def check(self):
"""
Checks the optimization algorithm's settings and raises an exception if
something is wrong.
"""
Optimizer.check(self)
if self.expand<=1.0:
raise Exception, DbgMsg("NMOPT", "Expansion coefficient should be gerater than 1.")
if self.reflect>self.expand:
raise Exception, DbgMsg("NMOPT", "Reflection coefficient should be smaller than expansion coefficient.")
if self.reflect<=0.0:
raise Exception, DbgMsg("NMOPT", "Reflection coefficient should be greater than 0.")
if (self.outerContract<=0.0) or (self.outerContract>=self.reflect):
raise Exception, DbgMsg("NMOPT", "Outer contraction coefficient should be between 0 and reflection coefficient.")
if (self.innerContract>=0.0) or (self.innerContract<=-1.0):
raise Exception, DbgMsg("NMOPT", "Inner contraction coefficient must be from (-1,0).")
if (self.shrink<=0.0) or (self.shrink>=1.0):
raise Exception, DbgMsg("NMOPT", "Shrink coefficient must be from (0,1).")
if self.reltol<0:
raise Exception, DbgMsg("NMOPT", "Negative relative tolerance.")
if self.ftol<0:
raise Exception, DbgMsg("NMOPT", "Negative f tolerance.")
if (self.xtol<0).any():
raise Exception, DbgMsg("NMOPT", "Negative x tolerance.")
def reset(self, x0):
"""
Puts the optimizer in its initial state and sets the initial point to
be the 1-dimensional array or list *x0*. The length of the array
becomes the dimension of the optimization problem
(:attr:`ndim` member).
The initial simplex is built around *x0* by calling the
:meth:`buildSimplex` method with default values for the *rel* and *abs*
arguments.
If *x0* is a 2-dimensional array or list of size
(*ndim*+1) times *ndim* it specifies the initial simplex.
A corresponding grid is created by calling the :meth:`buildGrid` method.
The initial value of the natural logarithm of the simplex side vectors
determinant is calculated and stored.
"""
# Debug message
if self.debug:
DbgMsgOut("GRNMOPT", "Resetting.")
# Make it an array
x0=array(x0)
# Is x0 a point or a simplex?
if x0.ndim==1:
# Point
# Set x now
NelderMead.reset(self, x0)
if self.debug:
DbgMsgOut("GRNMOPT", "Generating initial simplex from initial point.")
sim=self.buildSimplex(x0)
self._setSimplex(sim)
self.delta=self.buildGrid()
self.z=x0
else:
# Simplex or error (handled in _setSimplex())
self._setSimplex(x0)
self.delta=self.buildGrid()
self.z=x0[0,:]
if self.debug:
DbgMsgOut("GRNMOPT", "Using specified initial simplex.")
# Set x to first point in simplex after it was checked in _setSimplex()
Optimizer.reset(self, x0[0,:])
# Reset point moves counter
self.simplexmoves=zeros(self.ndim+1)
# Make x tolerance an array
self.xtol=array(self.xtol)
def test():
p = ParamRange(np.array([[-1, 1, 10], [0, 5, 10], [-2, 1.1, 10]]))
s = Store('testga.giclog')
pars = {'threads': 0, 'size': 20, 'time': 0.1}
model = Model() # test implementation that return product of params
model.perfect = 10
gapars = {'crossover': .9, 'mutation': .05, 'transposition': .001, 'minprop': 0}
alg = GA_Prop(gapars, p)
o = Optimizer(pars, model, alg, s)
o.run()
def __init__(self, f, x0, range=None, h=0.5, emax=1e-8, imax=1000):
'''
Initializes the optimizer.
To create an optimizer of this type, instantiate the class with the
parameters given below:
:Parameters:
f
A one variable only function to be optimized. The function should
have only one parameter and return the function value.
x0
First estimate of the minimum. Since this is a linear method, this
should be a ``float`` or ``int``.
range
A range of values might be passed to the algorithm, but it is not
necessary. If supplied, this parameter should be a tuples of two
values, ``(x0, x1)``, where ``x0`` is the start of the interval, and
``x1`` its end. Obviously, ``x0`` should be smaller than ``x1``.
