Source code for cvxpy.problems.problem

"""
Copyright 2013 Steven Diamond, 2017 Akshay Agrawal

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""

import cvxpy.settings as s
from cvxpy import error
from cvxpy.problems.objective import Minimize, Maximize
from cvxpy.reductions.chain import Chain
from cvxpy.reductions.dqcp2dcp import dqcp2dcp
from cvxpy.reductions.eval_params import EvalParams
from cvxpy.reductions.flip_objective import FlipObjective
from cvxpy.reductions.solvers.solving_chain import construct_solving_chain
from cvxpy.interface.matrix_utilities import scalar_value
from cvxpy.reductions.solvers import bisection
from cvxpy.reductions.solvers import defines as slv_def
from cvxpy.utilities.deterministic import unique_list
import cvxpy.utilities.performance_utils as perf
from cvxpy.constraints import Equality, Inequality, NonPos, Zero
import cvxpy.utilities as u

from collections import namedtuple
import numpy as np


SolveResult = namedtuple(
    'SolveResult',
    ['opt_value', 'status', 'primal_values', 'dual_values'])


class Cache(object):
    def __init__(self):
        self.key = None
        self.solving_chain = None
        self.param_cone_prog = None
        self.inverse_data = None

    def invalidate(self):
        self.key = None
        self.solving_chain = None
        self.param_cone_prog = None
        self.inverse_data = None

    def make_key(self, solver, gp):
        return (solver, gp)


[docs]class Problem(u.Canonical): """A convex optimization problem. Problems are immutable, save for modification through the specification of :class:`~cvxpy.expressions.constants.parameters.Parameter` Parameters ---------- objective : Minimize or Maximize The problem's objective. constraints : list The constraints on the problem variables. """ # The solve methods available. REGISTERED_SOLVE_METHODS = {} def __init__(self, objective, constraints=None): if constraints is None: constraints = [] # Check that objective is Minimize or Maximize. if not isinstance(objective, (Minimize, Maximize)): raise error.DCPError("Problem objective must be Minimize or Maximize.") # Constraints and objective are immutable. self._objective = objective self._constraints = [c for c in constraints] self._value = None self._status = None self._solution = None self._cache = Cache() self._solver_cache = {} # Information about the shape of the problem and its constituent parts self._size_metrics = None # Benchmarks reported by the solver: self._solver_stats = None self.args = [self._objective, self._constraints] @property def value(self): """float : The value from the last time the problem was solved (or None if not solved). """ if self._value is None: return None else: return scalar_value(self._value) @property def status(self): """str : The status from the last time the problem was solved; one of optimal, infeasible, or unbounded (with or without suffix inaccurate). """ return self._status @property def solution(self): """Solution : The solution from the last time the problem was solved. """ return self._solution @property def objective(self): """Minimize or Maximize : The problem's objective. Note that the objective cannot be reassigned after creation, and modifying the objective after creation will result in undefined behavior. """ return self._objective @property def constraints(self): """A shallow copy of the problem's constraints. Note that constraints cannot be reassigned, appended to, or otherwise modified after creation, except through parameters. """ return self._constraints[:]
[docs] @perf.compute_once def is_dcp(self): """Does the problem satisfy DCP rules? """ return all( expr.is_dcp() for expr in self.constraints + [self.objective])
[docs] @perf.compute_once def is_dpp(self): """Does the problem satisfy DPP rules? """ return all( expr.is_dpp() for expr in self.constraints + [self.objective])
[docs] @perf.compute_once def is_dgp(self): """Does the problem satisfy DGP rules? """ return all( expr.is_dgp() for expr in self.constraints + [self.objective])
[docs] @perf.compute_once def is_dqcp(self): """Does the problem satisfy the DQCP rules? """ return all( expr.is_dqcp() for expr in self.constraints + [self.objective])
