514 lines
19 KiB
Python
514 lines
19 KiB
Python
|
"""
|
||
|
|
This module implements the Sequential Least Squares Programming optimization
|
||
|
|
algorithm (SLSQP), originally developed by Dieter Kraft.
|
||
|
|
See http://www.netlib.org/toms/733
|
||
|
|
|
||
|
|
Functions
|
||
|
|
---------
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
approx_jacobian
|
||
|
|
fmin_slsqp
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
__all__ = ['approx_jacobian', 'fmin_slsqp']
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from scipy.optimize._slsqp import slsqp
|
||
|
|
from numpy import (zeros, array, linalg, append, concatenate, finfo,
|
||
|
|
sqrt, vstack, isfinite, atleast_1d)
|
||
|
|
from ._optimize import (OptimizeResult, _check_unknown_options,
|
||
|
|
_prepare_scalar_function, _clip_x_for_func,
|
||
|
|
_check_clip_x)
|
||
|
|
from ._numdiff import approx_derivative
|
||
|
|
from ._constraints import old_bound_to_new, _arr_to_scalar
|
||
|
|
from scipy._lib._array_api import atleast_nd, array_namespace
|
||
|
|
|
||
|
|
# deprecated imports to be removed in SciPy 1.13.0
|
||
|
|
from numpy import exp, inf # noqa: F401
|
||
|
|
|
||
|
|
|
||
|
|
__docformat__ = "restructuredtext en"
|
||
|
|
|
||
|
|
_epsilon = sqrt(finfo(float).eps)
|
||
|
|
|
||
|
|
|
||
|
|
def approx_jacobian(x, func, epsilon, *args):
|
||
|
|
"""
|
||
|
|
Approximate the Jacobian matrix of a callable function.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
x : array_like
|
||
|
|
The state vector at which to compute the Jacobian matrix.
|
||
|
|
func : callable f(x,*args)
|
||
|
|
The vector-valued function.
|
||
|
|
epsilon : float
|
||
|
|
The perturbation used to determine the partial derivatives.
|
||
|
|
args : sequence
|
||
|
|
Additional arguments passed to func.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
An array of dimensions ``(lenf, lenx)`` where ``lenf`` is the length
|
||
|
|
of the outputs of `func`, and ``lenx`` is the number of elements in
|
||
|
|
`x`.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The approximation is done using forward differences.
|
||
|
|
|
||
|
|
"""
|
||
|
|
# approx_derivative returns (m, n) == (lenf, lenx)
|
||
|
|
jac = approx_derivative(func, x, method='2-point', abs_step=epsilon,
|
||
|
|
args=args)
|
||
|
|
# if func returns a scalar jac.shape will be (lenx,). Make sure
|
||
|
|
# it's at least a 2D array.
|
||
|
|
return np.atleast_2d(jac)
|
||
|
|
|
||
|
|
|
||
|
|
def fmin_slsqp(func, x0, eqcons=(), f_eqcons=None, ieqcons=(), f_ieqcons=None,
|
||
|
|
bounds=(), fprime=None, fprime_eqcons=None,
|
||
|
|
fprime_ieqcons=None, args=(), iter=100, acc=1.0E-6,
|
||
|
|
iprint=1, disp=None, full_output=0, epsilon=_epsilon,
|
||
|
|
callback=None):
|
||
|
|
"""
|
||
|
|
Minimize a function using Sequential Least Squares Programming
|
||
|
|
|
||
|
|
Python interface function for the SLSQP Optimization subroutine
|
||
|
|
originally implemented by Dieter Kraft.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
func : callable f(x,*args)
|
||
|
|
Objective function. Must return a scalar.
|
||
|
|
x0 : 1-D ndarray of float
|
||
|
|
Initial guess for the independent variable(s).
|
||
|
|
eqcons : list, optional
|
||
|
|
A list of functions of length n such that
|
||
|
|
eqcons[j](x,*args) == 0.0 in a successfully optimized
|
||
|
|
problem.
|
||
|
|
f_eqcons : callable f(x,*args), optional
|
||
|
|
Returns a 1-D array in which each element must equal 0.0 in a
|
||
|
|
successfully optimized problem. If f_eqcons is specified,
|
||
|
|
eqcons is ignored.
|
||
|
|
ieqcons : list, optional
|
||
|
|
A list of functions of length n such that
|
||
|
|
ieqcons[j](x,*args) >= 0.0 in a successfully optimized
|
||
|
|
problem.
