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Fixed database typo and removed unnecessary class identifier.

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Batuhan Berk Başoğlu 2020-10-14 10:10:37 -04:00
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"""Constraints definition for minimize."""
import numpy as np
from ._hessian_update_strategy import BFGS
from ._differentiable_functions import (
VectorFunction, LinearVectorFunction, IdentityVectorFunction)
from .optimize import OptimizeWarning
from warnings import warn
from numpy.testing import suppress_warnings
from scipy.sparse import issparse
class NonlinearConstraint(object):
"""Nonlinear constraint on the variables.
The constraint has the general inequality form::
lb <= fun(x) <= ub
Here the vector of independent variables x is passed as ndarray of shape
(n,) and ``fun`` returns a vector with m components.
It is possible to use equal bounds to represent an equality constraint or
infinite bounds to represent a one-sided constraint.
Parameters
----------
fun : callable
The function defining the constraint.
The signature is ``fun(x) -> array_like, shape (m,)``.
lb, ub : array_like
Lower and upper bounds on the constraint. Each array must have the
shape (m,) or be a scalar, in the latter case a bound will be the same
for all components of the constraint. Use ``np.inf`` with an
appropriate sign to specify a one-sided constraint.
Set components of `lb` and `ub` equal to represent an equality
constraint. Note that you can mix constraints of different types:
interval, one-sided or equality, by setting different components of
`lb` and `ub` as necessary.
jac : {callable, '2-point', '3-point', 'cs'}, optional
Method of computing the Jacobian matrix (an m-by-n matrix,
where element (i, j) is the partial derivative of f[i] with
respect to x[j]). The keywords {'2-point', '3-point',
'cs'} select a finite difference scheme for the numerical estimation.
A callable must have the following signature:
``jac(x) -> {ndarray, sparse matrix}, shape (m, n)``.
Default is '2-point'.
hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy, None}, optional
Method for computing the Hessian matrix. The keywords
{'2-point', '3-point', 'cs'} select a finite difference scheme for
numerical estimation. Alternatively, objects implementing
`HessianUpdateStrategy` interface can be used to approximate the
Hessian. Currently available implementations are:
- `BFGS` (default option)
- `SR1`
A callable must return the Hessian matrix of ``dot(fun, v)`` and
must have the following signature:
``hess(x, v) -> {LinearOperator, sparse matrix, array_like}, shape (n, n)``.
Here ``v`` is ndarray with shape (m,) containing Lagrange multipliers.
keep_feasible : array_like of bool, optional
Whether to keep the constraint components feasible throughout
iterations. A single value set this property for all components.
Default is False. Has no effect for equality constraints.
finite_diff_rel_step: None or array_like, optional
Relative step size for the finite difference approximation. Default is
None, which will select a reasonable value automatically depending
on a finite difference scheme.
finite_diff_jac_sparsity: {None, array_like, sparse matrix}, optional
Defines the sparsity structure of the Jacobian matrix for finite
difference estimation, its shape must be (m, n). If the Jacobian has
only few non-zero elements in *each* row, providing the sparsity
structure will greatly speed up the computations. A zero entry means
that a corresponding element in the Jacobian is identically zero.
If provided, forces the use of 'lsmr' trust-region solver.
If None (default) then dense differencing will be used.
Notes
-----
Finite difference schemes {'2-point', '3-point', 'cs'} may be used for
approximating either the Jacobian or the Hessian. We, however, do not allow
its use for approximating both simultaneously. Hence whenever the Jacobian
is estimated via finite-differences, we require the Hessian to be estimated
using one of the quasi-Newton strategies.
The scheme 'cs' is potentially the most accurate, but requires the function
to correctly handles complex inputs and be analytically continuable to the
complex plane. The scheme '3-point' is more accurate than '2-point' but
requires twice as many operations.
