Coverage for local/lib/python2.7/site-packages/sage/numerical/backends/glpk

cpdef int add_variables(self, int number, lower_bound=0.0, upper_bound=None, binary=False, continuous=False, integer=False, obj=0.0, names=None) except -1:

"""

Add ``number`` new variables.

This amounts to adding new columns to the matrix. By default,

the variables are both positive, real and their coefficient in

the objective function is 0.0.

INPUT:

- ``n`` - the number of new variables (must be > 0)

- ``lower_bound`` - the lower bound of the variable (default: 0)

- ``upper_bound`` - the upper bound of the variable (default: ``None``)

- ``binary`` - ``True`` if the variable is binary (default: ``False``).

- ``continuous`` - ``True`` if the variable is binary (default: ``True``).

- ``integer`` - ``True`` if the variable is binary (default: ``False``).

- ``obj`` - (optional) coefficient of all variables in the objective function (default: 0.0)

- ``names`` - optional list of names (default: ``None``)

OUTPUT: The index of the variable created last.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.ncols()

sage: p.add_variables(5)

sage: p.ncols()

sage: p.add_variables(2, lower_bound=-2.0, integer=True, obj=42.0, names=['a','b'])

TESTS:

Check that arguments are used::

sage: p.col_bounds(5) # tol 1e-8

(-2.0, None)

sage: p.is_variable_integer(5)

True

sage: p.col_name(5)

'a'

sage: p.objective_coefficient(5)

42.0

"""

cdef int vtype = int(bool(binary)) + int(bool(continuous)) + int(bool(integer))

if vtype == 0:

continuous = True

elif vtype != 1:

raise ValueError("Exactly one parameter of 'binary', 'integer' and 'continuous' must be 'True'.")

glp_add_cols(self.lp, number)

cdef int n_var

n_var = glp_get_num_cols(self.lp)

cdef int i

for 0<= i < number:

self.variable_lower_bound(n_var - i - 1, lower_bound)

self.variable_upper_bound(n_var - i - 1, upper_bound)

if continuous:

glp_set_col_kind(self.lp, n_var - i, GLP_CV)

elif binary:

glp_set_col_kind(self.lp, n_var - i, GLP_BV)

elif integer:

glp_set_col_kind(self.lp, n_var - i, GLP_IV)

if obj:

self.objective_coefficient(n_var - i - 1, obj)

if names is not None:

glp_set_col_name(self.lp, n_var - i, names[number - i - 1])

return n_var - 1

cpdef set_variable_type(self, int variable, int vtype):

"""

Set the type of a variable

INPUT:

- ``variable`` (integer) -- the variable's id

- ``vtype`` (integer) :

* 1 Integer

* 0 Binary

* -1 Real

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.ncols()

sage: p.add_variable()

sage: p.set_variable_type(0,1)

sage: p.is_variable_integer(0)

True

"""

if vtype==1:

glp_set_col_kind(self.lp, variable+1, GLP_IV)

elif vtype==0:

glp_set_col_kind(self.lp, variable+1, GLP_BV)

else:

glp_set_col_kind(self.lp, variable+1, GLP_CV)

cpdef set_sense(self, int sense):

"""

Set the direction (maximization/minimization).

INPUT:

- ``sense`` (integer) :

* +1 => Maximization

* -1 => Minimization

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.is_maximization()

True

sage: p.set_sense(-1)

sage: p.is_maximization()

False

"""

if sense == 1:

glp_set_obj_dir(self.lp, GLP_MAX)

else:

glp_set_obj_dir(self.lp, GLP_MIN)

cpdef objective_coefficient(self, int variable, coeff=None):

"""

Set or get the coefficient of a variable in the objective function

INPUT:

- ``variable`` (integer) -- the variable's id

- ``coeff`` (double) -- its coefficient or ``None`` for

reading (default: ``None``)

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variable()

sage: p.objective_coefficient(0)

0.0

sage: p.objective_coefficient(0,2)

sage: p.objective_coefficient(0)

2.0

"""

if coeff is None:

return glp_get_obj_coef(self.lp, variable + 1)

else:

glp_set_obj_coef(self.lp, variable + 1, coeff)

cpdef problem_name(self, char * name = NULL):

"""

Return or define the problem's name

INPUT:

- ``name`` (``char *``) -- the problem's name. When set to

``NULL`` (default), the method returns the problem's name.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.problem_name("There once was a french fry")

sage: print(p.problem_name())

There once was a french fry

"""

cdef char * n

if name == NULL:

n = <char *> glp_get_prob_name(self.lp)

if n == NULL:

return ""

else:

return n

else:

if len(name) > 255:

raise ValueError("Problem name for GLPK must not be longer than 255 characters.")

glp_set_prob_name(self.lp, name)

cpdef set_objective(self, list coeff, d = 0.0):

"""

Set the objective function.

INPUT:

- ``coeff`` - a list of real values, whose ith element is the

coefficient of the ith variable in the objective function.

- ``d`` (double) -- the constant term in the linear function (set to `0` by default)

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(5)

sage: p.set_objective([1, 1, 2, 1, 3])

sage: [p.objective_coefficient(x) for x in range(5)]

[1.0, 1.0, 2.0, 1.0, 3.0]

"""

cdef int i

for i,v in enumerate(coeff):

glp_set_obj_coef(self.lp, i+1, v)

glp_set_obj_coef(self.lp, 0, d)

self.obj_constant_term = d

cpdef set_verbosity(self, int level):

"""

Set the verbosity level

INPUT:

- ``level`` (integer) -- From 0 (no verbosity) to 3.

EXAMPLES::

sage: p.<x> = MixedIntegerLinearProgram(solver="GLPK")

sage: p.add_constraint(10 * x[0] <= 1)

sage: p.add_constraint(5 * x[1] <= 1)

sage: p.set_objective(x[0] + x[1])

sage: p.solve()

0.30000000000000004

sage: p.get_backend().set_verbosity(3)

sage: p.solve()

GLPK Integer Optimizer, v4.63

2 rows, 2 columns, 2 non-zeros

0 integer variables, none of which are binary

Preprocessing...

Objective value = 3.000000000e-01

INTEGER OPTIMAL SOLUTION FOUND BY MIP PREPROCESSOR

0.30000000000000004

sage: p.<x> = MixedIntegerLinearProgram(solver="GLPK/exact")

sage: p.add_constraint(10 * x[0] <= 1)

sage: p.add_constraint(5 * x[1] <= 1)

sage: p.set_objective(x[0] + x[1])

sage: p.solve()

0.3

sage: p.get_backend().set_verbosity(2)

sage: p.solve()

* 2: objval = 0.3 (0)

0.3

sage: p.get_backend().set_verbosity(3)

sage: p.solve()

glp_exact: 2 rows, 2 columns, 2 non-zeros

GNU MP bignum library is being used

* 2: objval = 0.3 (0)

OPTIMAL SOLUTION FOUND

0.3

"""

if level == 0:

self.iocp.msg_lev = GLP_MSG_OFF

self.smcp.msg_lev = GLP_MSG_OFF

elif level == 1:

self.iocp.msg_lev = GLP_MSG_ERR

self.smcp.msg_lev = GLP_MSG_ERR

elif level == 2:

self.iocp.msg_lev = GLP_MSG_ON

self.smcp.msg_lev = GLP_MSG_ON

else:

self.iocp.msg_lev = GLP_MSG_ALL

self.smcp.msg_lev = GLP_MSG_ALL

cpdef remove_constraint(self, int i):

r"""

Remove a constraint from self.

INPUT:

- ``i`` -- index of the constraint to remove

EXAMPLES::

sage: p = MixedIntegerLinearProgram(solver='GLPK')

sage: x, y = p['x'], p['y']

sage: p.add_constraint(2*x + 3*y <= 6)

sage: p.add_constraint(3*x + 2*y <= 6)

sage: p.add_constraint(x >= 0)

sage: p.set_objective(x + y + 7)

sage: p.set_integer(x); p.set_integer(y)

sage: p.solve()

9.0

sage: p.remove_constraint(0)

sage: p.solve()

10.0

Removing fancy constraints does not make Sage crash::

sage: MixedIntegerLinearProgram(solver = "GLPK").remove_constraint(-2)

Traceback (most recent call last):

...

ValueError: The constraint's index i must satisfy 0 <= i < number_of_constraints

"""

cdef int rows[2]

if i < 0 or i >= glp_get_num_rows(self.lp):

raise ValueError("The constraint's index i must satisfy 0 <= i < number_of_constraints")

rows[1] = i + 1

glp_del_rows(self.lp, 1, rows)

glp_std_basis(self.lp)

cpdef remove_constraints(self, constraints):

r"""

Remove several constraints.

INPUT:

- ``constraints`` -- an iterable containing the indices of the rows to remove.

EXAMPLES::

sage: p = MixedIntegerLinearProgram(solver='GLPK')

sage: x, y = p['x'], p['y']

sage: p.add_constraint(2*x + 3*y <= 6)

sage: p.add_constraint(3*x + 2*y <= 6)

sage: p.add_constraint(x >= 0)

sage: p.set_objective(x + y + 7)

sage: p.set_integer(x); p.set_integer(y)

sage: p.solve()

9.0

sage: p.remove_constraints([0])

sage: p.solve()

10.0

sage: p.get_values([x,y])

[0.0, 3.0]

TESTS:

Removing fancy constraints does not make Sage crash::

sage: MixedIntegerLinearProgram(solver= "GLPK").remove_constraints([0, -2])

Traceback (most recent call last):

...

ValueError: The constraint's index i must satisfy 0 <= i < number_of_constraints

"""

cdef int i, c

cdef int m = len(constraints)

cdef int * rows = <int *>sig_malloc((m + 1) * sizeof(int *))

cdef int nrows = glp_get_num_rows(self.lp)

for i in xrange(m):

c = constraints[i]

if c < 0 or c >= nrows:

sig_free(rows)

raise ValueError("The constraint's index i must satisfy 0 <= i < number_of_constraints")

rows[i+1] = c + 1

glp_del_rows(self.lp, m, rows)

sig_free(rows)

glp_std_basis(self.lp)

cpdef add_linear_constraint(self, coefficients, lower_bound, upper_bound, name=None):

"""

Add a linear constraint.

