# 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.

    :SeeAlso:
      - scikits.openopt, which offers a unified syntax to call this and other solvers
      
      - fmin, fmin_powell, fmin_cg, fmin_bfgs, fmin_ncg :
         multivariate local optimizers

      - leastsq : nonlinear least squares minimizer

      - fmin_l_bfgs_b, fmin_tnc, fmin_cobyla : constrained
        multivariate optimizers

      - anneal, brute : global optimizers

      - fminbound, brent, golden, bracket : local scalar minimizers

      - fsolve : n-dimenstional root-finding

      - brentq, brenth, ridder, bisect, newton : one-dimensional root-finding

      - fixed_point : scalar fixed-point finder

"""
    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 == None, the lower bounds are removed.
                if up == 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 == None:
        scale = []

    if offset == None:
        offset = []

    if maxfun == 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()