在Python中生成Hermite_e多项式的伪Vandermonde矩阵和x、y、z复数数组点

要生成Hermite_e多项式和x、y、z样本点的伪Vandermonde矩阵，请使用Python Numpy中的hermite_e.hermevander3d()方法。该方法返回伪Vandermonde矩阵。参数x、y、z是具有相同形状的点坐标数组。根据元素是否是复数，dtypes将被转换为float64或complex128。标量将转换为1-D数组。参数deg是形式为[x_deg, y_deg, z_deg]的最大度数的列表。

步骤

首先，导入所需的库−

import numpy as np
from numpy.polynomial import hermite_e as H

使用numpy.array()方法创建具有相同形状的点坐标数组-

x = np.array([-2.+2.j, -1.+2.j])
y = np.array([0.+2.j, 1.+2.j])
z = np.array([2.+2.j, 3. + 3.j])

显示数组 –

print("Array1...\n",x)
print("\nArray2...\n",y)
print("\nArray3...\n",z)

显示数据类型−

print("\nArray1 datatype...\n",x.dtype)
print("\nArray2 datatype...\n",y.dtype)
print("\nArray3 datatype...\n",z.dtype)

检查两个数组的维度 –

print("\nDimensions of Array1...\n",x.ndim)
print("\nDimensions of Array2...\n",y.ndim)
print("\nDimensions of Array3...\n",z.ndim)

检查两个数组的形状-

print("\nShape of Array1...\n",x.shape)
print("\nShape of Array2...\n",y.shape)
print("\nShape of Array3...\n",z.shape)

使用 hermite_e.hermevander3d() 方法来生成 Hermite_e 多项式和 x、y、z 样本点的伪 Vandermonde 矩阵。

x_deg, y_deg, z_deg = 2, 3, 4
print("\nResult...\n",H.hermevander3d(x,y,z, [x_deg, y_deg, z_deg]))

示例

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([-2.+2.j, -1.+2.j])
y = np.array([0.+2.j, 1.+2.j])
z = np.array([2.+2.j, 3. + 3.j])

# 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_e.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]))

输出

Array1...
   [-2.+2.j -1.+2.j]

Array2...
   [0.+2.j 1.+2.j]
   
Array3...
   [2.+2.j 3.+3.j]

Array1 datatype...
complex128

Array2 datatype...
complex128

Array3 datatype...
complex128

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...
   [[ 1.0000e+00 +0.000e+00j 2.0000e+00 +2.000e+00j  -1.0000e+00  +8.000e+00j
     -2.2000e+01 +1.000e+01j -6.1000e+01-4.800e+01j   0.0000e+00  +2.000e+00j
     -4.0000e+00 +4.000e+00j -1.6000e+01-2.000e+00j  -2.0000e+01 -4.400e+01j
      9.6000e+01 -1.220e+02j -5.0000e+00+0.000e+00j  -1.0000e+01 -1.000e+01j
      5.0000e+00 -4.000e+01j  1.1000e+02 -5.000e+01j  3.0500e+02 +2.400e+02j
      0.0000e+00 -1.400e+01j  2.8000e+01 -2.800e+01j  1.1200e+02 +1.400e+01j
      1.4000e+02 +3.080e+02j -6.7200e+02 +8.540e+02j -2.0000e+00 +2.000e+00j
     -8.0000e+00 +0.000e+00j -1.4000e+01 -1.800e+01j  2.4000e+01 -6.400e+01j
      2.1800e+02 -2.600e+01j -4.0000e+00 -4.000e+00j  0.0000e+00 -1.600e+01j
      3.6000e+01 -2.800e+01j  1.2800e+02 +4.800e+01j  5.2000e+01 +4.360e+02j
      1.0000e+01 -1.000e+01j  4.0000e+01 +0.000e+00j  7.0000e+01 +9.000e+01j
     -1.2000e+02 +3.200e+02j -1.0900e+03 +1.300e+02j  2.8000e+01 +2.800e+01j
      0.0000e+00 +1.120e+02j -2.5200e+02 +1.960e+02j -8.9600e+02 -3.360e+02j
     -3.6400e+02 -3.052e+03j -1.0000e+00 -8.000e+00j  1.4000e+01 -1.800e+01j
      6.5000e+01 +0.000e+00j  1.0200e+02 +1.660e+02j -3.2300e+02 +5.360e+02j
      1.6000e+01 -2.000e+00j  3.6000e+01 +2.800e+01j  0.0000e+00 +1.300e+02j
     -3.3200e+02 +2.040e+02j -1.0720e+03 -6.460e+02j  5.0000e+00 +4.000e+01j
     -7.0000e+01 +9.000e+01j -3.2500e+02 +0.000e+00j -5.1000e+02 -8.300e+02j
      1.6150e+03 -2.680e+03j -1.1200e+02 +1.400e+01j -2.5200e+02 -1.960e+02j
      0.0000e+00 -9.100e+02j  2.3240e+03 -1.428e+03j  7.5040e+03 +4.522e+03j]
    [ 1.0000e+00 +0.000e+00j  3.0000e+00 +3.000e+00j -1.0000e+00 +1.800e+01j
     -6.3000e+01 +4.500e+01j -3.2100e+02 -1.080e+02j  1.0000e+00 +2.000e+00j
     -3.0000e+00 +9.000e+00j -3.7000e+01 +1.600e+01j -1.5300e+02 -8.100e+01j
     -1.0500e+02 -7.500e+02j -4.0000e+00 +4.000e+00j -2.4000e+01 +0.000e+00j
     -6.8000e+01 -7.600e+01j  7.2000e+01 -4.320e+02j  1.7160e+03 -8.520e+02j
     -1.4000e+01 -8.000e+00j -1.8000e+01 -6.600e+01j  1.5800e+02 -2.440e+02j
     1.2420e+03  -1.260e+02j  3.6300e+03 +4.080e+03j -1.0000e+00 +2.000e+00j
    -9.0000e+00  +3.000e+00j -3.5000e+01 -2.000e+01j -2.7000e+01 -1.710e+02j
     5.3700e+02 -5.340e+02j  -5.0000e+00 +0.000e+00j -1.5000e+01 -1.500e+01j
     5.0000e+00 -9.000e+01j   3.1500e+02 -2.250e+02j  1.6050e+03 +5.400e+02j
    -4.0000e+00 -1.200e+01j   2.4000e+01 -4.800e+01j  2.2000e+02 -6.000e+01j
     7.9200e+02 +5.760e+02j  -1.2000e+01 +4.284e+03j  3.0000e+01 -2.000e+01j
     1.5000e+02 +3.000e+01j   3.3000e+02 +5.600e+02j -9.9000e+02  +2.610e+03j
    -1.1790e+04 +3.180e+03j  -4.0000e+00 -4.000e+00j  0.0000e+00  -2.400e+01j
     7.6000e+01 -6.800e+01j   4.3200e+02 +7.200e+01j  8.5200e+02  +1.716e+03j
     4.0000e+00 -1.200e+01j   4.8000e+01 -2.400e+01j  2.1200e+02  +8.400e+01j
     2.8800e+02 +9.360e+02j  -2.5800e+03 +3.420e+03j  3.2000e+01  +0.000e+00j
     9.6000e+01 +9.600e+01j  -3.2000e+01 +5.760e+02j -2.0160e+03  +1.440e+03j
   -1.0272e+04 -3.456e+03j   2.4000e+01  +8.800e+01j -1.9200e+02  +3.360e+02j
   -1.6080e+03 +3.440e+02j  -5.4720e+03  -4.464e+03j  1.8000e+03  -3.084e+04j]]