INPUT:

- ``coefficients`` an iterable with ``(c,v)`` pairs where ``c``

is a variable index (integer) and ``v`` is a value (real

value).

- ``lower_bound`` - a lower bound, either a real value or ``None``

- ``upper_bound`` - an upper bound, either a real value or ``None``

- ``name`` - an optional name for this row (default: ``None``)

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(5)

sage: p.add_linear_constraint(list(zip(range(5), range(5))), 2.0, 2.0)

sage: p.row(0)

([4, 3, 2, 1], [4.0, 3.0, 2.0, 1.0])

sage: p.row_bounds(0)

(2.0, 2.0)

sage: p.add_linear_constraint(list(zip(range(5), range(5))), 1.0, 1.0, name='foo')

sage: p.row_name(1)

'foo'

TESTS:

This used to crash Sage, but was fixed in :trac:`19525`::

sage: p = MixedIntegerLinearProgram(solver="glpk")

sage: q = MixedIntegerLinearProgram(solver="glpk")

sage: q.add_constraint(p.new_variable()[0] <= 1)

Traceback (most recent call last):

...

GLPKError: glp_set_mat_row: i = 1; len = 1; invalid row length

Error detected in file api/prob1.c at line ...

"""

if lower_bound is None and upper_bound is None:

raise ValueError("At least one of 'upper_bound' or 'lower_bound' must be set.")

glp_add_rows(self.lp, 1)

cdef int n = glp_get_num_rows(self.lp)

cdef MemoryAllocator mem = MemoryAllocator()

cdef int * row_i

cdef double * row_values

row_i = <int*>mem.allocarray(len(coefficients)+1, sizeof(int))

row_values = <double*>mem.allocarray(len(coefficients)+1, sizeof(double))

cdef Py_ssize_t i = 1

for c,v in coefficients:

row_i[i] = c+1

row_values[i] = v

i += 1

sig_on()

glp_set_mat_row(self.lp, n, len(coefficients), row_i, row_values)

sig_off()

if upper_bound is not None and lower_bound is None:

glp_set_row_bnds(self.lp, n, GLP_UP, upper_bound, upper_bound)

elif lower_bound is not None and upper_bound is None:

glp_set_row_bnds(self.lp, n, GLP_LO, lower_bound, lower_bound)

elif upper_bound is not None and lower_bound is not None:

if lower_bound == upper_bound:

glp_set_row_bnds(self.lp, n, GLP_FX, lower_bound, upper_bound)

else:

glp_set_row_bnds(self.lp, n, GLP_DB, lower_bound, upper_bound)

if name is not None:

glp_set_row_name(self.lp, n, name)

cpdef add_linear_constraints(self, int number, lower_bound, upper_bound, names=None):

"""

Add ``'number`` linear constraints.

INPUT:

- ``number`` (integer) -- the number of constraints to add.

- ``lower_bound`` - a lower bound, either a real value or ``None``

- ``upper_bound`` - an upper bound, either a real value or ``None``

- ``names`` - an optional list of names (default: ``None``)

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(5)

sage: p.add_linear_constraints(5, None, 2)

sage: p.row(4)

([], [])

sage: p.row_bounds(4)

(None, 2.0)

sage: p.add_linear_constraints(2, None, 2, names=['foo','bar'])

"""

if lower_bound is None and upper_bound is None:

raise ValueError("At least one of 'upper_bound' or 'lower_bound' must be set.")

glp_add_rows(self.lp, number)

cdef int n = glp_get_num_rows(self.lp)

cdef int i

for 0<= i < number:

if upper_bound is not None and lower_bound is None:

glp_set_row_bnds(self.lp, n-i, GLP_UP, upper_bound, upper_bound)

elif lower_bound is not None and upper_bound is None:

glp_set_row_bnds(self.lp, n-i, GLP_LO, lower_bound, lower_bound)

elif upper_bound is not None and lower_bound is not None:

if lower_bound == upper_bound:

glp_set_row_bnds(self.lp, n-i, GLP_FX, lower_bound, upper_bound)

else:

glp_set_row_bnds(self.lp, n-i, GLP_DB, lower_bound, upper_bound)

if names is not None:

glp_set_row_name(self.lp, n-i, names[number-i-1])

cpdef row(self, int index):

r"""

Return a row

INPUT:

- ``index`` (integer) -- the constraint's id.

OUTPUT:

A pair ``(indices, coeffs)`` where ``indices`` lists the

entries whose coefficient is nonzero, and to which ``coeffs``

associates their coefficient on the model of the

``add_linear_constraint`` method.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(5)

sage: p.add_linear_constraint(list(zip(range(5), range(5))), 2, 2)

sage: p.row(0)

([4, 3, 2, 1], [4.0, 3.0, 2.0, 1.0])

sage: p.row_bounds(0)

(2.0, 2.0)

"""

cdef int n = glp_get_num_cols(self.lp)

cdef MemoryAllocator mem = MemoryAllocator()

cdef int * c_indices = <int*>mem.allocarray(n+1, sizeof(int))

cdef double * c_values = <double*>mem.allocarray(n+1, sizeof(double))

cdef list indices = []

cdef list values = []

cdef int i,j

i = glp_get_mat_row(self.lp, index + 1, c_indices, c_values)

for 0 < j <= i:

indices.append(c_indices[j]-1)

values.append(c_values[j])

return (indices, values)

cpdef row_bounds(self, int index):

"""

Return the bounds of a specific constraint.

INPUT:

- ``index`` (integer) -- the constraint's id.

OUTPUT:

A pair ``(lower_bound, upper_bound)``. Each of them can be set

to ``None`` if the constraint is not bounded in the

corresponding direction, and is a real value otherwise.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(5)

sage: p.add_linear_constraint(list(zip(range(5), range(5))), 2, 2)

sage: p.row(0)

([4, 3, 2, 1], [4.0, 3.0, 2.0, 1.0])

sage: p.row_bounds(0)

(2.0, 2.0)

"""

cdef double ub

cdef double lb

ub = glp_get_row_ub(self.lp, index + 1)

lb = glp_get_row_lb(self.lp, index +1)

return (

(lb if lb != -DBL_MAX else None),

(ub if ub != +DBL_MAX else None)

)

cpdef col_bounds(self, int index):

"""

Return the bounds of a specific variable.

INPUT:

- ``index`` (integer) -- the variable's id.

OUTPUT:

A pair ``(lower_bound, upper_bound)``. Each of them can be set

to ``None`` if the variable is not bounded in the

corresponding direction, and is a real value otherwise.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variable()

sage: p.col_bounds(0)

(0.0, None)

sage: p.variable_upper_bound(0, 5)

sage: p.col_bounds(0)

(0.0, 5.0)

"""

cdef double ub

cdef double lb

ub = glp_get_col_ub(self.lp, index +1)

lb = glp_get_col_lb(self.lp, index +1)

return (

(lb if lb != -DBL_MAX else None),

(ub if ub != +DBL_MAX else None)

)

cpdef add_col(self, list indices, list coeffs):

"""

Add a column.

INPUT:

- ``indices`` (list of integers) -- this list contains the

indices of the constraints in which the variable's

coefficient is nonzero

- ``coeffs`` (list of real values) -- associates a coefficient

to the variable in each of the constraints in which it

appears. Namely, the ith entry of ``coeffs`` corresponds to

the coefficient of the variable in the constraint

represented by the ith entry in ``indices``.

.. NOTE::

``indices`` and ``coeffs`` are expected to be of the same

length.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.ncols()

sage: p.nrows()

sage: p.add_linear_constraints(5, 0, None)

sage: p.add_col(range(5), range(5))

sage: p.nrows()

"""

glp_add_cols(self.lp, 1)

cdef int n = glp_get_num_cols(self.lp)

cdef int * col_i

cdef double * col_values

col_i = <int *> sig_malloc((len(indices)+1) * sizeof(int))

col_values = <double *> sig_malloc((len(indices)+1) * sizeof(double))

for i,v in enumerate(indices):

col_i[i+1] = v+1

for i,v in enumerate(coeffs):

col_values[i+1] = v

glp_set_mat_col(self.lp, n, len(indices), col_i, col_values)

glp_set_col_bnds(self.lp, n, GLP_LO, 0,0)

cpdef int solve(self) except -1:

"""

Solve the problem.

Sage uses GLPK's implementation of the branch-and-cut algorithm

(``glp_intopt``) to solve the mixed-integer linear program.

This algorithm can be requested explicitly by setting the solver

parameter "simplex_or_intopt" to "intopt_only".

(If all variables are continuous, the algorithm reduces to solving the

linear program by the simplex method.)

EXAMPLES::

sage: lp = MixedIntegerLinearProgram(solver = 'GLPK', maximization = False)

sage: x, y = lp[0], lp[1]

sage: lp.add_constraint(-2*x + y <= 1)

sage: lp.add_constraint(x - y <= 1)

sage: lp.add_constraint(x + y >= 2)

sage: lp.set_objective(x + y)

sage: lp.set_integer(x)

sage: lp.set_integer(y)

sage: lp.solve()

2.0

sage: lp.get_values([x, y])

[1.0, 1.0]

.. NOTE::

This method raises ``MIPSolverException`` exceptions when

the solution can not be computed for any reason (none

exists, or the LP solver was not able to find it, etc...)

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_linear_constraints(5, 0, None)

sage: p.add_col(range(5), range(5))

sage: p.solve()

sage: p.objective_coefficient(0,1)

sage: p.solve()

Traceback (most recent call last):

...

MIPSolverException: ...

.. WARNING::

Sage uses GLPK's ``glp_intopt`` to find solutions.

This routine sometimes FAILS CATASTROPHICALLY

when given a system it cannot solve. (:trac:`12309`.)

Here, "catastrophic" can mean either "infinite loop" or

segmentation fault. Upstream considers this behavior

"essentially innate" to their design, and suggests

preprocessing it with ``glp_simplex`` first.

Thus, if you suspect that your system is infeasible,

set the ``preprocessing`` option first.

