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Fix failure to set hasTimestamp on final part

author	Chris Cannam
date	Wed, 16 May 2012 11:44:39 +0100
parents	8b6102e2a9b0
children

rev	line source
max@0	1 <!-- <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> -->
max@0	2 <html>
max@0	3 <head>
max@0	4 <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type">
max@0	5 <title>Armadillo: C++ linear algebra library</title>
max@0	6 <link type="text/css" rel="stylesheet" href="style.css">
max@0	7 <link rel="icon" href="armadillo_icon.png" type="image/png">
max@0	8 </head>
max@0	9 <body>
max@0	10 <center>
max@0	11 <table style="text-align: left; width: 80%; margin-left: auto; margin-right: auto;" border="0" cellpadding="0" cellspacing="0">
max@0	12 <tbody>
max@0	13 <tr>
max@0	14 <td style="vertical-align: top;">
max@0	15
max@0	16 <table style="text-align: left; width: 100%;" border="0" cellpadding="0" cellspacing="0">
max@0	17 <tbody>
max@0	18 <tr>
max@0	19 <td style="text-align: left; vertical-align: top;">
max@0	20 <font size=+2><b>Reference for Armadillo 2.4.4</b></font>
max@0	21 <br>
max@0	22 <font size=-1><b>(Loco Lounge Lizard)</b></font>
max@0	23 </td>
max@0	24 <td style="text-align: right; vertical-align: top;">
max@0	25 <b><a href="http://arma.sourceforge.net">to Armadillo home page</a></b>
max@0	26 <br>
max@0	27 <b><a href="http://nicta.com.au">to NICTA home page</a></b>
max@0	28 </td>
max@0	29 </tr>
max@0	30 </tbody>
max@0	31 </table>
max@0	32 <hr>
max@0	33 <br>
max@0	34 <br>
max@0	35 <a name="top"></a>
max@0	36 <a style="display:scroll; position:fixed; bottom:5px; right:5px;" href="#top"><font size=-1>[top]</font></a>
max@0	37
max@0	38
max@0	39 <!-- BEGIN CONTENT -->
max@0	40
max@0	41
max@0	42 <b>Preamble</b>
max@0	43 <br>
max@0	44 <br>
max@0	45 <table border="0" cellpadding="0" cellspacing="0">
max@0	46 <tbody>
max@0	47 <tr>
max@0	48 <td style="text-align: left; vertical-align: top; width: 50%;">
max@0	49 <ul>
max@0	50 <li>
max@0	51 To aid the conversion of Matlab/Octave programs,
max@0	52 there is a <a href="#syntax">syntax conversion table</a>
max@0	53 </li>
max@0	54 <br>
max@0	55 <li>
max@0	56 First time users may want to have a look at a short <a href="#example_prog">example program</a>
max@0	57 </li>
max@0	58 <br>
max@0	59 <li>
max@0	60 If you find any bugs or regressions, please <a href="http://arma.sourceforge.net/faq.html">report them</a>
max@0	61 </li>
max@0	62 <br>
max@0	63 <li>
max@0	64 <b>Caveat:</b> the API for version 2.x has <a href="#api_changes">changes & additions</a> compared to version 1.2;
max@0	65 see also the list of <a href="#deprecated">deprecated</a> functionality
max@0	66 </li>
max@0	67 </ul>
max@0	68 </td>
max@0	69 <td>
max@0	70
max@0	71 </td>
max@0	72 <td class="line" style="vertical-align: top;">
max@0	73 <br>
max@0	74 </td>
max@0	75 <td style="text-align: left; vertical-align: top; width: 45%;">
max@0	76 <ul>
max@0	77 <li>
max@0	78 If you use Armadillo in your research and/or software,
max@0	79 we would appreciate a citation to the following tech report:
max@0	80 <br>
max@0	81 <br>
max@0	82 <font size=-1>
max@0	83 Conrad Sanderson.
max@0	84 <br>
max@0	85 <i><a href="armadillo_nicta_2010.pdf">Armadillo: An Open Source C++ Linear Algebra Library for Fast Prototyping and Computationally Intensive Experiments</a></i>.
max@0	86 <br>
max@0	87 Technical Report, NICTA, 2010.
max@0	88 </font>
max@0	89 </li>
max@0	90 </ul>
max@0	91 </td>
max@0	92 </tr>
max@0	93 </tbody>
max@0	94 </table>
max@0	95
max@0	96 <br>
max@0	97 <br>
max@0	98
max@0	99 <b>Matrix, Vector, Cube and Field Classes</b>
max@0	100 <ul>
max@0	101 <a href="#Mat">Mat<<i>type</i>>, mat and cx_mat</a> ·
max@0	102 <a href="#Col">Col<<i>type</i>>, colvec and vec</a> ·
max@0	103 <a href="#Row">Row<<i>type</i>>, rowvec</a> ·
max@0	104 <a href="#Cube">Cube<<i>type</i>>, cube</a> ·
max@0	105 <a href="#field">field<<i>object type</i>></a>
max@0	106 </ul>
max@0	107 <br>
max@0	108
max@0	109 <b>Member Functions & Variables</b>
max@0	110 <ul>
max@0	111 <a href="#attributes">attributes</a> ·
max@0	112 <a href="#colptr">colptr</a> ·
max@0	113 <a href="#copy_size">copy_size</a> ·
max@0	114 <a href="#diag">diag</a> ·
max@0	115 <a href="#element_access">element access</a> ·
max@0	116 <a href="#element_initialisation">element initialisation</a> ·
max@0	117 <a href="#eye_member">eye</a> ·
max@0	118 <a href="#fill">fill</a> ·
max@0	119 <a href="#insert">insert rows/cols/slices</a> ·
max@0	120 <a href="#in_range">in_range</a> ·
max@0	121 <a href="#is_empty">is_empty</a> ·
max@0	122 <a href="#is_finite">is_finite</a> ·
max@0	123 <a href="#is_square">is_square</a> ·
max@0	124 <a href="#is_vec">is_vec</a> ·
max@0	125 <a href="#iterators_mat">iterators (matrices)</a> ·
max@0	126 <a href="#iterators_cube">iterators (cubes)</a> ·
max@0	127 <a href="#memptr">memptr</a> ·
max@0	128 <a href="#min_and_max_member">min/max</a> ·
max@0	129 <a href="#ones_member">ones</a> ·
max@0	130 <a href="#operators">operators</a> ·
max@0	131 <a href="#print">print</a> ·
max@0	132 <a href="#raw_print">raw_print</a> ·
max@0	133 <a href="#randu_randn_member">randu/randn</a> ·
max@0	134 <a href="#reset">reset</a> ·
max@0	135 <a href="#reshape_member">reshape</a> ·
max@0	136 <a href="#resize_member">resize</a> ·
max@0	137 <a href="#save_load_mat">save/load (matrices & cubes)</a> ·
max@0	138 <a href="#save_load_field">save/load (fields)</a> ·
max@0	139 <a href="#set_imag">set_imag/real</a> ·
max@0	140 <a href="#set_size">set_size</a> ·
max@0	141 <a href="#shed">shed rows/cols/slices</a> ·
max@0	142 <a href="#stl_container_fns">STL container functions</a> ·
max@0	143 <a href="#submat">submatrix views</a> ·
max@0	144 <a href="#subcube">subcube views</a> ·
max@0	145 <a href="#subfield">subfield views</a> ·
max@0	146 <a href="#swap_rows">swap_rows/cols</a> ·
max@0	147 <a href="#t_st_members">t/st (transpose)</a> ·
max@0	148 <a href="#zeros_member">zeros</a>
max@0	149 </ul>
max@0	150 <br>
max@0	151
max@0	152 <b>Other Classes</b>
max@0	153 <ul>
max@0	154 <a href="#running_stat">running_stat<<i>type</i>></a> ·
max@0	155 <a href="#running_stat_vec">running_stat_vec<<i>type</i>></a> ·
max@0	156 <a href="#wall_clock">wall_clock</a>
max@0	157 </ul>
max@0	158 <br>
max@0	159
max@0	160 <b>Generated Vectors/Matrices/Cubes</b>
max@0	161 <ul>
max@0	162 <a href="#eye_standalone">eye</a> ·
max@0	163 <a href="#linspace">linspace</a> ·
max@0	164 <a href="#ones_standalone">ones</a> ·
max@0	165 <a href="#randu_randn_standalone">randu/randn</a> ·
max@0	166 <a href="#repmat">repmat</a> ·
max@0	167 <a href="#toeplitz">toeplitz/toeplitz_circ</a> ·
max@0	168 <a href="#zeros_standalone">zeros</a>
max@0	169 </ul>
max@0	170 <br>
max@0	171
max@0	172 <b>Functions Individually Applied to Each Element of a Matrix/Cube</b>
max@0	173 <ul>
max@0	174 <a href="#abs">abs</a> ·
max@0	175 <a href="#eps">eps</a> ·
max@0	176 <a href="#misc_fns">misc functions (exp, log, pow, sqrt, ...)</a> ·
max@0	177 <a href="#trig_fns">trigonometric functions (cos, sin, ...)</a>
max@0	178 </ul>
max@0	179 <br>
max@0	180
max@0	181 <b>Scalar Valued Functions of Vectors/Matrices/Cubes</b>
max@0	182 <ul>
max@0	183 <a href="#accu">accu</a> ·
max@0	184 <a href="#as_scalar">as_scalar</a> ·
max@0	185 <a href="#det">det</a> ·
max@0	186 <a href="#dot">dot/cdot/norm_dot</a> ·
max@0	187 <a href="#log_det">log_det</a> ·
max@0	188 <a href="#norm">norm</a> ·
max@0	189 <a href="#rank">rank</a> ·
max@0	190 <a href="#trace">trace</a>
max@0	191 </ul>
max@0	192 <br>
max@0	193
max@0	194 <b>Scalar/Vector Valued Functions of Vectors/Matrices</b>
max@0	195 <ul>
max@0	196 <a href="#diagvec">diagvec</a> ·
max@0	197 <a href="#min_and_max">min/max</a> ·
max@0	198 <a href="#prod">prod</a> ·
max@0	199 <a href="#sum">sum</a> ·
max@0	200 <a href="#stats_fns">statistics (mean, stddev, ...)</a>
max@0	201 </ul>
max@0	202 <br>
max@0	203
max@0	204 <b>Vector/Matrix/Cube Valued Functions of Vectors/Matrices/Cubes</b>
max@0	205 <ul>
max@0	206 <a href="#conv">conv</a> ·
max@0	207 <a href="#conv_to">conv_to</a> ·
max@0	208 <a href="#conj">conj</a> ·
max@0	209 <a href="#cor">cor</a> ·
max@0	210 <a href="#cov">cov</a> ·
max@0	211 <a href="#cross">cross</a> ·
max@0	212 <a href="#cumsum">cumsum</a> ·
max@0	213 <a href="#diagmat">diagmat</a> ·
max@0	214 <a href="#find">find</a> ·
max@0	215 <a href="#flip">fliplr/flipud</a> ·
max@0	216 <a href="#imag_real">imag/real</a> ·
max@0	217 <a href="#join">join rows/cols/slices</a> ·
max@0	218 <a href="#kron">kron</a> ·
max@0	219 <a href="#reshape">reshape</a> ·
max@0	220 <a href="#resize">resize</a> ·
max@0	221 <a href="#shuffle">shuffle</a> ·
max@0	222 <a href="#sort">sort</a> ·
max@0	223 <a href="#sort_index">sort_index</a> ·
max@0	224 <a href="#symmat">symmatu/symmatl</a> ·
max@0	225 <a href="#strans">strans</a> ·
max@0	226 <a href="#trans">trans</a> ·
max@0	227 <a href="#trimat">trimatu/trimatl</a>
max@0	228 </ul>
max@0	229 <br>
max@0	230
max@0	231 <b>Decompositions, Inverses and Equation Solvers</b>
max@0	232 <ul>
max@0	233 <a href="#chol">chol</a> ·
max@0	234 <a href="#eig_sym">eig_sym</a> ·
max@0	235 <a href="#eig_gen">eig_gen</a> ·
max@0	236 <a href="#inv">inv</a> ·
max@0	237 <a href="#lu">lu</a> ·
max@0	238 <a href="#pinv">pinv</a> ·
max@0	239 <a href="#princomp">princomp</a> ·
max@0	240 <a href="#qr">qr</a> ·
max@0	241 <a href="#solve">solve</a> ·
max@0	242 <a href="#svd">svd</a> ·
max@0	243 <a href="#svd_econ">svd_econ</a> ·
max@0	244 <a href="#syl">syl</a>
max@0	245 </ul>
max@0	246 <br>
max@0	247
max@0	248 <b>Miscellaneous</b>
max@0	249 <ul>
max@0	250 <a href="#is_finite_standalone">is_finite()</a> ·
max@0	251 <a href="#logging">logging of errors/warnings</a> ·
max@0	252 <a href="#math_constants">math constants (pi, ...)</a> ·
max@0	253 <a href="#phys_constants">physical constants (speed of light, ...)</a> ·
max@0	254 <a href="#log_add">log_add</a> ·
max@0	255 <a href="#uword">uword/sword</a> ·
max@0	256 <a href="#cx_float_double">cx_float/cx_double</a> ·
max@0	257 <a href="#syntax">Matlab/Armadillo syntax differences</a> ·
max@0	258 <a href="#example_prog">example program</a> ·
max@0	259 <!--<a href="#catching_exceptions">catching exceptions</a> ·-->
max@0	260 <a href="#api_changes">API changes</a>
max@0	261 </ul>
max@0	262 <br>
max@0	263
max@0	264 <br>
max@0	265 <br>
max@0	266 <hr class="greyline">
max@0	267 <hr class="greyline">
max@0	268 <br>
max@0	269 <br>
max@0	270 <font size=+1><b>Matrix, Vector, Cube and Field Classes</b></font>
max@0	271 <br>
max@0	272 <br>
max@0	273 <hr class="greyline">
max@0	274 <br>
max@0	275
max@0	276 <a name="Mat"></a><b>Mat<</b><i>type</i><b>></b>
max@0	277 <br><b>mat</b>
max@0	278 <br><b>cx_mat</b>
max@0	279 <ul>
max@0	280 <li>
max@0	281 The root template matrix class is <b>Mat<</b><i>type</i><b>></b>, where <i>type</i> can be one of:
max@0	282 <i>char</i>, <i>int</i>, <i>float</i>, <i>double</i>, <i>std::complex<double></i>, etc.
max@0	283 </li>
max@0	284 <br>
max@0	285 <li>
max@0	286 For convenience the following typedefs have been defined:
max@0	287 <ul>
max@0	288 <table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
max@0	289 <tbody>
max@0	290 <tr>
max@0	291 <td style="vertical-align: top;">
max@0	292 umat
max@0	293 </td>
max@0	294 <td style="vertical-align: top;">
max@0	295  =
max@0	296 </td>
max@0	297 <td style="vertical-align: top;">
max@0	298 Mat<<a href="#uword">uword</a>>
max@0	299 </td>
max@0	300 </tr>
max@0	301 <tr>
max@0	302 <td style="vertical-align: top;">
max@0	303 imat
max@0	304 </td>
max@0	305 <td style="vertical-align: top;">
max@0	306  =
max@0	307 </td>
max@0	308 <td style="vertical-align: top;">
max@0	309 Mat<<a href="#uword">sword</a>>
max@0	310 </td>
max@0	311 </tr>
max@0	312 <tr>
max@0	313 <td style="vertical-align: top;">
max@0	314 fmat
max@0	315 </td>
max@0	316 <td style="vertical-align: top;">
max@0	317  =
max@0	318 </td>
max@0	319 <td style="vertical-align: top;">
max@0	320 Mat<float>
max@0	321 </td>
max@0	322 </tr>
max@0	323 <tr>
max@0	324 <td style="vertical-align: top;">
max@0	325 mat
max@0	326 </td>
max@0	327 <td style="vertical-align: top;">
max@0	328  =
max@0	329 </td>
max@0	330 <td style="vertical-align: top;">
max@0	331 Mat<double>
max@0	332 </td>
max@0	333 </tr>
max@0	334 <tr>
max@0	335 <td style="vertical-align: top;">
max@0	336 cx_fmat
max@0	337 </td>
max@0	338 <td style="vertical-align: top;">
max@0	339  =
max@0	340 </td>
max@0	341 <td style="vertical-align: top;">
max@0	342 Mat<<a href="#cx_float_double">cx_float</a>>
max@0	343 </td>
max@0	344 </tr>
max@0	345 <tr>
max@0	346 <td style="vertical-align: top;">
max@0	347 cx_mat
max@0	348 </td>
max@0	349 <td style="vertical-align: top;">
max@0	350  =
max@0	351 </td>
max@0	352 <td style="vertical-align: top;">
max@0	353 Mat<<a href="#cx_float_double">cx_double</a>>
max@0	354 </td>
max@0	355 </tr>
max@0	356 </tbody>
max@0	357 </table>
max@0	358 </ul>
max@0	359 </li>
max@0	360 <br>
max@0	361 <li>
max@0	362 In this documentation the <i>mat</i> type is used for convenience;
max@0	363 it is possible to use other types instead, eg. <i>fmat</i>
max@0	364 </li>
max@0	365 <br>
max@0	366 <li>
max@0	367 Functions which are wrappers for LAPACK or ATLAS functions (generally matrix decompositions) are only valid for the following types:
max@0	368 <i>fmat</i>, <i>mat</i>, <i>cx_fmat</i>, <i>cx_mat</i>
max@0	369 </li>
max@0	370 <br>
max@0	371 <li>
max@0	372 Elements are stored with column-major ordering (ie. column by column)
max@0	373 </li>
max@0	374 <br>
max@0	375 <a name="constructors_mat"></a>
max@0	376 <li>
max@0	377 Constructors:
max@0	378 <ul>
max@0	379 <li>mat()</li>
max@0	380 <li>mat(n_rows, n_cols)</li>
max@0	381 <li>mat(mat)</li>
max@0	382 <li>mat(vec)</li>
max@0	383 <li>mat(rowvec)</li>
max@0	384 <li>mat(string)</li>
max@0	385 <li>mat(initialiser_list)   (C++11 only)</li>
max@0	386 <li>cx_mat(mat,mat)   (for constructing a complex matrix out of two real matrices)</li>
max@0	387 </ul>
max@0	388 </li>
max@0	389 <br>
max@0	390 <li>
max@0	391 The string format for the constructor is elements separated by spaces, and rows denoted by semicolons.
max@0	392 For example, the 2x2 identity matrix can be created using the format string <code>"1 0; 0 1"</code>.
max@0	393 While string based initialisation is compact, directly setting the elements or using <a href="#element_initialisation">element initialisation</a> is considerably faster.
max@0	394 </li>
max@0	395 <br>
max@0	396 <a name="adv_constructors_mat"></a>
max@0	397 <li>
max@0	398 Advanced constructors:
max@0	399 <br>
max@0	400 <br>
max@0	401 <ul>
max@0	402 <li>mat(aux_mem*, n_rows, n_cols, copy_aux_mem = true, strict = true)
max@0	403 <br>
max@0	404 <br>
max@0	405 <ul>
max@0	406 Create a matrix using data from writeable auxiliary memory.
max@0	407 By default the matrix allocates its own memory and copies data from the auxiliary memory (for safety).
max@0	408 However, if <i>copy_aux_mem</i> is set to <i>false</i>,
max@0	409 the matrix will instead directly use the auxiliary memory (ie. no copying).
max@0	410 This is faster, but can be dangerous unless you know what you're doing!
max@0	411 <br>
max@0	412 <br>
max@0	413 The <i>strict</i> variable comes into effect only if <i>copy_aux_mem</i> is set to <i>false</i>
max@0	414 (ie. the matrix is directly using auxiliary memory).
max@0	415 If <i>strict</i> is set to <i>true</i>,
max@0	416 the matrix will be bound to the auxiliary memory for its lifetime;
max@0	417 the number of elements in the matrix can't be changed (directly or indirectly).
max@0	418 If <i>strict</i> is set to <i>false</i>, the matrix will not be bound to the auxiliary memory for its lifetime,
max@0	419 ie., the size of the matrix can be changed.
max@0	420 If the requested number of elements is different to the size of the auxiliary memory,
max@0	421 new memory will be allocated and the auxiliary memory will no longer be used.
max@0	422 </ul>
max@0	423 </li>
max@0	424 <br>
max@0	425 <li>mat(const aux_mem*, n_rows, n_cols)
max@0	426 <br>
max@0	427 <br>
max@0	428 <ul>
max@0	429 Create a matrix by copying data from read-only auxiliary memory.
max@0	430 </ul>
max@0	431 </li>
max@0	432 <a name="adv_constructors_mat_fixed"></a>
max@0	433 <br>
max@0	434 <li>mat::fixed<n_rows, n_cols>
max@0	435 <br>
max@0	436 <br>
max@0	437 <ul>
max@0	438 Create a fixed size matrix, with the size specified via template arguments.
max@0	439 Memory for the matrix is allocated at compile time.
max@0	440 This is generally faster than dynamic memory allocation, but the size of the matrix can't be changed afterwards (directly or indirectly).
max@0	441 <br>
max@0	442 <br>
max@0	443 For convenience, there are several pre-defined typedefs for each matrix type
max@0	444 (where the types are: <i>umat</i>, <i>imat</i>, <i>fmat</i>, <i>mat</i>, <i>cx_fmat</i>, <i>cx_mat</i>).
max@0	445 The typedefs specify a square matrix size, ranging from 2x2 to 9x9.
max@0	446 The typedefs were defined by simply appending a two digit form of the size to the matrix type
max@0	447 -- for example, <i>mat33</i> is equivalent to <i>mat::fixed<3,3></i>,
max@0	448 while <i>cx_mat44</i> is equivalent to <i>cx_mat::fixed<4,4></i>.
max@0	449 </ul>
max@0	450 </li>
max@0	451 <br>
max@0	452 <li>mat::fixed<n_rows, n_cols>(const aux_mem*)
max@0	453 <br>
max@0	454 <br>
max@0	455 <ul>
max@0	456 Create a fixed size matrix, with the size specified via template arguments,
max@0	457 and copying data from auxiliary memory.
max@0	458 </ul>
max@0	459 </li>
max@0	460 </ul>
max@0	461 </li>
max@0	462 <br>
max@0	463 <br>
max@0	464 <li>
max@0	465 Examples:
max@0	466 <ul>
max@0	467 <pre>
max@0	468 mat A = randu<mat>(5,5);
max@0	469 double x = A(1,2);
max@0	470
max@0	471 mat B = A + A;
max@0	472 mat C = A * B;
max@0	473 mat D = A % B;
max@0	474
max@0	475 cx_mat X(A,B);
max@0	476
max@0	477 B.zeros();
max@0	478 B.set_size(10,10);
max@0	479 B.zeros(5,6);
max@0	480
max@0	481 //
max@0	482 // fixed size matrices:
max@0	483
max@0	484 mat::fixed<5,6> F;
max@0	485 F.ones();
max@0	486
max@0	487 mat44 G;
max@0	488 G.randn();
max@0	489
max@0	490 cout << mat22().randu() << endl;
max@0	491
max@0	492 //
max@0	493 // constructing matrices from
max@0	494 // auxiliary (external) memory:
max@0	495
max@0	496 double aux_mem[24];
max@0	497 mat H(aux_mem, 4, 6, false);
max@0	498 </pre>
max@0	499 </ul>
max@0	500 </li>
max@0	501 <br>
max@0	502 <li><b>Caveat:</b>
max@0	503 For mathematical correctness, scalars are treated as 1x1 matrices during initialisation.
max@0	504 As such, the code below <b>will not</b> generate a 5x5 matrix with every element equal to 123.0:
max@0	505 <ul>
max@0	506 <pre>
max@0	507 mat A(5,5);
max@0	508 A = 123.0;
max@0	509 </pre>
max@0	510 </ul>
max@0	511 Use the following code instead:
max@0	512 <ul>
max@0	513 <pre>
max@0	514 mat A(5,5);
max@0	515 A.fill(123.0);
max@0	516 </pre>
max@0	517 </ul>
max@0	518 Or:
max@0	519 <ul>
max@0	520 <pre>
max@0	521 mat A = 123.0 * ones<mat>(5,5);
max@0	522 </pre>
max@0	523 </ul>
max@0	524 <br>
max@0	525 <li>
max@0	526 See also:
max@0	527 <ul>
max@0	528 <li><a href="#attributes">matrix attributes</a></li>
max@0	529 <li><a href="#element_access">accessing elements</a></li>
max@0	530 <li><a href="#element_initialisation">initialising elements</a></li>
max@0	531 <li><a href="#operators">math & relational operators</a></li>
max@0	532 <li><a href="#submat">submatrix views</a></li>
max@0	533 <li><a href="#save_load_mat">saving & loading matrices</a></li>
max@0	534 <li><a href="#print">printing matrices</a></li>
max@0	535 <li><a href="#iterators_mat">STL-style element iterators</a></li>
max@0	536 <li><a href="http://www.cplusplus.com/doc/tutorial/other_data_types/">explanation of <i>typedef</i></a> (cplusplus.com)
max@0	537 <li><a href="#Col">Col class</a></li>
max@0	538 <li><a href="#Row">Row class</a></li>
max@0	539 <li><a href="#Cube">Cube class</a></li>
max@0	540 </ul>
max@0	541 </li>
max@0	542 <br>
max@0	543 </ul>
max@0	544 <hr class="greyline">
max@0	545 <br>
max@0	546
max@0	547 <a name="Col"></a><b>Col<</b><i>type</i><b>></b>
max@0	548 <br><b>colvec</b>
max@0	549 <br><b>vec</b>
max@0	550 <ul>
max@0	551 <li>
max@0	552 Classes for column vectors (matrices with one column)
max@0	553 </li>
max@0	554 <br>
max@0	555 <li>The <b>Col<</b><i>type</i><b>></b> class is derived from the <b>Mat<</b><i>type</i><b>></b> class
max@0	556 and inherits most of the member functions
max@0	557 </li>
max@0	558 <br>
max@0	559 <li>
max@0	560 For convenience the following typedefs have been defined:
max@0	561 <ul>
max@0	562 <table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
max@0	563 <tbody>
max@0	564 <tr>
max@0	565 <td style="vertical-align: top;">
max@0	566 uvec, ucolvec
max@0	567 </td>
max@0	568 <td style="vertical-align: top;">
max@0	569  =
max@0	570 </td>
max@0	571 <td style="vertical-align: top;">
max@0	572 Col<<a href="#uword">uword</a>>
max@0	573 </td>
max@0	574 </tr>
max@0	575 <tr>
max@0	576 <td style="vertical-align: top;">
max@0	577 ivec, icolvec
max@0	578 </td>
max@0	579 <td style="vertical-align: top;">
max@0	580  =
max@0	581 </td>
max@0	582 <td style="vertical-align: top;">
max@0	583 Col<<a href="#uword">sword</a>>
max@0	584 </td>
max@0	585 </tr>
max@0	586 <tr>
max@0	587 <td style="vertical-align: top;">
max@0	588 fvec, fcolvec
max@0	589 </td>
max@0	590 <td style="vertical-align: top;">
max@0	591  =
max@0	592 </td>
max@0	593 <td style="vertical-align: top;">
max@0	594 Col<float>
max@0	595 </td>
max@0	596 </tr>
max@0	597 <tr>
max@0	598 <td style="vertical-align: top;">
max@0	599 vec, colvec
max@0	600 </td>
max@0	601 <td style="vertical-align: top;">
max@0	602  =
max@0	603 </td>
max@0	604 <td style="vertical-align: top;">
max@0	605 Col<double>
max@0	606 </td>
max@0	607 </tr>
max@0	608 <tr>
max@0	609 <td style="vertical-align: top;">
max@0	610 cx_fvec, cx_fcolvec
max@0	611 </td>
max@0	612 <td style="vertical-align: top;">
max@0	613  =
max@0	614 </td>
max@0	615 <td style="vertical-align: top;">
max@0	616 Col<<a href="#cx_float_double">cx_float</a>>
max@0	617 </td>
max@0	618 </tr>
max@0	619 <tr>
max@0	620 <td style="vertical-align: top;">
max@0	621 cx_vec, cx_colvec
max@0	622 </td>
max@0	623 <td style="vertical-align: top;">
max@0	624  =
max@0	625 </td>
max@0	626 <td style="vertical-align: top;">
max@0	627 Col<<a href="#cx_float_double">cx_double</a>>
max@0	628 </td>
max@0	629 </tr>
max@0	630 </tbody>
max@0	631 </table>
max@0	632 </ul>
max@0	633 </li>
max@0	634 <br>
max@0	635 <li>
max@0	636 In this documentation, the <b><i>vec</i></b> and <b><i>colvec</i></b> types have the <b>same meaning</b> and are used <b>interchangeably</b>
max@0	637 </li>
max@0	638 <br>
max@0	639 <li>
max@0	640 In this documentation, the types <i>vec</i> or <i>colvec</i> are used for convenience; it is possible to use other types instead, eg. <i>fvec</i>, <i>fcolvec</i>
max@0	641 </li>
max@0	642 <br>
max@0	643 <li>
max@0	644 Functions which take <i>Mat</i> as input can generally also take <i>Col</i> as input.
max@0	645 Main exceptions are functions which require square matrices
max@0	646 </li>
max@0	647 <br>
max@0	648 <li>
max@0	649 Constructors
max@0	650 <ul>
max@0	651 <li>vec(n_elem=0)</li>
max@0	652 <li>vec(vec)</li>
max@0	653 <li>vec(mat)   (a <i>std::logic_error</i> exception is thrown if the given matrix has more than one column)</li>
max@0	654 <li>vec(string)   (elements separated by spaces)</li>
max@0	655 <li>vec(initialiser_list)   (C++11 only)</li>
max@0	656 </ul>
max@0	657 </li>
max@0	658 <br>
max@0	659 <a name="adv_constructors_col"></a>
max@0	660 <li>
max@0	661 Advanced constructors:
max@0	662 <br>
max@0	663 <br>
max@0	664 <ul>
max@0	665 <li>vec(aux_mem*, number_of_elements, copy_aux_mem = true, strict = true)
max@0	666 <br>
max@0	667 <br>
max@0	668 <ul>
max@0	669 Create a column vector using data from writeable auxiliary memory.
max@0	670 By default the vector allocates its own memory and copies data from the auxiliary memory (for safety).
max@0	671 However, if <i>copy_aux_mem</i> is set to <i>false</i>,
max@0	672 the vector will instead directly use the auxiliary memory (ie. no copying).
max@0	673 This is faster, but can be dangerous unless you know what you're doing!
max@0	674 <br>
max@0	675 <br>
max@0	676 The <i>strict</i> variable comes into effect only if <i>copy_aux_mem</i> is set to <i>false</i>
max@0	677 (ie. the vector is directly using auxiliary memory).
max@0	678 If <i>strict</i> is set to <i>true</i>,
max@0	679 the vector will be bound to the auxiliary memory for its lifetime;
max@0	680 the number of elements in the vector can't be changed (directly or indirectly).
max@0	681 If <i>strict</i> is set to <i>false</i>, the vector will not be bound to the auxiliary memory for its lifetime,
max@0	682 ie., the vector's size can be changed.
max@0	683 If the requested number of elements is different to the size of the auxiliary memory,
max@0	684 new memory will be allocated and the auxiliary memory will no longer be used.
max@0	685 </ul>
max@0	686 </li>
max@0	687 <br>
max@0	688 <li>vec(const aux_mem*, number_of_elements)
max@0	689 <br>
max@0	690 <br>
max@0	691 <ul>
max@0	692 Create a column vector by copying data from read-only auxiliary memory.
max@0	693 </ul>
max@0	694 </li>
max@0	695 <br>
max@0	696 <li>vec::fixed<number_of_elements>
max@0	697 <br>
max@0	698 <br>
max@0	699 <ul>
max@0	700 Create a fixed size column vector, with the size specified via the template argument.
max@0	701 Memory for the vector is allocated at compile time.
max@0	702 This is generally faster than dynamic memory allocation, but the size of the vector can't be changed afterwards (directly or indirectly).
max@0	703 <br>
max@0	704 <br>
max@0	705 For convenience, there are several pre-defined typedefs for each vector type
max@0	706 (where the types are: <i>uvec</i>, <i>ivec</i>, <i>fvec</i>, <i>vec</i>, <i>cx_fvec</i>, <i>cx_vec</i> as well as the corresponding <i>colvec</i> versions).
max@0	707 The pre-defined typedefs specify vector sizes ranging from 2 to 9.
max@0	708 The typedefs were defined by simply appending a single digit form of the size to the vector type
max@0	709 -- for example, <i>vec3</i> is equivalent to <i>vec::fixed<3></i>,
max@0	710 while <i>cx_vec4</i> is equivalent to <i>cx_vec::fixed<4></i>.
max@0	711 </ul>
max@0	712 </li>
max@0	713 <br>
max@0	714 <li>vec::fixed<number_of_elements>(const aux_mem*)
max@0	715 <br>
max@0	716 <br>
max@0	717 <ul>
max@0	718 Create a fixed size column vector, with the size specified via the template argument,
max@0	719 and copying data from auxiliary memory.
max@0	720 </ul>
max@0	721 </li>
max@0	722 </ul>
max@0	723 </li>
max@0	724 <br>
max@0	725 <br>
max@0	726 <li>
max@0	727 Examples:
max@0	728 <ul>
max@0	729 <pre>
max@0	730 vec x(10);
max@0	731 vec y = zeros<vec>(10,1);
max@0	732
max@0	733 mat A = randu<mat>(10,10);
max@0	734 vec z = A.col(5); // extract a column vector
max@0	735 </pre>
max@0	736 </ul>
max@0	737 </li>
max@0	738 <br>
max@0	739 <li><b>Caveat:</b>
max@0	740 For mathematical correctness, scalars are treated as 1x1 matrices during initialisation.
max@0	741 As such, the code below <b>will not</b> generate a column vector with every element equal to 123.0:
max@0	742 <ul>
max@0	743 <pre>
max@0	744 vec q(5);
max@0	745 q = 123.0;
max@0	746 </pre>
max@0	747 </ul>
max@0	748 Use the following code instead:
max@0	749 <ul>
max@0	750 <pre>
max@0	751 vec q(5);
max@0	752 q.fill(123.0);
max@0	753 </pre>
max@0	754 </ul>
max@0	755 Or:
max@0	756 <ul>
max@0	757 <pre>
max@0	758 vec q = 123.0 * ones<vec>(5,1);
max@0	759 </pre>
max@0	760 </ul>
max@0	761 </li>
max@0	762 <br>
max@0	763 <li>See also:
max@0	764 <ul>
max@0	765 <li><a href="#Mat">Mat class</a></li>
max@0	766 <li><a href="#Row">Row class</a></li>
max@0	767 </ul>
max@0	768 </li>
max@0	769 <br>
max@0	770 </ul>
max@0	771 <hr class="greyline"><br>
max@0	772
max@0	773 <a name="Row"></a>
max@0	774 <b>Row<</b><i>type</i><b>></b>
max@0	775 <br><b>rowvec</b>
max@0	776 <ul>
max@0	777 <li>
max@0	778 Classes for row vectors (matrices with one row)
max@0	779 </li>
max@0	780 <br>
max@0	781 <li>The template <b>Row<</b><i>type</i><b>></b> class is derived from the <b>Mat<</b><i>type</i><b>></b> class
max@0	782 and inherits most of the member functions
max@0	783 </li>
max@0	784 <br>
max@0	785 <li>
max@0	786 For convenience the following typedefs have been defined:
max@0	787 <ul>
max@0	788 <table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
max@0	789 <tbody>
max@0	790 <tr>
max@0	791 <td style="vertical-align: top;">
max@0	792 urowvec
max@0	793 </td>
max@0	794 <td style="vertical-align: top;">
max@0	795  =
max@0	796 </td>
max@0	797 <td style="vertical-align: top;">
max@0	798 Row<<a href="#uword">uword</a>>
max@0	799 </td>
max@0	800 </tr>
max@0	801 <tr>
max@0	802 <td style="vertical-align: top;">
max@0	803 irowvec
max@0	804 </td>
max@0	805 <td style="vertical-align: top;">
max@0	806  =
max@0	807 </td>
max@0	808 <td style="vertical-align: top;">
max@0	809 Row<<a href="#uword">sword</a>>
max@0	810 </td>
max@0	811 </tr>
max@0	812 <tr>
max@0	813 <td style="vertical-align: top;">
max@0	814 frowvec
max@0	815 </td>
max@0	816 <td style="vertical-align: top;">
max@0	817  =
max@0	818 </td>
max@0	819 <td style="vertical-align: top;">
max@0	820 Row<float>
max@0	821 </td>
max@0	822 </tr>
max@0	823 <tr>
max@0	824 <td style="vertical-align: top;">
max@0	825 rowvec
max@0	826 </td>
max@0	827 <td style="vertical-align: top;">
max@0	828  =
max@0	829 </td>
max@0	830 <td style="vertical-align: top;">
max@0	831 Row<double>
max@0	832 </td>
max@0	833 </tr>
max@0	834 <tr>
max@0	835 <td style="vertical-align: top;">
max@0	836 cx_frowvec
max@0	837 </td>
max@0	838 <td style="vertical-align: top;">
max@0	839  =
max@0	840 </td>
max@0	841 <td style="vertical-align: top;">
max@0	842 Row<<a href="#cx_float_double">cx_float</a>>
max@0	843 </td>
max@0	844 </tr>
max@0	845 <tr>
max@0	846 <td style="vertical-align: top;">
max@0	847 cx_rowvec
max@0	848 </td>
max@0	849 <td style="vertical-align: top;">
max@0	850  =
max@0	851 </td>
max@0	852 <td style="vertical-align: top;">
max@0	853 Row<<a href="#cx_float_double">cx_double</a>>
max@0	854 </td>
max@0	855 </tr>
max@0	856 </tbody>
max@0	857 </table>
max@0	858 </ul>
max@0	859 </li>
max@0	860 <br>
max@0	861 <li>
max@0	862 In this documentation, the <i>rowvec</i> type is used for convenience;
max@0	863 it is possible to use other types instead, eg. <i>frowvec</i>
max@0	864 </li>
max@0	865 <br>
max@0	866 <li>
max@0	867 Functions which take <i>Mat</i> as input can generally also take <i>Row</i> as input.
max@0	868 Main exceptions are functions which require square matrices
max@0	869 </li>
max@0	870 <br>
max@0	871 <li>
max@0	872 Constructors
max@0	873 <ul>
max@0	874 <li>rowvec(n_elem=0)</li>
max@0	875 <li>rowvec(rowvec)</li>
max@0	876 <li>rowvec(mat)   (a <i>std::logic_error</i> exception is thrown if the given matrix has more than one row)</li>
max@0	877 <li>rowvec(string)   (elements separated by spaces)</li>
max@0	878 <li>rowvec(initialiser_list)   (C++11 only)</li>
max@0	879 </ul>
max@0	880 </li>
max@0	881 <br>
max@0	882 <a name="adv_constructors_row"></a>
max@0	883 <li>
max@0	884 Advanced constructors:
max@0	885 <br>
max@0	886 <br>
max@0	887 <ul>
max@0	888 <li>rowvec(aux_mem*, number_of_elements, copy_aux_mem = true, strict = true)
max@0	889 <br>
max@0	890 <br>
max@0	891 <ul>
max@0	892 Create a row vector using data from writeable auxiliary memory.
max@0	893 By default the vector allocates its own memory and copies data from the auxiliary memory (for safety).
max@0	894 However, if <i>copy_aux_mem</i> is set to <i>false</i>,
max@0	895 the vector will instead directly use the auxiliary memory (ie. no copying).
max@0	896 This is faster, but can be dangerous unless you know what you're doing!
max@0	897 <br>
max@0	898 <br>
max@0	899 The <i>strict</i> variable comes into effect only if <i>copy_aux_mem</i> is set to <i>false</i>
max@0	900 (ie. the vector is directly using auxiliary memory).
max@0	901 If <i>strict</i> is set to <i>true</i>,
max@0	902 the vector will be bound to the auxiliary memory for its lifetime;
max@0	903 the number of elements in the vector can't be changed (directly or indirectly).
max@0	904 If <i>strict</i> is set to <i>false</i>, the vector will not be bound to the auxiliary memory for its lifetime,
max@0	905 ie., the vector's size can be changed.
max@0	906 If the requested number of elements is different to the size of the auxiliary memory,
max@0	907 new memory will be allocated and the auxiliary memory will no longer be used.
max@0	908 </ul>
max@0	909 </li>
max@0	910 <br>
max@0	911 <li>rowvec(const aux_mem*, number_of_elements)
max@0	912 <br>
max@0	913 <br>
max@0	914 <ul>
max@0	915 Create a row vector by copying data from read-only auxiliary memory.
max@0	916 </ul>
max@0	917 </li>
max@0	918 <br>
max@0	919 <li>rowvec::fixed<number_of_elements>
max@0	920 <br>
max@0	921 <br>
max@0	922 <ul>
max@0	923 Create a fixed size row vector, with the size specified via the template argument.
max@0	924 Memory for the vector is allocated at compile time.
max@0	925 This is generally faster than dynamic memory allocation, but the size of the vector can't be changed afterwards (directly or indirectly).
max@0	926 <br>
max@0	927 <br>
max@0	928 For convenience, there are several pre-defined typedefs for each vector type
max@0	929 (where the types are: <i>urowvec</i>, <i>irowvec</i>, <i>frowvec</i>, <i>rowvec</i>, <i>cx_frowvec</i>, <i>cx_rowvec</i>).
max@0	930 The pre-defined typedefs specify vector sizes ranging from 2 to 9.
max@0	931 The typedefs were defined by simply appending a single digit form of the size to the vector type
max@0	932 -- for example, <i>rowvec3</i> is equivalent to <i>rowvec::fixed<3></i>,
max@0	933 while <i>cx_rowvec4</i> is equivalent to <i>cx_rowvec::fixed<4></i>.
max@0	934 </ul>
max@0	935 </li>
max@0	936 <br>
max@0	937 <li>rowvec::fixed<number_of_elements>(const aux_mem*)
max@0	938 <br>
max@0	939 <br>
max@0	940 <ul>
max@0	941 Create a fixed size row vector, with the size specified via the template argument,
max@0	942 and copying data from auxiliary memory.
max@0	943 </ul>
max@0	944 </li>
max@0	945 </ul>
max@0	946 </li>
max@0	947 <br>
max@0	948 <br>
max@0	949 <li>
max@0	950 Examples:
max@0	951 <ul>
max@0	952 <pre>
max@0	953 rowvec x(10);
max@0	954 rowvec y = zeros<mat>(1,10);
max@0	955
max@0	956 mat A = randu<mat>(10,10);
max@0	957 rowvec z = A.row(5); // extract a row vector
max@0	958 </pre>
max@0	959 </ul>
max@0	960 </li>
max@0	961 <br>
max@0	962 <li>
max@0	963 <b>Caveat:</b>
max@0	964 For mathematical correctness, scalars are treated as 1x1 matrices during initialisation.
max@0	965 As such, the code below <b>will not</b> generate a row vector with every element equal to 123.0:
max@0	966 <ul>
max@0	967 <pre>
max@0	968 rowvec r(5);
max@0	969 r = 123.0;
max@0	970 </pre>
max@0	971 </ul>
max@0	972 Use the following code instead:
max@0	973 <ul>
max@0	974 <pre>
max@0	975 rowvec r(5);
max@0	976 r.fill(123.0);
max@0	977 </pre>
max@0	978 </ul>
max@0	979 Or:
max@0	980 <ul>
max@0	981 <pre>
max@0	982 rowvec r = 123.0 * ones<rowvec>(1,5);
max@0	983 </pre>
max@0	984 </ul>
max@0	985 <br>
max@0	986 <li>See also:
max@0	987 <ul>
max@0	988 <li><a href="#Mat">Mat class</a></li>
max@0	989 <li><a href="#Col">Col class</a></li>
max@0	990 </ul>
max@0	991 </li>
max@0	992 <br>
max@0	993 </ul>
max@0	994 <hr class="greyline">
max@0	995 <br>
max@0	996
max@0	997 <a name="Cube"></a>
max@0	998 <b>Cube<</b><i>type</i><b>></b>
max@0	999 <br><b>cube</b>
max@0	1000 <br><b>cx_cube</b>
max@0	1001 <ul>
max@0	1002 <li>
max@0	1003 Classes for cubes, also known as "3D matrices"
max@0	1004 </li>
max@0	1005 <br>
max@0	1006 <li>
max@0	1007 The root template cube class is <b>Cube<</b><i>type</i><b>></b>, where <i>type</i> can be one of:
max@0	1008 <i>char</i>, <i>int</i>, <i>float</i>, <i>double</i>, <i>std::complex<double></i>, etc
max@0	1009 </li>
max@0	1010 <br>
max@0	1011 <li>
max@0	1012 For convenience the following typedefs have been defined:
max@0	1013 <ul>
max@0	1014 <table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
max@0	1015 <tbody>
max@0	1016 <tr>
max@0	1017 <td style="vertical-align: top;">
max@0	1018 ucube
max@0	1019 </td>
max@0	1020 <td style="vertical-align: top;">
max@0	1021  =
max@0	1022 </td>
max@0	1023 <td style="vertical-align: top;">
max@0	1024 Cube<<a href="#uword">uword</a>>
max@0	1025 </td>
max@0	1026 </tr>
max@0	1027 <tr>
max@0	1028 <td style="vertical-align: top;">
max@0	1029 icube
max@0	1030 </td>
max@0	1031 <td style="vertical-align: top;">
max@0	1032  =
max@0	1033 </td>
max@0	1034 <td style="vertical-align: top;">
max@0	1035 Cube<<a href="#uword">sword</a>>
max@0	1036 </td>
max@0	1037 </tr>
max@0	1038 <tr>
max@0	1039 <td style="vertical-align: top;">
max@0	1040 fcube
max@0	1041 </td>
max@0	1042 <td style="vertical-align: top;">
max@0	1043  =
max@0	1044 </td>
max@0	1045 <td style="vertical-align: top;">
max@0	1046 Cube<float>
max@0	1047 </td>
max@0	1048 </tr>
max@0	1049 <tr>
max@0	1050 <td style="vertical-align: top;">
max@0	1051 cube
max@0	1052 </td>
max@0	1053 <td style="vertical-align: top;">
max@0	1054  =
max@0	1055 </td>
max@0	1056 <td style="vertical-align: top;">
max@0	1057 Cube<double>
max@0	1058 </td>
max@0	1059 </tr>
max@0	1060 <tr>
max@0	1061 <td style="vertical-align: top;">
max@0	1062 cx_fcube
max@0	1063 </td>
max@0	1064 <td style="vertical-align: top;">
max@0	1065  =
max@0	1066 </td>
max@0	1067 <td style="vertical-align: top;">
max@0	1068 Cube<<a href="#cx_float_double">cx_float</a>>
max@0	1069 </td>
max@0	1070 </tr>
max@0	1071 <tr>
max@0	1072 <td style="vertical-align: top;">
max@0	1073 cx_cube
max@0	1074 </td>
max@0	1075 <td style="vertical-align: top;">
max@0	1076  =
max@0	1077 </td>
max@0	1078 <td style="vertical-align: top;">
max@0	1079 Cube<<a href="#cx_float_double">cx_double</a>>
max@0	1080 </td>
max@0	1081 </tr>
max@0	1082 </tbody>
max@0	1083 </table>
max@0	1084 </ul>
max@0	1085 </li>
max@0	1086 <br>
max@0	1087 <li>
max@0	1088 In this documentation the <i>cube</i> type is used for convenience;
max@0	1089 it is possible to use other types instead, eg. <i>fcube</i>
max@0	1090 </li>
max@0	1091 <br>
max@0	1092 <li>
max@0	1093 Cube data is stored as a set of slices (matrices) stored contiguously within memory.
max@0	1094 Within each slice, elements are stored with column-major ordering (ie. column by column)
max@0	1095 </li>
max@0	1096 <br>
max@0	1097 <li>
max@0	1098 Each slice can be interpreted as a matrix, hence functions which take <i>Mat</i> as input can generally also take cube slices as input
max@0	1099 </li>
max@0	1100 <br>
max@0	1101 <a name="constructors_cube"></a>
max@0	1102 <li>
max@0	1103 Constructors:
max@0	1104 <ul>
max@0	1105 cube()
max@0	1106 <br>cube(cube)
max@0	1107 <br>cube(n_rows, n_cols, n_slices)
max@0	1108 <br>cx_cube(cube, cube) (for constructing a complex cube out of two real cubes)
max@0	1109 </ul>
max@0	1110 </li>
max@0	1111 <br>
max@0	1112
max@0	1113 <a name="adv_constructors_cube"></a>
max@0	1114 <li>
max@0	1115 Advanced constructors:
max@0	1116 <br>
max@0	1117 <br>
max@0	1118 <ul>
max@0	1119 <li>
max@0	1120 cube::fixed<n_rows, n_cols, n_slices>
max@0	1121 <br>
max@0	1122 <br>
max@0	1123 <ul>
max@0	1124 Create a fixed size cube, with the size specified via template arguments.
max@0	1125 Memory for the cube is allocated at compile time.
max@0	1126 This is generally faster than dynamic memory allocation, but the size of the cube can't be changed afterwards (directly or indirectly).
max@0	1127 </ul>
max@0	1128 </li>
max@0	1129 <br>
max@0	1130 <li>cube(aux_mem*, n_rows, n_cols, n_slices, copy_aux_mem = true, strict = true)
max@0	1131 <br>
max@0	1132 <br>
max@0	1133 <ul>
max@0	1134 Create a cube using data from writeable auxiliary memory.
max@0	1135 By default the cube allocates its own memory and copies data from the auxiliary memory (for safety).
max@0	1136 However, if <i>copy_aux_mem</i> is set to <i>false</i>,
max@0	1137 the cube will instead directly use the auxiliary memory (ie. no copying).
max@0	1138 This is faster, but can be dangerous unless you know what you're doing!
max@0	1139 <br>
max@0	1140 <br>
max@0	1141 The <i>strict</i> variable comes into effect only if <i>copy_aux_mem</i> is set to <i>false</i>
max@0	1142 (ie. the cube is directly using auxiliary memory).
max@0	1143 If <i>strict</i> is set to <i>true</i>,
max@0	1144 the cube will be bound to the auxiliary memory for its lifetime;
max@0	1145 the number of elements in the cube can't be changed (directly or indirectly).
max@0	1146 If <i>strict</i> is set to <i>false</i>, the cube will not be bound to the auxiliary memory for its lifetime,
max@0	1147 ie., the size of the cube can be changed.
max@0	1148 If the requested number of elements is different to the size of the auxiliary memory,
max@0	1149 new memory will be allocated and the auxiliary memory will no longer be used.
max@0	1150 </ul>
max@0	1151 </li>
max@0	1152 <br>
max@0	1153 <li>cube(const aux_mem*, n_rows, n_cols, n_slices)
max@0	1154 <br>
max@0	1155 <br>
max@0	1156 <ul>
max@0	1157 Create a cube by copying data from read-only auxiliary memory.
