<html lang="en">
<head>
<title>Row-major Format - FFTW 3.3.3</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="FFTW 3.3.3">
<meta name="generator" content="makeinfo 4.13">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" title="Multi-dimensional Array Format">
<link rel="prev" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format" title="Multi-dimensional Array Format">
<link rel="next" href="Column_002dmajor-Format.html#Column_002dmajor-Format" title="Column-major Format">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<!--
This manual is for FFTW
(version 3.3.3, 25 November 2012).
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">
<a name="Row-major-Format"></a>
<a name="Row_002dmajor-Format"></a>
<p>
Next: <a rel="next" accesskey="n" href="Column_002dmajor-Format.html#Column_002dmajor-Format">Column-major Format</a>,
Previous: <a rel="previous" accesskey="p" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>,
Up: <a rel="up" accesskey="u" href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>
<hr>
</div>
<h4 class="subsection">3.2.1 Row-major Format</h4>
<p><a name="index-row_002dmajor-115"></a>
The multi-dimensional arrays passed to <code>fftw_plan_dft</code> etcetera
are expected to be stored as a single contiguous block in
<dfn>row-major</dfn> order (sometimes called “C order”). Basically, this
means that as you step through adjacent memory locations, the first
dimension's index varies most slowly and the last dimension's index
varies most quickly.
<p>To be more explicit, let us consider an array of rank d whose
dimensions are n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>. Now, we specify a location in the array by a
sequence of d (zero-based) indices, one for each dimension:
(i<sub>0</sub>, i<sub>1</sub>, i<sub>2</sub>,..., i<sub>d-1</sub>). If the array is stored in row-major
order, then this element is located at the position
i<sub>d-1</sub> + n<sub>d-1</sub> * (i<sub>d-2</sub> + n<sub>d-2</sub> * (... + n<sub>1</sub> * i<sub>0</sub>)).
<p>Note that, for the ordinary complex DFT, each element of the array
must be of type <code>fftw_complex</code>; i.e. a (real, imaginary) pair of
(double-precision) numbers.
<p>In the advanced FFTW interface, the physical dimensions n from
which the indices are computed can be different from (larger than)
the logical dimensions of the transform to be computed, in order to
transform a subset of a larger array.
<a name="index-advanced-interface-116"></a>Note also that, in the advanced interface, the expression above is
multiplied by a <dfn>stride</dfn> to get the actual array index—this is
useful in situations where each element of the multi-dimensional array
is actually a data structure (or another array), and you just want to
transform a single field. In the basic interface, however, the stride
is 1.
<a name="index-stride-117"></a>
<!-- =========> -->
</body></html>
