在Python中生成Hermite多项式的伪范德蒙矩阵

要生成Hermite多项式的伪范德蒙德矩阵，请使用Python Numpy中的hermite.hermvander2d()方法。该方法返回伪范德蒙德矩阵。

参数x，y是点坐标的数组，所有的形状相同。根据元素是否为复数，将dtype转换为float64或complex128。标量转换为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([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)

要生成Hermite多项式的伪Vandermonde矩阵，请使用Python Numpy中的hermite.hermvander2d()函数。

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

# Check the Shape of both the arrays
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...
   [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...
   [[1.000e+00 6.000e+00 3.400e+01 1.800e+02 2.000e+00 1.200e+01 6.800e+01
    3.600e+02 2.000e+00 1.200e+01 6.800e+01 3.600e+02]
   [1.000e+00 8.000e+00 6.200e+01 4.640e+02 4.000e+00 3.200e+01 2.480e+02
    1.856e+03 1.400e+01 1.120e+02 8.680e+02 6.496e+03]]