[docs] @perf.compute_once def is_qp(self): """Is problem a quadratic program? """ for c in self.constraints: if not (isinstance(c, (Equality, Zero)) or c.args[0].is_pwl()): return False for var in self.variables(): if var.is_psd() or var.is_nsd(): return False return (self.is_dcp() and self.objective.args[0].is_qpwa())
@perf.compute_once def is_mixed_integer(self): return any(v.attributes['boolean'] or v.attributes['integer'] for v in self.variables())
[docs] @perf.compute_once def variables(self): """Accessor method for variables. Returns ------- list of :class:`~cvxpy.expressions.variable.Variable` A list of the variables in the problem. """ vars_ = self.objective.variables() for constr in self.constraints: vars_ += constr.variables() return unique_list(vars_)
[docs] @perf.compute_once def parameters(self): """Accessor method for parameters. Returns ------- list of :class:`~cvxpy.expressions.constants.parameter.Parameter` A list of the parameters in the problem. """ params = self.objective.parameters() for constr in self.constraints: params += constr.parameters() return unique_list(params)
[docs] @perf.compute_once def constants(self): """Accessor method for parameters. Returns ------- list of :class:`~cvxpy.expressions.constants.constant.Constant` A list of the constants in the problem. """ const_dict = {} constants_ = self.objective.constants() for constr in self.constraints: constants_ += constr.constants() # Note that numpy matrices are not hashable, so we use the built-in # function "id" const_dict = {id(constant): constant for constant in constants_} return list(const_dict.values())
[docs] def atoms(self): """Accessor method for atoms. Returns ------- list of :class:`~cvxpy.atoms.Atom` A list of the atom types in the problem; note that this list contains classes, not instances. """ atoms = self.objective.atoms() for constr in self.constraints: atoms += constr.atoms() return unique_list(atoms)
@property def size_metrics(self): """:class:`~cvxpy.problems.problem.SizeMetrics` : Information about the problem's size. """ if self._size_metrics is None: self._size_metrics = SizeMetrics(self) return self._size_metrics @property def solver_stats(self): """:class:`~cvxpy.problems.problem.SolverStats` : Information returned by the solver. """ return self._solver_stats
[docs] def solve(self, *args, **kwargs): """Solves the problem using the specified method. Populates the :code:`status` and :code:`value` attributes on the problem object as a side-effect. Parameters ---------- solver : str, optional The solver to use. For example, 'ECOS', 'SCS', or 'OSQP'. verbose : bool, optional Overrides the default of hiding solver output. gp : bool, optional If True, parses the problem as a disciplined geometric program instead of a disciplined convex program. qcp : bool, optional If True, parses the problem as a disciplined quasiconvex program instead of a disciplined convex program. requires_grad : bool, optional Makes it possible to compute gradients with respect to parameters by calling `.backward()` after solving, or to compute perturbations to the variables by calling `.derivative()`. When True, the solver must be SCS, and gp, qcp must be false; a DPPError is thrown when problem is not DPP. solver_specific_opts : dict, optional A dict of options that will be passed to the specific solver. In general, these options will override any default settings imposed by cvxpy. method : function, optional A custom solve method to use. Returns ------- float The optimal value for the problem, or a string indicating why the problem could not be solved. Raises ------ cvxpy.error.DCPError Raised if the problem is not DCP and `gp` is False. cvxpy.error.DGPError Raised if the problem is not DGP and `gp` is True. cvxpy.error.SolverError Raised if no suitable solver exists among the installed solvers, or if an unanticipated error is encountered. """ func_name = kwargs.pop("method", None) if func_name is not None: solve_func = Problem.REGISTERED_SOLVE_METHODS[func_name] else: solve_func = Problem._solve return solve_func(self, *args, **kwargs)
[docs] @classmethod def register_solve(cls, name, func): """Adds a solve method to the Problem class. Parameters ---------- name : str The keyword for the method. func : function The function that executes the solve method. This function must take as its first argument the problem instance to solve. """ cls.REGISTERED_SOLVE_METHODS[name] = func
