def lmdif(fcn,
x0,
xmin,
xmax,
ftol=EPSILON,
xtol=EPSILON,
gtol=EPSILON,
maxfev=None,
epsfcn=EPSILON,
factor=100.0,
numcores=1,
verbose=0):
class fdJac:
def __init__(self, func, fvec, pars):
self.func = func
self.fvec = fvec
epsmch = numpy.float_(numpy.finfo(numpy.float).eps)
self.eps = numpy.sqrt(max(epsmch, epsfcn))
self.h = self.calc_h(pars)
self.pars = numpy.copy(pars)
return
def __call__(self, param):
wa = self.func(param[1:])
return (wa - self.fvec) / self.h[int(param[0])]
def calc_h(self, pars):
nn = len(pars)
h = numpy.empty((nn, ))
for ii in range(nn):
h[ii] = self.eps * pars[ii]
if h[ii] == 0.0:
h[ii] = self.eps
if pars[ii] + h[ii] > xmax[ii]:
h[ii] = -h[ii]
return h
def calc_params(self):
h = self.calc_h(self.pars)
params = []
for ii in range(len(h)):
tmp_pars = numpy.copy(self.pars)
tmp_pars[ii] += h[ii]
tmp_pars = numpy.append(ii, tmp_pars)
params.append(tmp_pars)
return tuple(params)
x, xmin, xmax = _check_args(x0, xmin, xmax)
if maxfev is None:
maxfev = 256 * len(x)
def stat_cb0(pars):
return fcn(pars)[0]
def stat_cb1(pars):
return fcn(pars)[1]
def fcn_parallel(pars, fvec):
fd_jac = fdJac(stat_cb1, fvec, pars)
params = fd_jac.calc_params()
fjac = parallel_map(fd_jac, params, numcores)
return numpy.concatenate(fjac)
num_parallel_map, fcn_parallel_counter = func_counter(fcn_parallel)
# TO DO: reduce 1 model eval by passing the resulting 'fvec' to cpp_lmdif
m = numpy.asanyarray(stat_cb1(x)).size
error = []
n = len(x)
fjac = numpy.empty((m * n, ))
x, fval, nfev, info, fjac = \
_saoopt.cpp_lmdif(stat_cb1, fcn_parallel_counter, numcores, m, x, ftol,
xtol, gtol, maxfev, epsfcn, factor, verbose, xmin,
xmax, fjac)
if info > 0:
fjac = numpy.reshape(numpy.ravel(fjac, order='F'), (m, n), order='F')
if m != n:
covar = fjac[:n, :n]
else:
covar = fjac
if _par_at_boundary(xmin, x, xmax, xtol):
nm_result = neldermead(fcn,
x,
xmin,
xmax,
ftol=numpy.sqrt(ftol),
maxfev=maxfev - nfev,
finalsimplex=2,
iquad=0,
verbose=0)
nfev += nm_result[4]['nfev']
x = nm_result[1]
fval = nm_result[2]
if error:
raise error.pop()
if 0 == info:
info = 1
elif info >= 1 or info <= 4:
info = 0
else:
info = 3
status, msg = _get_saofit_msg(maxfev, info)
if info == 0:
rv = (status, x, fval, msg, {
'info': info,
'nfev': nfev,
'covar': covar,
'num_parallel_map': num_parallel_map[0]
})
else:
rv = (status, x, fval, msg, {
'info': info,
'nfev': nfev,
'num_parallel_map': num_parallel_map[0]
})
return rv
def func( counter, singleparnum, lock=None ):
# nfev contains the number of times it was fitted
nfev, counter_cb = func_counter( fit_cb )
#
# These are the bounds to be returned by this method
#
conf_int = [ [], [] ]
error_flags = []
