Mercurial > hg > batch-feature-extraction-tool
diff Lib/fftw-3.2.1/doc/html/.svn/text-base/Multi_002dDimensional-DFTs-of-Real-Data.html.svn-base @ 15:585caf503ef5 tip
Tidy up for ROLI
| author | Geogaddi\David <d.m.ronan@qmul.ac.uk> |
|---|---|
| date | Tue, 17 May 2016 18:50:19 +0100 |
| parents | 636c989477e7 |
| children |
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--- a/Lib/fftw-3.2.1/doc/html/.svn/text-base/Multi_002dDimensional-DFTs-of-Real-Data.html.svn-base Wed May 04 11:02:59 2016 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,132 +0,0 @@ -<html lang="en"> -<head> -<title>Multi-Dimensional DFTs of Real Data - FFTW 3.2.1</title> -<meta http-equiv="Content-Type" content="text/html"> -<meta name="description" content="FFTW 3.2.1"> -<meta name="generator" content="makeinfo 4.8"> -<link title="Top" rel="start" href="index.html#Top"> -<link rel="up" href="Tutorial.html#Tutorial" title="Tutorial"> -<link rel="prev" href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" title="One-Dimensional DFTs of Real Data"> -<link rel="next" href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data" title="More DFTs of Real Data"> -<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> -<!-- -This manual is for FFTW -(version 3.2.1, 5 February 2009). - -Copyright (C) 2003 Matteo Frigo. - -Copyright (C) 2003 Massachusetts Institute of Technology. - - Permission is granted to make and distribute verbatim copies of - this manual provided the copyright notice and this permission - notice are preserved on all copies. - - Permission is granted to copy and distribute modified versions of - this manual under the conditions for verbatim copying, provided - that the entire resulting derived work is distributed under the - terms of a permission notice identical to this one. - - Permission is granted to copy and distribute translations of this - manual into another language, under the above conditions for - modified versions, except that this permission notice may be - stated in a translation approved by the Free Software Foundation. - --> -<meta http-equiv="Content-Style-Type" content="text/css"> -<style type="text/css"><!-- - pre.display { font-family:inherit } - pre.format { font-family:inherit } - pre.smalldisplay { font-family:inherit; font-size:smaller } - pre.smallformat { font-family:inherit; font-size:smaller } - pre.smallexample { font-size:smaller } - pre.smalllisp { font-size:smaller } - span.sc { font-variant:small-caps } - span.roman { font-family:serif; font-weight:normal; } - span.sansserif { font-family:sans-serif; font-weight:normal; } ---></style> -</head> -<body> -<div class="node"> -<p> -<a name="Multi-Dimensional-DFTs-of-Real-Data"></a> -<a name="Multi_002dDimensional-DFTs-of-Real-Data"></a> -Next: <a rel="next" accesskey="n" href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data">More DFTs of Real Data</a>, -Previous: <a rel="previous" accesskey="p" href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data">One-Dimensional DFTs of Real Data</a>, -Up: <a rel="up" accesskey="u" href="Tutorial.html#Tutorial">Tutorial</a> -<hr> -</div> - -<h3 class="section">2.4 Multi-Dimensional DFTs of Real Data</h3> - -<p>Multi-dimensional DFTs of real data use the following planner routines: - -<pre class="example"> fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1, - double *in, fftw_complex *out, - unsigned flags); - fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2, - double *in, fftw_complex *out, - unsigned flags); - fftw_plan fftw_plan_dft_r2c(int rank, const int *n, - double *in, fftw_complex *out, - unsigned flags); -</pre> - <p><a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-58"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-59"></a><a name="index-fftw_005fplan_005fdft_005fr2c-60"></a> -as well as the corresponding <code>c2r</code> routines with the input/output -types swapped. These routines work similarly to their complex -analogues, except for the fact that here the complex output array is cut -roughly in half and the real array requires padding for in-place -transforms (as in 1d, above). - - <p>As before, <code>n</code> is the logical size of the array, and the -consequences of this on the the format of the complex arrays deserve -careful attention. -<a name="index-r2c_002fc2r-multi_002ddimensional-array-format-61"></a>Suppose that the real data has dimensions n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> (in row-major order). -Then, after an r2c transform, the output is an n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1) array of -<code>fftw_complex</code> values in row-major order, corresponding to slightly -over half of the output of the corresponding complex DFT. (The division -is rounded down.) The ordering of the data is otherwise exactly the -same as in the complex-DFT case. - - <p>Since the complex data is slightly larger than the real data, some -complications arise for in-place transforms. In this case, the final -dimension of the real data must be padded with extra values to -accommodate the size of the complex data—two values if the last -dimension is even and one if it is odd. -<a name="index-padding-62"></a>That is, the last dimension of the real data must physically contain -2 * (n<sub>d-1</sub>/2+1)<code>double</code> values (exactly enough to hold the complex data). -This physical array size does not, however, change the <em>logical</em> -array size—only -n<sub>d-1</sub>values are actually stored in the last dimension, and -n<sub>d-1</sub>is the last dimension passed to the plan-creation routine. - - <p>For example, consider the transform of a two-dimensional real array of -size <code>n0</code> by <code>n1</code>. The output of the r2c transform is a -two-dimensional complex array of size <code>n0</code> by <code>n1/2+1</code>, where -the <code>y</code> dimension has been cut nearly in half because of -redundancies in the output. Because <code>fftw_complex</code> is twice the -size of <code>double</code>, the output array is slightly bigger than the -input array. Thus, if we want to compute the transform in place, we -must <em>pad</em> the input array so that it is of size <code>n0</code> by -<code>2*(n1/2+1)</code>. If <code>n1</code> is even, then there are two padding -elements at the end of each row (which need not be initialized, as they -are only used for output). - - <p>The following illustration depicts the input and output arrays just -described, for both the out-of-place and in-place transforms (with the -arrows indicating consecutive memory locations): - - <div class="block-image"><img src="rfftwnd.png" alt="rfftwnd.png"></div> - - <p>These transforms are unnormalized, so an r2c followed by a c2r -transform (or vice versa) will result in the original data scaled by -the number of real data elements—that is, the product of the -(logical) dimensions of the real data. -<a name="index-normalization-63"></a> -(Because the last dimension is treated specially, if it is equal to -<code>1</code> the transform is <em>not</em> equivalent to a lower-dimensional -r2c/c2r transform. In that case, the last complex dimension also has -size <code>1</code> (<code>=1/2+1</code>), and no advantage is gained over the -complex transforms.) - -<!-- --> -</body></html> -