cond(x, p=None)

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

Notes

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

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 used in the condition number computation:

===== ============================ p norm for matrices ===== ============================ None 2-norm, computed directly using the SVD '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 sing. value) -2 smallest singular value ===== ============================

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

Returns

c : {float, inf}

The condition number of the matrix. May be infinite.

Compute the condition number of a matrix.

See Also

numpy.linalg.norm

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

See :

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GitHub : /numpy/linalg/linalg.py#1669
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