max@0	1158 </ul>
max@0	1159 </li>
max@0	1160 </ul>
max@0	1161 </li>
max@0	1162 <br>
max@0	1163 <br>
max@0	1164 <li>
max@0	1165 Examples:
max@0	1166 <ul>
max@0	1167 <pre>
max@0	1168 cube x(1,2,3);
max@0	1169 cube y = randu<cube>(4,5,6);
max@0	1170
max@0	1171 mat A = y.slice(1); // extract a slice from the cube
max@0	1172 // (each slice is a matrix)
max@0	1173
max@0	1174 mat B = randu<mat>(4,5);
max@0	1175 y.slice(2) = B; // set a slice in the cube
max@0	1176
max@0	1177 cube q = y + y; // cube addition
max@0	1178 cube r = y % y; // element-wise cube multiplication
max@0	1179
max@0	1180 cube::fixed<4,5,6> f;
max@0	1181 f.ones();
max@0	1182 </pre>
max@0	1183 </ul>
max@0	1184 </li>
max@0	1185 <br>
max@0	1186 <li>
max@0	1187 <b>Caveats</b>
max@0	1188 <br>
max@0	1189 <br>
max@0	1190 <ul>
max@0	1191 <li>
max@0	1192 The size of individual slices can't be changed.
max@0	1193 For example, the following <b>will not</b> work:
max@0	1194 <ul>
max@0	1195 <pre>
max@0	1196 cube c(5,6,7);
max@0	1197 c.slice(0) = randu<mat>(10,20); // wrong size
max@0	1198 </pre>
max@0	1199 </ul>
max@0	1200 </li>
max@0	1201 <li>
max@0	1202 For mathematical correctness, scalars are treated as 1x1x1 cubes during initialisation.
max@0	1203 As such, the code below <b>will not</b> generate a cube with every element equal to 123.0:
max@0	1204 <ul>
max@0	1205 <pre>
max@0	1206 cube c(5,6,7);
max@0	1207 c = 123.0;
max@0	1208 </pre>
max@0	1209 </ul>
max@0	1210 Use the following code instead:
max@0	1211 <ul>
max@0	1212 <pre>
max@0	1213 cube c(5,6,7);
max@0	1214 c.fill(123.0);
max@0	1215 </pre>
max@0	1216 </ul>
max@0	1217 Or:
max@0	1218 <ul>
max@0	1219 <pre>
max@0	1220 cube c = 123.0 * ones<cube>(5,6,7);
max@0	1221 </pre>
max@0	1222 </ul>
max@0	1223 </li>
max@0	1224 </ul>
max@0	1225 <br>
max@0	1226 <li>
max@0	1227 See also:
max@0	1228 <ul>
max@0	1229 <li><a href="#attributes">cube attributes</a></li>
max@0	1230 <li><a href="#element_access">accessing elements</a></li>
max@0	1231 <li><a href="#operators">math & relational operators</a></li>
max@0	1232 <li><a href="#subcube">subcube views and slices</a></li>
max@0	1233 <li><a href="#save_load_mat">saving & loading cubes</a></li>
max@0	1234 <li><a href="#iterators_cube">STL-style element iterators</a></li>
max@0	1235 <li><a href="#Mat">Mat class</a></li>
max@0	1236 </ul>
max@0	1237 </li>
max@0	1238 <br>
max@0	1239 </ul>
max@0	1240 <hr class="greyline">
max@0	1241 <br>
max@0	1242
max@0	1243 <a name="field"></a>
max@0	1244 <b>field<</b><i>object type</i><b>></b>
max@0	1245 <ul>
max@0	1246 <li>
max@0	1247 Class for one and two dimensional fields of arbitrary objects
max@0	1248 </li>
max@0	1249 <br>
max@0	1250 <li>
max@0	1251 Constructors (where <i>object type</i> is another class, eg. <i>std::string</i>, <i>mat</i>, <i>vec</i>, <i>rowvec</i>, etc):
max@0	1252 <ul>
max@0	1253 field<<i>object type</i>>(n_elem=0)
max@0	1254 <br>field<<i>object type</i>>(n_rows, n_cols)
max@0	1255 <br>field<<i>object type</i>>(field<<i>object type</i>>)
max@0	1256 </ul>
max@0	1257 </li>
max@0	1258 <br>
max@0	1259 <li>
max@0	1260 Examples:
max@0	1261 <ul>
max@0	1262 <pre>
max@0	1263 // create a field of strings
max@0	1264 field<std::string> S(3,2);
max@0	1265
max@0	1266 S(0,0) = "hello";
max@0	1267 S(1,0) = "there";
max@0	1268
max@0	1269 // string fields can be saved as plain text files
max@0	1270 S.save("string_field");
max@0	1271
max@0	1272 // create a vec field with 3 rows and 2 columns
max@0	1273 field<vec> F(3,2);
max@0	1274
max@0	1275 // access components of the field
max@0	1276 F(0,0) = vec(5);
max@0	1277 F(1,1) = randu<vec>(6);
max@0	1278 F(2,0).set_size(7);
max@0	1279
max@0	1280 // access element 1 of the vec stored at 2,0
max@0	1281 double x = F(2,0)(1);
max@0	1282
max@0	1283 // copy rows
max@0	1284 F.row(0) = F.row(2);
max@0	1285
max@0	1286 // extract a row of vecs from F
max@0	1287 field<vec> G = F.row(1);
max@0	1288
max@0	1289 // print the field to the standard output
max@0	1290 G.print("G =");
max@0	1291
max@0	1292 // save the field to a binary file
max@0	1293 G.save("vec_field");
max@0	1294 </pre>
max@0	1295 </ul>
max@0	1296 </li>
max@0	1297 <br>
max@0	1298 <li>See also:
max@0	1299 <ul>
max@0	1300 <li><a href="#attributes">field attributes</a></li>
max@0	1301 <li><a href="#subfield">subfield views</a></li>
max@0	1302 <li><a href="#save_load_field">saving/loading fields</a></li>
max@0	1303 <li><a href="http://cplusplus.com/reference/string/string/">string class in the standard C++ library</a> (cplusplus.com)</li>
max@0	1304 </ul>
max@0	1305 </li>
max@0	1306 <br>
max@0	1307 </ul>
max@0	1308 <hr class="greyline">
max@0	1309 <hr class="greyline">
max@0	1310 <br>
max@0	1311 <br>
max@0	1312 <font size=+1><b>Member Functions & Variables</b></font>
max@0	1313 <br>
max@0	1314 <br>
max@0	1315 <hr class="greyline">
max@0	1316 <br>
max@0	1317
max@0	1318 <a name="attributes"></a>
max@0	1319
max@0	1320 <b>attributes</b>
max@0	1321 <ul>
max@0	1322 <table style="text-align: left;" border="0" cellpadding="0" cellspacing="0">
max@0	1323 <tbody>
max@0	1324 <tr>
max@0	1325 <td>
max@0	1326 <b>.n_rows</b>
max@0	1327 </td>
max@0	1328 <td>  </td>
max@0	1329 <td>
max@0	1330 (number of rows)
max@0	1331 </td>
max@0	1332 </tr>
max@0	1333 <tr>
max@0	1334 <td>
max@0	1335 <b>.n_cols</b>
max@0	1336 </td>
max@0	1337 <td>  </td>
max@0	1338 <td>
max@0	1339 (number of columns)
max@0	1340 </td>
max@0	1341 </tr>
max@0	1342 <tr>
max@0	1343 <td>
max@0	1344 <b>.n_elem</b>
max@0	1345 </td>
max@0	1346 <td>  </td>
max@0	1347 <td>
max@0	1348 (total number of elements)
max@0	1349 </td>
max@0	1350 </tr>
max@0	1351 <tr>
max@0	1352 <td>
max@0	1353 <b>.n_slices</b>
max@0	1354 </td>
max@0	1355 <td>  </td>
max@0	1356 <td>
max@0	1357 (number of slices)
max@0	1358 </td>
max@0	1359 </tr>
max@0	1360 </tbody>
max@0	1361 </table>
max@0	1362 </ul>
max@0	1363 <br>
max@0	1364 <ul>
max@0	1365 <li>
max@0	1366 Member variables which are read-only;
max@0	1367 to change the size, use
max@0	1368 <a href="#set_size">.set_size()</a>,
max@0	1369 <a href="#copy_size">.copy_size()</a>,
max@0	1370 <a href="#zeros_member">.zeros()</a>,
max@0	1371 <a href="#ones_member">.ones()</a>,
max@0	1372 or
max@0	1373 <a href="#reset">.reset()</a>
max@0	1374 </li>
max@0	1375 <br>
max@0	1376 <li><i>n_rows</i>, <i>n_cols</i> and <i>n_elem</i> are applicable to <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i> and <i>field</i> classes</li>
max@0	1377 <br>
max@0	1378 <li><i>n_slices</i> is applicable only to the <i>Cube</i> class</li>
max@0	1379 <br>
max@0	1380 <li>
max@0	1381 For the <i>Col</i> and <i>Row</i> classes, <i>n_elem</i> also indicates vector length</li>
max@0	1382 <br>
max@0	1383 <li>The variables are of type <a href="#uword">uword</a></li>
max@0	1384 <br>
max@0	1385 <li>
max@0	1386 Examples:
max@0	1387 <ul>
max@0	1388 <pre>
max@0	1389 mat X(4,5);
max@0	1390 cout << "X has " << X.n_cols << " columns" << endl;
max@0	1391 </pre>
max@0	1392 </ul>
max@0	1393 </li>
max@0	1394 <br>
max@0	1395 <li>
max@0	1396 See also:
max@0	1397 <ul>
max@0	1398 <li><a href="#set_size">.set_size()</a></li>
max@0	1399 <li><a href="#copy_size">.copy_size()</a></li>
max@0	1400 <li><a href="#zeros_member">.zeros()</a></li>
max@0	1401 <li><a href="#ones_member">.ones()</a></li>
max@0	1402 <li><a href="#reset">.reset()</a></li>
max@0	1403 </ul>
max@0	1404 </li>
max@0	1405 <br>
max@0	1406 </ul>
max@0	1407 <hr class="greyline"><br>
max@0	1408
max@0	1409 <a name="colptr"></a>
max@0	1410 <b>.colptr(col_number)</b>
max@0	1411 <ul>
max@0	1412 <li>
max@0	1413 Member function of <i>Mat</i>
max@0	1414 </li>
max@0	1415 <br>
max@0	1416 <li>
max@0	1417 Obtain a raw pointer to the memory used by the specified column
max@0	1418 </li>
max@0	1419 <br>
max@0	1420 <li>
max@0	1421 As soon as the size of the matrix is changed, the pointer is no longer valid
max@0	1422 </li>
max@0	1423 <br>
max@0	1424 <li>This function is not recommended for use unless you know what you're doing
max@0	1425 -- you may wish to use <a href="#submat">submatrix views</a> instead
max@0	1426 </li>
max@0	1427 <br>
max@0	1428 <li>
max@0	1429 Examples:
max@0	1430 <ul>
max@0	1431 <pre>
max@0	1432 mat A = randu<mat>(5,5);
max@0	1433
max@0	1434 double* mem = A.colptr(2);
max@0	1435 </pre>
max@0	1436 </ul>
max@0	1437 </li>
max@0	1438 <br>
max@0	1439 <li>
max@0	1440 See also:
max@0	1441 <ul>
max@0	1442 <li><a href="#memptr">.memptr()</a></li>
max@0	1443 <li><a href="#submat">submatrix access</a></li>
max@0	1444 <li><a href="#iterators_mat">iterators (matrices)</a></li>
max@0	1445 <li><a href="#adv_constructors_mat">advanced constructors (matrices)</a></li>
max@0	1446 </ul>
max@0	1447 </li>
max@0	1448 <br>
max@0	1449 </ul>
max@0	1450 <hr class="greyline"><br>
max@0	1451
max@0	1452 <a name="copy_size"></a>
max@0	1453 <b>.copy_size(A)</b>
max@0	1454 <ul>
max@0	1455 <li>
max@0	1456 Member function of <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i> and <i>field</i>
max@0	1457 </li>
max@0	1458 <br>
max@0	1459 <li>
max@0	1460 Set the size to be the same as object <i>A</i>
max@0	1461 </li>
max@0	1462 <br>
max@0	1463 <li>
max@0	1464 Object <i>A</i> must be of the same root type as the object being modified
max@0	1465 (eg. you can't set the size of a matrix by providing a cube)
max@0	1466 </li>
max@0	1467 <br>
max@0	1468 <li>
max@0	1469 Examples:
max@0	1470 <ul>
max@0	1471 <pre>
max@0	1472 mat A = randu<mat>(5,6);
max@0	1473 mat B;
max@0	1474 B.copy_size(A);
max@0	1475
max@0	1476 cout << B.n_rows << endl;
max@0	1477 cout << B.n_cols << endl;
max@0	1478 </pre>
max@0	1479 </ul>
max@0	1480 </li>
max@0	1481 </ul>
max@0	1482 <br>
max@0	1483 <hr class="greyline"><br>
max@0	1484
max@0	1485 <a name="diag"></a>
max@0	1486 <b>.diag(k=0)</b>
max@0	1487 <ul>
max@0	1488 <li>
max@0	1489 Member function of <i>Mat</i>.
max@0	1490 </li>
max@0	1491 <br>
max@0	1492 <li>
max@0	1493 Read/write access to the <i>k</i>-th diagonal in a matrix
max@0	1494 </li>
max@0	1495 <br>
max@0	1496 <li>The argument <i>k</i> is optional -- by default the main diagonal is accessed (<i>k=0</i>)</li>
max@0	1497 <br>
max@0	1498 <li>For <i>k > 0</i>, the <i>k</i>-th super-diagonal is accessed (top-right corner)</li>
max@0	1499 <br>
max@0	1500 <li>For <i>k < 0</i>, the <i>k</i>-th sub-diagonal is accessed (bottom-left corner)</li>
max@0	1501 <br>
max@0	1502 <li>
max@0	1503 An extracted diagonal is interpreted as a column vector
max@0	1504 </li>
max@0	1505 <br>
max@0	1506 <li>
max@0	1507 Examples:
max@0	1508 <ul>
max@0	1509 <pre>
max@0	1510 mat X = randu<mat>(5,5);
max@0	1511
max@0	1512 vec a = X.diag();
max@0	1513 vec b = X.diag(1);
max@0	1514 vec c = X.diag(-2);
max@0	1515
max@0	1516 X.diag() = randu<vec>(5);
max@0	1517 X.diag() += 6;
max@0	1518 </pre>
max@0	1519 </ul>
max@0	1520 </li>
max@0	1521 <br>
max@0	1522 <li>
max@0	1523 See also:
max@0	1524 <ul>
max@0	1525 <li><a href="#diagvec">diagvec()</a></li>
max@0	1526 <li><a href="#submat">submatrix views</a></li>
max@0	1527 </ul>
max@0	1528 </li>
max@0	1529 </ul>
max@0	1530 <br>
max@0	1531 <hr class="greyline"><br>
max@0	1532
max@0	1533 <a name="element_access"></a>
max@0	1534 <b>element/object access via (), [] and .at()</b>
max@0	1535 <ul>
max@0	1536 <li>
max@0	1537 Provide access to individual elements or objects stored in a container object
max@0	1538 (ie., <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i>, <i>field</i>)<br>
max@0	1539 <br>
max@0	1540 <ul>
max@0	1541 <table style="text-align: left; width: 100%;"
max@0	1542 border="0" cellpadding="2" cellspacing="2">
max@0	1543 <tbody>
max@0	1544 <tr>
max@0	1545 <td style="vertical-align: top;">
max@0	1546 <pre>(n)</pre>
max@0	1547 </td>
max@0	1548 <td style="vertical-align: top;"> <br>
max@0	1549 </td>
max@0	1550 <td style="vertical-align: top;">
max@0	1551 For <i>vec</i> and <i>rowvec</i>, access the <i>n</i>-th element.
max@0	1552 For <i>mat</i>, <i>cube</i> and <i>field</i>, access the <i>n</i>-th element/object under the assumption of a flat layout,
max@0	1553 with column-major ordering of data (ie. column by column).
max@0	1554 A <i>std::logic_error</i> exception is thrown if the requested element is out of bounds.
max@0	1555 The bounds check can be optionally disabled at compile-time (see below).
max@0	1556 </td>
max@0	1557 </tr>
max@0	1558 <tr>
max@0	1559 <td> </td>
max@0	1560 <td> </td>
max@0	1561 <td> </td>
max@0	1562 </tr>
max@0	1563 <tr>
max@0	1564 <td style="vertical-align: top;">
max@0	1565 <pre>.at(n) and [n]</pre>
max@0	1566 </td>
max@0	1567 <td style="vertical-align: top;"><br>
max@0	1568 </td>
max@0	1569 <td style="vertical-align: top;">
max@0	1570 As for <i>(n)</i>, but without a bounds check.
max@0	1571 Not recommended for use unless your code has been thoroughly debugged.
max@0	1572 </td>
max@0	1573 </tr>
max@0	1574 <tr>
max@0	1575 <td> </td>
max@0	1576 <td> </td>
max@0	1577 <td> </td>
max@0	1578 </tr>
max@0	1579 <tr>
max@0	1580 <td style="vertical-align: top;">
max@0	1581 <pre>(i,j)</pre>
max@0	1582 </td>
max@0	1583 <td style="vertical-align: top;"><br>
max@0	1584 </td>
max@0	1585 <td style="vertical-align: top;">
max@0	1586 For <i>mat</i> and <i>field</i> classes, access the element/object stored at the <i>i</i>-th row and <i>j</i>-th column.
max@0	1587 A <i>std::logic_error</i> exception is thrown if the requested element is out of bounds.
max@0	1588 The bounds check can be optionally disabled at compile-time (see below).
max@0	1589 </td>
max@0	1590 </tr>
max@0	1591 <tr>
max@0	1592 <td> </td>
max@0	1593 <td> </td>
max@0	1594 <td> </td>
max@0	1595 </tr>
max@0	1596 <tr>
max@0	1597 <td style="vertical-align: top;">
max@0	1598 <pre>.at(i,j)</pre>
max@0	1599 </td>
max@0	1600 <td style="vertical-align: top;"><br>
max@0	1601 </td>
max@0	1602 <td style="vertical-align: top;">
max@0	1603 As for <i>(i,j)</i>, but without a bounds check.
max@0	1604 Not recommended for use unless your code has been thoroughly debugged.
max@0	1605 </td>
max@0	1606 <td style="vertical-align: top;"><br>
max@0	1607 </td>
max@0	1608 </tr>
max@0	1609 <tr>
max@0	1610 <td> </td>
max@0	1611 <td> </td>
max@0	1612 <td> </td>
max@0	1613 </tr>
max@0	1614 <tr>
max@0	1615 <td style="vertical-align: top;">
max@0	1616 <pre>(i,j,k)</pre>
max@0	1617 </td>
max@0	1618 <td style="vertical-align: top;"><br>
max@0	1619 </td>
max@0	1620 <td style="vertical-align: top;">
max@0	1621 Cube only: access the element stored at the <i>i</i>-th row, <i>j</i>-th column and <i>k</i>-th slice.
max@0	1622 A <i>std::logic_error</i> exception is thrown if the requested element is out of bounds.
max@0	1623 The bounds check can be optionally disabled at compile-time (see below).
max@0	1624 </td>
max@0	1625 </tr>
max@0	1626 <tr>
max@0	1627 <td> </td>
max@0	1628 <td> </td>
max@0	1629 <td> </td>
max@0	1630 </tr>
max@0	1631 <tr>
max@0	1632 <td style="vertical-align: top;">
max@0	1633 <pre>.at(i,j,k)</pre>
max@0	1634 </td>
max@0	1635 <td style="vertical-align: top;"><br>
max@0	1636 </td>
max@0	1637 <td style="vertical-align: top;">
max@0	1638 As for <i>(i,j,k)</i>, but without a bounds check.
max@0	1639 Not recommended for use unless your code has been thoroughly debugged.</td>
max@0	1640 </tr>
max@0	1641 </tbody>
max@0	1642 </table>
max@0	1643 </ul>
max@0	1644 </li>
max@0	1645 <br>
max@0	1646 <li>
max@0	1647 The bounds checks used by the <i>(n)</i>, <i>(i,j)</i> and <i>(i,j,k)</i> access forms
max@0	1648 can be disabled by defining <i>ARMA_NO_DEBUG</i> or <i>NDEBUG</i> macros
max@0	1649 before including the <i>armadillo</i> header file (eg. <i>#define ARMA_NO_DEBUG</i>).
max@0	1650 Disabling the bounds checks is not recommended until your code has been thoroughly debugged
max@0	1651 -- it's better to write correct code first, and then maximise its speed.
max@0	1652 </li>
max@0	1653 <br>
max@0	1654 <li>
max@0	1655 Examples:
max@0	1656 <ul>
max@0	1657 <pre>
max@0	1658 mat A = randu<mat>(10,10);
max@0	1659 A(9,9) = 123.0;
max@0	1660 double x = A.at(9,9);
max@0	1661 double y = A[99];
max@0	1662
max@0	1663 vec p = randu<vec>(10,1);
max@0	1664 p(9) = 123.0;
max@0	1665 double z = p[9];
max@0	1666 </pre>
max@0	1667 </ul>
max@0	1668 </li>
max@0	1669 <br>
max@0	1670 <li>See also:
max@0	1671 <ul>
max@0	1672 <li><a href="#in_range">.in_range()</a></li>
max@0	1673 <li><a href="#iterators_mat">iterators (matrices)</a></li>
max@0	1674 <li><a href="#iterators_cube">iterators (cubes)</a></li>
max@0	1675 </ul>
max@0	1676 </li>
max@0	1677 <br>
max@0	1678 </ul>
max@0	1679 <hr class="greyline"><br>
max@0	1680
max@0	1681 <a name="element_initialisation"></a>
max@0	1682 <b>element initialisation</b>
max@0	1683 <ul>
max@0	1684 <li>
max@0	1685 Instances of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>field</i> classes can be initialised via repeated use of the << operator
max@0	1686 </li>
max@0	1687 <br>
max@0	1688 <li>
max@0	1689 Special element <i>endr</i> indicates "end of row" (conceptually similar to <i>std::endl</i>)
max@0	1690 </li>
max@0	1691 <br>
max@0	1692 <li>
max@0	1693 Setting elements via << is a bit slower than directly <a href="#element_access">accessing</a> the elements,
max@0	1694 but code using << is generally more readable as well as being easier to write
max@0	1695 </li>
max@0	1696 <br>
max@0	1697 <li>
max@0	1698 If you have a C++11 compiler, instances of <i>Mat</i>, <i>Col</i> and <i>Row</i> classes can be also initialised via initialiser lists;
max@0	1699 this requires support for the C++11 standard to be <a href="#added_in_24">explicitly enabled</a>
max@0	1700 </li>
max@0	1701 <br>
max@0	1702 <li>
max@0	1703 Examples:
max@0	1704 <ul>
max@0	1705 <pre>
max@0	1706 mat A;
max@0	1707
max@0	1708 A << 1 << 2 << 3 << endr
max@0	1709 << 4 << 5 << 6 << endr;
max@0	1710
max@0	1711 mat B = { 1, 2, 3, 4, 5, 6 }; // C++11 only
max@0	1712 B.reshape(2,3);
max@0	1713 </pre>
max@0	1714 </ul>
max@0	1715 </li>
max@0	1716 <br>
max@0	1717 <li>
max@0	1718 See also:
max@0	1719 <ul>
max@0	1720 <li><a href="#element_access">element access</a></li>
max@0	1721 <li><a href="#print">.print()</a></li>
max@0	1722 <li><a href="#save_load_mat">saving & loading matrices</a></li>
max@0	1723 <li><a href="#adv_constructors_mat">advanced constructors (matrices)</a></li>
max@0	1724 </ul>
max@0	1725 </li>
max@0	1726 <br>
max@0	1727 </ul>
max@0	1728 <hr class="greyline"><br>
max@0	1729
max@0	1730 <a name="eye_member"></a>
max@0	1731 <b>.eye()</b>
max@0	1732 <br>
max@0	1733 <b>.eye(n_rows, n_cols)</b>
max@0	1734 <ul>
max@0	1735 <li>
max@0	1736 Set the elements along the main diagonal to one and off-diagonal elements set to zero,
max@0	1737 optionally first resizing to specified dimensions
max@0	1738 </li>
max@0	1739 <br>
max@0	1740 <li>
max@0	1741 An identity matrix is generated when <i>n_rows</i> = <i>n_cols</i>
max@0	1742 </li>
max@0	1743 <br>
max@0	1744 <li>
max@0	1745 Examples:
max@0	1746 <ul>
max@0	1747 <pre>
max@0	1748 mat A(5,5);
max@0	1749 A.eye();
max@0	1750
max@0	1751 mat B;
max@0	1752 B.eye(5,5);
max@0	1753 </pre>
max@0	1754 </ul>
max@0	1755 </li>
max@0	1756 <br>
max@0	1757 <li>See also:
max@0	1758 <ul>
max@0	1759 <li><a href="#eye_standalone">eye()</a> (standalone function)</li>
max@0	1760 <li><a href="#diagmat">diagmat()</a></li>
max@0	1761 <li><a href="#diagvec">diagvec()</a></li>
max@0	1762 <li><a href="#ones_member">.ones()</a></li>
max@0	1763 </ul>
max@0	1764 </li>
max@0	1765 <br>
max@0	1766 </ul>
max@0	1767 <hr class="greyline"><br>
max@0	1768
max@0	1769 <a name="fill"></a>
max@0	1770 <b>.fill(value)</b>
max@0	1771 <ul>
max@0	1772 <li>
max@0	1773 Member function of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>Cube</i> classes.
max@0	1774 </li>
max@0	1775 <br>
max@0	1776 <li>Sets the elements to a specified value.
max@0	1777 The type of value must match the type of elements used by the container object
max@0	1778 (eg. for <i>mat</i> the type is double)
max@0	1779 </li>
max@0	1780 <br>
max@0	1781 <li>
max@0	1782 Examples:
max@0	1783 <ul>
max@0	1784 <pre>
max@0	1785 mat A(5,5);
max@0	1786 A.fill(123.0);
max@0	1787 </pre>
max@0	1788 </ul>
max@0	1789 </li>
max@0	1790 <br>
max@0	1791 <li>
max@0	1792 See also:
max@0	1793 <ul>
max@0	1794 <li><a href="#ones_member">.ones()</a></li>
max@0	1795 <li><a href="#zeros_member">.zeros()</a></li>
max@0	1796 <li><a href="#randu_randn_member">.randu() & .randn()</a></li>
max@0	1797 </ul>
max@0	1798 </li>
max@0	1799 <br>
max@0	1800 </ul>
max@0	1801 <hr class="greyline"><br>
max@0	1802
max@0	1803 <a name="in_range"></a>
max@0	1804 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	1805 <tbody>
max@0	1806 <tr>
max@0	1807 <td style="vertical-align: top;"><b>.in_range(</b> i <b>)</b></td>
max@0	1808 <td style="vertical-align: top;"><br>
max@0	1809 </td>
max@0	1810 <td style="vertical-align: top;">(member of <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i> and <i>field</i>)
max@0	1811 </td>
max@0	1812 </tr>
max@0	1813 <tr>
max@0	1814 <td style="vertical-align: top;"><b>.in_range( span(</b>start<b>,</b> end<b>) )</b></td>
max@0	1815 <td style="vertical-align: top;"><br>
max@0	1816 </td>
max@0	1817 <td style="vertical-align: top;">(member of <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i> and <i>field</i>)
max@0	1818 </td>
max@0	1819 </tr>
max@0	1820 <tr>
max@0	1821 <td>
max@0	1822
max@0	1823 </td>
max@0	1824 </tr>
max@0	1825 <tr>
max@0	1826 <td style="vertical-align: top;"><b>.in_range(</b> row<b>,</b> col <b>)</b></td>
max@0	1827 <td style="vertical-align: top;"><br>
max@0	1828 </td>
max@0	1829 <td style="vertical-align: top;">(member of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>field</i>)
max@0	1830 </td>
max@0	1831 </tr>
max@0	1832 <tr>
max@0	1833 <td style="vertical-align: top;"><b>.in_range( <font size=-1>span(</b>start_row<b>,</b> end_row<b>), span(</b>start_col<b>,</b> end_col<b>)</font> )</b></td>
max@0	1834 <td style="vertical-align: top;"><br>
max@0	1835 </td>
max@0	1836 <td style="vertical-align: top;">(member of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>field</i>)
max@0	1837 </td>
max@0	1838 </tr>
max@0	1839 <tr>
max@0	1840 <td>
max@0	1841
max@0	1842 </td>
max@0	1843 </tr>
max@0	1844 <tr>
max@0	1845 <td style="vertical-align: top;"><b>.in_range(</b> row<b>,</b> col<b>,</b> slice <b>)</b></td>
max@0	1846 <td style="vertical-align: top;"><br>
max@0	1847 </td>
max@0	1848 <td style="vertical-align: top;">(member of <i>Cube</i>)
max@0	1849 </td>
max@0	1850 </tr>
max@0	1851 <tr>
max@0	1852 <td style="vertical-align: top;"><b>.in_range( <font size=-1>span(</b>start_row<b>,</b> end_row<b>), span(</b>start_col<b>,</b> end_col<b>), span(</b>start_slice<b>,</b> end_slice<b>)</font> )</b></td>
max@0	1853 <td style="vertical-align: top;"><br>
max@0	1854 </td>
max@0	1855 <td style="vertical-align: top;">(member of <i>Cube</i>)
max@0	1856 </td>
max@0	1857 </tr>
max@0	1858 </tbody>
max@0	1859 </table>
max@0	1860 <br>
max@0	1861 <ul>
max@0	1862 <li>Returns <i>true</i> if the given location or span is currently valid
max@0	1863 </li>
max@0	1864 <br>
max@0	1865 <li>Returns <i>false</i> if the object is empty, the location is out of bounds, or the span is out of bounds
max@0	1866 </li>
max@0	1867 <br>
max@0	1868 <li>
max@0	1869 Instances of <i>span(a,b)</i> can be replaced by:
max@0	1870 <ul>
max@0	1871 <li><i>span()</i> or <i>span::all</i>, to indicate the entire range</li>
max@0	1872 <li><i>span(a)</i>, to indicate a particular row, column or slice</li>
max@0	1873 </ul>
max@0	1874 </li>
max@0	1875 <br>
max@0	1876 <li>
max@0	1877 Examples:
max@0	1878 <ul>
max@0	1879 <pre>
max@0	1880 mat A = randu<mat>(4,5);
max@0	1881
max@0	1882 cout << A.in_range(0,0) << endl; // true
max@0	1883 cout << A.in_range(3,4) << endl; // true
max@0	1884 cout << A.in_range(4,5) << endl; // false
max@0	1885 </pre>
max@0	1886 </ul>
max@0	1887 </li>
max@0	1888 <br>
max@0	1889 <li>
max@0	1890 See also:
max@0	1891 <ul>
max@0	1892 <li><a href="#element_access">element access</a></li>
max@0	1893 <li><a href="#submat">submatrix views</a></li>
max@0	1894 <li><a href="#subcube">subcube views</a></li>
max@0	1895 <li><a href="#subfield">subfield views</a></li>
max@0	1896 <li><a href="#set_size">.set_size()</a></li>
max@0	1897 </ul>
max@0	1898 </li>
max@0	1899 <br>
max@0	1900 </ul>
max@0	1901 <hr class="greyline"><br>
max@0	1902
max@0	1903 <a name="is_empty"></a>
max@0	1904 <b>.is_empty()</b>
max@0	1905 <ul>
max@0	1906 <li>
max@0	1907 Member function of <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i> and <i>field</i> classes
max@0	1908 </li>
max@0	1909 <br>
max@0	1910 <li>Returns true if the object has no elements
max@0	1911 </li>
max@0	1912 <br>
max@0	1913 <li>Returns false if the object has one or more elements
max@0	1914 </li>
max@0	1915 <br>
max@0	1916 <li>
max@0	1917 Examples:
max@0	1918 <ul>
max@0	1919 <pre>
max@0	1920 mat A = randu<mat>(5,5);
max@0	1921 cout << A.is_empty() << endl;
max@0	1922
max@0	1923 A.reset();
max@0	1924 cout << A.is_empty() << endl;
max@0	1925 </pre>
max@0	1926 </ul>
max@0	1927 </li>
max@0	1928 <br>
max@0	1929 <li>
max@0	1930 See also:
max@0	1931 <ul>
max@0	1932 <li><a href="#is_square">.is_square()</a></li>
max@0	1933 <li><a href="#is_vec">.is_vec()</a></li>
max@0	1934 <li><a href="#reset">.reset()</a></li>
max@0	1935 </ul>
max@0	1936 </li>
max@0	1937 <br>
max@0	1938 </ul>
max@0	1939 <hr class="greyline"><br>
max@0	1940
max@0	1941 <a name="is_finite"></a>
max@0	1942 <b>.is_finite()</b>
max@0	1943 <ul>
max@0	1944 <li>
max@0	1945 Member function of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>Cube</i> classes
max@0	1946 </li>
max@0	1947 <br>
max@0	1948 <li>Returns <i>true</i> if all elements of the object are finite
max@0	1949 </li>
max@0	1950 <br>
max@0	1951 <li>Returns <i>false</i> if at least one of the elements of the object is non-finite (±infinity or NaN)
max@0	1952 </li>
max@0	1953 <br>
max@0	1954 <li>
max@0	1955 Examples:
max@0	1956 <ul>
max@0	1957 <pre>
max@0	1958 mat A = randu<mat>(5,5);
max@0	1959 mat B = randu<mat>(5,5);
max@0	1960
max@0	1961 B(1,1) = math::nan()
max@0	1962
max@0	1963 cout << A.is_finite() << endl;
max@0	1964 cout << B.is_finite() << endl;
max@0	1965 </pre>
max@0	1966 </ul>
max@0	1967 </li>
max@0	1968 <br>
max@0	1969 <li>
max@0	1970 See also:
max@0	1971 <ul>
max@0	1972 <li><a href="#math_constants">math::nan()</a></li>
max@0	1973 <li><a href="#math_constants">math::inf()</a></li>
max@0	1974 <li><a href="#is_finite_standalone">is_finite()</a> (standalone function)</li>
max@0	1975 </ul>
max@0	1976 </li>
max@0	1977 <br>
max@0	1978 </ul>
max@0	1979 <hr class="greyline"><br>
max@0	1980
max@0	1981 <a name="is_square"></a>
max@0	1982 <b>.is_square()</b>
max@0	1983 <ul>
max@0	1984 <li>
max@0	1985 Member function of the <i>Mat</i> class
max@0	1986 </li>
max@0	1987 <br>
max@0	1988 <li>Returns <i>true</i> if the matrix is square, ie., number of rows is equal to the number of columns
max@0	1989 </li>
max@0	1990 <br>
max@0	1991 <li>Returns <i>false</i> if the matrix is not square
max@0	1992 </li>
max@0	1993 <br>
max@0	1994 <li>
max@0	1995 Examples:
max@0	1996 <ul>
max@0	1997 <pre>
max@0	1998 mat A = randu<mat>(5,5);
max@0	1999 mat B = randu<mat>(6,7);
max@0	2000
max@0	2001 cout << A.is_square() << endl;
max@0	2002 cout << B.is_square() << endl;
max@0	2003 </pre>
max@0	2004 </ul>
max@0	2005 </li>
max@0	2006 <br>
max@0	2007 <li>
max@0	2008 See also:
max@0	2009 <ul>
max@0	2010 <li><a href="#is_empty">.is_empty()</a></li>
max@0	2011 <li><a href="#is_vec">.is_vec()</a></li>
max@0	2012 </ul>
max@0	2013 </li>
max@0	2014 </ul>
max@0	2015 <br>
max@0	2016 <hr class="greyline"><br>
max@0	2017
max@0	2018 <a name="is_vec"></a>
max@0	2019 <b>.is_vec()</b>
max@0	2020 <br><b>.is_colvec()</b>
max@0	2021 <br><b>.is_rowvec()</b>
max@0	2022 <ul>
max@0	2023 <li>
max@0	2024 Member functions of the <i>Mat</i> class
max@0	2025 </li>
max@0	2026 <br>
max@0	2027
max@0	2028 <li>.is_vec():
max@0	2029 <ul>
max@0	2030 <li>Returns <i>true</i> if the matrix can be interpreted as a vector (either column or row vector)
max@0	2031 </li>
max@0	2032 <li>Returns <i>false</i> if the matrix does not have exactly one column or one row
max@0	2033 </li>
max@0	2034 </ul>
max@0	2035 </li>
max@0	2036 <br>
max@0	2037
max@0	2038 <li>.is_colvec():
max@0	2039 <ul>
max@0	2040 <li>Returns <i>true</i> if the matrix can be interpreted as a column vector
max@0	2041 </li>
max@0	2042 <li>Returns <i>false</i> if the matrix does not have exactly one column
max@0	2043 </li>
max@0	2044 </ul>
max@0	2045 </li>
max@0	2046 <br>
max@0	2047
max@0	2048 <li>.is_rowvec():
max@0	2049 <ul>
max@0	2050 <li>Returns <i>true</i> if the matrix can be interpreted as a row vector
max@0	2051 </li>
max@0	2052 <li>Returns <i>false</i> if the matrix does not have exactly one row
max@0	2053 </li>
max@0	2054 </ul>
max@0	2055 </li>
max@0	2056 <br>
max@0	2057
max@0	2058 <li><b>Caveat:</b> do not assume that the vector has elements if these functions return <i>true</i> -- it is possible to have an empty vector (eg. 0x1)
max@0	2059 </li>
max@0	2060 <br>
max@0	2061 <li>
max@0	2062 Examples:
max@0	2063 <ul>
max@0	2064 <pre>
max@0	2065 mat A = randu<mat>(1,5);
max@0	2066 mat B = randu<mat>(5,1);
max@0	2067 mat C = randu<mat>(5,5);
max@0	2068
max@0	2069 cout << A.is_vec() << endl;
max@0	2070 cout << B.is_vec() << endl;
max@0	2071 cout << C.is_vec() << endl;
max@0	2072 </pre>
max@0	2073 </ul>
max@0	2074 </li>
max@0	2075 <br>
max@0	2076 <li>
max@0	2077 See also:
max@0	2078 <ul>
max@0	2079 <li><a href="#is_empty">.is_empty()</a></li>
max@0	2080 <li><a href="#is_square">.is_square()</a></li>
max@0	2081 </ul>
max@0	2082 </li>
max@0	2083 </ul>
max@0	2084 <br>
max@0	2085 <hr class="greyline"><br>
max@0	2086
max@0	2087 <a name="insert"></a>
max@0	2088 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	2089 <tbody>
max@0	2090 <tr>
max@0	2091 <td style="vertical-align: top;">
max@0	2092 <b>.insert_rows( </b>row_number, X<b> )</b>
max@0	2093 <br>
max@0	2094 <b>.insert_rows( </b>row_number, number_of_rows, set_to_zero = true<b> )</b>
max@0	2095 </td>
max@0	2096 <td style="vertical-align: top;"><br></td>
max@0	2097 <td style="vertical-align: top;">(member functions of <i>Mat</i> and <i>Col</i>)
max@0	2098 </td>
max@0	2099 </tr>
max@0	2100 <tr>
max@0	2101 <td> </td>
max@0	2102 </tr>
max@0	2103 <tr>
max@0	2104 <td style="vertical-align: top;">
max@0	2105 <b>.insert_cols( </b>col_number, X<b> )</b>
max@0	2106 <br>
max@0	2107 <b>.insert_cols( </b>col_number, number_of_cols, set_to_zero = true<b> )</b>
max@0	2108 </td>
max@0	2109 <td style="vertical-align: top;"><br></td>
max@0	2110 <td style="vertical-align: top;">(member functions of <i>Mat</i> and <i>Row</i>)
max@0	2111 </td>
max@0	2112 </tr>
max@0	2113 <tr>
max@0	2114 <td> </td>
max@0	2115 </tr>
max@0	2116 <tr>
max@0	2117 <td style="vertical-align: top;">
max@0	2118 <b>.insert_slices( </b>slice_number, X<b> )</b>
max@0	2119 <br>
max@0	2120 <b>.insert_slices( </b>slice_number, number_of_slices, set_to_zero = true<b> )</b>
max@0	2121 </td>
max@0	2122 <td style="vertical-align: top;"><br></td>
max@0	2123 <td style="vertical-align: top;">(member functions of <i>Cube</i>)
max@0	2124 </td>
max@0	2125 </tr>
max@0	2126 </tbody>
max@0	2127 </table>
max@0	2128 <br>
max@0	2129 <ul>
max@0	2130 <li>
max@0	2131 Functions with the <i>X</i> argument: insert a copy of X at the specified row/column/slice
max@0	2132 <ul>
max@0	2133 <li>if inserting rows, X must have the same number of columns as the recipient object</li>
max@0	2134 <li>if inserting columns, X must have the same number of rows as the recipient object</li>
max@0	2135 <li>if inserting slices, X must have the same number of rows and columns as the recipient object (ie. all slices must have the same size)</li>
max@0	2136 </ul>
max@0	2137 </li>
max@0	2138 <br>
max@0	2139 <li>
max@0	2140 Functions with the <i>number_of_...</i> argument: expand the object by creating new rows/columns/slices.
max@0	2141 By default, the new rows/columns/slices are set to zero.
max@0	2142 If <i>set_to_zero</i> is <i>false</i>, the memory used by the new rows/columns/slices will not be initialised.
max@0	2143 </li>
max@0	2144 <br>
max@0	2145 <li>
max@0	2146 Examples:
max@0	2147 <ul>
max@0	2148 <pre>
max@0	2149 mat A = randu<mat>(5,10);
max@0	2150 mat B = ones<mat>(5,2);
max@0	2151
max@0	2152 // at column 2, insert a copy of B;
max@0	2153 // A will now have 12 columns
max@0	2154 A.insert_cols(2, B);
max@0	2155
max@0	2156 // at column 1, insert 5 zeroed columns;
max@0	2157 // B will now have 7 columns
max@0	2158 B.insert_cols(1, 5);
max@0	2159 </pre>
max@0	2160 </ul>
max@0	2161 </li>
max@0	2162 <br>
max@0	2163 <li>
max@0	2164 See also:
max@0	2165 <ul>
max@0	2166 <li><a href="#shed">shed rows/columns/slices</a></li>
max@0	2167 <li><a href="#join">join rows/columns/slices</a></li>
max@0	2168 <li><a href="#resize_member">.resize()</a></li>
max@0	2169 <li><a href="#submat">submatrix views</a></li>
max@0	2170 <li><a href="#subcube">subcube views</a></li>
max@0	2171 </ul>
max@0	2172 </li>
max@0	2173 <br>
max@0	2174 </ul>
max@0	2175 <hr class="greyline"><br>
max@0	2176
max@0	2177 <a name="iterators_mat"></a>
max@0	2178 <b>iterators (matrices & vectors)</b>
max@0	2179 <ul>
max@0	2180 <li>
max@0	2181 STL-style iterators and associated member functions of the <i>Mat</i>, <i>Col</i> and <i>Row</i> classes
max@0	2182 </li>
max@0	2183 <br>
max@0	2184 <li>
max@0	2185 iterator types:
max@0	2186 <br>
max@0	2187 <br>
max@0	2188 <ul>
max@0	2189 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	2190 <tbody>
max@0	2191 <tr>
max@0	2192 <td style="vertical-align: top;">
max@0	2193 <b>mat::iterator</b>
max@0	2194 <br>
max@0	2195 <b>vec::iterator</b>
max@0	2196 <br>
max@0	2197 <b>rowvec::iterator</b>
max@0	2198 </td>
max@0	2199 <td style="vertical-align: top;"> <br>
max@0	2200 </td>
max@0	2201 <td style="vertical-align: top;">
max@0	2202 random access iterators, for read/write access to elements
max@0	2203 (which are stored column by column)
max@0	2204 </td>
max@0	2205 </tr>
max@0	2206 <tr>
max@0	2207 <td style="vertical-align: top;">
max@0	2208
max@0	2209 </td>
max@0	2210 <td style="vertical-align: top;"> <br>
max@0	2211 </td>
max@0	2212 <td style="vertical-align: top;">
max@0	2213
max@0	2214 </td>
max@0	2215 </tr>
max@0	2216 <tr>
max@0	2217 <td style="vertical-align: top;">
max@0	2218 <b>mat::const_iterator</b>
max@0	2219 <br>
max@0	2220 <b>vec::const_iterator</b>
max@0	2221 <br>
max@0	2222 <b>rowvec::const_iterator</b>
max@0	2223 </td>
max@0	2224 <td style="vertical-align: top;"> <br>
max@0	2225 </td>
max@0	2226 <td style="vertical-align: top;">
max@0	2227 random access iterators, for read-only access to elements
max@0	2228 (which are stored column by column)
max@0	2229 </td>
max@0	2230 </tr>
max@0	2231 <tr>
max@0	2232 <td style="vertical-align: top;">
max@0	2233
max@0	2234 </td>
max@0	2235 <td style="vertical-align: top;"> <br>
max@0	2236 </td>
max@0	2237 <td style="vertical-align: top;">
max@0	2238
max@0	2239 </td>
max@0	2240 </tr>
max@0	2241 <tr>
max@0	2242 <td style="vertical-align: top;">
max@0	2243 <b>mat::col_iterator</b>
max@0	2244 <br>
max@0	2245 <b>vec::col_iterator</b>
max@0	2246 <br>
max@0	2247 <b>rowvec::col_iterator</b>
max@0	2248 </td>
max@0	2249 <td style="vertical-align: top;"> <br>
max@0	2250 </td>
max@0	2251 <td style="vertical-align: top;">
max@0	2252 random access iterators, for read/write access to the elements of a specific column
max@0	2253 </td>
max@0	2254 </tr>
max@0	2255 <tr>
max@0	2256 <td style="vertical-align: top;">
max@0	2257
max@0	2258 </td>
max@0	2259 <td style="vertical-align: top;"> <br>
max@0	2260 </td>
max@0	2261 <td style="vertical-align: top;">
max@0	2262
max@0	2263 </td>
max@0	2264 </tr>
max@0	2265 <tr>
max@0	2266 <td style="vertical-align: top;">
max@0	2267 <b>mat::const_col_iterator</b>
max@0	2268 <br>
max@0	2269 <b>vec::const_col_iterator</b>
max@0	2270 <br>
max@0	2271 <b>rowvec::const_col_iterator</b>
max@0	2272 </td>
max@0	2273 <td style="vertical-align: top;"> <br>
max@0	2274 </td>
max@0	2275 <td style="vertical-align: top;">
max@0	2276 random access iterators, for read-only access to the elements of a specific column
max@0	2277 </td>
max@0	2278 </tr>
max@0	2279 <tr>
max@0	2280 <td style="vertical-align: top;">
max@0	2281
max@0	2282 </td>
max@0	2283 <td style="vertical-align: top;"> <br>
max@0	2284 </td>
max@0	2285 <td style="vertical-align: top;">
max@0	2286
max@0	2287 </td>
max@0	2288 </tr>
max@0	2289 <tr>
max@0	2290 <td style="vertical-align: top;">
max@0	2291 <b>mat::row_iterator</b>
max@0	2292 </td>
max@0	2293 <td style="vertical-align: top;"> <br>
max@0	2294 </td>
max@0	2295 <td style="vertical-align: top;">
max@0	2296 rudimentary forward iterator, for read/write access to the elements of a specific row
max@0	2297 </td>
max@0	2298 </tr>
max@0	2299 <tr>
max@0	2300 <td style="vertical-align: top;">
max@0	2301
max@0	2302 </td>
max@0	2303 <td style="vertical-align: top;"> <br>
max@0	2304 </td>
max@0	2305 <td style="vertical-align: top;">
max@0	2306
max@0	2307 </td>
max@0	2308 </tr>
max@0	2309 <tr>
max@0	2310 <td style="vertical-align: top;">
max@0	2311 <b>mat::const_row_iterator</b>
max@0	2312 </td>
max@0	2313 <td style="vertical-align: top;"> <br>
max@0	2314 </td>
max@0	2315 <td style="vertical-align: top;">
max@0	2316 rudimentary forward iterator, for read-only access to the elements of a specific row
max@0	2317 </td>
max@0	2318 </tr>
max@0	2319 <tr>
max@0	2320 <td style="vertical-align: top;">
max@0	2321
max@0	2322 </td>
max@0	2323 <td style="vertical-align: top;"> <br>
max@0	2324 </td>
max@0	2325 <td style="vertical-align: top;">
max@0	2326
max@0	2327 </td>
max@0	2328 </tr>
max@0	2329 <tr>
max@0	2330 <td style="vertical-align: top;">
max@0	2331 <b>vec::row_iterator</b>
max@0	2332 <br>
max@0	2333 <b>rowvec::row_iterator</b>
max@0	2334 </td>
max@0	2335 <td style="vertical-align: top;"> <br>
max@0	2336 </td>
max@0	2337 <td style="vertical-align: top;">
max@0	2338 random access iterators, for read/write access to the elements of a specific row
max@0	2339 </td>
max@0	2340 </tr>
max@0	2341 <tr>
max@0	2342 <td style="vertical-align: top;">
max@0	2343
max@0	2344 </td>
max@0	2345 <td style="vertical-align: top;"> <br>
max@0	2346 </td>
max@0	2347 <td style="vertical-align: top;">
max@0	2348
max@0	2349 </td>
max@0	2350 </tr>
max@0	2351 <tr>
max@0	2352 <td style="vertical-align: top;">
max@0	2353 <b>vec::const_row_iterator</b>
max@0	2354 <br>
max@0	2355 <b>rowvec::const_row_iterator</b>
max@0	2356 </td>
max@0	2357 <td style="vertical-align: top;"> <br>
max@0	2358 </td>
max@0	2359 <td style="vertical-align: top;">
max@0	2360 random access iterators, for read-only access to the elements of a specific row
max@0	2361 </td>
max@0	2362 </tr>
max@0	2363 </tbody>
max@0	2364 </table>
max@0	2365 </ul>
max@0	2366 </li>
max@0	2367 <br>
max@0	2368 <br>
max@0	2369 <li>
max@0	2370 Member functions:
max@0	2371 <br>
max@0	2372 <br>
max@0	2373 <ul>
max@0	2374 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	2375 <tbody>
max@0	2376 <tr>
max@0	2377 <td style="vertical-align: top;">
max@0	2378 <b>.begin()</b>
max@0	2379 </td>
max@0	2380 <td style="vertical-align: top;"> <br>
max@0	2381 </td>
max@0	2382 <td style="vertical-align: top;">
max@0	2383 iterator referring to the first element
max@0	2384 </td>
max@0	2385 </tr>
max@0	2386 <tr>
max@0	2387 <td style="vertical-align: top;">
max@0	2388 <b>.end()</b>
max@0	2389 </td>
max@0	2390 <td style="vertical-align: top;"> <br>
max@0	2391 </td>
max@0	2392 <td style="vertical-align: top;">
max@0	2393 iterator referring to the <i>past-the-end</i> element
max@0	2394 </td>
max@0	2395 </tr>
max@0	2396 <tr>
max@0	2397 <td>
max@0	2398
max@0	2399 </td>
max@0	2400 </tr>
max@0	2401 <tr>
max@0	2402 <td style="vertical-align: top;">
max@0	2403 <b>.begin_row(</b><i>row_number</i><b>)</b>
max@0	2404 </td>
max@0	2405 <td style="vertical-align: top;"> <br>
max@0	2406 </td>
max@0	2407 <td style="vertical-align: top;">
max@0	2408 iterator referring to the first element of the specified row
max@0	2409 </td>
max@0	2410 </tr>
max@0	2411 <tr>
max@0	2412 <td style="vertical-align: top;">
max@0	2413 <b>.end_row(</b><i>row_number</i><b>)</b>
max@0	2414 </td>
max@0	2415 <td style="vertical-align: top;"> <br>
max@0	2416 </td>
max@0	2417 <td style="vertical-align: top;">
max@0	2418 iterator referring to the <i>past-the-end</i> element of the specified row
max@0	2419 </td>
max@0	2420 </tr>
max@0	2421 <tr>
max@0	2422 <td>
max@0	2423
max@0	2424 </td>
max@0	2425 </tr>
max@0	2426 <tr>
max@0	2427 <td style="vertical-align: top;">
max@0	2428 <b>.begin_col(</b><i>col_number</i><b>)</b>
max@0	2429 </td>
max@0	2430 <td style="vertical-align: top;"> <br>
max@0	2431 </td>
max@0	2432 <td style="vertical-align: top;">
max@0	2433 iterator referring to the first element of the specified column
max@0	2434 </td>
max@0	2435 </tr>
max@0	2436 <tr>
max@0	2437 <td style="vertical-align: top;">
max@0	2438 <b>.end_col(</b><i>col_number</i><b>)</b>
max@0	2439 </td>
max@0	2440 <td style="vertical-align: top;"> <br>
max@0	2441 </td>
max@0	2442 <td style="vertical-align: top;">
max@0	2443 iterator referring to the <i>past-the-end</i> element of the specified column
max@0	2444 </td>
max@0	2445 </tr>
max@0	2446 </tbody>
max@0	2447 </table>
max@0	2448 </ul>
max@0	2449 </li>
max@0	2450 <br>
max@0	2451 <br>
max@0	2452 <li>
max@0	2453 Examples:
max@0	2454 <ul>
max@0	2455 <pre>
max@0	2456 mat X = randu<mat>(5,5);
max@0	2457
max@0	2458
max@0	2459 mat::iterator a = X.begin();
max@0	2460 mat::iterator b = X.end();
max@0	2461
max@0	2462 for(mat::iterator i=a; i!=b; ++i)
max@0	2463 {
max@0	2464 cout << *i << endl;
max@0	2465 }
max@0	2466
max@0	2467
max@0	2468 mat::col_iterator c = X.begin_col(1); // start of column 1
max@0	2469 mat::col_iterator d = X.end_col(3); // end of column 3
max@0	2470
max@0	2471 for(mat::col_iterator i=c; i!=d; ++i)
max@0	2472 {
max@0	2473 cout << *i << endl;
max@0	2474 (*i) = 123.0;
max@0	2475 }
max@0	2476 </pre>
max@0	2477 </ul>
max@0	2478 </li>
max@0	2479 <br>
max@0	2480 <li>
max@0	2481 See also:
max@0	2482 <ul>
max@0	2483 <li><a href="#stl_container_fns">STL container functions</a></li>
max@0	2484 <li><a href="http://cplusplus.com/reference/std/iterator/">iterator at cplusplus.com</a></li>
max@0	2485 <li><a href="#element_access">element access</a></li>
max@0	2486 </ul>
max@0	2487 </li>
max@0	2488 <br>
max@0	2489 </ul>
max@0	2490 <hr class="greyline"><br>
max@0	2491
max@0	2492 <a name="iterators_cube"></a>
max@0	2493 <b>iterators (cubes)</b>
max@0	2494 <ul>
max@0	2495 <li>
max@0	2496 STL-style iterators and associated member functions of the <i>Cube</i> class
max@0	2497 </li>
max@0	2498 <br>
max@0	2499 <li>
max@0	2500 iterator types:
max@0	2501 <br>
max@0	2502 <br>
max@0	2503 <ul>
max@0	2504 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	2505 <tbody>
max@0	2506 <tr>
max@0	2507 <td style="vertical-align: top;">
max@0	2508 <b>cube::iterator</b>
max@0	2509 </td>
max@0	2510 <td style="vertical-align: top;"> <br>
max@0	2511 </td>
max@0	2512 <td style="vertical-align: top;">
max@0	2513 random access iterator, for read/write access to elements;
max@0	2514 the elements are ordered slice by slice;
max@0	2515 the elements within each slice are ordered column by column
max@0	2516 </td>
max@0	2517 </tr>
max@0	2518 <tr>
max@0	2519 <td style="vertical-align: top;">
max@0	2520
max@0	2521 </td>
max@0	2522 <td style="vertical-align: top;"> <br>
max@0	2523 </td>
max@0	2524 <td style="vertical-align: top;">
max@0	2525
max@0	2526 </td>
max@0	2527 </tr>
max@0	2528 <tr>
max@0	2529 <td style="vertical-align: top;">
max@0	2530 <b>cube::const_iterator</b>
max@0	2531 </td>
max@0	2532 <td style="vertical-align: top;"> <br>
max@0	2533 </td>
max@0	2534 <td style="vertical-align: top;">
max@0	2535 random access iterators, for read-only access to elements
max@0	2536 </td>
max@0	2537 </tr>
max@0	2538 <tr>
max@0	2539 <td style="vertical-align: top;">
max@0	2540
max@0	2541 </td>
max@0	2542 <td style="vertical-align: top;"> <br>
max@0	2543 </td>
max@0	2544 <td style="vertical-align: top;">
max@0	2545
max@0	2546 </td>
max@0	2547 </tr>
max@0	2548 <tr>
max@0	2549 <td style="vertical-align: top;">
max@0	2550 <b>cube::slice_iterator</b>
max@0	2551 </td>
max@0	2552 <td style="vertical-align: top;"> <br>
max@0	2553 </td>
max@0	2554 <td style="vertical-align: top;">
max@0	2555 random access iterator, for read/write access to the elements of a particular slice;
max@0	2556 the elements are ordered column by column
max@0	2557 </td>
max@0	2558 </tr>
max@0	2559 <tr>
max@0	2560 <td style="vertical-align: top;">
max@0	2561
max@0	2562 </td>
max@0	2563 <td style="vertical-align: top;"> <br>
max@0	2564 </td>
max@0	2565 <td style="vertical-align: top;">
max@0	2566
max@0	2567 </td>
max@0	2568 </tr>
max@0	2569 <tr>
max@0	2570 <td style="vertical-align: top;">
max@0	2571 <b>cube::const_slice_iterator</b>
max@0	2572 </td>
max@0	2573 <td style="vertical-align: top;"> <br>
max@0	2574 </td>
max@0	2575 <td style="vertical-align: top;">
max@0	2576 random access iterators, for read-only access to the elements of a particular slice
max@0	2577 </td>
max@0	2578 </tr>
max@0	2579 </tbody>
max@0	2580 </table>
max@0	2581 </ul>
max@0	2582 </li>
max@0	2583 <br>
max@0	2584 <br>
max@0	2585 <li>
max@0	2586 Member functions:
max@0	2587 <br>
max@0	2588 <br>
max@0	2589 <ul>
max@0	2590 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	2591 <tbody>
max@0	2592 <tr>
max@0	2593 <td style="vertical-align: top;">
max@0	2594 <b>.begin()</b>
max@0	2595 </td>
max@0	2596 <td style="vertical-align: top;"> <br>
max@0	2597 </td>
max@0	2598 <td style="vertical-align: top;">
max@0	2599 iterator referring to the first element
max@0	2600 </td>
max@0	2601 </tr>
max@0	2602 <tr>
max@0	2603 <td style="vertical-align: top;">
max@0	2604 <b>.end()</b>
max@0	2605 </td>
max@0	2606 <td style="vertical-align: top;"> <br>
max@0	2607 </td>
max@0	2608 <td style="vertical-align: top;">
max@0	2609 iterator referring to the <i>past-the-end</i> element
max@0	2610 </td>
max@0	2611 </tr>
max@0	2612 <tr>
max@0	2613 <td>
max@0	2614
max@0	2615 </td>
max@0	2616 </tr>
max@0	2617 <tr>
max@0	2618 <td style="vertical-align: top;">
max@0	2619 <b>.begin_slice(</b><i>slice_number</i><b>)</b>
max@0	2620 </td>
max@0	2621 <td style="vertical-align: top;"> <br>
max@0	2622 </td>
max@0	2623 <td style="vertical-align: top;">
max@0	2624 iterator referring to the first element of the specified slice
max@0	2625 </td>
max@0	2626 </tr>
max@0	2627 <tr>
max@0	2628 <td style="vertical-align: top;">
max@0	2629 <b>.end_slice(</b><i>slice_number</i><b>)</b>
max@0	2630 </td>
max@0	2631 <td style="vertical-align: top;"> <br>
max@0	2632 </td>
max@0	2633 <td style="vertical-align: top;">
max@0	2634 iterator referring to the <i>past-the-end</i> element of the specified slice
max@0	2635 </td>
max@0	2636 </tr>
max@0	2637 </tbody>
max@0	2638 </table>
max@0	2639 </ul>
max@0	2640 </li>
max@0	2641 <br>
max@0	2642 <br>
max@0	2643 <li>
max@0	2644 Examples:
max@0	2645 <ul>
max@0	2646 <pre>
max@0	2647 cube X = randu<cube>(2,3,4);
max@0	2648
max@0	2649
max@0	2650 cube::iterator a = X.begin();
max@0	2651 cube::iterator b = X.end();
max@0	2652
max@0	2653 for(cube::iterator i=a; i!=b; ++i)
max@0	2654 {
max@0	2655 cout << *i << endl;
max@0	2656 }
max@0	2657
max@0	2658
max@0	2659 cube::slice_iterator c = X.begin_slice(1); // start of slice 1
max@0	2660 cube::slice_iterator d = X.end_slice(2); // end of slice 2
max@0	2661
max@0	2662 for(cube::slice_iterator i=c; i!=d; ++i)
max@0	2663 {
max@0	2664 cout << *i << endl;
max@0	2665 (*i) = 123.0;
max@0	2666 }
max@0	2667 </pre>
max@0	2668 </ul>
max@0	2669 </li>
max@0	2670 <br>
max@0	2671 <li>
max@0	2672 See also:
max@0	2673 <ul>
max@0	2674 <li><a href="http://cplusplus.com/reference/std/iterator/">iterator at cplusplus.com</a></li>
max@0	2675 <li><a href="#element_access">element access</a></li>
max@0	2676 </ul>
max@0	2677 </li>
max@0	2678 <br>
max@0	2679 </ul>
max@0	2680 <hr class="greyline"><br>
max@0	2681
max@0	2682 <a name="memptr"></a>
max@0	2683 <b>.memptr()</b>
max@0	2684 <ul>
max@0	2685 <li>
max@0	2686 Member function of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>Cube</i> classes
max@0	2687 </li>
max@0	2688 <br>
max@0	2689 <li>
max@0	2690 Obtain a raw pointer to the memory used for storing elements. Not recommended for use unless you know what you're doing!
