# TNC Python interface
# @(#) $Jeannot: tnc.py,v 1.11 2005/01/28 18:27:31 js Exp $
# Copyright (c) 2004-2005, Jean-Sebastien Roy (js@jeannot.org)
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"""
TNC: A python interface to the TNC non-linear optimizer
TNC is a non-linear optimizer. To use it, you must provide a function to
minimize. The function must take one argument: the list of coordinates where to
evaluate the function; and it must return either a tuple, whose first element is the
value of the function, and whose second argument is the gradient of the function
(as a list of values); or None, to abort the minimization.
"""
from scipy.optimize import moduleTNC
from numpy import asarray,inf,array
MSG_NONE = 0 # No messages
MSG_ITER = 1 # One line per iteration
MSG_INFO = 2 # Informational messages
MSG_VERS = 4 # Version info
MSG_EXIT = 8 # Exit reasons
MSG_ALL = MSG_ITER + MSG_INFO + MSG_VERS + MSG_EXIT
MSGS = {
MSG_NONE : "No messages",
MSG_ITER : "One line per iteration",
MSG_INFO : "Informational messages",
MSG_VERS : "Version info",
MSG_EXIT : "Exit reasons",
MSG_ALL : "All messages"
}
INFEASIBLE = -1 # Infeasible (low > up)
LOCALMINIMUM = 0 # Local minima reach (|pg| ~= 0)
FCONVERGED = 1 # Converged (|f_n-f_(n-1)| ~= 0)
XCONVERGED = 2 # Converged (|x_n-x_(n-1)| ~= 0)
MAXFUN = 3 # Max. number of function evaluations reach
LSFAIL = 4 # Linear search failed
CONSTANT = 5 # All lower bounds are equal to the upper bounds
NOPROGRESS = 6 # Unable to progress
USERABORT = 7 # User requested end of minimization
RCSTRINGS = {
INFEASIBLE : "Infeasible (low > up)",
LOCALMINIMUM : "Local minima reach (|pg| ~= 0)",
FCONVERGED : "Converged (|f_n-f_(n-1)| ~= 0)",
XCONVERGED : "Converged (|x_n-x_(n-1)| ~= 0)",
MAXFUN : "Max. number of function evaluations reach",
LSFAIL : "Linear search failed",
CONSTANT : "All lower bounds are equal to the upper bounds",
NOPROGRESS : "Unable to progress",
USERABORT : "User requested end of minimization"
}
# Changes to interface made by Travis Oliphant, Apr. 2004 for inclusion in
# SciPy
import optimize
approx_fprime = optimize.approx_fprime
def fmin_tnc(func, x0, fprime=None, args=(), approx_grad=0,
bounds=None, epsilon=1e-8, scale=None, offset=None,
messages=MSG_ALL, maxCGit=-1, maxfun=None, eta=-1,
stepmx=0, accuracy=0, fmin=0, ftol=-1, xtol=-1, pgtol=-1,
rescale=-1):
"""Minimize a function with variables subject to bounds, using
gradient information.
Parameters
----------
func : callable func(x, *args)
Function to minimize. Should return f and g, where f is
the value of the function and g its gradient (a list of
floats). If the function returns None, the minimization
is aborted.
x0 : list of floats
Initial estimate of minimum.
fprime : callable fprime(x, *args)
Gradient of func. If None, then func must return the
function value and the gradient (f,g = func(x, *args)).
args : tuple
Arguments to pass to function.
approx_grad : bool
If true, approximate the gradient numerically.
bounds : list
(min, max) pairs for each element in x, defining the
bounds on that parameter. Use None or +/-inf for one of
min or max when there is no bound in that direction.
scale : list of floats
Scaling factors to apply to each variable. If None, the
factors are up-low for interval bounded variables and
1+|x] fo the others. Defaults to None
offset : float
Value to substract from each variable. If None, the
offsets are (up+low)/2 for interval bounded variables
and x for the others.
messages :
Bit mask used to select messages display during
minimization values defined in the MSGS dict. Defaults to
MGS_ALL.
maxCGit : int
Maximum number of hessian*vector evaluations per main
iteration. If maxCGit == 0, the direction chosen is
-gradient if maxCGit < 0, maxCGit is set to
max(1,min(50,n/2)). Defaults to -1.
maxfun : int
Maximum number of function evaluation. if None, maxfun is
set to max(100, 10*len(x0)). Defaults to None.
eta : float
Severity of the line search. if < 0 or > 1, set to 0.25.