When this parameter is present, the algorithm will not let the
estimates fall outside the given interval.
h
The initial step of the search. Defaults to 0.5
emax
Maximum allowed error. The algorithm stops as soon as the error is
below this level. The error is absolute.
imax
Maximum number of iterations, the algorithm stops as soon this
number of iterations are executed, no matter what the error is at
the moment.
'''
Optimizer.__init__(self)
self.__f = f
self.__x = x0
self.range = range
'''Holds the range for the estimates. If this attribute is set, the
algorithm will never let the estimates fall outside the given
interval.'''
self.__h = h
self.__emax = float(emax)
self.__imax = int(imax)
def __init__(self, function, debug=0, fstop=None, maxiter=None, reflect=1.0, expand=2.0, outerContract=0.5, innerContract=-0.5, shrink=0.5, reltol=1e-15, ftol=1e-15, xtol=1e-9, simplex=None, looseContraction=False): Optimizer.__init__(self, function, debug, fstop, maxiter) # Coefficients self.reflect=reflect self.expand=expand self.outerContract=outerContract self.innerContract=innerContract self.shrink=shrink # Stopping condition self.reltol=reltol self.ftol=ftol self.xtol=xtol # Simplex self.simplex=simplex # Modifications self.looseContraction=looseContraction
def __init__(self, f, x0, emax=1e-8, imax=1000):
'''
Initializes the optimizer.
To create an optimizer of this type, instantiate the class with the
parameters given below:
:Parameters:
f
A one variable only function to be optimized. The function should
have only one parameter and return the function value.
x0
First estimate of the minimum. The Fibonacci search needs two
estimates to partition the interval. Thus, the first estimate must
be a duple ``(xl, xh)``, with the property that ``xl < xh``. Be
aware, however, that no checking is done -- if the estimate doesn't
correspond to this condition, in some point an exception will be
raised.
Notice that, given the nature of the estimate of the Fibonacci
method, it is not necessary to have a specific parameter to restrict
the range of acceptable values -- it is already embedded in the
estimate. If you need to restrict your estimate between an interval,
just use its limits as ``xl`` and ``xh`` in the estimate.
emax
Maximum allowed error. The algorithm stops as soon as the error is
below this level. The error is absolute.
imax
Maximum number of iterations, the algorithm stops as soon this
number of iterations are executed, no matter what the error is at
the moment.
'''
Optimizer.__init__(self)
self.__f = f
self.__x = x0
self.__k1 = 1.
self.__k2 = 1.
self.__emax = float(emax)
self.__imax = int(imax)
def __init__(self, f, x0, ranges=None, df=None, h=0.1, emax=1e-5, imax=1000):
'''
Initializes the optimizer.
To create an optimizer of this type, instantiate the class with the
parameters given below:
:Parameters:
f
A multivariable function to be optimized. The function should have
only one parameter, a multidimensional line-vector, and return the
function value, a scalar.
x0
First estimate of the minimum. Estimates can be given in any format,
but internally they are converted to a one-dimension vector, where
each component corresponds to the estimate of that particular
variable. The vector is computed by flattening the array.
ranges
A range of values might be passed to the algorithm, but it is not
necessary. If supplied, this parameter should be a list of ranges
for each variable of the objective function. It is specified as a
list of tuples of two values, ``(x0, x1)``, where ``x0`` is the
start of the interval, and ``x1`` its end. Obviously, ``x0`` should
be smaller than ``x1``. It can also be given as a list with a simple
tuple in the same format. In that case, the same range will be
applied for every variable in the optimization.
df
A function to calculate the gradient vector of the cost function
``f``. Defaults to ``None``, if no gradient is supplied, then it is
estimated from the cost function using Euler equations.
h
Convergence step. This method does not takes into consideration the
possibility of varying the convergence step, to avoid Stiefel cages.
emax
Maximum allowed error. The algorithm stops as soon as the error is
below this level. The error is absolute.
imax
Maximum number of iterations, the algorithm stops as soon this
number of iterations are executed, no matter what the error is at
the moment.
