# Return the scaled companion matrix of a 1-D array of Chebyshev series coefficients using NumPy in Python

• Last Updated : 03 Jun, 2022

In this article, we will discuss how to return the scaled companion matrix of a 1D array of Chebyshev series coefficients in python.

## chebyshev.chebcompanion() method

chebyshev.chebcompanion() method provides the eigenvalue estimates than the unscaled case and for basis polynomials. We can say that the eigenvalues are guaranteed to be real if numpy.linalg.eigvalsh is used to obtain them. This method will take the coefficient array as a parameter which is a 1-D array of Chebyshev series coefficients ordered from low degree to high degree and return the  Scaled companion matrix of dimensions.

Syntax: chebyshev.chebcompanion(coefficient_array)

Parameters:

• coefficient_array: It will take coefficient array as parameter which is an1-D array of Chebyshev series coefficients ordered from low degree to high degree.

Return: Scaled companion matrix of dimensions (deg, deg)

### Example 1:

In this example, we are creating a one-dimensional array with 3 coefficients and returning the scaled companion matrix along with shape, dimensions, and datatype. It returned a 2D scaled companion matrix.

## Python3

 `# import packages``import` `numpy as np``from` `numpy.polynomial ``import` `chebyshev`` ` `# array of coefficients``c ``=` `np.array([``2``,``2``,``3``])``print``(c)`` ` `# shape of the array is``print``(``"Shape of the array is : "``,c.shape)`` ` `# dimension of the array``print``(``"The dimension of the array is : "``,c.ndim)`` ` `# Datatype of the array``print``(``"Datatype of our Array is : "``,c.dtype)`` ` `# return the scaled companion matrix ``# of a 1-D array ``print``(chebyshev.chebcompanion(c))`

Output:

```[2 2 3]
Shape of the array is :  (3,)
The dimension of the array is :  1
Datatype of our Array is :  int64
[[ 0.          0.23570226]
[ 0.70710678 -0.33333333]]```

### Example 2:

In this example, we are creating a one-dimensional array with 5  coefficients and returning the scaled companion matrix along with shape, dimensions and datatype.  It returned 2D scaled companion matrix.

## Python3

 `# import packages``import` `numpy as np``from` `numpy.polynomial ``import` `chebyshev`` ` `# array of coefficients``c ``=` `np.array([``1``,``2``,``3``,``4``,``5``])``print``(c)`` ` `# shape of the array is``print``(``"Shape of the array is : "``,c.shape)`` ` `# dimension of the array``print``(``"The dimension of the array is : "``,c.ndim)`` ` `# Datatype of the array``print``(``"Datatype of our Array is : "``,c.dtype)`` ` `# return the scaled companion matrix of ``# a 1-D array ``print``(chebyshev.chebcompanion(c))`

Output:

```[1 2 3 4 5]
Shape of the array is :  (5,)
The dimension of the array is :  1
Datatype of our Array is :  int64
[[ 0.          0.70710678  0.         -0.14142136]
[ 0.70710678  0.          0.5        -0.2       ]
[ 0.          0.5         0.          0.2       ]
[ 0.          0.          0.5        -0.4       ]]```

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