Examples
--------
Constrain ``x[0] < sin(x[1]) + 1.9``
>>> from scipy.optimize import NonlinearConstraint
>>> con = lambda x: x[0] - np.sin(x[1])
>>> nlc = NonlinearConstraint(con, -np.inf, 1.9)
"""
def __init__(self, fun, lb, ub, jac='2-point', hess=BFGS(),
keep_feasible=False, finite_diff_rel_step=None,
finite_diff_jac_sparsity=None):
self.fun = fun
self.lb = lb
self.ub = ub
self.finite_diff_rel_step = finite_diff_rel_step
self.finite_diff_jac_sparsity = finite_diff_jac_sparsity
self.jac = jac
self.hess = hess
self.keep_feasible = keep_feasible
class LinearConstraint(object):
"""Linear constraint on the variables.
The constraint has the general inequality form::
lb <= A.dot(x) <= ub
Here the vector of independent variables x is passed as ndarray of shape
(n,) and the matrix A has shape (m, n).
It is possible to use equal bounds to represent an equality constraint or
infinite bounds to represent a one-sided constraint.
Parameters
----------
A : {array_like, sparse matrix}, shape (m, n)
Matrix defining the constraint.
lb, ub : array_like
Lower and upper bounds on the constraint. Each array must have the
shape (m,) or be a scalar, in the latter case a bound will be the same
for all components of the constraint. Use ``np.inf`` with an
appropriate sign to specify a one-sided constraint.
Set components of `lb` and `ub` equal to represent an equality
constraint. Note that you can mix constraints of different types:
interval, one-sided or equality, by setting different components of
`lb` and `ub` as necessary.
keep_feasible : array_like of bool, optional
Whether to keep the constraint components feasible throughout
iterations. A single value set this property for all components.
Default is False. Has no effect for equality constraints.
"""
def __init__(self, A, lb, ub, keep_feasible=False):
self.A = A
self.lb = lb
self.ub = ub
self.keep_feasible = keep_feasible
class Bounds(object):
"""Bounds constraint on the variables.
The constraint has the general inequality form::
lb <= x <= ub
It is possible to use equal bounds to represent an equality constraint or
infinite bounds to represent a one-sided constraint.
Parameters
----------
lb, ub : array_like, optional
Lower and upper bounds on independent variables. Each array must
have the same size as x or be a scalar, in which case a bound will be
the same for all the variables. Set components of `lb` and `ub` equal
to fix a variable. Use ``np.inf`` with an appropriate sign to disable
bounds on all or some variables. Note that you can mix constraints of
different types: interval, one-sided or equality, by setting different
components of `lb` and `ub` as necessary.
keep_feasible : array_like of bool, optional
Whether to keep the constraint components feasible throughout
iterations. A single value set this property for all components.
Default is False. Has no effect for equality constraints.
"""
def __init__(self, lb, ub, keep_feasible=False):
self.lb = lb
self.ub = ub
self.keep_feasible = keep_feasible
def __repr__(self):
if np.any(self.keep_feasible):
return "{}({!r}, {!r}, keep_feasible={!r})".format(type(self).__name__, self.lb, self.ub, self.keep_feasible)
else:
return "{}({!r}, {!r})".format(type(self).__name__, self.lb, self.ub)
class PreparedConstraint(object):
"""Constraint prepared from a user defined constraint.
On creation it will check whether a constraint definition is valid and
the initial point is feasible. If created successfully, it will contain
the attributes listed below.
Parameters
----------
constraint : {NonlinearConstraint, LinearConstraint`, Bounds}
Constraint to check and prepare.
x0 : array_like
Initial vector of independent variables.
sparse_jacobian : bool or None, optional
If bool, then the Jacobian of the constraint will be converted
to the corresponded format if necessary. If None (default), such
conversion is not made.
finite_diff_bounds : 2-tuple, optional
Lower and upper bounds on the independent variables for the finite
difference approximation, if applicable. Defaults to no bounds.
Attributes
----------
fun : {VectorFunction, LinearVectorFunction, IdentityVectorFunction}
Function defining the constraint wrapped by one of the convenience
classes.
bounds : 2-tuple
Contains lower and upper bounds for the constraints --- lb and ub.
These are converted to ndarray and have a size equal to the number of
the constraints.
keep_feasible : ndarray
Array indicating which components must be kept feasible with a size
equal to the number of the constraints.
