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numpy.linalg.cond(x, p=None)[source] -
Compute the condition number of a matrix.
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:
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.
See also
Notes
The condition number of
xis defined as the norm ofxtimes the norm of the inverse ofx[R37]; the norm can be the usual L2-norm (root-of-sum-of-squares) or one of a number of other matrix norms.References
[R37] (1, 2) 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 >>> min(LA.svd(a, compute_uv=0))*min(LA.svd(LA.inv(a), compute_uv=0)) 0.70710678118654746
numpy.linalg.cond()
2017-01-10 18:14:42
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