在Python中生成Hermite_e多项式的Vandermonde矩阵

要生成Hermite_e多项式的Vandermonde矩阵，可以使用Python的Numpy库中的hermite_e.hermevander()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_e多项式的阶数。返回的数据类型与转换后的x数据类型相同。

参数x是一个点的数组。如果其中任何一个元素为复数，则将数据类型转换为float64或complex128。如果x是标量，则会将其转换为1维数组。参数deg是生成矩阵的阶数。

步骤

首先导入所需的库-

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

创建一个数组 –

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

显示数组 –

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

检查尺寸 –

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

获取数据类型 –

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

获取形状 −

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

使用Python的Numpy库中的hermite_e.hermevander()函数生成Hermite_e多项式的Vandermonde矩阵。

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

示例

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

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

# 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_e polynomial, use the hermite_e.hermevander() in Python Numpy
print("\nResult...\n",H.hermevander(x, 2))

输出

Our Array...
   [ 0 1 -1 2]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(4,)

Result...
   [[ 1. 0. -1.]
   [ 1. 1. 0.]
   [ 1. -1. 0.]
   [ 1. 2. 3.]]