gpkit.constraints package¶

Submodules¶

gpkit.constraints.array module¶

Implements ArrayConstraint

class gpkit.constraints.array.ArrayConstraint(constraints, left, oper, right)¶

Bases: gpkit.constraints.single_equation.SingleEquationConstraint, gpkit.constraints.set.ConstraintSet

A ConstraintSet for prettier array-constraint printing.

ArrayConstraint gets its sub method from ConstrainSet, and so left and right are only used for printing.

When created by NomialArray left and right are likely to be be either NomialArrays or Varkeys of VectorVariables.

gpkit.constraints.bounded module¶

Implements Bounded

class gpkit.constraints.bounded.Bounded(constraints, verbosity=1, eps=1e-30, lower=None, upper=None)¶

Bases: gpkit.constraints.set.ConstraintSet

Bounds contained variables so as to ensure dual feasibility.

constraints : iterable

constraints whose varkeys will be bounded

substitutions : dict

as in ConstraintSet.__init__

verbosity : int

how detailed of a warning to print: 0: nothing 1: print warnings

eps : float

default lower bound is eps, upper bound is 1/eps

lower : float

lower bound for all varkeys, replaces eps

upper : float

upper bound for all varkeys, replaces 1/eps

check_boundaries(result)¶: Creates (and potentially prints) a dictionary of unbounded variables.

process_result(result)¶: Add boundedness to the model’s solution

sens_from_dual(las, nus, result)¶: Return sensitivities while capturing the relevant lambdas

gpkit.constraints.bounded.varkey_bounds(varkeys, lower, upper)¶

Returns constraints list bounding all varkeys.

varkeys : iterable: list of varkeys to create bounds for
lower : float: lower bound for all varkeys
upper : float: upper bound for all varkeys

gpkit.constraints.costed module¶

Implement CostedConstraintSet

class gpkit.constraints.costed.CostedConstraintSet(cost, constraints, substitutions=None)¶

Bases: gpkit.constraints.set.ConstraintSet

A ConstraintSet with a cost

cost : gpkit.Posynomial constraints : Iterable substitutions : dict

constrained_varkeys()¶: Return all varkeys in the cost and non-ConstraintSet constraints

controlpanel(*args, **kwargs)¶

Easy model control in IPython / Jupyter

Like interact(), but with the ability to control sliders and their ranges live. args and kwargs are passed on to interact()

interact(ranges=None, fn_of_sol=None, **solvekwargs)¶

Easy model interaction in IPython / Jupyter

By default, this creates a model with sliders for every constant which prints a new solution table whenever the sliders are changed.

fn_of_sol : function: The function called with the solution after each solve that displays the result. By default prints a table.
ranges : dictionary {str: Slider object or tuple}: Determines which sliders get created. Tuple values may contain two or three floats: two correspond to (min, max), while three correspond to (min, step, max)
**solvekwargs: kwargs which get passed to the solve()/localsolve() method.

reset_varkeys()¶: Resets varkeys to what is in the cost and constraints

rootconstr_latex(excluded=None)¶: Latex showing cost, to be used when this is the top constraint

rootconstr_str(excluded=None)¶: String showing cost, to be used when this is the top constraint

gpkit.constraints.gp module¶

Implement the GeometricProgram class

class gpkit.constraints.gp.GeometricProgram(cost, constraints, substitutions, allow_missingbounds=False)¶

Bases: gpkit.constraints.costed.CostedConstraintSet, gpkit.nomials.data.NomialData

Standard mathematical representation of a GP.

cost : Constraint: Posynomial to minimize when solving
constraints : list of Posynomials: Constraints to maintain when solving (implicitly Posynomials <= 1) GeometricProgram does not accept equality constraints (e.g. x == 1);

instead use two inequality constraints (e.g. x <= 1, 1/x <= 1)
verbosity : int (optional): If verbosity is greater than zero, warns about missing bounds on creation.

solver_out and solver_log are set during a solve result is set at the end of a solve if solution status is optimal

>>> gp = gpkit.geometric_program.GeometricProgram(
                    # minimize
                    x,
                    [   # subject to
                        1/x  # <= 1, implicitly
                    ])
>>> gp.solve()

check_solution(cost, primal, nu, la, tol=0.001, abstol=1e-20)¶

Run a series of checks to mathematically confirm sol solves this GP

cost: float: cost returned by solver
primal: list: primal solution returned by solver
nu: numpy.ndarray: monomial lagrange multiplier
la: numpy.ndarray: posynomial lagrange multiplier

