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Generate a Pseudo Vandermonde matrix of the Legendre polynomial and x, y floating array of points in Python
<p>To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the legendre.legvander2d() method 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 Legendre polynomial. The dtype will be the same as the converted x.</p><p>The parameter, x, y is an array of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is a list of maximum degrees of the form [x_deg, y_deg].</p><h2>Steps</h2><p>At first, import the required library −</p><pre class="prettyprint notranslate">import numpy as np from numpy.polynomial import legendre as L</pre><p>Create arrays of point coordinates, all of the same shape using the numpy.array() method −</p><pre class="prettyprint notranslate">x = np.array([0.1, 1.4]) y = np.array([1.7, 2.8])</pre><p>Display the arrays −</p><pre class="prettyprint notranslate">print("Array1... ",x) print(" Array2... ",y)</pre><p>Display the datatype −</p><pre class="prettyprint notranslate">print(" Array1 datatype... ",x.dtype) print(" Array2 datatype... ",y.dtype)</pre><p>Check the Dimensions of both the arrays −</p><pre class="prettyprint notranslate">print(" Dimensions of Array1... ",x.ndim) print(" Dimensions of Array2... ",y.ndim)</pre><p>Check the Shape of both the arrays −</p><pre class="prettyprint notranslate">print(" Shape of Array1... ",x.shape) print(" Shape of Array2... ",y.shape)</pre><p>To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the legendre.legvander2d() method in Python Numpy −</p><pre class="prettyprint notranslate">x_deg, y_deg = 2, 3 print(" Result... ",L.legvander2d(x,y, [x_deg, y_deg]))</pre><h2>Example</h2><pre class="demo-code notranslate language-numpy" data-lang="numpy">import numpy as np from numpy.polynomial import legendre as L # Create arrays of point coordinates, all of the same shape using the numpy.array() method x = np.array([0.1, 1.4]) y = np.array([1.7, 2.8]) # Display the arrays print("Array1... ",x) print(" Array2... ",y) # Display the datatype print(" Array1 datatype... ",x.dtype) print(" Array2 datatype... ",y.dtype) # Check the Dimensions of both the arrays print(" Dimensions of Array1... ",x.ndim) print(" Dimensions of Array2... ",y.ndim) # Check the Shape of both the arrays print(" Shape of Array1... ",x.shape) print(" Shape of Array2... ",y.shape) # To generate a pseudo Vandermonde matrix of the Legendre polynomial, use the legendre.legvander2d() method in Python Numpy x_deg, y_deg = 2, 3 print(" Result... ",L.legvander2d(x,y, [x_deg, y_deg]))</pre><h2>Output</h2><pre class="result notranslate">Array1... [0.1 1.4] Array2... [1.7 2.8] Array1 datatype... float64 Array2 datatype... float64 Dimensions of Array1... 1 Dimensions of Array2... 1 Shape of Array1... (2,) Shape of Array2... (2,) Result... [[ 1.0000000e+00 1.7000000e+00 3.8350000e+00 9.7325000e+00 1.0000000e-01 1.7000000e-01 3.8350000e-01 9.7325000e-01 -4.8500000e-01 -8.2450000e-01 -1.8599750e+00 -4.7202625e+00] [ 1.0000000e+00 2.8000000e+00 1.1260000e+01 5.0680000e+01 1.4000000e+00 3.9200000e+00 1.5764000e+01 7.0952000e+01 2.4400000e+00 6.8320000e+00 2.7474400e+01 1.2365920e+02]]</pre>
Updated on 09-Mar-2022 06:34:11
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