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bundles / scipy latest / scipy / linalg / _special_matrices / companion

function

scipy.linalg._special_matrices:companion

source: /scipy/linalg/_special_matrices.py :454

Signature

def   companion ( a )

Summary

Create a companion matrix.

Extended Summary

Create the companion matrix [1] associated with the polynomial whose coefficients are given in a.

Array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details.

Parameters

a : (..., N) array_like

1-D array of polynomial coefficients. The length of a must be at least two, and a[0] must not be zero. M-dimensional arrays are treated as a batch: each slice along the last axis is a 1-D array of polynomial coefficients.

Returns

c : (..., N-1, N-1) ndarray

For 1-D input, the first row of c is -a[1:]/a[0], and the first sub-diagonal is all ones. The data-type of the array is the same as the data-type of 1.0*a[0]. For batch input, each slice of shape (N-1, N-1) along the last two dimensions of the output corresponds with a slice of shape (N,) along the last dimension of the input.

Raises

: ValueError

If any of the following are true: a) a.shape[-1] < 2; b) a[..., 0] == 0.

Notes

Examples

from scipy.linalg import companion
companion([1, -10, 31, -30])
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Aliases

  • scipy.linalg.companion

Referenced by

This package