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<a name="Data-changing"></a>
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<a name="Data-changing-1"></a>
<h2 class="section">6.7 Data changing</h2>
<a name="index-CumSum"></a>
<a name="index-Integral"></a>
<a name="index-Diff"></a>
<a name="index-Diff2"></a>
<a name="index-SinFFT"></a>
<a name="index-CosFFT"></a>
<a name="index-Hankel"></a>
<a name="index-Swap"></a>
<a name="index-Roll"></a>
<a name="index-Mirror"></a>
<a name="index-Sew"></a>
<a name="index-Smooth"></a>
<a name="index-Envelop"></a>
<a name="index-Norm"></a>
<a name="index-NormSl"></a>

<p>These functions change the data in some direction like differentiations, integrations and so on. The direction in which the change will applied is specified by the string parameter, which may contain &lsquo;<samp>x</samp>&rsquo;, &lsquo;<samp>y</samp>&rsquo; or &lsquo;<samp>z</samp>&rsquo; characters for 1-st, 2-nd and 3-d dimension correspondingly.
</p>
<p><a name="cumsum"></a>
</p><dl>
<dt><a name="index-cumsum"></a><u>MGL command:</u> <b>cumsum</b><i> dat 'dir'</i></dt>
<dt><a name="index-CumSum-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>CumSum</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-CumSum-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>CumSum</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fcumsum"></a><u>C function:</u> <code>void</code> <b>mgl_data_cumsum</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdatac_005fcumsum"></a><u>C function:</u> <code>void</code> <b>mgl_datac_cumsum</b><i> (<code>HADT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Cumulative summation of the data in given direction or directions.
</p></dd></dl>

<p><a name="integrate"></a>
</p><dl>
<dt><a name="index-integrate"></a><u>MGL command:</u> <b>integrate</b><i> dat 'dir'</i></dt>
<dt><a name="index-Integral-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Integral</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-Integral-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>Integral</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fintegral"></a><u>C function:</u> <code>void</code> <b>mgl_data_integral</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdatac_005fintegral"></a><u>C function:</u> <code>void</code> <b>mgl_datac_integral</b><i> (<code>HADT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Integrates (like cumulative summation) the data in given direction or directions.
</p></dd></dl>

<p><a name="diff"></a>
</p><dl>
<dt><a name="index-diff"></a><u>MGL command:</u> <b>diff</b><i> dat 'dir'</i></dt>
<dt><a name="index-Diff-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Diff</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-Diff-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>Diff</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fdiff"></a><u>C function:</u> <code>void</code> <b>mgl_data_diff</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdatac_005fdiff"></a><u>C function:</u> <code>void</code> <b>mgl_datac_diff</b><i> (<code>HADT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Differentiates the data in given direction or directions.
</p></dd></dl>

<dl>
<dt><a name="index-diff-1"></a><u>MGL command:</u> <b>diff</b><i> dat xdat ydat [zdat=0]</i></dt>
<dt><a name="index-Diff-3"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Diff</b><i> (<code>const mglDataA &amp;</code>x, <code>const mglDataA &amp;</code>y)</i></dt>
<dt><a name="index-Diff-4"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Diff</b><i> (<code>const mglDataA &amp;</code>x, <code>const mglDataA &amp;</code>y, <code>const mglDataA &amp;</code>z)</i></dt>
<dt><a name="index-mgl_005fdata_005fdiff_005fpar"></a><u>C function:</u> <code>void</code> <b>mgl_data_diff_par</b><i> (<code>HMDT</code> dat, <code>HCDT</code> x, <code>HCDT</code>y, <code>HCDT</code>z)</i></dt>
<dd><p>Differentiates the data specified parametrically in direction <var>x</var> with <var>y</var>, <var>z</var>=constant. Parametrical differentiation uses the formula (for 2D case): <em>da/dx = (a_j*y_i-a_i*y_j)/(x_j*y_i-x_i*y_j)</em> where <em>a_i=da/di, a_j=da/dj</em> denotes usual differentiation along 1st and 2nd dimensions. The similar formula is used for 3D case. Note, that you may change the order of arguments &ndash; for example, if you have 2D data a(i,j) which depend on coordinates {x(i,j), y(i,j)} then usual derivative along &lsquo;<samp>x</samp>&rsquo; will be <code>Diff(x,y);</code> and usual derivative along &lsquo;<samp>y</samp>&rsquo; will be <code>Diff(y,x);</code>.
</p></dd></dl>

