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git-svn-id: svn://scm.gforge.inria.fr/svnroot/paradiseo@40 331e1502-861f-0410-8da2-ba01fb791d7f
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<a class="el" href="dir_000007.html">contrib</a> / <a class="el" href="dir_000008.html">mathsym</a> / <a class="el" href="dir_000022.html">fun</a></div>
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<h1>sym_operations.cpp</h1><div class="fragment"><pre class="fragment">00001 <span class="comment">/* </span>
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00002 <span class="comment"> * Copyright (C) 2005 Maarten Keijzer</span>
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00003 <span class="comment"> *</span>
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00004 <span class="comment"> * This program is free software; you can redistribute it and/or modify</span>
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00005 <span class="comment"> * it under the terms of version 2 of the GNU General Public License as </span>
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00006 <span class="comment"> * published by the Free Software Foundation. </span>
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00007 <span class="comment"> *</span>
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00008 <span class="comment"> * This program is distributed in the hope that it will be useful,</span>
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00009 <span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
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00010 <span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span>
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00011 <span class="comment"> * GNU General Public License for more details.</span>
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00012 <span class="comment"> *</span>
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00013 <span class="comment"> * You should have received a copy of the GNU General Public License</span>
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00014 <span class="comment"> * along with this program; if not, write to the Free Software</span>
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00015 <span class="comment"> * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA</span>
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00016 <span class="comment"> */</span>
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00017
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00018 <span class="preprocessor">#include <FunDef.h></span>
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00019
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00020 <span class="keyword">using</span> <span class="keyword">namespace </span>std;
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00021
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00022 Sym simplify_constants(Sym sym) {
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00023
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00024 SymVec args = sym.args();
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00025 token_t token = sym.token();
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00026
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00027 <span class="keywordtype">bool</span> has_changed = <span class="keyword">false</span>;
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00028 <span class="keywordtype">bool</span> all_constants = <span class="keyword">true</span>;
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00029
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00030 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < args.size(); ++i) {
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00031
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00032 Sym arg = simplify_constants(args[i]);
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00033
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00034 <span class="keywordflow">if</span> (arg != args[i]) {
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00035 has_changed = <span class="keyword">true</span>;
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00036 }
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00037 args[i] = arg;
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00038
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00039 all_constants &= is_constant(args[i].token());
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00040 }
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00041
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00042 <span class="keywordflow">if</span> (args.size() == 0) {
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00043
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00044 <span class="keywordflow">if</span> (sym.token() == sum_token) <span class="keywordflow">return</span> SymConst(0.0);
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00045 <span class="keywordflow">if</span> (sym.token() == prod_token) <span class="keywordflow">return</span> SymConst(1.0);
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00046
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00047 <span class="keywordflow">return</span> sym; <span class="comment">// variable or constant</span>
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00048 }
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00049
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00050 <span class="keywordflow">if</span> (all_constants) {
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00051 <span class="comment">// evaluate </span>
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00052
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00053 vector<double> dummy;
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00054
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00055 <span class="keywordtype">double</span> v = ::eval(sym, dummy);
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00056
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00057 Sym result = SymConst(v);
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00058
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00059 <span class="keywordflow">return</span> result;
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00060 }
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00061
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00062 <span class="keywordflow">if</span> (has_changed) {
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00063 <span class="keywordflow">return</span> Sym(token, args);
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00064 }
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00065
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00066 <span class="keywordflow">return</span> sym;
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00067
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00068 }
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00069
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00070 <span class="comment">// currently only simplifies constants</span>
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00071 Sym simplify(Sym sym) {
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00072
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00073 <span class="keywordflow">return</span> simplify_constants(sym);
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00074
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00075 }
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00076
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00077 Sym derivative(token_t token, Sym x) {
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00078 Sym one = Sym(prod_token);
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00079
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00080 <span class="keywordflow">switch</span> (token) {
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00081 <span class="keywordflow">case</span> inv_token : <span class="keywordflow">return</span> Sym(inv_token, sqr(x));
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00082
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00083 <span class="keywordflow">case</span> sin_token : <span class="keywordflow">return</span> -cos(x);
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00084 <span class="keywordflow">case</span> cos_token : <span class="keywordflow">return</span> sin(x);
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00085 <span class="keywordflow">case</span> tan_token : <span class="keywordflow">return</span> one + sqr(tan(x));
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00086
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00087 <span class="keywordflow">case</span> asin_token : <span class="keywordflow">return</span> inv( sqrt(one - sqr(x)));
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00088 <span class="keywordflow">case</span> acos_token: <span class="keywordflow">return</span> -inv( sqrt(one - sqr(x)));
