simsopt.objectives package

Submodules

simsopt.objectives.functions module

This module provides a few minimal optimizable objects, each representing a function. These functions are mostly used for testing.

class simsopt.objectives.functions.Adder(n=3)

Bases: simsopt._core.optimizable.Optimizable

This class defines a minimal object that can be optimized. It has n degrees of freedom, and has a function that just returns the sum of these dofs. This class is used for testing.

J()

Returns the sum of the degrees of freedom.

dJ()
property df

Same as the function dJ(), but a property instead of a function.

property f

Same as the function J(), but a property instead of a function.

get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(xin)

This base Optimizable object has no degrees of freedom, so do nothing.

class simsopt.objectives.functions.Affine(nparams, nvals)

Bases: simsopt._core.optimizable.Optimizable

This class represents a random affine (i.e. linear plus constant) transformation from R^n to R^m.

J()
dJ()
get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(x)

This base Optimizable object has no degrees of freedom, so do nothing.

class simsopt.objectives.functions.Failer(nparams: int = 2, nvals: int = 3, fail_index: int = 2)

Bases: simsopt._core.optimizable.Optimizable

This class is used for testing failures of the objective function. This function always returns a vector with entries all 1.0, except that ObjectiveFailure will be raised on a specified evaluation.

Parameters

  • nparams – Number of input values.

  • nvals – Number of entries in the return vector.

  • fail_index – Which function evaluation to fail on.

J()
get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(x)

This base Optimizable object has no degrees of freedom, so do nothing.

class simsopt.objectives.functions.Identity(x=0.0)

Bases: simsopt._core.optimizable.Optimizable

This class represents a term in an objective function which is just the identity. It has one degree of freedom, and the output of the function is equal to this degree of freedom.

J()
dJ()
property df

Same as the function dJ(), but a property instead of a function.

property f

Same as the function J(), but a property instead of a function.

get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(xin)

This base Optimizable object has no degrees of freedom, so do nothing.

class simsopt.objectives.functions.Rosenbrock(b=100.0, x=0.0, y=0.0)

Bases: simsopt._core.optimizable.Optimizable

This class defines a minimal object that can be optimized.

dterm1()

Returns the gradient of term1

property dterm1prop

Same as dterm1, but a property rather than a callable function.

dterm2()

Returns the gradient of term2

property dterm2prop

Same as dterm2, but a property rather than a callable function.

dterms()

Returns the 2x2 Jacobian for term1 and term2.

f()

Returns the total function, squaring and summing the two terms.

get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(xin)

This base Optimizable object has no degrees of freedom, so do nothing.

term1()

Returns the first of the two quantities that is squared and summed.

property term1prop

Same as term1, but a property rather than a callable function.

term2()

Returns the second of the two quantities that is squared and summed.

property term2prop

Same as term2, but a property rather than a callable function.

terms()

Returns term1 and term2 together as a 2-element numpy vector.

class simsopt.objectives.functions.RosenbrockWithFailures(*args, fail_interval=8, **kwargs)

Bases: simsopt.objectives.functions.Rosenbrock

This class is similar to the Rosenbrock class, except that it fails (raising ObjectiveFailure) at regular intervals. This is useful for testing that the simsopt infrastructure handles failures in the expected way.

term1()

Returns the first of the two quantities that is squared and summed.

class simsopt.objectives.functions.TestObject1(val)

Bases: simsopt._core.optimizable.Optimizable

This is an optimizable object used for testing. It depends on two sub-objects, both of type Adder.

J()
dJ()
property df

Same as dJ() but a property instead of a function.

property f

Same as J() but a property instead of a function.

get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(x)

This base Optimizable object has no degrees of freedom, so do nothing.

class simsopt.objectives.functions.TestObject2(val1, val2)

Bases: simsopt._core.optimizable.Optimizable

This is an optimizable object used for testing. It depends on two sub-objects, both of type Adder.

J()
dJ()
property df

Same as dJ() but a property instead of a function.

property f

Same as J() but a property instead of a function.

get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(x)

This base Optimizable object has no degrees of freedom, so do nothing.

simsopt.objectives.least_squares module

This module provides the LeastSquaresProblem class, as well as the associated class LeastSquaresTerm.

class simsopt.objectives.least_squares.LeastSquaresProblem(terms, fail: Union[None, float] = 1000000000000.0)

Bases: object

This class represents a nonlinear-least-squares optimization problem. The class stores a list of LeastSquaresTerm objects.

Parameters

  • terms – Must be convertable to a list by the list() subroutine. Each entry of the resulting list must either have type LeastSquaresTerm or else be a list or tuple of the form (function, goal, weight) or (object, attribute_str, goal, weight).

  • fail – Should be None, a large positive float, or NaN. If not None, any ObjectiveFailure excpetions raised will be caught and the corresponding residual values will be replaced by this value.

f(x=None)

This method returns the vector of residuals for a given state vector x. This function is passed to scipy.optimize, and could be passed to other optimization algorithms too. This function differs from Dofs.f() because it shifts and scales the terms.

If the argument x is not supplied, the residuals will be evaluated for the present state vector. If x is supplied, then first set_dofs() will be called for each object to set the global state vector to x.

f_from_unshifted(f_unshifted)

This function takes a vector of function values, as returned by dofs, and shifts and scales them. This function does not actually evaluate the dofs.

jac(x=None, **kwargs)

This method gives the Jacobian of the residuals with respect to the parameters, if it is available, given the state vector x. This function is passed to scipy.optimize, and could be passed to other optimization algorithms too. This Jacobian differs from the one returned by Dofs() because it accounts for the ‘weight’ scale factors.

