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<a name="Make-another-data-1"></a>
<h2 class="section">6.6 Make another data</h2>
<a name="index-SubData"></a>
<a name="index-Column"></a>
<a name="index-Trace"></a>
<a name="index-Hist-4"></a>
<a name="index-Resize"></a>
<a name="index-Evaluate"></a>
<a name="index-Combine-2"></a>
<a name="index-Momentum"></a>
<a name="index-Sum"></a>
<a name="index-Min"></a>
<a name="index-Max"></a>
<a name="index-Roots"></a>

<p><a name="subdata"></a>
</p><dl>
<dt><a name="index-subdata"></a><u>MGL command:</u> <b>subdata</b><i> <small>RES</small> dat <code>xx [yy=: zz=:]</code></i></dt>
<dt><a name="index-SubData-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>SubData</b><i> (<code>mreal</code> xx, <code>mreal</code> yy=<code>-1</code>, <code>mreal</code> zz=<code>-1</code>) <code>const</code></i></dt>
<dt><a name="index-SubData-2"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>SubData</b><i> (<code>mreal</code> xx, <code>mreal</code> yy=<code>-1</code>, <code>mreal</code> zz=<code>-1</code>) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fsubdata"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_subdata</b><i> (<code>HCDT</code> dat, <code>mreal</code> xx, <code>mreal</code> yy, <code>mreal</code> zz)</i></dt>
<dd><p>Extracts sub-array data from the original data array keeping fixed positive index. For example <code>SubData(-1,2)</code> extracts 3d row (indexes are zero based), <code>SubData(4,-1)</code> extracts 5th column, <code>SubData(-1,-1,3)</code> extracts 4th slice and so on. If argument(s) are non-integer then linear interpolation between slices is used. In MGL version this command usually is used as inline one <code>dat(xx,yy,zz)</code>.
</p></dd></dl>

<dl>
<dt><a name="index-subdata-1"></a><u>MGL command:</u> <b>subdata</b><i> <small>RES</small> dat xdat [ydat=: zdat=:]</i></dt>
<dt><a name="index-SubData-3"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>SubData</b><i> (<code>const mglDataA &amp;</code>xx, <code>const mglDataA &amp;</code>yy, <code>const mglDataA &amp;</code>zz) <code>const</code></i></dt>
<dt><a name="index-SubData-4"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>SubData</b><i> (<code>const mglDataA &amp;</code>xx, <code>const mglDataA &amp;</code>yy, <code>const mglDataA &amp;</code>zz) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fsubdata_005fext"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_subdata_ext</b><i> (<code>HCDT</code> dat, <code>HCDT</code> xx, <code>HCDT</code> yy, <code>HCDT</code> zz)</i></dt>
<dd><p>Extracts sub-array data from the original data array for indexes specified by arrays <var>xx</var>, <var>yy</var>, <var>zz</var> (indirect access). This function work like previous one for 1D arguments or numbers, and resulting array dimensions are equal dimensions of 1D arrays for corresponding direction. For 2D and 3D arrays in arguments, the resulting array have the same dimensions as input arrays. The dimensions of all argument must be the same (or to be scalar 1*1*1) if they are 2D or 3D arrays. In MGL version this command usually is used as inline one <code>dat(xx,yy,zz)</code>.
</p></dd></dl>

<p><a name="column"></a>
</p><dl>
<dt><a name="index-column"></a><u>MGL command:</u> <b>column</b><i> <small>RES</small> dat 'eq'</i></dt>
<dt><a name="index-Column-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Column</b><i> (<code>const char *</code>eq) <code>const</code></i></dt>
<dt><a name="index-Column-2"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Column</b><i> (<code>const char *</code>eq) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fcolumn"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_column</b><i> (<code>HCDT</code> dat, <code>const char *</code>eq)</i></dt>
<dd><p>Get column (or slice) of the data filled by formula <var>eq</var> on column ids. For example, <code>Column(&quot;n*w^2/exp(t)&quot;);</code>. The column ids must be defined first by <a href="mathgl_en_55.html#idset">idset</a> function or read from files. In MGL version this command usually is used as inline one <code>dat('eq')</code>.
</p></dd></dl>