RuntimeWarning, if any problems are found

gen()¶: Generates nomial and solve data (A, p_idxs) from posynomials

solve(solver=None, verbosity=1, warn_on_check=False, process_result=True, **kwargs)¶

Solves a GeometricProgram and returns the solution.

solver : str or function (optional): By default uses one of the solvers found during installation. If set to “mosek”, “mosek_cli”, or “cvxopt”, uses that solver. If set to a function, passes that function cs, A, p_idxs, and k.
verbosity : int (optional): If greater than 0, prints solver name and solve time.
**kwargs :: Passed to solver constructor and solver function.

result : dict

A dictionary containing the translated solver result; keys below.

cost : float

The value of the objective at the solution.

variables : dict

The value of each variable at the solution.

sensitivities : dict

monomials : array of floats: Each monomial’s dual variable value at the solution.
posynomials : array of floats: Each posynomials’s dual variable value at the solution.

varkeys¶: The GP’s varkeys, created when necessary.

gpkit.constraints.gp.check_mono_eq_bounds(missingbounds, meq_bounds)¶: Bounds variables with monomial equalities

gpkit.constraints.gp.genA(exps, varlocs, meq_idxs)¶

Generates A matrix from exps and varidxs

exps : list of Hashvectors

Exponents for each monomial in a GP

varidxs : dict

Locations of each variable in exps

A : sparse Cootmatrix

Exponents of the various free variables for each monomial: rows of A are monomials, columns of A are variables.

missingbounds : dict

Keys: variables that lack bounds. Values: which bounds are missed.

gpkit.constraints.model module¶

Implements Model

class gpkit.constraints.model.Model(cost=None, constraints=None, *args, **kwargs)¶

Bases: gpkit.constraints.costed.CostedConstraintSet

Symbolic representation of an optimization problem.

The Model class is used both directly to create models with constants and sweeps, and indirectly inherited to create custom model classes.

cost : Posynomial (optional): Defaults to Monomial(1).
constraints : ConstraintSet or list of constraints (optional): Defaults to an empty list.
substitutions : dict (optional): This dictionary will be substituted into the problem before solving, and also allows the declaration of sweeps and linked sweeps.
name : str (optional): Allows “naming” a model in a way similar to inherited instances, and overrides the inherited name if there is one.

program is set during a solve solution is set at the end of a solve

as_gpconstr(x0)¶: Returns approximating constraint, keeping name and num

autosweep(sweeps, tol=0.01, samplepoints=100, **solveargs)¶

Autosweeps {var: (start, end)} pairs in sweeps to tol.

Returns swept and sampled solutions. The original simplex tree can be accessed at sol.bst

debug(solver=None, verbosity=1, **solveargs)¶

Attempts to diagnose infeasible models.

If a model debugs but errors in a process_result call, debug again with process_results=False

gp(constants=None, **kwargs)¶

Return program version of self

program: NomialData: Class to return, e.g. GeometricProgram or SequentialGeometricProgram
return_attr: string: attribute to return in addition to the program

localsolve(solver=None, verbosity=1, skipsweepfailures=False, **kwargs)¶

Forms a mathematical program and attempts to solve it.

solver : string or function (optional): If None, uses the default solver found in installation.
verbosity : int (optional): If greater than 0 prints runtime messages. Is decremented by one and then passed to programs.
skipsweepfailures : bool (optional): If True, when a solve errors during a sweep, skip it.

**kwargs : Passed to solver

sol : SolutionArray: See the SolutionArray documentation for details.

ValueError if the program is invalid. RuntimeWarning if an error occurs in solving or parsing the solution.

name = None¶

naming = None¶

num = None¶

program = None¶

solution = None¶

solve(solver=None, verbosity=1, skipsweepfailures=False, **kwargs)¶

Forms a mathematical program and attempts to solve it.

solver : string or function (optional): If None, uses the default solver found in installation.
verbosity : int (optional): If greater than 0 prints runtime messages. Is decremented by one and then passed to programs.
skipsweepfailures : bool (optional): If True, when a solve errors during a sweep, skip it.

**kwargs : Passed to solver

sol : SolutionArray: See the SolutionArray documentation for details.

