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/* ASCEND modelling environment |
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Copyright (C) 2008 Carnegie Mellon University |
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|
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This program is free software; you can redistribute it and/or modify |
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it under the terms of the GNU General Public License as published by |
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the Free Software Foundation; either version 2, or (at your option) |
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any later version. |
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|
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This program is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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GNU General Public License for more details. |
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|
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You should have received a copy of the GNU General Public License |
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along with this program; if not, write to the Free Software |
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Foundation, Inc., 59 Temple Place - Suite 330, |
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Boston, MA 02111-1307, USA. |
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*/ |
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|
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#include <math.h> |
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|
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#include "ideal.h" |
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|
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#ifdef TEST |
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#include <assert.h> |
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#include <stdlib.h> |
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#include <stdio.h> |
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#endif |
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|
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/*--------------------------------------------- |
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IDEAL COMPONENT RELATIONS |
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*/ |
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|
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/* |
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Hypothesis: |
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in calculating the ideal component relations, we have some integration |
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constants that ultimately allow the arbitrary scales of h and s to |
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be specified. Hence we can ignore components of helm_ideal that |
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are either constant or linear in tau, and work them out later when we |
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stick in the values of data->c and data->m. |
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*/ |
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|
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/** |
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Ideal component of helmholtz function |
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*/ |
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double helm_ideal(double tau, double delta, const IdealData *data){ |
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|
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const IdealPowTerm *pt; |
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const IdealExpTerm *et; |
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|
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unsigned i; |
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double sum = log(delta) - log(tau) + data->c + data->m * tau; |
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double term; |
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|
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//fprintf(stderr,"constant = %f, linear = %f", data->c, data->m); |
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//fprintf(stderr,"initial terms = %f\n",sum); |
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pt = &(data->pt[0]); |
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for(i = 0; i<data->np; ++i, ++pt){ |
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double a = pt->a0; |
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double t = pt->t0; |
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if(t == 0){ |
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term = a*log(tau) /* + a */; /* term ignored, see above */ |
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}else if(t == 1){ |
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term = /* a * tau */ - a * tau * log(tau); /* term ignored, see above */ |
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}else{ |
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term = a * pow(tau,t) / ((t - 1) * t); |
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} |
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//fprintf(stderr,"i = %d: a0 = %f, t0 = %f, term = %f\n",i,pt->a0, pt->t0, term); |
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sum += pt->a0 * pow(tau, pt->t0); |
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} |
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|
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/* 'exponential' terms */ |
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et = &(data->et[0]); |
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for(i=0; i<data->ne; ++i, ++et){ |
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sum += et->b * log( 1 - exp(-et->B * tau)); |
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} |
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|
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return sum; |
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} |
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|
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/** |
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Partial dervivative of ideal component of helmholtz residual function with |
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respect to tau. |
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*/ |
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double helm_ideal_tau(double tau, double delta, const IdealData *data){ |
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const IdealPowTerm *pt; |
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const IdealExpTerm *et; |
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|
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unsigned i; |
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double term; |
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double sum = -1./tau + data->m; |
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|
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pt = &(data->pt[0]); |
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for(i = 0; i<data->np; ++i, ++pt){ |
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double a = pt->a0; |
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double t = pt->t0; |
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if(t==0){ |
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term = a / tau - a*t*pow(tau,t-1)/(t-1); |
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}else if(t==1){ |
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term = -a*log(tau); |
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}else{ |
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term = a*t*pow(tau,t-1)/(t-1); |
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} |
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sum += term; |
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} |
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|
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/* 'exponential' terms */ |
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et = &(data->et[0]); |
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for(i=0; i<data->ne; ++i, ++et){ |
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sum += et->b * et->B / (1 - exp(-tau*et->B)); |
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} |
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return sum; |
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} |
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