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Generate a Pseudo Vandermonde matrix of the Laguerre polynomial and x, y, z floating array of points in Python
To generate a pseudo Vandermonde matrix of the Laguerre polynomial with x, y, z sample points, use the laguerre.lagvander3d() in Python Numpy. The parameter, x, y, z 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, z_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([1.5, 2.3]) y = np.array([3.7, 4.4]) z = np.array([5.3, 6.6])
Display the arrays −
print("Array1...\n",x)
print("\nArray2...\n",y)
print("\nArray3...\n",z)Display the datatype −
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
print("\nArray3 datatype...\n",z.dtype)Check the Dimensions of both the arrays −
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)Check the Shape of both the arrays −
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)To generate a pseudo Vandermonde matrix of the Laguerre polynomial with x, y, z sample points, use the laguerre.lagvander3d() in Python −
x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",L.lagvander3d(x,y,z, [x_deg, y_deg, z_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([1.5, 2.3])
y = np.array([3.7, 4.4])
z = np.array([5.3, 6.6])
# Display the arrays
print("Array1...\n",x)
print("\nArray2...\n",y)
print("\nArray3...\n",z)
# Display the datatype
print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
print("\nArray3 datatype...\n",z.dtype)
# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)
# Check the Shape of both the arrays
print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)
# To generate a pseudo Vandermonde matrix of the Laguerre polynomial with x, y, z sample points, use the laguerre.lagvander3d() in Python Numpy
x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",L.lagvander3d(x,y,z, [x_deg, y_deg, z_deg]))Output
Array1... [1.5 2.3] Array2... [3.7 4.4] Array3... [5.3 6.6] Array1 datatype... float64 Array2 datatype... float64 Array3 datatype... float64 Dimensions of Array1... 1 Dimensions of Array2... 1 Dimensions of Array3... 1 Shape of Array1... (2,) Shape of Array2... (2,) Shape of Array3... (2,) Result... [[ 1. -4.3 4.445 2.42216667 -2.30432917 -2.7 11.61 -12.0015 -6.53985 6.22168875 0.445 -1.9135 1.978025 1.07786417 -1.02542648 1.99283333 -8.56918333 8.85814417 4.82697447 -4.59214397 -0.5 2.15 -2.2225 -1.21108333 1.15216458 1.35 -5.805 6.00075 3.269925 -3.11084437 -0.2225 0.95675 -0.9890125 -0.53893208 0.51271324 -0.99641667 4.28459167 -4.42907208 -2.41348724 2.29607199 -0.875 3.7625 -3.889375 -2.11939583 2.01628802 2.3625 -10.15875 10.5013125 5.72236875 -5.44397766 -0.389375 1.6743125 -1.73077188 -0.94313115 0.89724817 -1.74372917 7.49803542 -7.75087615 -4.22360266 4.01812598] [ 1. -5.6 9.58 -1.376 -7.3226 -3.4 19.04 -32.572 4.6784 24.89684 1.88 -10.528 18.0104 -2.58688 -13.766488 2.64266667 -14.79893333 25.31674667 -3.63630933 -19.35119093 -1.3 7.28 -12.454 1.7888 9.51938 4.42 -24.752 42.3436 -6.08192 -32.365892 -2.444 13.6864 -23.41352 3.362944 17.8964344 -3.43546667 19.23861333 -32.91177067 4.72720213 25.15654821 -0.955 5.348 -9.1489 1.31408 6.993083 3.247 -18.1832 31.10626 -4.467872 -23.7764822 -1.7954 10.05424 -17.199932 2.4704704 13.14699604 -2.52374667 14.13298133 -24.17749307 3.47267541 18.48038734]]
Updated on: 07-Mar-2022
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