<p><a name="resize"></a>
</p><dl>
<dt><a name="index-resize"></a><u>MGL command:</u> <b>resize</b><i> <small>RES</small> dat <code>mx [my=1 mz=1]</code></i></dt>
<dt><a name="index-Resize-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Resize</b><i> (<code>int</code> mx, <code>int</code> my=<code>1</code>, <code>int</code> mz=<code>1</code>, <code>mreal</code> x1=<code>0</code>, <code>mreal</code> x2=<code>1</code>, <code>mreal</code> y1=<code>0</code>, <code>mreal</code> y2=<code>1</code>, <code>mreal</code> z1=<code>0</code>, <code>mreal</code> z2=<code>1</code>) <code>const</code></i></dt>
<dt><a name="index-Resize-2"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Resize</b><i> (<code>int</code> mx, <code>int</code> my=<code>1</code>, <code>int</code> mz=<code>1</code>, <code>mreal</code> x1=<code>0</code>, <code>mreal</code> x2=<code>1</code>, <code>mreal</code> y1=<code>0</code>, <code>mreal</code> y2=<code>1</code>, <code>mreal</code> z1=<code>0</code>, <code>mreal</code> z2=<code>1</code>) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fresize"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_resize</b><i> (<code>HCDT</code> dat, <code>int</code> mx, <code>int</code> my, <code>int</code> mz)</i></dt>
<dt><a name="index-mgl_005fdata_005fresize_005fbox"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_resize_box</b><i> (<code>HCDT</code> dat, <code>int</code> mx, <code>int</code> my, <code>int</code> mz, <code>mreal</code> x1, <code>mreal</code> x2, <code>mreal</code> y1, <code>mreal</code> y2, <code>mreal</code> z1, <code>mreal</code> z2)</i></dt>
<dd><p>Resizes the data to new size <var>mx</var>, <var>my</var>, <var>mz</var> from box (part) [<var>x1</var>,<var>x2</var>] x [<var>y1</var>,<var>y2</var>] x [<var>z1</var>,<var>z2</var>] of original array. Initially x,y,z coordinates are supposed to be in [0,1].
</p></dd></dl>

<p><a name="evaluate"></a>
</p><dl>
<dt><a name="index-evaluate"></a><u>MGL command:</u> <b>evaluate</b><i> <small>RES</small> dat idat [<code>norm=on</code>]</i></dt>
<dt><a name="index-evaluate-1"></a><u>MGL command:</u> <b>evaluate</b><i> <small>RES</small> dat idat jdat [<code>norm=on</code>]</i></dt>
<dt><a name="index-evaluate-2"></a><u>MGL command:</u> <b>evaluate</b><i> <small>RES</small> dat idat jdat kdat [<code>norm=on</code>]</i></dt>
<dt><a name="index-Evaluate-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Evaluate</b><i> (<code>const mglDataA &amp;</code>idat, <code>bool</code> norm=<code>true</code>) <code>const</code></i></dt>
<dt><a name="index-Evaluate-2"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Evaluate</b><i> (<code>const mglDataA &amp;</code>idat, <code>const mglDataA &amp;</code>jdat, <code>bool</code> norm=<code>true</code>) <code>const</code></i></dt>
<dt><a name="index-Evaluate-3"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Evaluate</b><i> (<code>const mglDataA &amp;</code>idat, <code>const mglDataA &amp;</code>jdat, <code>const mglDataA &amp;</code>kdat, <code>bool</code> norm=<code>true</code>) <code>const</code></i></dt>
<dt><a name="index-Evaluate-4"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Evaluate</b><i> (<code>const mglDataA &amp;</code>idat, <code>bool</code> norm=<code>true</code>) <code>const</code></i></dt>
<dt><a name="index-Evaluate-5"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Evaluate</b><i> (<code>const mglDataA &amp;</code>idat, <code>const mglDataA &amp;</code>jdat, <code>bool</code> norm=<code>true</code>) <code>const</code></i></dt>
<dt><a name="index-Evaluate-6"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Evaluate</b><i> (<code>const mglDataA &amp;</code>idat, <code>const mglDataA &amp;</code>jdat, <code>const mglDataA &amp;</code>kdat, <code>bool</code> norm=<code>true</code>) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fevaluate"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_evaluate</b><i> (<code>HCDT</code> dat, <code>HCDT</code> idat, <code>HCDT</code> jdat, <code>HCDT</code> kdat, <code>int</code> norm)</i></dt>
<dd><p>Gets array which values is result of interpolation of original array for coordinates from other arrays. All dimensions must be the same for data <var>idat</var>, <var>jdat</var>, <var>kdat</var>. Coordinates from <var>idat</var>, <var>jdat</var>, <var>kdat</var> are supposed to be normalized in range [0,1] (if <var>norm</var>=<code>true</code>) or in ranges [0,nx], [0,ny], [0,nz] correspondingly.
</p></dd></dl>

