symjax.tensor.linalg.cond¶

symjax.tensor.linalg.cond(x, p=None)[source]¶

Compute the condition number of a matrix.

LAX-backend implementation of cond(). Original docstring below.

This function is capable of returning the condition number using one of seven different norms, depending on the value of p (see Parameters below).

Parameters:	x ((.., M, N) array_like) – The matrix whose condition number is sought. p ({None, 1, -1, 2, -2, inf, -inf, 'fro'}, optional) – Order of the norm:
Returns:	c – The condition number of the matrix. May be infinite.
Return type:	{float, inf}

See also

numpy.linalg.norm()

Notes

The condition number of x is defined as the norm of x times the norm of the inverse of x [1]; the norm can be the usual L2-norm (root-of-sum-of-squares) or one of a number of other matrix norms.

References

[1]	G. Strang, Linear Algebra and Its Applications, Orlando, FL, Academic Press, Inc., 1980, pg. 285.

Examples

>>> from numpy import linalg as LA
>>> a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]])
>>> a
array([[ 1,  0, -1],
       [ 0,  1,  0],
       [ 1,  0,  1]])
>>> LA.cond(a)
1.4142135623730951
>>> LA.cond(a, 'fro')
3.1622776601683795
>>> LA.cond(a, np.inf)
2.0
>>> LA.cond(a, -np.inf)
1.0
>>> LA.cond(a, 1)
2.0
>>> LA.cond(a, -1)
1.0
>>> LA.cond(a, 2)
1.4142135623730951
>>> LA.cond(a, -2)
0.70710678118654746 # may vary
>>> min(LA.svd(a, compute_uv=False))*min(LA.svd(LA.inv(a), compute_uv=False))
0.70710678118654746 # may vary