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<h4 class="subsection">4.3.6 Real-to-Real Transform Kinds</h4>
<p><a name="index-kind-_0028r2r_0029-212"></a>
FFTW currently supports 11 different r2r transform kinds, specified by
one of the constants below. For the precise definitions of these
transforms, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>. For a more colloquial
introduction to these transform kinds, see <a href="More-DFTs-of-Real-Data.html#More-DFTs-of-Real-Data">More DFTs of Real Data</a>.
<p>For dimension of size <code>n</code>, there is a corresponding “logical”
dimension <code>N</code> that determines the normalization (and the optimal
factorization); the formula for <code>N</code> is given for each kind below.
Also, with each transform kind is listed its corrsponding inverse
transform. FFTW computes unnormalized transforms: a transform followed
by its inverse will result in the original data multiplied by <code>N</code>
(or the product of the <code>N</code>'s for each dimension, in
multi-dimensions).
<a name="index-normalization-213"></a>
<ul>
<li><a name="index-FFTW_005fR2HC-214"></a><code>FFTW_R2HC</code> computes a real-input DFT with output in
“halfcomplex” format, i.e. real and imaginary parts for a transform of
size <code>n</code> stored as:
<p align=center>
r<sub>0</sub>, r<sub>1</sub>, r<sub>2</sub>, ..., r<sub>n/2</sub>, i<sub>(n+1)/2-1</sub>, ..., i<sub>2</sub>, i<sub>1</sub>
</p>(Logical <code>N=n</code>, inverse is <code>FFTW_HC2R</code>.)
<li><a name="index-FFTW_005fHC2R-215"></a><code>FFTW_HC2R</code> computes the reverse of <code>FFTW_R2HC</code>, above.
(Logical <code>N=n</code>, inverse is <code>FFTW_R2HC</code>.)
<li><a name="index-FFTW_005fDHT-216"></a><code>FFTW_DHT</code> computes a discrete Hartley transform.
(Logical <code>N=n</code>, inverse is <code>FFTW_DHT</code>.)
<a name="index-discrete-Hartley-transform-217"></a>
<li><a name="index-FFTW_005fREDFT00-218"></a><code>FFTW_REDFT00</code> computes an REDFT00 transform, i.e. a DCT-I.
(Logical <code>N=2*(n-1)</code>, inverse is <code>FFTW_REDFT00</code>.)
<a name="index-discrete-cosine-transform-219"></a><a name="index-DCT-220"></a>
<li><a name="index-FFTW_005fREDFT10-221"></a><code>FFTW_REDFT10</code> computes an REDFT10 transform, i.e. a DCT-II (sometimes called “the” DCT).
(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT01</code>.)
<li><a name="index-FFTW_005fREDFT01-222"></a><code>FFTW_REDFT01</code> computes an REDFT01 transform, i.e. a DCT-III (sometimes called “the” IDCT, being the inverse of DCT-II).
(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT=10</code>.)
<a name="index-IDCT-223"></a>
<li><a name="index-FFTW_005fREDFT11-224"></a><code>FFTW_REDFT11</code> computes an REDFT11 transform, i.e. a DCT-IV.
(Logical <code>N=2*n</code>, inverse is <code>FFTW_REDFT11</code>.)
<li><a name="index-FFTW_005fRODFT00-225"></a><code>FFTW_RODFT00</code> computes an RODFT00 transform, i.e. a DST-I.
(Logical <code>N=2*(n+1)</code>, inverse is <code>FFTW_RODFT00</code>.)
<a name="index-discrete-sine-transform-226"></a><a name="index-DST-227"></a>
<li><a name="index-FFTW_005fRODFT10-228"></a><code>FFTW_RODFT10</code> computes an RODFT10 transform, i.e. a DST-II.
(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT01</code>.)
<li><a name="index-FFTW_005fRODFT01-229"></a><code>FFTW_RODFT01</code> computes an RODFT01 transform, i.e. a DST-III.
(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT=10</code>.)
<li><a name="index-FFTW_005fRODFT11-230"></a><code>FFTW_RODFT11</code> computes an RODFT11 transform, i.e. a DST-IV.
(Logical <code>N=2*n</code>, inverse is <code>FFTW_RODFT11</code>.)
</ul>
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