使用Python生成具有复数点坐标的Hermite多项式的伪Vandermonde矩阵

要生成Hermite多项式的伪Vandermonde矩阵，请使用Python Numpy中的hermite.hermvander2d()方法。该方法返回伪Vandermonde矩阵。参数x、y是具有相同形状的点坐标数组。根据元素是否为复数，数据类型将转换为float64或complex128。标量将转换为1-D数组。参数deg是形式为[x_deg, y_deg]的最大度的列表。

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])

显示数组 –

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)

检查两个数组的维度 –

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.hermvander2d()函数生成Hermite多项式的伪Vandermonde矩阵。该方法返回伪Vandermonde矩阵：

x_deg, y_deg = 2, 3
print("\nResult...\n",H.hermvander2d(x,y, [x_deg, y_deg]))

示例

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([-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 polynomial, use the hermite.hermvander2d() in Python Numpy
# The method returns the pseudo-Vandermonde matrix.

x_deg, y_deg = 2, 3
print("\nResult...\n",H.hermvander2d(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...
   [[ 1.000e+00 +0.j  2.000e+00  +4.j  -1.400e+01 +16.j  -1.000e+02 -40.j
     -4.000e+00 +4.j -2.400e+01  -8.j  -8.000e+00 -120.j  5.600e+02 -240.j
     -2.000e+00 -32.j 1.240e+02  -72.j  5.400e+02 +416.j -1.080e+03 +3280.j]
   [ 1.000e+00  +0.j  4.000e+00  +4.j  -2.000e+00 +32.j  -1.520e+02 +104.j
    -2.000e+00  +4.j -2.400e+01  +8.j  -1.240e+02 -72.j  -1.120e+02 -816.j
    -1.400e+01  -16.j 8.000e+00  -120.j 5.400e+02 -416.j  3.792e+03 +976.j]]