

# Copyright 2010 by Philipp Kraft
# This file is part of cmf.
#
#   cmf is free software: you can redistribute it and/or modify
#   it under the terms of the GNU General Public License as published by
#   the Free Software Foundation, either version 2 of the License, or
#   (at your option) any later version.
#
#   cmf is distributed in the hope that it will be useful,
#   but WITHOUT ANY WARRANTY; without even the implied warranty of
#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#   GNU General Public License for more details.
#
#   You should have received a copy of the GNU General Public License
#   along with cmf.  If not, see <http://www.gnu.org/licenses/>.
#   
from __future__ import division

'''
Fits cmf retention curves objects into a measured pF curve

Created on 07.10.2009

@author: philkraf
'''
import cmf
import numpy as np
import scipy.optimize as opt
import random
def get_error_bc(params, pF,theta):
    bc=cmf.BrooksCoreyRetentionCurve(1,params[0],params[1],params[2])
    model_wetness=bc.Wetness_pF(pF)
    err = np.sum((theta - params[0] * model_wetness)**2)
    return err
            

def fit_bc(pF,theta,count=20,verbose=False):
    """Fits a Brooks-Corey retention curve into data
    pF: a sequence of pF values
    theta: an array of water contents
    """
    theta_mean=np.mean(theta)
    ns_denom=np.sum((theta-theta_mean)**2)
    best_f=1e12
    for i in range(count):
        x0=np.array(( random.uniform(0.01,1.0), random.uniform(1.0,20),random.uniform(0.01,1.0)))
        x_opt, f_opt,n_iter,n_eval, warn = opt.fmin(get_error_bc, x0 = x0, args=(pF,theta),full_output=1, disp=0)
        if f_opt<best_f:
            if verbose: print "%i: x=%s f=%0.12g iter=%i, eval=%i" % (i,x_opt,1-f_opt/ns_denom,n_iter,n_eval) 
            bc=cmf.BrooksCoreyRetentionCurve(1.,x_opt[0],x_opt[1],x_opt[2])
            best_f=f_opt

    return bc, 1-best_f/ns_denom

def make_vgm(params):
    try:
        vgm=cmf.VanGenuchtenMualem(1.0)
        vgm.Phi = params[0]
        vgm.alpha = params[1]
        vgm.n = params[2]
        if len(params)>3:
            vgm.theta_r = params[3]
        return vgm
    except RuntimeError:
        return None
    

def get_error_vgm(params,pF,theta):
    vgm=make_vgm(params)
    if vgm:
        model_theta=vgm.theta(vgm.Wetness_pF(pF))
        err = np.sum((theta - model_theta)**2)
        var = np.sum((theta - np.mean(theta))**2)
        return err/var
    else:
        return 100.0 # return a really bad error for illegal cases
def fit_vgm(pF,theta,variable_m=False, count=20, fitlevel=None,verbose=False):
    """Fits a Van Genuchten / Mualem retention curve into data
    pF: a sequence of pF values
    theta: an array of water contents
    alpha_range: a 2-sequence holding the range for alpha values
    n_range: a 2-sequence holding the range for n values
    """
    theta_mean=np.mean(theta)
    ns_denom=np.sum((theta-theta_mean)**2)

    best_f=1e120
    for i in range(count):
        x0=[ random.uniform(0.01,0.99), random.uniform(0.0001,1.9),random.uniform(1.01,3.9),random.uniform()]
        x0[-1]*=x0[0]
        if variable_m: x0.append(1-1/random.uniform(1.01,5))
        x_opt, f_opt,n_iter,n_eval, warn = opt.fmin(get_error_vgm, x0 = np.array(x0), args=(pF,theta),full_output=1, disp=0)
        if f_opt<best_f:
            if verbose: print "%i: x=%s f=%0.12g iter=%i, eval=%i" % (i,x_opt,f_opt,n_iter,n_eval) 
            vgm=cmf.VanGenuchtenMualem(1,*x_opt)
            best_f=f_opt
            if fitlevel and best_f<fitlevel:
                break
    theta_mean=np.mean(theta)
    return vgm,best_f

def narrowparameters_vgm(pF,theta,phi,alpha,n,theta_r=[0.0,0.0],count=10000,perc=10.):
    """
    Narrows the parameter space down to the best perc (default=10) percent of the results
    pF: A sequence of pF values matching theta
    theta: A sequence of water content values for the corresponding pF values
    phi: A distribution of porosity values, only the range is used
    alpha: A distribution of VanGenuchten alpha values, only the range is used
    n: A distribution of VanGenuchten n values, only the range is used
    count: Number of random values to be drawn in the range of the parameters
    perc: percentile of best fitting parameters
    
