Generate a Pseudo Vandermonde matrix of the Laguerre polynomial and x, y 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([1, 2])
y = np.array([3, 4])

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 array −

print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)

Check the Shape of both the array −

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([1, 2])
y = np.array([3, 4])

# 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 array
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)

# Check the Shape of both the array
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...
   [1 2]

Array2...
   [3 4]

Array1 datatype...
int64

Array2 datatype...
int64

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Result...
   [[ 1. -2.        -0.5 1.          0.   -0.
     -0. 0.         -0.5 1.          0.25 -0.5 ]
   [ 1. -3.          1.  2.33333333 -1.     3.
    -1. -2.33333333 -1.  3.         -1.    -2.33333333]]

AmitDiwan

e

Updated on: 04-Mar-2022

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