|
||
|
|
f_ieqcons : callable f(x,*args), optional
|
||
|
|
Returns a 1-D ndarray in which each element must be greater or
|
||
|
|
equal to 0.0 in a successfully optimized problem. If
|
||
|
|
f_ieqcons is specified, ieqcons is ignored.
|
||
|
|
bounds : list, optional
|
||
|
|
A list of tuples specifying the lower and upper bound
|
||
|
|
for each independent variable [(xl0, xu0),(xl1, xu1),...]
|
||
|
|
Infinite values will be interpreted as large floating values.
|
||
|
|
fprime : callable `f(x,*args)`, optional
|
||
|
|
A function that evaluates the partial derivatives of func.
|
||
|
|
fprime_eqcons : callable `f(x,*args)`, optional
|
||
|
|
A function of the form `f(x, *args)` that returns the m by n
|
||
|
|
array of equality constraint normals. If not provided,
|
||
|
|
the normals will be approximated. The array returned by
|
||
|
|
fprime_eqcons should be sized as ( len(eqcons), len(x0) ).
|
||
|
|
fprime_ieqcons : callable `f(x,*args)`, optional
|
||
|
|
A function of the form `f(x, *args)` that returns the m by n
|
||
|
|
array of inequality constraint normals. If not provided,
|
||
|
|
the normals will be approximated. The array returned by
|
||
|
|
fprime_ieqcons should be sized as ( len(ieqcons), len(x0) ).
|
||
|
|
args : sequence, optional
|
||
|
|
Additional arguments passed to func and fprime.
|
||
|
|
iter : int, optional
|
||
|
|
The maximum number of iterations.
|
||
|
|
acc : float, optional
|
||
|
|
Requested accuracy.
|
||
|
|
iprint : int, optional
|
||
|
|
The verbosity of fmin_slsqp :
|
||
|
|
|
||
|
|
* iprint <= 0 : Silent operation
|
||
|
|
* iprint == 1 : Print summary upon completion (default)
|
||
|
|
* iprint >= 2 : Print status of each iterate and summary
|
||
|
|
disp : int, optional
|
||
|
|
Overrides the iprint interface (preferred).
|
||
|
|
full_output : bool, optional
|
||
|
|
If False, return only the minimizer of func (default).
|
||
|
|
Otherwise, output final objective function and summary
|
||
|
|
information.
|
||
|
|
epsilon : float, optional
|
||
|
|
The step size for finite-difference derivative estimates.
|
||
|
|
callback : callable, optional
|
||
|
|
Called after each iteration, as ``callback(x)``, where ``x`` is the
|
||
|
|
current parameter vector.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : ndarray of float
|
||
|
|
The final minimizer of func.
|
||
|
|
fx : ndarray of float, if full_output is true
|
||
|
|
The final value of the objective function.
|
||
|
|
its : int, if full_output is true
|
||
|
|
The number of iterations.
|
||
|
|
imode : int, if full_output is true
|
||
|
|
The exit mode from the optimizer (see below).
|
||
|
|
smode : string, if full_output is true
|
||
|
|
Message describing the exit mode from the optimizer.
|
||
|
|
|
||
|
|
See also
|
||
|
|
--------
|
||
|
|
minimize: Interface to minimization algorithms for multivariate
|
||
|
|
functions. See the 'SLSQP' `method` in particular.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Exit modes are defined as follows ::
|
||
|
|
|
||
|
|
-1 : Gradient evaluation required (g & a)
|
||
|
|
0 : Optimization terminated successfully
|
||
|
|
1 : Function evaluation required (f & c)
|
||
|
|
2 : More equality constraints than independent variables
|
||
|
|
3 : More than 3*n iterations in LSQ subproblem
|
||
|
|
4 : Inequality constraints incompatible
|
||
|
|
5 : Singular matrix E in LSQ subproblem
|
||
|
|
6 : Singular matrix C in LSQ subproblem
|
||
|
|
7 : Rank-deficient equality constraint subproblem HFTI
|
||
|
|
8 : Positive directional derivative for linesearch
|
||
|
|
9 : Iteration limit reached
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
Examples are given :ref:`in the tutorial <tutorial-sqlsp>`.