<p><a name="solve"></a>
</p><dl>
<dt><a name="index-solve"></a><u>MGL command:</u> <b>solve</b><i> <small>RES</small> dat <code>val</code> 'dir' [<code>norm=on</code>]</i></dt>
<dt><a name="index-solve-1"></a><u>MGL command:</u> <b>solve</b><i> <small>RES</small> dat <code>val</code> 'dir' idat [<code>norm=on</code>]</i></dt>
<dt><a name="index-Solve"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Solve</b><i> (<code>mreal</code> val, <code>char</code> dir, <code>bool</code> norm=<code>true</code>) <code>const</code></i></dt>
<dt><a name="index-Solve-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Solve</b><i> (<code>mreal</code> val, <code>char</code> dir, <code>const mglDataA &amp;</code>idat, <code>bool</code> norm=<code>true</code>) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fsolve"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_solve</b><i> (<code>HCDT</code> dat, <code>mreal</code> val, <code>char</code> dir, <code>HCDT</code> idat, <code>int</code> norm)</i></dt>
<dd><p>Gets array which values is indexes (roots) along given direction <var>dir</var>, where interpolated values of data <var>dat</var> are equal to <var>val</var>. Output data will have the sizes of <var>dat</var> in directions transverse to <var>dir</var>. If data <var>idat</var> is provided then its values are used as starting points. This allows to find several branches by consequentive calls. Indexes are supposed to be normalized in range [0,1] (if <var>norm</var>=<code>true</code>) or in ranges [0,nx], [0,ny], [0,nz] correspondingly. See <a href="mathgl_en_12.html#Solve-sample">Solve sample</a>, for sample code and picture.
</p></dd></dl>

<p><a name="hist"></a>
</p><dl>
<dt><a name="index-hist-3"></a><u>MGL command:</u> <b>hist</b><i> <small>RES</small> dat <code>num v1 v2 [nsub=0]</code></i></dt>
<dt><a name="index-hist-4"></a><u>MGL command:</u> <b>hist</b><i> <small>RES</small> dat wdat <code>num v1 v2 [nsub=0]</code></i></dt>
<dt><a name="index-Hist-5"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Hist</b><i> (<code>int</code> n, <code>mreal</code> v1=<code>0</code>, <code>mreal</code> v2=<code>1</code>, <code>int</code> nsub=<code>0</code>) <code>const</code></i></dt>
<dt><a name="index-Hist-6"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Hist</b><i> (<code>const mglDataA &amp;</code>w, <code>int</code> n, <code>mreal</code> v1=<code>0</code>, <code>mreal</code> v2=<code>1</code>, <code>int</code> nsub=<code>0</code>) <code>const</code></i></dt>
<dt><a name="index-Hist-7"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Hist</b><i> (<code>int</code> n, <code>mreal</code> v1=<code>0</code>, <code>mreal</code> v2=<code>1</code>, <code>int</code> nsub=<code>0</code>) <code>const</code></i></dt>
<dt><a name="index-Hist-8"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Hist</b><i> (<code>const mglDataA &amp;</code>w, <code>int</code> n, <code>mreal</code> v1=<code>0</code>, <code>mreal</code> v2=<code>1</code>, <code>int</code> nsub=<code>0</code>) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fhist"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_hist</b><i> (<code>HCDT</code> dat, <code>int</code> n, <code>mreal</code> v1, <code>mreal</code> v2, <code>int</code> nsub)</i></dt>
<dt><a name="index-mgl_005fdata_005fhist_005fw"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_hist_w</b><i> (<code>HCDT</code> dat, <code>HCDT</code> w, <code>int</code> n, <code>mreal</code> v1, <code>mreal</code> v2, <code>int</code> nsub)</i></dt>
<dd><p>Creates <var>n</var>-th points distribution of the data values in range [<var>v1</var>, <var>v2</var>]. Array <var>w</var> specifies weights of the data elements (by default is 1). Parameter <var>nsub</var> define the number of additional interpolated points (for smoothness of histogram). See also <a href="mathgl_en_46.html#Data-manipulation">Data manipulation</a>
</p></dd></dl>