#
# If the user has requested a specific parameter to be
# calculated then 'ith_par' represents the index of the
# free parameter to deal with.
#
myargs.ith_par = singleparnum
fitcb = translated_fit_cb( counter_cb, myargs )
par_name = get_par_name( myargs.ith_par )
ith_covar_err = get_step_size( error_scales, upper_scales, counter,
pars[ myargs.ith_par ] )
trial_points = [ [ ], [ ] ]
fitcb = monitor_func( fitcb, trial_points )
bracket = ConfBracket( myargs, trial_points )
# the parameter name is set, may as well get the prefix
prefix = get_prefix( counter, par_name, ['-', '+' ] )
myfitcb = [ verbose_fitcb( fitcb,
ConfBlog(sherpablog,prefix[0],verbose,lock) ),
verbose_fitcb( fitcb,
ConfBlog(sherpablog,prefix[1],verbose,lock) ) ]
for dir in range( 2 ):
#
# trial_points stores the history of the points for the
# parameter which has been evaluated in order to locate
# the root. Note the first point is 'given' since the info
# of the minimum is crucial to the search.
#
bracket.trial_points[0].append( pars[ myargs.ith_par ] )
bracket.trial_points[1].append( - delta_stat )
myblog = ConfBlog( sherpablog, prefix[ dir ], verbose, lock,
debug )
# have to set the callback func otherwise disaster.
bracket.fcn = myfitcb[ dir ]
root = bracket( dir, iter, ith_covar_err, open_interval, maxiters,
eps, myblog )
myzero = root( eps, myblog )
delta_zero = get_delta_root( myzero, dir, pars[ myargs.ith_par ] )
conf_int[ dir ].append( delta_zero )
status_prefix = get_prefix( counter, par_name, ['lower bound',
'upper bound' ] )
print_status( myblog.blogger.info, verbose, status_prefix[ dir ],
delta_zero, lock )
error_flags.append( est_success )
#
# include the minimum point to seperate the -/+ interval
#
dict[ par_name ] = trial_points
return ( conf_int[ 0 ][0], conf_int[ 1 ][0], error_flags[0],
nfev[0], None )
def lmdif(fcn, x0, xmin, xmax, ftol=EPSILON, xtol=EPSILON, gtol=EPSILON,
maxfev=None, epsfcn=EPSILON, factor=100.0, numcores=1, verbose=0):
"""Levenberg-Marquardt optimization method.
The Levenberg-Marquardt method is an interface to the MINPACK
subroutine lmdif to find the local minimum of nonlinear least
squares functions of several variables by a modification of the
Levenberg-Marquardt algorithm [1]_.
Parameters
----------
fcn : function reference
Returns the current statistic and per-bin statistic value when
given the model parameters.
x0, xmin, xmax : sequence of number
The starting point, minimum, and maximum values for each
parameter.
ftol : number
The function tolerance to terminate the search for the minimum;
the default is FLT_EPSILON ~ 1.19209289551e-07, where
FLT_EPSILON is the smallest number x such that ``1.0 != 1.0 +
x``. The conditions are satisfied when both the actual and
predicted relative reductions in the sum of squares are, at
most, ftol.
xtol : number
The relative error desired in the approximate solution; default
is FLT_EPSILON ~ 1.19209289551e-07, where FLT_EPSILON
is the smallest number x such that ``1.0 != 1.0 + x``. The
conditions are satisfied when the relative error between two
consecutive iterates is, at most, `xtol`.
gtol : number
The orthogonality desired between the function vector and the
columns of the jacobian; default is FLT_EPSILON ~
1.19209289551e-07, where FLT_EPSILON is the smallest number x
such that ``1.0 != 1.0 + x``. The conditions are satisfied when
the cosine of the angle between fvec and any column of the
jacobian is, at most, `gtol` in absolute value.
maxfev : int or `None`
The maximum number of function evaluations; the default value
of `None` means to use ``1024 * n``, where `n` is the number of
free parameters.
epsfcn : number
This is used in determining a suitable step length for the
forward-difference approximation; default is FLT_EPSILON
~ 1.19209289551e-07, where FLT_EPSILON is the smallest number
x such that ``1.0 != 1.0 + x``. This approximation assumes that
the relative errors in the functions are of the order of
`epsfcn`. If `epsfcn` is less than the machine precision, it is
assumed that the relative errors in the functions are of the
order of the machine precision.
factor : int
Used in determining the initial step bound; default is 100. The
initial step bound is set to the product of `factor` and the
euclidean norm of diag*x if nonzero, or else to factor itself.
