X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fsymmetric_psd.py;h=89eba53c9687823a0882304a49d9ddefc1d009db;hb=7af2b9d146a6bf2fb8acc3c342983de577b417ce;hp=1b3dd8ab6d8905a1af202eec3816c46ece906561;hpb=f79e891ca154b0fa935a14001b0b6ed194425741;p=sage.d.git

diff --git a/mjo/cone/symmetric_psd.py b/mjo/cone/symmetric_psd.py
index 1b3dd8a..89eba53 100644
--- a/mjo/cone/symmetric_psd.py
+++ b/mjo/cone/symmetric_psd.py
@@ -1,4 +1,4 @@
-"""
+r"""
 The positive semidefinite cone `$S^{n}_{+}$` is the cone consisting of
 all symmetric positive-semidefinite matrices (as a subset of
 `$\mathbb{R}^{n \times n}$`
@@ -6,63 +6,6 @@ all symmetric positive-semidefinite matrices (as a subset of
 
 from sage.all import *
 
-def is_symmetric_psd(A):
-    """
-    Determine whether or not the matrix ``A`` is symmetric
-    positive-semidefinite.
-
-    INPUT:
-
-    - ``A`` - The matrix in question
-
-    OUTPUT:
-
-    Either ``True`` if ``A`` is symmetric positive-semidefinite, or
-    ``False`` otherwise.
-
-    SETUP::
-
-        sage: from mjo.cone.symmetric_psd import is_symmetric_psd
-
-    EXAMPLES:
-
-    Every completely positive matrix is symmetric
-    positive-semidefinite::
-
-        sage: v = vector(map(abs, random_vector(ZZ, 10)))
-        sage: A = v.column() * v.row()
-        sage: is_symmetric_psd(A)
-        True
-
-    The following matrix is symmetric but not positive semidefinite::
-
-        sage: A = matrix(ZZ, [[1, 2], [2, 1]])
-        sage: is_symmetric_psd(A)
-        False
-
-    This matrix isn't even symmetric::
-
-        sage: A = matrix(ZZ, [[1, 2], [3, 4]])
-        sage: is_symmetric_psd(A)
-        False
-
-    """
-
-    if A.base_ring() == SR:
-        msg = 'The matrix ``A`` cannot be symbolic.'
-        raise ValueError.new(msg)
-
-    # First make sure that ``A`` is symmetric.
-    if not A.is_symmetric():
-        return False
-
-    # If ``A`` is symmetric, we only need to check that it is positive
-    # semidefinite. For that we can consult its minimum eigenvalue,
-    # which should be zero or greater. Since ``A`` is symmetric, its
-    # eigenvalues are guaranteed to be real.
-    return min(A.eigenvalues()) >= 0
-
-
 def unit_eigenvectors(A):
     """
     Return the unit eigenvectors of a symmetric positive-definite matrix.
@@ -201,7 +144,7 @@ def factor_psd(A):
     return Q*root_D*Q.transpose()
 
 
-def random_psd(V, accept_zero=True, rank=None):
+def random_symmetric_psd(V, accept_zero=True, rank=None):
     """
     Generate a random symmetric positive-semidefinite matrix over the
     vector space ``V``. That is, the returned matrix will be a linear
@@ -242,42 +185,45 @@ def random_psd(V, accept_zero=True, rank=None):
 
     SETUP::
 
-        sage: from mjo.cone.symmetric_psd import is_symmetric_psd, random_psd
+        sage: from mjo.cone.symmetric_psd import random_symmetric_psd
 
     EXAMPLES:
 
     Well, it doesn't crash at least::
 
+        sage: set_random_seed()
         sage: V = VectorSpace(QQ, 2)
-        sage: A = random_psd(V)
+        sage: A = random_symmetric_psd(V)
         sage: A.matrix_space()
         Full MatrixSpace of 2 by 2 dense matrices over Rational Field
-        sage: is_symmetric_psd(A)
+        sage: A.is_positive_semidefinite()
         True
 
     A matrix with the desired rank is returned::
 
+        sage: set_random_seed()
         sage: V = VectorSpace(QQ, 5)
-        sage: A = random_psd(V,False,1)
+        sage: A = random_symmetric_psd(V,False,1)
         sage: A.rank()
         1
-        sage: A = random_psd(V,False,2)
+        sage: A = random_symmetric_psd(V,False,2)
         sage: A.rank()
         2
-        sage: A = random_psd(V,False,3)
+        sage: A = random_symmetric_psd(V,False,3)
         sage: A.rank()
         3
-        sage: A = random_psd(V,False,4)
+        sage: A = random_symmetric_psd(V,False,4)
         sage: A.rank()
         4
-        sage: A = random_psd(V,False,5)
+        sage: A = random_symmetric_psd(V,False,5)
         sage: A.rank()
         5
 
     If the user asks for a rank that's too high, we fail::
 
+        sage: set_random_seed()
         sage: V = VectorSpace(QQ, 2)
-        sage: A = random_psd(V,False,3)
+        sage: A = random_symmetric_psd(V,False,3)
         Traceback (most recent call last):
         ...
         ValueError: The ``rank`` must be between 0 and the dimension of ``V``.
@@ -303,19 +249,23 @@ def random_psd(V, accept_zero=True, rank=None):
         # Use the one the user gave us.
         rank_A = rank
 
-    # Begin with the zero matrix, and add projectors to it if we have any.
-    A = V.zero().column()*V.zero().row()
-
-    # Careful, begin at idx=1 so that we only generate a projector
-    # when rank_A is greater than zero.
-    while A.rank() < rank_A:
-        v = V.random_element()
-        A += v.column()*v.row()
-
-    if accept_zero or not A.is_zero():
-        # We either don't care what ``A`` is, or it's non-zero, so
-        # just return it.
-        return A
-    else:
-        # Uh oh, we need to generate a new one.
-        return random_psd(V, accept_zero, rank)
+    if n == 0 and not accept_zero:
+        # We're gonna loop forever trying to satisfy this...
+        raise ValueError('You must have accept_zero=True when V is trivial')
+
+    # Loop until we find a suitable "A" that will then be returned.
+    while True:
+        # Begin with the zero matrix, and add projectors to it if we
+        # have any.
+        A = matrix.zero(V.base_ring(), n, n)
+
+        # Careful, begin at idx=1 so that we only generate a projector
+        # when rank_A is greater than zero.
+        while A.rank() < rank_A:
+            v = V.random_element()
+            A += v.column()*v.row()
+
+        if accept_zero or not A.is_zero():
+            # We either don't care what ``A`` is, or it's non-zero, so
+            # just return it.
+            return A