'''
Optimizer.__init__(self)
self.__f = f
self.__x = array(x0).ravel()
if df is None:
self.__df = gradient(f)
else:
self.__df = df
self.__B = inv(hessian(self.__f)(self.x))
self.__h = h
# Determine ranges of the variables
if ranges is not None:
ranges = list(ranges)
if len(ranges) == 1:
ranges = array(ranges * len(x0[0]))
else:
ranges = array(ranges)
self.ranges = ranges
'''Holds the ranges for every variable. Although it is a writable
property, care should be taken in changing parameters before ending the
convergence.'''
self.__emax = float(emax)
self.__imax = int(imax)
def reset(self, x0):
"""
Puts the optimizer in its initial state and sets the initial point to
be the 1-dimensional array *x0*. The length of the array becomes the
dimension of the optimization problem (:attr:`ndim` member).
The initial simplex is built around *x0* by calling the
:meth:`buildSimplex` method with default values for the *rel* and
*abs* arguments.
If *x0* is a 2-dimensional array of size (*ndim*+1) times *ndim* it
specifies the initial simplex.
"""
# Debug message
if self.debug:
DbgMsgOut("NM", "Resetting.")
# Make it an array
x0=array(x0)
# Is x0 a point or a simplex?
if x0.ndim==1:
# Point
# Set x now
Optimizer.reset(self, x0)
if self.debug:
DbgMsgOut("NM", "Generating initial simplex from initial point.")
sim=self.buildSimplex(x0)
self._setSimplex(sim)
else:
# Simplex or error (handled in _setSimplex())
self._setSimplex(x0)
if self.debug:
DbgMsgOut("NM", "Using specified initial simplex.")
# Set x to first point in simplex after it was checked in _setSimplex()
Optimizer.reset(self, x0[0,:])
# Reset point moves counter
self.simplexmoves=zeros(self.ndim+1)
# Make x tolerance an array
self.xtol=array(self.xtol)
# Reset counters
self.nr=0
self.ne=0
self.noc=0
self.nic=0
self.ns=0
self.nrok=0
self.neok=0
self.nocok=0
self.nicok=0
self.icconv=0
self.occonv=0
def __init__(self,
f,
x0,
ranges=None,
df=None,
h=0.1,
emax=1e-5,
imax=1000):
'''
Initializes the optimizer.
To create an optimizer of this type, instantiate the class with the
parameters given below:
:Parameters:
f
A multivariable function to be optimized. The function should have
only one parameter, a multidimensional line-vector, and return the
function value, a scalar.
x0
First estimate of the minimum. Estimates can be given in any format,
but internally they are converted to a one-dimension vector, where
each component corresponds to the estimate of that particular
variable. The vector is computed by flattening the array.
ranges
A range of values might be passed to the algorithm, but it is not
necessary. If supplied, this parameter should be a list of ranges
for each variable of the objective function. It is specified as a
list of tuples of two values, ``(x0, x1)``, where ``x0`` is the
start of the interval, and ``x1`` its end. Obviously, ``x0`` should
be smaller than ``x1``. It can also be given as a list with a simple
tuple in the same format. In that case, the same range will be
applied for every variable in the optimization.
df
A function to calculate the gradient vector of the cost function
``f``. Defaults to ``None``, if no gradient is supplied, then it is
estimated from the cost function using Euler equations.
h
Convergence step. This method does not takes into consideration the
possibility of varying the convergence step, to avoid Stiefel cages.
emax
Maximum allowed error. The algorithm stops as soon as the error is
below this level. The error is absolute.
imax
Maximum number of iterations, the algorithm stops as soon this
number of iterations are executed, no matter what the error is at
the moment.