max@0	2691 </li>
max@0	2692 <br>
max@0	2693 <li>
max@0	2694 The function can be used for interfacing with libraries such as <a href="http://www.fftw.org/">FFTW</a>
max@0	2695 </li>
max@0	2696 <br>
max@0	2697 <li>
max@0	2698 As soon as the size of the matrix/vector/cube is changed, the pointer is no longer valid
max@0	2699 </li>
max@0	2700 <br>
max@0	2701 <li>
max@0	2702 Data for matrices is stored in a column-by-column order
max@0	2703 </li>
max@0	2704 <br>
max@0	2705 <li>
max@0	2706 Data for cubes is stored in a slice-by-slice (matrix-by-matrix) order
max@0	2707 </li>
max@0	2708 <br>
max@0	2709 <li>
max@0	2710 Examples:
max@0	2711 <ul>
max@0	2712 <pre>
max@0	2713 mat A = randu<mat>(5,5);
max@0	2714 const mat B = randu<mat>(5,5);
max@0	2715
max@0	2716 double* A_mem = A.memptr();
max@0	2717 const double* B_mem = B.memptr();
max@0	2718 </pre>
max@0	2719 </ul>
max@0	2720 </li>
max@0	2721 <br>
max@0	2722 <li>
max@0	2723 See also:
max@0	2724 <ul>
max@0	2725 <li><a href="#colptr">.colptr()</a></li>
max@0	2726 <li><a href="#iterators_mat">iterators (matrices)</a></li>
max@0	2727 <li><a href="#iterators_cube">iterators (cubes)</a></li>
max@0	2728 <li><a href="#adv_constructors_mat">advanced constructors (matrices)</a></li>
max@0	2729 <li><a href="#adv_constructors_cube">advanced constructors (cubes)</a></li>
max@0	2730 </ul>
max@0	2731 </li>
max@0	2732 <br>
max@0	2733 </ul>
max@0	2734 <hr class="greyline"><br>
max@0	2735
max@0	2736 <a name="min_and_max_member"></a>
max@0	2737 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	2738 <tbody>
max@0	2739 <tr>
max@0	2740 <td style="vertical-align: top;"><b>.min()</b></td>
max@0	2741 <td style="vertical-align: top;"><br>
max@0	2742 </td>
max@0	2743 <td style="vertical-align: top;">(member functions of <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i>)
max@0	2744 </td>
max@0	2745 </tr>
max@0	2746 <tr>
max@0	2747 <td style="vertical-align: top;"><b>.max()</b></td>
max@0	2748 <td style="vertical-align: top;"><br>
max@0	2749 </td>
max@0	2750 <td style="vertical-align: top;">
max@0	2751 </td>
max@0	2752 </tr>
max@0	2753 <tr>
max@0	2754 <td style="vertical-align: top;"> </td>
max@0	2755 <td style="vertical-align: top;"><br>
max@0	2756 </td>
max@0	2757 <td style="vertical-align: top;">
max@0	2758 </td>
max@0	2759 </tr>
max@0	2760 <tr>
max@0	2761 <td style="vertical-align: top;"><b>.min(</b> index_of_min_val <b>)</b></td>
max@0	2762 <td style="vertical-align: top;"><br>
max@0	2763 </td>
max@0	2764 <td style="vertical-align: top;">(member functions of <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i>)
max@0	2765 </td>
max@0	2766 </tr>
max@0	2767 <tr>
max@0	2768 <td style="vertical-align: top;"><b>.max(</b> index_of_max_val <b>)</b></td>
max@0	2769 <td style="vertical-align: top;"><br>
max@0	2770 </td>
max@0	2771 <td style="vertical-align: top;">
max@0	2772 </td>
max@0	2773 </tr>
max@0	2774 <tr>
max@0	2775 <td style="vertical-align: top;"> </td>
max@0	2776 <td style="vertical-align: top;"><br>
max@0	2777 </td>
max@0	2778 <td style="vertical-align: top;">
max@0	2779 </td>
max@0	2780 </tr>
max@0	2781 <tr>
max@0	2782 <td style="vertical-align: top;"><b>.min(</b> row_of_min_val<b>,</b> col_of_min_val <b>)</b></td>
max@0	2783 <td style="vertical-align: top;"><br>
max@0	2784 </td>
max@0	2785 <td style="vertical-align: top;">(member functions of <i>Mat</i>)
max@0	2786 </td>
max@0	2787 </tr>
max@0	2788 <tr>
max@0	2789 <td style="vertical-align: top;"><b>.max(</b> row_of_max_val<b>,</b> col_of_max_val <b>)</b></td>
max@0	2790 <td style="vertical-align: top;"><br>
max@0	2791 </td>
max@0	2792 <td style="vertical-align: top;">
max@0	2793 </td>
max@0	2794 </tr>
max@0	2795 <tr>
max@0	2796 <td style="vertical-align: top;"> </td>
max@0	2797 <td style="vertical-align: top;"><br>
max@0	2798 </td>
max@0	2799 <td style="vertical-align: top;">
max@0	2800 </td>
max@0	2801 </tr>
max@0	2802 <tr>
max@0	2803 <td style="vertical-align: top;"><b>.min(</b> row_of_min_val<b>,</b> col_of_min_val<b>,</b> slice_of_min_val <b>)</b></td>
max@0	2804 <td style="vertical-align: top;"><br>
max@0	2805 </td>
max@0	2806 <td style="vertical-align: top;">(member functions of <i>Cube</i>)
max@0	2807 </td>
max@0	2808 </tr>
max@0	2809 <tr>
max@0	2810 <td style="vertical-align: top;"><b>.max(</b> row_of_max_val<b>,</b> col_of_max_val<b>,</b> slice_of_max_val <b>)</b></td>
max@0	2811 <td style="vertical-align: top;"><br>
max@0	2812 </td>
max@0	2813 <td style="vertical-align: top;">
max@0	2814 </td>
max@0	2815 </tr>
max@0	2816 </tbody>
max@0	2817 </table>
max@0	2818 <ul>
max@0	2819 <br>
max@0	2820 <li>
max@0	2821 Without arguments: return the extremum value of an object
max@0	2822 </li>
max@0	2823 <br>
max@0	2824 <li>
max@0	2825 With one or more arguments: return the extremum value of an object and store the location of the extremum value in the provided variable(s)
max@0	2826 </li>
max@0	2827 <br>
max@0	2828 <li>
max@0	2829 The provided variables must be of type <a href="#uword">uword</a>.
max@0	2830 </li>
max@0	2831 <br>
max@0	2832 <li>
max@0	2833 Examples:
max@0	2834 <ul>
max@0	2835 <pre>
max@0	2836 vec v = randu<vec>(10);
max@0	2837
max@0	2838 cout << "min value is " << v.min() << endl;
max@0	2839
max@0	2840
max@0	2841 uword index;
max@0	2842 double min_val = v.min(index);
max@0	2843
max@0	2844 cout << "index of min value is " << index << endl;
max@0	2845
max@0	2846
max@0	2847 mat A = randu<mat>(5,5);
max@0	2848
max@0	2849 uword row;
max@0	2850 uword col;
max@0	2851 double min_val2 = A.max(row,col);
max@0	2852
max@0	2853 cout << "max value is at " << row << ',' << col << endl;
max@0	2854 </pre>
max@0	2855 </ul>
max@0	2856 </li>
max@0	2857 <br>
max@0	2858 <li>
max@0	2859 See also:
max@0	2860 <ul>
max@0	2861 <li><a href="#min_and_max">min() & max()</a> (standalone functions)</li>
max@0	2862 <li><a href="#running_stat">running_stat</a></li>
max@0	2863 <li><a href="#running_stat_vec">running_stat_vec</a></li>
max@0	2864 </ul>
max@0	2865 </li>
max@0	2866 <br>
max@0	2867 </ul>
max@0	2868 <hr class="greyline"><br>
max@0	2869
max@0	2870 <a name="ones_member"></a>
max@0	2871 <b>.ones()</b>
max@0	2872 <br><b>.ones(n_elem)</b>
max@0	2873 <br><b>.ones(n_rows, n_cols)</b>
max@0	2874 <br><b>.ones(n_rows, n_cols, n_slices)</b>
max@0	2875 <ul>
max@0	2876 <li>
max@0	2877 Set the elements of an object to one, optionally first resizing to specified dimensions
max@0	2878 </li>
max@0	2879 <br>
max@0	2880 <li>
max@0	2881 <i>.ones()</i> and <i>.ones(n_elem)</i> are member functions of <i>Col</i> and <i>Row</i>
max@0	2882 </li>
max@0	2883 <br>
max@0	2884 <li>
max@0	2885 <i>.ones()</i> and <i>.ones(n_rows, n_cols)</i> are member functions of <i>Mat</i>
max@0	2886 </li>
max@0	2887 <br>
max@0	2888 <li>
max@0	2889 <i>.ones()</i> and <i>.ones(n_rows, n_cols, n_slices)</i> are member functions of <i>Cube</i>
max@0	2890 </li>
max@0	2891 <br>
max@0	2892 <li>
max@0	2893 Examples:
max@0	2894 <ul>
max@0	2895 <pre>
max@0	2896 mat A = randu<mat>(5,10);
max@0	2897 A.ones(); // sets all elements to one
max@0	2898 A.ones(10,20); // sets the size to 10 rows and 20 columns
max@0	2899 // followed by setting all elements to one
max@0	2900 </pre>
max@0	2901 </ul>
max@0	2902 </li>
max@0	2903 <br>
max@0	2904 <li>
max@0	2905 See also:
max@0	2906 <ul>
max@0	2907 <li><a href="#ones_standalone">ones()</a> (standalone function)</li>
max@0	2908 <li><a href="#zeros_member">.zeros()</a></li>
max@0	2909 <li><a href="#fill">.fill()</a></li>
max@0	2910 </ul>
max@0	2911 </li>
max@0	2912 <br>
max@0	2913 </ul>
max@0	2914 <hr class="greyline"><br>
max@0	2915
max@0	2916 <a name="operators"></a>
max@0	2917 <b>operators:   +   -   *   /   %   ==   !=   <=   >=   <   ></b>
max@0	2918 <ul>
max@0	2919 <li>
max@0	2920 Overloaded operators for <i>mat</i>, <i>vec</i>, <i>rowvec</i> and <i>cube</i> classes
max@0	2921 </li>
max@0	2922 <br>
max@0	2923 <li>
max@0	2924 Meanings:
max@0	2925 <br>
max@0	2926 <br>
max@0	2927 <ul>
max@0	2928 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	2929 <tbody>
max@0	2930 <tr>
max@0	2931 <td style="vertical-align: top;"><b>+</b></td>
max@0	2932 <td style="vertical-align: top;">   <br>
max@0	2933 </td>
max@0	2934 <td style="vertical-align: top;">Addition of two objects</td>
max@0	2935 </tr>
max@0	2936 <tr>
max@0	2937 <td style="vertical-align: top;"><b>-</b></td>
max@0	2938 <td style="vertical-align: top;"><br>
max@0	2939 </td>
max@0	2940 <td style="vertical-align: top;">Subtraction of one object from another or negation of an object</td>
max@0	2941 </tr>
max@0	2942 <tr>
max@0	2943 <td style="vertical-align: top;"><b>/</b></td>
max@0	2944 <td style="vertical-align: top;"><br>
max@0	2945 </td>
max@0	2946 <td style="vertical-align: top;">Element-wise division of an object by another object or a scalar</td>
max@0	2947 </tr>
max@0	2948 <tr>
max@0	2949 <td style="vertical-align: top;"><b>*</b></td>
max@0	2950 <td style="vertical-align: top;"><br>
max@0	2951 </td>
max@0	2952 <td style="vertical-align: top;">Matrix multiplication of two objects; not applicable to the <i>cube</i> class unless multiplying a cube by a scalar</td>
max@0	2953 </tr>
max@0	2954 <tr>
max@0	2955 <td style="vertical-align: top;"><b>%</b></td>
max@0	2956 <td style="vertical-align: top;"><br>
max@0	2957 </td>
max@0	2958 <td style="vertical-align: top;"><a name="schur_product"></a>Schur product: element-wise multiplication of two objects</td>
max@0	2959 </tr>
max@0	2960 <tr>
max@0	2961 <td style="vertical-align: top;"><b>==</b></td>
max@0	2962 <td style="vertical-align: top;"><br>
max@0	2963 </td>
max@0	2964 <td style="vertical-align: top;">Element-wise equality evaluation of two objects; generates a matrix of type <i>umat</i> with entries that indicate whether at a given position the two elements from the two objects are equal (1) or not equal (0)</td>
max@0	2965 </tr>
max@0	2966 <tr>
max@0	2967 <td style="vertical-align: top;"><b>!=</b></td>
max@0	2968 <td style="vertical-align: top;"><br>
max@0	2969 </td>
max@0	2970 <td style="vertical-align: top;">Element-wise non-equality evaluation of two objects</td>
max@0	2971 </tr>
max@0	2972 <tr>
max@0	2973 <td style="vertical-align: top;"><b>>=</b></td>
max@0	2974 <td style="vertical-align: top;"><br>
max@0	2975 </td>
max@0	2976 <td style="vertical-align: top;">As for ==, but the check is for "greater than or equal to"</td>
max@0	2977 </tr>
max@0	2978 <tr>
max@0	2979 <td style="vertical-align: top;"><b><=</b></td>
max@0	2980 <td style="vertical-align: top;"><br>
max@0	2981 </td>
max@0	2982 <td style="vertical-align: top;">As for ==, but the check is for "less than or equal to"</td>
max@0	2983 </tr>
max@0	2984 <tr>
max@0	2985 <td style="vertical-align: top;"><b>></b></td>
max@0	2986 <td style="vertical-align: top;"><br>
max@0	2987 </td>
max@0	2988 <td style="vertical-align: top;">As for ==, but the check is for "greater than"</td>
max@0	2989 </tr>
max@0	2990 <tr>
max@0	2991 <td style="vertical-align: top;"><b><</b></td>
max@0	2992 <td style="vertical-align: top;"><br>
max@0	2993 </td>
max@0	2994 <td style="vertical-align: top;">As for ==, but the check is for "less than"</td>
max@0	2995 </tr>
max@0	2996 </tbody>
max@0	2997 </table>
max@0	2998 </ul>
max@0	2999 </li>
max@0	3000 <br>
max@0	3001 <li>
max@0	3002 A <i>std::logic_error</i> exception is thrown if incompatible object sizes are used
max@0	3003 </li>
max@0	3004 <br>
max@0	3005 <li>
max@0	3006 If the +, - and % operators are chained, Armadillo will try to avoid the generation of temporaries;
max@0	3007 no temporaries are generated if all given objects are of the same type and size
max@0	3008 </li>
max@0	3009 <br>
max@0	3010 <li>
max@0	3011 If the * operator is chained, Armadillo will try to find an efficient ordering of the matrix multiplications
max@0	3012 </li>
max@0	3013 <br>
max@0	3014 <li>
max@0	3015 <b>Caveat:</b> operators involving an equality comparison (ie., ==, !=, >=, <=)
max@0	3016 may not work as expected for floating point element types (ie., <i>float</i>, <i>double</i>)
max@0	3017 due to the necessarily limited precision of these types;
max@0	3018 in other words, these operators are (in general) not recommended for matrices of type <i>mat</i> or <i>fmat</i>
max@0	3019 </li>
max@0	3020 <br>
max@0	3021 <br>
max@0	3022 <li>
max@0	3023 Examples:
max@0	3024 <ul>
max@0	3025 <pre>
max@0	3026 mat A = randu<mat>(5,10);
max@0	3027 mat B = randu<mat>(5,10);
max@0	3028 mat C = randu<mat>(10,5);
max@0	3029
max@0	3030 mat P = A + B;
max@0	3031 mat Q = A - B;
max@0	3032 mat R = -B;
max@0	3033 mat S = A / 123.0;
max@0	3034 mat T = A % B;
max@0	3035 mat U = A * C;
max@0	3036
max@0	3037 // V is constructed without temporaries
max@0	3038 mat V = A + B + A + B;
max@0	3039
max@0	3040 imat AA = "1 2 3; 4 5 6; 7 8 9;";
max@0	3041 imat BB = "3 2 1; 6 5 4; 9 8 7;";
max@0	3042
max@0	3043 // compare elements
max@0	3044 umat ZZ = (AA >= BB);
max@0	3045 </pre>
max@0	3046 </ul>
max@0	3047 </li>
max@0	3048 <br>
max@0	3049 <li>
max@0	3050 See also:
max@0	3051 <ul>
max@0	3052 <li><a href="#accu">accu()</a></li>
max@0	3053 <li><a href="#as_scalar">as_scalar()</a></li>
max@0	3054 <li><a href="#find">find()</a></li>
max@0	3055 </ul>
max@0	3056 </li>
max@0	3057 <br>
max@0	3058 </ul>
max@0	3059 <hr class="greyline"><br>
max@0	3060
max@0	3061 <a name="print"></a>
max@0	3062 <b>.print(header="")</b>
max@0	3063 <br><b>.print(stream, header="")</b>
max@0	3064 <ul>
max@0	3065 <li>
max@0	3066 Member function of <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i> and <i>field</i>
max@0	3067 </li>
max@0	3068 <br>
max@0	3069 <li>
max@0	3070 The first form prints the contents of an object to the <i>std::cout</i> stream, with an optional header line
max@0	3071 </li>
max@0	3072 <br>
max@0	3073 <li>
max@0	3074 The second form prints to a user specified stream
max@0	3075 </li>
max@0	3076 <br>
max@0	3077 <li>
max@0	3078 It's also possible to print objects using the << stream operator
max@0	3079 </li>
max@0	3080 <br>
max@0	3081 <li>
max@0	3082 Elements of a field can only be printed if there is an associated <i>operator<<</i> function defined
max@0	3083 </li>
max@0	3084 <br>
max@0	3085 <li>
max@0	3086 Examples:
max@0	3087 <ul>
max@0	3088 <pre>
max@0	3089 mat A = randu<mat>(5,5);
max@0	3090 mat B = randu<mat>(6,6);
max@0	3091
max@0	3092 A.print();
max@0	3093
max@0	3094 // print a transposed version of A
max@0	3095 A.t().print();
max@0	3096
max@0	3097 // "B:" is the optional header line
max@0	3098 B.print("B:");
max@0	3099
max@0	3100 cout << A << endl;
max@0	3101 cout << "B:" << endl << B << endl;
max@0	3102 </pre>
max@0	3103 </ul>
max@0	3104 </li>
max@0	3105 <br>
max@0	3106 <li>
max@0	3107 See also:
max@0	3108 <ul>
max@0	3109 <li><a href="#raw_print">.raw_print()</a></li>
max@0	3110 <li><a href="#save_load_mat">saving & loading matrices</a></li>
max@0	3111 <li><a href="#element_initialisation">initialising elements</a></li>
max@0	3112 <li><a href="#logging">logging of errors and warnings</a></li>
max@0	3113 </ul>
max@0	3114 </li>
max@0	3115 <br>
max@0	3116 </ul>
max@0	3117 <hr class="greyline"><br>
max@0	3118
max@0	3119 <a name="raw_print"></a>
max@0	3120 <b>.raw_print(header="")</b>
max@0	3121 <br><b>.raw_print(stream, header="")</b>
max@0	3122 <ul>
max@0	3123 <li>
max@0	3124 Member function of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>Cube</i>
max@0	3125 </li>
max@0	3126 <br>
max@0	3127 <li>
max@0	3128 Similar to the <a href="#print">.print()</a> member function,
max@0	3129 with the difference being that no formatting of the output is done -- ie. the user can set the stream's parameters such as precision, cell width, etc.
max@0	3130 </li>
max@0	3131 <br>
max@0	3132 <li>
max@0	3133 If the cell width is set to zero, a space is printed between the elements
max@0	3134 </li>
max@0	3135 <br>
max@0	3136 <li>
max@0	3137 Examples:
max@0	3138 <ul>
max@0	3139 <pre>
max@0	3140 mat A = randu<mat>(5,5);
max@0	3141
max@0	3142 cout.precision(11);
max@0	3143 cout.setf(ios::fixed);
max@0	3144
max@0	3145 A.raw_print(cout, "A =");
max@0	3146 </pre>
max@0	3147 </ul>
max@0	3148 </li>
max@0	3149 </ul>
max@0	3150 <br>
max@0	3151 <hr class="greyline"><br>
max@0	3152
max@0	3153 <a name="randu_randn_member"></a>
max@0	3154 <b>.randu()</b>
max@0	3155 <br><b>.randu(n_elem)</b>
max@0	3156 <br><b>.randu(n_rows, n_cols)</b>
max@0	3157 <br><b>.randu(n_rows, n_cols, n_slices)</b>
max@0	3158 <br>
max@0	3159 <br>
max@0	3160 <b>.randn()</b>
max@0	3161 <br><b>.randn(n_elem)</b>
max@0	3162 <br><b>.randn(n_rows, n_cols)</b>
max@0	3163 <br><b>.randn(n_rows, n_cols, n_slices)</b>
max@0	3164 <ul>
max@0	3165 <li>
max@0	3166 Fill an object with random values, optionally first resizing to specified dimensions
max@0	3167 </li>
max@0	3168 <br>
max@0	3169 <li><i>.randu()</i> uses a uniform distribution in the [0,1] interval
max@0	3170 </li>
max@0	3171 <br>
max@0	3172 <li><i>.randn()</i> uses a normal/Gaussian distribution with zero mean and unit variance
max@0	3173 </li>
max@0	3174 <br>
max@0	3175 <li>
max@0	3176 To change the seed, use the <a href="http://cplusplus.com/reference/clibrary/cstdlib/srand/">std::srand()</a> function
max@0	3177 </li>
max@0	3178 <br>
max@0	3179 <li>
max@0	3180 Examples:
max@0	3181 <ul>
max@0	3182 <pre>
max@0	3183 mat A(4,5);
max@0	3184 A.randu();
max@0	3185
max@0	3186 mat B;
max@0	3187 B.randu(6,7);
max@0	3188 </pre>
max@0	3189 </ul>
max@0	3190 </li>
max@0	3191 <br>
max@0	3192 <li>
max@0	3193 See also:
max@0	3194 <ul>
max@0	3195 <li><a href="#randu_randn_standalone">randu() & randn()</a> (standalone functions)</li>
max@0	3196 <li><a href="#fill">.fill()</a></li>
max@0	3197 <li><a href="#ones_member">.ones()</a></li>
max@0	3198 <li><a href="#zeros_member">.zeros()</a></li>
max@0	3199 <li><a href="http://cplusplus.com/reference/clibrary/cstdlib/srand/">std::srand()</a></li>
max@0	3200 </ul>
max@0	3201 </li>
max@0	3202 <br>
max@0	3203 </ul>
max@0	3204 <hr class="greyline"><br>
max@0	3205
max@0	3206 <a name="reset"></a>
max@0	3207 <b>
max@0	3208 .reset()
max@0	3209 </b>
max@0	3210 <ul>
max@0	3211 <li>
max@0	3212 Member function of <i>Mat</i>, <i>Col</i>, <i>Row</i>, <i>Cube</i> and <i>field</i>
max@0	3213 </li>
max@0	3214 <br>
max@0	3215 <li>
max@0	3216 Causes an object to have no elements
max@0	3217 </li>
max@0	3218 <br>
max@0	3219 <li>
max@0	3220 Examples:
max@0	3221 <ul>
max@0	3222 <pre>
max@0	3223 mat A = randu<mat>(5, 5);
max@0	3224 A.reset();
max@0	3225 </pre>
max@0	3226 </ul>
max@0	3227 </li>
max@0	3228 <br>
max@0	3229 <li>See also:
max@0	3230 <ul>
max@0	3231 <li><a href="#set_size">.set_size()</a></li>
max@0	3232 <li><a href="#is_empty">.is_empty()</a></li>
max@0	3233 <li><a href="#zeros_member">.zeros()</a></li>
max@0	3234 </ul>
max@0	3235 </li>
max@0	3236 </ul>
max@0	3237 <br>
max@0	3238 <hr class="greyline"><br>
max@0	3239
max@0	3240 <a name="reshape_member"></a>
max@0	3241 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	3242 <tbody>
max@0	3243 <tr>
max@0	3244 <td style="vertical-align: top;"><b>.reshape(n_rows, n_cols, dim=0)</b></td>
max@0	3245 <td style="vertical-align: top;"><br>
max@0	3246 </td>
max@0	3247 <td style="vertical-align: top;">(member function of <i>Mat</i>, <i>Col</i>, <i>Row</i>)
max@0	3248 </td>
max@0	3249 </tr>
max@0	3250 <tr>
max@0	3251 <td style="vertical-align: top;"><b>.reshape(n_rows, n_cols, n_slices, dim=0)</b></td>
max@0	3252 <td style="vertical-align: top;"><br>
max@0	3253 </td>
max@0	3254 <td style="vertical-align: top;">(member function of <i>Cube</i>)
max@0	3255 </td>
max@0	3256 </tr>
max@0	3257 </tbody>
max@0	3258 </table>
max@0	3259 <br>
max@0	3260 <ul>
max@0	3261 <li>
max@0	3262 Recreate the object according to given size specifications,
max@0	3263 with the elements taken from the previous version of the object,
max@0	3264 either column-wise (dim=0) or row-wise (dim=1);
max@0	3265 the elements in the generated object are placed column-wise (ie. the first column is filled up before filling the second column)
max@0	3266 </li>
max@0	3267 <br>
max@0	3268 <li>
max@0	3269 The layout of the elements in the recreated object will be different to the layout in the previous version of the object
max@0	3270 </li>
max@0	3271 <br>
max@0	3272 <li>
max@0	3273 This function can be used to vectorise a matrix (ie. concatenate all the columns or rows)
max@0	3274 </li>
max@0	3275 <br>
max@0	3276 <li>
max@0	3277 The new total number of elements (according to the specified size) doesn't have to be the same as the previous total number of elements in the object
max@0	3278 </li>
max@0	3279 <br>
max@0	3280 <li>
max@0	3281 If the total number of elements in the previous version of the object is less than the specified size,
max@0	3282 the extra elements in the recreated object are set to zero
max@0	3283 </li>
max@0	3284 <br>
max@0	3285 <li>
max@0	3286 If the total number of elements in the previous version of the object is greater than the specified size,
max@0	3287 only a subset of the elements is taken
max@0	3288 </li>
max@0	3289 <br>
max@0	3290 <li>
max@0	3291 <b>Caveat:</b>
max@0	3292 .reshape() is slower than <a href="#set_size">.set_size()</a>, which doesn't preserve data
max@0	3293 </li>
max@0	3294 <br>
max@0	3295 <li>
max@0	3296 <b>Caveat:</b>
max@0	3297 if you wish to grow/shrink the object while preserving the elements <b>as well as</b> the layout of the elements,
max@0	3298 use <a href="#resize_member">.resize()</a> instead
max@0	3299 </li>
max@0	3300 <br>
max@0	3301 <li>
max@0	3302 Examples:
max@0	3303 <ul>
max@0	3304 <pre>
max@0	3305 mat A = randu<mat>(4,5);
max@0	3306 A.reshape(5,4);
max@0	3307
max@0	3308 // vectorise A into a column vector:
max@0	3309 A.reshape(A.n_elem, 1);
max@0	3310 </pre>
max@0	3311 </ul>
max@0	3312 </li>
max@0	3313 <br>
max@0	3314 <li>See also:
max@0	3315 <ul>
max@0	3316 <li><a href="#resize_member">.resize()</a></li>
max@0	3317 <li><a href="#set_size">.set_size()</a></li>
max@0	3318 <li><a href="#reset">.reset()</a></li>
max@0	3319 <li><a href="#reshape">reshape()</a> (standalone function)</li>
max@0	3320 </ul>
max@0	3321 </li>
max@0	3322 </ul>
max@0	3323 <br>
max@0	3324 <hr class="greyline"><br>
max@0	3325
max@0	3326 <a name="resize_member"></a>
max@0	3327 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	3328 <tbody>
max@0	3329 <tr>
max@0	3330 <td style="vertical-align: top;"><b>.resize(n_elem)</b></td>
max@0	3331 <td style="vertical-align: top;"><br>
max@0	3332 </td>
max@0	3333 <td style="vertical-align: top;">(member function of <i>Col</i>, <i>Row</i>)
max@0	3334 </td>
max@0	3335 </tr>
max@0	3336 <tr>
max@0	3337 <td style="vertical-align: top;"><b>.resize(n_rows, n_cols)</b></td>
max@0	3338 <td style="vertical-align: top;"><br>
max@0	3339 </td>
max@0	3340 <td style="vertical-align: top;">(member function of <i>Mat</i>)
max@0	3341 </td>
max@0	3342 </tr>
max@0	3343 <tr>
max@0	3344 <td style="vertical-align: top;"><b>.resize(n_rows, n_cols, n_slices)</b></td>
max@0	3345 <td style="vertical-align: top;"><br>
max@0	3346 </td>
max@0	3347 <td style="vertical-align: top;">(member function of <i>Cube</i>)
max@0	3348 </td>
max@0	3349 </tr>
max@0	3350 </tbody>
max@0	3351 </table>
max@0	3352 <br>
max@0	3353 <ul>
max@0	3354 <li>
max@0	3355 Recreate the object according to given size specifications, while preserving the elements as well as the layout of the elements
max@0	3356 </li>
max@0	3357 <br>
max@0	3358 <li>
max@0	3359 Can be used for growing or shrinking an object (ie. adding/removing rows, and/or columns, and/or slices)
max@0	3360 </li>
max@0	3361 <br>
max@0	3362 <li>
max@0	3363 <b>Caveat:</b>
max@0	3364 .resize() is slower than <a href="#set_size">.set_size()</a>, which doesn't preserve data
max@0	3365 </li>
max@0	3366 <br>
max@0	3367 <li>
max@0	3368 Examples:
max@0	3369 <ul>
max@0	3370 <pre>
max@0	3371 mat A = randu<mat>(4,5);
max@0	3372 A.resize(7,6);
max@0	3373 </pre>
max@0	3374 </ul>
max@0	3375 </li>
max@0	3376 <br>
max@0	3377 <li>
max@0	3378 This function was added in version 2.4.1
max@0	3379 </li>
max@0	3380 <br>
max@0	3381 <li>See also:
max@0	3382 <ul>
max@0	3383 <li><a href="#reshape_member">.reshape()</a></li>
max@0	3384 <li><a href="#set_size">.set_size()</a></li>
max@0	3385 <li><a href="#reset">.reset()</a></li>
max@0	3386 <li><a href="#insert">insert rows/cols/slices</a></li>
max@0	3387 <li><a href="#shed">shed rows/cols/slices</a></li>
max@0	3388 <li><a href="#resize">resize()</a> (standalone function)</li>
max@0	3389 </ul>
max@0	3390 </li>
max@0	3391 </ul>
max@0	3392 <br>
max@0	3393 <hr class="greyline"><br>
max@0	3394
max@0	3395 <a name="save_load_mat"></a>
max@0	3396 <b>
max@0	3397 .save(name, file_type = arma_binary)
max@0	3398 <br>
max@0	3399 .save(stream, file_type = arma_binary)
max@0	3400 <br>
max@0	3401 <br>
max@0	3402 .load(name, file_type = auto_detect)
max@0	3403 <br>
max@0	3404 .load(stream, file_type = auto_detect)
max@0	3405 <br>
max@0	3406 <br>
max@0	3407 .quiet_save(name, file_type = arma_binary)
max@0	3408 <br>
max@0	3409 .quiet_save(stream, file_type = arma_binary)
max@0	3410 <br>
max@0	3411 <br>
max@0	3412 .quiet_load(name, file_type = auto_detect)
max@0	3413 <br>
max@0	3414 .quiet_load(stream, file_type = auto_detect)
max@0	3415 </b>
max@0	3416 <ul>
max@0	3417 <li>Member functions of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>Cube</i> classes</li>
max@0	3418 <br>
max@0	3419 <li>Store/retrieve data in files or streams</li>
max@0	3420 <br>
max@0	3421 <li>On success, <i>save()</i>, <i>load()</i>, <i>quiet_save()</i>, and <i>quite_load()</i> will return a <i>bool</i> set to <i>true</i></li>
max@0	3422 <br>
max@0	3423 <li><i>save()</i> and <i>quiet_save()</i> will return a <i>bool</i> set to <i>false</i> if the saving process fails</li>
max@0	3424 <br>
max@0	3425 <li>
max@0	3426 <i>load()</i> and <i>quiet_load()</i> will return a <i>bool</i> set to <i>false</i> if the loading process fails;
max@0	3427 additionally, the object will be reset so it has no elements
max@0	3428 </li>
max@0	3429 <br>
max@0	3430 <li><i>load()</i> and <i>save()</i> will print warning messages if any problems are encountered</li>
max@0	3431 <br>
max@0	3432 <li><i>quiet_load()</i> and <i>quiet_save()</i> do not print any error messages</li>
max@0	3433 <br>
max@0	3434 <li>
max@0	3435 The following file formats are supported:
max@0	3436 <br>
max@0	3437 <br>
max@0	3438 <ul>
max@0	3439 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	3440 <tbody>
max@0	3441 <tr>
max@0	3442 <td style="vertical-align: top;"><b>auto_detect</b></td>
max@0	3443 <td style="vertical-align: top;"><br>
max@0	3444 </td>
max@0	3445 <td style="vertical-align: top;">
max@0	3446 for <i>load()</i> and <i>quiet_load()</i>:
max@0	3447 try to automatically detect the file type as one of the formats described below.
max@0	3448 This is the default operation.
max@0	3449 <br>
max@0	3450 <br>
max@0	3451 </td>
max@0	3452 </tr>
max@0	3453 <tr>
max@0	3454 <td style="vertical-align: top;"><b>raw_ascii</b></td>
max@0	3455 <td style="vertical-align: top;"><br>
max@0	3456 </td>
max@0	3457 <td style="vertical-align: top;">
max@0	3458 Numerical data stored in raw ASCII format, without a header.
max@0	3459 The numbers are separated by whitespace.
max@0	3460 The number of columns must be the same in each row.
max@0	3461 Data which was saved in Matlab/Octave using the <i>-ascii</i> option can be read in Armadillo, except for complex numbers.
max@0	3462 Complex numbers are stored in standard C++ notation (a tuple surrounded by brackets: eg. (1.23,4.56) indicates 1.24 + 4.56i).
max@0	3463 Cubes are loaded as one slice.
max@0	3464 <br>
max@0	3465 <br>
max@0	3466 </td>
max@0	3467 </tr>
max@0	3468 <tr>
max@0	3469 <td style="vertical-align: top;"><b>raw_binary</b></td>
max@0	3470 <td style="vertical-align: top;"><br>
max@0	3471 </td>
max@0	3472 <td style="vertical-align: top;">
max@0	3473 Numerical data stored in machine dependent raw binary format, without a header.
max@0	3474 Matrices are loaded to have one column,
max@0	3475 while cubes are loaded to have one slice with one column.
max@0	3476 The <a href="#reshape_member">.reshape()</a> function can be used to alter the size of the loaded matrix/cube without losing data.
max@0	3477 <br>
max@0	3478 <br>
max@0	3479 </td>
max@0	3480 </tr>
max@0	3481 <tr>
max@0	3482 <td style="vertical-align: top;"><b>arma_ascii</b></td>
max@0	3483 <td style="vertical-align: top;"><br>
max@0	3484 </td>
max@0	3485 <td style="vertical-align: top;">
max@0	3486 Numerical data stored in human readable text format, with a simple header to speed up loading.
max@0	3487 The header indicates the type of matrix as well as the number of rows and columns.
max@0	3488 For cubes, the header additionally specifies the number of slices.
max@0	3489 <br>
max@0	3490 <br>
max@0	3491 </td>
max@0	3492 </tr>
max@0	3493 <tr>
max@0	3494 <td style="vertical-align: top;"><b>arma_binary</b></td>
max@0	3495 <td style="vertical-align: top;"><br>
max@0	3496 </td>
max@0	3497 <td style="vertical-align: top;">
max@0	3498 Numerical data stored in machine dependent binary format, with a simple header to speed up loading.
max@0	3499 The header indicates the type of matrix as well as the number of rows and columns.
max@0	3500 For cubes, the header additionally specifies the number of slices.
max@0	3501 <br>
max@0	3502 <br>
max@0	3503 </td>
max@0	3504 </tr>
max@0	3505 <tr>
max@0	3506 <td style="vertical-align: top;"><b>csv_ascii</b></td>
max@0	3507 <td style="vertical-align: top;"><br>
max@0	3508 </td>
max@0	3509 <td style="vertical-align: top;">
max@0	3510 Numerical data stored in comma separated value (CSV) text format, without a header.
max@0	3511 Applicable to <i>Mat</i> only.
max@0	3512 <br>
max@0	3513 <br>
max@0	3514 </td>
max@0	3515 </tr>
max@0	3516 <tr>
max@0	3517 <td style="vertical-align: top;"><b>pgm_binary</b></td>
max@0	3518 <td style="vertical-align: top;"><br>
max@0	3519 </td>
max@0	3520 <td style="vertical-align: top;">
max@0	3521 Image data stored in Portable Gray Map (PGM) format.
max@0	3522 Applicable to <i>Mat</i> only.
max@0	3523 Saving <i>int</i>, <i>float</i> or <i>double</i> matrices is a lossy operation, as each element is copied and converted to an 8 bit representation.
max@0	3524 As such the matrix should have values in the [0,255] interval, otherwise the resulting image may not display correctly.
max@0	3525 <br>
max@0	3526 <br>
max@0	3527 </td>
max@0	3528 </tr>
max@0	3529 <tr>
max@0	3530 <td style="vertical-align: top;"><b>ppm_binary</b></td>
max@0	3531 <td style="vertical-align: top;"><br>
max@0	3532 </td>
max@0	3533 <td style="vertical-align: top;">
max@0	3534 Image data stored in Portable Pixel Map (PPM) format.
max@0	3535 Applicable to <i>Cube</i> only.
max@0	3536 Saving <i>int</i>, <i>float</i> or <i>double</i> matrices is a lossy operation, as each element is copied and converted to an 8 bit representation.
max@0	3537 As such the cube/field should have values in the [0,255] interval, otherwise the resulting image may not display correctly.
max@0	3538 </td>
max@0	3539 </tr>
max@0	3540 </tbody>
max@0	3541 </table>
max@0	3542 </ul>
max@0	3543 </li>
max@0	3544 <br>
max@0	3545 <br>
max@0	3546 <li>
max@0	3547 Examples:
max@0	3548 <ul>
max@0	3549 <pre>
max@0	3550 mat A = randu<mat>(5,5);
max@0	3551
max@0	3552 A.save("A1.mat"); // default save format is arma_binary
max@0	3553 A.save("A2.mat", arma_ascii);
max@0	3554
max@0	3555 mat B;
max@0	3556 // automatically detect format type
max@0	3557 B.load("A1.mat");
max@0	3558
max@0	3559 mat C;
max@0	3560 // force loading in the arma_ascii format
max@0	3561 C.load("A2.mat", arma_ascii);
max@0	3562
max@0	3563
max@0	3564 // example of saving/loading using a stream
max@0	3565 std::stringstream s;
max@0	3566 A.save(s);
max@0	3567
max@0	3568 mat D;
max@0	3569 D.load(s);
max@0	3570
max@0	3571
max@0	3572 // example of testing for success
max@0	3573 mat E;
max@0	3574 bool status = E.load("A2.mat");
max@0	3575
max@0	3576 if(status == true)
max@0	3577 {
max@0	3578 cout << "loaded okay" << endl;
max@0	3579 }
max@0	3580 else
max@0	3581 {
max@0	3582 cout << "problem with loading" << endl;
max@0	3583 }
max@0	3584 </pre>
max@0	3585 </ul>
max@0	3586 </li>
max@0	3587 <br>
max@0	3588 <li>See also:
max@0	3589 <ul>
max@0	3590 <li><a href="#save_load_field">saving/loading fields</a></li>
max@0	3591 </ul>
max@0	3592 </li>
max@0	3593 <br>
max@0	3594 </ul>
max@0	3595 <hr class="greyline"><br>
max@0	3596
max@0	3597 <a name="save_load_field"></a>
max@0	3598 <b>
max@0	3599 .save(name, file_type = arma_binary)
max@0	3600 <br>
max@0	3601 .save(stream, file_type = arma_binary)
max@0	3602 <br>
max@0	3603 <br>
max@0	3604 .load(name, file_type = auto_detect)
max@0	3605 <br>
max@0	3606 .load(stream, file_type = auto_detect)
max@0	3607 <br>
max@0	3608 <br>
max@0	3609 .quiet_save(name, file_type = arma_binary)
max@0	3610 <br>
max@0	3611 .quiet_save(stream, file_type = arma_binary)
max@0	3612 <br>
max@0	3613 <br>
max@0	3614 .quiet_load(name, file_type = auto_detect)
max@0	3615 <br>
max@0	3616 .quiet_load(stream, file_type = auto_detect)
max@0	3617 </b>
max@0	3618 <ul>
max@0	3619 <li>Member functions of the <i>field</i> class</li>
max@0	3620 <br>
max@0	3621 <li>Store/retrieve fields in files or stream</li>
max@0	3622 <br>
max@0	3623 <li>On success, save(), load(), quiet_save(), and quite_load() will return a <i>bool</i> set to <i>true</i></li>
max@0	3624 <br>
max@0	3625 <li>save() and quiet_save() will return a <i>bool</i> set to <i>false</i> if the saving process fails</li>
max@0	3626 <br>
max@0	3627 <li>
max@0	3628 load() and quiet_load() will return a <i>bool</i> set to <i>false</i> if the loading process fails;
max@0	3629 additionally, the field will be reset so it has no elements
max@0	3630 </li>
max@0	3631 <br>
max@0	3632 <li>load() and save() will print warning messages if any problems are encountered</li>
max@0	3633 <br>
max@0	3634 <li>quiet_load() and quiet_save() do not print any error messages</li>
max@0	3635 <br>
max@0	3636 <li>
max@0	3637 Fields with objects of type <i>std::string</i> are saved and loaded as raw text files.