<p><a name="momentum"></a>
</p><dl>
<dt><a name="index-momentum"></a><u>MGL command:</u> <b>momentum</b><i> <small>RES</small> dat 'how' ['dir'='z']</i></dt>
<dt><a name="index-Momentum-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Momentum</b><i> (<code>char</code> dir, <code>const char *</code>how) <code>const</code></i></dt>
<dt><a name="index-Momentum-2"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Momentum</b><i> (<code>char</code> dir, <code>const char *</code>how) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fmomentum"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_momentum</b><i> (<code>HCDT</code> dat, <code>char</code> dir, <code>const char *</code>how)</i></dt>
<dd><p>Gets momentum (1d-array) of the data along direction <var>dir</var>. String <var>how</var> contain kind of momentum. The momentum is defined like as
res_k = \sum_ij how(x_i,y_j,z_k) a_ij/ \sum_ij a_ij
if <var>dir</var>=&lsquo;<samp>z</samp>&rsquo; and so on. Coordinates &lsquo;<samp>x</samp>&rsquo;, &lsquo;<samp>y</samp>&rsquo;, &lsquo;<samp>z</samp>&rsquo; are data indexes normalized in range [0,1].
</p></dd></dl>

<p><a name="sum"></a>
</p><dl>
<dt><a name="index-sum"></a><u>MGL command:</u> <b>sum</b><i> <small>RES</small> dat 'dir'</i></dt>
<dt><a name="index-Sum-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Sum</b><i> (<code>const char *</code>dir) <code>const</code></i></dt>
<dt><a name="index-Sum-2"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Sum</b><i> (<code>const char *</code>dir) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fsum"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_sum</b><i> (<code>HCDT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Gets array which is the result of summation in given direction or direction(s).
</p></dd></dl>

<p><a name="max"></a>
</p><dl>
<dt><a name="index-max"></a><u>MGL command:</u> <b>max</b><i> <small>RES</small> dat 'dir'</i></dt>
<dt><a name="index-Max-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Max</b><i> (<code>const char *</code>dir) <code>const</code></i></dt>
<dt><a name="index-Max-2"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Max</b><i> (<code>const char *</code>dir) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fmax_005fdir"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_max_dir</b><i> (<code>HCDT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Gets array which is the maximal data values in given direction or direction(s).
</p></dd></dl>

<p><a name="min"></a>
</p><dl>
<dt><a name="index-min"></a><u>MGL command:</u> <b>min</b><i> <small>RES</small> dat 'dir'</i></dt>
<dt><a name="index-Min-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Min</b><i> (<code>const char *</code>dir) <code>const</code></i></dt>
<dt><a name="index-Min-2"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Min</b><i> (<code>const char *</code>dir) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fmin_005fdir"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_min_dir</b><i> (<code>HCDT</code> dat, <code>const char *</code>dir)</i></dt>
<dd><p>Gets array which is the maximal data values in given direction or direction(s).
</p></dd></dl>