'''
Optimizer.__init__(self)
self.__f = f
self.__x = array(x0).ravel()
if df is None:
self.__df = gradient(f)
else:
self.__df = df
self.__B = inv(hessian(self.__f)(self.x))
self.__h = h
# Determine ranges of the variables
if ranges is not None:
ranges = list(ranges)
if len(ranges) == 1:
ranges = array(ranges * len(x0[0]))
else:
ranges = array(ranges)
self.ranges = ranges
'''Holds the ranges for every variable. Although it is a writable
property, care should be taken in changing parameters before ending the
convergence.'''
self.__emax = float(emax)
self.__imax = int(imax)
def reset(self, x0):
"""
Puts the optimizer in its initial state and sets the initial point to
be the 1-dimensional array or list *x0*. The length of the array
becomes the dimension of the optimization problem
(:attr:`ndim` member).
The initial simplex is built around *x0* by calling the
:meth:`buildSimplex` method with default values for the *rel* and *abs*
arguments.
If *x0* is a 2-dimensional array or list of size
(*ndim*+1) times *ndim* it specifies the initial simplex.
The initial value of the natural logarithm of the simplex side vectors
determinant is calculated and stored. This value gets updated at every
simplex algorithm step. The only time it needs to be reevaluated is at
reshape. But that is also quite simple because the reshaped simplex
is orthogonal. The only place where a full determinant needs to be
calculated is here.
"""
# Debug message
if self.debug:
DbgMsgOut("SDNMOPT", "Resetting.")
# Make it an array
x0=array(x0)
# Is x0 a point or a simplex?
if x0.ndim==1:
# Point
# Set x now
NelderMead.reset(self, x0)
if self.debug:
DbgMsgOut("SDNMOPT", "Generating initial simplex from initial point.")
sim=self.buildSimplex(x0)
self._setSimplex(sim)
else:
# Simplex or error (handled in _setSimplex())
self._setSimplex(x0)
if self.debug:
DbgMsgOut("SDNMOPT", "Using specified initial simplex.")
# Set x to first point in simplex after it was checked in _setSimplex()
Optimizer.reset(self, x0[0,:])
# Reset point moves counter
self.simplexmoves=zeros(self.ndim+1)
# Calculate log(n! det([v])) where [v] are the n side vectors
# arranged as columns of a matrix
(v, l)=self.sortedSideVectors()
self.logDet=log(abs(det(v)))
# Initial h
self.h=1.0
# Make x tolerance an array
self.xtol=array(self.xtol)
def __init__(self, f, x0, ranges=None, h=0.5, emax=1e-8, imax=1000):
'''
Initializes the optimizer.
To create an optimizer of this type, instantiate the class with the
parameters given below:
:Parameters:
f
A multivariable function to be optimized. The function should have
only one parameter, a multidimensional line-vector, and return the
function value, a scalar.
x0
First estimate of the minimum. Estimates can be given in any format,
but internally they are converted to a one-dimension vector, where
each component corresponds to the estimate of that particular
variable. The vector is computed by flattening the array.
ranges
A range of values might be passed to the algorithm, but it is not
necessary. If supplied, this parameter should be a list of ranges
for each variable of the objective function. It is specified as a
list of tuples of two values, ``(x0, x1)``, where ``x0`` is the
start of the interval, and ``x1`` its end. Obviously, ``x0`` should
be smaller than ``x1``. It can also be given as a list with a simple
tuple in the same format. In that case, the same range will be
applied for every variable in the optimization.
h
The initial step of the search. Defaults to 0.5
emax
Maximum allowed error. The algorithm stops as soon as the error is
below this level. The error is absolute.
imax
Maximum number of iterations, the algorithm stops as soon this
number of iterations are executed, no matter what the error is at
the moment.