ValueError if the program is invalid. RuntimeWarning if an error occurs in solving or parsing the solution.

sp(constants=None, **kwargs)¶

Return program version of self

program: NomialData: Class to return, e.g. GeometricProgram or SequentialGeometricProgram
return_attr: string: attribute to return in addition to the program

subconstr_latex(excluded=None)¶: The collapsed appearance of a ConstraintBase

subconstr_str(excluded=None)¶: The collapsed appearance of a ConstraintBase

sweep(sweeps, **solveargs)¶: Sweeps {var: values} pairs in sweeps. Returns swept solutions.

verify_docstring()¶: Verifies docstring bounds are sufficient but not excessive.

gpkit.constraints.model.get_relaxed(relaxvals, mapped_list, min_return=1)¶: Determines which relaxvars are considered ‘relaxed’

gpkit.constraints.prog_factories module¶

Scripts for generating, solving and sweeping programs

gpkit.constraints.prog_factories.evaluate_linked(constants, linked)¶: Evaluates the values and gradients of linked variables.

gpkit.constraints.prog_factories.run_sweep(genfunction, self, solution, skipsweepfailures, constants, sweep, linked, solver, verbosity, **kwargs)¶: Runs through a sweep.

gpkit.constraints.relax module¶

Models for assessing primal feasibility

class gpkit.constraints.relax.ConstantsRelaxed(constraints, include_only=None, exclude=None)¶

Bases: gpkit.constraints.set.ConstraintSet

Relax constants in a constraintset.

constraints : iterable: Constraints which will be relaxed (made easier).
include_only : set: if declared, variable names must be on this list to be relaxed
exclude : set: if declared, variable names on this list will never be relaxed

relaxvars : Variable: The variables controlling the relaxation. A solved value of 1 means no relaxation was necessary or optimal for a particular constant. Higher values indicate the amount by which that constant has been made easier: e.g., a value of 1.5 means it was made 50 percent easier in the final solution than in the original problem. Of course, this can also be determined by looking at the constant’s new value directly.

process_result(result)¶

Does arbitrary computation / manipulation of a program’s result

There’s no guarantee what order different constraints will process results in, so any changes made to the program’s result should be careful not to step on other constraint’s toes.

check that an inequality was tight

add values computed from solved variables

class gpkit.constraints.relax.ConstraintsRelaxed(constraints)¶

Bases: gpkit.constraints.set.ConstraintSet

Relax constraints, as in Eqn. 11 of [Boyd2007].

constraints : iterable: Constraints which will be relaxed (made easier).

relaxvars : Variable: The variables controlling the relaxation. A solved value of 1 means no relaxation was necessary or optimal for a particular constraint. Higher values indicate the amount by which that constraint has been made easier: e.g., a value of 1.5 means it was made 50 percent easier in the final solution than in the original problem.

[Boyd2007] : “A tutorial on geometric programming”, Optim Eng 8:67-122

class gpkit.constraints.relax.ConstraintsRelaxedEqually(constraints)¶

Bases: gpkit.constraints.set.ConstraintSet

Relax constraints the same amount, as in Eqn. 10 of [Boyd2007].

constraints : iterable: Constraints which will be relaxed (made easier).

relaxvar : Variable: The variable controlling the relaxation. A solved value of 1 means no relaxation. Higher values indicate the amount by which all constraints have been made easier: e.g., a value of 1.5 means all constraints were 50 percent easier in the final solution than in the original problem.

[Boyd2007] : “A tutorial on geometric programming”, Optim Eng 8:67-122

gpkit.constraints.set module¶

Implements ConstraintSet

class gpkit.constraints.set.ConstraintSet(constraints, substitutions=None)¶

Bases: list

Recursive container for ConstraintSets and Inequalities

append(value)¶: L.append(object) – append object to end

as_gpconstr(x0)¶

Returns GPConstraint approximating this constraint at x0

When x0 is none, may return a default guess.

as_posyslt1(substitutions=None)¶: Returns list of posynomials which must be kept <= 1

as_view()¶: Return a ConstraintSetView of this ConstraintSet.

constrained_varkeys()¶: Return all varkeys in non-ConstraintSet constraints

flat(constraintsets=True)¶: Yields contained constraints, optionally including constraintsets.

idxlookup = None¶

latex(excluded=None)¶: LaTeX representation of a ConstraintSet.

process_result(result)¶

Does arbitrary computation / manipulation of a program’s result

There’s no guarantee what order different constraints will process results in, so any changes made to the program’s result should be careful not to step on other constraint’s toes.

check that an inequality was tight

add values computed from solved variables

reset_varkeys()¶: Goes through constraints and collects their varkeys.

rootconstr_latex(excluded=None)¶: The appearance of a ConstraintSet in addition to its contents

rootconstr_str(excluded=None)¶: The appearance of a ConstraintSet in addition to its contents

sens_from_dual(las, nus, result)¶

Computes constraint and variable sensitivities from dual solution

las : list: Sensitivity of each posynomial returned by self.as_posyslt1
nus: list of lists: Each posynomial’s monomial sensitivities

constraint_sens : dict: The interesting and computable sensitivities of this constraint
var_senss : dict: The variable sensitivities of this constraint

str_without(excluded=None)¶: String representation of a ConstraintSet.

