"""
Utility functions for working with CVXOPT matrices (instances of the
-``cvxopt.base.matrix`` class).
+class:`cvxopt.base.matrix` class).
"""
from math import sqrt
from cvxopt import matrix
from cvxopt.lapack import syev
+import options
+
def append_col(left, right):
"""
Append the matrix ``right`` to the right side of the matrix ``left``.
- EXAMPLES:
+ Parameters
+ ----------
+ left, right : matrix
+ The two matrices to append to one another.
+
+ Examples
+ --------
>>> A = matrix([1,2,3,4], (2,2))
>>> B = matrix([5,6,7,8,9,10], (2,3))
+ >>> print(A)
+ [ 1 3]
+ [ 2 4]
+ <BLANKLINE>
+ >>> print(B)
+ [ 5 7 9]
+ [ 6 8 10]
+ <BLANKLINE>
>>> print(append_col(A,B))
[ 1 3 5 7 9]
[ 2 4 6 8 10]
"""
Append the matrix ``bottom`` to the bottom of the matrix ``top``.
- EXAMPLES:
+ Parameters
+ ----------
+ top, bottom : matrix
+ The two matrices to append to one another.
+
+ Examples
+ --------
>>> A = matrix([1,2,3,4], (2,2))
>>> B = matrix([5,6,7,8,9,10], (3,2))
+ >>> print(A)
+ [ 1 3]
+ [ 2 4]
+ <BLANKLINE>
+ >>> print(B)
+ [ 5 8]
+ [ 6 9]
+ [ 7 10]
+ <BLANKLINE>
>>> print(append_row(A,B))
[ 1 3]
[ 2 4]
return matrix([top, bottom])
-def eigenvalues(real_matrix):
+def eigenvalues(symmat):
"""
- Return the eigenvalues of the given ``real_matrix``.
+ Return the eigenvalues of the given symmetric real matrix.
- EXAMPLES:
+ Parameters
+ ----------
+
+ symmat : matrix
+ The real symmetric matrix whose eigenvalues you want.
+
+
+ Raises
+ ------
+ TypeError
+ If the input matrix is not symmetric.
+
+ Examples
+ --------
>>> A = matrix([[2,1],[1,2]], tc='d')
>>> eigenvalues(A)
[1.0, 3.0]
+ If the input matrix is not symmetric, it may not have real
+ eigenvalues, and we don't know what to do::
+
+ >>> A = matrix([[1,2],[3,4]])
+ >>> eigenvalues(A)
+ Traceback (most recent call last):
+ ...
+ TypeError: input must be a symmetric real matrix
+
"""
- domain_dim = real_matrix.size[0] # Assume ``real_matrix`` is square.
+ if not norm(symmat.trans() - symmat) < options.ABS_TOL:
+ # Ensure that ``symmat`` is symmetric (and thus square).
+ raise TypeError('input must be a symmetric real matrix')
+
+ domain_dim = symmat.size[0]
eigs = matrix(0, (domain_dim, 1), tc='d')
- syev(real_matrix, eigs)
+ syev(symmat, eigs)
return list(eigs)
def identity(domain_dim):
"""
- Return a ``domain_dim``-by-``domain_dim`` dense integer identity
- matrix.
+ Create an identity matrix of the given dimensions.
- EXAMPLES:
+ Parameters
+ ----------
+
+ domain_dim : int
+ The dimension of the vector space on which the identity will act.
+
+ Returns
+ -------
+ matrix
+ A ``domain_dim``-by-``domain_dim`` dense integer identity matrix.
+
+ Examples
+ --------
>>> print(identity(3))
[ 1 0 0]
def inner_product(vec1, vec2):
"""
- Compute the (Euclidean) inner product of the two vectors ``vec1``
- and ``vec2``.
+ Compute the Euclidean inner product of two vectors.
+
+ Parameters
+ ----------
+
+ vec1, vec2 : matrix
+ The two vectors whose inner product you want.
- EXAMPLES:
+ Returns
+ -------
+ float
+ The inner product of ``vec1`` and ``vec2``.
+
+ Examples
+ --------
>>> x = [1,2,3]
>>> y = [3,4,1]
def norm(matrix_or_vector):
"""
- Return the Frobenius norm of ``matrix_or_vector``, which is the same
- thing as its Euclidean norm when it's a vector (when one of its
- dimensions is unity).
+ Return the Frobenius norm of a matrix or vector.
+
+ When the input is a vector, its matrix-Frobenius norm is the same
+ thing as its vector-Euclidean norm.
+
+ Parameters
+ ----------
+
+ matrix_or_vector : matrix
+ The matrix or vector whose norm you want.
+
+ Returns
+ -------
- EXAMPLES:
+ float
+ The norm of ``matrix_or_vector``.
+
+ Examples
+ --------
>>> v = matrix([1,1])
>>> print('{:.5f}'.format(norm(v)))
return sqrt(inner_product(matrix_or_vector, matrix_or_vector))
-def vec(real_matrix):
+def vec(mat):
"""
- Create a long vector in column-major order from ``real_matrix``.
+ Create a long vector in column-major order from ``mat``.
+
+ Parameters
+ ----------
+
+ mat : matrix
+ Any sort of real matrix that you want written as a long vector.
+
+ Returns
+ -------
+
+ matrix
+ An ``len(mat)``-by-``1`` long column vector containign the
+ entries of ``mat`` in column major order.
- EXAMPLES:
+ Examples
+ --------
>>> A = matrix([[1,2],[3,4]])
>>> print(A)
[ 4]
<BLANKLINE>
- Note that if ``real_matrix`` is a vector, this function is a no-op:
+ Note that if ``mat`` is a vector, this function is a no-op:
>>> v = matrix([1,2,3,4], (4,1))
>>> print(v)
<BLANKLINE>
"""
- return matrix(real_matrix, (len(real_matrix), 1))
+ return matrix(mat, (len(mat), 1))
projects / dunshire.git / blobdiff