[docs] def get_problem_data(self, solver, gp=False): """Returns the problem data used in the call to the solver. When a problem is solved, CVXPY creates a chain of reductions enclosed in a :class:`~cvxpy.reductions.solvers.solving_chain.SolvingChain`, and compiles it to some low-level representation that is compatible with the targeted solver. This method returns that low-level representation. For some solving chains, this low-level representation is a dictionary that contains exactly those arguments that were supplied to the solver; however, for other solving chains, the data is an intermediate representation that is compiled even further by the solver interfaces. A solution to the equivalent low-level problem can be obtained via the data by invoking the `solve_via_data` method of the returned solving chain, a thin wrapper around the code external to CVXPY that further processes and solves the problem. Invoke the unpack_results method to recover a solution to the original problem. For example: :: objective = ... constraints = ... problem = cp.Problem(objective, constraints) data, chain, inverse_data = problem.get_problem_data(cp.SCS) # calls SCS using `data` soln = chain.solve_via_data(problem, data) # unpacks the solution returned by SCS into `problem` problem.unpack_results(soln, chain, inverse_data) Alternatively, the `data` dictionary returned by this method contains enough information to bypass CVXPY and call the solver directly. For example: :: problem = cp.Problem(objective, constraints) data, _, _ = problem.get_problem_data(cp.SCS) import scs probdata = { 'A': data['A'], 'b': data['b'], 'c': data['c'], } cone_dims = data['dims'] cones = { "f": cone_dims.zero, "l": cone_dims.nonpos, "q": cone_dims.soc, "ep": cone_dims.exp, "s": cone_dims.psd, } soln = scs.solve(data, cones) The structure of the data dict that CVXPY returns depends on the solver. For details, consult the solver interfaces in `cvxpy/reductions/solvers`. Parameters ---------- solver : str The solver the problem data is for. gp : bool, optional If True, then parses the problem as a disciplined geometric program instead of a disciplined convex program. Returns ------- dict or object lowest level representation of problem SolvingChain The solving chain that created the data. list The inverse data generated by the chain. """ key = self._cache.make_key(solver, gp) if key != self._cache.key: self._cache.invalidate() solving_chain = self._construct_chain(solver=solver, gp=gp) self._cache.key = key self._cache.solving_chain = solving_chain self._solver_cache = {} else: solving_chain = self._cache.solving_chain if self._cache.param_cone_prog is not None: # fast path, bypasses application of reductions data, solver_inverse_data = solving_chain.solver.apply( self._cache.param_cone_prog) inverse_data = self._cache.inverse_data + [solver_inverse_data] else: data, inverse_data = solving_chain.apply(self) safe_to_cache = ( isinstance(data, dict) and s.PARAM_PROB in data and not any(isinstance(reduction, EvalParams) for reduction in solving_chain.reductions) ) if safe_to_cache: self._cache.param_cone_prog = data[s.PARAM_PROB] # the last datum in inverse_data corresponds to the solver, # so we shouldn't cache it self._cache.inverse_data = inverse_data[:-1] return data, solving_chain, inverse_data
def _find_candidate_solvers(self, solver=None, gp=False): """ Find candiate solvers for the current problem. If solver is not None, it checks if the specified solver is compatible with the problem passed. Parameters ---------- solver : string The name of the solver with which to solve the problem. If no solver is supplied (i.e., if solver is None), then the targeted solver may be any of those that are installed. If the problem is variable-free, then this parameter is ignored. gp : bool If True, the problem is parsed as a Disciplined Geometric Program instead of as a Disciplined Convex Program. Returns ------- dict A dictionary of compatible solvers divided in `qp_solvers` and `conic_solvers`. Raises ------ cvxpy.error.SolverError Raised if the problem is not DCP and `gp` is False. cvxpy.error.DGPError Raised