max@0	3638 The text files do not have a header.
max@0	3639 Each string is separated by a whitespace.
max@0	3640 load() and quiet_load() will only accept text files that have the same number of strings on each line.
max@0	3641 The strings can have variable lengths.
max@0	3642 </li>
max@0	3643 <br>
max@0	3644 <li>
max@0	3645 Other than storing string fields as text files, the following file formats are supported:
max@0	3646 <br>
max@0	3647 <br>
max@0	3648 <ul>
max@0	3649 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	3650 <tbody>
max@0	3651 <tr>
max@0	3652 <td style="vertical-align: top;"><b>auto_detect</b></td>
max@0	3653 <td style="vertical-align: top;"><br>
max@0	3654 </td>
max@0	3655 <td style="vertical-align: top;">
max@0	3656 <br>
max@0	3657 <li>
max@0	3658 load(): try to automatically detect the field format type as one of the formats described below.
max@0	3659 This is the default operation.
max@0	3660 </li>
max@0	3661 <br>
max@0	3662 </td>
max@0	3663 </tr>
max@0	3664 <tr>
max@0	3665 <td style="vertical-align: top;"><b>arma_binary</b></td>
max@0	3666 <td style="vertical-align: top;"><br>
max@0	3667 </td>
max@0	3668 <td style="vertical-align: top;">
max@0	3669 <br>
max@0	3670 <li>
max@0	3671 Objects are stored in machine dependent binary format.
max@0	3672 <li>
max@0	3673 Default type for fields of type <i>Mat</i>, <i>Col</i> or <i>Row</i>.
max@0	3674 </li>
max@0	3675 <li>
max@0	3676 Only applicable to fields of type <i>Mat</i>, <i>Col</i> or <i>Row</i>.
max@0	3677 </li>
max@0	3678 <br>
max@0	3679 </td>
max@0	3680 </tr>
max@0	3681 <tr>
max@0	3682 <td style="vertical-align: top;"><b>ppm_binary</b></td>
max@0	3683 <td style="vertical-align: top;"><br>
max@0	3684 </td>
max@0	3685 <td style="vertical-align: top;">
max@0	3686 <br>
max@0	3687 <li>
max@0	3688 Image data stored in Portable Pixmap Map (PPM) format.
max@0	3689 </li>
max@0	3690 <li>
max@0	3691 Only applicable to fields of type <i>Mat</i>, <i>Col</i> or <i>Row</i>.
max@0	3692 </li>
max@0	3693 <li>
max@0	3694 .load(): Loads the specified image and stores the red, green and blue components as three separate matrices.
max@0	3695 The resulting field is comprised of the three matrices,
max@0	3696 with the red, green and blue components in the first, second and third matrix, respectively.
max@0	3697 </li>
max@0	3698 <li>
max@0	3699 .save(): Saves a field with exactly three matrices of equal size as an image.
max@0	3700 It is assumed that the red, green and blue components are stored in the first, second and third matrix, respectively.
max@0	3701 Saving <i>int</i>, <i>float</i> or <i>double</i> matrices is a lossy operation,
max@0	3702 as each matrix element is copied and converted to an 8 bit representation.
max@0	3703 </li>
max@0	3704
max@0	3705 </td>
max@0	3706 </tr>
max@0	3707 </tbody>
max@0	3708 </table>
max@0	3709 </ul>
max@0	3710 </li>
max@0	3711 <br>
max@0	3712 <li>See also:
max@0	3713 <ul>
max@0	3714 <li><a href="#save_load_mat">saving/loading matrices and cubes</a></li>
max@0	3715 </ul>
max@0	3716 </li>
max@0	3717 <br>
max@0	3718 </ul>
max@0	3719 <hr class="greyline"><br>
max@0	3720
max@0	3721 <a name="set_imag"></a>
max@0	3722 <b>.set_imag(X)</b>
max@0	3723 <br>
max@0	3724 <b>.set_real(X)</b>
max@0	3725 <br>
max@0	3726 <ul>
max@0	3727 <li>Member functions of Mat, Col, Row and Cube</li>
max@0	3728 <br>
max@0	3729 <li>
max@0	3730 Set the imaginary/real part of an object
max@0	3731 </li>
max@0	3732 <br>
max@0	3733 <li>
max@0	3734 <i>X</i> must have the same size as the recipient object
max@0	3735 </li>
max@0	3736 <br>
max@0	3737 <li>
max@0	3738 Examples:
max@0	3739 <ul>
max@0	3740 <pre>
max@0	3741 mat A = randu<mat>(4,5);
max@0	3742 mat B = randu<mat>(4,5);
max@0	3743
max@0	3744 cx_mat C = zeros<mat>(4,5);
max@0	3745
max@0	3746 C.set_real(A);
max@0	3747 C.set_imag(B);
max@0	3748 </pre>
max@0	3749 </ul>
max@0	3750 </li>
max@0	3751 <br>
max@0	3752 <li>
max@0	3753 <b>Caveat:</b>
max@0	3754 if you want to directly construct a complex matrix out of two real matrices,
max@0	3755 the following code is faster:
max@0	3756 <ul>
max@0	3757 <pre>
max@0	3758 mat A = randu<mat>(4,5);
max@0	3759 mat B = randu<mat>(4,5);
max@0	3760
max@0	3761 cx_mat C = cx_mat(A,B);
max@0	3762 </pre>
max@0	3763 </ul>
max@0	3764 </li>
max@0	3765 <br>
max@0	3766 <li>See also:
max@0	3767 <ul>
max@0	3768 <li><a href="#constructors_mat">matrix constructors</a></li>
max@0	3769 <li><a href="#constructors_cube">cube constructors</a></li>
max@0	3770 <li><a href="#imag_real">imag() / real()</a></li>
max@0	3771 </ul>
max@0	3772 </li>
max@0	3773 <br>
max@0	3774 </ul>
max@0	3775 <hr class="greyline"><br>
max@0	3776
max@0	3777 <a name="set_size"></a>
max@0	3778 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	3779 <tbody>
max@0	3780 <tr>
max@0	3781 <td style="vertical-align: top;"><b>.set_size(n_elem)</b></td>
max@0	3782 <td style="vertical-align: top;"><br>
max@0	3783 </td>
max@0	3784 <td style="vertical-align: top;">(member function of <i>Col</i>, <i>Row</i>, and <i>field</i>)
max@0	3785 </td>
max@0	3786 </tr>
max@0	3787 <tr>
max@0	3788 <td style="vertical-align: top;"><b>.set_size(n_rows, n_cols)</b></td>
max@0	3789 <td style="vertical-align: top;"><br>
max@0	3790 </td>
max@0	3791 <td style="vertical-align: top;">(member function of <i>Mat</i> and <i>field</i>)
max@0	3792 </td>
max@0	3793 </tr>
max@0	3794 <tr>
max@0	3795 <td style="vertical-align: top;"><b>.set_size(n_rows, n_cols, n_slices)</b></td>
max@0	3796 <td style="vertical-align: top;"><br>
max@0	3797 </td>
max@0	3798 <td style="vertical-align: top;">(member function of <i>Cube</i>)
max@0	3799 </td>
max@0	3800 </tr>
max@0	3801 </tbody>
max@0	3802 </table>
max@0	3803 <br>
max@0	3804 <ul>
max@0	3805 <li>Changes the size of an object</li>
max@0	3806 <br>
max@0	3807 <li>
max@0	3808 If the requested number of elements is equal to the old number of elements, existing memory is reused
max@0	3809 </li>
max@0	3810 <br>
max@0	3811 <li>
max@0	3812 If the requested number of elements is not equal to the old number of elements, new memory is used
max@0	3813 </li>
max@0	3814 <br>
max@0	3815 <li>
max@0	3816 If you need to explicitly preserve data, use <a href="#reshape_member">.reshape()</a> or <a href="#resize_member">.resize()</a>
max@0	3817 </li>
max@0	3818 <br>
max@0	3819 <li>
max@0	3820 Examples:
max@0	3821 <ul>
max@0	3822 <pre>
max@0	3823 mat A;
max@0	3824 A.set_size(5,10);
max@0	3825
max@0	3826 vec q;
max@0	3827 q.set_size(100);
max@0	3828 </pre>
max@0	3829 </ul>
max@0	3830 </li>
max@0	3831 <br>
max@0	3832 <li>See also:
max@0	3833 <ul>
max@0	3834 <li><a href="#reset">.reset()</a></li>
max@0	3835 <li><a href="#reshape_member">.reshape()</a></li>
max@0	3836 <li><a href="#resize_member">.resize()</a></li>
max@0	3837 </ul>
max@0	3838 </li>
max@0	3839 </ul>
max@0	3840 <br>
max@0	3841 <hr class="greyline"><br>
max@0	3842
max@0	3843 <a name="shed"></a>
max@0	3844 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	3845 <tbody>
max@0	3846 <tr>
max@0	3847 <td style="vertical-align: top;">
max@0	3848 <b>.shed_row( </b>row_number<b> )</b>
max@0	3849 <br>
max@0	3850 <b>.shed_rows( </b>first_row, last_row<b> )</b>
max@0	3851 </td>
max@0	3852 <td style="vertical-align: top;"><br></td>
max@0	3853 <td style="vertical-align: top;">(member functions of <i>Mat</i> and <i>Col</i>)
max@0	3854 </td>
max@0	3855 </tr>
max@0	3856 <tr>
max@0	3857 <td> </td>
max@0	3858 </tr>
max@0	3859 <tr>
max@0	3860 <td style="vertical-align: top;">
max@0	3861 <b>.shed_col( </b>column_number<b> )</b>
max@0	3862 <br>
max@0	3863 <b>.shed_cols( </b>first_column, last_column<b> )</b>
max@0	3864 </td>
max@0	3865 <td style="vertical-align: top;"><br></td>
max@0	3866 <td style="vertical-align: top;">(member functions of <i>Mat</i> and <i>Row</i>)
max@0	3867 </td>
max@0	3868 </tr>
max@0	3869 <tr>
max@0	3870 <td> </td>
max@0	3871 </tr>
max@0	3872 <tr>
max@0	3873 <td style="vertical-align: top;">
max@0	3874 <b>.shed_slice( </b>slice_number<b> )</b>
max@0	3875 <br>
max@0	3876 <b>.shed_slices( </b>first_slice, last_slice<b> )</b>
max@0	3877 </td>
max@0	3878 <td style="vertical-align: top;"><br></td>
max@0	3879 <td style="vertical-align: top;">(member functions of <i>Cube</i>)
max@0	3880 </td>
max@0	3881 </tr>
max@0	3882 </tbody>
max@0	3883 </table>
max@0	3884 <br>
max@0	3885 <ul>
max@0	3886 <li>
max@0	3887 Single argument functions:
max@0	3888 remove the specified row/column/slice
max@0	3889 </li>
max@0	3890 <br>
max@0	3891 <li>
max@0	3892 Two argument functions:
max@0	3893 remove the specified range of rows/columns/slices
max@0	3894 </li>
max@0	3895 <br>
max@0	3896 <li>
max@0	3897 Examples:
max@0	3898 <ul>
max@0	3899 <pre>
max@0	3900 mat A = randu<mat>(5,10);
max@0	3901
max@0	3902 A.shed_row(2);
max@0	3903 A.shed_cols(2,4);
max@0	3904 </pre>
max@0	3905 </ul>
max@0	3906 </li>
max@0	3907 <br>
max@0	3908 <li>
max@0	3909 See also:
max@0	3910 <ul>
max@0	3911 <li><a href="#insert">insert rows/columns/slices</a></li>
max@0	3912 <li><a href="#join">join rows/columns/slices</a></li>
max@0	3913 <li><a href="#resize_member">.resize()</a></li>
max@0	3914 <li><a href="#submat">submatrix views</a></li>
max@0	3915 <li><a href="#subcube">subcube views</a></li>
max@0	3916 <li><a href="http://thesaurus.com/browse/shed"><i>shed</i> in thesaurus.com</a></li>
max@0	3917 </ul>
max@0	3918 </li>
max@0	3919 <br>
max@0	3920 </ul>
max@0	3921 <hr class="greyline"><br>
max@0	3922
max@0	3923 <a name="stl_container_fns"></a>
max@0	3924 <b>STL container functions</b>
max@0	3925 <ul>
max@0	3926 <li><i>Mat</i>, <i>Col</i> and <i>Row</i> classes provide the following member functions that mimic the containers in the C++ Standard Template Library:<br>
max@0	3927 <br>
max@0	3928
max@0	3929 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	3930 <tbody>
max@0	3931 <tr>
max@0	3932 <td style="vertical-align: top;">
max@0	3933 <b>.clear()</b>
max@0	3934 </td>
max@0	3935 <td style="vertical-align: top;"> <br>
max@0	3936 </td>
max@0	3937 <td style="vertical-align: top;">
max@0	3938 causes an object to have no elements
max@0	3939 </td>
max@0	3940 </tr>
max@0	3941 <tr>
max@0	3942 <td style="vertical-align: top;">
max@0	3943
max@0	3944 </td>
max@0	3945 <td style="vertical-align: top;"> <br>
max@0	3946 </td>
max@0	3947 <td style="vertical-align: top;">
max@0	3948
max@0	3949 </td>
max@0	3950 </tr>
max@0	3951 <tr>
max@0	3952 <td style="vertical-align: top;">
max@0	3953 <b>.empty()</b>
max@0	3954 </td>
max@0	3955 <td style="vertical-align: top;"> <br>
max@0	3956 </td>
max@0	3957 <td style="vertical-align: top;">
max@0	3958 returns true if the object has no elements; returns false if the object has one or more elements
max@0	3959 </td>
max@0	3960 </tr>
max@0	3961 <tr>
max@0	3962 <td style="vertical-align: top;">
max@0	3963
max@0	3964 </td>
max@0	3965 <td style="vertical-align: top;"> <br>
max@0	3966 </td>
max@0	3967 <td style="vertical-align: top;">
max@0	3968
max@0	3969 </td>
max@0	3970 </tr>
max@0	3971 <tr>
max@0	3972 <td style="vertical-align: top;">
max@0	3973 <b>.size()</b>
max@0	3974 </td>
max@0	3975 <td style="vertical-align: top;"> <br>
max@0	3976 </td>
max@0	3977 <td style="vertical-align: top;">
max@0	3978 returns the total number of elements
max@0	3979 </td>
max@0	3980 </tr>
max@0	3981 </tbody>
max@0	3982 </table>
max@0	3983 </li>
max@0	3984 <br>
max@0	3985 <li>
max@0	3986 Examples:
max@0	3987 <ul>
max@0	3988 <pre>
max@0	3989 mat A = randu<mat>(5,5);
max@0	3990 cout << A.size() << endl;
max@0	3991
max@0	3992 A.clear();
max@0	3993 cout << A.empty() << endl;
max@0	3994 </pre>
max@0	3995 </ul>
max@0	3996 </li>
max@0	3997 <br>
max@0	3998 <li>
max@0	3999 See also:
max@0	4000 <ul>
max@0	4001 <li><a href="#iterators_mat">iterators (matrices)</a></li>
max@0	4002 <li><a href="#attributes">matrix and vector attributes</a></li>
max@0	4003 <li><a href="#is_empty">.is_empty()</a></li>
max@0	4004 <li><a href="#reset">.reset()</a></li>
max@0	4005 </ul>
max@0	4006 </li>
max@0	4007 <br>
max@0	4008 </ul>
max@0	4009 <hr class="greyline"><br>
max@0	4010
max@0	4011 <a name="submat"></a>
max@0	4012 <b>submatrix views</b>
max@0	4013 <ul>
max@0	4014 <li>A collection of member functions of <i>Mat</i>, <i>Col</i> and <i>Row</i> classes that provide submatrix views<br>
max@0	4015 <br>
max@0	4016 <li>For a matrix or vector <i>X</i>, the subviews are accessed as:</li>
max@0	4017 <br>
max@0	4018 <ul>
max@0	4019 X.<b>col( </b>col_number<b> )</b><br>
max@0	4020 X<b>(</b> <b>span::all,</b> col_number <b>)</b><br>
max@0	4021 X<b>(</b> <b>span(</b>first_row<b>,</b> last_row<b>),</b> col_number <b>)</b><br>
max@0	4022 <br>
max@0	4023 X.<b>unsafe_col( </b>col_number<b> )</b><br>
max@0	4024 <br>
max@0	4025 X.<b>row( </b>row_number<b> )</b><br>
max@0	4026 X<b>(</b> row_number<b>,</b> <b>span::all</b> <b>)</b><br>
max@0	4027 X<b>(</b> row_number<b>,</b> <b>span(</b>first_col<b>,</b> last_col<b>) )</b><br>
max@0	4028 <br>
max@0	4029 X.<b>cols( </b>first_col<b>,</b> last_col<b> )</b><br>
max@0	4030 X.<b>rows( </b>first_row<b>,</b> last_row<b> )</b><br>
max@0	4031 <br>
max@0	4032 X.<b>submat( </b>first_row<b>,</b> first_col<b>,</b> last_row<b>,</b> last_col<b> )</b><br>
max@0	4033 X.<b>submat( span(</b>first_row<b>,</b> last_row<b>), span(</b>first_col<b>,</b> last_col<b>) )</b><br>
max@0	4034 <br>
max@0	4035 X<b>( span(</b>first_row<b>,</b> last_row<b>), span(</b>first_col<b>,</b> last_col<b>) )</b><br>
max@0	4036 <br>
max@0	4037 X.<b>elem(</b> vector_of_indices <b>)</b>
max@0	4038 </ul>
max@0	4039 </li>
max@0	4040 <br>
max@0	4041 <li>For a vector <i>V</i> (column or row vector), there is an additional method:</li>
max@0	4042 <!-- <li>For a vector <i>V</i> (column or row vector), there are three additional methods:</li> -->
max@0	4043 <br>
max@0	4044 <ul>
max@0	4045 V.<b>subvec( </b>first_index<b>,</b> last_index<b> )</b><br>
max@0	4046 <!--
max@0	4047 V.<b>subvec( span(</b>first_index<b>,</b> last_index<b>) )</b><br>
max@0	4048 <br>
max@0	4049 V<b>( span(</b>first_index<b>,</b> last_index<b>) )</b><br>
max@0	4050 -->
max@0	4051 </ul>
max@0	4052 <br>
max@0	4053 <li>
max@0	4054 Instances of <i>span::all</i>, to indicate an entire range, can be replaced by <i>span()</i>, where no number is specified
max@0	4055 </li>
max@0	4056 <br>
max@0	4057 <li>
max@0	4058 In the function <i>X.elem(vector_of_indices)</i>,
max@0	4059 elements specified in <i>vector_of_indices</i> are accessed.
max@0	4060 <i>X</i> is interpreted as one long vector,
max@0	4061 with column-by-column ordering of the elements of <i>X</i>.
max@0	4062 The <i>vector_of_indices</i> must evaluate to be a vector of type <i><a href="#Col">uvec</a></i>
max@0	4063 (eg., generated by <i><a href="#find">find()</a></i>).
max@0	4064 The aggregate set of the specified elements is treated as a column vector
max@0	4065 (eg., the output of <i>X.elem()</i> is always a column vector).
max@0	4066 </li>
max@0	4067 <br>
max@0	4068 <li>
max@0	4069 The function <i>.unsafe_col()</i> is provided for speed reasons and should be used only if you know what you're doing.
max@0	4070 The function creates a seemingly independent <i>Col</i> vector object (eg. <i>vec</i>),
max@0	4071 but the vector actually uses memory from the existing matrix object.
max@0	4072 As such, the created <i>Col</i> vector is currently not alias safe
max@0	4073 and does not take into account that the parent matrix object could be deleted.
max@0	4074 If deleted memory is accessed through the created <i>Col</i> vector,
max@0	4075 it will cause memory corruption and/or a crash.
max@0	4076 </li>
max@0	4077 <br>
max@0	4078 <li>
max@0	4079 Examples:
max@0	4080 <ul>
max@0	4081 <pre>
max@0	4082 mat A = zeros<mat>(5,10);
max@0	4083
max@0	4084 A.submat(0,1,2,3) = randu<mat>(3,3);
max@0	4085
max@0	4086 // the following three statements
max@0	4087 // access the same part of A
max@0	4088 mat B = A.submat(0,1,2,3);
max@0	4089 mat C = A.submat( span(0,2), span(1,3) );
max@0	4090 mat D = A( span(0,2), span(1,3) );
max@0	4091
max@0	4092 // the following two statements
max@0	4093 // access the same part of A
max@0	4094 A.col(1) = randu<mat>(5,1);
max@0	4095 A(span::all, 1) = randu<mat>(5,1);
max@0	4096
max@0	4097 mat X = randu<mat>(5,5);
max@0	4098
max@0	4099 // get all elements of X that are greater than 0.5
max@0	4100 vec q = X.elem( find(X > 0.5) );
max@0	4101
max@0	4102 // set four specific elements of X to 1
max@0	4103 uvec indices;
max@0	4104 indices << 2 << 3 << 6 << 8;
max@0	4105
max@0	4106 X.elem(indices) = ones<vec>(4);
max@0	4107 </pre>
max@0	4108 </ul>
max@0	4109 </li>
max@0	4110 <br>
max@0	4111 <li>
max@0	4112 See also:
max@0	4113 <ul>
max@0	4114 <li><a href="#diag">.diag()</a></li>
max@0	4115 <li><a href="#colptr">.colptr()</a></li>
max@0	4116 <li><a href="#in_range">.in_range()</a></li>
max@0	4117 <li><a href="#find">find()</a></li>
max@0	4118 <li><a href="#join">join rows/columns/slices</a></li>
max@0	4119 <li><a href="#shed">shed rows/columns/slices</a></li>
max@0	4120 <li><a href="#insert">insert rows/columns/slices</a></li>
max@0	4121 <li><a href="#subcube">subcube views</a></li>
max@0	4122 </ul>
max@0	4123 </li>
max@0	4124 <br>
max@0	4125 </ul>
max@0	4126 <hr class="greyline"><br>
max@0	4127
max@0	4128 <a name="subcube"></a>
max@0	4129 <b>subcube views and slices</b>
max@0	4130 <ul>
max@0	4131 <li>A collection of member functions of the <i>Cube</i> class that provide subcube views<br>
max@0	4132 <br>
max@0	4133 <li>For a cube <i>Q</i>, the subviews are accessed as:</li>
max@0	4134 <br>
max@0	4135 <ul>
max@0	4136 Q.<b>slice( </b>slice_number <b>)</b><br>
max@0	4137 Q.<b>slices( </b>first_slice<b>,</b> last_slice <b>)</b><br>
max@0	4138 <br>
max@0	4139 Q.<b>subcube( </b>first_row<b>,</b> first_col<b>,</b> first_slice<b>, </b>last_row<b>,</b> last_col<b>, </b>last_slice <b>)</b><br>
max@0	4140 Q.<b>subcube( span(</b>first_row<b>,</b> last_row<b>), span(</b>first_col<b>,</b> last_col<b>), span(</b>first_slice<b>,</b> last_slice<b>) )</b><br>
max@0	4141 <br>
max@0	4142 Q<b>( span(</b>first_row<b>,</b> last_row<b>), span(</b>first_col<b>,</b> last_col<b>), span(</b>first_slice<b>,</b> last_slice<b>) )</b><br>
max@0	4143 </ul>
max@0	4144 </li>
max@0	4145 <br>
max@0	4146 <li>
max@0	4147 Instances of <i>span(a,b)</i> can be replaced by:
max@0	4148 <ul>
max@0	4149 <li><i>span()</i> or <i>span::all</i>, to indicate the entire range</li>
max@0	4150 <li><i>span(a)</i>, to indicate a particular row, column or slice</li>
max@0	4151 </ul>
max@0	4152 </li>
max@0	4153 <br>
max@0	4154 <li>
max@0	4155 An individual slice, accessed via <i>.slice()</i>, is an instance of the <i>Mat</i> class
max@0	4156 (a reference to a matrix is provided)
max@0	4157 </li>
max@0	4158 <br>
max@0	4159 <li>
max@0	4160 Examples:
max@0	4161 <ul>
max@0	4162 <pre>
max@0	4163 cube A = randu<cube>(2,3,4);
max@0	4164 mat B = A.slice(1);
max@0	4165
max@0	4166 A.slice(0) = randu<mat>(2,3);
max@0	4167 A.slice(0)(1,2) = 99.0;
max@0	4168
max@0	4169 A.subcube(0,0,1, 1,1,2) = randu<cube>(2,2,2);
max@0	4170 A( span(0,1), span(0,1), span(1,2) ) = randu<cube>(2,2,2);
max@0	4171
max@0	4172 </pre>
max@0	4173 </ul>
max@0	4174 </li>
max@0	4175 <br>
max@0	4176 <li>
max@0	4177 See also:
max@0	4178 <ul>
max@0	4179 <li><a href="#in_range">.in_range()</a></li>
max@0	4180 <li><a href="#join">join slices</a></li>
max@0	4181 <li><a href="#shed">shed slices</a></li>
max@0	4182 <li><a href="#insert">insert slices</a></li>
max@0	4183 <li><a href="#submat">submatrix views</a></li>
max@0	4184 </ul>
max@0	4185 </li>
max@0	4186 <br>
max@0	4187 </ul>
max@0	4188 <hr class="greyline"><br>
max@0	4189
max@0	4190 <a name="subfield"></a>
max@0	4191 <b>subfield views</b>
max@0	4192 <ul>
max@0	4193 <li>A collection of member functions of the <i>field</i> class that provide subfield views<br>
max@0	4194 <br>
max@0	4195 <li>For a field <i>F</i>, the subfields are accessed as:</li>
max@0	4196 <br>
max@0	4197 <ul>
max@0	4198 F.<b>row( </b>row_number <b>)</b><br>
max@0	4199 F.<b>col( </b>col_number <b>)</b><br>
max@0	4200 <br>
max@0	4201 F.<b>rows( </b>first_row<b>,</b> last_row <b>)</b><br>
max@0	4202 F.<b>cols( </b>first_col<b>,</b> last_col <b>)</b><br>
max@0	4203 <br>
max@0	4204 F.<b>subfield( </b>first_row<b>,</b> first_col<b>,</b> last_row<b>,</b> last_col <b>)</b><br>
max@0	4205 F.<b>subfield( span(</b>first_row<b>,</b> last_row<b>), span(</b>first_col<b>,</b> last_col<b>) )</b><br>
max@0	4206 <br>
max@0	4207 F<b>( span(</b>first_row<b>,</b> last_row<b>), span(</b>first_col<b>,</b> last_col<b>) )</b><br>
max@0	4208 </ul>
max@0	4209 </li>
max@0	4210 <br>
max@0	4211 <li>
max@0	4212 Instances of <i>span(a,b)</i> can be replaced by:
max@0	4213 <ul>
max@0	4214 <li><i>span()</i> or <i>span::all</i>, to indicate the entire range</li>
max@0	4215 <li><i>span(a)</i>, to indicate a particular row or column</li>
max@0	4216 </ul>
max@0	4217 </li>
max@0	4218 <br>
max@0	4219 <li>
max@0	4220 See also:
max@0	4221 <ul>
max@0	4222 <li><a href="#in_range">.in_range()</a></li>
max@0	4223 <li><a href="#submat">submatrix views</a></li>
max@0	4224 <li><a href="#subcube">subcube views</a></li>
max@0	4225 </ul>
max@0	4226 </li>
max@0	4227 <br>
max@0	4228 </ul>
max@0	4229 <hr class="greyline"><br>
max@0	4230
max@0	4231 <a name="swap_rows"></a>
max@0	4232 <b>
max@0	4233 .swap_rows(row1, row2)
max@0	4234 <br>.swap_cols(col1, col2)
max@0	4235 </b>
max@0	4236 <ul>
max@0	4237 <li>
max@0	4238 Member functions of <i>Mat</i>, <i>Col</i> and <i>Row</i> classes
max@0	4239 </li>
max@0	4240 <br>
max@0	4241 <li>
max@0	4242 Swap the contents of specified rows or columns
max@0	4243 </li>
max@0	4244 <br>
max@0	4245 <li>
max@0	4246 Examples:
max@0	4247 <ul>
max@0	4248 <pre>
max@0	4249 mat X = randu<mat>(5,5);
max@0	4250 X.swap_rows(0,4);
max@0	4251 </pre>
max@0	4252 </ul>
max@0	4253 </li>
max@0	4254 <br>
max@0	4255 <li>
max@0	4256 See also:
max@0	4257 <ul>
max@0	4258 <li><a href="#flip">fliplr() & flipud()</a></li>
max@0	4259 </ul>
max@0	4260 </li>
max@0	4261 <br>
max@0	4262 </ul>
max@0	4263 <hr class="greyline"><br>
max@0	4264
max@0	4265 <a name="t_st_members"></a>
max@0	4266 <b>
max@0	4267 .t()
max@0	4268 <br>.st()
max@0	4269 </b>
max@0	4270 <ul>
max@0	4271 <li>
max@0	4272 Member functions of any expression involving matrices or vectors
max@0	4273 </li>
max@0	4274 <br>
max@0	4275 <li>
max@0	4276 <i>.t()</i> provides a transposed copy of the object; if a given object has complex elements, a Hermitian transpose is done (ie. the conjugate of the elements is taken during the transpose operation)
max@0	4277 </li>
max@0	4278 <br>
max@0	4279 <li>
max@0	4280 <i>.st()</i> provides a transposed copy of the object, without taking the conjugate of the elements (complex matrices)
max@0	4281 </li>
max@0	4282 <br>
max@0	4283 <li>
max@0	4284 For non-complex objects, the <i>.t()</i> and <i>.st()</i> functions are equivalent
max@0	4285 </li>
max@0	4286 <br>
max@0	4287 <li>
max@0	4288 Examples:
max@0	4289 <ul>
max@0	4290 <pre>
max@0	4291 mat A = randu<mat>(4,5);
max@0	4292 mat B = A.t();
max@0	4293 </pre>
max@0	4294 </ul>
max@0	4295 </li>
max@0	4296 <br>
max@0	4297 <li>
max@0	4298 The <i>.t()</i> and <i>.st()</i> functions were added in version 2.4
max@0	4299 </li>
max@0	4300 <br>
max@0	4301 <li>
max@0	4302 See also:
max@0	4303 <ul>
max@0	4304 <li><a href="#trans">trans()</a></li>
max@0	4305 <li><a href="#strans">strans()</a></li>
max@0	4306 </ul>
max@0	4307 </li>
max@0	4308 <br>
max@0	4309 </ul>
max@0	4310 <hr class="greyline"><br>
max@0	4311
max@0	4312 <a name="zeros_member"></a>
max@0	4313 <b>.zeros()</b>
max@0	4314 <br><b>.zeros(n_elem)</b>
max@0	4315 <br><b>.zeros(n_rows, n_cols)</b>
max@0	4316 <br><b>.zeros(n_rows, n_cols, n_slices)</b>
max@0	4317 <ul>
max@0	4318 <li>
max@0	4319 Set the elements of an object to zero, optionally first resizing to specified dimensions
max@0	4320 </li>
max@0	4321 <br>
max@0	4322 <li>
max@0	4323 <i>.zeros()</i> and <i>.zeros(n_elem)</i> are member function of <i>Col</i> and <i>Row</i>
max@0	4324 </li>
max@0	4325 <br>
max@0	4326 <li>
max@0	4327 <i>.zeros()</i> and <i>.zeros(n_rows, n_cols)</i> are member functions of <i>Mat</i>
max@0	4328 </li>
max@0	4329 <br>
max@0	4330 <li>
max@0	4331 <i>.zeros()</i> and <i>.zeros(n_rows, n_cols, n_slices)</i> are member functions of <i>Cube</i>
max@0	4332 </li>
max@0	4333 <br>
max@0	4334 <li>
max@0	4335 Examples:
max@0	4336 <ul>
max@0	4337 <pre>
max@0	4338 mat A = randu<mat>(5,10);
max@0	4339 A.zeros(); // sets all elements to zero
max@0	4340 A.zeros(10,20); // sets the size to 10 rows and 20 columns
max@0	4341 // followed by setting all elements to zero
max@0	4342 </pre>
max@0	4343 </ul>
max@0	4344 </li>
max@0	4345 <br>
max@0	4346 <li>
max@0	4347 See also:
max@0	4348 <ul>
max@0	4349 <li><a href="#zeros_standalone">zeros()</a> (standalone function)</li>
max@0	4350 <li><a href="#ones_member">.ones()</a></li>
max@0	4351 <li><a href="#fill">.fill()</a></li>
max@0	4352 <li><a href="#reset">.reset()</a></li>
max@0	4353 </ul>
max@0	4354 </li>
max@0	4355 <br>
max@0	4356 </ul>
max@0	4357 <hr class="greyline">
max@0	4358
max@0	4359
max@0	4360 <hr class="greyline">
max@0	4361 <br>
max@0	4362 <br>
max@0	4363 <font size=+1><b>Other Classes</b></font>
max@0	4364 <br>
max@0	4365 <br>
max@0	4366 <hr class="greyline">
max@0	4367 <br>
max@0	4368
max@0	4369 <a name="running_stat"></a>
max@0	4370 <b>running_stat<</b><i>type</i><b>></b>
max@0	4371 <ul>
max@0	4372 <li>
max@0	4373 Class for keeping statistics of a continuously sampled one dimensional process/signal.
max@0	4374 Useful if the storage of individual samples (scalars) is not necessary or desired.
max@0	4375 Also useful if the number of samples is not known beforehand or exceeds available memory.
max@0	4376 </li>
max@0	4377 <br>
max@0	4378 <li>
max@0	4379 <i>type</i> should be one of: <i>float</i>, <i>double</i>, <i><a href="#cx_float_double">cx_float</a></i>, <i><a href="#cx_float_double">cx_double</a></i>
max@0	4380 </li>
max@0	4381 <br>
max@0	4382 <li>
max@0	4383 Member functions:
max@0	4384 <ul>
max@0	4385 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	4386 <tbody>
max@0	4387 <tr>
max@0	4388 <td style="vertical-align: top;">
max@0	4389 <b>.operator()(</b>scalar<b>)</b>
max@0	4390 </td>
max@0	4391 <td style="vertical-align: top;"> <br>
max@0	4392 </td>
max@0	4393 <td style="vertical-align: top;">
max@0	4394 update the statistics so far using the given scalar
max@0	4395 </td>
max@0	4396 </tr>
max@0	4397 <tr>
max@0	4398 <td style="vertical-align: top;">
max@0	4399 <b>.mean()</b>
max@0	4400 </td>
max@0	4401 <td style="vertical-align: top;"> <br>
max@0	4402 </td>
max@0	4403 <td style="vertical-align: top;">
max@0	4404 get the mean or average value so far
max@0	4405 </td>
max@0	4406 </tr>
max@0	4407 <tr>
max@0	4408 <td style="vertical-align: top;">
max@0	4409 <b>.var(</b>norm_type=0<b>)</b>
max@0	4410 </td>
max@0	4411 <td style="vertical-align: top;"> <br>
max@0	4412 </td>
max@0	4413 <td style="vertical-align: top;">
max@0	4414 get the variance so far
max@0	4415 </td>
max@0	4416 </tr>
max@0	4417 <tr>
max@0	4418 <td style="vertical-align: top;">
max@0	4419 <b>.stddev(</b>norm_type=0<b>)</b>
max@0	4420 </td>
max@0	4421 <td style="vertical-align: top;"> <br>
max@0	4422 </td>
max@0	4423 <td style="vertical-align: top;">
max@0	4424 get the standard deviation so far
max@0	4425 </td>
max@0	4426 </tr>
max@0	4427 <tr>
max@0	4428 <td style="vertical-align: top;">
max@0	4429 <b>.min()</b>
max@0	4430 </td>
max@0	4431 <td style="vertical-align: top;"> <br>
max@0	4432 </td>
max@0	4433 <td style="vertical-align: top;">
max@0	4434 get the minimum value so far
max@0	4435 </td>
max@0	4436 </tr>
max@0	4437 <tr>
max@0	4438 <td style="vertical-align: top;">
max@0	4439 <b>.max()</b>
max@0	4440 </td>
max@0	4441 <td style="vertical-align: top;"> <br>
max@0	4442 </td>
max@0	4443 <td style="vertical-align: top;">
max@0	4444 get the maximum value so far
max@0	4445 </td>
max@0	4446 </tr>
max@0	4447 <tr>
max@0	4448 <td style="vertical-align: top;">
max@0	4449 <b>.reset()</b>
max@0	4450 </td>
max@0	4451 <td style="vertical-align: top;"> <br>
max@0	4452 </td>
max@0	4453 <td style="vertical-align: top;">
max@0	4454 reset all statistics and set the number of samples to zero
max@0	4455 </td>
max@0	4456 </tr>
max@0	4457 <tr>
max@0	4458 <td style="vertical-align: top;">
max@0	4459 <b>.count()</b>
max@0	4460 </td>
max@0	4461 <td style="vertical-align: top;"> <br>
max@0	4462 </td>
max@0	4463 <td style="vertical-align: top;">
max@0	4464 get the number of samples so far
max@0	4465 </td>
max@0	4466 </tr>
max@0	4467 </tbody>
max@0	4468 </table>
max@0	4469 </ul>
max@0	4470 </li>
max@0	4471 <br>
max@0	4472 <li>
max@0	4473 For the .var() and .stddev() functions, the default <i>norm_type=0</i> performs normalisation using <i>N-1</i>
max@0	4474 (where <i>N</i> is the number of samples so far),
max@0	4475 providing the best unbiased estimator.
max@0	4476 Using <i>norm_type=1</i> causes normalisation to be done using <i>N</i>, which provides the second moment around the mean.
max@0	4477 </li>
max@0	4478 <br>
max@0	4479 <li>
max@0	4480 The return type of .count() depends on the underlying form of <i>type</i>: it is either <i>float</i> or <i>double</i>.
max@0	4481 </li>
max@0	4482 <br>
max@0	4483 <li>
max@0	4484 Examples:
max@0	4485 <ul>
max@0	4486 <pre>
max@0	4487 running_stat<double> stats;
max@0	4488
max@0	4489 for(uword i=0; i<10000; ++i)
max@0	4490 {
max@0	4491 double sample = double(rand())/RAND_MAX;
max@0	4492 stats(sample);
max@0	4493 }
max@0	4494
max@0	4495 cout << "mean = " << stats.mean() << endl;
max@0	4496 cout << "var = " << stats.var() << endl;
max@0	4497 cout << "min = " << stats.min() << endl;
max@0	4498 cout << "max = " << stats.max() << endl;
max@0	4499 </pre>
max@0	4500 </ul>
max@0	4501 </li>
max@0	4502 <br>
max@0	4503 <li>See also:
max@0	4504 <ul>
max@0	4505 <li><a href="#stats_fns">statistics functions</a></li>
max@0	4506 <li><a href="#running_stat_vec">running_stat_vec</a></li>
max@0	4507 </ul>
max@0	4508 </li>
max@0	4509 </ul>
max@0	4510 <br>
max@0	4511 <hr class="greyline"><br>
max@0	4512
max@0	4513 <a name="running_stat_vec"></a>
max@0	4514 <b>running_stat_vec<</b><i>type</i><b>>(calc_cov = false)</b>
max@0	4515 <ul>
max@0	4516 <li>
max@0	4517 Class for keeping statistics of a continuously sampled multi-dimensional process/signal.
max@0	4518 Useful if the storage of individual samples is not necessary or desired.
max@0	4519 Also useful if the number of samples is not known beforehand or exceeds available memory.
max@0	4520 </li>
max@0	4521 <br>
max@0	4522 <li>
max@0	4523 This class is similar to <i>running_stat</i>, with the difference being that vectors are processed instead of single values.
max@0	4524 </li>
max@0	4525 <br>
max@0	4526 <li>
max@0	4527 <i>type</i> must match the element type used by the sample vectors
max@0	4528 (ie. it must be one of <i>float</i>, <i>double</i>, <i><a href="#cx_float_double">cx_float</a></i>, <i><a href="#cx_float_double">cx_double</a></i>)
max@0	4529 </li>
max@0	4530 <br>
max@0	4531 <li>
max@0	4532 <i>type</i> can be inferred via the use of the <i>elem_type</i> member typedef of a vector class.
max@0	4533 For example, <i>fvec::elem_type</i> will be interpreted as <i>float</i>,
max@0	4534 while <i>cx_vec::elem_type</i> will be interpreted as <i><a href="#cx_float_double">cx_double</a></i>.
max@0	4535 </li>
max@0	4536 <br>
max@0	4537 <li>
max@0	4538 Member functions:
max@0	4539 <ul>
max@0	4540 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	4541 <tbody>
max@0	4542 <tr>
max@0	4543 <td style="vertical-align: top;">
max@0	4544 <b>.operator()(</b>vector<b>)</b>
max@0	4545 </td>
max@0	4546 <td style="vertical-align: top;"> <br>
max@0	4547 </td>
max@0	4548 <td style="vertical-align: top;">
max@0	4549 update the statistics so far using the given vector
max@0	4550 </td>
max@0	4551 </tr>
max@0	4552 <tr>
max@0	4553 <td style="vertical-align: top;">
max@0	4554 <b>.mean()</b>
max@0	4555 </td>
max@0	4556 <td style="vertical-align: top;"> <br>
max@0	4557 </td>
max@0	4558 <td style="vertical-align: top;">
max@0	4559 get the mean vector so far
max@0	4560 </td>
max@0	4561 </tr>
max@0	4562 <tr>
max@0	4563 <td style="vertical-align: top;">
max@0	4564 <b>.var(</b>norm_type=0<b>)</b>
max@0	4565 </td>
max@0	4566 <td style="vertical-align: top;"> <br>
max@0	4567 </td>
max@0	4568 <td style="vertical-align: top;">
max@0	4569 get the vector of variances so far
max@0	4570 </td>
max@0	4571 </tr>
max@0	4572 <tr>
max@0	4573 <td style="vertical-align: top;">
max@0	4574 <b>.stddev(</b>norm_type=0<b>)</b>
max@0	4575 </td>
max@0	4576 <td style="vertical-align: top;"> <br>
max@0	4577 </td>
max@0	4578 <td style="vertical-align: top;">
max@0	4579 get the vector of standard deviations so far
max@0	4580 </td>
max@0	4581 </tr>
max@0	4582 <tr>
max@0	4583 <td style="vertical-align: top;">
max@0	4584 <b>.min()</b>
max@0	4585 </td>
max@0	4586 <td style="vertical-align: top;"> <br>
max@0	4587 </td>
max@0	4588 <td style="vertical-align: top;">
max@0	4589 get the vector of minimum values so far
max@0	4590 </td>
max@0	4591 </tr>
max@0	4592 <tr>
max@0	4593 <td style="vertical-align: top;">
max@0	4594 <b>.max()</b>
max@0	4595 </td>
max@0	4596 <td style="vertical-align: top;"> <br>
max@0	4597 </td>
max@0	4598 <td style="vertical-align: top;">
max@0	4599 get the vector of maximum values so far
max@0	4600 </td>
max@0	4601 </tr>
max@0	4602 <tr>
max@0	4603 <td style="vertical-align: top;">
max@0	4604 <b>.cov(</b>norm_type=0<b>)</b>
max@0	4605 </td>
max@0	4606 <td style="vertical-align: top;"> <br>
max@0	4607 </td>
max@0	4608 <td style="vertical-align: top;">
max@0	4609 get the covariance matrix so far
max@0	4610 <br>NOTE: this only works if <i>calc_cov</i> is set to <i>true</i> during the construction of the class
max@0	4611 </td>
max@0	4612 </tr>
max@0	4613 <tr>
max@0	4614 <td style="vertical-align: top;">
max@0	4615 <b>.reset()</b>
max@0	4616 </td>
max@0	4617 <td style="vertical-align: top;"> <br>
max@0	4618 </td>
max@0	4619 <td style="vertical-align: top;">
max@0	4620 reset all statistics and set the number of samples to zero
max@0	4621 </td>
max@0	4622 </tr>
max@0	4623 <tr>
max@0	4624 <td style="vertical-align: top;">
max@0	4625 <b>.count()</b>
max@0	4626 </td>
max@0	4627 <td style="vertical-align: top;"> <br>
max@0	4628 </td>
max@0	4629 <td style="vertical-align: top;">
max@0	4630 get the number of samples so far
max@0	4631 </td>
max@0	4632 </tr>
max@0	4633 </tbody>
max@0	4634 </table>
max@0	4635 </ul>
max@0	4636 </li>
max@0	4637 <br>
max@0	4638 <li>
max@0	4639 For the .var() and .stddev() functions, the default <i>norm_type=0</i> performs normalisation using <i>N-1</i>
max@0	4640 (where <i>N</i> is the number of samples so far),
max@0	4641 providing the best unbiased estimator.
max@0	4642 Using <i>norm_type=1</i> causes normalisation to be done using <i>N</i>, which provides the second moment around the mean.
max@0	4643 </li>
max@0	4644 <br>
max@0	4645 <li>
max@0	4646 The return type of .count() depends on the underlying form of <i>type</i>: it is either <i>float</i> or <i>double</i>.
max@0	4647 </li>
max@0	4648 <br>
max@0	4649 <li>
max@0	4650 Examples:
max@0	4651 <ul>
max@0	4652 <pre>
max@0	4653 running_stat_vec<rowvec::elem_type> stats;
max@0	4654
max@0	4655 rowvec sample;
max@0	4656
max@0	4657 for(uword i=0; i<10000; ++i)
max@0	4658 {
max@0	4659 sample = randu<rowvec>(5);
max@0	4660 stats(sample);
max@0	4661 }
max@0	4662
max@0	4663 cout << "mean = " << stats.mean() << endl;
max@0	4664 cout << "var = " << stats.var() << endl;
max@0	4665 cout << "min = " << stats.min() << endl;
max@0	4666 cout << "max = " << stats.max() << endl;
max@0	4667
max@0	4668 //
max@0	4669 //
max@0	4670
max@0	4671 running_stat_vec<rowvec::elem_type> more_stats(true);
max@0	4672
max@0	4673 for(uword i=0; i<20; ++i)
max@0	4674 {
max@0	4675 sample = randu<rowvec>(3);
max@0	4676
max@0	4677 sample(1) -= sample(0);
max@0	4678 sample(2) += sample(1);
max@0	4679
max@0	4680 more_stats(sample);
max@0	4681 }
max@0	4682
max@0	4683 cout << "covariance matrix = " << endl;
max@0	4684 cout << more_stats.cov() << endl;
max@0	4685
max@0	4686 rowvec sd = more_stats.stddev();
max@0	4687
max@0	4688 cout << "correlations = " << endl;
max@0	4689 cout << more_stats.cov() / (trans(sd) * sd);
max@0	4690 </pre>
max@0	4691 </ul>
max@0	4692 </li>
max@0	4693 <br>
max@0	4694 <li>See also:
max@0	4695 <ul>
max@0	4696 <li><a href="#cov">cov()</a></li>
max@0	4697 <li><a href="#cor">cor()</a></li>
max@0	4698 <li><a href="#running_stat">running_stat</a></li>
max@0	4699 <li><a href="#stats_fns">statistics functions</a></li>
max@0	4700 </ul>
max@0	4701 </li>
max@0	4702 </ul>
max@0	4703 <br>
max@0	4704 <hr class="greyline"><br>
max@0	4705
max@0	4706 <a name="wall_clock"></a>
max@0	4707 <b>wall_clock</b>
max@0	4708 <ul>
max@0	4709 <li>
max@0	4710 Simple wall clock timer class, for measuring the number of elapsed seconds between two intervals
max@0	4711 </li>
max@0	4712 <br>
max@0	4713 <li>
max@0	4714 Examples:
max@0	4715 <ul>
max@0	4716 <pre>
max@0	4717 wall_clock timer;
max@0	4718
max@0	4719 mat A = randu<mat>(4,4);
max@0	4720 mat B = randu<mat>(4,4);
max@0	4721 mat C;
max@0	4722
max@0	4723 timer.tic();
max@0	4724 for(uword i=0; i<100000; ++i)
max@0	4725 C = A + B + A + B;
max@0	4726
max@0	4727 double n_secs = timer.toc();
max@0	4728 cout << "took " << n_secs << " seconds" << endl;
max@0	4729 </pre>
max@0	4730 </ul>
max@0	4731 </li>
max@0	4732 </ul>
max@0	4733 <br>
max@0	4734 <hr class="greyline">
max@0	4735
max@0	4736 <hr class="greyline">
max@0	4737 <br>
max@0	4738 <br>
max@0	4739 <font size=+1><b>Generated Vectors/Matrices</b></font>
max@0	4740 <br>
max@0	4741 <br>
max@0	4742 <hr class="greyline">
max@0	4743 <br>
max@0	4744
max@0	4745 <a name="eye_standalone"></a>
max@0	4746 <b>eye(n_rows, n_cols)</b>
max@0	4747 <ul>
max@0	4748 <li>
max@0	4749 Generate a matrix with the elements along the main diagonal set to one
max@0	4750 and off-diagonal elements set to zero
max@0	4751 </li>
max@0	4752 <br>
max@0	4753 <li>
max@0	4754 An identity matrix is generated when <i>n_rows</i> = <i>n_cols</i>
max@0	4755 </li>
max@0	4756 <br>
max@0	4757 <li>
max@0	4758 Usage:
max@0	4759 <ul>
max@0	4760 <li>
max@0	4761 <i>matrix_type</i> X = eye<<i>matrix_type</i>>(n_rows, n_cols)
max@0	4762 </li>
max@0	4763 </ul>
max@0	4764 </li>
max@0	4765 <br>
max@0	4766 <li>
max@0	4767 Examples:
max@0	4768 <ul>
max@0	4769 <pre>
max@0	4770 mat A = eye<mat>(5,5);
max@0	4771 mat B = 123.0 * eye<mat>(5,5);
max@0	4772 </pre>
max@0	4773 </ul>
max@0	4774 </li>
max@0	4775 <br>
max@0	4776 <li>See also:
max@0	4777 <ul>
max@0	4778 <li><a href="#eye_member">.eye()</a> (member function of Mat)</li>
max@0	4779 <li><a href="#ones_standalone">ones()</a></li>
max@0	4780 <li><a href="#diagmat">diagmat()</a></li>
max@0	4781 <li><a href="#diagvec">diagvec()</a></li>
max@0	4782 </ul>
max@0	4783 </li>
max@0	4784 <br>
max@0	4785 </ul>
max@0	4786 <hr class="greyline"><br>
max@0	4787
max@0	4788 <a name="linspace"></a>
max@0	4789 <b>linspace(start, end, N=100)</b>
max@0	4790 <ul>
max@0	4791 <li>
max@0	4792 Generate a vector with <i>N</i> elements;
max@0	4793 the values of the elements linearly increase from <i>start</i> upto (and including) <i>end</i>
max@0	4794 <br>
max@0	4795 </li>
max@0	4796 <br>
max@0	4797 <li>
max@0	4798 Usage:
max@0	4799 <ul>
max@0	4800 <li><i>vector_type</i> v = linspace<<i>vector_type</i>>(start, end, N)</li>
max@0	4801 <li><i>matrix_type</i> X = linspace<<i>matrix_type</i>>(start, end, N)</li>
max@0	4802 </ul>
max@0	4803 </li>
max@0	4804 <br>
max@0	4805 <li>
max@0	4806 If a <i>matrix_type</i> is specified, the resultant matrix will have one column
max@0	4807 </li>
max@0	4808 <br>
max@0	4809 <li>
max@0	4810 Examples:
max@0	4811 <ul>
max@0	4812 <pre>
max@0	4813 vec v = linspace<vec>(10, 20, 5);
max@0	4814 mat X = linspace<mat>(10, 20, 5);
max@0	4815 </pre>
max@0	4816 </ul>
max@0	4817 </li>
max@0	4818 </ul>
max@0	4819 <br>
max@0	4820 <hr class="greyline"><br>
max@0	4821
max@0	4822 <a name="ones_standalone"></a>
max@0	4823 <b>
max@0	4824 ones(n_elem)
max@0	4825 <br>ones(n_rows, n_cols)
max@0	4826 <br>ones(n_rows, n_cols, n_slices)
max@0	4827 </b>
max@0	4828 <ul>
max@0	4829 <li>
max@0	4830 Generate a vector, matrix or cube with all elements set to one
max@0	4831 </li>
max@0	4832 <br>
max@0	4833 <li>
max@0	4834 Usage:
max@0	4835 <ul>
max@0	4836 <li><i>vector_type</i> v = ones<<i>vector_type</i>>(n_elem)</li>
max@0	4837 <li><i>matrix_type</i> X = ones<<i>matrix_type</i>>(n_rows, n_cols)</li>
max@0	4838 <li><i>cube_type</i> Q = ones<<i>cube_type</i>>(n_rows, n_cols, n_slices)</li>
max@0	4839 </ul>
max@0	4840 </li>
max@0	4841 <br>
max@0	4842 <li>
max@0	4843 Examples:
max@0	4844 <ul>
max@0	4845 <pre>
max@0	4846 vec v = ones<vec>(10);
max@0	4847 mat A = ones<mat>(5,6);
max@0	4848 cube Q = ones<cube>(5,6,7);
max@0	4849
max@0	4850 mat B = 123.0 * ones<mat>(5,6);
max@0	4851 </pre>
max@0	4852 </ul>
max@0	4853 </li>
max@0	4854 <br>
max@0	4855 <li>
max@0	4856 See also:
max@0	4857 <ul>
max@0	4858 <li><a href="#ones_member">.ones()</a> (member function of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>Cube</i>)</li>
max@0	4859 <li><a href="#eye_standalone">eye()</a></li>
max@0	4860 </ul>
max@0	4861 </li>
max@0	4862 </ul>
max@0	4863 <br>
max@0	4864 <hr class="greyline"><br>
max@0	4865
max@0	4866 <a name="randu_randn_standalone"></a>
max@0	4867 <b>randu(n_elem)</b>
max@0	4868 <br><b>randu(n_rows, n_cols)</b>
max@0	4869 <br><b>randu(n_rows, n_cols, n_slices)</b>
max@0	4870 <br>
max@0	4871 <br><b>randn(n_elem)</b>
max@0	4872 <br><b>randn(n_rows, n_cols)</b>
max@0	4873 <br><b>randn(n_rows, n_cols, n_slices)</b>
max@0	4874 <ul>
max@0	4875 <li>
max@0	4876 Generate a vector, matrix or cube with the elements set to random values
max@0	4877 </li>
max@0	4878 <br>
max@0	4879 <li><i>randu()</i> uses a uniform distribution in the [0,1] interval
max@0	4880 </li>
max@0	4881 <br>
max@0	4882 <li><i>randn()</i> uses a normal/Gaussian distribution with zero mean and unit variance
max@0	4883 </li>
max@0	4884 <br>
max@0	4885 <li>
max@0	4886 Usage:
max@0	4887 <ul>
max@0	4888 <li><i>vector_type</i> v = randu<<i>vector_type</i>>(n_elem)</li>
max@0	4889 <li><i>matrix_type</i> X = randu<<i>matrix_type</i>>(n_rows, n_cols)</li>
max@0	4890 <li><i>cube_type</i> Q = randu<<i>cube_type</i>>(n_rows, n_cols, n_slices)</li>
max@0	4891 </ul>
max@0	4892 </li>
max@0	4893 <br>
max@0	4894 <li>
max@0	4895 To change the seed, use the <a href="http://cplusplus.com/reference/clibrary/cstdlib/srand/">std::srand()</a> function.