"""
def __init__(self, constraint, x0, sparse_jacobian=None,
finite_diff_bounds=(-np.inf, np.inf)):
if isinstance(constraint, NonlinearConstraint):
fun = VectorFunction(constraint.fun, x0,
constraint.jac, constraint.hess,
constraint.finite_diff_rel_step,
constraint.finite_diff_jac_sparsity,
finite_diff_bounds, sparse_jacobian)
elif isinstance(constraint, LinearConstraint):
fun = LinearVectorFunction(constraint.A, x0, sparse_jacobian)
elif isinstance(constraint, Bounds):
fun = IdentityVectorFunction(x0, sparse_jacobian)
else:
raise ValueError("`constraint` of an unknown type is passed.")
m = fun.m
lb = np.asarray(constraint.lb, dtype=float)
ub = np.asarray(constraint.ub, dtype=float)
if lb.ndim == 0:
lb = np.resize(lb, m)
if ub.ndim == 0:
ub = np.resize(ub, m)
keep_feasible = np.asarray(constraint.keep_feasible, dtype=bool)
if keep_feasible.ndim == 0:
keep_feasible = np.resize(keep_feasible, m)
if keep_feasible.shape != (m,):
raise ValueError("`keep_feasible` has a wrong shape.")
mask = keep_feasible & (lb != ub)
f0 = fun.f
if np.any(f0[mask] < lb[mask]) or np.any(f0[mask] > ub[mask]):
raise ValueError("`x0` is infeasible with respect to some "
"inequality constraint with `keep_feasible` "
"set to True.")
self.fun = fun
self.bounds = (lb, ub)
self.keep_feasible = keep_feasible
def violation(self, x):
"""How much the constraint is exceeded by.
Parameters
----------
x : array-like
Vector of independent variables
Returns
-------
excess : array-like
How much the constraint is exceeded by, for each of the
constraints specified by `PreparedConstraint.fun`.
"""
with suppress_warnings() as sup:
sup.filter(UserWarning)
ev = self.fun.fun(np.asarray(x))
excess_lb = np.maximum(self.bounds[0] - ev, 0)
excess_ub = np.maximum(ev - self.bounds[1], 0)
return excess_lb + excess_ub
def new_bounds_to_old(lb, ub, n):
"""Convert the new bounds representation to the old one.
The new representation is a tuple (lb, ub) and the old one is a list
containing n tuples, ith containing lower and upper bound on a ith
variable.
If any of the entries in lb/ub are -np.inf/np.inf they are replaced by
None.
"""
lb = np.asarray(lb)
ub = np.asarray(ub)
if lb.ndim == 0:
lb = np.resize(lb, n)
if ub.ndim == 0:
ub = np.resize(ub, n)
lb = [float(x) if x > -np.inf else None for x in lb]
ub = [float(x) if x < np.inf else None for x in ub]
return list(zip(lb, ub))
def old_bound_to_new(bounds):
"""Convert the old bounds representation to the new one.
The new representation is a tuple (lb, ub) and the old one is a list
containing n tuples, ith containing lower and upper bound on a ith
variable.
If any of the entries in lb/ub are None they are replaced by
-np.inf/np.inf.
"""
lb, ub = zip(*bounds)
lb = np.array([float(x) if x is not None else -np.inf for x in lb])
ub = np.array([float(x) if x is not None else np.inf for x in ub])
return lb, ub
def strict_bounds(lb, ub, keep_feasible, n_vars):
"""Remove bounds which are not asked to be kept feasible."""
strict_lb = np.resize(lb, n_vars).astype(float)
strict_ub = np.resize(ub, n_vars).astype(float)
keep_feasible = np.resize(keep_feasible, n_vars)
strict_lb[~keep_feasible] = -np.inf
strict_ub[~keep_feasible] = np.inf
return strict_lb, strict_ub
def new_constraint_to_old(con, x0):
"""
Converts new-style constraint objects to old-style constraint dictionaries.