subconstr_latex(excluded=None)¶: The collapsed appearance of a ConstraintSet

subconstr_str(excluded=None)¶: The collapsed appearance of a ConstraintSet

unique_varkeys = frozenset([])¶

variables_byname(key)¶: Get all variables with a given name

varkeys = None¶

class gpkit.constraints.set.ConstraintSetView(constraintset, index=())¶

Bases: object

Class to access particular views on a set’s variables

gpkit.constraints.set.add_meq_bounds(bounded, meq_bounded)¶: Iterates through meq_bounds until convergence

gpkit.constraints.set.raise_badelement(cns, i, constraint)¶: Identify the bad element and raise a ValueError

gpkit.constraints.set.raise_elementhasnumpybools(constraint)¶: Identify the bad subconstraint array and raise a ValueError

gpkit.constraints.sgp module¶

Implement the SequentialGeometricProgram class

class gpkit.constraints.sgp.SequentialGeometricProgram(cost, constraints, substitutions)¶

Bases: gpkit.constraints.costed.CostedConstraintSet

Prepares a collection of signomials for a SP solve.

cost : Posynomial: Objective to minimize when solving
constraints : list of Constraint or SignomialConstraint objects: Constraints to maintain when solving (implicitly Signomials <= 1)
verbosity : int (optional): Currently has no effect: SequentialGeometricPrograms don’t know anything new after being created, unlike GeometricPrograms.

gps is set during a solve result is set at the end of a solve

>>> gp = gpkit.geometric_program.SequentialGeometricProgram(
                    # minimize
                    x,
                    [   # subject to
                        1/x - y/x,  # <= 1, implicitly
                        y/10  # <= 1
                    ])
>>> gp.solve()

gp(x0=None, mutategp=False)¶: The GP approximation of this SP at x0.

init_gp(substitutions, x0=None)¶: Generates a simplified GP representation for later modification

localsolve(solver=None, verbosity=1, x0=None, reltol=0.0001, iteration_limit=50, mutategp=True, **kwargs)¶

Locally solves a SequentialGeometricProgram and returns the solution.

solver : str or function (optional): By default uses one of the solvers found during installation. If set to “mosek”, “mosek_cli”, or “cvxopt”, uses that solver. If set to a function, passes that function cs, A, p_idxs, and k.
verbosity : int (optional): If greater than 0, prints solve time and number of iterations. Each GP is created and solved with verbosity one less than this, so if greater than 1, prints solver name and time for each GP.
x0 : dict (optional): Initial location to approximate signomials about.
reltol : float: Iteration ends when this is greater than the distance between two consecutive solve’s objective values.
iteration_limit : int: Maximum GP iterations allowed.
*args, **kwargs :: Passed to solver function.

result : dict: A dictionary containing the translated solver result.

gpkit.constraints.sigeq module¶

Implements SignomialEquality

class gpkit.constraints.sigeq.SignomialEquality(left, right)¶

Bases: gpkit.constraints.set.ConstraintSet

A constraint of the general form posynomial == posynomial

gpkit.constraints.single_equation module¶

Implements SingleEquationConstraint

class gpkit.constraints.single_equation.SingleEquationConstraint(left, oper, right)¶

Bases: object

Constraint expressible in a single equation.

func_opers = {'<=': <built-in function le>, '=': <built-in function eq>, '>=': <built-in function ge>}¶

latex(excluded=None)¶: Latex representation without attributes in excluded list

latex_opers = {'<=': '\\leq', '=': '=', '>=': '\\geq'}¶

process_result(result)¶: Process solver results

str_without(excluded=None)¶: String representation without attributes in excluded list

subconstr_latex(excluded)¶: The collapsed latex of a constraint

subconstr_str(excluded)¶: The collapsed string of a constraint

gpkit.constraints.single_equation.trycall(obj, attr, arg, default)¶: Try to call method of an object, returning default if it does not exist

gpkit.constraints.tight module¶

Implements Tight

class gpkit.constraints.tight.Tight(constraints, reltol=None, raiseerror=False, printwarning=False, **kwargs)¶

Bases: gpkit.constraints.set.ConstraintSet

ConstraintSet whose inequalities must result in an equality.

process_result(result)¶: Checks that all constraints are satisfied with equality

reltol = 1e-06¶

Module contents¶

Contains ConstraintSet and related classes and objects