max@0	4896 </li>
max@0	4897 <br>
max@0	4898 <li>
max@0	4899 Examples:
max@0	4900 <ul>
max@0	4901 <pre>
max@0	4902 vec v = randu<vec>(5);
max@0	4903 mat A = randu<mat>(5,6);
max@0	4904 cube Q = randu<cube>(5,6,7);
max@0	4905 </pre>
max@0	4906 </ul>
max@0	4907 </li>
max@0	4908 <li>See also:
max@0	4909 <ul>
max@0	4910 <li><a href="#randu_randn_member">.randu() & .randn()</a> (member functions)</li>
max@0	4911 <li><a href="#ones_standalone">ones()</a></li>
max@0	4912 <li><a href="#zeros_standalone">zeros()</a></li>
max@0	4913 <li><a href="#shuffle">shuffle()</a></li>
max@0	4914 <li><a href="http://cplusplus.com/reference/clibrary/cstdlib/srand/">std::srand()</a></li>
max@0	4915 <li><a href="#api_changes">API changes</a></li>
max@0	4916 </ul>
max@0	4917 </li>
max@0	4918 <br>
max@0	4919 </ul>
max@0	4920 <hr class="greyline"><br>
max@0	4921
max@0	4922 <a name="repmat"></a>
max@0	4923 <b>repmat(A, num_copies_per_row, num_copies_per_col)</b>
max@0	4924 <ul>
max@0	4925 <li>Generate a matrix by replicating matrix A in a block-like fashion</li>
max@0	4926 <br>
max@0	4927 <li>The generated matrix has the following size:
max@0	4928 <ul>
max@0	4929 rows = num_copies_per_row * A.n_rows
max@0	4930 <br>
max@0	4931 cols = num_copies_per_col * A.n_cols
max@0	4932 </ul>
max@0	4933 </li>
max@0	4934 <br>
max@0	4935 <li>
max@0	4936 Examples:
max@0	4937 <ul>
max@0	4938 <pre>
max@0	4939 mat A = randu<mat>(2, 3);
max@0	4940
max@0	4941 mat B = repmat(A, 4, 5);
max@0	4942 </pre>
max@0	4943 </ul>
max@0	4944 </li>
max@0	4945 <br>
max@0	4946 </ul>
max@0	4947 <hr class="greyline">
max@0	4948 <br>
max@0	4949
max@0	4950 <a name="toeplitz"></a>
max@0	4951 <b>toeplitz(A)</b>
max@0	4952 <br><b>toeplitz(A,B)</b>
max@0	4953 <br><b>circ_toeplitz(A)</b>
max@0	4954 <ul>
max@0	4955 <li>
max@0	4956 toeplitz(): generate a Toeplitz matrix, with the first column specified by <i>A</i>, and (optionally) the first row specified by <i>B</i>
max@0	4957 </li>
max@0	4958 <br>
max@0	4959 <li>
max@0	4960 circ_toeplitz(): generate a circulant Toeplitz matrix
max@0	4961 </li>
max@0	4962 <br>
max@0	4963 <li>
max@0	4964 A and B must be vectors
max@0	4965 </li>
max@0	4966 <br>
max@0	4967 <li>
max@0	4968 Examples:
max@0	4969 <ul>
max@0	4970 <pre>
max@0	4971 vec A = randu<vec>(5);
max@0	4972 mat X = toeplitz(A);
max@0	4973 mat Y = circ_toeplitz(A);
max@0	4974 </pre>
max@0	4975 </ul>
max@0	4976 </li>
max@0	4977 <br>
max@0	4978 <li>See also:
max@0	4979 <ul>
max@0	4980 <li><a href="http://mathworld.wolfram.com/ToeplitzMatrix.html">Toeplitz matrix in MathWorld</a></li>
max@0	4981 <li><a href="http://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz matrix in Wikipedia</a></li>
max@0	4982 <li><a href="http://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix in Wikipedia</a></li>
max@0	4983 </ul>
max@0	4984 </li>
max@0	4985 <br>
max@0	4986 </ul>
max@0	4987 <hr class="greyline">
max@0	4988 <br>
max@0	4989
max@0	4990 <a name="zeros_standalone"></a>
max@0	4991 <b>zeros(n_elem)</b>
max@0	4992 <br><b>zeros(n_rows, n_cols)</b>
max@0	4993 <br><b>zeros(n_rows, n_cols, n_slices)</b>
max@0	4994 <ul>
max@0	4995 <li>
max@0	4996 Generate a vector, matrix or cube with the elements set to zero
max@0	4997 </li>
max@0	4998 <br>
max@0	4999 <li>
max@0	5000 Usage:
max@0	5001 <ul>
max@0	5002 <li><i>vector_type</i> v = zeros<<i>vector_type</i>>(n_elem)</li>
max@0	5003 <li><i>matrix_type</i> X = zeros<<i>matrix_type</i>>(n_rows, n_cols)</li>
max@0	5004 <li><i>cube_type</i> X = zeros<<i>cube_type</i>>(n_rows, n_cols, n_slices)</li>
max@0	5005 </ul>
max@0	5006 </li>
max@0	5007 <br>
max@0	5008 <li>
max@0	5009 Examples:
max@0	5010 <ul>
max@0	5011 <pre>
max@0	5012 vec v = zeros<vec>(5);
max@0	5013 mat A = zeros<mat>(5,6);
max@0	5014 cube Q = zeros<cube>(5,6,7);
max@0	5015 </pre>
max@0	5016 </ul>
max@0	5017 </li>
max@0	5018 <br>
max@0	5019 <li>
max@0	5020 See also:
max@0	5021 <ul>
max@0	5022 <li><a href="#zeros_member">.zeros()</a> (member function of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>Cube</i>)</li>
max@0	5023 <li><a href="#ones_member">.ones()</a> (member function of <i>Mat</i>, <i>Col</i>, <i>Row</i> and <i>Cube</i>)</li>
max@0	5024 <li><a href="#ones_standalone">ones()</a></li>
max@0	5025 </ul>
max@0	5026 </li>
max@0	5027 </ul>
max@0	5028 <br>
max@0	5029 <hr class="greyline">
max@0	5030
max@0	5031 <hr class="greyline">
max@0	5032 <br>
max@0	5033 <br>
max@0	5034 <font size=+1><b>Functions Individually Applied to Each Element of a Matrix/Cube</b></font>
max@0	5035 <br>
max@0	5036 <br>
max@0	5037 <hr class="greyline">
max@0	5038 <br>
max@0	5039
max@0	5040 <a name="abs"></a>
max@0	5041 <b>abs(mat)</b>
max@0	5042 <br><b>abs(cube)</b>
max@0	5043 <br><b>abs(cx_mat)</b>
max@0	5044 <br><b>abs(cx_cube)</b>
max@0	5045 <ul>
max@0	5046 <li>
max@0	5047 Obtain the magnitude of each element
max@0	5048 </li>
max@0	5049 <br>
max@0	5050 <li>
max@0	5051 Usage for non-complex matrices:
max@0	5052 <ul>
max@0	5053 <li><i>matrix_type</i> Y = abs(X)</li>
max@0	5054 <li>X and Y must have the same <i>matrix_type</i></li>
max@0	5055 </ul>
max@0	5056 </li>
max@0	5057 <br>
max@0	5058 <li>
max@0	5059 Usage for non-complex cubes:
max@0	5060 <ul>
max@0	5061 <li><i>cube_type</i> Y = abs(X)</li>
max@0	5062 <li>X and Y must have the same <i>cube_type</i></li>
max@0	5063 </ul>
max@0	5064 </li>
max@0	5065 <br>
max@0	5066 <li>
max@0	5067 Usage for complex matrices:
max@0	5068 <ul>
max@0	5069 <li><i>non_complex_matrix_type</i> Y = abs(X)</li>
max@0	5070 <li>X must be a have complex matrix type, eg., <i>cx_mat</i> or <i>cx_fmat</i></li>
max@0	5071 <li>The type of Y must be related to the type of X,
max@0	5072 eg., if X has the type <i>cx_mat</i>, then the type of Y must be <i>mat</i>
max@0	5073 </ul>
max@0	5074 </li>
max@0	5075 <br>
max@0	5076 <li>
max@0	5077 Usage for complex cubes:
max@0	5078 <ul>
max@0	5079 <li><i>non_complex_cube_type</i> Y = abs(X)</li>
max@0	5080 <li>X must be a have complex cube type, eg., <i>cx_cube</i> or <i>cx_fcube</i></li>
max@0	5081 <li>The type of Y must be related to the type of X,
max@0	5082 eg., if X has the type <i>cx_cube</i>, then the type of Y must be <i>cube</i>
max@0	5083 </ul>
max@0	5084 </li>
max@0	5085 <br>
max@0	5086 <li>
max@0	5087 Examples:
max@0	5088 <ul>
max@0	5089 <pre>
max@0	5090 mat A = randu<mat>(5,5);
max@0	5091 mat B = abs(A);
max@0	5092
max@0	5093 cx_mat X = randu<cx_mat>(5,5);
max@0	5094 mat Y = abs(X);
max@0	5095 </pre>
max@0	5096 </ul>
max@0	5097 </li>
max@0	5098 </ul>
max@0	5099 <br>
max@0	5100 <hr class="greyline"><br>
max@0	5101
max@0	5102 <a name="eps"></a>
max@0	5103 <b>eps(X)</b>
max@0	5104 <ul>
max@0	5105 <li>
max@0	5106 Obtain the positive distance of the absolute value of each element of <i>X</i> to the next largest representable floating point number
max@0	5107 </li>
max@0	5108 <br>
max@0	5109 <li>
max@0	5110 <i>X</i> can be a scalar (eg. <i>double</i>), vector or matrix
max@0	5111 </li>
max@0	5112 <br>
max@0	5113 <li>
max@0	5114 Examples:
max@0	5115 <ul>
max@0	5116 <pre>
max@0	5117 mat A = randu<mat>(4,5);
max@0	5118 mat B = eps(A);
max@0	5119 </pre>
max@0	5120 </ul>
max@0	5121 </li>
max@0	5122 <br>
max@0	5123 <li>
max@0	5124 See also:
max@0	5125 <ul>
max@0	5126 <li><a href="#math_constants">math::eps()</a></li>
max@0	5127 <li><a href="http://mathworld.wolfram.com/Floating-PointArithmetic.html">Floating-Point Arithmetic in MathWorld</a></li>
max@0	5128 <li><a href="http://en.wikipedia.org/wiki/IEEE_754-2008">IEEE Standard for Floating-Point Arithmetic in Wikipedia</a></li>
max@0	5129
max@0	5130 </ul>
max@0	5131 </li>
max@0	5132 </ul>
max@0	5133 <br>
max@0	5134 <hr class="greyline"><br>
max@0	5135
max@0	5136 <a name="misc_fns"></a>
max@0	5137 <b>
max@0	5138 miscellaneous functions:
max@0	5139 <br>  exp, exp2, exp10, trunc_exp,
max@0	5140 <br>  log, log2, log10, trunc_log,
max@0	5141 <br>  pow, sqrt, square
max@0	5142 <br>  floor, ceil
max@0	5143 </b>
max@0	5144 <br>
max@0	5145 <ul>
max@0	5146 <li>
max@0	5147 Apply a function to each element
max@0	5148 </li>
max@0	5149 <br>
max@0	5150 <li>
max@0	5151 Usage:
max@0	5152 <ul>
max@0	5153 <li>
max@0	5154 <i>matrix_type</i> B = misc_fn(A)
max@0	5155 </li>
max@0	5156 <li>
max@0	5157 <i>cube_type</i> B = misc_fn(A)
max@0	5158 </li>
max@0	5159 <li>
max@0	5160 A and B must have the same <i>matrix_type/cube_type</i>
max@0	5161 </li>
max@0	5162 <li>
max@0	5163 misc_fn(A) is one of:
max@0	5164 <ul>
max@0	5165
max@0	5166 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	5167 <tbody>
max@0	5168 <tr>
max@0	5169 <td style="vertical-align: top;">
max@0	5170 exp(A)<sup> </sup>
max@0	5171 </td>
max@0	5172 <td style="vertical-align: top;">
max@0	5173
max@0	5174 </td>
max@0	5175 <td style="vertical-align: top;">
max@0	5176 base-e exponential, <i>e<sup>x</sup></i>
max@0	5177 </td>
max@0	5178 </tr>
max@0	5179 <tr>
max@0	5180 <td style="vertical-align: top;">
max@0	5181 exp2(A)<sup> </sup>
max@0	5182 </td>
max@0	5183 <td style="vertical-align: top;">
max@0	5184
max@0	5185 </td>
max@0	5186 <td style="vertical-align: top;">
max@0	5187 base-2 exponential, <i>2<sup>x</sup></i>
max@0	5188 </td>
max@0	5189 </tr>
max@0	5190 <tr>
max@0	5191 <td style="vertical-align: top;">
max@0	5192 exp10(A)<sup> </sup>
max@0	5193 </td>
max@0	5194 <td style="vertical-align: top;">
max@0	5195
max@0	5196 </td>
max@0	5197 <td style="vertical-align: top;">
max@0	5198 base-10 exponential, <i>10<sup>x</sup></i>
max@0	5199 </td>
max@0	5200 </tr>
max@0	5201 <tr>
max@0	5202 <td style="vertical-align: top;">
max@0	5203 trunc_exp(A)
max@0	5204 </td>
max@0	5205 <td style="vertical-align: top;">
max@0	5206
max@0	5207 </td>
max@0	5208 <td style="vertical-align: top;">
max@0	5209 base-e exponential,
max@0	5210 truncated to avoid infinity
max@0	5211 <br>
max@0	5212 <font size=-1>(only for elements with type <i>float</i> or <i>double</i>)</font>
max@0	5213 </td>
max@0	5214 </tr>
max@0	5215 <tr>
max@0	5216 <td style="vertical-align: top;">
max@0	5217 log(A)<sub> </sub>
max@0	5218 </td>
max@0	5219 <td style="vertical-align: top;">
max@0	5220
max@0	5221 </td>
max@0	5222 <td style="vertical-align: top;">
max@0	5223 natural log, <i>log<sub>e</sub> x</i>
max@0	5224 </td>
max@0	5225 </tr>
max@0	5226 <tr>
max@0	5227 <td style="vertical-align: top;">
max@0	5228 log2(A)<sub> </sub>
max@0	5229 </td>
max@0	5230 <td style="vertical-align: top;">
max@0	5231
max@0	5232 </td>
max@0	5233 <td style="vertical-align: top;">
max@0	5234 base-2 log, <i>log<sub>2</sub> x</i>
max@0	5235 </td>
max@0	5236 </tr>
max@0	5237 <tr>
max@0	5238 <td style="vertical-align: top;">
max@0	5239 log10(A)<sub> </sub>
max@0	5240 </td>
max@0	5241 <td style="vertical-align: top;">
max@0	5242
max@0	5243 </td>
max@0	5244 <td style="vertical-align: top;">
max@0	5245 base-10 log, <i>log<sub>10</sub> x</i>
max@0	5246 </td>
max@0	5247 </tr>
max@0	5248 <tr>
max@0	5249 <td style="vertical-align: top;">
max@0	5250 trunc_log(A)
max@0	5251 </td>
max@0	5252 <td style="vertical-align: top;">
max@0	5253
max@0	5254 </td>
max@0	5255 <td style="vertical-align: top;">
max@0	5256 natural log,
max@0	5257 truncated to avoid ±infinity
max@0	5258 <br>
max@0	5259 <font size=-1>(only for elements with type <i>float</i> or <i>double</i>)</font>
max@0	5260 </td>
max@0	5261 </tr>
max@0	5262 <tr>
max@0	5263 <td style="vertical-align: top;">
max@0	5264 pow(A, p)<sup> </sup>
max@0	5265 </td>
max@0	5266 <td style="vertical-align: top;">
max@0	5267
max@0	5268 </td>
max@0	5269 <td style="vertical-align: top;">
max@0	5270 raise to the power of p, <i>x<sup>p</sup></i>
max@0	5271 </td>
max@0	5272 </tr>
max@0	5273 <tr>
max@0	5274 <td style="vertical-align: top;">
max@0	5275 sqrt(A)<sup> </sup>
max@0	5276 </td>
max@0	5277 <td style="vertical-align: top;">
max@0	5278
max@0	5279 </td>
max@0	5280 <td style="vertical-align: top;">
max@0	5281 square root, <i>x<sup>½</sup></i>
max@0	5282 </td>
max@0	5283 </tr>
max@0	5284 <tr>
max@0	5285 <td style="vertical-align: top;">
max@0	5286 square(A)<sup> </sup>
max@0	5287 </td>
max@0	5288 <td style="vertical-align: top;">
max@0	5289
max@0	5290 </td>
max@0	5291 <td style="vertical-align: top;">
max@0	5292 square, <i>x<sup>2</sup></i>
max@0	5293 </td>
max@0	5294 </tr>
max@0	5295 <tr>
max@0	5296 <td style="vertical-align: top;">
max@0	5297 floor(A)
max@0	5298 </td>
max@0	5299 <td style="vertical-align: top;">
max@0	5300
max@0	5301 </td>
max@0	5302 <td style="vertical-align: top;">
max@0	5303 largest integral value that is not greater than the input value
max@0	5304 </td>
max@0	5305 </tr>
max@0	5306 <tr>
max@0	5307 <td style="vertical-align: top;">
max@0	5308 ceil(A)
max@0	5309 </td>
max@0	5310 <td style="vertical-align: top;">
max@0	5311
max@0	5312 </td>
max@0	5313 <td style="vertical-align: top;">
max@0	5314 smallest integral value that is not less than the input value
max@0	5315 </td>
max@0	5316 </tr>
max@0	5317 </tbody>
max@0	5318 </table>
max@0	5319
max@0	5320
max@0	5321 </ul>
max@0	5322 </li>
max@0	5323
max@0	5324 </ul>
max@0	5325 </li>
max@0	5326 <br>
max@0	5327 <li>
max@0	5328 Examples:
max@0	5329 <ul>
max@0	5330 <pre>
max@0	5331 mat A = randu<mat>(5,5);
max@0	5332 mat B = exp(A);
max@0	5333 </pre>
max@0	5334 </ul>
max@0	5335 </li>
max@0	5336 </ul>
max@0	5337 <br>
max@0	5338 <hr class="greyline"><br>
max@0	5339
max@0	5340 <a name="trig_fns"></a>
max@0	5341 <b>trigonometric functions (cos, sin, tan, ...)</b>
max@0	5342 <ul>
max@0	5343 <li>
max@0	5344 Apply a trigonometric function to each element
max@0	5345 </li>
max@0	5346 <br>
max@0	5347 <li>
max@0	5348 Usage:
max@0	5349 <ul>
max@0	5350 <li>
max@0	5351 <i>matrix_type</i> Y = trig_fn(X)
max@0	5352 </li>
max@0	5353 <li>
max@0	5354 <i>cube_type</i> Y = trig_fn(X)
max@0	5355 </li>
max@0	5356 <li>
max@0	5357 X and Y must have the same <i>matrix_type/cube_type</i>
max@0	5358 </li>
max@0	5359 <li>
max@0	5360 trig_fn is one of:
max@0	5361 <ul>
max@0	5362 <li>
max@0	5363 cos family: <i>cos</i>, <i>acos</i>, <i>cosh</i>, <i>acosh</i>
max@0	5364 </li>
max@0	5365 <li>
max@0	5366 sin family: <i>sin</i>, <i>asin</i>, <i>sinh</i>, <i>asinh</i>
max@0	5367 </li>
max@0	5368 <li>
max@0	5369 tan family: <i>tan</i>, <i>atan</i>, <i>tanh</i>, <i>atanh</i>
max@0	5370 </li>
max@0	5371 </ul>
max@0	5372 </li>
max@0	5373
max@0	5374 </ul>
max@0	5375 </li>
max@0	5376 <br>
max@0	5377 <li>
max@0	5378 Examples:
max@0	5379 <ul>
max@0	5380 <pre>
max@0	5381 mat X = randu<mat>(5,5);
max@0	5382 mat Y = cos(X);
max@0	5383 </pre>
max@0	5384 </ul>
max@0	5385 </li>
max@0	5386 </ul>
max@0	5387 <br>
max@0	5388 <hr class="greyline">
max@0	5389
max@0	5390 <hr class="greyline">
max@0	5391 <br>
max@0	5392 <br>
max@0	5393 <font size=+1><b>Scalar Valued Functions of Vectors/Matrices/Cubes</b></font>
max@0	5394 <br>
max@0	5395 <br>
max@0	5396 <hr class="greyline">
max@0	5397 <br>
max@0	5398
max@0	5399 <a name="accu"></a>
max@0	5400 <b>accu(mat)</b>
max@0	5401 <br><b>accu(cube)</b>
max@0	5402 <ul>
max@0	5403 <li>
max@0	5404 Accumulate (sum) all elements
max@0	5405 </li>
max@0	5406 <br>
max@0	5407 <li>
max@0	5408 Examples:
max@0	5409 <ul>
max@0	5410 <pre>
max@0	5411 mat A = randu<mat>(5,5);
max@0	5412 double x = accu(A);
max@0	5413
max@0	5414 mat B = randu<mat>(5,5);
max@0	5415 double y = accu(A % B);
max@0	5416
max@0	5417 // operator % performs element-wise multiplication,
max@0	5418 // hence accu(A % B) is a "multiply-and-accumulate"
max@0	5419 // operation
max@0	5420 </pre>
max@0	5421 </ul>
max@0	5422 </li>
max@0	5423 <br>
max@0	5424 <li>
max@0	5425 See also:
max@0	5426 <ul>
max@0	5427 <li><a href="#sum">sum()</a></li>
max@0	5428 <li><a href="#cumsum">cumsum()</a></li>
max@0	5429 <li><a href="#as_scalar">as_scalar()</a></li>
max@0	5430 </ul>
max@0	5431 </li>
max@0	5432 <br>
max@0	5433 </ul>
max@0	5434 <hr class="greyline"><br>
max@0	5435
max@0	5436 <a name="as_scalar"></a>
max@0	5437 <b>as_scalar(expression)</b>
max@0	5438 <ul>
max@0	5439 <li>
max@0	5440 Evaluate an expression that results in a 1x1 matrix,
max@0	5441 followed by converting the 1x1 matrix to a pure scalar
max@0	5442 </li>
max@0	5443 <br>
max@0	5444 <li>
max@0	5445 If a binary or trinary expression is given (ie. 2 or 3 terms),
max@0	5446 the function will try to exploit the fact that the result is a 1x1 matrix
max@0	5447 by using optimised expression evaluations
max@0	5448 </li>
max@0	5449 <br>
max@0	5450 <li>
max@0	5451 Examples:
max@0	5452 <ul>
max@0	5453 <pre>
max@0	5454 rowvec r = randu<rowvec>(5);
max@0	5455 colvec q = randu<colvec>(5);
max@0	5456 mat X = randu<mat>(5,5);
max@0	5457
max@0	5458 // examples of some expressions
max@0	5459 // for which optimised implementations exist
max@0	5460
max@0	5461 double a = as_scalar(r*q);
max@0	5462 double b = as_scalar(rXq);
max@0	5463 double c = as_scalar(rdiagmat(X)q);
max@0	5464 double d = as_scalar(rinv(diagmat(X))q);
max@0	5465 </pre>
max@0	5466 </ul>
max@0	5467 </li>
max@0	5468 <br>
max@0	5469 <li>
max@0	5470 See also:
max@0	5471 <ul>
max@0	5472 <li><a href="#accu">accu()</a></li>
max@0	5473 <li><a href="#conv_to">conv_to()</a></li>
max@0	5474 <li><a href="#dot">dot()</a></li>
max@0	5475 <li><a href="#norm">norm()</a></li>
max@0	5476 <li><a href="#reshape">reshape()</a></li>
max@0	5477 <li><a href="#resize">resize()</a></li>
max@0	5478 </ul>
max@0	5479 </li>
max@0	5480 <br>
max@0	5481 </ul>
max@0	5482 <hr class="greyline"><br>
max@0	5483
max@0	5484 <a name="det"></a>
max@0	5485 <b>det(A, slow = <i>false</i>)</b>
max@0	5486 <ul>
max@0	5487 <li>
max@0	5488 Determinant of square matrix <i>A</i>
max@0	5489 </li>
max@0	5490 <br>
max@0	5491 <li>
max@0	5492 If <i>A</i> is not square, a <i>std::logic_error</i> exception is thrown
max@0	5493 </li>
max@0	5494 <br>
max@0	5495 <li>
max@0	5496 <b>Caveat</b>: for large matrices you may want to use <a href="#log_det">log_det()</a> instead
max@0	5497 </li>
max@0	5498 <br>
max@0	5499 <li>
max@0	5500 For matrix sizes ≤ 4x4, a fast algorithm is used by default.
max@0	5501 In rare instances, the fast algorithm might be less precise than the standard algorithm.
max@0	5502 To force the use of the standard algorithm, set the <i>slow</i> argument to <i>true</i>
max@0	5503 </li>
max@0	5504 <br>
max@0	5505 <li>
max@0	5506 Examples:
max@0	5507 <ul>
max@0	5508 <pre>
max@0	5509 mat A = randu<mat>(5,5);
max@0	5510 double x = det(A);
max@0	5511
max@0	5512 mat44 B = randu<mat>(4,4);
max@0	5513
max@0	5514 double y = det(B); // use fast algorithm by default
max@0	5515 double z = det(B, true); // use slow algorithm
max@0	5516 </pre>
max@0	5517 </ul>
max@0	5518 </li>
max@0	5519 <br>
max@0	5520 <li>
max@0	5521 See also:
max@0	5522 <ul>
max@0	5523 <li><a href="#log_det">log_det()</a></li>
max@0	5524 <li><a href="http://mathworld.wolfram.com/Determinant.html">determinant in MathWorld</a></li>
max@0	5525 <li><a href="http://en.wikipedia.org/wiki/Determinant">determinant in Wikipedia</a></li>
max@0	5526 </ul>
max@0	5527 </li>
max@0	5528 <br>
max@0	5529 </ul>
max@0	5530 <hr class="greyline"><br>
max@0	5531
max@0	5532 <a name="dot"></a>
max@0	5533 <b>dot(A, B)</b>
max@0	5534 <br><b>cdot(A, B)</b>
max@0	5535 <br><b>norm_dot(A, B)</b>
max@0	5536 <ul>
max@0	5537 <li>
max@0	5538 <i>dot(A,B)</i>: dot product of A and B, under the assumption that A and B are vectors with the same number of elements
max@0	5539 </li>
max@0	5540 <br>
max@0	5541 <li>
max@0	5542 <i>cdot(A,B)</i>: as per <i>dot(A,B)</i>, but the complex conjugate of A is used
max@0	5543 </li>
max@0	5544 <br>
max@0	5545 <li>
max@0	5546 <i>norm_dot(A,B)</i>: normalised version of <i>dot(A,B)</i>
max@0	5547 </li>
max@0	5548 <br>
max@0	5549 <li>
max@0	5550 Examples:
max@0	5551 <ul>
max@0	5552 <pre>
max@0	5553 vec a = randu<vec>(10);
max@0	5554 vec b = randu<vec>(10);
max@0	5555
max@0	5556 double x = dot(a,b);
max@0	5557 </pre>
max@0	5558 </ul>
max@0	5559 </li>
max@0	5560 <br>
max@0	5561 <li>See also:
max@0	5562 <ul>
max@0	5563 <li><a href="#as_scalar">as_scalar()</a></li>
max@0	5564 <li><a href="#cross">cross()</a></li>
max@0	5565 <li><a href="#conj">conj()</a></li>
max@0	5566 <li><a href="#norm">norm()</a></li>
max@0	5567 </ul>
max@0	5568 </li>
max@0	5569 <br>
max@0	5570 </ul>
max@0	5571 <hr class="greyline"><br>
max@0	5572
max@0	5573 <a name="log_det"></a>
max@0	5574 <b>log_det(val, sign, A)</b>
max@0	5575 <ul>
max@0	5576 <li>
max@0	5577 Log determinant of square matrix <i>A</i>, such that the determinant is equal to <i>exp(val)*sign</i>
max@0	5578 </li>
max@0	5579 <br>
max@0	5580 <li>
max@0	5581 If <i>A</i> is not square, a <i>std::logic_error</i> exception is thrown
max@0	5582 </li>
max@0	5583 <br>
max@0	5584 <li>
max@0	5585 Examples:
max@0	5586 <ul>
max@0	5587 <pre>
max@0	5588 mat A = randu<mat>(5,5);
max@0	5589
max@0	5590 double val;
max@0	5591 double sign;
max@0	5592
max@0	5593 log_det(val, sign, A);
max@0	5594 </pre>
max@0	5595 </ul>
max@0	5596 </li>
max@0	5597 <br>
max@0	5598 <li>
max@0	5599 See also:
max@0	5600 <ul>
max@0	5601 <li><a href="#det">det()</a></li>
max@0	5602 <li><a href="http://mathworld.wolfram.com/Determinant.html">determinant in MathWorld</a></li>
max@0	5603 <li><a href="http://en.wikipedia.org/wiki/Determinant">determinant in Wikipedia</a></li>
max@0	5604 </ul>
max@0	5605 </li>
max@0	5606 <br>
max@0	5607 </ul>
max@0	5608 <hr class="greyline"><br>
max@0	5609
max@0	5610 <a name="norm"></a>
max@0	5611 <b>
max@0	5612 norm(X, p)
max@0	5613 </b>
max@0	5614 <ul>
max@0	5615 <li>
max@0	5616 Compute the <i>p</i>-norm of <i>X</i>, where <i>X</i> can be a vector or a matrix
max@0	5617 </li>
max@0	5618 <br>
max@0	5619 <li>
max@0	5620 For vectors, <i>p</i> is an integer ≥1, or one of: "-inf", "inf", "fro"
max@0	5621 </li>
max@0	5622 <br>
max@0	5623 <li>
max@0	5624 For matrices, <i>p</i> is one of: 1, 2, "inf", "fro"
max@0	5625 </li>
max@0	5626 <br>
max@0	5627 <li>
max@0	5628 "-inf" is the minimum norm, "inf" is the maximum norm, while "fro" is the Frobenius norm
max@0	5629 </li>
max@0	5630 <br>
max@0	5631 <li>
max@0	5632 To obtain the zero norm or Hamming norm (ie. the number of non-zero elements),
max@0	5633 you may want to use this expression: <a href="#accu">accu</a>(X != 0).
max@0	5634 </li>
max@0	5635 <br>
max@0	5636 <li>
max@0	5637 Examples:
max@0	5638 <ul>
max@0	5639 <pre>
max@0	5640 vec q = randu<vec>(5);
max@0	5641 double x = norm(q, 2);
max@0	5642 double y = norm(q, "inf");
max@0	5643 </pre>
max@0	5644 </ul>
max@0	5645 </li>
max@0	5646 <br>
max@0	5647 <li>
max@0	5648 See also:
max@0	5649 <ul>
max@0	5650 <li><a href="#dot">dot()</a></li>
max@0	5651 <li><a href="http://en.wikipedia.org/wiki/Norm_(mathematics)">Vector Norm in Wikipedia</a></li>
max@0	5652 <li><a href="http://mathworld.wolfram.com/VectorNorm.html">Vector Norm in MathWorld</a></li>
max@0	5653 <li><a href="http://en.wikipedia.org/wiki/Matrix_norm">Matrix Norm in Wikipedia</a></li>
max@0	5654 <li><a href="http://mathworld.wolfram.com/MatrixNorm.html">Matrix Norm in MathWorld</a></li>
max@0	5655 </ul>
max@0	5656 </li>
max@0	5657 <br>
max@0	5658 </ul>
max@0	5659 <hr class="greyline"><br>
max@0	5660
max@0	5661 <a name="rank"></a>
max@0	5662 <b>rank(X, tolerance = default)</b>
max@0	5663
max@0	5664 <ul>
max@0	5665 <li>Returns the rank of matrix <i>X</i></li><br>
max@0	5666 <li>Any singular values less than default tolerance are treated as zero</li><br>
max@0	5667 <li>The default tolerance is <i>max(X.n_rows, X.n_cols)*eps(sigma)</i>,
max@0	5668 where <i>sigma</i> is the largest singular value of <i>X</i>
max@0	5669 </li><br>
max@0	5670 <li>The computation is based on singular value decomposition;
max@0	5671 if the decomposition fails, a <i>std::runtime_error</i> exception is thrown</li><br>
max@0	5672 <li>
max@0	5673 Examples:
max@0	5674 <ul>
max@0	5675 <pre>
max@0	5676 mat A = randu<mat>(4,5);
max@0	5677 uword r = rank(A);
max@0	5678 </pre>
max@0	5679 </ul>
max@0	5680 </li>
max@0	5681 <br>
max@0	5682 <li>
max@0	5683 See also:
max@0	5684 <ul>
max@0	5685 <li><a href="#eps">eps()</a></li>
max@0	5686 <li><a href="http://mathworld.wolfram.com/MatrixRank.html">Rank in MathWorld</a></li>
max@0	5687 <li><a href="http://en.wikipedia.org/wiki/Rank_(linear_algebra)">Rank in Wikipedia</a></li>
max@0	5688 </ul>
max@0	5689 </li>
max@0	5690 </ul>
max@0	5691 <br>
max@0	5692 <hr class="greyline"><br>
max@0	5693
max@0	5694 <a name="trace"></a>
max@0	5695 <b>trace(mat)</b>
max@0	5696 <ul>
max@0	5697 <li>
max@0	5698 Sum of the diagonal elements of a square matrix
max@0	5699 </li>
max@0	5700 <br>
max@0	5701 <li>
max@0	5702 A <i>std::logic_error</i> exception is thrown if the given matrix is not square
max@0	5703 </li>
max@0	5704 <br>
max@0	5705 <li>
max@0	5706 Examples:
max@0	5707 <ul>
max@0	5708 <pre>
max@0	5709 mat A = randu<mat>(5,5);
max@0	5710 double x = trace(A);
max@0	5711 </pre>
max@0	5712 </ul>
max@0	5713 </li>
max@0	5714 <br>
max@0	5715 <li>
max@0	5716 See also:
max@0	5717 <ul>
max@0	5718 <li><a href="#diag">.diag()</a></li>
max@0	5719 <li><a href="#diagvec">diagvec()</a></li>
max@0	5720 <li><a href="#sum">sum()</a></li>
max@0	5721 </ul>
max@0	5722 </li>
max@0	5723 <br>
max@0	5724 </ul>
max@0	5725 <hr class="greyline">
max@0	5726
max@0	5727 <hr class="greyline">
max@0	5728 <br>
max@0	5729 <br>
max@0	5730 <font size=+1><b>Scalar/Vector Valued Functions of Vectors/Matrices</b></font>
max@0	5731 <br>
max@0	5732 <br>
max@0	5733 <hr class="greyline">
max@0	5734 <br>
max@0	5735
max@0	5736 <a name="diagvec"></a>
max@0	5737 <b>diagvec(A, k=0)</b>
max@0	5738 <ul>
max@0	5739 <li>
max@0	5740 Extract the <i>k</i>-th diagonal from matrix <i>A</i>
max@0	5741 </li>
max@0	5742 <br>
max@0	5743 <li>
max@0	5744 The argument <i>k</i> is optional -- by default the main diagonal is extracted (<i>k=0</i>)
max@0	5745 </li>
max@0	5746 <br>
max@0	5747 <li>For <i>k > 0</i>, the <i>k</i>-th super-diagonal is extracted (top-right corner)</li>
max@0	5748 <br>
max@0	5749 <li>For <i>k < 0</i>, the <i>k</i>-th sub-diagonal is extracted (bottom-left corner)</li>
max@0	5750 <br>
max@0	5751 <li>
max@0	5752 An extracted a diagonal is interpreted as a column vector
max@0	5753 </li>
max@0	5754 <br>
max@0	5755 <li>
max@0	5756 Examples:
max@0	5757 <ul>
max@0	5758 <pre>
max@0	5759 mat A = randu<mat>(5,5);
max@0	5760 vec d = diagvec(A);
max@0	5761 </pre>
max@0	5762 </ul>
max@0	5763 </li>
max@0	5764 <br>
max@0	5765 <li>See also:
max@0	5766 <ul>
max@0	5767 <li><a href="#diag">.diag()</a></li>
max@0	5768 <li><a href="#diagmat">diagmat()</a></li>
max@0	5769 </ul>
max@0	5770 </li>
max@0	5771 <br>
max@0	5772 </ul>
max@0	5773 <hr class="greyline">
max@0	5774 <br>
max@0	5775
max@0	5776 <a name="min_and_max"></a>
max@0	5777 <b>min(mat, dim=0)</b>
max@0	5778 <br><b>min(rowvec)</b>
max@0	5779 <br><b>min(colvec)</b>
max@0	5780 <br>
max@0	5781 <br><b>max(mat, dim=0)</b>
max@0	5782 <br><b>max(rowvec)</b>
max@0	5783 <br><b>max(colvec)</b>
max@0	5784 <ul>
max@0	5785 <li>
max@0	5786 For a matrix argument, return the extremum value for each column (dim=0), or each row (dim=1)
max@0	5787 </li>
max@0	5788 <br>
max@0	5789 <li>
max@0	5790 For a vector argument, return the extremum value
max@0	5791 </li>
max@0	5792 <br>
max@0	5793 <li>
max@0	5794 Examples:
max@0	5795 <ul>
max@0	5796 <pre>
max@0	5797 colvec q = randu<colvec>(10,1);
max@0	5798 double x = max(q);
max@0	5799
max@0	5800 mat A = randu<mat>(10,10);
max@0	5801 rowvec b = max(A);
max@0	5802
max@0	5803 // same result as max(A)
max@0	5804 // the 0 explicitly indicates
max@0	5805 // "traverse across rows"
max@0	5806 rowvec c = max(A,0);
max@0	5807
max@0	5808 // the 1 explicitly indicates
max@0	5809 // "traverse across columns"
max@0	5810 colvec d = max(A,1);
max@0	5811
max@0	5812 // find the overall maximum value
max@0	5813 double y = max(max(A));
max@0	5814 </pre>
max@0	5815 </ul>
max@0	5816 </li>
max@0	5817 <br>
max@0	5818 <li>
max@0	5819 See also:
max@0	5820 <ul>
max@0	5821 <li><a href="#min_and_max_member">.min() & .max()</a> (member functions of Mat and Cube)</li>
max@0	5822 <li><a href="#running_stat">running_stat</a></li>
max@0	5823 <li><a href="#running_stat_vec">running_stat_vec</a></li>
max@0	5824 </ul>
max@0	5825 </li>
max@0	5826 <br>
max@0	5827 </ul>
max@0	5828 <hr class="greyline"><br>
max@0	5829
max@0	5830 <a name="prod"></a>
max@0	5831 <b>prod(mat, dim=0)</b>
max@0	5832 <br><b>prod(rowvec)</b>
max@0	5833 <br><b>prod(colvec)</b>
max@0	5834 <ul>
max@0	5835 <li>
max@0	5836 For a matrix argument, return the product of elements in each column (dim=0), or each row (dim=1)
max@0	5837 </li>
max@0	5838 <br>
max@0	5839 <li>
max@0	5840 For a vector argument, return the product of all elements
max@0	5841 </li>
max@0	5842 <br>
max@0	5843 <li>
max@0	5844 Examples:
max@0	5845 <ul>
max@0	5846 <pre>
max@0	5847 colvec q = randu<colvec>(10,1);
max@0	5848 double x = prod(q);
max@0	5849
max@0	5850 mat A = randu<mat>(10,10);
max@0	5851 rowvec b = prod(A);
max@0	5852
max@0	5853 // same result as prod(A)
max@0	5854 // the 0 explicitly indicates
max@0	5855 // "traverse across rows"
max@0	5856 rowvec c = prod(A,0);
max@0	5857
max@0	5858 // the 1 explicitly indicates
max@0	5859 // "traverse across columns"
max@0	5860 colvec d = prod(A,1);
max@0	5861
max@0	5862 // find the overall product
max@0	5863 double y = prod(prod(A));
max@0	5864 </pre>
max@0	5865 </ul>
max@0	5866 </li>
max@0	5867 <br>
max@0	5868 <li>
max@0	5869 See also:
max@0	5870 <ul>
max@0	5871 <li><a href="#schur_product">Schur product</a></li>
max@0	5872 </ul>
max@0	5873 </li>
max@0	5874 </ul>
max@0	5875 <br>
max@0	5876 <hr class="greyline"><br>
max@0	5877
max@0	5878
max@0	5879 <a name="sum"></a>
max@0	5880 <b>sum(mat, dim=0)</b>
max@0	5881 <br><b>sum(rowvec)</b>
max@0	5882 <br><b>sum(colvec)</b>
max@0	5883 <ul>
max@0	5884 <li>
max@0	5885 For a matrix argument, return the sum of elements in each column (dim=0), or each row (dim=1)
max@0	5886 </li>
max@0	5887 <br>
max@0	5888 <li>
max@0	5889 For a vector argument, return the sum of all elements
max@0	5890 </li>
max@0	5891 <br>
max@0	5892 <li>
max@0	5893 To get a sum of all the elements regardless of the argument type (ie. matrix or vector),
max@0	5894 you may wish to use <a href="#accu">accu()</a> instead
max@0	5895 </li>
max@0	5896 <br>
max@0	5897 <li>
max@0	5898 Examples:
max@0	5899 <ul>
max@0	5900 <pre>
max@0	5901 colvec q = randu<colvec>(10,1);
max@0	5902 double x = sum(q);
max@0	5903
max@0	5904 mat A = randu<mat>(10,10);
max@0	5905 rowvec b = sum(A);
max@0	5906
max@0	5907 // same result as sum(A)
max@0	5908 // the 0 explicitly indicates
max@0	5909 // "traverse across rows"
max@0	5910 rowvec c = sum(A,0);
max@0	5911
max@0	5912 // the 1 explicitly indicates
max@0	5913 // "traverse across columns"
max@0	5914 colvec d = sum(A,1);
max@0	5915
max@0	5916 // find the overall sum
max@0	5917 double y = sum(sum(A));
max@0	5918 </pre>
max@0	5919 </ul>
max@0	5920 </li>
max@0	5921 <br>
max@0	5922 <li>
max@0	5923 See also:
max@0	5924 <ul>
max@0	5925 <li><a href="#accu">accu()</a></li>
max@0	5926 <li><a href="#cumsum">cumsum()</a></li>
max@0	5927 <li><a href="#trace">trace()</a></li>
max@0	5928 <li><a href="#as_scalar">as_scalar()</a></li>
max@0	5929 </ul>
max@0	5930 </li>
max@0	5931 <br>
max@0	5932 </ul>
max@0	5933 <hr class="greyline"><br>
max@0	5934
max@0	5935
max@0	5936 <a name="stats_fns"></a>
max@0	5937 <b>statistics: mean, median, stddev, var</b>
max@0	5938
max@0	5939 <ul>
max@0	5940 <table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
max@0	5941 <tbody>
max@0	5942 <tr>
max@0	5943 <td style="vertical-align: top;">
max@0	5944 <b>mean(mat, dim=0)</b>
max@0	5945 <br><b>mean(colvec)</b>
max@0	5946 <br><b>mean(rowvec)</b>
max@0	5947 <br>
max@0	5948 <br>
max@0	5949 </td>
max@0	5950 <td style="vertical-align: top;">
max@0	5951
max@0	5952 </td>
max@0	5953 <td style="vertical-align: top;">
max@0	5954 mean (average value)
max@0	5955 </td>
max@0	5956 </tr>
max@0	5957 <tr>
max@0	5958 <td style="vertical-align: top;">
max@0	5959 <b>median(mat, dim=0)</b>
max@0	5960 <br><b>median(colvec)</b>
max@0	5961 <br><b>median(rowvec)</b>
max@0	5962 <br>
max@0	5963 <br>
max@0	5964 </td>
max@0	5965 <td style="vertical-align: top;">
max@0	5966
max@0	5967 </td>
max@0	5968 <td style="vertical-align: top;">
max@0	5969 median
max@0	5970 </td>
max@0	5971 </tr>
max@0	5972 <tr>
max@0	5973 <td style="vertical-align: top;">
max@0	5974 <b>stddev(mat, norm_type=0, dim=0)</b>
max@0	5975 <br><b>stddev(colvec, norm_type=0)</b>
max@0	5976 <br><b>stddev(rowvec, norm_type=0)</b>
max@0	5977 <br>
max@0	5978 <br>
max@0	5979 </td>
max@0	5980 <td style="vertical-align: top;">
max@0	5981
max@0	5982 </td>
max@0	5983 <td style="vertical-align: top;">
max@0	5984 standard deviation
max@0	5985 </td>
max@0	5986 </tr>
max@0	5987 <tr>
max@0	5988 <td style="vertical-align: top;">
max@0	5989 <b>var(mat, norm_type=0, dim=0)</b>
max@0	5990 <br><b>var(colvec, norm_type=0)</b>
max@0	5991 <br><b>var(rowvec, norm_type=0)</b>
max@0	5992 <br>
max@0	5993 <br>
max@0	5994 </td>
max@0	5995 <td style="vertical-align: top;">
max@0	5996
max@0	5997 </td>
max@0	5998 <td style="vertical-align: top;">
max@0	5999 variance
max@0	6000 </td>
max@0	6001 </tr>
max@0	6002 </tbody>
max@0	6003 </table>
max@0	6004 <br>
max@0	6005 <li>
max@0	6006 For a matrix argument, find a particular statistic for each column (<i>dim=0</i>), or each row (<i>dim=1</i>)
max@0	6007 </li>
max@0	6008 <br>
max@0	6009 <li>
max@0	6010 For a vector argument, return a particular statistic calculated using all the elements of the vector
max@0	6011 </li>
max@0	6012 <br>
max@0	6013 <li>
max@0	6014 For the var() and stddev() functions, the default <i>norm_type=0</i> performs normalisation using <i>N-1</i> (where <i>N</i> is the number of samples),
max@0	6015 providing the best unbiased estimator.
max@0	6016 Using <i>norm_type=1</i> causes normalisation to be done using <i>N</i>, which provides the second moment around the mean
max@0	6017 </li>
max@0	6018 <br>
max@0	6019 <li>
max@0	6020 Examples:
max@0	6021 <ul>
max@0	6022 <pre>
max@0	6023 mat A = randu<mat>(5,5);
max@0	6024 mat B = mean(A);
max@0	6025 mat C = var(A);
max@0	6026 double m = mean(mean(A));
max@0	6027
max@0	6028 vec q = randu<vec>(5);
max@0	6029 double v = var(q);
max@0	6030 </pre>
max@0	6031 </ul>
max@0	6032 </li>
max@0	6033 <br>
max@0	6034 <li>
max@0	6035 See also:
max@0	6036 <ul>
max@0	6037 <li><a href="#cov">cov()</a></li>
max@0	6038 <li><a href="#cor">cor()</a></li>
max@0	6039 <li><a href="#running_stat">running_stat</a></li>
max@0	6040 <li><a href="#running_stat_vec">running_stat_vec</a></li>
max@0	6041 </ul>
max@0	6042 </li>
max@0	6043 </ul>
max@0	6044 <br>
max@0	6045 <hr class="greyline">
max@0	6046
max@0	6047 <hr class="greyline">
max@0	6048 <br>
max@0	6049 <br>
max@0	6050 <font size=+1><b>Vector/Matrix/Cube Valued Functions of Vectors/Matrices/Cubes</b></font>
max@0	6051 <br>
max@0	6052 <br>
max@0	6053 <hr class="greyline">
max@0	6054 <br>
max@0	6055
max@0	6056 <a name="conv"></a>
max@0	6057 <b>
max@0	6058 C = conv(A, B)
max@0	6059 </b>
max@0	6060 <ul>
max@0	6061 <li>
max@0	6062 Convolution of vectors A and B.
