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t/31312/interactive simplex method improve support for base fields other than qq #36

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merged 2 commits into from
May 8, 2024
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t/31312/interactive simplex method improve support for base fields other than qq #36

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2ca6131
fix doc tests
ComboProblem May 1, 2024
cb67d63
removed RDF import; updated doc test to include RDF
ComboProblem May 8, 2024
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53 changes: 47 additions & 6 deletions src/sage/numerical/interactive_simplex_method.py
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Original file line number Diff line number Diff line change
Expand Up @@ -200,7 +200,6 @@
from sage.rings.infinity import Infinity
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
from sage.rings.rational_field import QQ
from sage.rings.real_double import RDF
from sage.rings.integer_ring import ZZ
from sage.structure.all import SageObject
from sage.symbolic.ring import SR
Expand Down Expand Up @@ -302,7 +301,7 @@ def _latex_product(coefficients, variables,
sage: var("x, y") # needs sage.symbolic
(x, y)
sage: print(_latex_product([-1, 3], [x, y])) # needs sage.symbolic
- \mspace{-6mu}&\mspace{-6mu} x \mspace{-6mu}&\mspace{-6mu} + \mspace{-6mu}&\mspace{-6mu} 3 y
- \mspace{-6mu}&\mspace{-6mu} 1 x \mspace{-6mu}&\mspace{-6mu} + \mspace{-6mu}&\mspace{-6mu} 3 y
"""
entries = []
for c, v in zip(coefficients, variables):
Expand Down Expand Up @@ -1174,10 +1173,14 @@ def dual(self, y=None):
objective_constant_term=self._constant_term)

@cached_method
def feasible_set(self):
def feasible_set(self, backend=None):
r"""
Return the feasible set of ``self``.

INPUT:

- (optional) a backend for :mod:`Polyhedron <sage.geometry.polyhedron.constructor>`

OUTPUT:

- a :mod:`Polyhedron <sage.geometry.polyhedron.constructor>`
Expand All @@ -1191,7 +1194,18 @@ def feasible_set(self):
sage: P.feasible_set()
A 2-dimensional polyhedron in QQ^2
defined as the convex hull of 4 vertices
"""
sage: P.feasible_set(backend='cdd')
A 2-dimensional polyhedron in QQ^2
defined as the convex hull of 4 vertices
sage: from sage.rings.real_double import RDF
sage: A = ([RDF(1),RDF(1)], [RDF(3), RDF(1)])
sage: b = (1000, 1500)
sage: c = (10, 5)
sage: P = InteractiveLPProblem(A, b, c, ["C", "B"], variable_type=">=")
sage: P.feasible_set()
A 2-dimensional polyhedron in RDF^2
defined as the convex hull of 4 vertices
"""
ieqs = []
eqns = []
for a, r, b in zip(self.A().rows(), self._constraint_types, self.b()):
Expand All @@ -1206,6 +1220,8 @@ def feasible_set(self):
ieqs.append([0] + list(-n))
elif r == ">=":
ieqs.append([0] + list(n))
if backend is not None:
return Polyhedron(ieqs=ieqs, eqns=eqns, backend=backend)
return Polyhedron(ieqs=ieqs, eqns=eqns)

def is_bounded(self):
Expand Down Expand Up @@ -2653,6 +2669,31 @@ def run_simplex_method(self):
Entering: $x_{2}$. Leaving: $x_{3}$.
...
The optimal value: $6250$. An optimal solution: $\left(250,\,750\right)$.

TESTS::

sage: from sage.rings.real_double import RDF
sage: A = ([RDF(1), RDF(1)], [RDF(3), RDF(1)], [RDF(-1), RDF(-1)])
sage: b = (RDF(1000), RDF(1500), RDF(-400))
sage: c = (RDF(10), RDF(5))
sage: P = InteractiveLPProblemStandardForm(A, b, c)
sage: P.run_simplex_method()
\begin{equation*}
...
\end{equation*}
The initial dictionary is infeasible, solving auxiliary problem.
...
Entering: $x_{0}$. Leaving: $x_{5}$.
...
Entering: $x_{1}$. Leaving: $x_{0}$.
...
Back to the original problem.
...
Entering: $x_{5}$. Leaving: $x_{4}$.
...
Entering: $x_{2}$. Leaving: $x_{3}$.
...
The optimal value: $6250.0$. An optimal solution: $\left(249.99999999999997,\,750.0\right)$.
"""
output = []
d = self.initial_dictionary()
Expand Down Expand Up @@ -4002,8 +4043,8 @@ def _latex_(self):
\renewcommand{\arraystretch}{1.5} %notruncate
\begin{array}{|rcrcrcr|}
\hline
x_{3} \mspace{-6mu}&\mspace{-6mu} = \mspace{-6mu}&\mspace{-6mu} 1000 \mspace{-6mu}&\mspace{-6mu} - \mspace{-6mu}&\mspace{-6mu} x_{1} \mspace{-6mu}&\mspace{-6mu} - \mspace{-6mu}&\mspace{-6mu} x_{2}\\
x_{4} \mspace{-6mu}&\mspace{-6mu} = \mspace{-6mu}&\mspace{-6mu} 1500 \mspace{-6mu}&\mspace{-6mu} - \mspace{-6mu}&\mspace{-6mu} 3 x_{1} \mspace{-6mu}&\mspace{-6mu} - \mspace{-6mu}&\mspace{-6mu} x_{2}\\
x_{3} \mspace{-6mu}&\mspace{-6mu} = \mspace{-6mu}&\mspace{-6mu} 1000 \mspace{-6mu}&\mspace{-6mu} - \mspace{-6mu}&\mspace{-6mu} 1 x_{1} \mspace{-6mu}&\mspace{-6mu} - \mspace{-6mu}&\mspace{-6mu} 1 x_{2}\\
x_{4} \mspace{-6mu}&\mspace{-6mu} = \mspace{-6mu}&\mspace{-6mu} 1500 \mspace{-6mu}&\mspace{-6mu} - \mspace{-6mu}&\mspace{-6mu} 3 x_{1} \mspace{-6mu}&\mspace{-6mu} - \mspace{-6mu}&\mspace{-6mu} 1 x_{2}\\
\hline
z \mspace{-6mu}&\mspace{-6mu} = \mspace{-6mu}&\mspace{-6mu} 0 \mspace{-6mu}&\mspace{-6mu} + \mspace{-6mu}&\mspace{-6mu} 10 x_{1} \mspace{-6mu}&\mspace{-6mu} + \mspace{-6mu}&\mspace{-6mu} 5 x_{2}\\
\hline
Expand Down