EXAMPLES::

sage: lp = MixedIntegerLinearProgram(solver = "GLPK")

sage: v = lp.new_variable(nonnegative=True)

sage: lp.add_constraint(v[1] +v[2] -2.0 *v[3], max=-1.0)

sage: lp.add_constraint(v[0] -4.0/3 *v[1] +1.0/3 *v[2], max=-1.0/3)

sage: lp.add_constraint(v[0] +0.5 *v[1] -0.5 *v[2] +0.25 *v[3], max=-0.25)

sage: lp.solve()

0.0

sage: lp.add_constraint(v[0] +4.0 *v[1] -v[2] +v[3], max=-1.0)

sage: lp.solve()

Traceback (most recent call last):

...

GLPKError: Assertion failed: ...

sage: lp.solver_parameter("simplex_or_intopt", "simplex_then_intopt")

sage: lp.solve()

Traceback (most recent call last):

...

MIPSolverException: GLPK: Problem has no feasible solution

If we switch to "simplex_only", the integrality constraints are ignored,

and we get an optimal solution to the continuous relaxation.

EXAMPLES::

sage: lp = MixedIntegerLinearProgram(solver = 'GLPK', maximization = False)

sage: x, y = lp[0], lp[1]

sage: lp.add_constraint(-2*x + y <= 1)

sage: lp.add_constraint(x - y <= 1)

sage: lp.add_constraint(x + y >= 2)

sage: lp.set_objective(x + y)

sage: lp.set_integer(x)

sage: lp.set_integer(y)

sage: lp.solver_parameter("simplex_or_intopt", "simplex_only") # use simplex only

sage: lp.solve()

2.0

sage: lp.get_values([x, y])

[1.5, 0.5]

If one solves a linear program and wishes to access dual information

(`get_col_dual` etc.) or tableau data (`get_row_stat` etc.),

one needs to switch to "simplex_only" before solving.

GLPK also has an exact rational simplex solver. The only

access to data is via double-precision floats, however. It

reconstructs rationals from doubles and also provides results

as doubles.

EXAMPLES::

sage: lp.solver_parameter("simplex_or_intopt", "exact_simplex_only") # use exact simplex only

sage: lp.solve()

2.0

sage: lp.get_values([x, y])

[1.5, 0.5]

If you need the rational solution, you need to retrieve the

basis information via ``get_col_stat`` and ``get_row_stat``

and calculate the corresponding basic solution. Below we only

test that the basis information is indeed available.

Calculating the corresponding basic solution is left as an

exercise.

EXAMPLES::

sage: lp.get_backend().get_row_stat(0)

sage: lp.get_backend().get_col_stat(0)

Below we test that integers that can be exactly represented by

IEEE 754 double-precision floating point numbers survive the

rational reconstruction done by ``glp_exact`` and the subsequent

conversion to double-precision floating point numbers.

EXAMPLES::

sage: lp = MixedIntegerLinearProgram(solver = 'GLPK', maximization = True)

sage: test = 2^53 - 43

sage: lp.solver_parameter("simplex_or_intopt", "exact_simplex_only") # use exact simplex only

sage: x = lp[0]

sage: lp.add_constraint(x <= test)

sage: lp.set_objective(x)

sage: lp.solve() == test # yes, we want an exact comparison here

True

sage: lp.get_values(x) == test # yes, we want an exact comparison here

True

Below we test that GLPK backend can detect unboundedness in

"simplex_only" mode (:trac:`18838`).

EXAMPLES::

sage: lp = MixedIntegerLinearProgram(maximization=True, solver = "GLPK")

sage: lp.set_objective(lp[0])

sage: lp.solver_parameter("simplex_or_intopt", "simplex_only")

sage: lp.solve()

Traceback (most recent call last):

...

MIPSolverException: GLPK: Problem has unbounded solution

sage: lp.set_objective(lp[1])

sage: lp.solver_parameter("primal_v_dual", "GLP_DUAL")

sage: lp.solve()

Traceback (most recent call last):

...

MIPSolverException: GLPK: Problem has unbounded solution

sage: lp.solver_parameter("simplex_or_intopt", "simplex_then_intopt")

sage: lp.solve()

Traceback (most recent call last):

...

MIPSolverException: GLPK: The LP (relaxation) problem has no dual feasible solution

sage: lp.solver_parameter("simplex_or_intopt", "intopt_only")

sage: lp.solve()

Traceback (most recent call last):

...

MIPSolverException: GLPK: The LP (relaxation) problem has no dual feasible solution

sage: lp.set_max(lp[1],5)

sage: lp.solve()

5.0

Solving a LP within the acceptable gap. No exception is raised, even if

the result is not optimal. To do this, we try to compute the maximum

number of disjoint balls (of diameter 1) in a hypercube::

sage: g = graphs.CubeGraph(9)

sage: p = MixedIntegerLinearProgram(solver="GLPK")

sage: p.solver_parameter("mip_gap_tolerance",100)

sage: b = p.new_variable(binary=True)

sage: p.set_objective(p.sum(b[v] for v in g))

sage: for v in g:

....: p.add_constraint(b[v]+p.sum(b[u] for u in g.neighbors(v)) <= 1)

sage: p.add_constraint(b[v] == 1) # Force an easy non-0 solution

sage: p.solve() # rel tol 100

Same, now with a time limit::

sage: p.solver_parameter("mip_gap_tolerance",1)

sage: p.solver_parameter("timelimit",3.0)

sage: p.solve() # rel tol 100

"""

cdef int solve_status

cdef int solution_status

global solve_status_msg

global solution_status_msg

if (self.simplex_or_intopt == glp_simplex_only

or self.simplex_or_intopt == glp_simplex_then_intopt

or self.simplex_or_intopt == glp_exact_simplex_only):

if self.simplex_or_intopt == glp_exact_simplex_only:

solve_status = glp_exact(self.lp, self.smcp)

else:

solve_status = glp_simplex(self.lp, self.smcp)

solution_status = glp_get_status(self.lp)

if ((self.simplex_or_intopt == glp_intopt_only)

or (self.simplex_or_intopt == glp_simplex_then_intopt) and (solution_status != GLP_UNDEF) and (solution_status != GLP_NOFEAS)):

sig_on()

solve_status = glp_intopt(self.lp, self.iocp)

solution_status = glp_mip_status(self.lp)

sig_off()

if solution_status == GLP_OPT:

pass

elif (solution_status == GLP_FEAS) and (solve_status == GLP_ETMLIM or solve_status == GLP_EITLIM \

or solve_status == GLP_EMIPGAP or solve_status == GLP_EOBJLL or solve_status == GLP_EOBJUL):

# no exception when time limit or iteration limit or mip gap tolerances or objective limits reached.

pass

elif solution_status == GLP_UNDEF:

raise MIPSolverException("GLPK: "+solve_status_msg.get(solve_status, "unknown error during call to GLPK : "+str(solve_status)))

else:

raise MIPSolverException("GLPK: "+solution_status_msg.get(solution_status, "unknown error during call to GLPK : "+str(solution_status)))

return 0

cpdef get_objective_value(self):

"""

Returns the value of the objective function.

.. NOTE::

Behaviour is undefined unless ``solve`` has been called before.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(2)

sage: p.add_linear_constraint([[0, 1], [1, 2]], None, 3)

sage: p.set_objective([2, 5])

sage: p.solve()

sage: p.get_objective_value()

7.5

sage: p.get_variable_value(0) # abs tol 1e-15

0.0

sage: p.get_variable_value(1)

1.5

"""

if (self.simplex_or_intopt != glp_simplex_only

and self.simplex_or_intopt != glp_exact_simplex_only):

return glp_mip_obj_val(self.lp)

else:

return glp_get_obj_val(self.lp)

cpdef best_known_objective_bound(self):

r"""

Return the value of the currently best known bound.

This method returns the current best upper (resp. lower) bound on the

optimal value of the objective function in a maximization

(resp. minimization) problem. It is equal to the output of

:meth:`get_objective_value` if the MILP found an optimal solution, but

it can differ if it was interrupted manually or after a time limit (cf

:meth:`solver_parameter`).

.. NOTE::

Has no meaning unless ``solve`` has been called before.

EXAMPLES::

sage: g = graphs.CubeGraph(9)

sage: p = MixedIntegerLinearProgram(solver="GLPK")

sage: p.solver_parameter("mip_gap_tolerance",100)

sage: b = p.new_variable(binary=True)

sage: p.set_objective(p.sum(b[v] for v in g))

sage: for v in g:

....: p.add_constraint(b[v]+p.sum(b[u] for u in g.neighbors(v)) <= 1)

sage: p.add_constraint(b[v] == 1) # Force an easy non-0 solution

sage: p.solve() # rel tol 100

1.0

sage: backend = p.get_backend()

sage: backend.best_known_objective_bound() # random

48.0

"""

return self.search_tree_data.best_bound

cpdef get_relative_objective_gap(self):

r"""

Return the relative objective gap of the best known solution.

For a minimization problem, this value is computed by

`(\texttt{bestinteger} - \texttt{bestobjective}) / (1e-10 +

|\texttt{bestobjective}|)`, where ``bestinteger`` is the value returned

by :meth:`get_objective_value` and ``bestobjective`` is the value

returned by :meth:`best_known_objective_bound`. For a maximization

problem, the value is computed by `(\texttt{bestobjective} -

\texttt{bestinteger}) / (1e-10 + |\texttt{bestobjective}|)`.

.. NOTE::

Has no meaning unless ``solve`` has been called before.

EXAMPLES::

sage: g = graphs.CubeGraph(9)

sage: p = MixedIntegerLinearProgram(solver="GLPK")

sage: p.solver_parameter("mip_gap_tolerance",100)

sage: b = p.new_variable(binary=True)

sage: p.set_objective(p.sum(b[v] for v in g))

sage: for v in g:

....: p.add_constraint(b[v]+p.sum(b[u] for u in g.neighbors(v)) <= 1)

sage: p.add_constraint(b[v] == 1) # Force an easy non-0 solution

sage: p.solve() # rel tol 100

1.0

sage: backend = p.get_backend()

sage: backend.get_relative_objective_gap() # random

46.99999999999999

TESTS:

Just make sure that the variable *has* been defined, and is not just

undefined::

sage: backend.get_relative_objective_gap() > 1

True

"""

return self.search_tree_data.mip_gap

cpdef get_variable_value(self, int variable):

"""

Returns the value of a variable given by the solver.