|
||
|
|
|
||
|
|
"""
|
||
|
|
if disp is not None:
|
||
|
|
iprint = disp
|
||
|
|
|
||
|
|
opts = {'maxiter': iter,
|
||
|
|
'ftol': acc,
|
||
|
|
'iprint': iprint,
|
||
|
|
'disp': iprint != 0,
|
||
|
|
'eps': epsilon,
|
||
|
|
'callback': callback}
|
||
|
|
|
||
|
|
# Build the constraints as a tuple of dictionaries
|
||
|
|
cons = ()
|
||
|
|
# 1. constraints of the 1st kind (eqcons, ieqcons); no Jacobian; take
|
||
|
|
# the same extra arguments as the objective function.
|
||
|
|
cons += tuple({'type': 'eq', 'fun': c, 'args': args} for c in eqcons)
|
||
|
|
cons += tuple({'type': 'ineq', 'fun': c, 'args': args} for c in ieqcons)
|
||
|
|
# 2. constraints of the 2nd kind (f_eqcons, f_ieqcons) and their Jacobian
|
||
|
|
# (fprime_eqcons, fprime_ieqcons); also take the same extra arguments
|
||
|
|
# as the objective function.
|
||
|
|
if f_eqcons:
|
||
|
|
cons += ({'type': 'eq', 'fun': f_eqcons, 'jac': fprime_eqcons,
|
||
|
|
'args': args}, )
|
||
|
|
if f_ieqcons:
|
||
|
|
cons += ({'type': 'ineq', 'fun': f_ieqcons, 'jac': fprime_ieqcons,
|
||
|
|
'args': args}, )
|
||
|
|
|
||
|
|
res = _minimize_slsqp(func, x0, args, jac=fprime, bounds=bounds,
|
||
|
|
constraints=cons, **opts)
|
||
|
|
if full_output:
|
||
|
|
return res['x'], res['fun'], res['nit'], res['status'], res['message']
|
||
|
|
else:
|
||
|
|
return res['x']
|
||
|
|
|
||
|
|
|
||
|
|
def _minimize_slsqp(func, x0, args=(), jac=None, bounds=None,
|
||
|
|
constraints=(),
|
||
|
|
maxiter=100, ftol=1.0E-6, iprint=1, disp=False,
|
||
|
|
eps=_epsilon, callback=None, finite_diff_rel_step=None,
|
||
|
|
**unknown_options):
|
||
|
|
"""
|
||
|
|
Minimize a scalar function of one or more variables using Sequential
|
||
|
|
Least Squares Programming (SLSQP).
|
||
|
|
|
||
|
|
Options
|
||
|
|
-------
|
||
|
|
ftol : float
|
||
|
|
Precision goal for the value of f in the stopping criterion.
|
||
|
|
eps : float
|
||
|
|
Step size used for numerical approximation of the Jacobian.
|
||
|
|
disp : bool
|
||
|
|
Set to True to print convergence messages. If False,
|
||
|
|
`verbosity` is ignored and set to 0.
|
||
|
|
maxiter : int
|
||
|
|
Maximum number of iterations.
|
||
|
|
finite_diff_rel_step : None or array_like, optional
|
||
|
|
If `jac in ['2-point', '3-point', 'cs']` the relative step size to
|
||
|
|
use for numerical approximation of `jac`. The absolute step
|
||
|
|
size is computed as ``h = rel_step * sign(x) * max(1, abs(x))``,
|
||
|
|
possibly adjusted to fit into the bounds. For ``method='3-point'``
|
||
|
|
the sign of `h` is ignored. If None (default) then step is selected
|
||
|
|
automatically.
|
||
|
|
"""
|
||
|
|
_check_unknown_options(unknown_options)
|
||
|
|
iter = maxiter - 1
|
||
|
|
acc = ftol
|
||
|
|
epsilon = eps
|
||
|
|
|
||
|
|
if not disp:
|
||
|
|
iprint = 0
|
||
|
|
|
||
|
|
# Transform x0 into an array.
|
||
|
|
xp = array_namespace(x0)
|
||
|
|
x0 = atleast_nd(x0, ndim=1, xp=xp)
|
||
|
|
dtype = xp.float64
|
||
|
|
if xp.isdtype(x0.dtype, "real floating"):
|
||
|
|
dtype = x0.dtype
|
||
|
|
x = xp.reshape(xp.astype(x0, dtype), -1)
|
||
|
|
|
||
|
|
# SLSQP is sent 'old-style' bounds, 'new-style' bounds are required by
|
||
|
|
# ScalarFunction
|
||
|
|
if bounds is None or len(bounds) == 0:
|
||
|
|
new_bounds = (-np.inf, np.inf)
|
||
|
|
else:
|
||
|
|
new_bounds = old_bound_to_new(bounds)
|
||
|
|
|
||
|
|
# clip the initial guess to bounds, otherwise ScalarFunction doesn't work
|
||
|
|
x = np.clip(x, new_bounds[0], new_bounds[1])
|
||
|
|
|
||
|
|
# Constraints are triaged per type into a dictionary of tuples
|
||
|
|
if isinstance(constraints, dict):
|
||
|
|
constraints = (constraints, )
|
||
|
|
|
||
|
|
cons = {'eq': (), 'ineq': ()}
|
||
|
|
for ic, con in enumerate(constraints):
|
||
|
|
# check type
|
||
|
|
try:
|
||
|
|
ctype = con['type'].lower()
|
||
|
|
except KeyError as e:
|
||
|
|
raise KeyError('Constraint %d has no type defined.' % ic) from e
|
||
|
|
except TypeError as e:
|
||
|
|
raise TypeError('Constraints must be defined using a '
|
||
|
|
'dictionary.') from e
|
||
|
|
except AttributeError as e:
|
||
|
|
raise TypeError("Constraint's type must be a string.") from e
|
||
|
|
else:
|
||
|
|
if ctype not in ['eq', 'ineq']:
|
||
|
|
raise ValueError("Unknown constraint type '%s'." % con['type'])
|
||
|
|
|
||
|
|
# check function
|
||
|
|
if 'fun' not in con:
|
||
|
|
raise ValueError('Constraint %d has no function defined.' % ic)
|
||
|
|
|
||
|
|
# check Jacobian
|
||
|
|
cjac = con.get('jac')
|
||
|
|
if cjac is None:
|
||
|
|
# approximate Jacobian function. The factory function is needed
|
||
|
|
# to keep a reference to `fun`, see gh-4240.
|
||
|
|
def cjac_factory(fun):
|
||
|
|
def cjac(x, *args):
|
||
|
|
x = _check_clip_x(x, new_bounds)
|
||
|
|
|
||
|
|
if jac in ['2-point', '3-point', 'cs']:
|
||
|
|
return approx_derivative(fun, x, method=jac, args=args,
|
||
|
|
rel_step=finite_diff_rel_step,
|
||
|
|
bounds=new_bounds)
|
||
|
|
else:
|
||
|
|
return approx_derivative(fun, x, method='2-point',
|
||
|
|
abs_step=epsilon, args=args,
|
||
|
|
bounds=new_bounds)
|
||
|
|
|
||
|
|
return cjac
|
||
|
|
cjac = cjac_factory(con['fun'])
|
||
|
|
|
||
|
|
# update constraints' dictionary
|
||
|
|
cons[ctype] += ({'fun': con['fun'],
|
||
|
|
'jac': cjac,
|
||
|
|
'args': con.get('args', ())}, )
|
||
|
|
|
||
|
|
exit_modes = {-1: "Gradient evaluation required (g & a)",
|
||
|
|
0: "Optimization terminated successfully",
|
||
|
|
1: "Function evaluation required (f & c)",
|
||
|
|
2: "More equality constraints than independent variables",
|
||
|
|
3: "More than 3*n iterations in LSQ subproblem",
|
||
|
|
4: "Inequality constraints incompatible",
|
||
|
|
5: "Singular matrix E in LSQ subproblem",
|
||
|
|
6: "Singular matrix C in LSQ subproblem",
|
||
|
|
7: "Rank-deficient equality constraint subproblem HFTI",
|
||
|
|
8: "Positive directional derivative for linesearch",
|
||
|
|
9: "Iteration limit reached"}
|
||
|
|
|
||
|
|
# Set the parameters that SLSQP will need
|
||
|
|
# meq, mieq: number of equality and inequality constraints
|
||
|
|
meq = sum(map(len, [atleast_1d(c['fun'](x, *c['args']))
|
||
|
|
for c in cons['eq']]))
|
||
|
|
mieq = sum(map(len, [atleast_1d(c['fun'](x, *c['args']))
|
||
|
|
for c in cons['ineq']]))
|
||
|
|
# m = The total number of constraints
|
||
|
|
m = meq + mieq
|
||
|
|
# la = The number of constraints, or 1 if there are no constraints
|
||
|
|
la = array([1, m]).max()
|
||
|
|
# n = The number of independent variables
|
||
|
|
n = len(x)
|
||
|
|
|
||
|
|
# Define the workspaces for SLSQP
|
||
|
|
n1 = n + 1
|
||
|
|
mineq = m - meq + n1 + n1
|
||
|
|
len_w = (3*n1+m)*(n1+1)+(n1-meq+1)*(mineq+2) + 2*mineq+(n1+mineq)*(n1-meq) \
|
||
|
|
+ 2*meq + n1 + ((n+1)*n)//2 + 2*m + 3*n + 3*n1 + 1
|
||
|
|
len_jw = mineq
|
||
|
|
w = zeros(len_w)
|
||
|
|
jw = zeros(len_jw)
|
||
|
|
|
||
|
|
# Decompose bounds into xl and xu
|
||
|
|
if bounds is None or len(bounds) == 0:
|
||
|
|
xl = np.empty(n, dtype=float)
|
||
|
|
xu = np.empty(n, dtype=float)
|
||
|
|
xl.fill(np.nan)
|
||
|
|
xu.fill(np.nan)
|
||
|
|
else:
|
||
|
|
bnds = array([(_arr_to_scalar(l), _arr_to_scalar(u))
|
||
|
|
for (l, u) in bounds], float)
|
||
|
|
if bnds.shape[0] != n:
|
||
|
|
raise IndexError('SLSQP Error: the length of bounds is not '
|
||
|
|
'compatible with that of x0.')