    Returns:
    phi,alpha,n,vgm_err: New distribution of phi, alpha, n and the corrseponding errors
                         for the best perc% of the results
                         
    Usage:
        # Create a priori range
        phi, n, alpha = 
    """
    phi,alpha,n,theta_r = [np.random.uniform(np.amin(arg),np.amax(arg),count) for arg in [phi,alpha,n,theta_r]]
    vgm_err = np.array([get_error_vgm((phi_,alpha_,n_),pF,theta) for phi_,alpha_,n_ in zip(phi,alpha,n)]) 
    res_perc = np.percentile(vgm_err[np.isfinite(vgm_err)],perc)
    take = vgm_err<res_perc
    minmax = lambda x: (x.min(),x.max())
    print "Best %g%% has an error value < %g" % (perc,res_perc)
    for arg,narg in zip([phi,alpha,n,theta_r,vgm_err],'phi alpha n theta_r vgm_error'.split()):
        print narg, ': %g - %g' % minmax(arg[take])
    print "Error for mean value: %g" % get_error_vgm((phi.mean(),alpha.mean(),n.mean()),pF,theta)
    return [arg[take] for arg in [phi,alpha,n,theta_r,vgm_err]]
    
def narrowparameters_bc(pF,theta,phi,b,w_x,count=10000,perc=10.):
    """
    Narrows the parameter space down to the best perc (default=10) percent of the results
    pF: A sequence of pF values matching theta
    theta: A sequence of water content values for the corresponding pF values
    phi: A distribution of porosity values, only the range is used
    alpha: A distribution of VanGenuchten alpha values, only the range is used
    n: A distribution of VanGenuchten n values, only the range is used
    count: Number of random values to be drawn in the range of the parameters
    perc: percentile of best fitting parameters
    
    Returns:
    phi,alpha,n,vgm_err: New distribution of phi, alpha, n and the corrseponding errors
                         for the best perc% of the results
    """
    phi,b,w_x= [np.random.uniform(arg.min(),arg.max(),count) for arg in [phi,b,w_x]]
    vgm_err = np.array([get_error_bc((phi_,b_,w_x_ * phi_),pF,theta) for phi_,b_,w_x_ in zip(phi,b,w_x)]) 
    res_perc = np.percentile(vgm_err[np.isfinite(vgm_err)],perc)
    take = vgm_err<res_perc
    minmax = lambda x: (x.min(),x.max())
    print "Best %g%% has an error value < %g" % (perc,res_perc)
    for arg,narg in zip([phi,b,w_x,vgm_err],'phi b w_x vgm_error'.split()):
        print narg, ': %g - %g' % minmax(arg[take])
    print "Error for mean value: %g" % get_error_bc((phi.mean(),b.mean(),(w_x*phi).mean()),pF,theta)
    return [arg[take] for arg in [phi,b,w_x,vgm_err]]
      
if __name__=='__main__':
    theta5 = [0.324615604527165,0.4482,0.4708,0.4801,0.4806,0.4864,0.582851086403064]
    theta15 = [0.342471569196674,0.4394,0.4676,0.4826,0.4856,0.4907,0.566714937861957]
    theta25 = [0.364151497261831,0.4624,0.4945,0.5089,0.5101,0.512,0.539286123841295]

    pF = [4.2,3,2.5,2,1.8,1.4,-1]
    phi=[0.4,0.6]
    alpha=[0.0001,1.0]
    n=[1.001,3]
    theta_r=[0.0,0.3]
#%%    
def plot_vgms(pF,theta,phi,alpha,n,theta_r):
    from pylab import plot,ioff,ion,draw
    ioff()
    pF_dense= np.arange(-1,7,0.01)
    for params in zip(phi,alpha,n,theta_r):
        vgm = make_vgm(params)
        plot(pF_dense,vgm.theta(vgm.Wetness_pF(pF_dense)),'k-',alpha=0.1)
    plot(pF,theta,'ro')
    ion()
    draw()
    
    
    