numpy.linalg.cond¶
- 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 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