dpnp.linalg.cond

dpnp.linalg.cond(x, p=None)

Compute the condition number of a matrix.

For full documentation refer to numpy.linalg.cond.

Parameters:

• x ({dpnp.ndarray, usm_ndarray}) -- The matrix whose condition number is sought.

• p ({None, 1, -1, 2, -2, inf, -inf, "fro"}, optional) --

  Order of the norm used in the condition number computation:

  p	norm for matrices
  None	2-norm
  'fro'	Frobenius norm
  inf	max(sum(abs(x), axis=1))
  -inf	min(sum(abs(x), axis=1))
  1	max(sum(abs(x), axis=0))
  -1	min(sum(abs(x), axis=0))
  2	2-norm (largest singular value)
  -2	smallest singular value

  inf means the dpnp.inf object, and the Frobenius norm is the root-of-sum-of-squares norm.

  Default: None.

Returns:

out -- The condition number of the matrix. May be infinite.

Return type:

dpnp.ndarray

See also

dpnp.linalg.norm

Matrix or vector norm.

Notes

This function will raise dpnp.linalg.LinAlgError on singular input when using any of the norm: 1, -1, inf, -inf, or 'fro'. In contrast, numpy.linalg.cond will fill the result array with inf values for each 2D batch in the input array that is singular when using these norms.

Examples

>>> import dpnp as np
>>> a = np.array([[1, 0, -1], [0, 1, 0], [1, 0, 1]])
>>> a
array([[ 1,  0, -1],
       [ 0,  1,  0],
       [ 1,  0,  1]])
>>> np.linalg.cond(a)
array(1.41421356)
>>> np.linalg.cond(a, 'fro')
array(3.16227766)
>>> np.linalg.cond(a, np.inf)
array(2.)
>>> np.linalg.cond(a, -np.inf)
array(1.)
>>> np.linalg.cond(a, 1)
array(2.)
>>> np.linalg.cond(a, -1)
array(1.)
>>> np.linalg.cond(a, 2)
array(1.41421356)
>>> np.linalg.cond(a, -2)
array(0.70710678) # may vary
>>> x = min(np.linalg.svd(a, compute_uv=False))
>>> y = min(np.linalg.svd(np.linalg.inv(a), compute_uv=False))
>>> x * y
array(0.70710678) # may vary