max@0	6063 </li>
max@0	6064 <br>
max@0	6065 <li>
max@0	6066 If A and B are polynomial coefficient vectors, convolving them is equivalent to multiplying the two polynomials
max@0	6067 </li>
max@0	6068 <br>
max@0	6069 <li>
max@0	6070 The convolution operation is also equivalent to FIR filtering
max@0	6071 </li>
max@0	6072 <br>
max@0	6073 <li>
max@0	6074 The orientation of the result vector is the same as the orientation of A (ie. column or row vector)
max@0	6075 </li>
max@0	6076 <br>
max@0	6077 <li>
max@0	6078 Examples:
max@0	6079 <ul>
max@0	6080 <pre>
max@0	6081 vec A = randu<vec>(128) - 0.5;
max@0	6082 vec B = randu<vec>(128) - 0.5;
max@0	6083
max@0	6084 vec C = conv(A,B);
max@0	6085 </pre>
max@0	6086 </ul>
max@0	6087 </li>
max@0	6088 <br>
max@0	6089 <li>
max@0	6090 See also:
max@0	6091 <ul>
max@0	6092 <li><a href="http://mathworld.wolfram.com/Convolution.html">Convolution in MathWorld</a></li>
max@0	6093 <li><a href="http://en.wikipedia.org/wiki/Convolution">Convolution in Wikipedia</a></li>
max@0	6094 <li><a href="http://en.wikipedia.org/wiki/Finite_impulse_response">FIR filter in Wikipedia</a></li>
max@0	6095 <li><a href="#cor">cor()</a></li>
max@0	6096 </ul>
max@0	6097 </li>
max@0	6098 </ul>
max@0	6099 <br>
max@0	6100 <hr class="greyline"><br>
max@0	6101
max@0	6102 <a name="conv_to"></a>
max@0	6103 <b>
max@0	6104 conv_to<<i>type</i>>::from(X)
max@0	6105 </b>
max@0	6106 <ul>
max@0	6107 <li>
max@0	6108 A form of casting
max@0	6109 </li>
max@0	6110 <br>
max@0	6111 <li>
max@0	6112 Convert between matrix/vector types (eg. <i>mat</i> to <i>fmat</i>), as well as cube types (eg. <i>cube</i> to <i>fcube</i>)
max@0	6113 </li>
max@0	6114 <br>
max@0	6115 <li>
max@0	6116 Conversion between <i>std::vector</i> and Armadillo matrices/vectors is also possible
max@0	6117 </li>
max@0	6118 <br>
max@0	6119 <li>
max@0	6120 Conversion of a <i>mat</i> object into <i>colvec</i>, <i>rowvec</i> or <i>std::vector</i> is possible if the object can be interpreted as a vector
max@0	6121 </li>
max@0	6122 <br>
max@0	6123 <li>
max@0	6124 Examples:
max@0	6125 <ul>
max@0	6126 <pre>
max@0	6127 mat A = randu<mat>(5,5);
max@0	6128 fmat B = conv_to<fmat>::from(A);
max@0	6129
max@0	6130 typedef std::vector<double> stdvec;
max@0	6131
max@0	6132 stdvec x(3);
max@0	6133 x[0] = 0.0; x[1] = 1.0; x[2] = 2.0;
max@0	6134
max@0	6135 colvec y = conv_to< colvec >::from(x);
max@0	6136 stdvec z = conv_to< stdvec >::from(y);
max@0	6137 </pre>
max@0	6138 </ul>
max@0	6139 </li>
max@0	6140 <br>
max@0	6141 <li>
max@0	6142 See also:
max@0	6143 <ul>
max@0	6144 <li><a href="#as_scalar">as_scalar()</a></li>
max@0	6145 <li><a href="#reshape">reshape()</a></li>
max@0	6146 <li><a href="#resize">resize()</a></li>
max@0	6147 <li><a href="#adv_constructors_mat">advanced constructors (matrices)</a></li>
max@0	6148 <li><a href="#adv_constructors_cube">advanced constructors (cubes)</a></li>
max@0	6149 </ul>
max@0	6150 </li>
max@0	6151 <br>
max@0	6152 </ul>
max@0	6153 <hr class="greyline"><br>
max@0	6154
max@0	6155 <a name="conj"></a>
max@0	6156 <b>conj(cx_mat)</b>
max@0	6157 <br><b>conj(cx_cube)</b>
max@0	6158 <ul>
max@0	6159 <li>
max@0	6160 Obtain the complex conjugate of each element in a complex matrix/cube
max@0	6161 </li>
max@0	6162 <br>
max@0	6163 <li>
max@0	6164 Examples:
max@0	6165 <ul>
max@0	6166 <pre>
max@0	6167 cx_mat X = randu<cx_mat>(5,5);
max@0	6168 cx_mat Y = conj(X);
max@0	6169 </pre>
max@0	6170 </ul>
max@0	6171 </li>
max@0	6172 <br>
max@0	6173 <li>See also:
max@0	6174 <ul>
max@0	6175 <li><a href="#trans">trans()</a></li>
max@0	6176 </ul>
max@0	6177 </li>
max@0	6178 <br>
max@0	6179 </ul>
max@0	6180 <hr class="greyline"><br>
max@0	6181
max@0	6182 <a name="cor"></a>
max@0	6183 <b>cor(X, Y, norm_type=0)</b>
max@0	6184 <br><b>cor(X, norm_type=0)</b>
max@0	6185 <ul>
max@0	6186 <li>
max@0	6187 For two matrix arguments <i>X</i> and <i>Y</i>,
max@0	6188 if each row of <i>X</i> and <i>Y</i> is an observation and each column is a variable,
max@0	6189 the <i>(i,j)</i>-th entry of <i>cor(X,Y)</i> is the correlation coefficient between the <i>i</i>-th variable in <i>X</i> and the <i>j</i>-th variable in <i>Y</i>
max@0	6190 </li>
max@0	6191 <br>
max@0	6192 <li>
max@0	6193 For vector arguments, the type of vector is ignored and each element in the vector is treated as an observation
max@0	6194 </li>
max@0	6195 <br>
max@0	6196 <li>
max@0	6197 For matrices, <i>X</i> and <i>Y</i> must have the same dimensions
max@0	6198 </li>
max@0	6199 <br>
max@0	6200 <li>
max@0	6201 For vectors, <i>X</i> and <i>Y</i> must have the same number of elements
max@0	6202 </li>
max@0	6203 <br>
max@0	6204 <li>
max@0	6205 <i>cor(X)</i> is equivalent to <i>cor(X, X)</i>, also called autocorrelation
max@0	6206 </li>
max@0	6207 <br>
max@0	6208 <li>
max@0	6209 The default <i>norm_type=0</i> performs normalisation of the correlation matrix using <i>N-1</i> (where <i>N</i> is the number of observations).
max@0	6210 Using <i>norm_type=1</i> causes normalisation to be done using <i>N</i>
max@0	6211 </li>
max@0	6212 <br>
max@0	6213 <li>
max@0	6214 Examples:
max@0	6215 <ul>
max@0	6216 <pre>
max@0	6217 mat X = randu<mat>(4,5);
max@0	6218 mat Y = randu<mat>(4,5);
max@0	6219
max@0	6220 mat R = cor(X,Y);
max@0	6221 </pre>
max@0	6222 </ul>
max@0	6223 </li>
max@0	6224 <br>
max@0	6225 <li>
max@0	6226 See also:
max@0	6227 <ul>
max@0	6228 <li><a href="http://mathworld.wolfram.com/Correlation.html">Correlation in MathWorld</a></li>
max@0	6229 <li><a href="http://mathworld.wolfram.com/Autocorrelation.html">Autocorrelation in MathWorld</a></li>
max@0	6230 <li><a href="#cov">cov()</a></li>
max@0	6231 <li><a href="#conv">conv()</a></li>
max@0	6232 </ul>
max@0	6233 </li>
max@0	6234 </ul>
max@0	6235 <br>
max@0	6236 <hr class="greyline"><br>
max@0	6237
max@0	6238 <a name="cov"></a>
max@0	6239 <b>cov(X, Y, norm_type=0)</b>
max@0	6240 <br><b>cov(X, norm_type=0)</b>
max@0	6241 <ul>
max@0	6242 <li>
max@0	6243 For two matrix arguments <i>X</i> and <i>Y</i>,
max@0	6244 if each row of <i>X</i> and <i>Y</i> is an observation and each column is a variable,
max@0	6245 the <i>(i,j)</i>-th entry of <i>cov(X,Y)</i> is the covariance between the <i>i</i>-th variable in <i>X</i> and the <i>j</i>-th variable in <i>Y</i>
max@0	6246 </li>
max@0	6247 <br>
max@0	6248 <li>
max@0	6249 For vector arguments, the type of vector is ignored and each element in the vector is treated as an observation
max@0	6250 </li>
max@0	6251 <br>
max@0	6252 <li>
max@0	6253 For matrices, <i>X</i> and <i>Y</i> must have the same dimensions
max@0	6254 </li>
max@0	6255 <br>
max@0	6256 <li>
max@0	6257 For vectors, <i>X</i> and <i>Y</i> must have the same number of elements
max@0	6258 </li>
max@0	6259 <br>
max@0	6260 <li>
max@0	6261 <i>cov(X)</i> is equivalent to <i>cov(X, X)</i>
max@0	6262 </li>
max@0	6263 <br>
max@0	6264 <li>
max@0	6265 The default <i>norm_type=0</i> performs normalisation using <i>N-1</i> (where <i>N</i> is the number of observations),
max@0	6266 providing the best unbiased estimation of the covariance matrix (if the observations are from a normal distribution).
max@0	6267 Using <i>norm_type=1</i> causes normalisation to be done using <i>N</i>, which provides the second moment matrix of the observations about their mean
max@0	6268 </li>
max@0	6269 <br>
max@0	6270 <li>
max@0	6271 Examples:
max@0	6272 <ul>
max@0	6273 <pre>
max@0	6274 mat X = randu<mat>(4,5);
max@0	6275 mat Y = randu<mat>(4,5);
max@0	6276
max@0	6277 mat C = cov(X,Y);
max@0	6278 </pre>
max@0	6279 </ul>
max@0	6280 </li>
max@0	6281 <br>
max@0	6282 <li>
max@0	6283 See also:
max@0	6284 <ul>
max@0	6285 <li><a href="#running_stat_vec">running_stat_vec</a></li>
max@0	6286 <li><a href="#stats_fns">statistics functions</a></li>
max@0	6287 <li><a href="http://mathworld.wolfram.com/Covariance.html">Covariance in MathWorld</a></li>
max@0	6288 <li><a href="#cor">cor()</a></li>
max@0	6289 </ul>
max@0	6290 </li>
max@0	6291 </ul>
max@0	6292 <br>
max@0	6293 <hr class="greyline"><br>
max@0	6294
max@0	6295 <a name="cross"></a>
max@0	6296 <b>cross(A, B)</b>
max@0	6297 <ul>
max@0	6298 <li>
max@0	6299 Calculate the cross product between A and B, under the assumption that A and B are 3 dimensional vectors
max@0	6300 </li>
max@0	6301 <br>
max@0	6302 <li>
max@0	6303 Examples:
max@0	6304 <ul>
max@0	6305 <pre>
max@0	6306 vec a = randu<vec>(3);
max@0	6307 vec b = randu<vec>(3);
max@0	6308
max@0	6309 vec c = cross(a,b);
max@0	6310 </pre>
max@0	6311 </ul>
max@0	6312 </li>
max@0	6313 <br>
max@0	6314 <li>
max@0	6315 See also:
max@0	6316 <ul>
max@0	6317 <li><a href="#dot">dot()</a></li>
max@0	6318 <li><a href="http://en.wikipedia.org/wiki/Cross_product">Cross product in Wikipedia</a></li>
max@0	6319 <li><a href="http://mathworld.wolfram.com/CrossProduct.html">Cross product in MathWorld</a></li>
max@0	6320 </ul>
max@0	6321 </li>
max@0	6322 </ul>
max@0	6323 <br>
max@0	6324 <hr class="greyline"><br>
max@0	6325
max@0	6326 <a name="cumsum"></a>
max@0	6327 <b>cumsum(mat, dim=0)</b>
max@0	6328 <br><b>cumsum(rowvec)</b>
max@0	6329 <br><b>cumsum(colvec)</b>
max@0	6330 <ul>
max@0	6331 <li>
max@0	6332 For a matrix argument, return a matrix containing the cumulative sum of elements in each column (dim=0, the default), or each row (dim=1)
max@0	6333 </li>
max@0	6334 <br>
max@0	6335 <li>
max@0	6336 For a vector argument, return a vector of the same orientation, containing the cumulative sum of elements
max@0	6337 </li>
max@0	6338 <br>
max@0	6339 <li>
max@0	6340 Examples:
max@0	6341 <ul>
max@0	6342 <pre>
max@0	6343 mat A = randu<mat>(5,5);
max@0	6344 mat B = cumsum(A);
max@0	6345
max@0	6346 vec x = randu<vec>(10);
max@0	6347 vec y = cumsum(x);
max@0	6348 </pre>
max@0	6349 </ul>
max@0	6350 </li>
max@0	6351 <br>
max@0	6352 <li>
max@0	6353 See also:
max@0	6354 <ul>
max@0	6355 <li><a href="#accu">accu()</a></li>
max@0	6356 <li><a href="#sum">sum()</a></li>
max@0	6357 </ul>
max@0	6358 </li>
max@0	6359 <br>
max@0	6360 </ul>
max@0	6361 <hr class="greyline"><br>
max@0	6362
max@0	6363 <a name="diagmat"></a>
max@0	6364 <b>diagmat(mat)</b>
max@0	6365 <br><b>diagmat(rowvec)</b>
max@0	6366 <br><b>diagmat(colvec)</b>
max@0	6367 <ul>
max@0	6368 <li>
max@0	6369 Interpret a matrix or vector as a diagonal matrix
max@0	6370 </li>
max@0	6371 <br>
max@0	6372 <li>
max@0	6373 For <i>mat</i>, given matrix must be square; the main diagonal is copied and all other elements in the generated matrix are set to zero
max@0	6374 </li>
max@0	6375 <br>
max@0	6376 <li>
max@0	6377 For <i>colvec</i> and <i>rowvec</i>, elements of the vector are placed on the main diagonal in the generated matrix and all other elements are set to zero
max@0	6378 </li>
max@0	6379 <br>
max@0	6380 <li>
max@0	6381 Examples:
max@0	6382 <ul>
max@0	6383 <pre>
max@0	6384 mat A = randu<mat>(5,5);
max@0	6385 mat B = diagmat(A);
max@0	6386 mat C = A*diagmat(A);
max@0	6387
max@0	6388 rowvec q = randu<rowvec>(5);
max@0	6389 colvec r = randu<colvec>(5);
max@0	6390 mat X = diagmat(q)*diagmat(r);
max@0	6391 </pre>
max@0	6392 </ul>
max@0	6393 </li>
max@0	6394 <br>
max@0	6395 <li>
max@0	6396 See also:
max@0	6397 <ul>
max@0	6398 <li><a href="#diagvec">diagvec()</a></li>
max@0	6399 <li><a href="#trimat">trimatu() / trimatl()</a></li>
max@0	6400 <li><a href="#symmat">symmatu() / symmatl()</a></li>
max@0	6401 <li><a href="#reshape">reshape()</a></li>
max@0	6402 </ul>
max@0	6403 </li>
max@0	6404 <br>
max@0	6405 </ul>
max@0	6406 <hr class="greyline">
max@0	6407 <br>
max@0	6408
max@0	6409 <a name="find"></a>
max@0	6410 <b>find(X, k=0, s="first")</b>
max@0	6411 <ul>
max@0	6412 <li>Return a column vector of the indices of non-zero elements of <i>X</i></li>
max@0	6413 <br>
max@0	6414 <li>The output vector must have the type <a href="#Col">uvec</a> or <a href="#Mat">umat</a>
max@0	6415 (ie. the indices are stored as unsigned integers of type <a href="#uword">uword</a>)
max@0	6416 </li>
max@0	6417 <br>
max@0	6418 <li>
max@0	6419 The input matrix <i>X</i> is interpreted as a vector, with column-by-column ordering of the elements of <i>X</i>
max@0	6420 </li>
max@0	6421 <br>
max@0	6422 <li>Relational operators can be used instead of <i>X</i>, eg. <i>A > 0.5</i>
max@0	6423 </li>
max@0	6424 <br>
max@0	6425 <li>If <i>k=0</i> (default), return the indices of all non-zero elements, otherwise return at most <i>k</i> of their indices</li>
max@0	6426 <br>
max@0	6427 <li>If <i>s="first"</i> (default), return at most the first <i>k</i> indices of the non-zero elements
max@0	6428 </li>
max@0	6429 <br>
max@0	6430 <li>If <i>s="last"</i>, return at most the last <i>k</i> indices of the non-zero elements
max@0	6431 </li>
max@0	6432 <br>
max@0	6433 <li>
max@0	6434 Examples:
max@0	6435 <ul>
max@0	6436 <pre>
max@0	6437 mat A = randu<mat>(5,5);
max@0	6438 mat B = randu<mat>(5,5);
max@0	6439
max@0	6440 uvec q1 = find(A > B);
max@0	6441 uvec q2 = find(A > 0.5);
max@0	6442 uvec q3 = find(A > 0.5, 3, "last");
max@0	6443 </pre>
max@0	6444 </ul>
max@0	6445 </li>
max@0	6446 <br>
max@0	6447 <li>
max@0	6448 See also:
max@0	6449 <ul>
max@0	6450 <li><a href="#conv_to">conv_to()</a> (convert between matrix/vector types)</li>
max@0	6451 <li><a href="#submat">submatrix views</a></li>
max@0	6452 <li><a href="#sort_index">sort_index()</a></li>
max@0	6453 </ul>
max@0	6454 </li>
max@0	6455 <br>
max@0	6456 </ul>
max@0	6457 <hr class="greyline">
max@0	6458 <br>
max@0	6459
max@0	6460 <a name="flip"></a>
max@0	6461 <b>fliplr(mat)</b>
max@0	6462 <br><b>flipud(mat)</b>
max@0	6463 <ul>
max@0	6464 <li>
max@0	6465 fliplr(): generate a copy of the input matrix, with the order of the columns reversed
max@0	6466 </li>
max@0	6467 <br>
max@0	6468 <li>
max@0	6469 flipud(): generate a copy of the input matrix, with the order of the rows reversed
max@0	6470 </li>
max@0	6471 <br>
max@0	6472 <li>
max@0	6473 Examples:
max@0	6474 <ul>
max@0	6475 <pre>
max@0	6476 mat A = randu<mat>(5,5);
max@0	6477
max@0	6478 mat B = fliplr(A);
max@0	6479 mat C = flipud(A);
max@0	6480 </pre>
max@0	6481 </ul>
max@0	6482 </li>
max@0	6483 <br>
max@0	6484 <li>
max@0	6485 See also:
max@0	6486 <ul>
max@0	6487 <li><a href="#swap_rows">.swap_rows() & .swap_cols()</a> (member functions of <i>Mat</i>, <i>Col</i> and <i>Row</i> classes)</li>
max@0	6488 </ul>
max@0	6489 </li>
max@0	6490 <br>
max@0	6491 </ul>
max@0	6492 <hr class="greyline"><br>
max@0	6493
max@0	6494 <a name="imag_real"></a>
max@0	6495 <b>imag(cx_mat)</b>
max@0	6496 <br><b>imag(cx_cube)</b>
max@0	6497 <br>
max@0	6498 <br><b>real(cx_mat)</b>
max@0	6499 <br><b>real(cx_cube)</b>
max@0	6500 <ul>
max@0	6501 <li>
max@0	6502 Extract the imaginary/real part of a complex matrix/cube
max@0	6503 </li>
max@0	6504 <br>
max@0	6505 <li>
max@0	6506 Examples:
max@0	6507 <ul>
max@0	6508 <pre>
max@0	6509 cx_mat C = randu<cx_mat>(5,5);
max@0	6510
max@0	6511 mat A = imag(C);
max@0	6512 mat B = real(C);
max@0	6513 </pre>
max@0	6514 </ul>
max@0	6515 </li>
max@0	6516 <br>
max@0	6517 <li><b>Caveat:</b> versions 4.4, 4.5 and 4.6 of the GCC C++ compiler have a bug when using the <i>-std=c++0x</i> compiler option (ie. experimental support for C++11);
max@0	6518 to work around this bug, preface Armadillo's imag() and real() with the <i>arma</i> namespace qualification, eg. arma::imag(C)
max@0	6519 </li>
max@0	6520 <br>
max@0	6521 <li>See also:
max@0	6522 <ul>
max@0	6523 <li><a href="#set_imag">set_imag() / set_real()</a></li>
max@0	6524 </ul>
max@0	6525 </li>
max@0	6526 <br>
max@0	6527 </ul>
max@0	6528 <hr class="greyline"><br>
max@0	6529
max@0	6530 <a name="join"></a>
max@0	6531 <b>join_rows(mat A, mat B)</b>
max@0	6532 <br><b>join_cols(mat A, mat B)</b>
max@0	6533 <br><b>join_slices(cube A, cube B)</b>
max@0	6534 <ul>
max@0	6535 <li>
max@0	6536 join_rows():
max@0	6537 for two matrices A and B, append each row of B to its respective row of A;
max@0	6538 matrices A and B must have the same number of rows
max@0	6539 </li>
max@0	6540 <br>
max@0	6541 <li>
max@0	6542 join_cols():
max@0	6543 for two matrices A and B, append each column of B to its respective column of A;
max@0	6544 matrices A and B must have the same number of columns
max@0	6545 </li>
max@0	6546 <br>
max@0	6547 <li>
max@0	6548 join_slices():
max@0	6549 for two cubes A and B, append the slices of B to the slices of A;
max@0	6550 cubes A and B have the same number of rows and columns (ie. all slices must have the same size)
max@0	6551 </li>
max@0	6552 <br>
max@0	6553 <li>
max@0	6554 Examples:
max@0	6555 <ul>
max@0	6556 <pre>
max@0	6557 mat A = randu<mat>(4,5);
max@0	6558 mat B = randu<mat>(4,6);
max@0	6559 mat C = randu<mat>(6,5);
max@0	6560
max@0	6561 mat X = join_rows(A,B);
max@0	6562 mat Y = join_cols(A,C);
max@0	6563 </pre>
max@0	6564 </ul>
max@0	6565 </li>
max@0	6566 <br>
max@0	6567 <li>
max@0	6568 See also:
max@0	6569 <ul>
max@0	6570 <li><a href="#shed">shed rows/columns/slices</a></li>
max@0	6571 <li><a href="#insert">insert rows/columns/slices</a></li>
max@0	6572 <li><a href="#submat">submatrix views</a></li>
max@0	6573 <li><a href="#subcube">subcube views</a></li>
max@0	6574 </ul>
max@0	6575 </li>
max@0	6576 <br>
max@0	6577 </ul>
max@0	6578 <hr class="greyline"><br>
max@0	6579
max@0	6580 <a name="kron"></a>
max@0	6581 <b>kron(A,B)</b>
max@0	6582
max@0	6583 <ul>
max@0	6584 <li>Kronecker tensor product.</li>
max@0	6585 <br>
max@0	6586 <li>Using matrix <i>A</i> (with <i>n</i> rows and <i>p</i> columns) and matrix <i>B</i> (with <i>m</i> rows and <i>q</i> columns),
max@0	6587 <i>kron(A,B)</i> returns a matrix (with <i>nm</i> rows and <i>pq</i> columns) which denotes the tensor product of <i>A</i> and <i>B</i>
max@0	6588 </li>
max@0	6589 <br>
max@0	6590 <li>
max@0	6591 Examples:
max@0	6592 <ul>
max@0	6593 <pre>
max@0	6594 mat A = randu<mat>(4,5);
max@0	6595 mat B = randu<mat>(5,4);
max@0	6596
max@0	6597 mat K = kron(A,B);
max@0	6598 </pre>
max@0	6599 </ul>
max@0	6600 </li>
max@0	6601 <br>
max@0	6602 <li>
max@0	6603 See also:
max@0	6604 <ul>
max@0	6605 <li><a href="http://mathworld.wolfram.com/KroneckerProduct.html">Kronecker Product in MathWorld</a></li>
max@0	6606 </ul>
max@0	6607 </li>
max@0	6608 </ul>
max@0	6609 <br>
max@0	6610 <hr class="greyline"><br>
max@0	6611
max@0	6612 <a name="reshape"></a>
max@0	6613 <b>reshape(mat, n_rows, n_cols, dim=0)</b>
max@0	6614 <br><b>reshape(cube, n_rows, n_cols, n_slices, dim=0)</b>
max@0	6615 <ul>
max@0	6616 <li>
max@0	6617 Generate a matrix/cube sized according to given size specifications,
max@0	6618 whose elements are taken from the given matrix/cube, either column-wise (dim=0) or row-wise (dim=1);
max@0	6619 the elements in the generated object are placed column-wise (ie. the first column is filled up before filling the second column)
max@0	6620 </li>
max@0	6621 <br>
max@0	6622 <li>
max@0	6623 The layout of the elements in the generated object will be different to the layout in the given object
max@0	6624 </li>
max@0	6625 <br>
max@0	6626 <li>
max@0	6627 This function can be used to create a vector representation of a matrix (ie. concatenate all the columns or rows)
max@0	6628 </li>
max@0	6629 <br>
max@0	6630 <li>
max@0	6631 The total number of elements in the generated matrix/cube doesn't have to be the same as the total number of elements in the given matrix/cube
max@0	6632 </li>
max@0	6633 <br>
max@0	6634 <li>
max@0	6635 If the total number of elements in the given matrix/cube is less than the specified size,
max@0	6636 the remaining elements in the generated matrix/cube are set to zero
max@0	6637 </li>
max@0	6638 <br>
max@0	6639 <li>
max@0	6640 If the total number of elements in the given matrix/cube is greater than the specified size,
max@0	6641 only a subset of elements is taken from the given matrix/cube
max@0	6642 </li>
max@0	6643 <br>
max@0	6644 <li>
max@0	6645 <b>Caveat:</b>
max@0	6646 reshape() is slower than <a href="#set_size">.set_size()</a>, which doesn't preserve data
max@0	6647 </li>
max@0	6648 <br>
max@0	6649 <li>
max@0	6650 <b>Caveat:</b>
max@0	6651 if you wish to grow/shrink a matrix while preserving the elements <b>as well as</b> the layout of the elements,
max@0	6652 use <a href="#resize">resize()</a> instead
max@0	6653 </li>
max@0	6654 <br>
max@0	6655 <li>
max@0	6656 Examples:
max@0	6657 <ul>
max@0	6658 <pre>
max@0	6659 mat A = randu<mat>(10, 5);
max@0	6660 mat B = reshape(A, 5, 10);
max@0	6661 </pre>
max@0	6662 </ul>
max@0	6663 </li>
max@0	6664 <br>
max@0	6665 <li>
max@0	6666 See also:
max@0	6667 <ul>
max@0	6668 <li><a href="#reshape_member">.reshape()</a> (member function of Mat and Cube)</li>
max@0	6669 <li><a href="#set_size">.set_size()</a> (member function of Mat and Cube)</li>
max@0	6670 <li><a href="#resize">resize()</a></li>
max@0	6671 <li><a href="#as_scalar">as_scalar()</a></li>
max@0	6672 <li><a href="#conv_to">conv_to()</a></li>
max@0	6673 <li><a href="#diagmat">diagmat()</a></li>
max@0	6674 </ul>
max@0	6675 </li>
max@0	6676 <br>
max@0	6677 </ul>
max@0	6678 <hr class="greyline"><br>
max@0	6679
max@0	6680 <a name="resize"></a>
max@0	6681 <b>resize(mat, n_rows, n_cols)</b>
max@0	6682 <br><b>resize(cube, n_rows, n_cols, n_slices)</b>
max@0	6683 <ul>
max@0	6684 <li>
max@0	6685 Generate a matrix/cube sized according to given size specifications,
max@0	6686 whose elements as well as the layout of the elements are taken from the given matrix/cube
max@0	6687 </li>
max@0	6688 <br>
max@0	6689 <li>
max@0	6690 <b>Caveat:</b>
max@0	6691 resize() is slower than <a href="#set_size">.set_size()</a>, which doesn't preserve data
max@0	6692 </li>
max@0	6693 <br>
max@0	6694 <li>
max@0	6695 Examples:
max@0	6696 <ul>
max@0	6697 <pre>
max@0	6698 mat A = randu<mat>(4, 5);
max@0	6699 mat B = resize(A, 7, 6);
max@0	6700 </pre>
max@0	6701 </ul>
max@0	6702 </li>
max@0	6703 <br>
max@0	6704 <li>
max@0	6705 This function was added in version 2.4.1
max@0	6706 </li>
max@0	6707 <br>
max@0	6708 <li>
max@0	6709 See also:
max@0	6710 <ul>
max@0	6711 <li><a href="#resize_member">.resize()</a> (member function of Mat and Cube)</li>
max@0	6712 <li><a href="#set_size">.set_size()</a> (member function of Mat and Cube)</li>
max@0	6713 <li><a href="#reshape">reshape()</a></li>
max@0	6714 <li><a href="#as_scalar">as_scalar()</a></li>
max@0	6715 <li><a href="#conv_to">conv_to()</a></li>
max@0	6716 </ul>
max@0	6717 </li>
max@0	6718 <br>
max@0	6719 </ul>
max@0	6720 <hr class="greyline"><br>
max@0	6721
max@0	6722 <a name="shuffle"></a>
max@0	6723 <b>shuffle(mat, dim=0)</b>
max@0	6724 <br><b>shuffle(rowvec, dim=0)</b>
max@0	6725 <br><b>shuffle(colvec, dim=0)</b>
max@0	6726 <ul>
max@0	6727 <li>
max@0	6728 Shuffle the rows (dim=0) or columns (dim=1) of a matrix or vector
max@0	6729 </li>
max@0	6730 <br>
max@0	6731 <li>
max@0	6732 Examples:
max@0	6733 <ul>
max@0	6734 <pre>
max@0	6735 mat A = randu<mat>(4,5);
max@0	6736 mat B = shuffle(A);
max@0	6737 </pre>
max@0	6738 </ul>
max@0	6739 </li>
max@0	6740 <br>
max@0	6741 <li>
max@0	6742 See also:
max@0	6743 <ul>
max@0	6744 <li><a href="#randu_randn_standalone">randu() / randn()</a></li>
max@0	6745 <li><a href="#sort">sort()</a></li>
max@0	6746 </ul>
max@0	6747 </li>
max@0	6748 <br>
max@0	6749 </ul>
max@0	6750 <hr class="greyline"><br>
max@0	6751
max@0	6752 <a name="sort"></a>
max@0	6753 <b>sort(mat, sort_type=0, dim=0)</b>
max@0	6754 <br><b>sort(rowvec, sort_type=0)</b>
max@0	6755 <br><b>sort(colvec, sort_type=0)</b>
max@0	6756 <ul>
max@0	6757 <li>For a matrix argument, return a matrix with the elements of the input matrix sorted in each column (<i>dim=0</i>), or each row (<i>dim=1</i>)</li>
max@0	6758 <br>
max@0	6759 <li><i>sort_type=0</i> (default) indicates an ascending sort</li>
max@0	6760 <br>
max@0	6761 <li><i>sort_type=1</i> indicates a descending sort</li>
max@0	6762 <br>
max@0	6763 <li>For a vector argument, return a vector which is a sorted version of the input vector</li>
max@0	6764 <br>
max@0	6765 <li>
max@0	6766 Examples:
max@0	6767 <ul>
max@0	6768 <pre>
max@0	6769 mat A = randu<mat>(10,10);
max@0	6770 mat B = sort(A);
max@0	6771 </pre>
max@0	6772 </ul>
max@0	6773 </li>
max@0	6774 <li>
max@0	6775 See also:
max@0	6776 <ul>
max@0	6777 <li><a href="#sort_index">sort_index()</a></li>
max@0	6778 <li><a href="#shuffle">shuffle()</a></li>
max@0	6779 <li><a href="#randu_randn_standalone">randu() / randn()</a></li>
max@0	6780 </ul>
max@0	6781 </li>
max@0	6782 <br>
max@0	6783 </ul>
max@0	6784 <hr class="greyline"><br>
max@0	6785
max@0	6786 <a name="sort_index"></a>
max@0	6787 <b>sort_index(colvec, sort_type=0)</b>
max@0	6788 <br><b>sort_index(rowvec, sort_type=0)</b>
max@0	6789 <ul>
max@0	6790 <li>Return a vector which describes the sorted order of the given vector's elements
max@0	6791 (ie. it contains the indices of the given vector's elements)
max@0	6792 </li>
max@0	6793 <br>
max@0	6794 <li>The output vector must have the type <a href="#Col">uvec</a> or <a href="#Mat">umat</a>
max@0	6795 (ie. the indices are stored as unsigned integers of type <a href="#uword">uword</a>)
max@0	6796 </li>
max@0	6797 <br>
max@0	6798 <li><i>sort_type=0</i> (default) indicates an ascending sort</li>
max@0	6799 <br>
max@0	6800 <li><i>sort_type=1</i> indicates a descending sort</li>
max@0	6801 <br>
max@0	6802 <li>
max@0	6803 Examples:
max@0	6804 <ul>
max@0	6805 <pre>
max@0	6806 vec q = randu<vec>(10);
max@0	6807 uvec indices = sort_index(q);
max@0	6808 </pre>
max@0	6809 </ul>
max@0	6810 </li>
max@0	6811 <br>
max@0	6812 <li>
max@0	6813 See also:
max@0	6814 <ul>
max@0	6815 <li><a href="#find">find()</a></li>
max@0	6816 <li><a href="#sort">sort()</a></li>
max@0	6817 </ul>
max@0	6818 </li>
max@0	6819 <br>
max@0	6820 </ul>
max@0	6821 <hr class="greyline"><br>
max@0	6822
max@0	6823 <a name="symmat"></a>
max@0	6824 <b>symmatu(A)</b>
max@0	6825 <br><b>symmatl(A)</b>
max@0	6826 <ul>
max@0	6827 <li>
max@0	6828 <i>symmatu(A)</i>: interpret square matrix <i>A</i> as symmetric, reflecting the upper triangle to the lower triangle
max@0	6829 </li>
max@0	6830 <br>
max@0	6831 <li>
max@0	6832 <i>symmatl(A)</i>: interpret square matrix <i>A</i> as symmetric, reflecting the lower triangle to the upper triangle
max@0	6833 </li>
max@0	6834 <br>
max@0	6835 <li>
max@0	6836 If <i>A</i> is non-square, a <i>std::logic_error</i> exception is thrown
max@0	6837 </li>
max@0	6838 <br>
max@0	6839 <li>
max@0	6840 Examples:
max@0	6841 <ul>
max@0	6842 <pre>
max@0	6843 mat A = randu<mat>(5,5);
max@0	6844
max@0	6845 mat B = symmatu(A);
max@0	6846 mat C = symmatl(A);
max@0	6847 </pre>
max@0	6848 </ul>
max@0	6849 </li>
max@0	6850 <br>
max@0	6851 <li>See also:
max@0	6852 <ul>
max@0	6853 <li><a href="#diagmat">diagmat()</a></li>
max@0	6854 <li><a href="#trimat">trimatu() / trimatl()</a></li>
max@0	6855 <li><a href="http://en.wikipedia.org/wiki/Symmetric_matrix">Symmetric matrix in Wikipedia</a></li>
max@0	6856 </ul>
max@0	6857 </li>
max@0	6858 </ul>
max@0	6859 <br>
max@0	6860 <hr class="greyline"><br>
max@0	6861
max@0	6862 <a name="strans"></a>
max@0	6863 <b>strans(mat)</b>
max@0	6864 <br><b>strans(colvec)</b>
max@0	6865 <br><b>strans(rowvec)</b>
max@0	6866 <ul>
max@0	6867 <li>
max@0	6868 Simple matrix transpose, without taking the conjugate of the elements (complex matrices)
max@0	6869 </li>
max@0	6870 <br>
max@0	6871 <li>
max@0	6872 Use <a href="#trans">trans()</a> instead, unless you explicitly need to take the transpose of a complex matrix without taking the conjugate of the elements
max@0	6873 </li>
max@0	6874 <br>
max@0	6875 <li>See also:
max@0	6876 <ul>
max@0	6877 <li><a href="#t_st_members">.st()</a></li>
max@0	6878 <li><a href="#trans">trans()</a></li>
max@0	6879 </ul>
max@0	6880 </li>
max@0	6881 </ul>
max@0	6882 <br>
max@0	6883 <hr class="greyline"><br>
max@0	6884
max@0	6885
max@0	6886 <a name="trans"></a>
max@0	6887 <b>trans(mat)</b>
max@0	6888 <br><b>trans(colvec)</b>
max@0	6889 <br><b>trans(rowvec)</b>
max@0	6890 <ul>
max@0	6891 <li>
max@0	6892 Matrix transpose / Hermitian transpose
max@0	6893 </li>
max@0	6894 <br>
max@0	6895 <li>
max@0	6896 If a given object has real elements, a normal transpose is done
max@0	6897 </li>
max@0	6898 <br>
max@0	6899 <li>
max@0	6900 If a given object has complex elements, a Hermitian transpose is done (ie. the conjugate of the elements is taken during the transpose operation)
max@0	6901 </li>
max@0	6902 <br>
max@0	6903 <li>
max@0	6904 <b>Caveat:</b> for complex matrices, the functionality of trans() has changed in version 2.0:
max@0	6905 <ul>
max@0	6906 <li>in version 1.2.x and earlier, trans() does not take the conjugate of complex elements</li>
max@0	6907 <li>in version 1.2.x and earlier, the deprecated htrans() function is used for the Hermitian transpose</li>
max@0	6908 </ul>
max@0	6909 </li>
max@0	6910 <br>
max@0	6911 <li>
max@0	6912 Examples:
max@0	6913 <ul>
max@0	6914 <pre>mat A = randu<mat>(5,10);
max@0	6915 mat B = trans(A);
max@0	6916 </pre>
max@0	6917 </ul>
max@0	6918 </li>
max@0	6919 <br>
max@0	6920 <li>See also:
max@0	6921 <ul>
max@0	6922 <li><a href="#t_st_members">.t()</a></li>
max@0	6923 <li><a href="#strans">strans()</a></li>
max@0	6924 </ul>
max@0	6925 </li>
max@0	6926 </ul>
max@0	6927 <br>
max@0	6928 <hr class="greyline"><br>
max@0	6929
max@0	6930
max@0	6931 <a name="trimat"></a>
max@0	6932 <b>trimatu(A)</b>
max@0	6933 <br><b>trimatl(A)</b>
max@0	6934 <ul>
max@0	6935 <li>
max@0	6936 trimatu(A): interpret square matrix A as upper triangular
max@0	6937 </li>
max@0	6938 <br>
max@0	6939 <li>
max@0	6940 trimatl(A): interpret square matrix A as lower triangular
max@0	6941 </li>
max@0	6942 <br>
max@0	6943 <li>
max@0	6944 A <i>std::logic_error</i> exception is thrown if A is non-square
max@0	6945 </li>
max@0	6946 <br>
max@0	6947 <li>
max@0	6948 Examples:
max@0	6949 <ul>
max@0	6950 <pre>mat A = randu<mat>(5,5);
max@0	6951 mat U = trimatu(A);
max@0	6952 mat L = trimatl(A);
max@0	6953
max@0	6954 // tell the inv() function to look only
max@0	6955 // at the upper triangular part
max@0	6956 mat X = inv( trimatu(U) );
max@0	6957 </pre>
max@0	6958 </ul>
max@0	6959 </li>
max@0	6960 <br>
max@0	6961 <li>See also:
max@0	6962 <ul>
max@0	6963 <li><a href="#symmat">symmatu() / symmatl()</a></li>
max@0	6964 <li><a href="#diagmat">diagmat()</a></li>
max@0	6965 <li><a href="#inv">inv()</a></li>
max@0	6966 <li><a href="#solve">solve()</a></li>
max@0	6967 <li><a href="http://mathworld.wolfram.com/TriangularMatrix.html">Triangular matrix in MathWorld</a></li>
max@0	6968 <li><a href="http://en.wikipedia.org/wiki/Triangular_matrix">Triangular matrix in Wikipedia</a></li>
max@0	6969 </ul>
max@0	6970 </li>
max@0	6971 </ul>
max@0	6972 <br>
max@0	6973 <hr class="greyline">
max@0	6974
max@0	6975
max@0	6976 <hr class="greyline">
max@0	6977 <br>
max@0	6978 <br>
max@0	6979 <font size=+1><b>Decompositions, Inverses and Equation Solvers</b></font>
max@0	6980 <br>
max@0	6981 <br>
max@0	6982 <hr class="greyline">
max@0	6983 <br>
max@0	6984
max@0	6985 <a name="chol"></a>
max@0	6986 <b>R = chol(X)</b>
max@0	6987 <br><b>chol(R, X)</b>
max@0	6988 <ul>
max@0	6989 <li>
max@0	6990 Cholesky decomposition of <i>X</i>, such that <i>trans(R)*R = X</i>
max@0	6991 </li>
max@0	6992 <br>
max@0	6993 <li>
max@0	6994 X must be a symmetric, positive-definite matrix
max@0	6995 </li>
max@0	6996 <br>
max@0	6997 <li>If the decomposition fails, <i>R</i> is reset and:
max@0	6998 <ul>
max@0	6999 <li><i>chol(X)</i> throws a <i>std::runtime_error</i> exception</li>
max@0	7000 <li><i>chol(R,X)</i> returns a bool set to <i>false</i></li>
max@0	7001 </ul>
max@0	7002 </li>
max@0	7003 <br>
max@0	7004 <li>
max@0	7005 Examples:
max@0	7006 <ul>
max@0	7007 <pre>
max@0	7008 mat X = randu<mat>(5,5);
max@0	7009 mat Y = trans(X)*X;
max@0	7010
max@0	7011 mat R = chol(Y);
max@0	7012 </pre>
max@0	7013 </ul>
max@0	7014 </li>
max@0	7015 <br>
max@0	7016 <li>
max@0	7017 See also:
max@0	7018 <ul>
max@0	7019 <li><a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">Cholesky decomposition in MathWorld</a></li>
max@0	7020 </ul>
max@0	7021 </li>
max@0	7022 </ul>
max@0	7023 <br>
max@0	7024 <hr class="greyline"><br>
max@0	7025
max@0	7026 <a name="eig_sym"></a>
max@0	7027 <b>vec eigval = eig_sym(mat X)</b>
max@0	7028 <br><b>vec eigval = eig_sym(cx_mat X)</b>
max@0	7029 <br>
max@0	7030 <br><b>eig_sym(vec eigval, mat X)</b>
max@0	7031 <br><b>eig_sym(vec eigval, cx_mat X)</b>
max@0	7032 <br>
max@0	7033 <br><b>eig_sym(vec eigval, mat eigvec, mat X)</b>
max@0	7034 <br><b>eig_sym(vec eigval, cx_mat eigvec, cx_mat X)</b>
max@0	7035 <ul>
max@0	7036 <li>
max@0	7037 Eigen decomposition of symmetric/hermitian matrix <i>X</i></li>
max@0	7038 <br>
max@0	7039 <li>The eigenvalues and corresponding eigenvectors are stored in <i>eigval</i> and <i>eigvec</i>, respectively</li>
max@0	7040 <br>
max@0	7041 <li>
max@0	7042 The eigenvalues are in ascending order
max@0	7043 </li>
max@0	7044 <br>
max@0	7045 <li>If <i>X</i> is not square, a <i>std::logic_error</i> exception is thrown</li>
max@0	7046 <br>
max@0	7047 <li>If the decomposition fails, the output objects are reset and:
max@0	7048 <ul>
max@0	7049 <li><i>eig_sym(X)</i> throws a <i>std::runtime_error</i> exception</li>
max@0	7050 <li><i>eig_sym(eigval, X)</i> and <i>eig_sym(eigval, eigvec, X)</i> return a bool set to <i>false</i></li>
max@0	7051 </ul>
max@0	7052 </li>
max@0	7053 <br>
max@0	7054 <li>There is currently no check whether <i>X</i> is symmetric</li>
max@0	7055 <br>
max@0	7056 <li>
max@0	7057 Examples:
max@0	7058 <ul>
max@0	7059 <pre>
max@0	7060 mat A = randu<mat>(10,10);
max@0	7061 mat B = trans(A)*A; // generate a symmetric matrix
max@0	7062
max@0	7063 vec eigval;
max@0	7064 mat eigvec;
max@0	7065
max@0	7066 eig_sym(eigval, eigvec, B);
max@0	7067 </pre>
max@0	7068 </ul>
max@0	7069 </li>
max@0	7070 <br>
max@0	7071 <li>
max@0	7072 See also:
max@0	7073 <ul>
max@0	7074 <li><a href="#eig_gen">eig_gen()</a></li>
max@0	7075 <li><a href="#svd">svd()</a></li>
max@0	7076 <li><a href="#svd_econ">svd_econ()</a></li>
max@0	7077 <li><a href="http://mathworld.wolfram.com/EigenDecomposition.html">eigen decomposition in MathWorld</a></li>
max@0	7078 </ul>
max@0	7079 </li>
max@0	7080 <br>
max@0	7081 </ul>
max@0	7082 <hr class="greyline"><br>
max@0	7083
max@0	7084 <a name="eig_gen"></a>
max@0	7085 <b>eig_gen(cx_vec eigval, cx_mat eigvec, mat X, side='r')</b>
max@0	7086 <br>
max@0	7087 <b>eig_gen(cx_vec eigval, cx_mat eigvec, cx_mat X, side='r')</b>
max@0	7088 <br>
max@0	7089 <br>
max@0	7090 <b>eig_gen(cx_vec eigval, mat l_eigvec, mat r_eigvec, mat X)</b>
max@0	7091 <br>
max@0	7092 <b>eig_gen(cx_vec eigval, cx_mat l_eigvec, cx_mat r_eigvec, cx_mat X)</b>
max@0	7093 <ul>
max@0	7094 <li>
max@0	7095 Eigen decomposition of general (non-symmetric/non-hermitian) square matrix <i>X</i></li>
max@0	7096 <br>
max@0	7097 <li>The eigenvalues and corresponding eigenvectors are stored in <i>eigval</i> and <i>eigvec</i>, respectively</li>
max@0	7098 <br>
max@0	7099 <li>
max@0	7100 For the first two forms, <i>side='r'</i> (default) specifies that right eigenvectors are computed,
max@0	7101 while <i>side='l'</i> specifies that left eigenvectors are computed
max@0	7102 </li>
max@0	7103 <br>
max@0	7104 <li>For the last two forms, both left and right eigenvectors are computed</li>
max@0	7105 <br>
max@0	7106 <li>
max@0	7107 The eigenvalues are not guaranteed to be ordered
max@0	7108 </li>
max@0	7109 <br>
max@0	7110 <li>If <i>X</i> is not square, a <i>std::logic_error</i> exception is thrown</li>
max@0	7111 <br>
max@0	7112 <li>If the decomposition fails, the output objects are reset and <i>eig_gen()</i> returns a bool set to <i>false</i></li>
max@0	7113 <br>
max@0	7114 <li>
max@0	7115 Examples:
max@0	7116 <ul>
max@0	7117 <pre>
max@0	7118 mat A = randu<mat>(10,10);
max@0	7119
max@0	7120 cx_vec eigval;
max@0	7121 cx_mat eigvec;
max@0	7122
max@0	7123 eig_gen(eigval, eigvec, A);
max@0	7124 </pre>
max@0	7125 </ul>
max@0	7126 </li>
max@0	7127 <br>
max@0	7128 <li>
max@0	7129 See also:
max@0	7130 <ul>
max@0	7131 <li><a href="#eig_sym">eig_sym()</a></li>
max@0	7132 <li><a href="#svd">svd()</a></li>
max@0	7133 <li><a href="#svd_econ">svd_econ()</a></li>
max@0	7134 <li><a href="http://mathworld.wolfram.com/EigenDecomposition.html">eigen decomposition in MathWorld</a></li>
max@0	7135 </ul>
max@0	7136 </li>
max@0	7137 </ul>
max@0	7138 <br>
max@0	7139 <hr class="greyline"><br>
max@0	7140
max@0	7141 <a name="inv"></a>
max@0	7142 <b>B = inv(A, slow = <i>false</i>)</b>
max@0	7143 <br>
max@0	7144 <b>inv(B, A, slow = <i>false</i>)</b>
max@0	7145 <ul>
max@0	7146 <li>
max@0	7147 Inverse of square matrix <i>A</i>
max@0	7148 </li>
max@0	7149 <br>
max@0	7150 <li>
max@0	7151 If <i>A</i> is known to be a triangular matrix,
max@0	7152 the inverse can be computed faster by explicitly marking the matrix as triangular
max@0	7153 through <a href="#trimat">trimatu()</a> or <a href="#trimat">trimatl()</a>
max@0	7154 </li>
max@0	7155 <br>
max@0	7156 <li>
max@0	7157 If <i>A</i> is known to be a positive-definite symmetric matrix,
max@0	7158 the inverse can be computed faster by explicitly marking the matrix using sympd()
max@0	7159 </li>
max@0	7160 <br>
max@0	7161 <li>
max@0	7162 If <i>A</i> is not square, a <i>std::logic_error</i> exception is thrown
max@0	7163 </li>
max@0	7164 <br>
max@0	7165 <li>If <i>A</i> appears to be singular, <i>B</i> is reset and:
max@0	7166 <ul>
max@0	7167 <li><i>inv(A)</i> throws a <i>std::runtime_error</i> exception</li>
max@0	7168 <li><i>inv(B,A)</i> returns a bool set to <i>false</i></li>
max@0	7169 </ul>
max@0	7170 </li>
max@0	7171 <br>
max@0	7172 <li>
max@0	7173 If you want to solve a system of linear equations, eg., <i>X = inv(A)*B</i>,
max@0	7174 the <a href="#solve">solve()</a> function is generally more efficient
max@0	7175 </li>
max@0	7176 <br>
max@0	7177 <li>
max@0	7178 For matrix sizes ≤ 4x4, a fast inverse algorithm is used by default.
max@0	7179 In rare instances, the fast algorithm might be less precise than the standard algorithm.
max@0	7180 To force the use of the standard algorithm, set the <i>slow</i> argument to <i>true</i>
max@0	7181 </li>
max@0	7182 <br>
max@0	7183 <li>
max@0	7184 Examples:
max@0	7185 <ul>
max@0	7186 <pre>
max@0	7187 mat A = randu<mat>(5,5);
max@0	7188 mat B = inv(A);
max@0	7189
max@0	7190
max@0	7191 // Diagonal elements in C are set to the
max@0	7192 // reciprocal of the corresponding elements in A.
max@0	7193 // Off-diagonal elements in C are set to zero.