.. NOTE::

Behaviour is undefined unless ``solve`` has been called before.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(2)

sage: p.add_linear_constraint([[0, 1], [1, 2]], None, 3)

sage: p.set_objective([2, 5])

sage: p.solve()

sage: p.get_objective_value()

7.5

sage: p.get_variable_value(0) # abs tol 1e-15

0.0

sage: p.get_variable_value(1)

1.5

"""

if (self.simplex_or_intopt != glp_simplex_only

and self.simplex_or_intopt != glp_exact_simplex_only):

return glp_mip_col_val(self.lp, variable+1)

else:

return glp_get_col_prim(self.lp, variable+1)

cpdef get_row_prim(self, int i):

r"""

Returns the value of the auxiliary variable associated with i-th row.

.. NOTE::

Behaviour is undefined unless ``solve`` has been called before.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.solve()

sage: lp.get_objective_value()

280.0

sage: lp.get_row_prim(0)

24.0

sage: lp.get_row_prim(1)

20.0

sage: lp.get_row_prim(2)

8.0

"""

return glp_get_row_prim(self.lp, i+1)

cpdef int ncols(self):

"""

Return the number of columns/variables.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.ncols()

sage: p.add_variables(2)

sage: p.ncols()

"""

return glp_get_num_cols(self.lp)

cpdef int nrows(self):

"""

Return the number of rows/constraints.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.nrows()

sage: p.add_linear_constraints(2, 2, None)

sage: p.nrows()

"""

return glp_get_num_rows(self.lp)

cpdef col_name(self, int index):

"""

Return the ``index`` th col name

INPUT:

- ``index`` (integer) -- the col's id

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variable(name='I am a variable')

sage: p.col_name(0)

'I am a variable'

"""

cdef char * s

glp_create_index(self.lp)

s = <char*> glp_get_col_name(self.lp, index + 1)

if s != NULL:

return s

else:

return ""

cpdef row_name(self, int index):

"""

Return the ``index`` th row name

INPUT:

- ``index`` (integer) -- the row's id

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_linear_constraints(1, 2, None, names=['Empty constraint 1'])

sage: p.row_name(0)

'Empty constraint 1'

"""

cdef char * s

glp_create_index(self.lp)

s = <char*> glp_get_row_name(self.lp, index + 1)

if s != NULL:

return s

else:

return ""

cpdef bint is_variable_binary(self, int index):

"""

Test whether the given variable is of binary type.

INPUT:

- ``index`` (integer) -- the variable's id

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.ncols()

sage: p.add_variable()

sage: p.set_variable_type(0,0)

sage: p.is_variable_binary(0)

True

"""

return glp_get_col_kind(self.lp, index + 1) == GLP_BV

cpdef bint is_variable_integer(self, int index):

"""

Test whether the given variable is of integer type.

INPUT:

- ``index`` (integer) -- the variable's id

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.ncols()

sage: p.add_variable()

sage: p.set_variable_type(0,1)

sage: p.is_variable_integer(0)

True

"""

return glp_get_col_kind(self.lp, index + 1) == GLP_IV

cpdef bint is_variable_continuous(self, int index):

"""

Test whether the given variable is of continuous/real type.

INPUT:

- ``index`` (integer) -- the variable's id

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.ncols()

sage: p.add_variable()

sage: p.is_variable_continuous(0)

True

sage: p.set_variable_type(0,1)

sage: p.is_variable_continuous(0)

False

"""

return glp_get_col_kind(self.lp, index + 1) == GLP_CV

cpdef bint is_maximization(self):

"""

Test whether the problem is a maximization

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.is_maximization()

True

sage: p.set_sense(-1)

sage: p.is_maximization()

False

"""

return glp_get_obj_dir(self.lp) == GLP_MAX

cpdef variable_upper_bound(self, int index, value = False):

"""

Return or define the upper bound on a variable

INPUT:

- ``index`` (integer) -- the variable's id

- ``value`` -- real value, or ``None`` to mean that the

variable has not upper bound. When set to ``False``

(default), the method returns the current value.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variable()

sage: p.col_bounds(0)

(0.0, None)

sage: p.variable_upper_bound(0, 5)

sage: p.col_bounds(0)

(0.0, 5.0)

TESTS:

:trac:`14581`::

sage: P = MixedIntegerLinearProgram(solver="GLPK")

sage: x = P["x"]

sage: P.set_max(x, 0)

sage: P.get_max(x)

0.0

Check that :trac:`10232` is fixed::

sage: p = get_solver(solver="GLPK")

sage: p.variable_upper_bound(2)

Traceback (most recent call last):

...

GLPKError: ...

sage: p.variable_upper_bound(3, 5)

Traceback (most recent call last):

...

GLPKError: ...

sage: p.add_variable()

sage: p.variable_upper_bound(0, 'hey!')

Traceback (most recent call last):

...

TypeError: a float is required

"""

cdef double x

cdef double min

cdef double dvalue

if value is False:

sig_on()

x = glp_get_col_ub(self.lp, index +1)

sig_off()

if x == DBL_MAX:

return None

else:

return x

else:

sig_on()

min = glp_get_col_lb(self.lp, index + 1)

sig_off()

if value is None:

sig_on()

if min == -DBL_MAX:

glp_set_col_bnds(self.lp, index + 1, GLP_FR, 0, 0)

else:

glp_set_col_bnds(self.lp, index + 1, GLP_LO, min, 0)

sig_off()

else:

dvalue = <double?> value

sig_on()

if min == -DBL_MAX:

glp_set_col_bnds(self.lp, index + 1, GLP_UP, 0, dvalue)

elif min == dvalue:

glp_set_col_bnds(self.lp, index + 1, GLP_FX, dvalue, dvalue)

else:

glp_set_col_bnds(self.lp, index + 1, GLP_DB, min, dvalue)

sig_off()

cpdef variable_lower_bound(self, int index, value = False):

"""

Return or define the lower bound on a variable

INPUT:

- ``index`` (integer) -- the variable's id

- ``value`` -- real value, or ``None`` to mean that the

variable has not lower bound. When set to ``False``

(default), the method returns the current value.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variable()

sage: p.col_bounds(0)

(0.0, None)

sage: p.variable_lower_bound(0, 5)

sage: p.col_bounds(0)

(5.0, None)

TESTS:

:trac:`14581`::

sage: P = MixedIntegerLinearProgram(solver="GLPK")

sage: x = P["x"]

sage: P.set_min(x, 5)

sage: P.set_min(x, 0)

sage: P.get_min(x)

0.0

Check that :trac:`10232` is fixed::

sage: p = get_solver(solver="GLPK")

sage: p.variable_lower_bound(2)

Traceback (most recent call last):

...

GLPKError: ...

sage: p.variable_lower_bound(3, 5)

Traceback (most recent call last):

...

GLPKError: ...

sage: p.add_variable()

sage: p.variable_lower_bound(0, 'hey!')

Traceback (most recent call last):

...

TypeError: a float is required

"""

cdef double x

cdef double max

cdef double dvalue

if value is False:

sig_on()

x = glp_get_col_lb(self.lp, index +1)

sig_off()

if x == -DBL_MAX:

return None

else:

return x

else:

sig_on()

max = glp_get_col_ub(self.lp, index + 1)

sig_off()

if value is None:

sig_on()

if max == DBL_MAX:

glp_set_col_bnds(self.lp, index + 1, GLP_FR, 0.0, 0.0)

else:

glp_set_col_bnds(self.lp, index + 1, GLP_UP, 0.0, max)

sig_off()

else:

dvalue = <double?> value

sig_on()

if max == DBL_MAX:

glp_set_col_bnds(self.lp, index + 1, GLP_LO, value, 0.0)

elif max == value:

glp_set_col_bnds(self.lp, index + 1, GLP_FX, value, value)

else:

glp_set_col_bnds(self.lp, index + 1, GLP_DB, value, max)

sig_off()

cpdef write_lp(self, char * filename):

"""

Write the problem to a .lp file

INPUT:

- ``filename`` (string)

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(2)

sage: p.add_linear_constraint([[0, 1], [1, 2]], None, 3)

sage: p.set_objective([2, 5])

sage: p.write_lp(os.path.join(SAGE_TMP, "lp_problem.lp"))

Writing problem data to ...

9 lines were written

"""

glp_write_lp(self.lp, NULL, filename)

cpdef write_mps(self, char * filename, int modern):

"""

Write the problem to a .mps file

INPUT:

- ``filename`` (string)

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(2)

sage: p.add_linear_constraint([[0, 1], [1, 2]], None, 3)

sage: p.set_objective([2, 5])

sage: p.write_mps(os.path.join(SAGE_TMP, "lp_problem.mps"), 2)

Writing problem data to ...

17 records were written

"""

glp_write_mps(self.lp, modern, NULL, filename)

cpdef __copy__(self):

"""

Returns a copy of self.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = MixedIntegerLinearProgram(solver = "GLPK")

sage: b = p.new_variable()

sage: p.add_constraint(b[1] + b[2] <= 6)

sage: p.set_objective(b[1] + b[2])

sage: copy(p).solve()

6.0

"""

cdef GLPKBackend p = type(self)(maximization = (1 if self.is_maximization() else -1))

p.simplex_or_intopt = self.simplex_or_intopt

p.iocp.tm_lim = self.iocp.tm_lim

glp_copy_prob(p.lp, self.lp, 1)

return p

cpdef solver_parameter(self, name, value = None):

"""

Return or define a solver parameter

INPUT:

- ``name`` (string) -- the parameter

- ``value`` -- the parameter's value if it is to be defined,

or ``None`` (default) to obtain its current value.

You can supply the name of a parameter and its value using either a

string or a ``glp_`` constant (which are defined as Cython variables of

this module).

In most cases, you can use the same name for a parameter as that given

in the GLPK documentation, which is available by downloading GLPK from

<http://www.gnu.org/software/glpk/>. The exceptions relate to parameters

common to both methods; these require you to append ``_simplex`` or

``_intopt`` to the name to resolve ambiguity, since the interface allows

access to both.

We have also provided more meaningful names, to assist readability.

Parameter **names** are specified in lower case.

To use a constant instead of a string, prepend ``glp_`` to the name.

For example, both ``glp_gmi_cuts`` or ``"gmi_cuts"`` control whether

to solve using Gomory cuts.

Parameter **values** are specified as strings in upper case,

or as constants in lower case. For example, both ``glp_on`` and ``"GLP_ON"``

specify the same thing.

