raise NotImplementedError
+ def ball_radius(self, point):
+ """
+ Return the radius of a ball around ``point`` in this cone.
+
+ Since a radius cannot be negative, the ``point`` must be
+ contained in this cone; otherwise, an error is raised.
+
+ Parameters
+ ----------
+
+ point : matrix
+ A point contained in this cone.
+
+ Returns
+ -------
+
+ float
+ A radius ``r`` such that the ball of radius ``r`` centered at
+ ``point`` is contained entirely within this cone.
+
+ Raises
+ ------
+
+ NotImplementedError
+ Always, this method must be implemented in subclasses.
+
+ Examples
+ --------
+
+ >>> K = SymmetricCone(5)
+ >>> K.ball_radius(matrix([1,1,1,1,1]))
+ Traceback (most recent call last):
+ ...
+ NotImplementedError
+
+ """
+ raise NotImplementedError
+
def dimension(self):
"""
return all([x > -options.ABS_TOL for x in point])
+ def ball_radius(self, point):
+ """
+ Return the radius of a ball around ``point`` in this cone.
+
+ Since a radius cannot be negative, the ``point`` must be
+ contained in this cone; otherwise, an error is raised.
+
+ The minimum distance from ``point`` to the complement of this
+ cone will always occur at its projection onto that set. It is
+ not hard to see that the projection is directly along one of the
+ coordinates, and so the minimum distance from ``point`` to the
+ boundary of this cone is the smallest coordinate of
+ ``point``. Therefore any radius less than that will work; we
+ divide it in half somewhat arbitrarily.
+
+ Parameters
+ ----------
+
+ point : matrix
+ A point contained in this cone.
+
+ Returns
+ -------
+
+ float
+ A radius ``r`` such that the ball of radius ``r`` centered at
+ ``point`` is contained entirely within this cone.
+
+ Raises
+ ------
+
+ TypeError
+ If ``point`` is not a :class:`cvxopt.base.matrix`.
+
+ TypeError
+ If ``point`` has the wrong dimensions.
+
+ ValueError
+ if ``point`` is not contained in this cone.
+
+ Examples
+ --------
+
+ >>> K = NonnegativeOrthant(5)
+ >>> K.ball_radius(matrix([1,2,3,4,5]))
+ 0.5
+
+ """
+ if not isinstance(point, matrix):
+ raise TypeError('the given point is not a cvxopt.base.matrix')
+ if not point.size == (self.dimension(), 1):
+ raise TypeError('the given point has the wrong dimensions')
+ if not point in self:
+ raise ValueError('the given point does not lie in the cone')
+
+ return min(list(point)) / 2.0
+
+
class IceCream(SymmetricCone):
"""
return norm(radius) < (height + options.ABS_TOL)
+ def ball_radius(self, point):
+ r"""
+ Return the radius of a ball around ``point`` in this cone.
+
+ Since a radius cannot be negative, the ``point`` must be
+ contained in this cone; otherwise, an error is raised.
+
+ The minimum distance from ``point`` to the complement of this
+ cone will always occur at its projection onto that set. It is
+ not hard to see that the projection is at a "down and out" angle
+ of :math:`\pi/4` towards the outside of the cone. If one draws a
+ right triangle involving the ``point`` and that projection, it
+ becomes clear that the distance between ``point`` and its
+ projection is a factor of :math:`1/\sqrt(2)` times the "horizontal"
+ distance from ``point`` to boundary of this cone. For simplicity
+ we take :math:`1/2` instead.
+
+ Parameters
+ ----------
+
+ point : matrix
+ A point contained in this cone.
+
+ Returns
+ -------
+
+ float
+ A radius ``r`` such that the ball of radius ``r`` centered at
+ ``point`` is contained entirely within this cone.
+
+ Raises
+ ------
+
+ TypeError
+ If ``point`` is not a :class:`cvxopt.base.matrix`.
+
+ TypeError
+ If ``point`` has the wrong dimensions.
+
+ ValueError
+ if ``point`` is not contained in this cone.
+
+ Examples
+ --------
+
+ The height of ``x`` below is one (its first coordinate), and so
+ the radius of the circle obtained from a height-one cross
+ section is also one. Note that the last two coordinates of ``x``
+ are half of the way to the boundary of the cone, and in the
+ direction of a 30-60-90 triangle. If one follows those
+ coordinates, they hit at :math:`\left(1, \frac{\sqrt(3)}{2},
+ \frac{1}{2}\right)` having unit norm. Thus the "horizontal"
+ distance to the boundary of the cone is :math:`1 - \left\lVert x
+ \right\rVert`, which simplifies to :math:`1/2`. And rather than
+ involve a square root, we divide by two for a final safe radius
+ of :math:`1/4`.
+
+ >>> from math import sqrt
+ >>> K = IceCream(3)
+ >>> x = matrix([1, sqrt(3)/4.0, 1/4.0])
+ >>> K.ball_radius(x)
+ 0.25
+
+ """
+ if not isinstance(point, matrix):
+ raise TypeError('the given point is not a cvxopt.base.matrix')
+ if not point.size == (self.dimension(), 1):
+ raise TypeError('the given point has the wrong dimensions')
+ if not point in self:
+ raise ValueError('the given point does not lie in the cone')
+
+ height = point[0]
+ radius = norm(point[1:])
+ return (height - radius) / 2.0
+
class SymmetricPSD(SymmetricCone):
r"""
def cvxopt_dims(self):
"""
- Return a dictionary of dimensions corresponding to the factors
- of this cartesian product. The format of this dictionary is
- described in the CVXOPT user's guide:
-
- http://cvxopt.org/userguide/coneprog.html#linear-cone-programs
+ Return a dictionary of dimensions corresponding to the
+ factors of this cartesian product. The format of this dictionary
+ is described in the `CVXOPT user's guide
+ <http://cvxopt.org/userguide/coneprog.html#linear-cone-programs>`_.
Returns
-------
projects / dunshire.git / blobdiff