在Python中使用复数坐标的Hermite_e多项式生成伪Vandermonde矩阵

要生成Hermite_e多项式的伪Vandermonde矩阵，可以使用Python Numpy中的hermite_e.hermevander2d()方法。该方法返回伪Vandermonde矩阵。参数x，y是一个具有相同形状的点坐标数组。元素的数据类型将根据是否存在复数来转换为float64或complex128。标量将转换为1-D数组。参数deg是形式为[x_deg，y_deg]的最大次数列表。

步骤

首先，导入所需的库−

import numpy as np
from numpy.polynomial import hermite 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([1.+2.j, 2.+2.j])

展示数组 –

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

显示数据类型 –

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

检查两个数组的尺寸 –

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

检查两个数组的形状 –

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

使用Python Numpy中的hermite_e.hermevander2d()函数生成Hermite_e多项式的伪范德蒙矩阵 −

x_deg, y_deg = 2, 3
print("\nResult...\n",H.hermevander2d(x,y, [x_deg, y_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([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 Hermite_e polynomial, use the hermite_e.hermevander2d() in Python Numpy
# The method returns the pseudo-Vandermonde matrix.

x_deg, y_deg = 2, 3
print("\nResult...\n",H.hermevander2d(x,y, [x_deg, y_deg]))

输出

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  1.  +2.j  -4. +4.j -14. -8.j  -2. +2.j  -6. -2.j
     0. -16.j  44. -12.j -1. -8.j  15. -10.j 36. +28.j -50.+120.j]
   [ 1.  +0.j  2.  +2.j  -1. +8.j -22. +10.j -1. +2.j  -6.  +2.j
   -15. -10.j  2. -54.j  -4. -4.j  0. -16.j  36. -28.j 128. +48.j]]