# Generate a Vandermonde matrix of the Hermite_e polynomial with complex array of points in Python

PythonNumpyServer Side ProgrammingProgramming

<p>To generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.hermvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1,), where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted x.</p><p>The parameter, x returns an Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. The parameter, deg is the degree of the resulting matrix.</p><h2>Steps</h2><p>At first, import the required library &minus;</p><pre class="prettyprint notranslate">import numpy as np from numpy.polynomial import hermite_e as H</pre><p>Create an array &minus;</p><pre class="prettyprint notranslate">x = np.array([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j])</pre><p>Display the array &minus;</p><pre class="prettyprint notranslate">print(&quot;Our Array... &quot;,c)</pre><p>Check the Dimensions &minus;</p><pre class="prettyprint notranslate">print(&quot; Dimensions of our Array... &quot;,c.ndim)</pre><p>Get the Datatype &minus;</p><pre class="prettyprint notranslate">print(&quot; Datatype of our Array object... &quot;,c.dtype)</pre><p>Get the Shape &minus;</p><pre class="prettyprint notranslate">print(&quot; Shape of our Array object... &quot;,c.shape)</pre><p>To generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.hermvander() in Python Numpy &minus;</p><pre class="prettyprint notranslate">print(&quot; Result... &quot;,H.hermevander(x, 2))</pre><h2>Example</h2><pre class="demo-code notranslate language-numpy" data-lang="numpy">import numpy as np from numpy.polynomial import hermite_e as H # Create an array x = np.array([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j]) # Display the array print(&quot;Our Array... &quot;,x) # Check the Dimensions print(&quot; Dimensions of our Array... &quot;,x.ndim) # Get the Datatype print(&quot; Datatype of our Array object... &quot;,x.dtype) # Get the Shape print(&quot; Shape of our Array object... &quot;,x.shape) # To generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.hermvander() in Python Numpy print(&quot; Result... &quot;,H.hermevander(x, 2))</pre><h2>Output</h2><pre class="result notranslate">Our Array... &nbsp; &nbsp;[-2.+2.j -1.+2.j 0.+2.j 1.+2.j 2.+2.j] Dimensions of our Array... 1 Datatype of our Array object... complex128 Shape of our Array object... (5,) Result... &nbsp; &nbsp;[[ 1.+0.j -2.+2.j -1.-8.j] &nbsp; &nbsp;[ 1.+0.j -1.+2.j -4.-4.j] &nbsp; &nbsp;[ 1.+0.j 0.+2.j -5.+0.j] &nbsp; &nbsp;[ 1.+0.j 1.+2.j -4.+4.j] &nbsp; &nbsp;[ 1.+0.j 2.+2.j -1.+8.j]]</pre>
Updated on 09-Mar-2022 05:35:29