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Chris@42: (version 3.3.5, 30 July 2016).
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Chris@42: <title>FFTW 3.3.5: Real-to-Real Transforms</title>
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Chris@42: <a name="Real_002dto_002dReal-Transforms"></a>
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Chris@42: Next: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@42: </div>
Chris@42: <hr>
Chris@42: <a name="Real_002dto_002dReal-Transforms-1"></a>
Chris@42: <h4 class="subsection">4.3.5 Real-to-Real Transforms</h4>
Chris@42: <a name="index-r2r-1"></a>
Chris@42:
Chris@42: <div class="example">
Chris@42: <pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
Chris@42: fftw_r2r_kind kind, unsigned flags);
Chris@42: fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
Chris@42: fftw_r2r_kind kind0, fftw_r2r_kind kind1,
Chris@42: unsigned flags);
Chris@42: fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
Chris@42: double *in, double *out,
Chris@42: fftw_r2r_kind kind0,
Chris@42: fftw_r2r_kind kind1,
Chris@42: fftw_r2r_kind kind2,
Chris@42: unsigned flags);
Chris@42: fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
Chris@42: const fftw_r2r_kind *kind, unsigned flags);
Chris@42: </pre></div>
Chris@42: <a name="index-fftw_005fplan_005fr2r_005f1d-1"></a>
Chris@42: <a name="index-fftw_005fplan_005fr2r_005f2d-1"></a>
Chris@42: <a name="index-fftw_005fplan_005fr2r_005f3d-1"></a>
Chris@42: <a name="index-fftw_005fplan_005fr2r-1"></a>
Chris@42:
Chris@42: <p>Plan a real input/output (r2r) transform of various kinds in zero or
Chris@42: more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@42: </p>
Chris@42: <p>Once you have created a plan for a certain transform type and
Chris@42: parameters, then creating another plan of the same type and parameters,
Chris@42: but for different arrays, is fast and shares constant data with the
Chris@42: first plan (if it still exists).
Chris@42: </p>
Chris@42: <p>The planner returns <code>NULL</code> if the plan cannot be created. A
Chris@42: non-<code>NULL</code> plan is always returned by the basic interface unless
Chris@42: you are using a customized FFTW configuration supporting a restricted
Chris@42: set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are
Chris@42: not defined).
Chris@42: <a name="index-FFTW_005fREDFT00-1"></a>
Chris@42: </p>
Chris@42: <a name="Arguments-2"></a>
Chris@42: <h4 class="subsubheading">Arguments</h4>
Chris@42: <ul>
Chris@42: <li> <code>rank</code> is the dimensionality of the transform (it should be the
Chris@42: size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
Chris@42: non-negative integer. The ‘<samp>_1d</samp>’, ‘<samp>_2d</samp>’, and ‘<samp>_3d</samp>’
Chris@42: planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
Chris@42: <code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
Chris@42: of one number from input to output.
Chris@42:
Chris@42: </li><li> <code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
Chris@42: respectively, gives the (physical) size of the transform dimensions.
Chris@42: They can be any positive integer.
Chris@42:
Chris@42: <ul class="no-bullet">
Chris@42: <li>- <a name="index-row_002dmajor-2"></a>
Chris@42: Multi-dimensional arrays are stored in row-major order with dimensions:
Chris@42: <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
Chris@42: <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
Chris@42: See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@42: </li><li>- FFTW is generally best at handling sizes of the form
Chris@42: 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@42: 11<sup>e</sup> 13<sup>f</sup>,where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
Chris@42: are arbitrary. Other sizes are computed by means of a slow,
Chris@42: general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>) performance even for prime sizes). (It is possible to customize FFTW
Chris@42: for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
Chris@42: Transforms whose sizes are powers of <em>2</em> are especially fast.
Chris@42: </li><li>- For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
Chris@42: size <em>n</em>, it is <em>n-1</em> or <em>n+1</em>, respectively, that
Chris@42: should be factorizable in the above form.
Chris@42: </li></ul>
Chris@42:
Chris@42: </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@42: transform, which may be the same (yielding an in-place transform).
Chris@42: <a name="index-in_002dplace-5"></a>
Chris@42: These arrays are overwritten during planning, unless
Chris@42: <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@42: initialized, but they must be allocated.)
Chris@42:
Chris@42: </li><li> <code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
Chris@42: <code>kind[rank]</code>, is the kind of r2r transform used for the
Chris@42: corresponding dimension. The valid kind constants are described in
Chris@42: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform,
Chris@42: what is computed is the separable product formed by taking each
Chris@42: transform kind along the corresponding dimension, one dimension after
Chris@42: another.
Chris@42:
Chris@42: </li><li> <a name="index-flags-4"></a>
Chris@42: <code>flags</code> is a bitwise OR (‘<samp>|</samp>’) of zero or more planner flags,
Chris@42: as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@42:
Chris@42: </li></ul>
Chris@42:
Chris@42: <hr>
Chris@42: <div class="header">
Chris@42: <p>
Chris@42: Next: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic Interface</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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