返回在Python中的1-D Chebyshev级数系数的缩放伴随矩阵

要返回多项式系数的1-D数组的缩放伴随矩阵，请返回Python Numpy中的chebyshev.chebcompanion()方法。 这些基础多项式被缩放，以便在c为Chebyshev基础多项式时，伴随矩阵是对称的。这比未缩放的情况提供了更好的特征值估计，并且对于基础多项式，如果使用numpy.linalg.eigvalsh来获得它们，则特征值保证是实数。该方法返回维度为（deg，deg）的缩放伴随矩阵。参数c是按低到高次序排列的1-D Chebyshev级数系数的数组。

步骤

首先，导入所需的库 –

import numpy as np
from numpy.polynomial import chebyshev as C

创建一个1D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)

得到形状 –

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

返回一个一维多项式系数数组的缩放伴随矩阵，可以使用Python Numpy中的chebyshev.chebcompanion()方法。

print("\nResult...\n",C.chebcompanion(c))

示例

import numpy as np
from numpy.polynomial import chebyshev as C

# 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 chebyshev.chebcompanion() method in Python Numpy
print("\nResult...\n",C.chebcompanion(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. 0.47140452]
   [ 0.70710678 -0.33333333]]