|
||
|
|
|
||
|
|
with np.errstate(invalid='ignore'):
|
||
|
|
bnderr = bnds[:, 0] > bnds[:, 1]
|
||
|
|
|
||
|
|
if bnderr.any():
|
||
|
|
raise ValueError('SLSQP Error: lb > ub in bounds %s.' %
|
||
|
|
', '.join(str(b) for b in bnderr))
|
||
|
|
xl, xu = bnds[:, 0], bnds[:, 1]
|
||
|
|
|
||
|
|
# Mark infinite bounds with nans; the Fortran code understands this
|
||
|
|
infbnd = ~isfinite(bnds)
|
||
|
|
xl[infbnd[:, 0]] = np.nan
|
||
|
|
xu[infbnd[:, 1]] = np.nan
|
||
|
|
|
||
|
|
# ScalarFunction provides function and gradient evaluation
|
||
|
|
sf = _prepare_scalar_function(func, x, jac=jac, args=args, epsilon=eps,
|
||
|
|
finite_diff_rel_step=finite_diff_rel_step,
|
||
|
|
bounds=new_bounds)
|
||
|
|
# gh11403 SLSQP sometimes exceeds bounds by 1 or 2 ULP, make sure this
|
||
|
|
# doesn't get sent to the func/grad evaluator.
|
||
|
|
wrapped_fun = _clip_x_for_func(sf.fun, new_bounds)
|
||
|
|
wrapped_grad = _clip_x_for_func(sf.grad, new_bounds)
|
||
|
|
|
||
|
|
# Initialize the iteration counter and the mode value
|
||
|
|
mode = array(0, int)
|
||
|
|
acc = array(acc, float)
|
||
|
|
majiter = array(iter, int)
|
||
|
|
majiter_prev = 0
|
||
|
|
|
||
|
|
# Initialize internal SLSQP state variables
|
||
|
|
alpha = array(0, float)
|
||
|
|
f0 = array(0, float)
|
||
|
|
gs = array(0, float)
|
||
|
|
h1 = array(0, float)
|
||
|
|
h2 = array(0, float)
|
||
|
|
h3 = array(0, float)
|
||
|
|
h4 = array(0, float)
|
||
|
|
t = array(0, float)
|
||
|
|
t0 = array(0, float)
|
||
|
|
tol = array(0, float)
|
||
|
|
iexact = array(0, int)
|
||
|
|
incons = array(0, int)
|
||
|
|
ireset = array(0, int)
|
||
|
|
itermx = array(0, int)
|
||
|
|
line = array(0, int)
|
||
|
|
n1 = array(0, int)
|
||
|
|
n2 = array(0, int)
|
||
|
|
n3 = array(0, int)
|
||
|
|
|
||
|
|
# Print the header if iprint >= 2
|
||
|
|
if iprint >= 2:
|
||
|
|
print("%5s %5s %16s %16s" % ("NIT", "FC", "OBJFUN", "GNORM"))
|
||
|
|
|
||
|
|
# mode is zero on entry, so call objective, constraints and gradients
|
||
|
|
# there should be no func evaluations here because it's cached from
|
||
|
|
# ScalarFunction
|
||
|
|
fx = wrapped_fun(x)
|
||
|
|
g = append(wrapped_grad(x), 0.0)
|
||
|
|
c = _eval_constraint(x, cons)
|
||
|
|
a = _eval_con_normals(x, cons, la, n, m, meq, mieq)
|
||
|
|
|
||
|
|
while 1:
|
||
|
|
# Call SLSQP
|
||
|
|
slsqp(m, meq, x, xl, xu, fx, c, g, a, acc, majiter, mode, w, jw,
|
||
|
|
alpha, f0, gs, h1, h2, h3, h4, t, t0, tol,
|
||
|
|
iexact, incons, ireset, itermx, line,
|
||
|
|
n1, n2, n3)
|
||
|
|
|
||
|
|
if mode == 1: # objective and constraint evaluation required
|
||
|
|
fx = wrapped_fun(x)
