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]]