返回Python中一维Chebyshev级数系数的缩放伴随矩阵


要返回一维多项式系数数组的缩放伴随矩阵,请在Python Numpy中返回chebyshev.chebcompanion()方法。基多项式已缩放,以便当c是Chebyshev基多项式时,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,并且对于基多项式,如果使用numpy.linalg.eigvalsh获得特征值,则保证特征值是实数。该方法返回维度为(deg, deg)的缩放伴随矩阵。参数c是从低到高阶排列的一维Chebyshev级数系数数组。

步骤

首先,导入所需的库:

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

创建一个一维系数数组:

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

显示数组:

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

检查维度:

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)

要返回一维多项式系数数组的缩放伴随矩阵,请在Python Numpy中返回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]]

更新于:2022年3月1日

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