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 arrayconstraint 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.

subinplace
(subs)¶ Substitutes in place, updating self.substitutions accordingly.
Keys substituted with subinplace are no longer present, so if such a key is also in self.substitutions that substitution is now orphaned. If subs[key] describes some key in the ConstraintSet (i.e. one key has been substituted for another), then a substitution is added, mapping the orphaned value to this new key; otherwise, an error is raised.

gpkit.constraints.bounded module¶
Implements Bounded

class
gpkit.constraints.bounded.
Bounded
(constraints, verbosity=1, eps=1e30, 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)¶ 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

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

subinplace
(subs)¶ Substitutes in place.

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=1e20)¶ 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, *args, **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.
 *args, **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.

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, substitutions=None)¶ 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, *args, **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.
*args, **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, *args, **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.
*args, **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.

zero_lower_unbounded_variables
()¶ Recursively substitutes 0 for variables that lack a lower bound

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.
run_sweep
(genfunction, self, solution, skipsweepfailures, constants, sweep, linked, solver, verbosity, *args, **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)¶

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 8:67122

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 8:67122
gpkit.constraints.set module¶
Implements ConstraintSet

class
gpkit.constraints.set.
ConstraintSet
(constraints, substitutions=None)¶ Bases:
list
Recursive container for ConstraintSets and Inequalities

append
(value)¶

as_gpconstr
(x0, substitutions=None)¶ 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

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

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)¶ 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

subinplace
(subs)¶ Substitutes in place, updating self.substitutions accordingly.
Keys substituted with subinplace are no longer present, so if such a key is also in self.substitutions that substitution is now orphaned. If subs[key] describes some key in the ConstraintSet (i.e. one key has been substituted for another), then a substitution is added, mapping the orphaned value to this new key; otherwise, an error is raised.

topvar
(key)¶ If a variable by a given name exists in the top model, return it

unique_varkeys
= frozenset([])¶

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

varkeys
= None¶


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
= {'<=': <builtin function le>, '=': <builtin function eq>, '>=': <builtin 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

sub
(subs)¶ Returns a substituted version of this constraint.

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, substitutions=None, reltol=None, raiseerror=False)¶ 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
= 1e06¶

Module contents¶
Contains ConstraintSet and related classes and objects