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Generate a Vandermonde matrix of the Hermite_e polynomial with complex array of points in Python
<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 −</p><pre class="prettyprint notranslate">import numpy as np from numpy.polynomial import hermite_e as H</pre><p>Create an array −</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 −</p><pre class="prettyprint notranslate">print("Our Array... ",c)</pre><p>Check the Dimensions −</p><pre class="prettyprint notranslate">print(" Dimensions of our Array... ",c.ndim)</pre><p>Get the Datatype −</p><pre class="prettyprint notranslate">print(" Datatype of our Array object... ",c.dtype)</pre><p>Get the Shape −</p><pre class="prettyprint notranslate">print(" Shape of our Array object... ",c.shape)</pre><p>To generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.hermvander() in Python Numpy −</p><pre class="prettyprint notranslate">print(" Result... ",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("Our Array... ",x) # Check the Dimensions print(" Dimensions of our Array... ",x.ndim) # Get the Datatype print(" Datatype of our Array object... ",x.dtype) # Get the Shape print(" Shape of our Array object... ",x.shape) # To generate a Vandermonde matrix of the Hermite_e polynomial, use the hermite_e.hermvander() in Python Numpy print(" Result... ",H.hermevander(x, 2))</pre><h2>Output</h2><pre class="result notranslate">Our Array... [-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... [[ 1.+0.j -2.+2.j -1.-8.j] [ 1.+0.j -1.+2.j -4.-4.j] [ 1.+0.j 0.+2.j -5.+0.j] [ 1.+0.j 1.+2.j -4.+4.j] [ 1.+0.j 2.+2.j -1.+8.j]]</pre>
Updated on 09-Mar-2022 05:35:29
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