Naturally, you can use ``True`` and ``False`` in cases where ``glp_on`` and ``glp_off``

would be used.

A list of parameter names, with their possible values:

**General-purpose parameters:**

.. list-table::

:widths: 30 70

* - ``timelimit``

- specify the time limit IN SECONDS. This affects both simplex

and intopt.

* - ``timelimit_simplex`` and ``timelimit_intopt``

- specify the time limit IN MILLISECONDS. (This is glpk's

default.)

* - ``simplex_or_intopt``

- specify which of ``simplex``, ``exact`` and ``intopt`` routines

in GLPK to use.

This is controlled by setting ``simplex_or_intopt`` to

``glp_simplex_only``, ``glp_exact_simplex_only``,

``glp_intopt_only`` and ``glp_simplex_then_intopt``, respectively.

The latter is useful to deal with a problem in GLPK where

problems with no solution hang when using integer optimization;

if you specify ``glp_simplex_then_intopt``,

sage will try simplex first, then perform integer optimization

only if a solution of the LP relaxation exists.

* - ``verbosity_intopt`` and ``verbosity_simplex``

- one of ``GLP_MSG_OFF``, ``GLP_MSG_ERR``, ``GLP_MSG_ON``, or

``GLP_MSG_ALL``. The default is ``GLP_MSG_OFF``.

* - ``output_frequency_intopt`` and ``output_frequency_simplex``

- the output frequency, in milliseconds. Default is 5000.

* - ``output_delay_intopt`` and ``output_delay_simplex``

- the output delay, in milliseconds, regarding the use of the

simplex method on the LP relaxation. Default is 10000.

**intopt-specific parameters:**

.. list-table::

:widths: 30 70

* - ``branching``

- - ``GLP_BR_FFV`` first fractional variable

- ``GLP_BR_LFV`` last fractional variable

- ``GLP_BR_MFV`` most fractional variable

- ``GLP_BR_DTH`` Driebeck-Tomlin heuristic (default)

- ``GLP_BR_PCH`` hybrid pseudocost heuristic

* - ``backtracking``

- - ``GLP_BT_DFS`` depth first search

- ``GLP_BT_BFS`` breadth first search

- ``GLP_BT_BLB`` best local bound (default)

- ``GLP_BT_BPH`` best projection heuristic

* - ``preprocessing``

- - ``GLP_PP_NONE``

- ``GLP_PP_ROOT`` preprocessing only at root level

- ``GLP_PP_ALL`` (default)

* - ``feasibility_pump``

- ``GLP_ON`` or ``GLP_OFF`` (default)

* - ``gomory_cuts``

- ``GLP_ON`` or ``GLP_OFF`` (default)

* - ``mixed_int_rounding_cuts``

- ``GLP_ON`` or ``GLP_OFF`` (default)

* - ``mixed_cover_cuts``

- ``GLP_ON`` or ``GLP_OFF`` (default)

* - ``clique_cuts``

- ``GLP_ON`` or ``GLP_OFF`` (default)

* - ``absolute_tolerance``

- (double) used to check if optimal solution to LP relaxation is

integer feasible. GLPK manual advises, "do not change... without

detailed understanding of its purpose."

* - ``relative_tolerance``

- (double) used to check if objective value in LP relaxation is not

better than best known integer solution. GLPK manual advises, "do

not change... without detailed understanding of its purpose."

* - ``mip_gap_tolerance``

- (double) relative mip gap tolerance. Default is 0.0.

* - ``presolve_intopt``

- ``GLP_ON`` (default) or ``GLP_OFF``.

* - ``binarize``

- ``GLP_ON`` or ``GLP_OFF`` (default)

**simplex-specific parameters:**

.. list-table::

:widths: 30 70

* - ``primal_v_dual``

- - ``GLP_PRIMAL`` (default)

- ``GLP_DUAL``

- ``GLP_DUALP``

* - ``pricing``

- - ``GLP_PT_STD`` standard (textbook)

- ``GLP_PT_PSE`` projected steepest edge (default)

* - ``ratio_test``

- - ``GLP_RT_STD`` standard (textbook)

- ``GLP_RT_HAR`` Harris' two-pass ratio test (default)

* - ``tolerance_primal``

- (double) tolerance used to check if basic solution is primal

feasible. GLPK manual advises, "do not change... without

detailed understanding of its purpose."

* - ``tolerance_dual``

- (double) tolerance used to check if basic solution is dual

feasible. GLPK manual advises, "do not change... without

detailed understanding of its purpose."

* - ``tolerance_pivot``

- (double) tolerance used to choose pivot. GLPK manual advises,

"do not change... without detailed understanding of its

purpose."

* - ``obj_lower_limit``

- (double) lower limit of the objective function. The default is

``-DBL_MAX``.

* - ``obj_upper_limit``

- (double) upper limit of the objective function. The default is

``DBL_MAX``.

* - ``iteration_limit``

- (int) iteration limit of the simplex algorithm. The default is

``INT_MAX``.

* - ``presolve_simplex``

- ``GLP_ON`` or ``GLP_OFF`` (default).

.. NOTE::

The coverage for GLPK's control parameters for simplex and integer optimization

is nearly complete. The only thing lacking is a wrapper for callback routines.

To date, no attempt has been made to expose the interior point methods.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.solver_parameter("timelimit", 60)

sage: p.solver_parameter("timelimit")

60.0

- Don't forget the difference between ``timelimit`` and ``timelimit_intopt``

sage: p.solver_parameter("timelimit_intopt")

60000

If you don't care for an integer answer, you can ask for an LP

relaxation instead. The default solver performs integer optimization,

but you can switch to the standard simplex algorithm through the

``glp_simplex_or_intopt`` parameter.

EXAMPLES::

sage: lp = MixedIntegerLinearProgram(solver = 'GLPK', maximization = False)

sage: x, y = lp[0], lp[1]

sage: lp.add_constraint(-2*x + y <= 1)

sage: lp.add_constraint(x - y <= 1)

sage: lp.add_constraint(x + y >= 2)

sage: lp.set_integer(x); lp.set_integer(y)

sage: lp.set_objective(x + y)

sage: lp.solve()

2.0

sage: lp.get_values([x,y])

[1.0, 1.0]

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.solve()

2.0

sage: lp.get_values([x,y])

[1.5, 0.5]

You can get GLPK to spout all sorts of information at you.

The default is to turn this off, but sometimes (debugging) it's very useful::

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_then_intopt)

sage: lp.solver_parameter(backend.glp_mir_cuts, backend.glp_on)

sage: lp.solver_parameter(backend.glp_msg_lev_intopt, backend.glp_msg_all)

sage: lp.solver_parameter(backend.glp_mir_cuts)

If you actually try to solve ``lp``, you will get a lot of detailed information.

"""

if type(name) == str:

if name == "out_frq" or name == "out_dly" or name == "tm_lim" or name == "msg_lev":

raise ValueError("To set parameter " + name + " you must specify the solver. Append either _simplex or _intopt.")

name = solver_parameter_names_dict[name]

if type(value) == str: value = solver_parameter_values[value]

if name == timelimit_intopt:

if value is None: return self.iocp.tm_lim

else: self.iocp.tm_lim = value

if name == timelimit_seconds:

if value is None: return self.iocp.tm_lim / 1000.0

else:

self.iocp.tm_lim = value * 1000.0

self.smcp.tm_lim = value * 1000.0

elif name == timelimit_simplex:

if value is None: return self.smcp.tm_lim

else: self.smcp.tm_lim = value

elif name == simplex_or_intopt:

if value is None: return self.simplex_or_intopt

if not value in (simplex_only,intopt_only,simplex_then_intopt,exact_simplex_only):

raise MIPSolverException("GLPK: invalid value for simplex_or_intopt; see documentation")

self.simplex_or_intopt = value

elif name == msg_lev_simplex:

if value is None: return self.smcp.msg_lev

else: self.smcp.msg_lev = value

elif name == msg_lev_intopt:

if value is None: return self.iocp.msg_lev

else: self.iocp.msg_lev = value

elif name == br_tech:

if value is None: return self.iocp.br_tech

else: self.iocp.br_tech = value

elif name == bt_tech:

if value is None: return self.iocp.bt_tech

else: self.iocp.bt_tech = value

elif name == pp_tech:

if value is None: return self.iocp.pp_tech

else: self.iocp.pp_tech = value

elif name == fp_heur:

if value is None: return self.iocp.fp_heur

else:

if value: value = GLP_ON

else: value = GLP_OFF

self.iocp.fp_heur = value

elif name == gmi_cuts:

if value is None: return self.iocp.gmi_cuts

else:

if value: value = GLP_ON

else: value = GLP_OFF

self.iocp.gmi_cuts = value

elif name == mir_cuts:

if value is None: return self.iocp.mir_cuts

else:

if value: value = GLP_ON

else: value = GLP_OFF

self.iocp.mir_cuts = value

elif name == cov_cuts:

if value is None: return self.iocp.cov_cuts

else:

if value: value = GLP_ON

else: value = GLP_OFF

self.iocp.cov_cuts = value

elif name == clq_cuts:

if value is None: return self.iocp.clq_cuts

else:

if value: value = GLP_ON

else: value = GLP_OFF

self.iocp.clq_cuts = value

elif name == tol_int:

if value is None: return self.iocp.tol_int

else: self.iocp.tol_int = value

elif name == tol_obj:

if value is None: return self.iocp.tol_obj

else: self.iocp.tol_obj = value

elif name == mip_gap:

if value is None: return self.iocp.mip_gap

else: self.iocp.mip_gap = value

elif name == tm_lim_intopt:

if value is None: return self.iocp.tm_lim

else: self.iocp.tm_lim = value

elif name == out_frq_intopt:

if value is None: return self.iocp.out_frq

else: self.iocp.out_frq = value

elif name == out_dly_intopt:

if value is None: return self.iocp.out_dly

else: self.iocp.out_dly = value

elif name == presolve_intopt:

if value is None: return self.iocp.presolve

else:

if value: value = GLP_ON

else: value = GLP_OFF

self.iocp.presolve = value

elif name == binarize:

if value is None: return self.iocp.binarize

else:

if value: value = GLP_ON

else: value = GLP_OFF

self.iocp.binarize = value

elif name == msg_lev_simplex:

if value is None: return self.smcp.msg_lev

else: self.smcp.msg_lev = value

elif name == meth:

if value is None: return self.smcp.meth

else: self.smcp.meth = value

elif name == pricing:

if value is None: return self.smcp.pricing

else: self.smcp.pricing = value

elif name == r_test:

if value is None: return self.smcp.r_test

else: self.smcp.r_test = value

elif name == tol_bnd:

if value is None: return self.smcp.tol_bnd

else: self.smcp.tol_bnd = value

elif name == tol_dj:

if value is None: return self.smcp.tol_dj

else: self.smcp.tol_dj = value

elif name == tol_piv:

if value is None: return self.smcp.tol_piv

else: self.smcp.tol_piv = value

elif name == obj_ll:

if value is None: return self.smcp.obj_ll

else: self.smcp.obj_ll = value

elif name == obj_ul:

if value is None: return self.smcp.obj_ul

else: self.smcp.obj_ul = value

elif name == it_lim:

if value is None: return self.smcp.it_lim

else: self.smcp.it_lim = value

elif name == tm_lim_simplex:

if value is None: return self.smcp.tm_lim

else: self.smcp.tm_lim = value

elif name == out_frq_simplex:

if value is None: return self.smcp.out_frq

else: self.smcp.out_frq = value

elif name == out_dly_simplex:

if value is None: return self.smcp.out_dly

else: self.smcp.out_dly = value

elif name == presolve_simplex:

if value is None: return self.smcp.presolve

else:

if value: value = GLP_ON

else: value = GLP_OFF

self.smcp.presolve = value

else:

raise ValueError("This parameter is not available.")