In most cases, `factor` should be from the interval (.1,100.).
numcores : int
The number of CPU cores to use. The default is `1`.
verbose: int
The amount of information to print during the fit. The default
is `0`, which means no output.
References
----------
.. [1] J.J. More, "The Levenberg Marquardt algorithm:
implementation and theory," in Lecture Notes in Mathematics
630: Numerical Analysis, G.A. Watson (Ed.),
Springer-Verlag: Berlin, 1978, pp.105-116.
"""
class fdJac:
def __init__(self, func, fvec, pars):
self.func = func
self.fvec = fvec
epsmch = numpy.finfo(float).eps
self.eps = numpy.sqrt(max(epsmch, epsfcn))
self.h = self.calc_h(pars)
self.pars = numpy.copy(pars)
return
def __call__(self, param):
wa = self.func(param[1:])
return (wa - self.fvec) / self.h[int(param[0])]
def calc_h(self, pars):
nn = len(pars)
h = numpy.empty((nn,))
for ii in range(nn):
h[ii] = self.eps * pars[ii]
if h[ii] == 0.0:
h[ii] = self.eps
if pars[ii] + h[ii] > xmax[ii]:
h[ii] = - h[ii]
return h
def calc_params(self):
h = self.calc_h(self.pars)
params = []
for ii in range(len(h)):
tmp_pars = numpy.copy(self.pars)
tmp_pars[ii] += h[ii]
tmp_pars = numpy.append(ii, tmp_pars)
params.append(tmp_pars)
return tuple(params)
x, xmin, xmax = _check_args(x0, xmin, xmax)
if maxfev is None:
maxfev = 256 * len(x)
def stat_cb0(pars):
return fcn(pars)[0]
def stat_cb1(pars):
return fcn(pars)[1]
def fcn_parallel(pars, fvec):
fd_jac = fdJac(stat_cb1, fvec, pars)
params = fd_jac.calc_params()
fjac = parallel_map(fd_jac, params, numcores)
return numpy.concatenate(fjac)
num_parallel_map, fcn_parallel_counter = func_counter(fcn_parallel)
# TO DO: reduce 1 model eval by passing the resulting 'fvec' to cpp_lmdif
m = numpy.asanyarray(stat_cb1(x)).size
error = []
n = len(x)
fjac = numpy.empty((m*n,))
x, fval, nfev, info, fjac = \
_saoopt.cpp_lmdif(stat_cb1, fcn_parallel_counter, numcores, m, x, ftol,
xtol, gtol, maxfev, epsfcn, factor, verbose, xmin,
xmax, fjac)
if info > 0:
fjac = numpy.reshape(numpy.ravel(fjac, order='F'), (m, n), order='F')
if m != n:
covar = fjac[:n, :n]
else:
covar = fjac
if _par_at_boundary(xmin, x, xmax, xtol):
nm_result = neldermead(fcn, x, xmin, xmax, ftol=numpy.sqrt(ftol),
maxfev=maxfev-nfev, finalsimplex=2, iquad=0,
verbose=0)
nfev += nm_result[4]['nfev']
x = nm_result[1]
fval = nm_result[2]
if error:
raise error.pop()
if 0 == info:
info = 1
elif info >= 1 or info <= 4:
info = 0
else:
info = 3
status, msg = _get_saofit_msg(maxfev, info)
if info == 0:
rv = (status, x, fval, msg, {'info': info, 'nfev': nfev,
'covar': covar,
'num_parallel_map': num_parallel_map[0]})
else:
rv = (status, x, fval, msg, {'info': info, 'nfev': nfev,
'num_parallel_map': num_parallel_map[0]})
return rv
def func(counter, singleparnum, lock=None):
# nfev contains the number of times it was fitted
nfev, counter_cb = func_counter(fit_cb)
#
# These are the bounds to be returned by this method
#
conf_int = [[], []]
error_flags = []