<p><a name="diff2"></a>
</p><dl>
<dt><a name="index-diff2"></a><u>MGL command:</u> <b>diff2</b><i> dat 'dir'</i></dt>
<dt><a name="index-Diff2-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Diff2</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-Diff2-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>Diff2</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fdiff2"></a><u>C function:</u> <code>void</code> <b>mgl_data_diff2</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdatac_005fdiff2"></a><u>C function:</u> <code>void</code> <b>mgl_datac_diff2</b><i> (<code>HADT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Double-differentiates (like Laplace operator) the data in given direction.
</p></dd></dl>

<p><a name="sinfft"></a>
</p><dl>
<dt><a name="index-sinfft"></a><u>MGL command:</u> <b>sinfft</b><i> dat 'dir'</i></dt>
<dt><a name="index-SinFFT-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>SinFFT</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fsinfft"></a><u>C function:</u> <code>void</code> <b>mgl_data_sinfft</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Do Sine transform of the data in given direction or directions. The Sine transform is <em>\sum a_j \sin(k j)</em> (see <a href="http://en.wikipedia.org/wiki/Discrete_sine_transform#DST-I">http://en.wikipedia.org/wiki/Discrete_sine_transform#DST-I</a>).
</p></dd></dl>

<p><a name="cosfft"></a>
</p><dl>
<dt><a name="index-cosfft"></a><u>MGL command:</u> <b>cosfft</b><i> dat 'dir'</i></dt>
<dt><a name="index-CosFFT-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>CosFFT</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fcosfft"></a><u>C function:</u> <code>void</code> <b>mgl_data_cosfft</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Do Cosine transform of the data in given direction or directions. The Cosine transform is <em>\sum a_j \cos(k j)</em> (see <a href="http://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-I">http://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-I</a>).
</p></dd></dl>

<dl>
<dt><a name="index-FFT"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>FFT</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdatac_005ffft"></a><u>C function:</u> <code>void</code> <b>mgl_datac_fft</b><i> (<code>HADT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Do Fourier transform of the data in given direction or directions. If <var>dir</var> contain &lsquo;<samp>i</samp>&rsquo; then inverse Fourier is used. The Fourier transform is <em>\sum a_j \exp(i k j)</em> (see <a href="http://en.wikipedia.org/wiki/Discrete_Fourier_transform">http://en.wikipedia.org/wiki/Discrete_Fourier_transform</a>).
</p></dd></dl>

<p><a name="hankel"></a>
</p><dl>
<dt><a name="index-hankel"></a><u>MGL command:</u> <b>hankel</b><i> dat 'dir'</i></dt>
<dt><a name="index-Hankel-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Hankel</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-Hankel-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>Hankel</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fhankel"></a><u>C function:</u> <code>void</code> <b>mgl_data_hankel</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdatac_005fhankel"></a><u>C function:</u> <code>void</code> <b>mgl_datac_hankel</b><i> (<code>HADT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Do Hankel transform of the data in given direction or directions. The Hankel transform is <em>\sum a_j J_0(k j)</em> (see <a href="http://en.wikipedia.org/wiki/Hankel_transform">http://en.wikipedia.org/wiki/Hankel_transform</a>).
</p></dd></dl>