if the problem is not DGP and `gp` is True. """ candidates = {'qp_solvers': [], 'conic_solvers': []} if solver is not None: if solver not in slv_def.INSTALLED_SOLVERS: raise error.SolverError("The solver %s is not installed." % solver) if solver in slv_def.CONIC_SOLVERS: candidates['conic_solvers'] += [solver] if solver in slv_def.QP_SOLVERS: candidates['qp_solvers'] += [solver] else: candidates['qp_solvers'] = [s for s in slv_def.INSTALLED_SOLVERS if s in slv_def.QP_SOLVERS] candidates['conic_solvers'] = [s for s in slv_def.INSTALLED_SOLVERS if s in slv_def.CONIC_SOLVERS] # If gp we must have only conic solvers if gp: if solver is not None and solver not in slv_def.CONIC_SOLVERS: raise error.SolverError( "When `gp=True`, `solver` must be a conic solver " "(received '%s'); try calling " % solver + " `solve()` with `solver=cvxpy.ECOS`." ) elif solver is None: candidates['qp_solvers'] = [] # No QP solvers allowed if self.is_mixed_integer(): candidates['qp_solvers'] = [ s for s in candidates['qp_solvers'] if slv_def.SOLVER_MAP_QP[s].MIP_CAPABLE] candidates['conic_solvers'] = [ s for s in candidates['conic_solvers'] if slv_def.SOLVER_MAP_CONIC[s].MIP_CAPABLE] if not candidates['conic_solvers'] and \ not candidates['qp_solvers']: raise error.SolverError( "Problem is mixed-integer, but candidate " "QP/Conic solvers (%s) are not MIP-capable." % [candidates['qp_solvers'], candidates['conic_solvers']]) return candidates def _construct_chain(self, solver=None, gp=False): """ Construct the chains required to reformulate and solve the problem. In particular, this function # finds the candidate solvers # constructs the solving chain that performs the numeric reductions and solves the problem. Parameters ---------- solver : str, optional The solver to use. Defaults to ECOS. gp : bool, optional If True, the problem is parsed as a Disciplined Geometric Program instead of as a Disciplined Convex Program. Returns ------- A solving chain """ candidate_solvers = self._find_candidate_solvers(solver=solver, gp=gp) return construct_solving_chain(self, candidate_solvers, gp=gp) def _invalidate_cache(self): self._cache_key = None self._solving_chain = None self._param_cone_prog = None self._inverse_data = None def _solve(self, solver=None, warm_start=True, verbose=False, gp=False, qcp=False, requires_grad=False, **kwargs): """Solves a DCP compliant optimization problem. Saves the values of primal and dual variables in the variable and constraint objects, respectively. Parameters ---------- solver : str, optional The solver to use. Defaults to ECOS. warm_start : bool, optional Should the previous solver result be used to warm start? verbose : bool, optional Overrides the default of hiding solver output. gp : bool, optional If True, parses the problem as a disciplined geometric program. qcp : bool, optional If True, parses the problem as a disciplined quasiconvex program. requires_grad : bool, optional Makes it possible to compute gradients with respect to parameters by calling `.backward()` after solving, or to compute perturbations to the variables by calling `.derivative()`. When True, the solver must be SCS, and gp, qcp must be False; a DPPError is thrown when problem is not DPP. kwargs : dict, optional A dict of options that will be passed to the specific solver. In general, these options will override any default settings imposed by cvxpy. Returns ------- float The optimal value for the problem, or a string indicating why the problem could not be solved. """ for parameter in self.parameters(): if parameter.value is None: raise error.ParameterError( "A Parameter (whose name is '%s') does not have a value " "associated with it; all Parameter objects must have " "values before solving a problem." % parameter.name()) if requires_grad: if not self.is_dpp(): raise error.DPPError("Problem is not DPP (when requires_grad " "is True, problem must be DPP).") elif gp: raise ValueError("Cannot compute gradients of DGP problems.") elif qcp: raise ValueError("Cannot compute gradients of DQCP problems.") elif solver is not None and solver not in [s.SCS, s.DIFFCP]: raise ValueError("When requires_grad is True, the only " "supported solver is SCS " "(received %s)." % solver) elif s.DIFFCP not in slv_def.INSTALLED_SOLVERS: