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Generate a Pseudo Vandermonde matrix of the Laguerre polynomial and x, y complex 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([-2.+2.j, -1.+2.j]) y = np.array([1.+2.j, 2.+2.j])
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([-2.+2.j, -1.+2.j])
y = np.array([1.+2.j, 2.+2.j])
# 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... [-2.+2.j -1.+2.j] Array2... [1.+2.j 2.+2.j] Array1 datatype... complex128 Array2 datatype... complex128 Dimensions of Array1... 1 Dimensions of Array2... 1 Shape of Array1... (2,) Shape of Array2... (2,) Result... [[ 1. +0.j 0. -2.j -2.5 -2.j -4.66666667 +0.33333333j 3. -2.j -4. -6.j -11.5 -1.j -13.33333333 +10.33333333j 5. -8.j -16. -10.j -28.5 +10.j -20.66666667 +39.j ] [ 1. +0.j -1. -2.j -3. +0.j -2.33333333 +3.33333333j 2. -2.j -6. -2.j -6. +6.j 2. +11.33333333j 1.5 -6.j -13.5 +3.j -4.5 +18.j 16.5 +19.j ]]
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