<p><a name="swap"></a>
</p><dl>
<dt><a name="index-swap"></a><u>MGL command:</u> <b>swap</b><i> dat 'dir'</i></dt>
<dt><a name="index-Swap-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Swap</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-Swap-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>Swap</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fswap"></a><u>C function:</u> <code>void</code> <b>mgl_data_swap</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdatac_005fswap"></a><u>C function:</u> <code>void</code> <b>mgl_datac_swap</b><i> (<code>HADT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Swaps the left and right part of the data in given direction (useful for Fourier spectrum).
</p></dd></dl>

<p><a name="roll"></a>
</p><dl>
<dt><a name="index-roll"></a><u>MGL command:</u> <b>roll</b><i> dat 'dir' num</i></dt>
<dt><a name="index-Roll-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Roll</b><i> (<code>char</code> dir, <code>num</code>)</i></dt>
<dt><a name="index-Roll-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>Roll</b><i> (<code>char</code> dir, <code>num</code>)</i></dt>
<dt><a name="index-mgl_005fdata_005froll"></a><u>C function:</u> <code>void</code> <b>mgl_data_roll</b><i> (<code>HMDT</code> dat, <code>char</code> dir, <code>num</code>)</i></dt>
<dt><a name="index-mgl_005fdatac_005froll"></a><u>C function:</u> <code>void</code> <b>mgl_datac_roll</b><i> (<code>HADT</code> dat, <code>char</code> dir, <code>num</code>)</i></dt>
<dd><p>Rolls the data along direction <var>dir</var>. Resulting array will be out[i] = ini[(i+<var>num</var>)%nx] if <code>dir='x'</code>.
</p></dd></dl>

<p><a name="mirror"></a>
</p><dl>
<dt><a name="index-mirror"></a><u>MGL command:</u> <b>mirror</b><i> dat 'dir'</i></dt>
<dt><a name="index-Mirror-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Mirror</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-Mirror-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>Mirror</b><i> (<code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdata_005fmirror"></a><u>C function:</u> <code>void</code> <b>mgl_data_mirror</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir)</i></dt>
<dt><a name="index-mgl_005fdatac_005fmirror"></a><u>C function:</u> <code>void</code> <b>mgl_datac_mirror</b><i> (<code>HADT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Mirror the left-to-right part of the data in given direction. Looks like change the value index <var>i</var>-&gt;<var>n-i</var>. Note, that the similar effect in graphics you can reach by using options (see section <a href="mathgl_en_27.html#Command-options">Command options</a>), for example, <code>surf dat; xrange 1 -1</code>.
</p></dd></dl>

<p><a name="sew"></a>
</p><dl>
<dt><a name="index-sew"></a><u>MGL command:</u> <b>sew</b><i> dat ['dir'='xyz' <code>da=2*pi</code>]</i></dt>
<dt><a name="index-Sew-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Sew</b><i> (<code>const char *</code>dir, <code>mreal</code> da=<code>2*M_PI</code>)</i></dt>
<dt><a name="index-mgl_005fdata_005fsew"></a><u>C function:</u> <code>void</code> <b>mgl_data_sew</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir, <code>mreal</code> da)</i></dt>
<dd><p>Remove value steps (like phase jumps after inverse trigonometric functions) with period <var>da</var> in given direction.
</p></dd></dl>

