def minimize_scalar(fun, bracket=None, bounds=None, args=(),
method='brent', options=None):
"""
Minimization of scalar function of one variable.
.. versionadded:: 0.11.0
Parameters
----------
fun : callable
Objective function.
Scalar function, must return a scalar.
bracket : sequence, optional
For methods 'brent' and 'golden', `bracket` defines the bracketing
interval and can either have three items `(a, b, c)` so that `a < b
< c` and `fun(b) < fun(a), fun(c)` or two items `a` and `c` which
are assumed to be a starting interval for a downhill bracket search
(see `bracket`); it doesn't always mean that the obtained solution
will satisfy `a <= x <= c`.
bounds : sequence, optional
For method 'bounded', `bounds` is mandatory and must have two items
corresponding to the optimization bounds.
args : tuple, optional
Extra arguments passed to the objective function.
method : str, optional
Type of solver. Should be one of
- 'Brent'
- 'Bounded'
- 'Golden'
options : dict, optional
A dictionary of solver options.
xtol : float
Relative error in solution `xopt` acceptable for
convergence.
ftol : float
Relative error in ``fun(xopt)`` acceptable for convergence.
maxiter : int
Maximum number of iterations to perform.
disp : bool
Set to True to print convergence messages.
Returns
-------
res : Result
The optimization result represented as a ``Result`` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. See
`Result` for a description of other attributes.
See also
--------
minimize: Interface to minimization algorithms for scalar multivariate
functions.
Notes
-----
This section describes the available solvers that can be selected by the
'method' parameter. The default method is *Brent*.
Method *Brent* uses Brent's algorithm to find a local minimum.
The algorithm uses inverse parabolic interpolation when possible to
speed up convergence of the golden section method.
Method *Golden* uses the golden section search technique. It uses
analog of the bisection method to decrease the bracketed interval. It
is usually preferable to use the *Brent* method.
Method *Bounded* can perform bounded minimization. It uses the Brent
method to find a local minimum in the interval x1 < xopt < x2.
Examples
--------
Consider the problem of minimizing the following function.
>>> def f(x):
... return (x - 2) * x * (x + 2)**2
Using the *Brent* method, we find the local minimum as:
>>> from scipy.optimize import minimize_scalar
>>> res = minimize_scalar(f)
>>> res.x
1.28077640403
Using the *Bounded* method, we find a local minimum with specified
bounds as:
>>> res = minimize_scalar(f, bounds=(-3, -1), method='bounded')
>>> res.x
-2.0000002026
"""
meth = method.lower()
if options is None:
options = {}
if meth == 'brent':
return _minimize_scalar_brent(fun, bracket, args, options)
elif meth == 'bounded':
if bounds is None:
raise ValueError('The `bounds` parameter is mandatory for '
'method `bounded`.')
return _minimize_scalar_bounded(fun, bounds, args, options)
elif meth == 'golden':
return _minimize_scalar_golden(fun, bracket, args, options)
else:
raise ValueError('Unknown solver %s' % method)
def minimize_scalar(fun, bracket=None, bounds=None, args=(),
method='brent', tol=None, options=None):
"""
Minimization of scalar function of one variable.
.. versionadded:: 0.11.0
Parameters
----------
fun : callable
Objective function.
Scalar function, must return a scalar.
bracket : sequence, optional
For methods 'brent' and 'golden', `bracket` defines the bracketing
interval and can either have three items `(a, b, c)` so that `a < b
< c` and `fun(b) < fun(a), fun(c)` or two items `a` and `c` which
are assumed to be a starting interval for a downhill bracket search
(see `bracket`); it doesn't always mean that the obtained solution
will satisfy `a <= x <= c`.
bounds : sequence, optional
For method 'bounded', `bounds` is mandatory and must have two items
corresponding to the optimization bounds.
args : tuple, optional
Extra arguments passed to the objective function.
method : str, optional
Type of solver. Should be one of
- 'Brent'
- 'Bounded'
- 'Golden'
tol : float, optional
Tolerance for termination. For detailed control, use solver-specific
options.
options : dict, optional
A dictionary of solver options.
xtol : float
Relative error in solution `xopt` acceptable for
convergence.
maxiter : int
Maximum number of iterations to perform.
disp : bool
Set to True to print convergence messages.
Returns
-------
res : Result
The optimization result represented as a ``Result`` object.
Important attributes are: ``x`` the solution array, ``success`` a
Boolean flag indicating if the optimizer exited successfully and
``message`` which describes the cause of the termination. See
`Result` for a description of other attributes.
See also
--------
minimize: Interface to minimization algorithms for scalar multivariate
functions.
Notes
-----
This section describes the available solvers that can be selected by the
'method' parameter. The default method is *Brent*.
Method *Brent* uses Brent's algorithm to find a local minimum.
The algorithm uses inverse parabolic interpolation when possible to
speed up convergence of the golden section method.
Method *Golden* uses the golden section search technique. It uses
analog of the bisection method to decrease the bracketed interval. It
is usually preferable to use the *Brent* method.
Method *Bounded* can perform bounded minimization. It uses the Brent
method to find a local minimum in the interval x1 < xopt < x2.
Examples
--------
Consider the problem of minimizing the following function.
>>> def f(x):
... return (x - 2) * x * (x + 2)**2
Using the *Brent* method, we find the local minimum as:
>>> from scipy.optimize import minimize_scalar
>>> res = minimize_scalar(f)
>>> res.x
1.28077640403
Using the *Bounded* method, we find a local minimum with specified
bounds as:
>>> res = minimize_scalar(f, bounds=(-3, -1), method='bounded')
>>> res.x
-2.0000002026
"""
meth = method.lower()
if options is None:
options = {}
if tol is not None:
options = dict(options)
options.setdefault('xtol', tol)
if meth == 'brent':
return _minimize_scalar_brent(fun, bracket, args, **options)
elif meth == 'bounded':
if bounds is None:
raise ValueError('The `bounds` parameter is mandatory for '
'method `bounded`.')
return _minimize_scalar_bounded(fun, bounds, args, **options)
elif meth == 'golden':
return _minimize_scalar_golden(fun, bracket, args, **options)
else:
raise ValueError('Unknown solver %s' % method)