|
||
|
|
c = _eval_constraint(x, cons)
|
||
|
|
|
||
|
|
if mode == -1: # gradient evaluation required
|
||
|
|
g = append(wrapped_grad(x), 0.0)
|
||
|
|
a = _eval_con_normals(x, cons, la, n, m, meq, mieq)
|
||
|
|
|
||
|
|
if majiter > majiter_prev:
|
||
|
|
# call callback if major iteration has incremented
|
||
|
|
if callback is not None:
|
||
|
|
callback(np.copy(x))
|
||
|
|
|
||
|
|
# Print the status of the current iterate if iprint > 2
|
||
|
|
if iprint >= 2:
|
||
|
|
print("%5i %5i % 16.6E % 16.6E" % (majiter, sf.nfev,
|
||
|
|
fx, linalg.norm(g)))
|
||
|
|
|
||
|
|
# If exit mode is not -1 or 1, slsqp has completed
|
||
|
|
if abs(mode) != 1:
|
||
|
|
break
|
||
|
|
|
||
|
|
majiter_prev = int(majiter)
|
||
|
|
|
||
|
|
# Optimization loop complete. Print status if requested
|
||
|
|
if iprint >= 1:
|
||
|
|
print(exit_modes[int(mode)] + " (Exit mode " + str(mode) + ')')
|
||
|
|
print(" Current function value:", fx)
|
||
|
|
print(" Iterations:", majiter)
|
||
|
|
print(" Function evaluations:", sf.nfev)
|
||
|
|
print(" Gradient evaluations:", sf.ngev)
|
||
|
|
|
||
|
|
return OptimizeResult(x=x, fun=fx, jac=g[:-1], nit=int(majiter),
|
||
|
|
nfev=sf.nfev, njev=sf.ngev, status=int(mode),
|
||
|
|
message=exit_modes[int(mode)], success=(mode == 0))
|
||
|
|
|
||
|
|
|
||
|
|
def _eval_constraint(x, cons):
|
||
|
|
# Compute constraints
|
||
|
|
if cons['eq']:
|
||
|
|
c_eq = concatenate([atleast_1d(con['fun'](x, *con['args']))
|
||
|
|
for con in cons['eq']])
|
||
|
|
else:
|
||
|
|
c_eq = zeros(0)
|
||
|
|
|
||
|
|
if cons['ineq']:
|
||
|
|
c_ieq = concatenate([atleast_1d(con['fun'](x, *con['args']))
|
||
|
|
for con in cons['ineq']])
|
||
|
|
else:
|
||
|
|
c_ieq = zeros(0)
|
||
|
|
|
||
|
|
# Now combine c_eq and c_ieq into a single matrix
|
||
|
|
c = concatenate((c_eq, c_ieq))
|
||
|
|
return c
|
||
|
|
|
||
|
|
|
||
|
|
def _eval_con_normals(x, cons, la, n, m, meq, mieq):
|
||
|
|
# Compute the normals of the constraints
|
||
|
|
if cons['eq']:
|
||
|
|
a_eq = vstack([con['jac'](x, *con['args'])
|
||
|
|
for con in cons['eq']])
|
||
|
|
else: # no equality constraint
|
||
|
|
a_eq = zeros((meq, n))
|
||
|
|
|
||
|
|
if cons['ineq']:
|
||
|
|
a_ieq = vstack([con['jac'](x, *con['args'])
|
||
|
|
for con in cons['ineq']])
|
||
|
|
else: # no inequality constraint
|
||
|
|
a_ieq = zeros((mieq, n))
|
||
|
|
|
||
|
|
# Now combine a_eq and a_ieq into a single a matrix
|
||
|
|
if m == 0: # no constraints
|
||
|
|
a = zeros((la, n))
|
||
|
|
else:
|
||
|
|
a = vstack((a_eq, a_ieq))
|
||
|
|
a = concatenate((a, zeros([la, 1])), 1)
|
||
|
|
|
||
|
|
return a
|