Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.3/doc/html/Complex-numbers.html @ 95:89f5e221ed7b

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add FFTW3
author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
parents
children
rev   line source
cannam@95 1 <html lang="en">
cannam@95 2 <head>
cannam@95 3 <title>Complex numbers - FFTW 3.3.3</title>
cannam@95 4 <meta http-equiv="Content-Type" content="text/html">
cannam@95 5 <meta name="description" content="FFTW 3.3.3">
cannam@95 6 <meta name="generator" content="makeinfo 4.13">
cannam@95 7 <link title="Top" rel="start" href="index.html#Top">
cannam@95 8 <link rel="up" href="Data-Types-and-Files.html#Data-Types-and-Files" title="Data Types and Files">
cannam@95 9 <link rel="prev" href="Data-Types-and-Files.html#Data-Types-and-Files" title="Data Types and Files">
cannam@95 10 <link rel="next" href="Precision.html#Precision" title="Precision">
cannam@95 11 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
cannam@95 12 <!--
cannam@95 13 This manual is for FFTW
cannam@95 14 (version 3.3.3, 25 November 2012).
cannam@95 15
cannam@95 16 Copyright (C) 2003 Matteo Frigo.
cannam@95 17
cannam@95 18 Copyright (C) 2003 Massachusetts Institute of Technology.
cannam@95 19
cannam@95 20 Permission is granted to make and distribute verbatim copies of
cannam@95 21 this manual provided the copyright notice and this permission
cannam@95 22 notice are preserved on all copies.
cannam@95 23
cannam@95 24 Permission is granted to copy and distribute modified versions of
cannam@95 25 this manual under the conditions for verbatim copying, provided
cannam@95 26 that the entire resulting derived work is distributed under the
cannam@95 27 terms of a permission notice identical to this one.
cannam@95 28
cannam@95 29 Permission is granted to copy and distribute translations of this
cannam@95 30 manual into another language, under the above conditions for
cannam@95 31 modified versions, except that this permission notice may be
cannam@95 32 stated in a translation approved by the Free Software Foundation.
cannam@95 33 -->
cannam@95 34 <meta http-equiv="Content-Style-Type" content="text/css">
cannam@95 35 <style type="text/css"><!--
cannam@95 36 pre.display { font-family:inherit }
cannam@95 37 pre.format { font-family:inherit }
cannam@95 38 pre.smalldisplay { font-family:inherit; font-size:smaller }
cannam@95 39 pre.smallformat { font-family:inherit; font-size:smaller }
cannam@95 40 pre.smallexample { font-size:smaller }
cannam@95 41 pre.smalllisp { font-size:smaller }
cannam@95 42 span.sc { font-variant:small-caps }
cannam@95 43 span.roman { font-family:serif; font-weight:normal; }
cannam@95 44 span.sansserif { font-family:sans-serif; font-weight:normal; }
cannam@95 45 --></style>
cannam@95 46 </head>
cannam@95 47 <body>
cannam@95 48 <div class="node">
cannam@95 49 <a name="Complex-numbers"></a>
cannam@95 50 <p>
cannam@95 51 Next:&nbsp;<a rel="next" accesskey="n" href="Precision.html#Precision">Precision</a>,
cannam@95 52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>,
cannam@95 53 Up:&nbsp;<a rel="up" accesskey="u" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>
cannam@95 54 <hr>
cannam@95 55 </div>
cannam@95 56
cannam@95 57 <h4 class="subsection">4.1.1 Complex numbers</h4>
cannam@95 58
cannam@95 59 <p>The default FFTW interface uses <code>double</code> precision for all
cannam@95 60 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
cannam@95 61 complex numbers as:
cannam@95 62
cannam@95 63 <pre class="example"> typedef double fftw_complex[2];
cannam@95 64 </pre>
cannam@95 65 <p><a name="index-fftw_005fcomplex-139"></a>
cannam@95 66 Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
cannam@95 67 element holds the imaginary part.
cannam@95 68
cannam@95 69 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
cannam@95 70 supports the C99 revision of the ANSI C standard, you can use C's new
cannam@95 71 native complex type (which is binary-compatible with the typedef above).
cannam@95 72 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
cannam@95 73 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
cannam@95 74 complex type and you can manipulate it with ordinary arithmetic
cannam@95 75 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
cannam@95 76 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
cannam@95 77 imaginary unit);
cannam@95 78 <a name="index-C99-140"></a>
cannam@95 79
cannam@95 80 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
cannam@95 81 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
cannam@95 82 committee has recently agreed to mandate that the storage format used
cannam@95 83 for this type be binary-compatible with the C99 type, i.e. an array
cannam@95 84 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
cannam@95 85 parts. (See report
cannam@95 86 <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf WG21/N1388</a>.) Although not part of the official standard as of this
cannam@95 87 writing, the proposal stated that: &ldquo;This solution has been tested with
cannam@95 88 all current major implementations of the standard library and shown to
cannam@95 89 be working.&rdquo; To the extent that this is true, if you have a variable
cannam@95 90 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
cannam@95 91 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
cannam@95 92 <a name="index-C_002b_002b-141"></a><a name="index-portability-142"></a>
cannam@95 93 <!-- =========> -->
cannam@95 94
cannam@95 95 </body></html>
cannam@95 96