raise ImportError( "The Python package diffcp must be installed to " "differentiate through problems. Please follow the " "installation instructions at " "https://github.com/cvxgrp/diffcp") else: solver = s.DIFFCP else: if gp and qcp: raise ValueError("At most one of `gp` and `qcp` can be True.") if qcp and not self.is_dcp(): if not self.is_dqcp(): raise error.DQCPError("The problem is not DQCP.") reductions = [dqcp2dcp.Dqcp2Dcp()] if type(self.objective) == Maximize: reductions = [FlipObjective()] + reductions chain = Chain(problem=self, reductions=reductions) soln = bisection.bisect( chain.reduce(), solver=solver, verbose=verbose, **kwargs) self.unpack(chain.retrieve(soln)) return self.value data, solving_chain, inverse_data = self.get_problem_data(solver, gp) solution = solving_chain.solve_via_data( self, data, warm_start, verbose, kwargs) self.unpack_results(solution, solving_chain, inverse_data) return self.value
[docs] def backward(self): """Compute the gradient of a solution with respect to parameters. This method differentiates through the solution map of the problem, to obtain the gradient of a solution with respect to the parameters. In other words, it calculates the sensitivities of the parameters with respect to perturbations in the optimal variable values. .backward() populates the .gradient attribute of each parameter as a side-effect. It can only be called after calling .solve() with `requires_grad=True`. Below is a simple example: :: import cvxpy as cp import numpy as np p = cp.Parameter() x = cp.Variable() quadratic = cp.square(x - 2 * p) problem = cp.Problem(cp.Minimize(quadratic), [x >= 0]) p.value = 3.0 problem.solve(requires_grad=True, eps=1e-10) # .backward() populates the .gradient attribute of the parameters problem.backward() # Because x* = 2 * p, dx*/dp = 2 np.testing.assert_allclose(p.gradient, 2.0) In the above example, the gradient could easily be computed by hand; however, .backward() can be used to differentiate through any DCP program (that is also DPP-compliant). This method uses the chain rule to evaluate the gradients of a scalar-valued function of the variables with respect to the parameters. For example, let x be a variable and p a parameter; x and p might be scalars, vectors, or matrices. Let f be a scalar-valued function, with z = f(x). Then this method computes dz/dp = (dz/dx) (dx/p). dz/dx is chosen to be the all ones vector by default, corresponding to choosing f to be the sum function. You can specify a custom value for dz/dx by setting the .gradient attribute on your variables. For example, :: import cvxpy as cp import numpy as np b = cp.Parameter() x = cp.Variable() quadratic = cp.square(x - 2 * b) problem = cp.Problem(cp.Minimize(quadratic), [x >= 0]) b.value = 3. problem.solve(requires_grad=True, eps=1e-10) x.gradient = 4. problem.backward() # dz/dp = dz/dx dx/dp = 4. * 2. == 8. np.testing.assert_allclose(b.gradient, 8.) The .gradient attribute on a variable can also be interpreted as a perturbation to its optimal value. Raises ------ ValueError if solve was not called with `requires_grad=True` SolverError if the problem is infeasible or unbounded """ if s.DIFFCP not in self._solver_cache: raise ValueError("backward can only be called after calling " "solve with `requires_grad=True`") elif self.status not in s.SOLUTION_PRESENT: raise error.SolverError("Backpropagating through " "infeasible/unbounded problems is not " "yet supported. Please file an issue on " "Github if you need this feature.") # TODO(akshayka): Backpropagate through dual variables as well. backward_cache = self._solver_cache[s.DIFFCP] DT = backward_cache["DT"] zeros = np.zeros(backward_cache["s"].shape) del_vars = {} for variable in self.variables(): if variable.gradient is None: del_vars[variable.id] = np.ones(variable.shape) else: del_vars[variable.id] = np.asarray(variable.gradient, dtype=np.float64) dx = self._cache.param_cone_prog.split_adjoint(del_vars) dA, db, dc = DT(dx, zeros, zeros) dparams = self._cache.param_cone_prog.apply_param_jac(dc, -dA, db) for parameter in self.parameters(): parameter.gradient = dparams[parameter.id]