#
# If the user has requested a specific parameter to be
# calculated then 'ith_par' represents the index of the
# free parameter to deal with.
#
myargs.ith_par = singleparnum
fitcb = translated_fit_cb(counter_cb, myargs)
par_name = get_par_name(myargs.ith_par)
ith_covar_err = get_step_size(error_scales, upper_scales, counter,
pars[myargs.ith_par])
trial_points = [[], []]
fitcb = monitor_func(fitcb, trial_points)
bracket = ConfBracket(myargs, trial_points)
# the parameter name is set, may as well get the prefix
prefix = get_prefix(counter, par_name, ['-', '+'])
myfitcb = [
verbose_fitcb(fitcb, ConfBlog(sherpablog, prefix[0], verbose,
lock)),
verbose_fitcb(fitcb, ConfBlog(sherpablog, prefix[1], verbose,
lock))
]
for dir in range(2):
#
# trial_points stores the history of the points for the
# parameter which has been evaluated in order to locate
# the root. Note the first point is 'given' since the info
# of the minimum is crucial to the search.
#
bracket.trial_points[0].append(pars[myargs.ith_par])
bracket.trial_points[1].append(-delta_stat)
myblog = ConfBlog(sherpablog, prefix[dir], verbose, lock, debug)
# have to set the callback func otherwise disaster.
bracket.fcn = myfitcb[dir]
root = bracket(dir, iter, ith_covar_err, open_interval, maxiters,
eps, myblog)
myzero = root(eps, myblog)
delta_zero = get_delta_root(myzero, dir, pars[myargs.ith_par])
conf_int[dir].append(delta_zero)
status_prefix = get_prefix(counter, par_name,
['lower bound', 'upper bound'])
print_status(myblog.blogger.info, verbose, status_prefix[dir],
delta_zero, lock)
error_flags.append(est_success)
#
# include the minimum point to seperate the -/+ interval
#
dict[par_name] = trial_points
return (conf_int[0][0], conf_int[1][0], error_flags[0], nfev[0], None)
def __init__(self, fcn):
self.nfev, self.fcn = func_counter(fcn)
def optneldermead(
afcn,
x0,
xmin,
xmax,
ftol=EPSILON,
maxfev=None,
initsimplex=0,
finalsimplex=None,
step=None,
multicore=False,
verbose=None,
):
x, xmin, xmax = _check_args(x0, xmin, xmax)
nfev, fcn = func_counter(afcn)
if step is None or (numpy.iterable(step) and len(step) != len(x)):
step = 1.2 * numpy.ones(x.shape, numpy.float_, numpy.isfortran(x))
elif numpy.isscalar(step):
step = step * numpy.ones(x.shape, numpy.float_, numpy.isfortran(x))
if maxfev is None:
maxfev = 1024 * len(x)
if finalsimplex is None:
finalsimplex = [0, 2]
if False == is_iterable(finalsimplex):
finalsimplex = [finalsimplex]
# For internal use only:
debug = True
def myloop(xxx, mymaxfev, mystep):
nms = classicNelderMead(fcn)
mynfev = 0
for myfinalsimplex in finalsimplex:
starttime = time.time()
result = nms(
xxx, xmin, xmax, mymaxfev - mynfev, ftol, mystep, initsimplex, myfinalsimplex, multicore, verbose
)
mynfev += result[3]
if 0 != result[0]:
return result[0], result[1], result[2], mynfev
if debug:
print "neldermead::myloop: result = ", result, " took ", time.time() - starttime, " secs"
