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Generate a Pseudo Vandermonde matrix of the Laguerre polynomial and x, y, z sample 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, 2]) y = np.array([3, 4]) z = np.array([5, 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, 2]) y = np.array([3, 4]) z = np.array([5, 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 2] Array2... [3 4] Array3... [5 6] Array1 datatype... int64 Array2 datatype... int64 Array3 datatype... int64 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. 3.5 2.66666667 -1.29166667 -2. 8. -7. -5.33333333 2.58333333 -0.5 2. -1.75 -1.33333333 0.64583333 1. -4. 3.5 2.66666667 -1.29166667 0. -0. 0. 0. -0. -0. 0. -0. -0. 0. -0. 0. -0. -0. 0. 0. - 0. 0. 0. -0. -0.5 2. -1.75 -1.33333333 0.64583333 1. -4. 3.5 2.66666667 -1.29166667 0.25 -1. 0.875 0.66666667 -0.32291667 -0.5 2. -1.75 -1.33333333 0.64583333] [ 1. -5. 7. 1. -5. -3. 15. -21. -3. 15. 1. -5. 7. 1. -5. 2.33333333 -11.66666667 16.33333333 2.33333333 -11.66666667 -1. 5. -7. -1. 5. 3. -15. 21. 3. -15. -1. 5. -7. -1. 5. -2.33333333 11.66666667 -16.33333333 -2.33333333 11.66666667 -1. 5. -7. -1. 5. 3. -15. 21. 3. -15. -1. 5. -7. -1. 5. -2.33333333 11.66666667 -16.33333333 -2.33333333 11.66666667]]
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