[docs] def derivative(self): """Apply the derivative of the solution map to perturbations in the parameters This method applies the derivative of the solution map to perturbations in the parameters, to obtain perturbations in the optimal values of the variables. In other words, it tells you how the optimal values of the variables would be changed. You can specify perturbations in a parameter by setting its .delta attribute (if unspecified, the perturbation defaults to 0). This method populates the .delta attribute of the variables as a side-effect. This method can only be called after calling .solve() with `requires_grad=True`. Below is a simple example: :: import cvxpy as cp import numpy as np p = cp.Parameter() x = cp.Variable() quadratic = cp.square(x - 2 * p) problem = cp.Problem(cp.Minimize(quadratic), [x >= 0]) p.value = 3.0 problem.solve(requires_grad=True, eps=1e-10) # .derivative() populates the .gradient attribute of the parameters problem.backward() p.delta = 1e-3 # Because x* = 2 * p, dx*/dp = 2, so (dx*/dp)(p.delta) == 2e-3 np.testing.assert_allclose(p.gradient, 2e-3) Raises ------ ValueError if solve was not called with `requires_grad=True` SolverError if the problem is infeasible or unbounded """ if s.DIFFCP not in self._solver_cache: raise ValueError("derivative can only be called after calling " "solve with `requires_grad=True`") elif self.status not in s.SOLUTION_PRESENT: raise ValueError("Differentiating through infeasible/unbounded " "problems is not yet supported. Please file an " "issue on Github if you need this feature.") # TODO(akshayka): Forward differentiate dual variables as well backward_cache = self._solver_cache[s.DIFFCP] param_cone_prog = self._cache.param_cone_prog D = backward_cache["D"] param_deltas = {} for parameter in self.parameters(): if parameter.delta is None: param_deltas[parameter.id] = np.zeros(parameter.shape) else: param_deltas[parameter.id] = np.asarray(parameter.delta, dtype=np.float64) dc, _, dA, db = param_cone_prog.apply_parameters(param_deltas, zero_offset=True) dx, _, _ = D(-dA, db, dc) dvars = param_cone_prog.split_solution( dx, [v.id for v in self.variables()]) for variable in self.variables(): variable.delta = dvars[variable.id]
def _clear_solution(self): for v in self.variables(): v.save_value(None) for c in self.constraints: for dv in c.dual_variables: dv.save_value(None) self._value = None self._status = None self._solution = None def unpack(self, solution): """Updates the problem state given a Solution. Updates problem.status, problem.value and value of primal and dual variables. If solution.status is in cvxpy.settins.ERROR, this method is a no-op. Parameters __________ solution : cvxpy.Solution A Solution object. Raises ------ ValueError If the solution object has an invalid status """ if solution.status in s.SOLUTION_PRESENT: for v in self.variables(): v.save_value(solution.primal_vars[v.id]) for c in self.constraints: if c.id in solution.dual_vars: c.save_dual_value(solution.dual_vars[c.id]) elif solution.status in s.INF_OR_UNB: for v in self.variables(): v.save_value(None) for constr in self.constraints: for dv in constr.dual_variables: dv.save_value(None) else: raise ValueError("Cannot unpack invalid solution: %s" % solution) self._value = solution.opt_val self._status = solution.status self._solution = solution
[docs] def unpack_results(self, solution, chain, inverse_data): """Updates the problem state given the solver results. Updates problem.status, problem.value and value of primal and dual variables. Parameters __________ solution : object The solution returned by applying the chain to the problem and invoking the solver on the resulting data. chain : SolvingChain A solving chain that was used to solve the problem. inverse_data : list The inverse data returned by applying the chain to the problem. Raises ------ cvxpy.error.SolverError If the solver failed """ solution = chain.invert(solution, inverse_data) if solution.status in s.ERROR: raise error.SolverError( "Solver '%s' failed. " % chain.solver.name() + "Try another solver, or solve with verbose=True for more " "information.") self.unpack(solution) self._solver_stats = SolverStats(self._solution.attr, chain.solver.name())