"""
if isinstance(con, NonlinearConstraint):
if (con.finite_diff_jac_sparsity is not None or
con.finite_diff_rel_step is not None or
not isinstance(con.hess, BFGS) or # misses user specified BFGS
con.keep_feasible):
warn("Constraint options `finite_diff_jac_sparsity`, "
"`finite_diff_rel_step`, `keep_feasible`, and `hess`"
"are ignored by this method.", OptimizeWarning)
fun = con.fun
if callable(con.jac):
jac = con.jac
else:
jac = None
else: # LinearConstraint
if con.keep_feasible:
warn("Constraint option `keep_feasible` is ignored by this "
"method.", OptimizeWarning)
A = con.A
if issparse(A):
A = A.todense()
fun = lambda x: np.dot(A, x)
jac = lambda x: A
# FIXME: when bugs in VectorFunction/LinearVectorFunction are worked out,
# use pcon.fun.fun and pcon.fun.jac. Until then, get fun/jac above.
pcon = PreparedConstraint(con, x0)
lb, ub = pcon.bounds
i_eq = lb == ub
i_bound_below = np.logical_xor(lb != -np.inf, i_eq)
i_bound_above = np.logical_xor(ub != np.inf, i_eq)
i_unbounded = np.logical_and(lb == -np.inf, ub == np.inf)
if np.any(i_unbounded):
warn("At least one constraint is unbounded above and below. Such "
"constraints are ignored.", OptimizeWarning)
ceq = []
if np.any(i_eq):
def f_eq(x):
y = np.array(fun(x)).flatten()
return y[i_eq] - lb[i_eq]
ceq = [{"type": "eq", "fun": f_eq}]
if jac is not None:
def j_eq(x):
dy = jac(x)
if issparse(dy):
dy = dy.todense()
dy = np.atleast_2d(dy)
return dy[i_eq, :]
ceq[0]["jac"] = j_eq
cineq = []
n_bound_below = np.sum(i_bound_below)
n_bound_above = np.sum(i_bound_above)
if n_bound_below + n_bound_above:
def f_ineq(x):
y = np.zeros(n_bound_below + n_bound_above)
y_all = np.array(fun(x)).flatten()
y[:n_bound_below] = y_all[i_bound_below] - lb[i_bound_below]
y[n_bound_below:] = -(y_all[i_bound_above] - ub[i_bound_above])
return y
cineq = [{"type": "ineq", "fun": f_ineq}]
if jac is not None:
def j_ineq(x):
dy = np.zeros((n_bound_below + n_bound_above, len(x0)))
dy_all = jac(x)
if issparse(dy_all):
dy_all = dy_all.todense()
dy_all = np.atleast_2d(dy_all)
dy[:n_bound_below, :] = dy_all[i_bound_below]
dy[n_bound_below:, :] = -dy_all[i_bound_above]
return dy
cineq[0]["jac"] = j_ineq
old_constraints = ceq + cineq
if len(old_constraints) > 1:
warn("Equality and inequality constraints are specified in the same "
"element of the constraint list. For efficient use with this "
"method, equality and inequality constraints should be specified "
"in separate elements of the constraint list. ", OptimizeWarning)
return old_constraints
def old_constraint_to_new(ic, con):
"""
Converts old-style constraint dictionaries to new-style constraint objects.
"""
# check type
try:
ctype = con['type'].lower()
except KeyError:
raise KeyError('Constraint %d has no type defined.' % ic)
except TypeError:
raise TypeError('Constraints must be a sequence of dictionaries.')
except AttributeError:
raise TypeError("Constraint's type must be a string.")
else:
if ctype not in ['eq', 'ineq']:
raise ValueError("Unknown constraint type '%s'." % con['type'])
if 'fun' not in con:
raise ValueError('Constraint %d has no function defined.' % ic)
lb = 0
if ctype == 'eq':
ub = 0
else:
ub = np.inf
jac = '2-point'
if 'args' in con:
args = con['args']
fun = lambda x: con['fun'](x, *args)
if 'jac' in con:
jac = lambda x: con['jac'](x, *args)
else:
fun = con['fun']
if 'jac' in con:
jac = con['jac']
return NonlinearConstraint(fun, lb, ub, jac)