scipy.linalg.companion

scipy.linalg.companion(a)

Create a companion matrix.

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

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.

Returns

c(N-1, N-1) ndarray

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].

Raises

ValueError

If any of the following are true: a) a.ndim != 1; b) a.size < 2; c) a[0] == 0.

Notes

New in version 0.8.0.

References

1

R. A. Horn & C. R. Johnson, Matrix Analysis. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7.

Examples

>>> from scipy.linalg import companion
>>> companion([1, -10, 31, -30])
array([[ 10., -31.,  30.],
       [  1.,   0.,   0.],
       [  0.,   1.,   0.]])