if multicore:
return result[0], result[1], result[2], mynfev + nfev[0]
else:
return result[0], result[1], result[2], mynfev
def myneldermead(xxx, mymaxfev, mystep, fold=numpy.float_(numpy.finfo(numpy.float_).max)):
result = myloop(xxx, mymaxfev, mystep)
mynfev = result[3]
fnew = result[2]
if (
fnew < fold * 0.995
and 0 == Knuth_close(fnew, fold, ftol)
and 0 == Knuth_close(fnew, fold, ftol)
and 0 == result[0]
and mynfev < mymaxfev
):
if debug:
print "neldermead: fnew = ", fnew, "\tfold = ", fold, "\tx = ", result[1]
result = myneldermead(result[1], mymaxfev - mynfev, step, fold=fnew)
mynfev += result[3]
return result[0], result[1], result[2], mynfev
# result = myneldermead( x, maxfev, step )
result = myloop(x, maxfev, step)
return get_result(result, maxfev)
def func_counter_bounds_wrappers(self, func, npar, xmin, xmax):
"""Wraps the calls to func_counter then func_bounds"""
nfev, afunc = func_counter(func)
myfunc = self.func_bounds(afunc, npar, xmin, xmax)
return nfev, myfunc
def __init__(self, fcn):
self.nfev, self.fcn = func_counter(fcn)
def optneldermead(afcn,
x0,
xmin,
xmax,
ftol=EPSILON,
maxfev=None,
initsimplex=0,
finalsimplex=None,
step=None,
multicore=False,
verbose=None):
x, xmin, xmax = _check_args(x0, xmin, xmax)
nfev, fcn = func_counter(afcn)
if step is None or (numpy.iterable(step) and len(step) != len(x)):
step = 1.2 * numpy.ones(x.shape, numpy.float_, numpy.isfortran(x))
elif numpy.isscalar(step):
step = step * numpy.ones(x.shape, numpy.float_, numpy.isfortran(x))
if maxfev is None:
maxfev = 1024 * len(x)
if finalsimplex is None:
finalsimplex = [0, 2]
if False == is_iterable(finalsimplex):
finalsimplex = [finalsimplex]
# For internal use only:
debug = True
def myloop(xxx, mymaxfev, mystep):
nms = classicNelderMead(fcn)
mynfev = 0
for myfinalsimplex in finalsimplex:
starttime = time.time()
result = nms(xxx, xmin, xmax, mymaxfev - mynfev, ftol, mystep,
initsimplex, myfinalsimplex, multicore, verbose)
mynfev += result[3]
if 0 != result[0]:
return result[0], result[1], result[2], mynfev
if debug:
print 'neldermead::myloop: result = ', result, ' took ', time.time(
) - starttime, ' secs'
if multicore:
return result[0], result[1], result[2], mynfev + nfev[0]
else:
return result[0], result[1], result[2], mynfev
def myneldermead(xxx,
mymaxfev,
mystep,
fold=numpy.float_(numpy.finfo(numpy.float_).max)):
result = myloop(xxx, mymaxfev, mystep)
mynfev = result[3]
fnew = result[2]
if fnew < fold * 0.995 and 0 == Knuth_close( fnew, fold, ftol ) and \
0 == Knuth_close( fnew, fold, ftol ) and \
0 == result[0] and mynfev < mymaxfev:
if debug:
print 'neldermead: fnew = ', fnew, '\tfold = ', fold, \
'\tx = ', result[ 1 ]
result = myneldermead(result[1],
mymaxfev - mynfev,
step,
fold=fnew)
mynfev += result[3]
return result[0], result[1], result[2], mynfev
#result = myneldermead( x, maxfev, step )
result = myloop(x, maxfev, step)
return get_result(result, maxfev)