cpdef bint is_variable_basic(self, int index):

"""

Test whether the given variable is basic.

This assumes that the problem has been solved with the simplex method

and a basis is available. Otherwise an exception will be raised.

INPUT:

- ``index`` (integer) -- the variable's id

EXAMPLES::

sage: p = MixedIntegerLinearProgram(maximization=True,\

solver="GLPK")

sage: x = p.new_variable(nonnegative=True)

sage: p.add_constraint(-x[0] + x[1] <= 2)

sage: p.add_constraint(8 * x[0] + 2 * x[1] <= 17)

sage: p.set_objective(5.5 * x[0] - 3 * x[1])

sage: b = p.get_backend()

sage: import sage.numerical.backends.glpk_backend as backend

sage: b.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: b.solve()

sage: b.is_variable_basic(0)

True

sage: b.is_variable_basic(1)

False

"""

return self.get_col_stat(index) == GLP_BS

cpdef bint is_variable_nonbasic_at_lower_bound(self, int index):

"""

Test whether the given variable is nonbasic at lower bound.

This assumes that the problem has been solved with the simplex method

and a basis is available. Otherwise an exception will be raised.

INPUT:

- ``index`` (integer) -- the variable's id

EXAMPLES::

sage: p = MixedIntegerLinearProgram(maximization=True,\

solver="GLPK")

sage: x = p.new_variable(nonnegative=True)

sage: p.add_constraint(-x[0] + x[1] <= 2)

sage: p.add_constraint(8 * x[0] + 2 * x[1] <= 17)

sage: p.set_objective(5.5 * x[0] - 3 * x[1])

sage: b = p.get_backend()

sage: import sage.numerical.backends.glpk_backend as backend

sage: b.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: b.solve()

sage: b.is_variable_nonbasic_at_lower_bound(0)

False

sage: b.is_variable_nonbasic_at_lower_bound(1)

True

"""

return self.get_col_stat(index) == GLP_NL

cpdef bint is_slack_variable_basic(self, int index):

"""

Test whether the slack variable of the given row is basic.

This assumes that the problem has been solved with the simplex method

and a basis is available. Otherwise an exception will be raised.

INPUT:

- ``index`` (integer) -- the variable's id

EXAMPLES::

sage: p = MixedIntegerLinearProgram(maximization=True,\

solver="GLPK")

sage: x = p.new_variable(nonnegative=True)

sage: p.add_constraint(-x[0] + x[1] <= 2)

sage: p.add_constraint(8 * x[0] + 2 * x[1] <= 17)

sage: p.set_objective(5.5 * x[0] - 3 * x[1])

sage: b = p.get_backend()

sage: import sage.numerical.backends.glpk_backend as backend

sage: b.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: b.solve()

sage: b.is_slack_variable_basic(0)

True

sage: b.is_slack_variable_basic(1)

False

"""

return self.get_row_stat(index) == GLP_BS

cpdef bint is_slack_variable_nonbasic_at_lower_bound(self, int index):

"""

Test whether the slack variable of the given row is nonbasic at lower bound.

This assumes that the problem has been solved with the simplex method

and a basis is available. Otherwise an exception will be raised.

INPUT:

- ``index`` (integer) -- the variable's id

EXAMPLES::

sage: p = MixedIntegerLinearProgram(maximization=True,\

solver="GLPK")

sage: x = p.new_variable(nonnegative=True)

sage: p.add_constraint(-x[0] + x[1] <= 2)

sage: p.add_constraint(8 * x[0] + 2 * x[1] <= 17)

sage: p.set_objective(5.5 * x[0] - 3 * x[1])

sage: b = p.get_backend()

sage: import sage.numerical.backends.glpk_backend as backend

sage: b.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: b.solve()

sage: b.is_slack_variable_nonbasic_at_lower_bound(0)

False

sage: b.is_slack_variable_nonbasic_at_lower_bound(1)

True

"""

return self.get_row_stat(index) == GLP_NU

cpdef int print_ranges(self, char * filename = NULL) except -1:

r"""

Print results of a sensitivity analysis

If no filename is given as an input the results of the

sensitivity analysis are displayed on the screen. If a

filename is given they are written to a file.

INPUT:

- ``filename`` -- (optional) name of the file

OUTPUT:

Zero if the operations was successful otherwise nonzero.

.. NOTE::

This method is only effective if an optimal solution has been found

for the lp using the simplex algorithm. In all other cases an error

message is printed.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(2)

sage: p.add_linear_constraint(list(zip([0, 1], [1, 2])), None, 3)

sage: p.set_objective([2, 5])

sage: import sage.numerical.backends.glpk_backend as backend

sage: p.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: p.print_ranges()

glp_print_ranges: optimal basic solution required

sage: p.solve()

sage: p.print_ranges()

Write sensitivity analysis report to ...

GLPK ... - SENSITIVITY ANALYSIS REPORT Page 1

Problem:

Objective: 7.5 (MAXimum)

No. Row name St Activity Slack Lower bound Activity Obj coef Obj value at Limiting

Marginal Upper bound range range break point variable

------ ------------ -- ------------- ------------- ------------- ------------- ------------- ------------- ------------

1 NU 3.00000 . -Inf . -2.50000 .

2.50000 3.00000 +Inf +Inf +Inf

GLPK ... - SENSITIVITY ANALYSIS REPORT Page 2

Problem:

Objective: 7.5 (MAXimum)

No. Column name St Activity Obj coef Lower bound Activity Obj coef Obj value at Limiting

Marginal Upper bound range range break point variable

------ ------------ -- ------------- ------------- ------------- ------------- ------------- ------------- ------------

1 NL . 2.00000 . -Inf -Inf +Inf

-.50000 +Inf 3.00000 2.50000 6.00000

2 BS 1.50000 5.00000 . -Inf 4.00000 6.00000

. +Inf 1.50000 +Inf +Inf

End of report

"""

from sage.misc.all import SAGE_TMP

if filename == NULL:

fname = SAGE_TMP+"/ranges.tmp"

else:

fname = filename

res = glp_print_ranges(self.lp, 0, 0, 0, fname)

if filename == NULL:

if res == 0:

with open(fname) as f:

for line in f:

print(line, end=" ")

print("\n")

return res

cpdef double get_row_dual(self, int variable):

r"""

Returns the dual value of a constraint.

The dual value of the ith row is also the value of the ith variable

of the dual problem.

The dual value of a constraint is the shadow price of the constraint.

The shadow price is the amount by which the objective value will change

if the constraints bounds change by one unit under the precondition

that the basis remains the same.

INPUT:

- ``variable`` -- The number of the constraint

.. NOTE::

Behaviour is undefined unless ``solve`` has been called before.

If the simplex algorithm has not been used for solving 0.0 will

be returned.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.solve()

sage: lp.get_row_dual(0) # tolerance 0.00001

0.0

sage: lp.get_row_dual(1) # tolerance 0.00001

10.0

"""

if self.simplex_or_intopt == simplex_only:

return glp_get_row_dual(self.lp, variable+1)

else:

return 0.0

cpdef double get_col_dual(self, int variable):

"""

Returns the dual value (reduced cost) of a variable

The dual value is the reduced cost of a variable.

The reduced cost is the amount by which the objective coefficient

of a non basic variable has to change to become a basic variable.

INPUT:

- ``variable`` -- The number of the variable

.. NOTE::

Behaviour is undefined unless ``solve`` has been called before.

If the simplex algorithm has not been used for solving just a

0.0 will be returned.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: p = get_solver(solver = "GLPK")

sage: p.add_variables(3)

sage: p.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: p.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: p.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: p.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: p.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: p.solve()

sage: p.get_col_dual(1)

-5.0

"""

if self.simplex_or_intopt == simplex_only:

return glp_get_col_dual(self.lp, variable+1)

else:

return 0.0

cpdef int get_row_stat(self, int i) except? -1:

"""

Retrieve the status of a constraint.

INPUT:

- ``i`` -- The index of the constraint

OUTPUT:

- Returns current status assigned to the auxiliary variable associated with i-th row:

* GLP_BS = 1 basic variable

* GLP_NL = 2 non-basic variable on lower bound

* GLP_NU = 3 non-basic variable on upper bound

* GLP_NF = 4 non-basic free (unbounded) variable

* GLP_NS = 5 non-basic fixed variable

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.solve()

sage: lp.get_row_stat(0)

sage: lp.get_row_stat(1)

sage: lp.get_row_stat(-1)

Traceback (most recent call last):

...

ValueError: The constraint's index i must satisfy 0 <= i < number_of_constraints

"""

if i < 0 or i >= glp_get_num_rows(self.lp):

raise ValueError("The constraint's index i must satisfy 0 <= i < number_of_constraints")

return glp_get_row_stat(self.lp, i+1)

cpdef int get_col_stat(self, int j) except? -1:

"""

Retrieve the status of a variable.