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00089 <span class="keywordflow">case</span> atan_token : <span class="keywordflow">return</span> inv( sqrt(one + sqr(x)));
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00090
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00091 <span class="keywordflow">case</span> cosh_token : <span class="keywordflow">return</span> -sinh(x);
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00092 <span class="keywordflow">case</span> sinh_token : <span class="keywordflow">return</span> cosh(x);
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00093 <span class="keywordflow">case</span> tanh_token : <span class="keywordflow">return</span> one - sqr( tanh(x) );
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00094
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00095 <span class="keywordflow">case</span> asinh_token : <span class="keywordflow">return</span> inv( sqrt( one + sqr(x) ));
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00096 <span class="keywordflow">case</span> acosh_token : <span class="keywordflow">return</span> inv( sqrt(x-one) * sqrt(x + one) );
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00097 <span class="keywordflow">case</span> atanh_token : <span class="keywordflow">return</span> inv(one - sqr(x));
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00098
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00099 <span class="keywordflow">case</span> exp_token : <span class="keywordflow">return</span> exp(x);
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00100 <span class="keywordflow">case</span> log_token : <span class="keywordflow">return</span> inv(x);
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00101
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00102 <span class="keywordflow">case</span> sqr_token : <span class="keywordflow">return</span> SymConst(2.0) * x;
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00103 <span class="keywordflow">case</span> sqrt_token : <span class="keywordflow">return</span> SymConst(0.5) * inv( sqrt(x));
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00104 <span class="keywordflow">default</span> :
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00105 <span class="keywordflow">throw</span> differentiation_error();
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00106 }
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00107
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00108 <span class="keywordflow">return</span> x;
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00109 }
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00110
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00111 <span class="keyword">extern</span> Sym differentiate(Sym sym, token_t dx) {
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00112
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00113 token_t token = sym.token();
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00114
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00115 Sym zero = Sym(sum_token);
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00116 Sym one = Sym(prod_token);
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00117
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00118 <span class="keywordflow">if</span> (token == dx) {
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00119 <span class="keywordflow">return</span> one;
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00120 }
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00121
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00122 SymVec args = sym.args();
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00123
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00124 <span class="keywordflow">if</span> (args.size() == 0) { <span class="comment">// df/dx with f != x</span>
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00125 <span class="keywordflow">return</span> zero;
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00126 }
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00127
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00128 <span class="keywordflow">switch</span> (token) {
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00129
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00130 <span class="keywordflow">case</span> sum_token:
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00131 {
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00132 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < args.size(); ++i) {
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00133 args[i] = differentiate(args[i], dx);
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00134 }
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00135
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00136 <span class="keywordflow">if</span> (args.size() == 1) <span class="keywordflow">return</span> args[0];
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00137 <span class="keywordflow">return</span> Sym(sum_token, args);
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00138 }
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00139 <span class="keywordflow">case</span> min_token :
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00140 {
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00141 <span class="keywordflow">return</span> -differentiate(args[0],dx);
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00142 }
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00143 <span class="keywordflow">case</span> prod_token:
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00144 {
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00145 <span class="keywordflow">if</span> (args.size() == 1) <span class="keywordflow">return</span> differentiate(args[0], dx);
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00146
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00147 <span class="keywordflow">if</span> (args.size() == 2) {
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00148 <span class="keywordflow">return</span> args[0] * differentiate(args[1], dx) + args[1] * differentiate(args[0], dx);
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00149 }
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00150 <span class="comment">// else </span>
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00151 Sym c = args.back();
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00152 args.pop_back();
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00153 Sym f = Sym(prod_token, args);
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00154 Sym df = differentiate( f, dx);
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00155
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00156 <span class="keywordflow">return</span> c * df + f * differentiate(c,dx);
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00157 }
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00158 <span class="keywordflow">case</span> pow_token :
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00159 {
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00160 <span class="keywordflow">return</span> pow(args[0], args[1]) * args[1] * inv(args[0]);
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00161 }
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00162 <span class="keywordflow">case</span> ifltz_token :
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00163 { <span class="comment">// cannot be differentiated</span>
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00164 <span class="keywordflow">throw</span> differentiation_error(); <span class="comment">// TODO define proper exception</span>
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00165 }
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00166
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00167 <span class="keywordflow">default</span>: <span class="comment">// unary function: apply chain rule</span>
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00168 {
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00169 Sym arg = args[0];
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00170 <span class="keywordflow">return</span> derivative(token, arg) * differentiate(arg, dx);
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00171 }
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00172 }
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00173
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00174 }
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</pre></div><hr size="1"><address style="align: right;"><small>Generated on Thu Oct 19 05:06:42 2006 for EO by
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<a href="http://www.doxygen.org/index.html">
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<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.3.9.1 </small></address>
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