在Python中返回1-D Hermite系数数组的缩放伴随矩阵

要返回1-D多项式系数数组的缩放伴随矩阵，在Python的Numpy中使用hermite_e.hermecompanion()方法。基础多项式被缩放，以使得伴随矩阵在c是Hermite_e基础多项式时对称。这比不缩放的情况下提供更好的特征值估计，并且对于基础多项式，特征值保证是实数，如果使用numpy.linalg.eigvalsh来获取它们。

该方法返回维度为（deg，deg）的缩放伴随矩阵。参数c是一个按照从低到高度的次序排列的1-D Hermite系列系数数组。

步骤

首先，导入所需的库-

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

创建一个一维系数数组 −

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

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)

要返回一个一维多项式系数数组的缩放伴随矩阵，请在Python中使用hermite_e.hermecompanion()方法 –

print("\nResult...\n",H.hermecompanion(c))

示例

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

# Create a 1D array of coefficients
c = np.array([1, 2, 3])

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

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

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

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

# To return the scaled companion matrix of a 1-D array of polynomial coefficients, return the hermite_e.hermecompanion() method in Python Numpy
print("\nResult...\n",H.hermecompanion(c))

输出

Our Array...
   [1 2 3]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(3,)

Result...
   [[ 0. 0.66666667]
   [ 1. -0.66666667]]