在Python中生成Hermite_e多项式的伪Vandermonde矩阵

要生成Hermite_e多项式的伪Vandermonde矩阵，请使用Python Numpy中的hermite_e.hermevander2d()方法。该方法返回伪Vandermonde矩阵。参数x、y是坐标点的数组，形状相同。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是最大度数的列表，形式为[x_deg, y_deg]。

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([1, 2])
y = np.array([3, 4])

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)

要生成Hermite_e多项式的伪Vandermonde矩阵，在Python Numpy中使用hermite_e.hermevander2d()函数−

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([1, 2])
y = np.array([3, 4])

# 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

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

输出

Array1...
   [1 2]

Array2...
   [3 4]

Array1 datatype...
int64

Array2 datatype...
int64

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(2,)

Shape of Array2...
(2,)

Result...
   [[ 1. 3. 8. 18. 1. 3. 8. 18. 0. 0. 0. 0.]
   [ 1. 4. 15. 52. 2. 8. 30. 104. 3. 12. 45. 156.]]