INPUT:

- ``j`` -- The index of the variable

OUTPUT:

- Returns current status assigned to the structural variable associated with j-th column:

* GLP_BS = 1 basic variable

* GLP_NL = 2 non-basic variable on lower bound

* GLP_NU = 3 non-basic variable on upper bound

* GLP_NF = 4 non-basic free (unbounded) variable

* GLP_NS = 5 non-basic fixed variable

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.solve()

sage: lp.get_col_stat(0)

sage: lp.get_col_stat(1)

sage: lp.get_col_stat(100)

Traceback (most recent call last):

...

ValueError: The variable's index j must satisfy 0 <= j < number_of_variables

"""

if j < 0 or j >= glp_get_num_cols(self.lp):

raise ValueError("The variable's index j must satisfy 0 <= j < number_of_variables")

return glp_get_col_stat(self.lp, j+1)

cpdef set_row_stat(self, int i, int stat):

r"""

Set the status of a constraint.

INPUT:

- ``i`` -- The index of the constraint

- ``stat`` -- The status to set to

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.solve()

sage: lp.get_row_stat(0)

sage: lp.set_row_stat(0, 3)

sage: lp.get_row_stat(0)

"""

if i < 0 or i >= glp_get_num_rows(self.lp):

raise ValueError("The constraint's index i must satisfy 0 <= i < number_of_constraints")

glp_set_row_stat(self.lp, i+1, stat)

cpdef set_col_stat(self, int j, int stat):

r"""

Set the status of a variable.

INPUT:

- ``j`` -- The index of the constraint

- ``stat`` -- The status to set to

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.solve()

sage: lp.get_col_stat(0)

sage: lp.set_col_stat(0, 2)

sage: lp.get_col_stat(0)

"""

if j < 0 or j >= glp_get_num_cols(self.lp):

raise ValueError("The variable's index j must satisfy 0 <= j < number_of_variables")

glp_set_col_stat(self.lp, j+1, stat)

cpdef int warm_up(self):

r"""

Warm up the basis using current statuses assigned to rows and cols.

OUTPUT:

- Returns the warming up status

* 0 The operation has been successfully performed.

* GLP_EBADB The basis matrix is invalid.

* GLP_ESING The basis matrix is singular within the working precision.

* GLP_ECOND The basis matrix is ill-conditioned.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.solve()

sage: lp.get_objective_value()

280.0

sage: lp.set_row_stat(0,3)

sage: lp.set_col_stat(1,1)

sage: lp.warm_up()

"""

return glp_warm_up(self.lp)

cpdef eval_tab_row(self, int k):

r"""

Computes a row of the current simplex tableau.

A row corresponds to some basic variable specified by the parameter

``k`` as follows:

- if `0 \leq k \leq m-1`, the basic variable is `k`-th auxiliary

variable,

- if `m \leq k \leq m+n-1`, the basic variable is `(k-m)`-th structual

variable,

where `m` is the number of rows and `n` is the number of columns in the

specified problem object.

.. NOTE::

The basis factorization must exist.

Otherwise, a ``MIPSolverException`` will be raised.

INPUT:

- ``k`` (integer) -- the id of the basic variable.

OUTPUT:

A pair ``(indices, coeffs)`` where ``indices`` lists the

entries whose coefficient is nonzero, and to which ``coeffs``

associates their coefficient in the computed row

of the current simplex tableau.

.. NOTE::

Elements in ``indices`` have the same sense as index ``k``.

All these variables are non-basic by definition.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.eval_tab_row(0)

Traceback (most recent call last):

...

MIPSolverException: ...

sage: lp.solve()

sage: lp.eval_tab_row(0)

([1, 2, 4], [-2.0, 8.0, -2.0])

sage: lp.eval_tab_row(3)

([1, 2, 4], [-0.5, 1.5, -1.25])

sage: lp.eval_tab_row(5)

([1, 2, 4], [2.0, -4.0, 2.0])

sage: lp.eval_tab_row(1)

Traceback (most recent call last):

...

MIPSolverException: ...

sage: lp.eval_tab_row(-1)

Traceback (most recent call last):

...

ValueError: ...

"""

cdef int n = glp_get_num_cols(self.lp)

cdef int i,j

if k < 0 or k >= n + glp_get_num_rows(self.lp):

raise ValueError("k = %s; Variable number out of range" % k)

cdef MemoryAllocator mem = MemoryAllocator()

cdef int * c_indices = <int*>mem.allocarray(n+1, sizeof(int))

cdef double * c_values = <double*>mem.allocarray(n+1, sizeof(double))

try:

sig_on() # to catch GLPKError

i = glp_eval_tab_row(self.lp, k + 1, c_indices, c_values)

sig_off()

except GLPKError:

raise MIPSolverException('GLPK: basis factorization does not exist; or variable must be basic')

indices = [c_indices[j+1] - 1 for j in range(i)]

values = [c_values[j+1] for j in range(i)]

return (indices, values)

cpdef eval_tab_col(self, int k):

r"""

Computes a column of the current simplex tableau.

A (column) corresponds to some non-basic variable specified by the

parameter ``k`` as follows:

- if `0 \leq k \leq m-1`, the non-basic variable is `k`-th auxiliary

variable,

- if `m \leq k \leq m+n-1`, the non-basic variable is `(k-m)`-th

structual variable,

where `m` is the number of rows and `n` is the number of columns

in the specified problem object.

.. NOTE::

The basis factorization must exist.

Otherwise a ``MIPSolverException`` will be raised.

INPUT:

- ``k`` (integer) -- the id of the non-basic variable.

OUTPUT:

A pair ``(indices, coeffs)`` where ``indices`` lists the

entries whose coefficient is nonzero, and to which ``coeffs``

associates their coefficient in the computed column

of the current simplex tableau.

.. NOTE::

Elements in ``indices`` have the same sense as index `k`.

All these variables are basic by definition.

EXAMPLES::

sage: from sage.numerical.backends.generic_backend import get_solver

sage: lp = get_solver(solver = "GLPK")

sage: lp.add_variables(3)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [8, 6, 1])), None, 48)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [4, 2, 1.5])), None, 20)

sage: lp.add_linear_constraint(list(zip([0, 1, 2], [2, 1.5, 0.5])), None, 8)

sage: lp.set_objective([60, 30, 20])

sage: import sage.numerical.backends.glpk_backend as backend

sage: lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)

sage: lp.eval_tab_col(1)

Traceback (most recent call last):

...

MIPSolverException: ...

sage: lp.solve()

sage: lp.eval_tab_col(1)

([0, 5, 3], [-2.0, 2.0, -0.5])

sage: lp.eval_tab_col(2)

([0, 5, 3], [8.0, -4.0, 1.5])

sage: lp.eval_tab_col(4)

([0, 5, 3], [-2.0, 2.0, -1.25])

sage: lp.eval_tab_col(0)

Traceback (most recent call last):

...

MIPSolverException: ...

sage: lp.eval_tab_col(-1)

Traceback (most recent call last):

...

ValueError: ...

"""

cdef int m = glp_get_num_rows(self.lp)

cdef int i,j

if k < 0 or k >= m + glp_get_num_cols(self.lp):

raise ValueError("k = %s; Variable number out of range" % k)

cdef MemoryAllocator mem = MemoryAllocator()

cdef int * c_indices = <int*>mem.allocarray(m+1, sizeof(int))

cdef double * c_values = <double*>mem.allocarray(m+1, sizeof(double))

try:

sig_on() # To catch GLPKError

i = glp_eval_tab_col(self.lp, k + 1, c_indices, c_values)

sig_off()

except GLPKError:

raise MIPSolverException('GLPK: basis factorization does not exist; or variable must be non-basic')

indices = [c_indices[j+1] - 1 for j in range(i)]

values = [c_values[j+1] for j in range(i)]

return (indices, values)

def __dealloc__(self):

"""

Destructor

"""

glp_delete_prob(self.lp)

sig_free(self.iocp)

sig_free(self.smcp)

cdef void glp_callback(glp_tree* tree, void* info):

r"""

A callback routine called by glp_intopt

This function fills the ``search_tree_data`` structure of a ``GLPKBackend``

object. It is fed to ``glp_intopt`` (which calls it while the search tree is

being built) through ``iocp.cb_func``.

INPUT:

- ``tree`` -- a pointer toward ``glp_tree``, which is GLPK's search tree

- ``info`` -- a ``void *`` to let the function know *where* it should store

the data we need. The value of ``info`` is equal to the one stored in

iocp.cb_info.

"""

cdef search_tree_data_t * data = <search_tree_data_t *> info

data.mip_gap = glp_ios_mip_gap(tree)

cdef int node_id = glp_ios_best_node(tree)

data.best_bound = glp_ios_node_bound(tree, node_id)