<p><a name="combine"></a>
</p><dl>
<dt><a name="index-combine"></a><u>MGL command:</u> <b>combine</b><i> <small>RES</small> adat bdat</i></dt>
<dt><a name="index-Combine-3"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Combine</b><i> (<code>const mglDataA &amp;</code>a) <code>const</code></i></dt>
<dt><a name="index-Combine-4"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Combine</b><i> (<code>const mglDataA &amp;</code>a) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005fcombine"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_combine</b><i> (<code>HCDT</code> dat, <code>HCDT</code> a)</i></dt>
<dd><p>Returns direct multiplication of arrays (like, res[i,j] = this[i]*a[j] and so on).
</p></dd></dl>

<p><a name="trace"></a>
</p><dl>
<dt><a name="index-trace"></a><u>MGL command:</u> <b>trace</b><i> <small>RES</small> dat</i></dt>
<dt><a name="index-Trace-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Trace</b><i> () <code>const</code></i></dt>
<dt><a name="index-Trace-2"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Trace</b><i> () <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005ftrace"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_trace</b><i> (<code>HCDT</code> dat)</i></dt>
<dd><p>Gets array of diagonal elements a[i,i] (for 2D case) or a[i,i,i] (for 3D case) where i=0...nx-1. Function return copy of itself for 1D case. Data array must have dimensions ny,nz &gt;= nx or ny,nz = 1.
</p></dd></dl>

<dl>
<dt><a name="index-Real"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Real</b><i> () <code>const</code></i></dt>
<dt><a name="index-mgl_005fdatac_005freal"></a><u>C function:</u> <code>HMDT</code> <b>mgl_datac_real</b><i> (<code>HCDT</code> dat)</i></dt>
<dd><p>Gets array of real parts of the data.
</p></dd></dl>
<dl>
<dt><a name="index-Imag"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Imag</b><i> () <code>const</code></i></dt>
<dt><a name="index-mgl_005fdatac_005fimag"></a><u>C function:</u> <code>HMDT</code> <b>mgl_datac_imag</b><i> (<code>HCDT</code> dat)</i></dt>
<dd><p>Gets array of imaginary parts of the data.
</p></dd></dl>
<dl>
<dt><a name="index-Abs"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Abs</b><i> () <code>const</code></i></dt>
<dt><a name="index-mgl_005fdatac_005fabs"></a><u>C function:</u> <code>HMDT</code> <b>mgl_datac_abs</b><i> (<code>HCDT</code> dat)</i></dt>
<dd><p>Gets array of absolute values of the data.
</p></dd></dl>
<dl>
<dt><a name="index-Arg"></a><u>Method on <code>mglDataC</code>:</u> <code>mglData</code> <b>Arg</b><i> () <code>const</code></i></dt>
<dt><a name="index-mgl_005fdatac_005farg"></a><u>C function:</u> <code>HMDT</code> <b>mgl_datac_arg</b><i> (<code>HCDT</code> dat)</i></dt>
<dd><p>Gets array of arguments of the data.
</p></dd></dl>

<p><a name="roots"></a>
</p><dl>
<dt><a name="index-roots"></a><u>MGL command:</u> <b>roots</b><i> <small>RES</small> 'func' ini ['var'='x']</i></dt>
<dt><a name="index-roots-1"></a><u>MGL command:</u> <b>roots</b><i> <small>RES</small> 'func' <code>ini</code> ['var'='x']</i></dt>
<dt><a name="index-Roots-1"></a><u>Method on <code>mglData</code>:</u> <code>mglData</code> <b>Roots</b><i> (<code>const char *</code>func, <code>char</code> var) <code>const</code></i></dt>
<dt><a name="index-mgl_005fdata_005froots"></a><u>C function:</u> <code>HMDT</code> <b>mgl_data_roots</b><i> (<code>const char *</code>func, <code>HCDT</code> ini, <code>char</code> var)</i></dt>
<dt><a name="index-mgl_005ffind_005froot_005ftxt"></a><u>C function:</u> <code>mreal</code> <b>mgl_find_root_txt</b><i> (<code>const char *</code>func, <code>mreal</code> ini, <code>char</code> var)</i></dt>
<dd><p>Find roots of equation &rsquo;func&rsquo;=0 for variable <var>var</var> with initial guess <var>ini</var>. Secant method is used for root finding.
</p></dd></dl>


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