]>
gitweb.michael.orlitzky.com - dunshire.git/blob - src/dunshire/cones.py
2 Class definitions for all of the symmetric cones (and their superclass,
3 SymmetricCone) supported by CVXOPT.
6 from cvxopt
import matrix
7 from matrices
import eigenvalues
, norm
11 An instance of a symmetric (self-dual and homogeneous) cone.
13 There are three types of symmetric cones supported by CVXOPT:
15 1. The nonnegative orthant in the real n-space.
16 2. The Lorentz "ice cream" cone, or the second-order cone.
17 3. The cone of symmetric positive-semidefinite matrices.
19 This class is intended to encompass them all.
21 def __init__(self
, dimension
):
23 A generic constructor for symmetric cones.
25 When constructing a single symmetric cone (i.e. not a cartesian
26 product of them), the only information that we need is its
27 dimension. We take that dimension as a parameter, and store it
32 - ``dimension`` -- the dimension of this cone.
36 raise ValueError('cones must have dimension greater than zero')
38 self
._dimension
= dimension
41 def __contains__(self
, point
):
43 Return whether or not ``point`` belongs to this cone.
47 >>> K = SymmetricCone(5)
48 >>> matrix([1,2]) in K
49 Traceback (most recent call last):
54 raise NotImplementedError
56 def contains_strict(self
, point
):
58 Return whether or not ``point`` belongs to the interior
63 >>> K = SymmetricCone(5)
64 >>> K.contains_strict(matrix([1,2]))
65 Traceback (most recent call last):
69 raise NotImplementedError
73 Return the dimension of this symmetric cone.
75 The dimension of this symmetric cone is recorded during its
76 creation. This method simply returns the recorded value, and
77 should not need to be overridden in subclasses. We prefer to do
78 any special computation in ``__init__()`` and record the result
79 in ``self._dimension``.
83 >>> K = SymmetricCone(5)
88 return self
._dimension
91 class NonnegativeOrthant(SymmetricCone
):
93 The nonnegative orthant in ``n`` dimensions.
97 >>> K = NonnegativeOrthant(3)
99 Nonnegative orthant in the real 3-space
104 Output a human-readable description of myself.
106 tpl
= 'Nonnegative orthant in the real {:d}-space'
107 return tpl
.format(self
.dimension())
109 def __contains__(self
, point
):
111 Return whether or not ``point`` belongs to this cone.
115 An instance of the ``cvxopt.base.matrix`` class having
116 dimensions ``(n,1)`` where ``n`` is the dimension of this cone.
120 >>> K = NonnegativeOrthant(3)
121 >>> matrix([1,2,3]) in K
124 >>> K = NonnegativeOrthant(3)
125 >>> matrix([1,-0.1,3]) in K
128 >>> K = NonnegativeOrthant(3)
130 Traceback (most recent call last):
132 TypeError: the given point is not a cvxopt.base.matrix
134 >>> K = NonnegativeOrthant(3)
135 >>> matrix([1,2]) in K
136 Traceback (most recent call last):
138 TypeError: the given point has the wrong dimensions
141 if not isinstance(point
, matrix
):
142 raise TypeError('the given point is not a cvxopt.base.matrix')
143 if not point
.size
== (self
.dimension(), 1):
144 raise TypeError('the given point has the wrong dimensions')
146 return all([x
>= 0 for x
in point
])
149 def contains_strict(self
, point
):
151 Return whether or not ``point`` belongs to the interior of this
156 An instance of the ``cvxopt.base.matrix`` class having
157 dimensions ``(n,1)`` where ``n`` is the dimension of this cone.
161 >>> K = NonnegativeOrthant(3)
162 >>> K.contains_strict(matrix([1,2,3]))
165 >>> K = NonnegativeOrthant(3)
166 >>> K.contains_strict(matrix([1,0,1]))
169 >>> K = NonnegativeOrthant(3)
170 >>> K.contains_strict(matrix([1,-0.1,3]))
173 >>> K = NonnegativeOrthant(3)
174 >>> K.contains_strict([1,2,3])
175 Traceback (most recent call last):
177 TypeError: the given point is not a cvxopt.base.matrix
179 >>> K = NonnegativeOrthant(3)
180 >>> K.contains_strict(matrix([1,2]))
181 Traceback (most recent call last):
183 TypeError: the given point has the wrong dimensions
186 if not isinstance(point
, matrix
):
187 raise TypeError('the given point is not a cvxopt.base.matrix')
188 if not point
.size
== (self
.dimension(), 1):
189 raise TypeError('the given point has the wrong dimensions')
191 return all([x
> 0 for x
in point
])
195 class IceCream(SymmetricCone
):
197 The nonnegative orthant in ``n`` dimensions.
203 Lorentz "ice cream" cone in the real 3-space
208 Output a human-readable description of myself.
210 tpl
= 'Lorentz "ice cream" cone in the real {:d}-space'
211 return tpl
.format(self
.dimension())
214 def __contains__(self
, point
):
216 Return whether or not ``point`` belongs to this cone.
220 An instance of the ``cvxopt.base.matrix`` class having
221 dimensions ``(n,1)`` where ``n`` is the dimension of this cone.