<p><a name="smooth"></a>
</p><dl>
<dt><a name="index-smooth"></a><u>MGL command:</u> <b>smooth</b><i> data <code>type</code> ['dir'='xyz']</i></dt>
<dt><a name="index-Smooth-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Smooth</b><i> (<code>const char *</code>dir=<code>&quot;xyz&quot;</code>, <code>mreal</code> delta=<code>0</code>)</i></dt>
<dt><a name="index-Smooth-2"></a><u>Method on <code>mglDataC</code>:</u> <code>void</code> <b>Smooth</b><i> (<code>const char *</code>dir=<code>&quot;xyz&quot;</code>, <code>mreal</code> delta=<code>0</code>)</i></dt>
<dt><a name="index-mgl_005fdata_005fsmooth"></a><u>C function:</u> <code>void</code> <b>mgl_data_smooth</b><i> (<code>HMDT</code> dat, <code>const char *</code>dir, <code>mreal</code> delta)</i></dt>
<dt><a name="index-mgl_005fdatac_005fsmooth"></a><u>C function:</u> <code>void</code> <b>mgl_datac_smooth</b><i> (<code>HADT</code> dat, <code>const char *</code>dir, <code>mreal</code> delta)</i></dt>
<dd><p>Smooths the data on specified direction or directions. String <var>dirs</var> specifies the dimensions which will be smoothed. It may contain characters: &lsquo;<samp>x</samp>&rsquo; for 1st dimension, &lsquo;<samp>y</samp>&rsquo; for 2nd dimension, &lsquo;<samp>z</samp>&rsquo; for 3d dimension. If string <var>dir</var> contain: &lsquo;<samp>0</samp>&rsquo; then does nothing, &lsquo;<samp>3</samp>&rsquo; &ndash; linear averaging over 3 points, &lsquo;<samp>5</samp>&rsquo; &ndash; linear averaging over 5 points. By default quadratic averaging over 5 points is used.
</p></dd></dl>

<p><a name="envelop"></a>
</p><dl>
<dt><a name="index-envelop"></a><u>MGL command:</u> <b>envelop</b><i> dat ['dir'='x']</i></dt>
<dt><a name="index-Envelop-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Envelop</b><i> (<code>char</code> dir=<code>'x'</code>)</i></dt>
<dt><a name="index-mgl_005fdata_005fenvelop"></a><u>C function:</u> <code>void</code> <b>mgl_data_envelop</b><i> (<code>HMDT</code> dat, <code>char</code> dir)</i></dt>
<dd><p>Find envelop for data values along direction <var>dir</var>.
</p></dd></dl>

<p><a name="norm"></a>
</p><dl>
<dt><a name="index-norm"></a><u>MGL command:</u> <b>norm</b><i> dat <code>v1 v2 [sym=off dim=0]</code></i></dt>
<dt><a name="index-Norm-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>Norm</b><i> (<code>mreal</code> v1=<code>0</code>, <code>mreal</code> v2=<code>1</code>, <code>bool</code> sym=<code>false</code>, <code>int</code> dim=<code>0</code>)</i></dt>
<dd><p>Normalizes the data to range [<var>v1</var>,<var>v2</var>]. If flag <var>sym</var>=<code>true</code> then symmetrical interval [-max(|v1|,|v2|), max(|v1|,|v2|)] is used. Modification will be applied only for slices &gt;=<var>dim</var>.
</p></dd></dl>

<p><a name="normsl"></a>
</p><dl>
<dt><a name="index-normsl"></a><u>MGL command:</u> <b>normsl</b><i> dat <code>v1 v2</code> ['dir'='z' <code>keep=on sym=off</code>]</i></dt>
<dt><a name="index-NormSl-1"></a><u>Method on <code>mglData</code>:</u> <code>void</code> <b>NormSl</b><i> (<code>mreal</code> v1=<code>0</code>, <code>mreal</code> v2=<code>1</code>, <code>char</code> dir=<code>'z'</code>, <code>bool</code> keep_en=<code>true</code>, <code>bool</code> sym=<code>false</code>)</i></dt>
<dt><a name="index-mgl_005fdata_005fnorm_005fslice"></a><u>C function:</u> <code>void</code> <b>mgl_data_norm_slice</b><i> (<code>HMDT</code> dat, <code>mreal</code> v1, <code>mreal</code> v2, <code>char</code> dir, <code>int</code> keep_en, <code>int</code> sym)</i></dt>
<dd><p>Normalizes data slice-by-slice along direction <var>dir</var> the data in slices to range [<var>v1</var>,<var>v2</var>]. If flag <var>sym</var>=<code>true</code> then symmetrical interval [-max(|v1|,|v2|), max(|v1|,|v2|)] is used. If <var>keep_en</var> is set then maximal value of k-th slice will be limited by
<em>\sqrt\sum a_ij(k)/\sum a_ij(0)</em>.
</p></dd></dl>


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