Hermite_e polynomial and x, y, z sample points, use the hermite.hermevander3d() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The parameter, x, y, z are arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. The parameter, deg is the 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 hermite as H
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 Hermite_e polynomial and x, y, z sample points, use the hermite.hermevander3d() in Python Numpy −
x_deg, y_deg, z_deg = 2, 3, 4 print("\nResult...\n",H.hermevander3d(x,y,z, [x_deg, y_deg, z_deg]))
Example
import numpy as np from numpy.polynomial import hermite_e as H # 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 Hermite_e polynomial and x, y, z sample points, use the hermite.hermevander3d() in Python Numpy x_deg, y_deg, z_deg = 2, 3, 4 print("\nResult...\n",H.hermevander3d(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... [[1.00000e+00 5.00000e+00 2.40000e+01 1.10000e+02 4.78000e+02 3.00000e+00 1.50000e+01 7.20000e+01 3.30000e+02 1.43400e+03 8.00000e+00 4.00000e+01 1.92000e+02 8.80000e+02 3.82400e+03 1.80000e+01 9.00000e+01 4.32000e+02 1.98000e+03 8.60400e+03 1.00000e+00 5.00000e+00 2.40000e+01 1.10000e+02 4.78000e+02 3.00000e+00 1.50000e+01 7.20000e+01 3.30000e+02 1.43400e+03 8.00000e+00 4.00000e+01 1.92000e+02 8.80000e+02 3.82400e+03 1.80000e+01 9.00000e+01 4.32000e+02 1.98000e+03 8.60400e+03 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00] [1.00000e+00 6.00000e+00 3.50000e+01 1.98000e+02 1.08300e+03 4.00000e+00 2.40000e+01 1.40000e+02 7.92000e+02 4.33200e+03 1.50000e+01 9.00000e+01 5.25000e+02 2.97000e+03 1.62450e+04 5.20000e+01 3.12000e+02 1.82000e+03 1.02960e+04 5.63160e+04 2.00000e+00 1.20000e+01 7.00000e+01 3.96000e+02 2.16600e+03 8.00000e+00 4.80000e+01 2.80000e+02 1.58400e+03 8.66400e+03 3.00000e+01 1.80000e+02 1.05000e+03 5.94000e+03 3.24900e+04 1.04000e+02 6.24000e+02 3.64000e+03 2.05920e+04 1.12632e+05 3.00000e+00 1.80000e+01 1.05000e+02 5.94000e+02 3.24900e+03 1.20000e+01 7.20000e+01 4.20000e+02 2.37600e+03 1.29960e+04 4.50000e+01 2.70000e+02 1.57500e+03 8.91000e+03 4.87350e+04 1.56000e+02 9.36000e+02 5.46000e+03 3.08880e+04 1.68948e+05]]