Defaults to -1.
stepmx : float
Maximum step for the line search. May be increased during
call. If too small, it will be set to 10.0. Defaults to 0.
accuracy : float
Relative precision for finite difference calculations. If
<= machine_precision, set to sqrt(machine_precision).
Defaults to 0.
fmin : float
Minimum function value estimate. Defaults to 0.
ftol : float
Precision goal for the value of f in the stoping criterion.
If ftol < 0.0, ftol is set to 0.0 defaults to -1.
xtol : float
Precision goal for the value of x in the stopping
criterion (after applying x scaling factors). If xtol <
0.0, xtol is set to sqrt(machine_precision). Defaults to
-1.
pgtol : float
Precision goal for the value of the projected gradient in
the stopping criterion (after applying x scaling factors).
If pgtol < 0.0, pgtol is set to 1e-2 * sqrt(accuracy).
Setting it to 0.0 is not recommended. Defaults to -1.
rescale : float
Scaling factor (in log10) used to trigger f value
rescaling. If 0, rescale at each iteration. If a large
value, never rescale. If < 0, rescale is set to 1.3.
Returns
-------
x : list of floats
The solution.
nfeval : int
The number of function evaluations.
rc :
Return code as defined in the RCSTRINGS dict.
"""
x0 = asarray(x0, dtype=float).tolist()
n = len(x0)
if bounds is None:
bounds = [(None,None)] * n
if len(bounds) != n:
raise ValueError('length of x0 != length of bounds')
if approx_grad:
def func_and_grad(x):
x = asarray(x)
f = func(x, *args)
g = approx_fprime(x, func, epsilon, *args)
return f, list(g)
elif fprime is None:
def func_and_grad(x):
x = asarray(x)
f, g = func(x, *args)
return f, list(g)
else:
def func_and_grad(x):
x = asarray(x)
f = func(x, *args)
g = fprime(x, *args)
return f, list(g)
"""
low, up : the bounds (lists of floats)
if low is None, the lower bounds are removed.
if up is None, the upper bounds are removed.
low and up defaults to None
"""
low = [0]*n
up = [0]*n
for i in range(n):
if bounds[i] is None: l, u = -inf, inf
else:
l,u = bounds[i]
if l is None:
low[i] = -inf
else:
low[i] = l
if u is None:
up[i] = inf
else:
up[i] = u
if scale is None:
scale = []
if offset is None:
offset = []
if maxfun is None:
maxfun = max(100, 10*len(x0))
rc, nf, x = moduleTNC.minimize(func_and_grad, x0, low, up, scale, offset,
messages, maxCGit, maxfun, eta, stepmx, accuracy,
fmin, ftol, xtol, pgtol, rescale)
return array(x), nf, rc
if __name__ == '__main__':
# Examples for TNC
def example():
print "Example"
# A function to minimize
def function(x):
f = pow(x[0],2.0)+pow(abs(x[1]),3.0)
g = [0,0]
g[0] = 2.0*x[0]
g[1] = 3.0*pow(abs(x[1]),2.0)
if x[1]<0:
g[1] = -g[1]
return f, g
# Optimizer call
x, nf, rc = fmin_tnc(function, [-7, 3], bounds=([-10, 1], [10, 10]))
print "After", nf, "function evaluations, TNC returned:", RCSTRINGS[rc]
print "x =", x
print "exact value = [0, 1]"
print
example()
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