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Added symbolic differentiation

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maartenkeijzer 2005-10-09 07:03:35 +00:00
commit ffdce66c98
12 changed files with 186 additions and 61 deletions
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97
eo/contrib/mathsym/fun/sym_operations.cpp
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@ -74,3 +74,100 @@ Sym simplify(Sym sym) {
}
Sym derivative(token_t token, Sym x) {
Sym one = Sym(prod_token);
switch (token) {
case inv_token : return Sym(inv_token, sqr(x));
case sin_token : return -cos(x);
case cos_token : return sin(x);
case tan_token : return one + sqr(tan(x));
case asin_token : return inv( sqrt(one - sqr(x)));
case acos_token: return -inv( sqrt(one - sqr(x)));
case atan_token : return inv( sqrt(one + sqr(x)));
case cosh_token : return -sinh(x);
case sinh_token : return cosh(x);
case tanh_token : return one - sqr( tanh(x) );
case asinh_token : return inv( sqrt( one + sqr(x) ));
case acosh_token : return inv( sqrt(x-one) * sqrt(x + one) );
case atanh_token : return inv(one - sqr(x));
case exp_token : return exp(x);
case log_token : return inv(x);
case sqr_token : return SymConst(2.0) * x;
case sqrt_token : return SymConst(0.5) * inv( sqrt(x));
}
throw differentiation_error();
return x;
}
extern Sym differentiate(Sym sym, token_t dx) {
token_t token = sym.token();
Sym zero = Sym(sum_token);
Sym one = Sym(prod_token);
if (token == dx) {
return one;
}
SymVec args = sym.args();
if (args.size() == 0) { // df/dx with f != x
return zero;
}
switch (token) {
case sum_token:
{
for (unsigned i = 0; i < args.size(); ++i) {
args[i] = differentiate(args[i], dx);
}
if (args.size() == 1) return args[0];
return Sym(sum_token, args);
}
case min_token :
{
return -differentiate(args[0],dx);
}
case prod_token:
{
if (args.size() == 1) return differentiate(args[0], dx);
if (args.size() == 2) {
return args[0] * differentiate(args[1], dx) + args[1] * differentiate(args[0], dx);
}
// else
Sym c = args.back();
args.pop_back();
Sym f = Sym(prod_token, args);
Sym df = differentiate( f, dx);
return c * df + f * differentiate(c,dx);
}
case pow_token :
{
return pow(args[0], args[1]) * args[1] * inv(args[0]);
}
case ifltz_token :
{ // cannot be differentiated
throw differentiation_error(); // TODO define proper exception
}
default: // unary function: apply chain rule
{
Sym arg = args[0];
return derivative(token, arg) * differentiate(arg, dx);
}
}
}