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Generate a Pseudo Vandermonde matrix of the Laguerre polynomial and x, y floating array of points in Python
To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() 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 Laguerre polynomial. The dtype will be the same as the converted x.
The parameter, x, y 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 a list of maximum degrees of the form [x_deg, y_deg].
Steps
At first, import the required library −
import numpy as np from numpy.polynomial import laguerre 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...\n",x)
print("\nArray2...\n",y)Display the datatype −
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)Check the Dimensions of both the arrays −
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)Check the Shape of both the arrays −
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() in Python Numpy −
x_deg, y_deg = 2, 3
print("\nResult...\n",L.lagvander2d(x,y, [x_deg, y_deg]))Example
import numpy as np
from numpy.polynomial import laguerre 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...\n",x)
print("\nArray2...\n",y)
# Display the datatype
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
# Check the Shape of both the arrays
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
# To generate a pseudo Vandermonde matrix of the Laguerre polynomial, use the laguerre.lagvander2d() in Python Numpy
x_deg, y_deg = 2, 3
print("\nResult...\n",L.lagvander2d(x,y, [x_deg, y_deg]))Output
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. -0.7 -0.955 -0.58383333 0.9 -0.63
-0.8595 -0.52545 0.805 -0.5635 -0.768775 -0.46998583]
[ 1. -1.8 -0.68 0.70133333 -0.4 0.72
0.272 -0.28053333 -0.82 1.476 0.5576 -0.57509333]]
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