226 >>> matrix([1,0.5,0.5]) in K
230 >>> matrix([1,0,1]) in K
234 >>> matrix([1,1,1]) in K
239 Traceback (most recent call last):
241 TypeError: the given point is not a cvxopt.base.matrix
244 >>> matrix([1,2]) in K
245 Traceback (most recent call last):
247 TypeError: the given point has the wrong dimensions
250 if not isinstance(point
, matrix
):
251 raise TypeError('the given point is not a cvxopt.base.matrix')
252 if not point
.size
== (self
.dimension(), 1):
253 raise TypeError('the given point has the wrong dimensions')
256 if self
.dimension() == 1:
257 # In one dimension, the ice cream cone is the nonnegative
262 return height
>= norm(radius
)
265 def contains_strict(self
, point
):
267 Return whether or not ``point`` belongs to the interior
272 An instance of the ``cvxopt.base.matrix`` class having
273 dimensions ``(n,1)`` where ``n`` is the dimension of this cone.
278 >>> K.contains_strict(matrix([1,0.5,0.5]))
282 >>> K.contains_strict(matrix([1,0,1]))
286 >>> K.contains_strict(matrix([1,1,1]))
290 >>> K.contains_strict([1,2,3])
291 Traceback (most recent call last):
293 TypeError: the given point is not a cvxopt.base.matrix
296 >>> K.contains_strict(matrix([1,2]))
297 Traceback (most recent call last):
299 TypeError: the given point has the wrong dimensions
302 if not isinstance(point
, matrix
):
303 raise TypeError('the given point is not a cvxopt.base.matrix')
304 if not point
.size
== (self
.dimension(), 1):
305 raise TypeError('the given point has the wrong dimensions')
308 if self
.dimension() == 1:
309 # In one dimension, the ice cream cone is the nonnegative
314 return height
> norm(radius
)
317 class SymmetricPSD(SymmetricCone
):
319 The nonnegative orthant in ``n`` dimensions.
323 >>> K = SymmetricPSD(3)
325 Cone of symmetric positive-semidefinite matrices on the real 3-space
330 Output a human-readable description of myself.
332 tpl
= 'Cone of symmetric positive-semidefinite matrices ' \
333 'on the real {:d}-space'
334 return tpl
.format(self
.dimension())
337 def __contains__(self
, point
):
339 Return whether or not ``point`` belongs to this cone.
343 An instance of the ``cvxopt.base.matrix`` class having
344 dimensions ``(n,n)`` where ``n`` is the dimension of this cone.
345 Its type code must be 'd'.
349 >>> K = SymmetricPSD(2)
350 >>> matrix([[1,0],[0,1]], tc='d') in K
353 >>> K = SymmetricPSD(2)
354 >>> matrix([[0,0],[0,0]], tc='d') in K
357 >>> K = SymmetricPSD(2)
358 >>> [[1,2],[2,3]] in K
359 Traceback (most recent call last):
361 TypeError: the given point is not a cvxopt.base.matrix
363 >>> K = SymmetricPSD(3)
364 >>> matrix([[1,2],[3,4]], tc='d') in K
365 Traceback (most recent call last):
367 TypeError: the given point has the wrong dimensions
370 if not isinstance(point
, matrix
):
371 raise TypeError('the given point is not a cvxopt.base.matrix')
372 if not point
.size
== (self
.dimension(), self
.dimension()):
373 raise TypeError('the given point has the wrong dimensions')
374 return all([e
>= 0 for e
in eigenvalues(point
)])
377 def contains_strict(self
, point
):
379 Return whether or not ``point`` belongs to the interior
384 An instance of the ``cvxopt.base.matrix`` class having
385 dimensions ``(n,n)`` where ``n`` is the dimension of this cone.
386 Its type code must be 'd'.
390 >>> K = SymmetricPSD(2)
391 >>> K.contains_strict(matrix([[1,0],[0,1]], tc='d'))
394 >>> K = SymmetricPSD(2)
395 >>> K.contains_strict(matrix([[0,0],[0,0]], tc='d'))
398 >>> K = SymmetricPSD(2)
399 >>> K.contains_strict([[1,2],[2,3]])
400 Traceback (most recent call last):
402 TypeError: the given point is not a cvxopt.base.matrix
404 >>> K = SymmetricPSD(3)
405 >>> K.contains_strict(matrix([[1,2],[3,4]], tc='d'))
406 Traceback (most recent call last):
408 TypeError: the given point has the wrong dimensions
411 if not isinstance(point
, matrix
):
412 raise TypeError('the given point is not a cvxopt.base.matrix')
413 if not point
.size
== (self
.dimension(), self
.dimension()):
414 raise TypeError('the given point has the wrong dimensions')
415 return all([e
> 0 for e
in eigenvalues(point
)])
418 class CartesianProduct(SymmetricCone
):
420 A cartesian product of symmetric cones, which is itself a symmetric
425 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(2))
427 Cartesian product of dimension 5 with 2 factors:
428 * Nonnegative orthant in the real 3-space
429 * Lorentz "ice cream" cone in the real 2-space
432 def __init__(self
, *factors
):
433 my_dimension
= sum([f
.dimension() for f
in factors
])
434 super().__init
__(my_dimension
)