max@0	7194 mat C = inv( diagmat(A) );
max@0	7195
max@0	7196
max@0	7197 // tell inv() to look only at the upper triangular part of A
max@0	7198 mat D = inv( trimatu(A) );
max@0	7199
max@0	7200
max@0	7201 // tell inv() that AA is a symmetric positive definite matrix
max@0	7202 mat AA = A*trans(A);
max@0	7203 mat E = inv( sympd(AA) );
max@0	7204
max@0	7205
max@0	7206 mat44 F = randu<mat>(4,4);
max@0	7207
max@0	7208 mat G = inv(F); // use fast algorithm by default
max@0	7209 mat H = inv(F, true); // use slow algorithm
max@0	7210 </pre>
max@0	7211 </ul>
max@0	7212 </li>
max@0	7213 <br>
max@0	7214 <li>
max@0	7215 See also:
max@0	7216 <ul>
max@0	7217 <li><a href="#pinv">pinv()</a>
max@0	7218 <li><a href="#solve">solve()</a></li>
max@0	7219 <li><a href="#trimat">trimatu() / trimatl()</a></li>
max@0	7220 <li><a href="http://mathworld.wolfram.com/MatrixInverse.html">matrix inverse in MathWorld</a></li>
max@0	7221 <li><a href="http://en.wikipedia.org/wiki/Invertible_matrix">invertible matrix in Wikipedia</a></li>
max@0	7222 </ul>
max@0	7223 </li>
max@0	7224 </ul>
max@0	7225 <br>
max@0	7226 <hr class="greyline"><br>
max@0	7227
max@0	7228
max@0	7229
max@0	7230 <a name="lu"></a>
max@0	7231 <b>lu(mat L, mat U, mat P, mat X)</b>
max@0	7232 <br>
max@0	7233 <b>lu(mat L, mat U, mat X)</b>
max@0	7234 <ul>
max@0	7235 <li>
max@0	7236 Lower-upper decomposition (with partial pivoting) of matrix <i>X</i>
max@0	7237 </li>
max@0	7238 <br>
max@0	7239 <li>
max@0	7240 The first form provides
max@0	7241 a lower-triangular matrix <i>L</i>,
max@0	7242 an upper-triangular matrix <i>U</i>,
max@0	7243 and a permutation matrix <i>P</i>,
max@0	7244 such that <i>trans(P)LU = X</i>
max@0	7245 </li>
max@0	7246 <br>
max@0	7247 <li>
max@0	7248 The second form provides permuted <i>L</i> and <i>U</i>, such that <i>L*U = X</i>.
max@0	7249 Note that in this case <i>L</i> is generally not lower-triangular
max@0	7250 </li>
max@0	7251 <br>
max@0	7252 <li>
max@0	7253 If the decomposition fails, the output objects are reset and <i>lu()</i> returns a bool set to <i>false</i>
max@0	7254 </li>
max@0	7255 <br>
max@0	7256 <li>
max@0	7257 Examples:
max@0	7258 <ul>
max@0	7259 <pre>
max@0	7260 mat A = randu<mat>(5,5);
max@0	7261
max@0	7262 mat L, U, P;
max@0	7263
max@0	7264 lu(L, U, P, A);
max@0	7265
max@0	7266 mat B = trans(P)LU;
max@0	7267 </pre>
max@0	7268 </ul>
max@0	7269 </li>
max@0	7270 <br>
max@0	7271 <li>
max@0	7272 See also:
max@0	7273 <ul>
max@0	7274 <li><a href="http://en.wikipedia.org/wiki/LU_decomposition">LU decomposition in Wikipedia</a></li>
max@0	7275 <li><a href="http://mathworld.wolfram.com/LUDecomposition.html">LU decomposition in MathWorld</a></li>
max@0	7276 </ul>
max@0	7277 </li>
max@0	7278 </ul>
max@0	7279 <br>
max@0	7280 <hr class="greyline"><br>
max@0	7281
max@0	7282 <a name="pinv"></a>
max@0	7283 <b>B = pinv(A, tolerance = default)</b>
max@0	7284 <br><b>pinv(B, A, tolerance = default)</b>
max@0	7285 <ul>
max@0	7286 <li>Moore-Penrose pseudo-inverse of matrix <i>A</i></li>
max@0	7287 <br>
max@0	7288 <li>The computation is based on singular value decomposition;
max@0	7289 if the decomposition fails, <i>B</i> is reset and:
max@0	7290 <ul>
max@0	7291 <li><i>pinv(A)</i> throws a <i>std::runtime_error</i> exception</li>
max@0	7292 <li><i>pinv(B,A)</i> returns a bool set to <i>false</i></li>
max@0	7293 </ul>
max@0	7294 <br>
max@0	7295 <li>Any singular values less than <i>tol</i> are treated as zero</li>
max@0	7296 <br>
max@0	7297 <li>For matrix <i>A</i> with <i>m</i> rows and <i>n</i> columns,
max@0	7298 the default tolerance is <i>max(m,n)norm(A)math::eps()</i>,
max@0	7299 where <i>math::eps()</i> denotes the difference between 1 and the least value greater than 1 that is representable</li>
max@0	7300 <br>
max@0	7301 <li>
max@0	7302 Examples:
max@0	7303 <ul>
max@0	7304 <pre>
max@0	7305 mat A = randu<mat>(4,5);
max@0	7306 mat B = pinv(A);
max@0	7307 </pre>
max@0	7308 </ul>
max@0	7309 </li>
max@0	7310 <br>
max@0	7311 <li>
max@0	7312 See also:
max@0	7313 <ul>
max@0	7314 <li><a href="#inv">inv()</a></li>
max@0	7315 <li><a href="#math_constants">math::eps()</a></li>
max@0	7316 <li><a href="http://mathworld.wolfram.com/Pseudoinverse.html">Pseudoinverse in MathWorld</a></li>
max@0	7317 <li><a href="http://mathworld.wolfram.com/Moore-PenroseMatrixInverse.html">Moore-Penrose Matrix Inverse in MathWorld</a></li>
max@0	7318 <li><a href="http://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse">Moore-Penrose pseudoinverse in Wikipedia</a></li>
max@0	7319 </ul>
max@0	7320 </li>
max@0	7321 </ul>
max@0	7322 <br>
max@0	7323 <hr class="greyline"><br>
max@0	7324
max@0	7325 <a name="princomp"></a>
max@0	7326 <b>mat coeff = princomp(mat X)</b>
max@0	7327 <br><b>cx_mat coeff = princomp(cx_mat X)</b><br>
max@0	7328
max@0	7329 <br><b>princomp(mat coeff, mat X)</b>
max@0	7330 <br><b>princomp(cx_mat coeff, cx_mat X)</b><br>
max@0	7331
max@0	7332 <br><b>princomp(mat coeff, mat score, mat X)</b>
max@0	7333 <br><b>princomp(cx_mat coeff, cx_mat score, cx_mat X)</b><br>
max@0	7334
max@0	7335 <br><b>princomp(mat coeff, mat score, vec latent, mat X)</b>
max@0	7336 <br><b>princomp(cx_mat coeff, cx_mat score, vec latent, cx_mat X)</b><br>
max@0	7337
max@0	7338 <br><b>princomp(mat coeff, mat score, vec latent, vec tsquared, mat X)</b>
max@0	7339 <br><b>princomp(cx_mat coeff, cx_mat score, vec latent, cx_vec tsquared, cx_mat X)</b><br>
max@0	7340 <br>
max@0	7341 <ul>
max@0	7342 <li>Principal component analysis of matrix <i>X</i></li><br>
max@0	7343 <li>Each row of <i>X</i> is an observation and each column is a variable</li><br>
max@0	7344 <li>output objects:
max@0	7345 <ul>
max@0	7346 <li><i>coeff</i>: principal component coefficients</li>
max@0	7347 <li><i>score</i>: projected data</li>
max@0	7348 <li><i>latent</i>: eigenvalues of the covariance matrix of <i>X</i></li>
max@0	7349 <li><i>tsquared</i>: Hotteling's statistic for each sample</li>
max@0	7350 </ul>
max@0	7351 </li>
max@0	7352 <br>
max@0	7353 <li>The computation is based on singular value decomposition;
max@0	7354 if the decomposition fails, the output objects are reset and:
max@0	7355 <ul>
max@0	7356 <li><i>princomp(X)</i> throws a <i>std::runtime_error</i> exception</li>
max@0	7357 <li>remaining forms of <i>princomp()</i> return a bool set to <i>false</i></li>
max@0	7358 </ul>
max@0	7359 </li>
max@0	7360 <br>
max@0	7361 <li>
max@0	7362 Examples:
max@0	7363 <ul>
max@0	7364 <pre>
max@0	7365 mat A = randu<mat>(5,4);
max@0	7366
max@0	7367 mat coeff;
max@0	7368 mat score;
max@0	7369 vec latent;
max@0	7370 vec tsquared;
max@0	7371
max@0	7372 princomp(coeff, score, latent, tsquared, A);
max@0	7373 </pre>
max@0	7374 </ul>
max@0	7375 </li>
max@0	7376 <br>
max@0	7377 <li>
max@0	7378 See also:
max@0	7379 <ul>
max@0	7380 <li><a href="http://en.wikipedia.org/wiki/Principal_component_analysis">principal components analysis in Wikipedia</a></li>
max@0	7381 <li><a href="http://mathworld.wolfram.com/PrincipalComponentAnalysis.html">principal components analysis in MathWorld</a></li>
max@0	7382 </ul>
max@0	7383 </li>
max@0	7384 <br>
max@0	7385 </ul>
max@0	7386 <hr class="greyline"><br>
max@0	7387
max@0	7388 <a name="qr"></a>
max@0	7389 <b>qr(Q,R,X)</b>
max@0	7390 <ul>
max@0	7391 <li>
max@0	7392 Decomposition of matrix <i>X</i> into an orthogonal (<i>Q</i>) and a right triangular matrix (<i>R</i>), such that <i>Q*R = X</i>
max@0	7393 </li>
max@0	7394 <br>
max@0	7395 <li>
max@0	7396 If the decomposition fails, <i>Q</i> and <i>R</i> are reset and the function returns a bool set to <i>false</i>
max@0	7397 </li>
max@0	7398 <br>
max@0	7399 <li>
max@0	7400 Examples:
max@0	7401 <ul>
max@0	7402 <pre>
max@0	7403 mat X = randu<mat>(5,5);
max@0	7404 mat Q, R;
max@0	7405
max@0	7406 qr(Q,R,X);
max@0	7407 </pre>
max@0	7408 </ul>
max@0	7409 </li>
max@0	7410 <br>
max@0	7411 <li>
max@0	7412 See also:
max@0	7413 <ul>
max@0	7414 <li><a href="http://mathworld.wolfram.com/QRDecomposition.html">QR decomposition in MathWorld</a></li>
max@0	7415 <li><a href="http://octave.sourceforge.net/octave/function/qr.html">QR decomposition in Octave</a></li>
max@0	7416 </ul>
max@0	7417 </li>
max@0	7418 </ul>
max@0	7419 <br>
max@0	7420 <hr class="greyline"><br>
max@0	7421
max@0	7422 <a name="solve"></a>
max@0	7423 <b>X = solve(A, B, slow = false)</b>
max@0	7424 <br><b>solve(X, A, B, slow = false)</b>
max@0	7425 <ul>
max@0	7426 <li>Solve a system of linear equations, ie., <i>A*X = B</i>, where <i>X</i> is unknown</li>
max@0	7427 <br>
max@0	7428 <li>For a square matrix <i>A</i>, this function is conceptually the same as <i>X = inv(A)*B</i>, but is more efficient</li>
max@0	7429 <br>
max@0	7430 <li>Similar functionality to the "\" (left division operator) operator in Matlab/Octave, ie. <i>X = A \ B</i></li>
max@0	7431 <br>
max@0	7432 <li>The number of rows in <i>A</i> and <i>B</i> must be the same</li>
max@0	7433 <br>
max@0	7434 <li>
max@0	7435 If <i>A</i> is known to be a triangular matrix,
max@0	7436 the solution can be computed faster by explicitly marking the matrix as triangular
max@0	7437 through <a href="#trimat">trimatu()</a> or <a href="#trimat">trimatl()</a>
max@0	7438 </li>
max@0	7439 <br>
max@0	7440 <li>
max@0	7441 If <i>A</i> is non-square (and hence also non-triangular),
max@0	7442 solve() will also try to provide approximate solutions to under-determined as well as over-determined systems</li>
max@0	7443 <br>
max@0	7444 <li>
max@0	7445 If no solution is found, <i>X</i> is reset and:
max@0	7446 <ul>
max@0	7447 <li><i>solve(A,B)</i> throws a <i>std::runtime_error</i> exception</li>
max@0	7448 <li><i>solve(X,A,B)</i> returns a bool set to <i>false</i></li>
max@0	7449 </ul>
max@0	7450 </li>
max@0	7451 <br>
max@0	7452 <li>
max@0	7453 For matrix sizes ≤ 4x4, a fast algorithm is used by default.
max@0	7454 In rare instances, the fast algorithm might be less precise than the standard algorithm.
max@0	7455 To force the use of the standard algorithm, set the <i>slow</i> argument to <i>true</i>
max@0	7456 </li>
max@0	7457 <br>
max@0	7458 <li>
max@0	7459 <b>NOTE:</b> Old versions of the ATLAS library (eg. 3.6) can corrupt memory and crash your program;
max@0	7460 the standard LAPACK library and later versions of ATLAS (eg. 3.8) work without problems
max@0	7461 </li>
max@0	7462 <br>
max@0	7463 <li>
max@0	7464 Examples:
max@0	7465 <ul>
max@0	7466 <pre>
max@0	7467 mat A = randu<mat>(5,5);
max@0	7468 vec b = randu<vec>(5);
max@0	7469 mat B = randu<mat>(5,5);
max@0	7470
max@0	7471 vec x = solve(A, b);
max@0	7472 mat X = solve(A, B);
max@0	7473
max@0	7474 vec x2;
max@0	7475 solve(x2, A, b);
max@0	7476
max@0	7477 // tell solve() to look only at the upper triangular part of A
max@0	7478 mat Y = solve( trimatu(A), B );
max@0	7479
max@0	7480
max@0	7481 mat44 C = randu<mat>(4,4);
max@0	7482 mat44 D = randu<mat>(4,4);
max@0	7483
max@0	7484 mat E = solve(C, D); // use fast algorithm by default
max@0	7485 mat F = solve(C, D, true); // use slow algorithm
max@0	7486
max@0	7487 </pre>
max@0	7488 </ul>
max@0	7489 </li>
max@0	7490 <br>
max@0	7491 <li>
max@0	7492 See also:
max@0	7493 <ul>
max@0	7494 <li><a href="#inv">inv()</a></li>
max@0	7495 <li><a href="#syl">syl()</a></li>
max@0	7496 <li><a href="#trimat">trimatu() / trimatl()</a></li>
max@0	7497 <li><a href="http://mathworld.wolfram.com/LinearSystemofEquations.html">linear system of equations in MathWorld</a></li>
max@0	7498 <li><a href="http://en.wikipedia.org/wiki/Linear_system_of_equations">system of linear equations in Wikipedia</a></li>
max@0	7499 </ul>
max@0	7500 </li>
max@0	7501 <br>
max@0	7502 </ul>
max@0	7503 <hr class="greyline"><br>
max@0	7504
max@0	7505
max@0	7506 <a name="svd"></a>
max@0	7507 <b>vec s = svd(mat X)</b>
max@0	7508 <br><b>vec s = svd(cx_mat X)</b>
max@0	7509 <br>
max@0	7510 <br><b>svd(vec s, mat X)</b>,
max@0	7511 <br><b>svd(vec s, cx_mat X)</b>
max@0	7512 <br>
max@0	7513 <br><b>svd(mat U, vec s, mat V, mat X)</b>
max@0	7514 <br><b>svd(cx_mat U, vec s, cx_mat V, cx_mat X)</b>
max@0	7515 <ul>
max@0	7516 <li>
max@0	7517 The single and two argument versions compute the singular values of <i>X</i>
max@0	7518 </li>
max@0	7519 <br>
max@0	7520 <li>
max@0	7521 The four argument version computes the full singular value decomposition of <i>X</i>
max@0	7522 </li>
max@0	7523 <br>
max@0	7524 <li>If <i>X</i> is square, it can be reconstructed using <i>X = Udiagmat(s)trans(V)</i>
max@0	7525 </li>
max@0	7526 <br>
max@0	7527 <li>
max@0	7528 The singular values are in descending order
max@0	7529 </li>
max@0	7530 <br>
max@0	7531 <li>
max@0	7532 If the decomposition fails, the output objects are reset and:
max@0	7533 <ul>
max@0	7534 <li><i>svd(X)</i> throws a <i>std::runtime_error</i> exception</li>
max@0	7535 <li><i>svd(s,X)</i> and <i>svd(U,s,V,X)</i> return a bool set to <i>false</i></li>
max@0	7536 </ul>
max@0	7537 </li>
max@0	7538 <br>
max@0	7539 <li>
max@0	7540 <b>NOTE:</b> Old versions of the ATLAS library (eg. 3.6) can corrupt memory and crash your program;
max@0	7541 the standard LAPACK library and later versions of ATLAS (eg. 3.8) work without problems
max@0	7542 </li>
max@0	7543 <br>
max@0	7544 <li>
max@0	7545 Examples:
max@0	7546 <ul>
max@0	7547 <pre>
max@0	7548 mat X = randu<mat>(5,5);
max@0	7549
max@0	7550 mat U;
max@0	7551 vec s;
max@0	7552 mat V;
max@0	7553 svd(U,s,V,X);
max@0	7554 </pre>
max@0	7555 </ul>
max@0	7556 </li>
max@0	7557 <br>
max@0	7558 <li>
max@0	7559 See also:
max@0	7560 <ul>
max@0	7561 <li><a href="#svd_econ">svd_econ()</a></li>
max@0	7562 <li><a href="#eig_gen">eig_gen()</a></li>
max@0	7563 <li><a href="#eig_sym">eig_sym()</a></li>
max@0	7564 <li><a href="http://en.wikipedia.org/wiki/Singular_value_decomposition">singular value decomposition in Wikipedia</a></li>
max@0	7565 <li><a href="http://mathworld.wolfram.com/SingularValueDecomposition.html">singular value decomposition in MathWorld</a></li>
max@0	7566 </ul>
max@0	7567 </li>
max@0	7568 </ul>
max@0	7569 <br>
max@0	7570 <hr class="greyline">
max@0	7571 <br>
max@0	7572
max@0	7573 <a name="svd_econ"></a>
max@0	7574 <b>svd_econ(mat U, vec s, mat V, mat X, mode = 'b')</b>
max@0	7575 <br><b>svd_econ(cx_mat U, vec s, cx_mat V, cx_mat X, mode = 'b')</b>
max@0	7576 <ul>
max@0	7577 <li>
max@0	7578 Economical singular value decomposition of <i>X</i>
max@0	7579 </li>
max@0	7580 <br>
max@0	7581 <li>
max@0	7582 mode is one of:
max@0	7583 <ul>
max@0	7584 <li><i>'l'</i>: compute only left singular vectors</li>
max@0	7585 <li><i>'r'</i>: compute only right singular vectors</li>
max@0	7586 <li><i>'b'</i>: compute both left and right singular vectors (default)</li>
max@0	7587 </ul>
max@0	7588 </li>
max@0	7589 <br>
max@0	7590 <li>
max@0	7591 The singular values are in descending order
max@0	7592 </li>
max@0	7593 <br>
max@0	7594 <li>
max@0	7595 If the decomposition fails, the output objects are reset and bool set to <i>false</i> is returned
max@0	7596 </li>
max@0	7597 <br>
max@0	7598 <li>
max@0	7599 Examples:
max@0	7600 <ul>
max@0	7601 <pre>
max@0	7602 mat X = randu<mat>(4,5);
max@0	7603
max@0	7604 mat U;
max@0	7605 vec s;
max@0	7606 mat V;
max@0	7607 svd_econ(U, s, V, X, 'l');
max@0	7608 </pre>
max@0	7609 </ul>
max@0	7610 </li>
max@0	7611 <br>
max@0	7612 <li>
max@0	7613 See also:
max@0	7614 <ul>
max@0	7615 <li><a href="#svd">svd()</a></li>
max@0	7616 <li><a href="#eig_gen">eig_gen()</a></li>
max@0	7617 <li><a href="#eig_sym">eig_sym()</a></li>
max@0	7618 <li><a href="http://en.wikipedia.org/wiki/Singular_value_decomposition">singular value decomposition in Wikipedia</a></li>
max@0	7619 <li><a href="http://mathworld.wolfram.com/SingularValueDecomposition.html">singular value decomposition in MathWorld</a></li>
max@0	7620 </ul>
max@0	7621 </li>
max@0	7622 </ul>
max@0	7623 <br>
max@0	7624 <hr class="greyline">
max@0	7625 <br>
max@0	7626
max@0	7627 <a name="syl"></a>
max@0	7628 <b>X = syl(A, B, C)</b>
max@0	7629 <br><b>syl(X, A, B, C)</b>
max@0	7630 <ul>
max@0	7631 <li>Solve the Sylvester equation, ie., <i>AX + XB + C = 0</i>, where <i>X</i> is unknown.</li>
max@0	7632 <br>
max@0	7633 <li>Matrices <i>A</i>, <i>B</i> and <i>C</i> must be square sized.</li>
max@0	7634 <br>
max@0	7635 <li>
max@0	7636 If no solution is found, <i>X</i> is reset and:
max@0	7637 <ul>
max@0	7638 <li><i>syl(A,B,C)</i> throws a <i>std::runtime_error</i> exception</li>
max@0	7639 <li><i>svd(X,A,B,C)</i> returns a bool set to <i>false</i></li>
max@0	7640 </ul>
max@0	7641 </li>
max@0	7642 <br>
max@0	7643 <li>
max@0	7644 Examples:
max@0	7645 <ul>
max@0	7646 <pre>
max@0	7647 mat A = randu<mat>(5,5);
max@0	7648 mat B = randu<mat>(5,5);
max@0	7649 mat C = randu<mat>(5,5);
max@0	7650
max@0	7651 mat X1 = syl(A, B, C);
max@0	7652
max@0	7653 mat X2;
max@0	7654 syl(X2, A, B, C);
max@0	7655 </pre>
max@0	7656 </ul>
max@0	7657 </li>
max@0	7658 <br>
max@0	7659 <li>
max@0	7660 See also:
max@0	7661 <ul>
max@0	7662 <li><a href="#solve">solve()</a></li>
max@0	7663 <li><a href="http://en.wikipedia.org/wiki/Sylvester_equation">Sylvester equation in Wikipedia</a></li>
max@0	7664 </ul>
max@0	7665 </li>
max@0	7666 <br>
max@0	7667 </ul>
max@0	7668 <hr class="greyline">
max@0	7669
max@0	7670
max@0	7671 <hr class="greyline">
max@0	7672 <br>
max@0	7673 <br>
max@0	7674 <font size=+1><b>Miscellaneous</b></font>
max@0	7675 <br>
max@0	7676 <br>
max@0	7677 <hr class="greyline">
max@0	7678 <br>
max@0	7679
max@0	7680 <a name="is_finite_standalone"></a>
max@0	7681 <b>is_finite(X)</b>
max@0	7682 <ul>
max@0	7683 <li>
max@0	7684 Returns <i>true</i> if all elements in <i>X</i> are finite
max@0	7685 </li>
max@0	7686 <br>
max@0	7687 <li>
max@0	7688 Returns <i>false</i> if at least one element in <i>X</i> is non-finite (±infinity or NaN)
max@0	7689 </li>
max@0	7690 <br>
max@0	7691 <li>
max@0	7692 <i>X</i> can be a scalar (eg. <i>double</i>), vector, matrix or cube
max@0	7693 </li>
max@0	7694 <br>
max@0	7695 <li>
max@0	7696 Examples:
max@0	7697 <ul>
max@0	7698 <pre>
max@0	7699 mat A = randu<mat>(5,5);
max@0	7700 mat B = randu<mat>(5,5);
max@0	7701
max@0	7702 B(1,1) = math::nan();
max@0	7703
max@0	7704 cout << is_finite(A) << endl;
max@0	7705 cout << is_finite(B) << endl;
max@0	7706
max@0	7707 cout << is_finite( 0.123456789 ) << endl;
max@0	7708 cout << is_finite( math::nan() ) << endl;
max@0	7709 cout << is_finite( math::inf() ) << endl;
max@0	7710 </pre>
max@0	7711 </ul>
max@0	7712 </li>
max@0	7713 <br>
max@0	7714 <li>
max@0	7715 See also:
max@0	7716 <ul>
max@0	7717 <li><a href="#math_constants">math::nan()</a></li>
max@0	7718 <li><a href="#math_constants">math::inf()</a></li>
max@0	7719 <li><a href="#is_finite">.is_finite()</a> (member function of <i>Mat</i> and <i>Cube</i>)</li>
max@0	7720 </ul>
max@0	7721 </li>
max@0	7722 <br>
max@0	7723 </ul>
max@0	7724 <hr class="greyline"><br>
max@0	7725
max@0	7726 <a name="logging"></a>
max@0	7727 <b>logging of warnings and errors</b>
max@0	7728 <br>
max@0	7729 <br>
max@0	7730 <b>set_stream_err1(user_stream)</b><br>
max@0	7731 <b>set_stream_err2(user_stream)</b><br>
max@0	7732 <br>
max@0	7733 <b>std::ostream& x = get_stream_err1()</b>
max@0	7734 <br>
max@0	7735 <b>std::ostream& x = get_stream_err2()</b>
max@0	7736 <br>
max@0	7737 <ul>
max@0	7738 <li>
max@0	7739 By default, Armadillo prints warnings and messages associated with <i>std::logic_error</i> and <i>std::runtime_error</i> exceptions to the <i>std::cout</i> stream
max@0	7740 </li>
max@0	7741 <br>
max@0	7742 <li><b>set_stream_err1()</b>: change the stream for messages associated with <i>std::logic_error</i> exceptions (eg. out of bounds accesses)</li>
max@0	7743 <br>
max@0	7744 <li><b>set_stream_err2()</b>: change the stream for warnings and messages associated with <i>std::runtime_error</i> exceptions (eg. failed decompositions)</li>
max@0	7745 <br>
max@0	7746 <li><b>get_stream_err1()</b>: get a reference to the stream for messages associated with <i>std::logic_error</i> exceptions</li>
max@0	7747 <br>
max@0	7748 <li><b>get_stream_err2()</b>: get a reference to the stream for warnings and messages associated with <i>std::runtime_error</i> exceptions</li>
max@0	7749 <br>
max@0	7750 <li>
max@0	7751 Examples:
max@0	7752 <ul>
max@0	7753 <pre>
max@0	7754 // print "hello" to the current err1 stream
max@0	7755 get_stream_err1() << "hello" << endl;
max@0	7756
max@0	7757 // change the err2 stream to be a file
max@0	7758 ofstream f("my_log.txt");
max@0	7759 set_stream_err2(f);
max@0	7760
max@0	7761 // trying to invert a singular matrix
max@0	7762 // will print a message to the err2 stream
max@0	7763 // and throw an exception
max@0	7764 mat X = zeros<mat>(5,5);
max@0	7765 mat Y = inv(X);
max@0	7766
max@0	7767 // disable messages being printed to the err2 stream
max@0	7768 std::ostream nullstream(0);
max@0	7769 set_stream_err2(nullstream);
max@0	7770 </pre>
max@0	7771 </ul>
max@0	7772 </li>
max@0	7773 <br>
max@0	7774 <li>
max@0	7775 <b>Caveat</b>: set_stream_err1() and set_stream_err2() will not change the stream used by .print()
max@0	7776 </li>
max@0	7777 <br>
max@0	7778 <li>
max@0	7779 See also:
max@0	7780 <ul>
max@0	7781 <li><a href="#print">.print()</a></li>
max@0	7782 <li><a href="http://cplusplus.com/reference/iostream/cout/">std::cout</a></li>
max@0	7783 <li><a href="http://cplusplus.com/reference/iostream/ostream/">std::ostream</a></li>
max@0	7784 <li><a href="http://cplusplus.com/reference/std/stdexcept/logic_error/">std::logic_error</a></li>
max@0	7785 <li><a href="http://cplusplus.com/reference/std/stdexcept/runtime_error/">std::runtime_error</a></li>
max@0	7786 <li><a href="http://cplusplus.com/doc/tutorial/exceptions/">tutorial on exceptions</a></li>
max@0	7787 </ul>
max@0	7788 </li>
max@0	7789 <br>
max@0	7790 </ul>
max@0	7791 <hr class="greyline">
max@0	7792
max@0	7793
max@0	7794
max@0	7795 <a name="math_constants"></a>
max@0	7796 <b>math constants (pi, e, euler, gratio, sqrt2, eps, log_min, log_max, nan, inf)</b>
max@0	7797 <br>
max@0	7798 <ul>
max@0	7799 <li>
max@0	7800 Collection of constants, with their precision and/or value dependant on the numerical type and/or machine used.
max@0	7801 </li>
max@0	7802 <br>
max@0	7803 <li>
max@0	7804 The constants are stored as static functions in the <i>Math<type></i> class,
max@0	7805 where <i>type</i> is either <i>float</i> or <i>double</i>.
max@0	7806 </li>
max@0	7807 <br>
max@0	7808 <li>
max@0	7809 For convenience, <i>Math<float></i> has been typedefed as <i>fmath</i>,
max@0	7810 while <i>Math<double></i> has been typedefed as <i>math</i>.
max@0	7811 </li>
max@0	7812 <br>
max@0	7813 <li>
max@0	7814 Meaning of the constants:
max@0	7815 <ul>
max@0	7816 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	7817 <tbody>
max@0	7818 <tr>
max@0	7819 <td style="vertical-align: top;">
max@0	7820 math::pi()
max@0	7821 </td>
max@0	7822 <td style="vertical-align: top;">
max@0	7823
max@0	7824 </td>
max@0	7825 <td style="vertical-align: top;">
max@0	7826 π, the ratio of any circle's circumference to its diameter
max@0	7827 </td>
max@0	7828 </tr>
max@0	7829 <tr>
max@0	7830 <td style="vertical-align: top;">
max@0	7831 math::e()
max@0	7832 </td>
max@0	7833 <td style="vertical-align: top;">
max@0	7834
max@0	7835 </td>
max@0	7836 <td style="vertical-align: top;">
max@0	7837 base of the natural logarithm
max@0	7838 </td>
max@0	7839 </tr>
max@0	7840 <tr>
max@0	7841 <td style="vertical-align: top;">
max@0	7842 math::euler()
max@0	7843 </td>
max@0	7844 <td style="vertical-align: top;">
max@0	7845
max@0	7846 </td>
max@0	7847 <td style="vertical-align: top;">
max@0	7848 Euler's constant, aka Euler-Mascheroni constant
max@0	7849 </td>
max@0	7850 </tr>
max@0	7851 <tr>
max@0	7852 <td style="vertical-align: top;">
max@0	7853 math::gratio()
max@0	7854 </td>
max@0	7855 <td style="vertical-align: top;">
max@0	7856
max@0	7857 </td>
max@0	7858 <td style="vertical-align: top;">
max@0	7859 golden ratio
max@0	7860 </td>
max@0	7861 </tr>
max@0	7862 <tr>
max@0	7863 <td style="vertical-align: top;">
max@0	7864 math::sqrt2()
max@0	7865 </td>
max@0	7866 <td style="vertical-align: top;">
max@0	7867
max@0	7868 </td>
max@0	7869 <td style="vertical-align: top;">
max@0	7870 square root of 2
max@0	7871 </td>
max@0	7872 </tr>
max@0	7873 <tr>
max@0	7874 <td style="vertical-align: top;">
max@0	7875 math::eps()
max@0	7876 </td>
max@0	7877 <td style="vertical-align: top;">
max@0	7878
max@0	7879 </td>
max@0	7880 <td style="vertical-align: top;">
max@0	7881 the difference between 1 and the least value greater than 1 that is representable
max@0	7882 </td>
max@0	7883 </tr>
max@0	7884 <tr>
max@0	7885 <td style="vertical-align: top;">
max@0	7886 math::log_min()
max@0	7887 </td>
max@0	7888 <td style="vertical-align: top;">
max@0	7889
max@0	7890 </td>
max@0	7891 <td style="vertical-align: top;">
max@0	7892 log of minimum non-zero value
max@0	7893 </td>
max@0	7894 </tr>
max@0	7895 <tr>
max@0	7896 <td style="vertical-align: top;">
max@0	7897 math::log_max()
max@0	7898 </td>
max@0	7899 <td style="vertical-align: top;">
max@0	7900
max@0	7901 </td>
max@0	7902 <td style="vertical-align: top;">
max@0	7903 log of maximum value
max@0	7904 </td>
max@0	7905 </tr>
max@0	7906 <tr>
max@0	7907 <td style="vertical-align: top;">
max@0	7908 math::nan()
max@0	7909 </td>
max@0	7910 <td style="vertical-align: top;">
max@0	7911
max@0	7912 </td>
max@0	7913 <td style="vertical-align: top;">
max@0	7914 “not a number” (NaN)
max@0	7915 </td>
max@0	7916 </tr>
max@0	7917 <tr>
max@0	7918 <td style="vertical-align: top;">
max@0	7919 math::inf()
max@0	7920 </td>
max@0	7921 <td style="vertical-align: top;">
max@0	7922
max@0	7923 </td>
max@0	7924 <td style="vertical-align: top;">
max@0	7925 infinity
max@0	7926 </td>
max@0	7927 </tr>
max@0	7928 </tbody>
max@0	7929 </table>
max@0	7930 </ul>
max@0	7931 </li>
max@0	7932 <br>
max@0	7933 <li>
max@0	7934 <b>Caveat:</b>
max@0	7935 nan() is not equal to anything, even itself;
max@0	7936 if you wish to check whether a given number <i>x</i> is finite,
max@0	7937 use <a href="#is_finite_standalone">is_finite</a>(<i>x</i>).
max@0	7938 </li>
max@0	7939 <br>
max@0	7940 <li>
max@0	7941 Examples:
max@0	7942 <ul>
max@0	7943 <pre>
max@0	7944 cout << "2.0 * pi = " << 2.0 * math::pi() << endl;
max@0	7945
max@0	7946 cout << "log_max for floats = ";
max@0	7947 cout << fmath::log_max() << endl;
max@0	7948
max@0	7949 cout << "log_max for doubles = ";
max@0	7950 cout << math::log_max() << endl;
max@0	7951 </pre>
max@0	7952 </ul>
max@0	7953 </li>
max@0	7954 <li>
max@0	7955 See also:
max@0	7956 <ul>
max@0	7957 <li><a href="#phys_constants">physical constants</a></li>
max@0	7958 <li><a href="#is_finite_standalone">is_finite()</a></li>
max@0	7959 <li><a href="http://en.wikipedia.org/wiki/NaN">Wikipedia entry for NaN</a></li>
max@0	7960 <li><a href="http://cplusplus.com/reference/std/limits/numeric_limits/">std::numeric_limits</a></li>
max@0	7961 </ul>
max@0	7962 </li>
max@0	7963 </ul>
max@0	7964 <br>
max@0	7965 <hr class="greyline"><br>
max@0	7966
max@0	7967 <a name="phys_constants"></a>
max@0	7968 <b>physical constants (speed of light, etc)</b>
max@0	7969 <br>
max@0	7970 <ul>
max@0	7971 <li>
max@0	7972 Collection of fundamental physical constants,
max@0	7973 mainly taken from
max@0	7974 <a href="http://physics.nist.gov/cuu/Constants">NIST</a>
max@0	7975 and some from
max@0	7976 <a href="http://www.wolframalpha.com">WolframAlpha</a>
max@0	7977 on 2009-06-23.
max@0	7978 </li>
max@0	7979 <br>
max@0	7980 <li>
max@0	7981 Constants from NIST are in turn sourced from the <a href="http://physics.nist.gov/cuu/Constants/papers.html">2006 CODATA values</a>.
max@0	7982 </li>
max@0	7983 <br>
max@0	7984 <li>
max@0	7985 The constants are stored as static functions in the <i>Phy<type></i> class,
max@0	7986 where <i>type</i> is either <i>float</i> or <i>double</i>.
max@0	7987 </li>
max@0	7988 <br>
max@0	7989 <li>
max@0	7990 For convenience, <i>Phy<float></i> has been typedefed as <i>fphy</i>,
max@0	7991 while <i>Phy<double></i> has been typedefed as <i>phy</i>.
max@0	7992 </li>
max@0	7993 <br>
max@0	7994 <li>
max@0	7995 Meaning of the constants:
max@0	7996 <ul>
max@0	7997 <table style="text-align: left; width: 100%;" border="0" cellpadding="2" cellspacing="2">
max@0	7998 <tbody>
max@0	7999 <tr>
max@0	8000 <td style="vertical-align: top;">
max@0	8001 phy::m_u()
max@0	8002 </td>
max@0	8003 <td style="vertical-align: top;">
max@0	8004
max@0	8005 </td>
max@0	8006 <td style="vertical-align: top;">
max@0	8007 atomic mass constant (in kg)
max@0	8008 </td>
max@0	8009 </tr>
max@0	8010 <tr>
max@0	8011 <td style="vertical-align: top;">
max@0	8012 phy::N_A()
max@0	8013 </td>
max@0	8014 <td style="vertical-align: top;">
max@0	8015
max@0	8016 </td>
max@0	8017 <td style="vertical-align: top;">
max@0	8018 Avogadro constant
max@0	8019 </td>
max@0	8020 </tr>
max@0	8021 <tr>
max@0	8022 <td style="vertical-align: top;">
max@0	8023 phy::k()
max@0	8024 </td>
max@0	8025 <td style="vertical-align: top;">
max@0	8026
max@0	8027 </td>
max@0	8028 <td style="vertical-align: top;">
max@0	8029 Boltzmann constant (in joules per kelvin)
max@0	8030 </td>
max@0	8031 </tr>
max@0	8032 <tr>
max@0	8033 <td style="vertical-align: top;">
max@0	8034 phy::k_evk()
max@0	8035 </td>
max@0	8036 <td style="vertical-align: top;">
max@0	8037
max@0	8038 </td>
max@0	8039 <td style="vertical-align: top;">
max@0	8040 Boltzmann constant (in eV/K)
max@0	8041 </td>
max@0	8042 </tr>
max@0	8043 <tr>
max@0	8044 <td style="vertical-align: top;">
max@0	8045 phy::a_0()
max@0	8046 </td>
max@0	8047 <td style="vertical-align: top;">
max@0	8048
max@0	8049 </td>
max@0	8050 <td style="vertical-align: top;">
max@0	8051 Bohr radius (in meters)
max@0	8052 </td>
max@0	8053 </tr>
max@0	8054 <tr>
max@0	8055 <td style="vertical-align: top;">
max@0	8056 phy::mu_B()
max@0	8057 </td>
max@0	8058 <td style="vertical-align: top;">
max@0	8059
max@0	8060 </td>
max@0	8061 <td style="vertical-align: top;">
max@0	8062 Bohr magneton
max@0	8063 </td>
max@0	8064 </tr>
max@0	8065 <tr>
max@0	8066 <td style="vertical-align: top;">
max@0	8067 phy::Z_0()
max@0	8068 </td>
max@0	8069 <td style="vertical-align: top;">
max@0	8070
max@0	8071 </td>
max@0	8072 <td style="vertical-align: top;">
max@0	8073 characteristic impedance of vacuum (in ohms)
max@0	8074 </td>
max@0	8075 </tr>
max@0	8076 <tr>
max@0	8077 <td style="vertical-align: top;">
max@0	8078 phy::G_0()
max@0	8079 </td>
max@0	8080 <td style="vertical-align: top;">
max@0	8081
max@0	8082 </td>
max@0	8083 <td style="vertical-align: top;">
max@0	8084 conductance quantum (in siemens)
max@0	8085 </td>
max@0	8086 </tr>
max@0	8087 <tr>
max@0	8088 <td style="vertical-align: top;">
max@0	8089 phy::k_e()
max@0	8090 </td>
max@0	8091 <td style="vertical-align: top;">
max@0	8092
max@0	8093 </td>
max@0	8094 <td style="vertical-align: top;">
max@0	8095 Coulomb's constant (in meters per farad)
max@0	8096 </td>
max@0	8097 </tr>
max@0	8098 <tr>
max@0	8099 <td style="vertical-align: top;">
max@0	8100 phy::eps_0()
max@0	8101 </td>
max@0	8102 <td style="vertical-align: top;">
max@0	8103
max@0	8104 </td>
max@0	8105 <td style="vertical-align: top;">
max@0	8106 electric constant (in farads per meter)
max@0	8107 </td>
max@0	8108 </tr>
max@0	8109 <tr>
max@0	8110 <td style="vertical-align: top;">
max@0	8111 phy::m_e()
max@0	8112 </td>
max@0	8113 <td style="vertical-align: top;">
max@0	8114
max@0	8115 </td>
max@0	8116 <td style="vertical-align: top;">
max@0	8117 electron mass (in kg)
max@0	8118 </td>
max@0	8119 </tr>
max@0	8120 <tr>
max@0	8121 <td style="vertical-align: top;">
max@0	8122 phy::eV()
max@0	8123 </td>
max@0	8124 <td style="vertical-align: top;">
max@0	8125
max@0	8126 </td>
max@0	8127 <td style="vertical-align: top;">
max@0	8128 electron volt (in joules)
max@0	8129 </td>
max@0	8130 </tr>
max@0	8131 <tr>
max@0	8132 <td style="vertical-align: top;">
max@0	8133 phy::e()
max@0	8134 </td>
max@0	8135 <td style="vertical-align: top;">
max@0	8136
max@0	8137 </td>
max@0	8138 <td style="vertical-align: top;">
max@0	8139 elementary charge (in coulombs)
max@0	8140 </td>
max@0	8141 </tr>
max@0	8142 <tr>
max@0	8143 <td style="vertical-align: top;">
max@0	8144 phy::F()
max@0	8145 </td>
max@0	8146 <td style="vertical-align: top;">
max@0	8147
max@0	8148 </td>
max@0	8149 <td style="vertical-align: top;">
max@0	8150 Faraday constant (in coulombs)
max@0	8151 </td>
max@0	8152 </tr>
max@0	8153 <tr>
max@0	8154 <td style="vertical-align: top;">
max@0	8155 phy::alpha()
max@0	8156 </td>
max@0	8157 <td style="vertical-align: top;">
max@0	8158
max@0	8159 </td>
max@0	8160 <td style="vertical-align: top;">
max@0	8161 fine-structure constant
max@0	8162 </td>
max@0	8163 </tr>
max@0	8164 <tr>
max@0	8165 <td style="vertical-align: top;">
max@0	8166 phy::alpha_inv()
max@0	8167 </td>
max@0	8168 <td style="vertical-align: top;">
max@0	8169
max@0	8170 </td>
max@0	8171 <td style="vertical-align: top;">
max@0	8172 inverse fine-structure constant
max@0	8173 </td>
max@0	8174 </tr>
max@0	8175 <tr>
max@0	8176 <td style="vertical-align: top;">
max@0	8177 phy::K_J()
max@0	8178 </td>
max@0	8179 <td style="vertical-align: top;">
max@0	8180
max@0	8181 </td>
max@0	8182 <td style="vertical-align: top;">
max@0	8183 Josephson constant
max@0	8184 </td>
max@0	8185 </tr>
max@0	8186 <tr>
max@0	8187 <td style="vertical-align: top;">
max@0	8188 phy::mu_0()
max@0	8189 </td>
max@0	8190 <td style="vertical-align: top;">
max@0	8191
max@0	8192 </td>
max@0	8193 <td style="vertical-align: top;">
max@0	8194 magnetic constant (in henries per meter)
max@0	8195 </td>
max@0	8196 </tr>
max@0	8197 <tr>
max@0	8198 <td style="vertical-align: top;">
max@0	8199 phy::phi_0()
max@0	8200 </td>
max@0	8201 <td style="vertical-align: top;">
max@0	8202
max@0	8203 </td>
max@0	8204 <td style="vertical-align: top;">
max@0	8205 magnetic flux quantum (in webers)
max@0	8206 </td>
max@0	8207 </tr>
max@0	8208 <tr>
max@0	8209 <td style="vertical-align: top;">
max@0	8210 phy::R()
max@0	8211 </td>
max@0	8212 <td style="vertical-align: top;">
max@0	8213
max@0	8214 </td>
max@0	8215 <td style="vertical-align: top;">
max@0	8216 molar gas constant (in joules per mole kelvin)
max@0	8217 </td>
max@0	8218 </tr>
max@0	8219 <tr>
max@0	8220 <td style="vertical-align: top;">
max@0	8221 phy::G()
max@0	8222 </td>
max@0	8223 <td style="vertical-align: top;">
max@0	8224
max@0	8225 </td>
max@0	8226 <td style="vertical-align: top;">
max@0	8227 Newtonian constant of gravitation (in newton square meters per kilogram squared)
max@0	8228 </td>
max@0	8229 </tr>
max@0	8230 <tr>
max@0	8231 <td style="vertical-align: top;">
max@0	8232 phy::h()
max@0	8233 </td>
max@0	8234 <td style="vertical-align: top;">
max@0	8235
max@0	8236 </td>
max@0	8237 <td style="vertical-align: top;">
max@0	8238 Planck constant (in joule seconds)
max@0	8239 </td>
max@0	8240 </tr>
max@0	8241 <tr>
max@0	8242 <td style="vertical-align: top;">
max@0	8243 phy::h_bar()
max@0	8244 </td>
max@0	8245 <td style="vertical-align: top;">
max@0	8246
max@0	8247 </td>
max@0	8248 <td style="vertical-align: top;">
max@0	8249 Planck constant over 2 pi, aka reduced Planck constant (in joule seconds)
max@0	8250 </td>
max@0	8251 </tr>
max@0	8252 <tr>
max@0	8253 <td style="vertical-align: top;">
max@0	8254 phy::m_p()
max@0	8255 </td>
max@0	8256 <td style="vertical-align: top;">
max@0	8257
max@0	8258 </td>
max@0	8259 <td style="vertical-align: top;">
max@0	8260 proton mass (in kg)
max@0	8261 </td>
max@0	8262 </tr>
max@0	8263 <tr>
max@0	8264 <td style="vertical-align: top;">
max@0	8265 phy::R_inf()
max@0	8266 </td>
max@0	8267 <td style="vertical-align: top;">
max@0	8268
max@0	8269 </td>
max@0	8270 <td style="vertical-align: top;">
max@0	8271 Rydberg constant (in reciprocal meters)
max@0	8272 </td>
max@0	8273 </tr>
max@0	8274 <tr>
max@0	8275 <td style="vertical-align: top;">
max@0	8276 phy::c_0()
max@0	8277 </td>
max@0	8278 <td style="vertical-align: top;">
max@0	8279
max@0	8280 </td>
max@0	8281 <td style="vertical-align: top;">
max@0	8282 speed of light in vacuum (in meters per second)
max@0	8283 </td>
max@0	8284 </tr>
max@0	8285 <tr>
max@0	8286 <td style="vertical-align: top;">
max@0	8287 phy::sigma()
max@0	8288 </td>
max@0	8289 <td style="vertical-align: top;">
max@0	8290
max@0	8291 </td>
max@0	8292 <td style="vertical-align: top;">
max@0	8293 Stefan-Boltzmann constant
max@0	8294 </td>
max@0	8295 </tr>
max@0	8296 <tr>
max@0	8297 <td style="vertical-align: top;">
max@0	8298 phy::R_k()
max@0	8299 </td>
max@0	8300 <td style="vertical-align: top;">
max@0	8301
max@0	8302 </td>
max@0	8303 <td style="vertical-align: top;">
max@0	8304 von Klitzing constant (in ohms)
max@0	8305 </td>
max@0	8306 </tr>
max@0	8307 <tr>
max@0	8308 <td style="vertical-align: top;">
max@0	8309 phy::b()
max@0	8310 </td>
max@0	8311 <td style="vertical-align: top;">
max@0	8312
max@0	8313 </td>
max@0	8314 <td style="vertical-align: top;">
max@0	8315 Wien wavelength displacement law constant
max@0	8316 </td>
max@0	8317 </tr>
max@0	8318 </tbody>
max@0	8319 </table>
max@0	8320 </ul>
max@0	8321 </li>
max@0	8322 <br>
max@0	8323 <li>
max@0	8324 Examples:
max@0	8325 <ul>
max@0	8326 <pre>
max@0	8327 cout << "speed of light = " << phy::c_0() << endl;
max@0	8328 </pre>
max@0	8329 </ul>
max@0	8330 </li>
max@0	8331 <br>
max@0	8332 <li>
max@0	8333 See also:
max@0	8334 <ul>
max@0	8335 <li><a href="http://en.wikipedia.org/wiki/Physical_constant">physical constant</a> entry in Wikipedia</li>
max@0	8336 <li><a href="#math_constants">math constants</a></li>
max@0	8337 </ul>
max@0	8338 </li>
max@0	8339 </ul>
max@0	8340 <br>
max@0	8341 <hr class="greyline"><br>
max@0	8342
max@0	8343 <a name="log_add"></a>
max@0	8344 <b>log_add(log_a, log_b)</b>
max@0	8345 <ul>
max@0	8346 <li>
max@0	8347 Safe replacement for log(exp(log_a) + exp(log_b))
max@0	8348 </li>
max@0	8349 <br>
max@0	8350 <li>
max@0	8351 Usage:
max@0	8352 <ul>
max@0	8353 <li>
max@0	8354 <i>scalar_type</i> log_c = log_add(log_a, log_b)
max@0	8355 </li>
max@0	8356 <li>
max@0	8357 <i>scalar_type</i> is either <i>float</i> or <i>double</i>
max@0	8358 </li>
max@0	8359 <li>
max@0	8360 log_a, log_b and log_c must have the same type
max@0	8361 </li>
max@0	8362 </ul>
max@0	8363 </li>
max@0	8364 </ul>
max@0	8365 <br>
max@0	8366 <hr class="greyline"><br>
max@0	8367
max@0	8368 <a name="uword"></a>
max@0	8369 <b>uword</b>, <b>sword</b>
max@0	8370 <ul>
max@0	8371 <li>
max@0	8372 <i>uword</i> is a typedef for an unsigned integer with a minimum width of 32 bits; if <i>ARMA_64BIT_WORD</i> is enabled, the minimum width is 64 bits
max@0	8373 </li>
max@0	8374 <br>
max@0	8375 <li>
max@0	8376 <i>sword</i> is a typedef for a signed integer with a minimum width of 32 bits; if <i>ARMA_64BIT_WORD</i> is enabled, the minimum width is 64 bits
max@0	8377 </li>
max@0	8378 <br>
max@0	8379 <li>
max@0	8380 <i>ARMA_64BIT_WORD</i> can be enabled via editing <i>include/armadillo_bits/config.hpp</i>
max@0	8381 </li>
max@0	8382 <br>
max@0	8383 <li>See also:
max@0	8384 <ul>
max@0	8385 <li><a href="http://cplusplus.com/doc/tutorial/variables/">C++ variable types</a></li>
max@0	8386 <li><a href="http://www.cplusplus.com/doc/tutorial/other_data_types/">explanation of <i>typedef</i></a></li>
max@0	8387 <li><a href="#Mat">imat & umat</a> matrix types
max@0	8388 <li><a href="#Col">ivec & uvec</a> vector types
max@0	8389 </ul>
max@0	8390 </li>
max@0	8391 <br>
max@0	8392 </ul>
max@0	8393 <hr class="greyline"><br>
max@0	8394
max@0	8395 <a name="cx_float_double"></a>
max@0	8396 <b>cx_float</b>, <b>cx_double</b>
max@0	8397 <ul>
max@0	8398 <li>
max@0	8399 cx_float is a typedef for <i>std::complex<float></i>
max@0	8400 </li>
max@0	8401 <br>
max@0	8402 <li>
max@0	8403 cx_double is a typedef for <i>std::complex<double></i>
max@0	8404 </li>
max@0	8405 <br>
max@0	8406 <li>See also:
max@0	8407 <ul>
max@0	8408 <li><a href="http://cplusplus.com/reference/std/complex/">complex numbers in the standard C++ library</a></li>
max@0	8409 <li><a href="http://www.cplusplus.com/doc/tutorial/other_data_types/">explanation of <i>typedef</i></a></li>
max@0	8410 <li><a href="#Mat">cx_mat</a> matrix type
max@0	8411 <li><a href="#Col">cx_vec</a> vector type
max@0	8412 </ul>
max@0	8413 </li>
max@0	8414 <br>
max@0	8415 </ul>
max@0	8416
max@0	8417 <a name="syntax"></a>
max@0	8418 <hr class="greyline">
max@0	8419 <br>
max@0	8420 <b>
max@0	8421 Examples of Matlab/Octave syntax and conceptually corresponding Armadillo syntax
max@0	8422 </b>
max@0	8423 <br>