If the argument x is not supplied, the Jacobian will be evaluated for the present state vector. If x is supplied, then first set_dofs() will be called for each object to set the global state vector to x.

kwargs is passed to Dofs.fd_jac().

objective(x=None)

Return the value of the total objective function, by summing the terms.

If the argument x is not supplied, the objective will be evaluated for the present state vector. If x is supplied, then first set_dofs() will be called for each object to set the global state vector to x.

objective_from_shifted_f(f)

Given a vector of functions that has already been evaluated, and already shifted and scaled, convert the result to the overall scalar objective function, without any further function evaluations. This routine is useful if we have already evaluated the residuals and we want to convert the result to the overall scalar objective without the computational expense of further function evaluations.

objective_from_unshifted_f(f_unshifted)

Given a vector of functions that has already been evaluated, but not yet shifted and scaled, convert the result to the overall scalar objective function, without any further function evaluations. This routine is useful if we have already evaluated the residuals and we want to convert the result to the overall scalar objective without the computational expense of further function evaluations.

scale_dofs_jac(jmat)

Given a Jacobian matrix j for the Dofs() associated to this least-squares problem, return the scaled Jacobian matrix for the least-squares residual terms. This function does not actually compute the Dofs() Jacobian, since sometimes we would compute that directly whereas other times we might compute it with serial or parallel finite differences. The provided jmat is scaled in-place.

property x

Return the state vector.

class simsopt.objectives.least_squares.LeastSquaresTerm(f_in, goal, weight)

Bases: object

This class represents one term in a nonlinear-least-squares problem. A LeastSquaresTerm instance has 3 basic attributes: a function (called f_in), a goal value (called goal), and a weight (sigma). The overall value of the term is:

f_out = weight * (f_in - goal) ** 2.

f_out()

Return the overall value of this least-squares term.

classmethod from_sigma(f_in, goal, sigma)

Define the LeastSquaresTerm with sigma = 1 / sqrt(weight), so

f_out = ((f_in - goal) / sigma) ** 2.

Module contents

class simsopt.objectives.LeastSquaresProblem(terms, fail: Union[None, float] = 1000000000000.0)

Bases: object

This class represents a nonlinear-least-squares optimization problem. The class stores a list of LeastSquaresTerm objects.

Parameters

  • terms – Must be convertable to a list by the list() subroutine. Each entry of the resulting list must either have type LeastSquaresTerm or else be a list or tuple of the form (function, goal, weight) or (object, attribute_str, goal, weight).

  • fail – Should be None, a large positive float, or NaN. If not None, any ObjectiveFailure excpetions raised will be caught and the corresponding residual values will be replaced by this value.

f(x=None)

This method returns the vector of residuals for a given state vector x. This function is passed to scipy.optimize, and could be passed to other optimization algorithms too. This function differs from Dofs.f() because it shifts and scales the terms.

If the argument x is not supplied, the residuals will be evaluated for the present state vector. If x is supplied, then first set_dofs() will be called for each object to set the global state vector to x.

f_from_unshifted(f_unshifted)

This function takes a vector of function values, as returned by dofs, and shifts and scales them. This function does not actually evaluate the dofs.

jac(x=None, **kwargs)

This method gives the Jacobian of the residuals with respect to the parameters, if it is available, given the state vector x. This function is passed to scipy.optimize, and could be passed to other optimization algorithms too. This Jacobian differs from the one returned by Dofs() because it accounts for the ‘weight’ scale factors.

If the argument x is not supplied, the Jacobian will be evaluated for the present state vector. If x is supplied, then first set_dofs() will be called for each object to set the global state vector to x.

kwargs is passed to Dofs.fd_jac().

objective(x=None)

Return the value of the total objective function, by summing the terms.

If the argument x is not supplied, the objective will be evaluated for the present state vector. If x is supplied, then first set_dofs() will be called for each object to set the global state vector to x.

objective_from_shifted_f(f)

Given a vector of functions that has already been evaluated, and already shifted and scaled, convert the result to the overall scalar objective function, without any further function evaluations. This routine is useful if we have already evaluated the residuals and we want to convert the result to the overall scalar objective without the computational expense of further function evaluations.

objective_from_unshifted_f(f_unshifted)

Given a vector of functions that has already been evaluated, but not yet shifted and scaled, convert the result to the overall scalar objective function, without any further function evaluations. This routine is useful if we have already evaluated the residuals and we want to convert the result to the overall scalar objective without the computational expense of further function evaluations.

scale_dofs_jac(jmat)

Given a Jacobian matrix j for the Dofs() associated to this least-squares problem, return the scaled Jacobian matrix for the least-squares residual terms. This function does not actually compute the Dofs() Jacobian, since sometimes we would compute that directly whereas other times we might compute it with serial or parallel finite differences. The provided jmat is scaled in-place.

property x

Return the state vector.

class simsopt.objectives.LeastSquaresTerm(f_in, goal, weight)

Bases: object

This class represents one term in a nonlinear-least-squares problem. A LeastSquaresTerm instance has 3 basic attributes: a function (called f_in), a goal value (called goal), and a weight (sigma). The overall value of the term is:

f_out = weight * (f_in - goal) ** 2.

f_out()

Return the overall value of this least-squares term.

classmethod from_sigma(f_in, goal, sigma)

Define the LeastSquaresTerm with sigma = 1 / sqrt(weight), so

f_out = ((f_in - goal) / sigma) ** 2.