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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
123456789101112131415161718192021222324>>>fromnumpyimportlinalg as LA>>> a=np.array([[1,0,-1], [0,1,0], [1,0,1]])>>> aarray([[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()
2025-01-10 15:47:30
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