# parameter names

cdef enum solver_parameter_names:

timelimit_seconds, timelimit_simplex, timelimit_intopt, simplex_or_intopt, msg_lev_simplex,

msg_lev_intopt, br_tech, bt_tech, pp_tech, fp_heur, gmi_cuts,

mir_cuts, cov_cuts, clq_cuts, tol_int, tol_obj, mip_gap,

tm_lim_intopt, out_frq_intopt, out_dly_intopt, presolve_intopt,

binarize, meth, pricing, r_test, tol_bnd, tol_dj, tol_piv, obj_ll,

obj_ul, it_lim, tm_lim_simplex, out_frq_simplex, out_dly_simplex,

presolve_simplex

glp_tm_lim_simplex = timelimit_simplex

glp_tm_lim_intopt = timelimit_intopt

glp_simplex_or_intopt = simplex_or_intopt

glp_msg_lev_intopt = glp_verbosity_intopt = msg_lev_intopt

glp_msg_lev_simplex = glp_verbosity_simplex = msg_lev_simplex

glp_br_tech = glp_branching = br_tech

glp_bt_tech = glp_backtracking = bt_tech

glp_pp_tech = glp_preprocessing = pp_tech

glp_fp_heur = glp_feasibility_pump = fp_heur

glp_gmi_cuts = glp_gomory_cuts = gmi_cuts

glp_mir_cuts = glp_mixed_int_rounding_cuts = mir_cuts

glp_cov_cuts = glp_mixed_cover_cuts = cov_cuts

glp_clq_cuts = glp_clique_cuts = clq_cuts

glp_tol_int = glp_absolute_tolerance = tol_int

glp_tol_obj = glp_relative_tolerance = tol_obj

glp_mip_gap = glp_mip_gap_tolerance = mip_gap

glp_out_frq_intopt = glp_output_frequency_intopt = out_frq_intopt

glp_out_dly_intopt = glp_output_delay_intopt = out_dly_intopt

glp_presolve_intopt = presolve_intopt

glp_binarize = binarize

glp_meth = glp_primal_v_dual = meth

glp_pricing = pricing

glp_r_test = glp_ratio_test = r_test

glp_tol_bnd = glp_tolerance_primal = tol_bnd

glp_tol_dj = glp_tolerance_dual = tol_dj

glp_tol_piv = glp_tolerance_pivot = tol_piv

glp_obj_ll = glp_obj_lower_limit = obj_ll

glp_obj_ul = glp_obj_upper_limit = obj_ul

glp_it_lim = glp_iteration_limit = it_lim

glp_out_frq_simplex = glp_output_frequency_intopt = out_frq_simplex

glp_out_dly_simplex = glp_output_delay_simplex = out_dly_simplex

glp_presolve_simplex = presolve_simplex

solver_parameter_names_dict = {

'timelimit': timelimit_seconds,

'timelimit_intopt': timelimit_intopt,

'tm_lim_intopt': timelimit_intopt,

'timelimit_simplex': timelimit_simplex,

'tm_lim_simplex': timelimit_simplex,

'simplex_or_intopt': simplex_or_intopt,

'msg_lev_simplex': msg_lev_simplex, 'verbosity_simplex': msg_lev_simplex,

'msg_lev_intopt': msg_lev_intopt, 'verbosity_intopt': msg_lev_intopt,

'br_tech': br_tech, 'branching': br_tech,

'bt_tech': bt_tech, 'backtracking': bt_tech,

'pp_tech': pp_tech, 'preprocessing': pp_tech,

'fp_heur': fp_heur, 'feasibility_pump': fp_heur,

'gmi_cuts': gmi_cuts, 'gomory_cuts': gmi_cuts,

'mir_cuts': mir_cuts, 'mixed_int_rounding_cuts': mir_cuts,

'cov_cuts': cov_cuts, 'mixed_cover_cuts': cov_cuts,

'clq_cuts': clq_cuts, 'clique_cuts': clq_cuts,

'tol_int': tol_int, 'absolute_tolerance': tol_int,

'tol_obj': tol_obj, 'relative_tolerance': tol_obj,

'mip_gap': mip_gap, 'mip_gap_tolerance': mip_gap,

'out_frq_intopt': out_frq_intopt, 'output_frequency_intopt': out_frq_intopt,

'out_dly_intopt': out_dly_intopt, 'output_delay_intopt': out_dly_intopt,

'presolve_intopt': presolve_intopt, 'binarize': binarize,

'meth': meth, 'primal_v_dual': meth,

'pricing': pricing,

'r_test': r_test, 'ratio_test': r_test,

'tol_bnd': tol_bnd, 'tolerance_primal': tol_bnd,

'tol_dj': tol_dj, 'tolerance_dual': tol_dj,

'tol_piv': tol_piv, 'tolerance_pivot': tol_piv,

'obj_ll': obj_ll, 'obj_lower_limit': obj_ll,

'obj_ul': obj_ul, 'obj_upper_limit': obj_ul,

'it_lim': it_lim, 'iteration_limit': it_lim,

'out_frq_simplex': out_frq_simplex, 'output_frequency_intopt': out_frq_simplex,

'out_dly_simplex': out_dly_simplex, 'output_delay_simplex': out_dly_simplex,

'presolve_simplex': presolve_simplex

}

# parameter values

glp_msg_off = GLP_MSG_OFF

glp_msg_on = GLP_MSG_ON

glp_msg_err = GLP_MSG_ERR

glp_msg_all = GLP_MSG_ALL

glp_msg_dbg = GLP_MSG_DBG

glp_primal = GLP_PRIMAL

glp_dual = GLP_DUAL

glp_dualp = GLP_DUALP

glp_pt_std = GLP_PT_STD

glp_pt_pse = GLP_PT_PSE

glp_rt_std = GLP_RT_STD

glp_rt_har = GLP_RT_HAR

dbl_max = DBL_MAX

int_max = INT_MAX

glp_on = GLP_ON

glp_off = GLP_OFF

glp_br_ffv = GLP_BR_FFV

glp_br_lfv = GLP_BR_LFV

glp_br_mfv = GLP_BR_MFV

glp_br_dth = GLP_BR_DTH

glp_br_pch = GLP_BR_PCH

glp_bt_dfs = GLP_BT_DFS

glp_bt_bfs = GLP_BT_BFS

glp_bt_blb = GLP_BT_BLB

glp_bt_bph = GLP_BT_BPH

glp_pp_none = GLP_PP_NONE

glp_pp_root = GLP_PP_ROOT

glp_pp_all = GLP_PP_ALL

glp_max = GLP_MAX

glp_min = GLP_MIN

glp_up = GLP_UP

glp_fr = GLP_FR

glp_db = GLP_DB

glp_fx = GLP_FX

glp_lo = GLP_LO

glp_cv = GLP_CV

glp_iv = GLP_IV

glp_bv = GLP_BV

glp_mps_deck = GLP_MPS_DECK

glp_mps_file = GLP_MPS_FILE

glp_undef = GLP_UNDEF

glp_opt = GLP_OPT

glp_feas = GLP_FEAS

glp_nofeas = GLP_NOFEAS

glp_bs = GLP_BS

glp_nl = GLP_NL

glp_nu = GLP_NU

glp_nf = GLP_NF

cdef enum more_parameter_values:

simplex_only, simplex_then_intopt, intopt_only, exact_simplex_only

glp_simplex_only = simplex_only

glp_simplex_then_intopt = simplex_then_intopt

glp_intopt_only = intopt_only

glp_exact_simplex_only = exact_simplex_only

# dictionaries for those who prefer to use strings

solver_parameter_values = {

'simplex_only': simplex_only,

'simplex_then_intopt': simplex_then_intopt,

'intopt_only': intopt_only,

'exact_simplex_only': exact_simplex_only,

'GLP_MSG_OFF' : GLP_MSG_OFF,

'GLP_MSG_ON' : GLP_MSG_ON,

'GLP_MSG_ERR' : GLP_MSG_ERR,

'GLP_MSG_ALL' : GLP_MSG_ALL,

'GLP_MSG_DBG' : GLP_MSG_DBG,

'GLP_PRIMAL' : GLP_PRIMAL,

'GLP_DUAL' : GLP_DUAL,

'GLP_DUALP' : GLP_DUALP,

'GLP_PT_STD' : GLP_PT_STD,

'GLP_PT_PSE' : GLP_PT_PSE,

'GLP_RT_STD' : GLP_RT_STD,

'GLP_RT_HAR' : GLP_RT_HAR,

'DBL_MAX' : DBL_MAX,

'INT_MAX' : INT_MAX,

'GLP_ON' : GLP_ON,

'GLP_OFF' : GLP_OFF,

'GLP_BR_FFV' : GLP_BR_FFV,

'GLP_BR_LFV' : GLP_BR_LFV,

'GLP_BR_MFV' : GLP_BR_MFV,

'GLP_BR_DTH' : GLP_BR_DTH,

'GLP_BR_PCH' : GLP_BR_PCH,

'GLP_BT_DFS' : GLP_BT_DFS,

'GLP_BT_BFS' : GLP_BT_BFS,

'GLP_BT_BLB' : GLP_BT_BLB,

'GLP_BT_BPH' : GLP_BT_BPH,

'GLP_PP_NONE' : GLP_PP_NONE,

'GLP_PP_ROOT' : GLP_PP_ROOT,

'GLP_PP_ALL' : GLP_PP_ALL,

'GLP_MAX' : GLP_MAX,

'GLP_MIN' : GLP_MIN,

'GLP_UP' : GLP_UP,

'GLP_FR' : GLP_FR,

'GLP_DB' : GLP_DB,

'GLP_FX' : GLP_FX,

'GLP_LO' : GLP_LO,

'GLP_CV' : GLP_CV,

'GLP_IV' : GLP_IV,

'GLP_BV' : GLP_BV,

'GLP_MPS_DECK' : GLP_MPS_DECK,

'GLP_MPS_FILE' : GLP_MPS_FILE,

'GLP_UNDEF' : GLP_UNDEF,

'GLP_OPT' : GLP_OPT,

'GLP_FEAS' : GLP_FEAS,

'GLP_NOFEAS' : GLP_NOFEAS

}

cdef dict solve_status_msg = {

GLP_EBADB: "The initial basis specified in the problem object is invalid",

GLP_ESING: "The basis matrix corresponding to the initial basis is singular within the working precision",

GLP_ECOND: "The basis matrix corresponding to the initial basis is ill-conditioned, i.e. its condition number is too large",

GLP_EBOUND: "Some variables (auxiliary or structural) have incorrect bounds",

GLP_EFAIL: "Solver failure",

GLP_EOBJLL: "The objective lower limit has been reached",

GLP_EOBJUL: "The objective upper limit has been reached",

GLP_EITLIM: "The iteration limit has been exceeded",

GLP_ETMLIM: "The time limit has been exceeded",

GLP_ENOPFS: "The LP (relaxation) problem has no primal feasible solution",

GLP_ENODFS: "The LP (relaxation) problem has no dual feasible solution",

GLP_EROOT: "Optimal basis for initial LP relaxation is not provided",

GLP_ESTOP: "The search was prematurely terminated by application",

GLP_EMIPGAP: "The relative mip gap tolerance has been reached",

}

cdef dict solution_status_msg = {

GLP_UNDEF: "Solution is undefined",

GLP_FEAS: "Feasible solution found, while optimality has not been proven",

GLP_INFEAS: "Solution is infeasible",

GLP_NOFEAS: "Problem has no feasible solution",

GLP_OPT: "Solution is optimal",

GLP_UNBND: "Problem has unbounded solution",

}

Coverage for local/lib/python2.7/site-packages/sage/numerical/backends/glpk_backend.pyx : 77%

725 statements 561 run 164 missing 0 excluded