在Python中使用复数数组生成Hermite多项式的Vandermonde矩阵

要生成Hermite多项式的Vandermonde矩阵，可以使用Python Numpy中的chebyshev.hermvander()方法。该方法返回伪Vandermonde矩阵。返回矩阵的形状为x.shape + (deg + 1,)，其中最后一个索引是对应Hermite多项式的次数。dtype将与转换后的x相同。

参数x返回一个点数组。根据其中是否有复数元素，将其dtype转换为float64或complex128。如果x是标量，则将其转换为一维数组。参数deg是所得矩阵的次数。

步骤

首先，导入所需的库−

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

创建一个数组 –

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

显示数组 –

print("Our Array...\n",x)

检查尺寸−

print("\nDimensions of our Array...\n",x.ndim)

获取数据类型−

print("\nDatatype of our Array object...\n",x.dtype)

获取形状 –

print("\nShape of our Array object...\n",x.shape)

要生成一个Hermite多项式的Vandermonde矩阵，可以使用chebyshev.hermvander()函数。

print("\nResult...\n",H.hermvander(x, 2))

示例

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

# Create an array
x = np.array([-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j])

# Display the array
print("Our Array...\n",x)

# Check the Dimensions
print("\nDimensions of our Array...\n",x.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",x.dtype)

# Get the Shape
print("\nShape of our Array object...\n",x.shape)

# To generate a Vandermonde matrix of the Hermite polynomial, use the chebyshev.hermvander() in Python Numpy
print("\nResult...\n",H.hermvander(x, 2))

输出

Our Array...
   [-2.+2.j -1.+2.j 0.+2.j 1.+2.j 2.+2.j]

Dimensions of our Array...
1

Datatype of our Array object...
complex128

Shape of our Array object...
(5,)

Result...
   [[ 1. +0.j -4. +4.j -2.-32.j]
   [ 1. +0.j -2. +4.j -14.-16.j]
   [ 1. +0.j 0. +4.j -18. +0.j]
   [ 1. +0.j 2. +4.j -14.+16.j]
   [ 1. +0.j 4. +4.j -2.+32.j]]