435 self
._factors
= factors
439 Output a human-readable description of myself.
441 tpl
= 'Cartesian product of dimension {:d} with {:d} factors:'
442 tpl
+= '\n * {!s}' * len(self
.factors())
443 format_args
= [self
.dimension(), len(self
.factors())]
444 format_args
+= list(self
.factors())
445 return tpl
.format(*format_args
)
447 def __contains__(self
, point
):
449 Return whether or not ``point`` belongs to this cone.
453 An instance of the ``cvxopt.base.matrix`` class having
454 dimensions ``(n,1)`` where ``n`` is the dimension of this cone.
458 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
459 >>> matrix([1,2,3,1,0.5,0.5]) in K
462 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
463 >>> matrix([0,0,0,1,0,1]) in K
466 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
467 >>> matrix([1,1,1,1,1,1]) in K
470 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
471 >>> matrix([1,-1,1,1,0,1]) in K
474 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
475 >>> [1,2,3,4,5,6] in K
476 Traceback (most recent call last):
478 TypeError: the given point is not a cvxopt.base.matrix
480 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
481 >>> matrix([1,2]) in K
482 Traceback (most recent call last):
484 TypeError: the given point has the wrong dimensions
487 if not isinstance(point
, matrix
):
488 raise TypeError('the given point is not a cvxopt.base.matrix')
489 if not point
.size
== (self
.dimension(), 1):
490 raise TypeError('the given point has the wrong dimensions')
492 for factor
in self
.factors():
493 # Split off the components of ``point`` corresponding to
495 factor_part
= point
[0:factor
.dimension()]
496 if not factor_part
in factor
:
498 point
= point
[factor
.dimension():]
503 def contains_strict(self
, point
):
505 Return whether or not ``point`` belongs to the interior
510 An instance of the ``cvxopt.base.matrix`` class having
511 dimensions ``(n,1)`` where ``n`` is the dimension of this cone.
515 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
516 >>> K.contains_strict(matrix([1,2,3,1,0.5,0.5]))
519 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
520 >>> K.contains_strict(matrix([1,2,3,1,0,1]))
523 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
524 >>> K.contains_strict(matrix([0,1,1,1,0.5,0.5]))
527 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
528 >>> K.contains_strict(matrix([1,1,1,1,1,1]))
531 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
532 >>> K.contains_strict(matrix([1,-1,1,1,0,1]))
535 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
536 >>> K.contains_strict([1,2,3,4,5,6])
537 Traceback (most recent call last):
539 TypeError: the given point is not a cvxopt.base.matrix
541 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(3))
542 >>> K.contains_strict(matrix([1,2]))
543 Traceback (most recent call last):
545 TypeError: the given point has the wrong dimensions
548 if not isinstance(point
, matrix
):
549 raise TypeError('the given point is not a cvxopt.base.matrix')
550 if not point
.size
== (self
.dimension(), 1):
551 raise TypeError('the given point has the wrong dimensions')
553 for factor
in self
.factors():
554 # Split off the components of ``point`` corresponding to
556 factor_part
= point
[0:factor
.dimension()]
557 if not factor
.contains_strict(factor_part
):
559 point
= point
[factor
.dimension():]
566 Return a tuple containing the factors (in order) of this
571 >>> K = CartesianProduct(NonnegativeOrthant(3), IceCream(2))
578 def cvxopt_dims(self
):
580 Return a dictionary of dimensions corresponding to the factors
581 of this cartesian product. The format of this dictionary is
582 described in the CVXOPT user's guide:
584 http://cvxopt.org/userguide/coneprog.html#linear-cone-programs
588 >>> K = CartesianProduct(NonnegativeOrthant(3),
591 >>> d = K.cvxopt_dims()
592 >>> (d['l'], d['q'], d['s'])
596 dims
= {'l':0, 'q':[], 's':[]}
597 dims
['l'] += sum([K
.dimension()
598 for K
in self
.factors()
599 if isinstance(K
, NonnegativeOrthant
)])
600 dims
['q'] = [K
.dimension()
601 for K
in self
.factors()
602 if isinstance(K
, IceCream
)]
603 dims
['s'] = [K
.dimension()
604 for K
in self
.factors()
605 if isinstance(K
, SymmetricPSD
)]