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<p>
<a name="Complex-numbers"></a>
Next: <a rel="next" accesskey="n" href="Properties-of-complex-numbers.html">Properties of complex numbers</a>,
Up: <a rel="up" accesskey="u" href="Complex-Numbers.html">Complex Numbers</a>
<hr>
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<h3 class="section">5.1 Complex numbers</h3>
<p><a name="index-representations-of-complex-numbers-137"></a><a name="index-polar-form-of-complex-numbers-138"></a><a name="index-gsl_005fcomplex-139"></a>
Complex numbers are represented using the type <code>gsl_complex</code>. The
internal representation of this type may vary across platforms and
should not be accessed directly. The functions and macros described
below allow complex numbers to be manipulated in a portable way.
<p>For reference, the default form of the <code>gsl_complex</code> type is
given by the following struct,
<pre class="example"> typedef struct
{
double dat[2];
} gsl_complex;
</pre>
<p class="noindent">The real and imaginary part are stored in contiguous elements of a two
element array. This eliminates any padding between the real and
imaginary parts, <code>dat[0]</code> and <code>dat[1]</code>, allowing the struct to
be mapped correctly onto packed complex arrays.
<div class="defun">
— Function: gsl_complex <b>gsl_complex_rect</b> (<var>double x, double y</var>)<var><a name="index-gsl_005fcomplex_005frect-140"></a></var><br>
<blockquote><p>This function uses the rectangular cartesian components
(<var>x</var>,<var>y</var>) to return the complex number z = x + i y. An inline version of this function is used when <code>HAVE_INLINE</code> is defined.
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_polar</b> (<var>double r, double theta</var>)<var><a name="index-gsl_005fcomplex_005fpolar-141"></a></var><br>
<blockquote><p>This function returns the complex number z = r \exp(i \theta) = r
(\cos(\theta) + i \sin(\theta)) from the polar representation
(<var>r</var>,<var>theta</var>).
</p></blockquote></div>
<div class="defun">
— Macro: <b>GSL_REAL</b> (<var>z</var>)<var><a name="index-GSL_005fREAL-142"></a></var><br>
— Macro: <b>GSL_IMAG</b> (<var>z</var>)<var><a name="index-GSL_005fIMAG-143"></a></var><br>
<blockquote><p>These macros return the real and imaginary parts of the complex number
<var>z</var>.
</p></blockquote></div>
<div class="defun">
— Macro: <b>GSL_SET_COMPLEX</b> (<var>zp, x, y</var>)<var><a name="index-GSL_005fSET_005fCOMPLEX-144"></a></var><br>
<blockquote><p>This macro uses the cartesian components (<var>x</var>,<var>y</var>) to set the
real and imaginary parts of the complex number pointed to by <var>zp</var>.
For example,
<pre class="example"> GSL_SET_COMPLEX(&z, 3, 4)
</pre>
<p class="noindent">sets <var>z</var> to be 3 + 4i.
</p></blockquote></div>
<div class="defun">
— Macro: <b>GSL_SET_REAL</b> (<var>zp,x</var>)<var><a name="index-GSL_005fSET_005fREAL-145"></a></var><br>
— Macro: <b>GSL_SET_IMAG</b> (<var>zp,y</var>)<var><a name="index-GSL_005fSET_005fIMAG-146"></a></var><br>
<blockquote><p>These macros allow the real and imaginary parts of the complex number
pointed to by <var>zp</var> to be set independently.
</p></blockquote></div>
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