'''
Optimizer.__init__(self)
self.__f = f
self.__x = array(x0).ravel()
n = self.__x.size
self.__h = ones((n, ))
self.__h[0] = -0.5
self.__dx = h * eye(n, 1).reshape(self.__x.shape)
# Determine ranges of the variables
if ranges is not None:
ranges = list(ranges)
if len(ranges) == 1:
ranges = array(ranges * len(x0[0]))
else:
ranges = array(ranges)
self.ranges = ranges
'''Holds the ranges for every variable. Although it is a writable
property, care should be taken in changing parameters before ending the
convergence.'''
self.__emax = float(emax)
self.__imax = int(imax)
def reset(self, x0):
"""
Puts the optimizer in its initial state and sets the initial point to
be the 1-dimensional array or list *x0*. The length of the array
becomes the dimension of the optimization problem
(:attr:`ndim` member).
The initial simplex is built around *x0* by calling the
:meth:`buildSimplex` method with default values for the *rel* and *abs*
arguments.
If *x0* is a 2-dimensional array or list of size
(*ndim*+1) times *ndim* it specifies the initial simplex.
The initial value of the natural logarithm of the simplex side vectors
determinant is calculated and stored. This value gets updated at every
simplex algorithm step. The only time it needs to be reevaluated is at
reshape. But that is also quite simple because the reshaped simplex
is orthogonal. The only place where a full determinant needs to be
calculated is here.
"""
# Debug message
if self.debug:
DbgMsgOut("SDNMOPT", "Resetting.")
# Make it an array
x0 = array(x0)
# Is x0 a point or a simplex?
if x0.ndim == 1:
# Point
# Set x now
NelderMead.reset(self, x0)
if self.debug:
DbgMsgOut("SDNMOPT",
"Generating initial simplex from initial point.")
sim = self.buildSimplex(x0)
self._setSimplex(sim)
else:
# Simplex or error (handled in _setSimplex())
self._setSimplex(x0)
if self.debug:
DbgMsgOut("SDNMOPT", "Using specified initial simplex.")
# Set x to first point in simplex after it was checked in _setSimplex()
Optimizer.reset(self, x0[0, :])
# Reset point moves counter
self.simplexmoves = zeros(self.ndim + 1)
# Calculate log(n! det([v])) where [v] are the n side vectors
# arranged as columns of a matrix
(v, l) = self.sortedSideVectors()
self.logDet = log(abs(det(v)))
# Initial h
self.h = 1.0
# Make x tolerance an array
self.xtol = array(self.xtol)
def __init__(self, f, x0, ranges=None, h=0.5, emax=1e-8, imax=1000):
'''
Initializes the optimizer.
To create an optimizer of this type, instantiate the class with the
parameters given below:
:Parameters:
f
A multivariable function to be optimized. The function should have
only one parameter, a multidimensional line-vector, and return the
function value, a scalar.
x0
First estimate of the minimum. Estimates can be given in any format,
but internally they are converted to a one-dimension vector, where
each component corresponds to the estimate of that particular
variable. The vector is computed by flattening the array.
ranges
A range of values might be passed to the algorithm, but it is not
necessary. If supplied, this parameter should be a list of ranges
for each variable of the objective function. It is specified as a
list of tuples of two values, ``(x0, x1)``, where ``x0`` is the
start of the interval, and ``x1`` its end. Obviously, ``x0`` should
be smaller than ``x1``. It can also be given as a list with a simple
tuple in the same format. In that case, the same range will be
applied for every variable in the optimization.
h
The initial step of the search. Defaults to 0.5
emax
Maximum allowed error. The algorithm stops as soon as the error is
below this level. The error is absolute.
imax
Maximum number of iterations, the algorithm stops as soon this
number of iterations are executed, no matter what the error is at
the moment.
'''
Optimizer.__init__(self)
self.__f = f
self.__x = array(x0).ravel()
n = self.__x.size
self.__h = ones((n, ))
self.__h[0] = -0.5
self.__dx = h * eye(n, 1).reshape(self.__x.shape)
# Determine ranges of the variables
if ranges is not None:
ranges = list(ranges)
if len(ranges) == 1:
ranges = array(ranges * len(x0[0]))
else:
ranges = array(ranges)
self.ranges = ranges
'''Holds the ranges for every variable. Although it is a writable
property, care should be taken in changing parameters before ending the
convergence.'''
self.__emax = float(emax)
self.__imax = int(imax)