max@0	8424 <br>
max@0	8425 <ul>
max@0	8426 <table style="text-align: left;" border="0" cellpadding="2" cellspacing="2">
max@0	8427 <tbody>
max@0	8428 <tr>
max@0	8429 <td style="vertical-align: top;">
max@0	8430 <b>Matlab/Octave</b>
max@0	8431 </td>
max@0	8432 <td style="vertical-align: top;">
max@0	8433
max@0	8434 </td>
max@0	8435 <td style="vertical-align: top;">
max@0	8436 <b>Armadillo</b>
max@0	8437 </td>
max@0	8438 <td style="vertical-align: top;">
max@0	8439
max@0	8440 </td>
max@0	8441 <td style="vertical-align: top;">
max@0	8442 <b>Notes</b>
max@0	8443 </td>
max@0	8444 </tr>
max@0	8445 <tr>
max@0	8446 <td style="vertical-align: top;">
max@0	8447
max@0	8448 </td>
max@0	8449 <td style="vertical-align: top;">
max@0	8450
max@0	8451 </td>
max@0	8452 <td style="vertical-align: top;">
max@0	8453
max@0	8454 </td>
max@0	8455 <td style="vertical-align: top;">
max@0	8456
max@0	8457 </td>
max@0	8458 <td style="vertical-align: top;">
max@0	8459
max@0	8460 </td>
max@0	8461 </tr>
max@0	8462 <tr>
max@0	8463 <td style="vertical-align: top;">
max@0	8464 A(1, 1)
max@0	8465 </td>
max@0	8466 <td style="vertical-align: top;">
max@0	8467
max@0	8468 </td>
max@0	8469 <td style="vertical-align: top;">
max@0	8470 A(0, 0)
max@0	8471 </td>
max@0	8472 <td style="vertical-align: top;">
max@0	8473
max@0	8474 </td>
max@0	8475 <td style="vertical-align: top;">
max@0	8476 indexing in Armadillo starts at 0
max@0	8477 </td>
max@0	8478 </tr>
max@0	8479 <tr>
max@0	8480 <td style="vertical-align: top;">
max@0	8481 A(k, k)
max@0	8482 </td>
max@0	8483 <td style="vertical-align: top;">
max@0	8484
max@0	8485 </td>
max@0	8486 <td style="vertical-align: top;">
max@0	8487 A(k-1, k-1)
max@0	8488 </td>
max@0	8489 <td style="vertical-align: top;">
max@0	8490
max@0	8491 </td>
max@0	8492 <td style="vertical-align: top;">
max@0	8493
max@0	8494 </td>
max@0	8495 </tr>
max@0	8496 <tr>
max@0	8497 <td style="vertical-align: top;">
max@0	8498
max@0	8499 </td>
max@0	8500 <td style="vertical-align: top;">
max@0	8501
max@0	8502 </td>
max@0	8503 <td style="vertical-align: top;">
max@0	8504
max@0	8505 </td>
max@0	8506 <td style="vertical-align: top;">
max@0	8507
max@0	8508 </td>
max@0	8509 <td style="vertical-align: top;">
max@0	8510
max@0	8511 </td>
max@0	8512 </tr>
max@0	8513 <tr>
max@0	8514 <td style="vertical-align: top;">
max@0	8515 size(A,1)
max@0	8516 </td>
max@0	8517 <td style="vertical-align: top;">
max@0	8518
max@0	8519 </td>
max@0	8520 <td style="vertical-align: top;">
max@0	8521 A<a href="#attributes">.n_rows</a>
max@0	8522 </td>
max@0	8523 <td style="vertical-align: top;">
max@0	8524
max@0	8525 </td>
max@0	8526 <td style="vertical-align: top;">
max@0	8527 read only
max@0	8528 </td>
max@0	8529 </tr>
max@0	8530 <tr>
max@0	8531 <td style="vertical-align: top;">
max@0	8532 size(A,2)
max@0	8533 </td>
max@0	8534 <td style="vertical-align: top;">
max@0	8535
max@0	8536 </td>
max@0	8537 <td style="vertical-align: top;">
max@0	8538 A<a href="#attributes">.n_cols</a>
max@0	8539 </td>
max@0	8540 <td style="vertical-align: top;">
max@0	8541
max@0	8542 </td>
max@0	8543 <td style="vertical-align: top;">
max@0	8544
max@0	8545 </td>
max@0	8546 </tr>
max@0	8547 <tr>
max@0	8548 <td style="vertical-align: top;">
max@0	8549 size(Q,3)
max@0	8550 </td>
max@0	8551 <td style="vertical-align: top;">
max@0	8552
max@0	8553 </td>
max@0	8554 <td style="vertical-align: top;">
max@0	8555 Q<a href="#attributes">.n_slices</a>
max@0	8556 </td>
max@0	8557 <td style="vertical-align: top;">
max@0	8558
max@0	8559 </td>
max@0	8560 <td style="vertical-align: top;">
max@0	8561 Q is a <a href="#Cube">cube</a> (3D array)
max@0	8562 </td>
max@0	8563 </tr>
max@0	8564 <tr>
max@0	8565 <td style="vertical-align: top;">
max@0	8566 numel(A)
max@0	8567 </td>
max@0	8568 <td style="vertical-align: top;">
max@0	8569
max@0	8570 </td>
max@0	8571 <td style="vertical-align: top;">
max@0	8572 A<a href="#attributes">.n_elem</a>
max@0	8573 </td>
max@0	8574 <td style="vertical-align: top;">
max@0	8575
max@0	8576 </td>
max@0	8577 <td style="vertical-align: top;">
max@0	8578
max@0	8579 </td>
max@0	8580 </tr>
max@0	8581 <tr>
max@0	8582 <td style="vertical-align: top;">
max@0	8583
max@0	8584 </td>
max@0	8585 <td style="vertical-align: top;">
max@0	8586
max@0	8587 </td>
max@0	8588 <td style="vertical-align: top;">
max@0	8589
max@0	8590 </td>
max@0	8591 <td style="vertical-align: top;">
max@0	8592
max@0	8593 </td>
max@0	8594 <td style="vertical-align: top;">
max@0	8595
max@0	8596 </td>
max@0	8597 </tr>
max@0	8598 <tr>
max@0	8599 <td style="vertical-align: top;">
max@0	8600 A(:, k)
max@0	8601 </td>
max@0	8602 <td style="vertical-align: top;">
max@0	8603
max@0	8604 </td>
max@0	8605 <td style="vertical-align: top;">
max@0	8606 A<a href="#submat">.col</a>(k)
max@0	8607 </td>
max@0	8608 <td style="vertical-align: top;">
max@0	8609
max@0	8610 </td>
max@0	8611 <td style="vertical-align: top;">
max@0	8612 this is a conceptual example only;
max@0	8613 exact conversion from Matlab/Octave to Armadillo syntax
max@0	8614 will require taking into account that indexing starts at 0
max@0	8615 </td>
max@0	8616 </tr>
max@0	8617 <tr>
max@0	8618 <td style="vertical-align: top;">
max@0	8619 A(k, :)
max@0	8620 </td>
max@0	8621 <td style="vertical-align: top;">
max@0	8622
max@0	8623 </td>
max@0	8624 <td style="vertical-align: top;">
max@0	8625 A<a href="#submat">.row</a>(k)
max@0	8626 </td>
max@0	8627 <td style="vertical-align: top;">
max@0	8628
max@0	8629 </td>
max@0	8630 <td style="vertical-align: top;">
max@0	8631
max@0	8632 </td>
max@0	8633 </tr>
max@0	8634 <tr>
max@0	8635 <td style="vertical-align: top;">
max@0	8636 A(:, p:q)
max@0	8637 </td>
max@0	8638 <td style="vertical-align: top;">
max@0	8639
max@0	8640 </td>
max@0	8641 <td style="vertical-align: top;">
max@0	8642 A<a href="#submat">.cols</a>(p, q)
max@0	8643 </td>
max@0	8644 <td style="vertical-align: top;">
max@0	8645
max@0	8646 </td>
max@0	8647 <td style="vertical-align: top;">
max@0	8648
max@0	8649 </td>
max@0	8650 </tr>
max@0	8651 <tr>
max@0	8652 <td style="vertical-align: top;">
max@0	8653 A(p:q, :)
max@0	8654 </td>
max@0	8655 <td style="vertical-align: top;">
max@0	8656
max@0	8657 </td>
max@0	8658 <td style="vertical-align: top;">
max@0	8659 A<a href="#submat">.rows</a>(p, q)
max@0	8660 </td>
max@0	8661 <td style="vertical-align: top;">
max@0	8662
max@0	8663 </td>
max@0	8664 <td style="vertical-align: top;">
max@0	8665
max@0	8666 </td>
max@0	8667 </tr>
max@0	8668 <tr>
max@0	8669 <td style="vertical-align: top;">
max@0	8670
max@0	8671 </td>
max@0	8672 <td style="vertical-align: top;">
max@0	8673
max@0	8674 </td>
max@0	8675 <td style="vertical-align: top;">
max@0	8676
max@0	8677 </td>
max@0	8678 <td style="vertical-align: top;">
max@0	8679
max@0	8680 </td>
max@0	8681 <td style="vertical-align: top;">
max@0	8682
max@0	8683 </td>
max@0	8684 </tr>
max@0	8685 <tr>
max@0	8686 <td style="vertical-align: top;">
max@0	8687 A(p:q, r:s)
max@0	8688 </td>
max@0	8689 <td style="vertical-align: top;">
max@0	8690
max@0	8691 </td>
max@0	8692 <td style="vertical-align: top;">
max@0	8693 <font size=-1>
max@0	8694 A<a href="#submat">.submat</a>(p, r, q, s)
max@0	8695 </font>
max@0	8696 </td>
max@0	8697 <td style="vertical-align: top;">
max@0	8698
max@0	8699 </td>
max@0	8700 <td style="vertical-align: top;">
max@0	8701 <font size=-1>
max@0	8702 A.submat(first_row, first_col, last_row, last_col)
max@0	8703 </font>
max@0	8704 </td>
max@0	8705 </tr>
max@0	8706 <tr>
max@0	8707 <td style="vertical-align: top;">
max@0	8708
max@0	8709 </td>
max@0	8710 <td style="vertical-align: top;">
max@0	8711
max@0	8712 </td>
max@0	8713 <td style="vertical-align: top;">
max@0	8714 <font size=-1>
max@0	8715 or
max@0	8716 </font>
max@0	8717 </td>
max@0	8718 <td style="vertical-align: top;">
max@0	8719
max@0	8720 </td>
max@0	8721 <td style="vertical-align: top;">
max@0	8722
max@0	8723 </td>
max@0	8724 </tr>
max@0	8725 <tr>
max@0	8726 <td style="vertical-align: top;">
max@0	8727
max@0	8728 </td>
max@0	8729 <td style="vertical-align: top;">
max@0	8730
max@0	8731 </td>
max@0	8732 <td style="vertical-align: top;">
max@0	8733 <font size=-1>
max@0	8734 A( <a href="#submat">span</a>(p,q), <a href="#submat">span</a>(r,s) )
max@0	8735 </font>
max@0	8736 </td>
max@0	8737 <td style="vertical-align: top;">
max@0	8738
max@0	8739 </td>
max@0	8740 <td style="vertical-align: top;">
max@0	8741 <font size=-1>
max@0	8742 A( span(first_row, last_row), span(first_col, last_col) )
max@0	8743 </font>
max@0	8744 </td>
max@0	8745 </tr>
max@0	8746 <tr>
max@0	8747 <td style="vertical-align: top;">
max@0	8748
max@0	8749 </td>
max@0	8750 <td style="vertical-align: top;">
max@0	8751
max@0	8752 </td>
max@0	8753 <td style="vertical-align: top;">
max@0	8754
max@0	8755 </td>
max@0	8756 <td style="vertical-align: top;">
max@0	8757
max@0	8758 </td>
max@0	8759 <td style="vertical-align: top;">
max@0	8760
max@0	8761 </td>
max@0	8762 </tr>
max@0	8763 <tr>
max@0	8764 <td style="vertical-align: top;">
max@0	8765 Q(:, :, k)
max@0	8766 </td>
max@0	8767 <td style="vertical-align: top;">
max@0	8768
max@0	8769 </td>
max@0	8770 <td style="vertical-align: top;">
max@0	8771 Q<a href="#subcube">.slice</a>(k)
max@0	8772 </td>
max@0	8773 <td style="vertical-align: top;">
max@0	8774
max@0	8775 </td>
max@0	8776 <td style="vertical-align: top;">
max@0	8777 Q is a <a href="#Cube">cube</a> (3D array)
max@0	8778 </td>
max@0	8779 </tr>
max@0	8780 <tr>
max@0	8781 <td style="vertical-align: top;">
max@0	8782 Q(:, :, t:u)
max@0	8783 </td>
max@0	8784 <td style="vertical-align: top;">
max@0	8785
max@0	8786 </td>
max@0	8787 <td style="vertical-align: top;">
max@0	8788 Q<a href="#subcube">.slices</a>(t, u)
max@0	8789 </td>
max@0	8790 <td style="vertical-align: top;">
max@0	8791
max@0	8792 </td>
max@0	8793 <td style="vertical-align: top;">
max@0	8794
max@0	8795 </td>
max@0	8796 </tr>
max@0	8797 <tr>
max@0	8798 <td style="vertical-align: top;">
max@0	8799
max@0	8800 </td>
max@0	8801 <td style="vertical-align: top;">
max@0	8802
max@0	8803 </td>
max@0	8804 <td style="vertical-align: top;">
max@0	8805
max@0	8806 </td>
max@0	8807 <td style="vertical-align: top;">
max@0	8808
max@0	8809 </td>
max@0	8810 <td style="vertical-align: top;">
max@0	8811
max@0	8812 </td>
max@0	8813 </tr>
max@0	8814 <tr>
max@0	8815 <td style="vertical-align: top;">
max@0	8816 Q(p:q, r:s, t:u)
max@0	8817 </td>
max@0	8818 <td style="vertical-align: top;">
max@0	8819
max@0	8820 </td>
max@0	8821 <td style="vertical-align: top;">
max@0	8822 <font size=-1>
max@0	8823 Q<a href="#subcube">.subcube</a>(p, r, t, q, s, u)
max@0	8824 </font>
max@0	8825 </td>
max@0	8826 <td style="vertical-align: top;">
max@0	8827
max@0	8828 </td>
max@0	8829 <td style="vertical-align: top;">
max@0	8830 <font size=-1>
max@0	8831 .subcube(first_row, first_col, first_slice, last_row, last_col, last_slice)
max@0	8832 </font>
max@0	8833 </td>
max@0	8834 </tr>
max@0	8835 <tr>
max@0	8836 <td style="vertical-align: top;">
max@0	8837
max@0	8838 </td>
max@0	8839 <td style="vertical-align: top;">
max@0	8840
max@0	8841 </td>
max@0	8842 <td style="vertical-align: top;">
max@0	8843 <font size=-1>
max@0	8844 or
max@0	8845 </font>
max@0	8846 </td>
max@0	8847 <td style="vertical-align: top;">
max@0	8848
max@0	8849 </td>
max@0	8850 <td style="vertical-align: top;">
max@0	8851
max@0	8852 </td>
max@0	8853 </tr>
max@0	8854 <tr>
max@0	8855 <td style="vertical-align: top;">
max@0	8856
max@0	8857 </td>
max@0	8858 <td style="vertical-align: top;">
max@0	8859
max@0	8860 </td>
max@0	8861 <td style="vertical-align: top;">
max@0	8862 <font size=-1>
max@0	8863 Q( <a href="#subcube">span</a>(p,q), <a href="#subcube">span</a>(r,s), <a href="#subcube">span</a>(t,u) )
max@0	8864 </font>
max@0	8865 </td>
max@0	8866 <td style="vertical-align: top;">
max@0	8867
max@0	8868 </td>
max@0	8869 <td style="vertical-align: top;">
max@0	8870
max@0	8871 </td>
max@0	8872 </tr>
max@0	8873 <tr>
max@0	8874 <td style="vertical-align: top;">
max@0	8875
max@0	8876 </td>
max@0	8877 <td style="vertical-align: top;">
max@0	8878
max@0	8879 </td>
max@0	8880 <td style="vertical-align: top;">
max@0	8881
max@0	8882 </td>
max@0	8883 <td style="vertical-align: top;">
max@0	8884
max@0	8885 </td>
max@0	8886 <td style="vertical-align: top;">
max@0	8887
max@0	8888 </td>
max@0	8889 </tr>
max@0	8890 <tr>
max@0	8891 <td style="vertical-align: top;">
max@0	8892 A'
max@0	8893 </td>
max@0	8894 <td style="vertical-align: top;">
max@0	8895
max@0	8896 </td>
max@0	8897 <td style="vertical-align: top;">
max@0	8898 A<a href="#t_st_members">.t()</a> or <a href="#trans">trans</a>(A)
max@0	8899 </td>
max@0	8900 <td style="vertical-align: top;">
max@0	8901
max@0	8902 </td>
max@0	8903 <td style="vertical-align: top;">
max@0	8904 matrix transpose / Hermitian transpose
max@0	8905 <br>
max@0	8906 (for complex matrices, the conjugate of each element is taken)
max@0	8907 </td>
max@0	8908 </tr>
max@0	8909 <tr>
max@0	8910 <td style="vertical-align: top;">
max@0	8911 A.'
max@0	8912 </td>
max@0	8913 <td style="vertical-align: top;">
max@0	8914
max@0	8915 </td>
max@0	8916 <td style="vertical-align: top;">
max@0	8917 A<a href="#t_st_members">.st()</a> or <a href="#strans">strans</a>(A)
max@0	8918 </td>
max@0	8919 <td style="vertical-align: top;">
max@0	8920
max@0	8921 </td>
max@0	8922 <td style="vertical-align: top;">
max@0	8923 simple matrix transpose
max@0	8924 <br>
max@0	8925 (for complex matrices, the conjugate of each element is not taken)
max@0	8926 </td>
max@0	8927 </tr>
max@0	8928 <tr>
max@0	8929 <td style="vertical-align: top;">
max@0	8930
max@0	8931 </td>
max@0	8932 <td style="vertical-align: top;">
max@0	8933
max@0	8934 </td>
max@0	8935 <td style="vertical-align: top;">
max@0	8936
max@0	8937 </td>
max@0	8938 <td style="vertical-align: top;">
max@0	8939
max@0	8940 </td>
max@0	8941 <td style="vertical-align: top;">
max@0	8942
max@0	8943 </td>
max@0	8944 </tr>
max@0	8945 <tr>
max@0	8946 <td style="vertical-align: top;">
max@0	8947 A = zeros(size(A))
max@0	8948 </td>
max@0	8949 <td style="vertical-align: top;">
max@0	8950
max@0	8951 </td>
max@0	8952 <td style="vertical-align: top;">
max@0	8953 A<a href="#zeros_member">.zeros()</a>
max@0	8954 </td>
max@0	8955 <td style="vertical-align: top;">
max@0	8956
max@0	8957 </td>
max@0	8958 <td style="vertical-align: top;">
max@0	8959
max@0	8960 </td>
max@0	8961 </tr>
max@0	8962 <tr>
max@0	8963 <td style="vertical-align: top;">
max@0	8964 A = ones(size(A))
max@0	8965 </td>
max@0	8966 <td style="vertical-align: top;">
max@0	8967
max@0	8968 </td>
max@0	8969 <td style="vertical-align: top;">
max@0	8970 A.<a href="#ones_member">ones()</a>
max@0	8971 </td>
max@0	8972 <td style="vertical-align: top;">
max@0	8973
max@0	8974 </td>
max@0	8975 <td style="vertical-align: top;">
max@0	8976
max@0	8977 </td>
max@0	8978 </tr>
max@0	8979 <tr>
max@0	8980 <td style="vertical-align: top;">
max@0	8981 A = zeros(k)
max@0	8982 </td>
max@0	8983 <td style="vertical-align: top;">
max@0	8984
max@0	8985 </td>
max@0	8986 <td style="vertical-align: top;">
max@0	8987 A = <a href="#zeros_standalone">zeros</a><mat>(k,k)
max@0	8988 </td>
max@0	8989 <td style="vertical-align: top;">
max@0	8990
max@0	8991 </td>
max@0	8992 <td style="vertical-align: top;">
max@0	8993
max@0	8994 </td>
max@0	8995 </tr>
max@0	8996 <tr>
max@0	8997 <td style="vertical-align: top;">
max@0	8998 A = ones(k)
max@0	8999 </td>
max@0	9000 <td style="vertical-align: top;">
max@0	9001
max@0	9002 </td>
max@0	9003 <td style="vertical-align: top;">
max@0	9004 A = <a href="#ones_standalone">ones</a><mat>(k,k)
max@0	9005 </td>
max@0	9006 <td style="vertical-align: top;">
max@0	9007
max@0	9008 </td>
max@0	9009 <td style="vertical-align: top;">
max@0	9010
max@0	9011 </td>
max@0	9012 </tr>
max@0	9013 <tr>
max@0	9014 <td style="vertical-align: top;">
max@0	9015
max@0	9016 </td>
max@0	9017 <td style="vertical-align: top;">
max@0	9018
max@0	9019 </td>
max@0	9020 <td style="vertical-align: top;">
max@0	9021
max@0	9022 </td>
max@0	9023 <td style="vertical-align: top;">
max@0	9024
max@0	9025 </td>
max@0	9026 <td style="vertical-align: top;">
max@0	9027
max@0	9028 </td>
max@0	9029 </tr>
max@0	9030 <tr>
max@0	9031 <td style="vertical-align: top;">
max@0	9032 C = complex(A,B)
max@0	9033 </td>
max@0	9034 <td style="vertical-align: top;">
max@0	9035
max@0	9036 </td>
max@0	9037 <td style="vertical-align: top;">
max@0	9038 cx_mat C = <a href="#Mat">cx_mat</a>(A,B)
max@0	9039 </td>
max@0	9040 <td style="vertical-align: top;">
max@0	9041
max@0	9042 </td>
max@0	9043 <td style="vertical-align: top;">
max@0	9044
max@0	9045 </td>
max@0	9046 </tr>
max@0	9047 <tr>
max@0	9048 <td style="vertical-align: top;">
max@0	9049
max@0	9050 </td>
max@0	9051 <td style="vertical-align: top;">
max@0	9052
max@0	9053 </td>
max@0	9054 <td style="vertical-align: top;">
max@0	9055
max@0	9056 </td>
max@0	9057 <td style="vertical-align: top;">
max@0	9058
max@0	9059 </td>
max@0	9060 <td style="vertical-align: top;">
max@0	9061
max@0	9062 </td>
max@0	9063 </tr>
max@0	9064 <tr>
max@0	9065 <td style="vertical-align: top;">
max@0	9066 A .* B
max@0	9067 </td>
max@0	9068 <td style="vertical-align: top;">
max@0	9069
max@0	9070 </td>
max@0	9071 <td style="vertical-align: top;">
max@0	9072 A % B
max@0	9073 </td>
max@0	9074 <td style="vertical-align: top;">
max@0	9075
max@0	9076 </td>
max@0	9077 <td style="vertical-align: top;">
max@0	9078 <a href="#operators">element-wise multiplication</a>
max@0	9079 </td>
max@0	9080 </tr>
max@0	9081 <tr>
max@0	9082 <td style="vertical-align: top;">
max@0	9083 A ./ B
max@0	9084 </td>
max@0	9085 <td style="vertical-align: top;">
max@0	9086
max@0	9087 </td>
max@0	9088 <td style="vertical-align: top;">
max@0	9089 A / B
max@0	9090 </td>
max@0	9091 <td style="vertical-align: top;">
max@0	9092
max@0	9093 </td>
max@0	9094 <td style="vertical-align: top;">
max@0	9095 <a href="#operators">element-wise division</a>
max@0	9096 </td>
max@0	9097 </tr>
max@0	9098 <tr>
max@0	9099 <td style="vertical-align: top;">
max@0	9100 A \ B
max@0	9101 </td>
max@0	9102 <td style="vertical-align: top;">
max@0	9103
max@0	9104 </td>
max@0	9105 <td style="vertical-align: top;">
max@0	9106 <a href="#solve">solve</a>(A,B)
max@0	9107 </td>
max@0	9108 <td style="vertical-align: top;">
max@0	9109
max@0	9110 </td>
max@0	9111 <td style="vertical-align: top;">
max@0	9112 conceptually similar to <a href="#inv">inv</a>(A)*B, but more efficient
max@0	9113 </td>
max@0	9114 </tr>
max@0	9115 <tr>
max@0	9116 <td style="vertical-align: top;">
max@0	9117 A = A + 1;
max@0	9118 </td>
max@0	9119 <td style="vertical-align: top;">
max@0	9120
max@0	9121 </td>
max@0	9122 <td style="vertical-align: top;">
max@0	9123 A++
max@0	9124 </td>
max@0	9125 <td style="vertical-align: top;">
max@0	9126
max@0	9127 </td>
max@0	9128 <td style="vertical-align: top;">
max@0	9129
max@0	9130 </td>
max@0	9131 </tr>
max@0	9132 <tr>
max@0	9133 <td style="vertical-align: top;">
max@0	9134 A = A - 1;
max@0	9135 </td>
max@0	9136 <td style="vertical-align: top;">
max@0	9137
max@0	9138 </td>
max@0	9139 <td style="vertical-align: top;">
max@0	9140 A--
max@0	9141 </td>
max@0	9142 <td style="vertical-align: top;">
max@0	9143
max@0	9144 </td>
max@0	9145 <td style="vertical-align: top;">
max@0	9146
max@0	9147 </td>
max@0	9148 </tr>
max@0	9149 <tr>
max@0	9150 <td style="vertical-align: top;">
max@0	9151
max@0	9152 </td>
max@0	9153 <td style="vertical-align: top;">
max@0	9154
max@0	9155 </td>
max@0	9156 <td style="vertical-align: top;">
max@0	9157
max@0	9158 </td>
max@0	9159 <td style="vertical-align: top;">
max@0	9160
max@0	9161 </td>
max@0	9162 <td style="vertical-align: top;">
max@0	9163
max@0	9164 </td>
max@0	9165 </tr>
max@0	9166 <tr>
max@0	9167 <td style="vertical-align: top;">
max@0	9168 A = [ 1 2; 3 4; ]
max@0	9169 </td>
max@0	9170 <td style="vertical-align: top;">
max@0	9171
max@0	9172 </td>
max@0	9173 <td style="vertical-align: top;">
max@0	9174 A <font size=-1><<</font> 1 <font size=-1><<</font> 2 <font size=-1><<</font> endr<br>
max@0	9175    <font size=-1><<</font> 3 <font size=-1><<</font> 4 <font size=-1><<</font> endr;
max@0	9176 </td>
max@0	9177 <td style="vertical-align: top;">
max@0	9178
max@0	9179 </td>
max@0	9180 <td style="vertical-align: top;">
max@0	9181 <a href="#element_initialisation">element initialisation</a>,
max@0	9182 with special element <i>endr</i> indicating <i>end of row</i>
max@0	9183 </td>
max@0	9184 </tr>
max@0	9185 <tr>
max@0	9186 <td style="vertical-align: top;">
max@0	9187
max@0	9188 </td>
max@0	9189 <td style="vertical-align: top;">
max@0	9190
max@0	9191 </td>
max@0	9192 <td style="vertical-align: top;">
max@0	9193
max@0	9194 </td>
max@0	9195 <td style="vertical-align: top;">
max@0	9196
max@0	9197 </td>
max@0	9198 <td style="vertical-align: top;">
max@0	9199
max@0	9200 </td>
max@0	9201 </tr>
max@0	9202 <tr>
max@0	9203 <td style="vertical-align: top;">
max@0	9204 X = [ A  B ]
max@0	9205 </td>
max@0	9206 <td style="vertical-align: top;">
max@0	9207
max@0	9208 </td>
max@0	9209 <td style="vertical-align: top;">
max@0	9210 X = <a href="#join">join_rows</a>(A,B)
max@0	9211 </td>
max@0	9212 <td style="vertical-align: top;">
max@0	9213
max@0	9214 </td>
max@0	9215 <td style="vertical-align: top;">
max@0	9216
max@0	9217 </td>
max@0	9218 </tr>
max@0	9219 <tr>
max@0	9220 <td style="vertical-align: top;">
max@0	9221 X = [ A; B ]
max@0	9222 </td>
max@0	9223 <td style="vertical-align: top;">
max@0	9224
max@0	9225 </td>
max@0	9226 <td style="vertical-align: top;">
max@0	9227 X = <a href="#join">join_cols</a>(A,B)
max@0	9228 </td>
max@0	9229 <td style="vertical-align: top;">
max@0	9230
max@0	9231 </td>
max@0	9232 <td style="vertical-align: top;">
max@0	9233
max@0	9234 </td>
max@0	9235 </tr>
max@0	9236 <tr>
max@0	9237 <td style="vertical-align: top;">
max@0	9238
max@0	9239 </td>
max@0	9240 <td style="vertical-align: top;">
max@0	9241
max@0	9242 </td>
max@0	9243 <td style="vertical-align: top;">
max@0	9244
max@0	9245 </td>
max@0	9246 <td style="vertical-align: top;">
max@0	9247
max@0	9248 </td>
max@0	9249 <td style="vertical-align: top;">
max@0	9250
max@0	9251 </td>
max@0	9252 </tr>
max@0	9253 <tr>
max@0	9254 <td style="vertical-align: top;">
max@0	9255 A
max@0	9256 </td>
max@0	9257 <td style="vertical-align: top;">
max@0	9258
max@0	9259 </td>
max@0	9260 <td style="vertical-align: top;">
max@0	9261 cout <font size=-1><<</font> A <font size=-1><<</font> endl;
max@0	9262 <br>or
max@0	9263 <br>A<a href="#print">.print</a>("A =");
max@0	9264 </td>
max@0	9265 <td style="vertical-align: top;">
max@0	9266
max@0	9267 </td>
max@0	9268 <td style="vertical-align: top;">
max@0	9269
max@0	9270 </td>
max@0	9271 </tr>
max@0	9272 <tr>
max@0	9273 <td style="vertical-align: top;">
max@0	9274
max@0	9275 </td>
max@0	9276 <td style="vertical-align: top;">
max@0	9277
max@0	9278 </td>
max@0	9279 <td style="vertical-align: top;">
max@0	9280
max@0	9281 </td>
max@0	9282 <td style="vertical-align: top;">
max@0	9283
max@0	9284 </td>
max@0	9285 <td style="vertical-align: top;">
max@0	9286
max@0	9287 </td>
max@0	9288 </tr>
max@0	9289 <tr>
max@0	9290 <td style="vertical-align: top;">
max@0	9291 save -ascii 'A.dat' A
max@0	9292 </td>
max@0	9293 <td style="vertical-align: top;">
max@0	9294
max@0	9295 </td>
max@0	9296 <td style="vertical-align: top;">
max@0	9297 A<a href="#save_load_mat">.save</a>("A.dat", raw_ascii);
max@0	9298 </td>
max@0	9299 <td style="vertical-align: top;">
max@0	9300
max@0	9301 </td>
max@0	9302 <td style="vertical-align: top;">
max@0	9303 Matlab/Octave matrices saved as ascii are readable by Armadillo (and vice-versa)
max@0	9304 </td>
max@0	9305 </tr>
max@0	9306 <tr>
max@0	9307 <td style="vertical-align: top;">
max@0	9308 load -ascii 'A.dat'
max@0	9309 </td>
max@0	9310 <td style="vertical-align: top;">
max@0	9311
max@0	9312 </td>
max@0	9313 <td style="vertical-align: top;">
max@0	9314 A<a href="#save_load_mat">.load</a>("A.dat", raw_ascii);
max@0	9315 </td>
max@0	9316 <td style="vertical-align: top;">
max@0	9317
max@0	9318 </td>
max@0	9319 <td style="vertical-align: top;">
max@0	9320
max@0	9321 </td>
max@0	9322 </tr>
max@0	9323 <tr>
max@0	9324 <td style="vertical-align: top;">
max@0	9325
max@0	9326 </td>
max@0	9327 <td style="vertical-align: top;">
max@0	9328
max@0	9329 </td>
max@0	9330 <td style="vertical-align: top;">
max@0	9331
max@0	9332 </td>
max@0	9333 <td style="vertical-align: top;">
max@0	9334
max@0	9335 </td>
max@0	9336 <td style="vertical-align: top;">
max@0	9337
max@0	9338 </td>
max@0	9339 </tr>
max@0	9340 <tr>
max@0	9341 <td style="vertical-align: top;">
max@0	9342 S = { 'abc'; 'def' }
max@0	9343 </td>
max@0	9344 <td style="vertical-align: top;">
max@0	9345
max@0	9346 </td>
max@0	9347 <td style="vertical-align: top;">
max@0	9348 <a href="#field">field</a><std::string> S(2);
max@0	9349 <br>S(0) = "abc";
max@0	9350 <br>S(1) = "def";
max@0	9351 </td>
max@0	9352 <td style="vertical-align: top;">
max@0	9353
max@0	9354 </td>
max@0	9355 <td style="vertical-align: top;">
max@0	9356 <a href="#field">fields</a> can store arbitrary objects, in a 1D or 2D layout
max@0	9357 </td>
max@0	9358 </tr>
max@0	9359 </tbody>
max@0	9360 </table>
max@0	9361 </ul>
max@0	9362 <br>
max@0	9363
max@0	9364 <a name="example_prog"></a>
max@0	9365 <hr class="greyline">
max@0	9366 <br>
max@0	9367 <b>example program</b>
max@0	9368 <br>
max@0	9369 <br>
max@0	9370 <ul>
max@0	9371 <li>
max@0	9372 If you save the program below as <i>example.cpp</i>,
max@0	9373 under Linux you can compile it using:
max@0	9374 <br>
max@0	9375 g++ example.cpp -o example -O1 -larmadillo
max@0	9376 </li>
max@0	9377 <ul>
max@0	9378 <pre>
max@0	9379 #include <iostream>
max@0	9380 #include <armadillo>
max@0	9381
max@0	9382 using namespace std;
max@0	9383 using namespace arma;
max@0	9384
max@0	9385 int main(int argc, char** argv)
max@0	9386 {
max@0	9387 mat A = randu<mat>(4,5);
max@0	9388 mat B = randu<mat>(4,5);
max@0	9389
max@0	9390 cout << A*trans(B) << endl;
max@0	9391
max@0	9392 return 0;
max@0	9393 }
max@0	9394 </pre>
max@0	9395 </ul>
max@0	9396 <li>
max@0	9397 You may also want to have a look at the example programs that come with the Armadillo archive.
max@0	9398 </li>
max@0	9399 <br>
max@0	9400 <li>
max@0	9401 As Armadillo is a template library, we strongly recommended to have optimisation enabled when compiling programs
max@0	9402 (eg. when compiling with GCC, use the -O1 or -O2 options).
max@0	9403 </li>
max@0	9404 </ul>
max@0	9405 <br>
max@0	9406
max@0	9407
max@0	9408 <!--
max@0	9409 <a name="catching_exceptions"></a>
max@0	9410 <hr class="greyline">
max@0	9411 <br>
max@0	9412 <b>how to catch std::runtime_error exceptions</b>
max@0	9413 <br>
max@0	9414 <br>
max@0	9415 <ul>
max@0	9416 <li>
max@0	9417 If a function such as <a href="#inv">inv()</a> fails to find a solution,
max@0	9418 an error message is printed and a <i>std::runtime_error</i> exception is thrown.
max@0	9419 If the exception is not caught, the program typically terminates.
max@0	9420 Below is an example of how to catch exceptions:
max@0	9421 <ul>
max@0	9422 <pre>
max@0	9423 #include <iostream>
max@0	9424 #include <armadillo>
max@0	9425
max@0	9426 using namespace std;
max@0	9427 using namespace arma;
max@0	9428
max@0	9429 int main(int argc, char** argv)
max@0	9430 {
max@0	9431 // create a non-invertible matrix
max@0	9432 mat A = zeros<mat>(5,5);
max@0	9433
max@0	9434 mat B;
max@0	9435
max@0	9436 try
max@0	9437 {
max@0	9438 B = inv(A);
max@0	9439 }
max@0	9440 catch (std::runtime_error& x)
max@0	9441 {
max@0	9442 cout << "caught an exception" << endl;
max@0	9443 }
max@0	9444
max@0	9445 return 0;
max@0	9446 }
max@0	9447 </pre>
max@0	9448 </ul>
max@0	9449 <li>
max@0	9450 See also:
max@0	9451 <ul>
max@0	9452 <li><a href="#logging">logging of warnings and errors</a></li>
max@0	9453 <li><a href="http://cplusplus.com/doc/tutorial/exceptions/">tutorial on exceptions</a></li>
max@0	9454 <li><a href="http://cplusplus.com/reference/std/stdexcept/runtime_error/">std::runtime_error</a></li>
max@0	9455 </ul>
max@0	9456 </li>
max@0	9457 <br>
max@0	9458 </ul>
max@0	9459 <br>
max@0	9460 -->
max@0	9461
max@0	9462 <a name="api_changes"></a>
max@0	9463 <hr class="greyline">
max@0	9464 <br>
max@0	9465 <b>API Changes, Additions and Deprecations</b>
max@0	9466 <br>
max@0	9467 <br>
max@0	9468 Armadillo's version number is X.Y.Z, where X is a major version, Y is a minor version, and Z is the patch level (indicating bug fixes).
max@0	9469 <br>
max@0	9470 <br>
max@0	9471 Within each major version (eg. 2.x), minor versions with an even number (eg. 2.2) are backwards compatible with earlier even minor versions (eg. 2.0).
max@0	9472 For example, code written for version 2.0 will work with version 2.2.
max@0	9473 However, as each minor version may have more features (ie. API extensions) than earlier versions,
max@0	9474 code written for version 2.2 doesn't necessarily work with 2.0.
max@0	9475 <br>
max@0	9476 <br>
max@0	9477 An odd minor version number (eg. 2.3) indicates an experimental version.
max@0	9478 Experimental versions are generally faster and have more functionality,
max@0	9479 but their APIs have not been finalised yet.
max@0	9480 <br>
max@0	9481 <br>
max@0	9482 In general, we don't like changes to existing APIs and prefer not to break any user software.
max@0	9483 However, to allow evolution and help code maintenance, we reserve the right to change the APIs in future major versions of Armadillo,
max@0	9484 while remaining backwards compatible wherever possible
max@0	9485 (eg. 3.0 may have slightly different APIs than 2.x).
max@0	9486 Also, in a rare instance the user API may need to be altered if a bug fix absolutely requires it.
max@0	9487 <br>
max@0	9488 <br>
max@0	9489 <br>
max@0	9490 <a name="deprecated"></a>
max@0	9491 Below is a list of deprecated functionality; this functionality will be <b>removed</b> in version 3.0:
max@0	9492 <ul>
max@0	9493 <li>
max@0	9494 <i>.print_trans()</i> and <i>.raw_print_trans()</i> are deprecated;
max@0	9495 <br>instead, you can chain <i>.t()</i> and <i>.print()</i> to achieve a similar result: <i>.t().print()</i>
max@0	9496 <br>
max@0	9497 </li>
max@0	9498 <li>
max@0	9499 support for tying writeable auxiliary (external) memory to fixed size matrices is deprecated;
max@0	9500 <br>instead, you can use standard matrices with <a href="#adv_constructors_mat">writeable auxiliary memory</a>,
max@0	9501 or initialise fixed size matrices by <a href="#adv_constructors_mat">copying the memory</a>.
max@0	9502 Using auxiliary memory with standard matrices is unaffected.
max@0	9503 <br>
max@0	9504 </li>
max@0	9505 </ul>
max@0	9506 <br>
max@0	9507 <br>
max@0	9508 Below is a list of additions and changes since prior versions of Armadillo:
max@0	9509 <ul>
max@0	9510 <a name="added_in_24"></a>
max@0	9511 <li>Added in 2.4:
max@0	9512 <ul>
max@0	9513 <li>shorter forms of transposes: <a href="#t_st_members">.t()</a> and <a href="#t_st_members">.st()</a></li>
max@0	9514 <li><a href="#resize_member">.resize()</a> and <a href="#resize">resize()</a> (added in 2.4.1)</li>
max@0	9515 <li>optional use of 64 bit indices (allowing matrices to have more than 4 billion elements),
max@0	9516 <br>enabled via ARMA_64BIT_WORD in <i>include/armadillo_bits/config.hpp</i></li>
max@0	9517 <li>experimental support for C++11 initialiser lists, enabled via ARMA_USE_CXX11 in <i>include/armadillo_bits/config.hpp</i></li>
max@0	9518 </ul>
max@0	9519 <br>
max@0	9520 <li>Changed in 2.4:
max@0	9521 <ul>
max@0	9522 <li>refactored code to eliminate warnings when using the Clang C++ compiler</li>
max@0	9523 <li><a href="#Mat">umat</a>, <a href="#Col">uvec</a>, <a href="#min_and_max_member">.min()</a> and <a href="#min_and_max_member">.max()</a>
max@0	9524 have been changed to use the <a href="#uword"><i>uword</i></a> type instead of the <i>u32</i> type;
max@0	9525 by default the <i>uword</i> and <i>u32</i> types are equivalent (ie. unsigned integer type with a minimum width 32 bits);
max@0	9526 however, when the use of 64 bit indices is enabled via ARMA_64BIT_WORD in <i>include/armadillo_bits/config.hpp</i>,
max@0	9527 the <i>uword</i> type then has a minimum width of 64 bits
max@0	9528 </ul>
max@0	9529 </li>
max@0	9530 <br>
max@0	9531 <li>Added in 2.2:
max@0	9532 <ul>
max@0	9533 <li><a href="#svd_econ">svd_econ()</a></li>
max@0	9534 <li><a href="#toeplitz">circ_toeplitz()</a></li>
max@0	9535 <li><a href="#is_vec">.is_colvec()</a> and <a href="#is_vec">.is_rowvec()</a></li>
max@0	9536 </ul>
max@0	9537 <br>
max@0	9538 <li>Changed in 2.0:
max@0	9539 <ul>
max@0	9540 <li><a href="#trans">trans()</a> now takes the complex conjugate when transposing a complex matrix</li>
max@0	9541 <li>Forms of
max@0	9542 <a href="#chol">chol()</a>, <a href="#eig_sym">eig_sym()</a>, <a href="#eig_gen">eig_gen()</a>,
max@0	9543 <a href="#inv">inv()</a>, <a href="#lu">lu()</a>, <a href="#pinv">pinv()</a>, <a href="#princomp">princomp()</a>,
max@0	9544 <a href="#qr">qr()</a>, <a href="#solve">solve()</a>, <a href="#svd">svd()</a>, <a href="#syl">syl()</a>
max@0	9545 that do not return a bool indicating success now throw <i>std::runtime_error</i> exceptions when failures are detected</li>
max@0	9546 <li>princomp_cov() has been removed; <a href="#eig_sym">eig_sym()</a> in conjunction with <a href="#cov">cov()</a> can be used instead</li>
max@0	9547 <li><a href="#is_vec">.is_vec()</a> now outputs <i>true</i> for empty vectors (eg. 0x1)</li>
max@0	9548 <li>set_log_stream() & get_log_stream() have been replaced by <a href="#logging">set_stream_err1()</a> & <a href="#logging">get_stream_err1()</a></li>
max@0	9549 </ul>
max@0	9550 <br>
max@0	9551 <li>Added in 2.0:
max@0	9552 <ul>
max@0	9553 <li><a href="#det">det()</a>, <a href="#inv">inv()</a> and <a href="#solve">solve()</a> can be forced to use more precise algorithms for tiny matrices (≤ 4x4)</li>
max@0	9554 <li><a href="#syl">syl()</a>, for solving Sylvester's equation</li>
max@0	9555 <li><a href="#strans">strans()</a>, for transposing a complex matrix without taking the complex conjugate</li>
max@0	9556 <li><a href="#symmat">symmatu()</a> and <a href="#symmat">symmatl()</a></li>
max@0	9557 <li>submatrices of <a href="#submat">submatrices</a></li>
max@0	9558 <li>faster <a href="#inv">inverse</a> of symmetric positive definite matrices</li>
max@0	9559 <li>faster element access for <a href="#adv_constructors_mat_fixed">fixed size</a> matrices</li>
max@0	9560 <li>faster multiplication of tiny matrices (eg. 4x4)</li>
max@0	9561 <li>faster compound expressions containing <a href="#submat">submatrices</a></li>
max@0	9562 <li>handling of arbitrarily sized empty matrices (eg. 5x0)</li>
max@0	9563 <li>.count() member function in <a href="#running_stat">running_stat</a> and <a href="#running_stat_vec">running_stat_vec</a></li>
max@0	9564 <li><a href="#save_load_mat">loading & saving</a> of matrices as CSV text files</li>
max@0	9565 </ul>
max@0	9566 <br>
max@0	9567 <li>Added in 1.2:
max@0	9568 <ul>
max@0	9569 <li><a href="#min_and_max_member">.min() & .max()</a> member functions of Mat and Cube</li>
max@0	9570 <li><a href="#misc_fns">floor()</a> and <a href="#misc_fns">ceil()</a></li>
max@0	9571 <li>representation of “not a number”: <a href="#math_constants">math::nan()</a></li>
max@0	9572 <li>representation of infinity: <a href="#math_constants">math::inf()</a></li>
max@0	9573 <li>standalone <a href="#is_finite_standalone">is_finite()</a></li>
max@0	9574 <li><a href="#in_range">.in_range()</a> can use <b>span()</b> arguments</li>
max@0	9575 <li><a href="#adv_constructors_mat">fixed size</a> matrices and vectors can use auxiliary (external) memory</li>
max@0	9576 <li><a href="#submat">submatrices</a> and <a href="#subfield">subfields</a> can be accessed via <i><b>X(</b> <b>span(</b>a,b<b>)</b>, <b>span(</b>c,d<b>)</b> <b>)</b></i></li>
max@0	9577 <li><a href="#subcube">subcubes</a> can be accessed via <i><b>X(</b> <b>span(</b>a,b<b>)</b>, <b>span(</b>c,d<b>)</b>, <b>span(</b>e,f<b>)</b> <b>)</b></i></li>
max@0	9578 <li>the two argument version of <i><b>span</b></i> can be replaced by
max@0	9579 <i><b>span::all</b></i> or <i><b>span()</b></i>, to indicate an entire range
max@0	9580 </li>
max@0	9581 <li>for cubes, the two argument version of <i><b>span</b></i> can be replaced by
max@0	9582 a single argument version, <i><b>span(</b>a<b>)</b></i>, to indicate a single column, row or slice
max@0	9583 </li>
max@0	9584 <li>arbitrary "flat" subcubes can be interpreted as matrices; for example:
max@0	9585 <ul>
max@0	9586 <pre>
max@0	9587 cube Q = randu<cube>(5,3,4);
max@0	9588 mat A = Q( span(1), span(1,2), span::all );
max@0	9589 // A has a size of 2x4
max@0	9590
max@0	9591 vec v = ones<vec>(4);
max@0	9592 Q( span(1), span(1), span::all ) = v;
max@0	9593 </pre>
max@0	9594 </ul>
max@0	9595 </li>
max@0	9596 <li>interpretation of matrices as triangular through <a href="#trimat">trimatu() / trimatl()</a></li>
max@0	9597 <li>explicit handling of triangular matrices by <a href="#solve">solve()</a> and <a href="#inv">inv()</a></li>
max@0	9598 <li>extended syntax for <a href="#submat">submatrices</a>, including access to elements whose indices are specified in a vector</li>
max@0	9599 <li>ability to change the stream used for <a href="#logging">logging</a> of errors and warnings</li>
max@0	9600 <li>ability to <a href="#save_load_mat">save/load matrices</a> in raw binary format</li>
max@0	9601 <li>cumulative sum function: <a href="#cumsum">cumsum()</a></li>
max@0	9602 </ul>
max@0	9603 </li>
max@0	9604 <br>
max@0	9605 <li>
max@0	9606 Changed in 1.0 (compared to earlier 0.x development versions):
max@0	9607 <ul>
max@0	9608 <li>
max@0	9609 the 3 argument version of <a href="#lu">lu()</a>,
max@0	9610 eg. lu(L,U,X),
max@0	9611 provides L and U which should be the same as produced by Octave 3.2
max@0	9612 (this was not the case in versions prior to 0.9.90)
max@0	9613 </li>
max@0	9614 <br>
max@0	9615 <li>
max@0	9616 rand() has been replaced by <a href="#randu_randn_standalone">randu()</a>;
max@0	9617 this has been done to avoid confusion with <a href="http://cplusplus.com/reference/clibrary/cstdlib/rand/">std::rand()</a>,
max@0	9618 which generates random numbers in a different interval
max@0	9619 </li>
max@0	9620 <br>
max@0	9621 <li>
max@0	9622 In versions earlier than 0.9.0,
max@0	9623 some multiplication operations directly converted result matrices with a size of 1x1 into scalars.
max@0	9624 This is no longer the case.
max@0	9625 If you know the result of an expression will be a 1x1 matrix and wish to treat it as a pure scalar,
max@0	9626 use the <a href="#as_scalar">as_scalar()</a> wrapping function
max@0	9627 </li>
max@0	9628 <br>
max@0	9629 <li>
max@0	9630 Almost all functions have been placed in the delayed operations framework (for speed purposes).
max@0	9631 This may affect code which assumed that the output of some functions was a pure matrix.
max@0	9632 The solution is easy, as explained below.
max@0	9633 <br>
max@0	9634 <br>
max@0	9635 In general, Armadillo queues operations before executing them.
max@0	9636 As such, the direct output of an operation or function cannot be assumed to be a directly accessible matrix.
max@0	9637 The queued operations are executed when the output needs to be stored in a matrix,
max@0	9638 eg. <i>mat B = trans(A)</i> or <i>mat B(trans(A))</i>.
max@0	9639 If you need to force the execution of the delayed operations,
max@0	9640 place the operation or function inside the corresponding Mat constructor.
max@0	9641 For example, if your code assumed that the output of some functions was a pure matrix,
max@0	9642 eg. <i>chol(m).diag()</i>, change the code to <i>mat(chol(m)).diag()</i>.
max@0	9643 Similarly, if you need to pass the result of an operation such as <i>A+B</i> to one of your own functions,
max@0	9644 use <i>my_function( mat(A+B) )</i>.
max@0	9645 </li>
max@0	9646 </ul>
max@0	9647 </li>
max@0	9648 <br>
max@0	9649 </ul>
max@0	9650 <br>
max@0	9651 <br>
max@0	9652
max@0	9653
max@0	9654 <!-- END CONTENT -->
max@0	9655
max@0	9656
max@0	9657 <hr>
max@0	9658 <br>
max@0	9659 <br>
max@0	9660
max@0	9661 </td>
max@0	9662 </tr>
max@0	9663 </tbody>
max@0	9664 </table>
max@0	9665 </center>
max@0	9666 </body>
max@0	9667 </html>

Mercurial > hg > segmenter-vamp-plugin

annotate armadillo-2.4.4/docs/index.html @ 36:cc18e9a13fe8 slimline