在Python中用浮点数组点生成埃尔米特多项式的Vandermonde矩阵

在Python中用浮点数组点生成埃尔米特多项式的Vandermonde矩阵

要生成埃尔米特多项式的Vandermonde矩阵，可以使用Python Numpy中的chebyshev.hermvander()方法。该方法返回伪Vandermonde矩阵。返回的矩阵的形状为x.shape + (deg + 1,)，其中最后一个索引是对应埃尔米特多项式的度数。dtype将与转换后的x相同。

参数x返回一个点的数组。dtype根据元素是否为复数进行转换为float64或complex128。如果x是标量，则转换为1-D数组。参数deg是结果矩阵的度数。

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([0, 3.5, -1.4, 2.5])

展示数组 –

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Hermite多项式的Vandermonde矩阵，请使用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([0, 3.5, -1.4, 2.5])

# 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...
   [ 0. 3.5 -1.4 2.5]

Dimensions of our Array...
1

Datatype of our Array object...
float64

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

Result...
   [[ 1. 0.  -2. ]
   [ 1.  7.  47. ]
   [ 1. -2.8 5.84]
   [ 1.  5.  23. ]]