+ def __contains__(self, point):
+ """
+ Return whether or not ``point`` belongs to this cone.
+
+ INPUT:
+
+ An instance of the ``cvxopt.base.matrix`` class having
+ dimensions ``(n,n)`` where ``n`` is the dimension of this cone.
+
+ EXAMPLES:
+
+ >>> K = SymmetricPSD(2)
+ >>> matrix([[1,0],[0,1]]) in K
+ True
+
+ >>> K = SymmetricPSD(2)
+ >>> matrix([[0,0],[0,0]]) in K
+ True
+
+ >>> K = SymmetricPSD(3)
+ >>> matrix([[2,-1,0],[-1,2,-1],[0,-1,2]]) in K
+ True
+
+ >>> K = SymmetricPSD(5)
+ >>> A = matrix([[5,4,3,2,1],
+ ... [4,5,4,3,2],
+ ... [3,4,5,4,3],
+ ... [2,3,4,5,4],
+ ... [1,2,3,4,5]])
+ >>> A in K
+ True
+
+ >>> K = SymmetricPSD(5)
+ >>> A = matrix([[1,0,0,0,0],
+ ... [0,1,0,0,0],
+ ... [0,0,0,0,0],
+ ... [0,0,0,1,0],
+ ... [0,0,0,0,1]])
+ >>> A in K
+ True
+
+ >>> K = SymmetricPSD(2)
+ >>> [[1,2],[2,3]] in K
+ Traceback (most recent call last):
+ ...
+ TypeError: the given point is not a cvxopt.base.matrix
+
+ >>> K = SymmetricPSD(3)
+ >>> matrix([[1,2],[3,4]]) in K
+ Traceback (most recent call last):
+ ...
+ TypeError: the given point has the wrong dimensions
+
+ """
+ if not isinstance(point, matrix):
+ raise TypeError('the given point is not a cvxopt.base.matrix')
+ if not point.size == (self.dimension(), self.dimension()):
+ raise TypeError('the given point has the wrong dimensions')
+ if not point.typecode == 'd':
+ point = matrix(point, (self.dimension(), self.dimension()), 'd')
+ return all([e >= 0 for e in eigenvalues(point)])
+
+
+ def contains_strict(self, point):
+ """
+ Return whether or not ``point`` belongs to the interior
+ of this cone.
+
+ INPUT:
+
+ An instance of the ``cvxopt.base.matrix`` class having
+ dimensions ``(n,n)`` where ``n`` is the dimension of this cone.
+ Its type code must be 'd'.
+
+ EXAMPLES:
+
+ >>> K = SymmetricPSD(2)
+ >>> K.contains_strict(matrix([[1,0],[0,1]]))
+ True
+
+ >>> K = SymmetricPSD(2)
+ >>> K.contains_strict(matrix([[0,0],[0,0]]))
+ False
+
+ >>> K = SymmetricPSD(3)
+ >>> matrix([[2,-1,0],[-1,2,-1],[0,-1,2]]) in K
+ True
+
+ >>> K = SymmetricPSD(5)
+ >>> A = matrix([[5,4,3,2,1],
+ ... [4,5,4,3,2],
+ ... [3,4,5,4,3],
+ ... [2,3,4,5,4],
+ ... [1,2,3,4,5]])
+ >>> A in K
+ True
+
+ >>> K = SymmetricPSD(5)
+ >>> A = matrix([[1,0,0,0,0],
+ ... [0,1,0,0,0],
+ ... [0,0,0,0,0],
+ ... [0,0,0,1,0],
+ ... [0,0,0,0,1]])
+ >>> K.contains_strict(A)
+ False
+
+ >>> K = SymmetricPSD(2)
+ >>> K.contains_strict([[1,2],[2,3]])
+ Traceback (most recent call last):
+ ...
+ TypeError: the given point is not a cvxopt.base.matrix
+
+ >>> K = SymmetricPSD(3)
+ >>> K.contains_strict(matrix([[1,2],[3,4]]))
+ Traceback (most recent call last):
+ ...
+ TypeError: the given point has the wrong dimensions
+
+ """
+ if not isinstance(point, matrix):
+ raise TypeError('the given point is not a cvxopt.base.matrix')
+ if not point.size == (self.dimension(), self.dimension()):
+ raise TypeError('the given point has the wrong dimensions')
+ if not point.typecode == 'd':
+ point = matrix(point, (self.dimension(), self.dimension()), 'd')
+ return all([e > 0 for e in eigenvalues(point)])
+
+