def __str__(self): if len(self.constraints) == 0: return str(self.objective) else: subject_to = "subject to " lines = [str(self.objective), subject_to + str(self.constraints[0])] for constr in self.constraints[1:]: lines += [len(subject_to) * " " + str(constr)] return '\n'.join(lines) def __repr__(self): return "Problem(%s, %s)" % (repr(self.objective), repr(self.constraints)) def __neg__(self): return Problem(-self.objective, self.constraints) def __add__(self, other): if other == 0: return self elif not isinstance(other, Problem): return NotImplemented return Problem(self.objective + other.objective, unique_list(self.constraints + other.constraints)) def __radd__(self, other): if other == 0: return self else: return NotImplemented def __sub__(self, other): if not isinstance(other, Problem): return NotImplemented return Problem(self.objective - other.objective, unique_list(self.constraints + other.constraints)) def __rsub__(self, other): if other == 0: return -self else: return NotImplemented def __mul__(self, other): if not isinstance(other, (int, float)): return NotImplemented return Problem(self.objective * other, self.constraints) __rmul__ = __mul__ def __div__(self, other): if not isinstance(other, (int, float)): return NotImplemented return Problem(self.objective * (1.0 / other), self.constraints) def is_constant(self): return False __truediv__ = __div__
[docs]class SolverStats(object): """Reports some of the miscellaneous information that is returned by the solver after solving but that is not captured directly by the Problem instance. Attributes ---------- solve_time : double The time (in seconds) it took for the solver to solve the problem. setup_time : double The time (in seconds) it took for the solver to setup the problem. num_iters : int The number of iterations the solver had to go through to find a solution. """ def __init__(self, results_dict, solver_name): self.solver_name = solver_name self.solve_time = None self.setup_time = None self.num_iters = None if s.SOLVE_TIME in results_dict: self.solve_time = results_dict[s.SOLVE_TIME] if s.SETUP_TIME in results_dict: self.setup_time = results_dict[s.SETUP_TIME] if s.NUM_ITERS in results_dict: self.num_iters = results_dict[s.NUM_ITERS]
[docs]class SizeMetrics(object): """Reports various metrics regarding the problem. Attributes ---------- num_scalar_variables : integer The number of scalar variables in the problem. num_scalar_data : integer The number of scalar constants and parameters in the problem. The number of constants used across all matrices, vectors, in the problem. Some constants are not apparent when the problem is constructed: for example, The sum_squares expression is a wrapper for a quad_over_lin expression with a constant 1 in the denominator. num_scalar_eq_constr : integer The number of scalar equality constraints in the problem. num_scalar_leq_constr : integer The number of scalar inequality constraints in the problem. max_data_dimension : integer The longest dimension of any data block constraint or parameter. max_big_small_squared : integer The maximum value of (big)(small)^2 over all data blocks of the problem, where (big) is the larger dimension and (small) is the smaller dimension for each data block. """ def __init__(self, problem): # num_scalar_variables self.num_scalar_variables = 0 for var in problem.variables(): self.num_scalar_variables += var.size # num_scalar_data, max_data_dimension, and max_big_small_squared self.max_data_dimension = 0 self.num_scalar_data = 0 self.max_big_small_squared = 0 for const in problem.constants()+problem.parameters(): big = 0 # Compute number of data self.num_scalar_data += const.size big = 1 if len(const.shape) == 0 else max(const.shape) small = 1 if len(const.shape) == 0 else min(const.shape) # Get max data dimension: if self.max_data_dimension < big: self.max_data_dimension = big max_big_small_squared = float(big)*(float(small)**2) if self.max_big_small_squared < max_big_small_squared: self.max_big_small_squared = max_big_small_squared # num_scalar_eq_constr self.num_scalar_eq_constr = 0 for constraint in problem.constraints: if isinstance(constraint, (Equality, Zero)): self.num_scalar_eq_constr += constraint.expr.size # num_scalar_leq_constr self.num_scalar_leq_constr = 0 for constraint in problem.constraints: if isinstance(constraint, (Inequality, NonPos)): self.num_scalar_leq_constr += constraint.expr.size