class:`cvxopt.base.matrix` class).
"""
+from copy import copy
from math import sqrt
from cvxopt import matrix
from cvxopt.lapack import gees, gesdd, syevr
domain_dim = symmat.size[0]
eigs = matrix(0, (domain_dim, 1), tc='d')
- syevr(symmat, eigs)
+
+ # Create a copy of ``symmat`` here because ``syevr`` clobbers it.
+ dummy = copy(symmat)
+ syevr(dummy, eigs)
return list(eigs)
--------
>>> v = matrix([1,1])
- >>> print('{:.5f}'.format(norm(v)))
- 1.41421
+ >>> norm(v)
+ 1.414...
>>> A = matrix([1,1,1,1], (2,2))
>>> norm(A)
- 2.0
+ 2.0...
"""
return sqrt(inner_product(matrix_or_vector, matrix_or_vector))
+def specnorm(mat):
+ """
+ Return the spectral norm of a matrix.
+
+ The spectral norm of a matrix is its largest singular value, and it
+ corresponds to the operator norm induced by the vector ``2``-norm.
+
+ Parameters
+ ----------
+
+ mat : matrix
+ The matrix whose spectral norm you want.
+
+ Examples:
+
+ >>> specnorm(identity(3))
+ 1.0
+
+ >>> specnorm(5*identity(4))
+ 5.0
+
+ """
+ num_eigs = min(mat.size)
+ eigs = matrix(0, (num_eigs, 1), tc='d')
+ typecode = 'd'
+ if any([isinstance(entry, complex) for entry in mat]):
+ typecode = 'z'
+ dummy = matrix(mat, mat.size, tc=typecode)
+ gesdd(dummy, eigs)
+
+ if len(eigs) > 0:
+ return eigs[0]
+ else:
+ return 0
+
+
def vec(mat):
"""
Create a long vector in column-major order from ``mat``.
Examples
--------
- >>> condition_number(identity(1, typecode='d'))
- 1.0
- >>> condition_number(identity(2, typecode='d'))
- 1.0
- >>> condition_number(identity(3, typecode='d'))
+ >>> condition_number(identity(3))
1.0
- >>> A = matrix([[2,1],[1,2]], tc='d')
+ >>> A = matrix([[2,1],[1,2]])
>>> abs(condition_number(A) - 3.0) < options.ABS_TOL
True
- >>> A = matrix([[2,1j],[-1j,2]], tc='z')
+ >>> A = matrix([[2,1j],[-1j,2]])
>>> abs(condition_number(A) - 3.0) < options.ABS_TOL
True
"""
num_eigs = min(mat.size)
eigs = matrix(0, (num_eigs, 1), tc='d')
- gesdd(mat, eigs)
+ typecode = 'd'
+ if any([isinstance(entry, complex) for entry in mat]):
+ typecode = 'z'
+ dummy = matrix(mat, mat.size, tc=typecode)
+ gesdd(dummy, eigs)
if len(eigs) > 0:
return eigs[0]/eigs[-1]