X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2Fdunshire%2Fmatrices.py;h=2006fd20427b999fd8061a74e89e03508b55f0f1;hb=4bf45d1711033bc419e1c48a7906f21de67ef791;hp=a33259e6f3e71f7a4b5f2d47234464d80a9a3199;hpb=56ea961887d507114174af5f92b8c3c77b0b7a50;p=dunshire.git

diff --git a/src/dunshire/matrices.py b/src/dunshire/matrices.py
index a33259e..2006fd2 100644
--- a/src/dunshire/matrices.py
+++ b/src/dunshire/matrices.py
@@ -5,6 +5,7 @@ Utility functions for working with CVXOPT matrices (instances of the
 
 from math import sqrt
 from cvxopt import matrix
+from cvxopt.lapack import syev
 
 def append_col(left, right):
     """
@@ -41,6 +42,24 @@ def append_row(top, bottom):
     """
     return matrix([top, bottom])
 
+
+def eigenvalues(real_matrix):
+    """
+    Return the eigenvalues of the given ``real_matrix``.
+
+    EXAMPLES:
+
+        >>> A = matrix([[2,1],[1,2]], tc='d')
+        >>> eigenvalues(A)
+        [1.0, 3.0]
+
+    """
+    domain_dim = real_matrix.size[0] # Assume ``real_matrix`` is square.
+    eigs = matrix(0, (domain_dim, 1), tc='d')
+    syev(real_matrix, eigs)
+    return list(eigs)
+
+
 def identity(domain_dim):
     """
     Return a ``domain_dim``-by-``domain_dim`` dense integer identity
@@ -64,6 +83,37 @@ def identity(domain_dim):
     return matrix(entries, (domain_dim, domain_dim))
 
 
+def inner_product(vec1, vec2):
+    """
+    Compute the (Euclidean) inner product of the two vectors ``vec1``
+    and ``vec2``.
+
+    EXAMPLES:
+
+        >>> x = [1,2,3]
+        >>> y = [3,4,1]
+        >>> inner_product(x,y)
+        14
+
+        >>> x = matrix([1,1,1])
+        >>> y = matrix([2,3,4], (1,3))
+        >>> inner_product(x,y)
+        9
+
+        >>> x = [1,2,3]
+        >>> y = [1,1]
+        >>> inner_product(x,y)
+        Traceback (most recent call last):
+        ...
+        TypeError: the lengths of vec1 and vec2 must match
+
+    """
+    if not len(vec1) == len(vec2):
+        raise TypeError('the lengths of vec1 and vec2 must match')
+
+    return sum([x*y for (x, y) in zip(vec1, vec2)])
+
+
 def norm(matrix_or_vector):
     """
     Return the Frobenius norm of ``matrix_or_vector``, which is the same
@@ -81,4 +131,43 @@ def norm(matrix_or_vector):
         2.0
 
     """
-    return sqrt(sum([x**2 for x in matrix_or_vector]))
+    return sqrt(inner_product(matrix_or_vector, matrix_or_vector))
+
+
+def vec(real_matrix):
+    """
+    Create a long vector in column-major order from ``real_matrix``.
+
+    EXAMPLES:
+
+        >>> A = matrix([[1,2],[3,4]])
+        >>> print(A)
+        [ 1  3]
+        [ 2  4]
+        <BLANKLINE>
+
+        >>> print(vec(A))
+        [ 1]
+        [ 2]
+        [ 3]
+        [ 4]
+        <BLANKLINE>
+
+    Note that if ``real_matrix`` is a vector, this function is a no-op:
+
+        >>> v = matrix([1,2,3,4], (4,1))
+        >>> print(v)
+        [ 1]
+        [ 2]
+        [ 3]
+        [ 4]
+        <BLANKLINE>
+        >>> print(vec(v))
+        [ 1]
+        [ 2]
+        [ 3]
+        [ 4]
+        <BLANKLINE>
+
+    """
+    return matrix(real_matrix, (len(real_matrix), 1))