eigenmath/taylor.cpp

151 lines
1.7 KiB
C++

/* Taylor expansion of a function
push(F)
push(X)
push(N)
push(A)
taylor()
*/
#include "stdafx.h"
#include "defs.h"
void
eval_taylor(void)
{
// 1st arg
p1 = cdr(p1);
push(car(p1));
eval();
// 2nd arg
p1 = cdr(p1);
push(car(p1));
eval();
p2 = pop();
if (p2 == symbol(NIL))
guess();
else
push(p2);
// 3rd arg
p1 = cdr(p1);
push(car(p1));
eval();
p2 = pop();
if (p2 == symbol(NIL))
push_integer(24); // default number of terms
else
push(p2);
// 4th arg
p1 = cdr(p1);
push(car(p1));
eval();
p2 = pop();
if (p2 == symbol(NIL))
push_integer(0); // default expansion point
else
push(p2);
taylor();
}
#define F p1
#define X p2
#define N p3
#define A p4
#define C p5
void
taylor(void)
{
int i, k;
save();
A = pop();
N = pop();
X = pop();
F = pop();
push(N);
k = pop_integer();
if (k == (int) 0x80000000) {
push_symbol(TAYLOR);
push(F);
push(X);
push(N);
push(A);
list(5);
restore();
return;
}
push(F); // f(a)
push(X);
push(A);
subst();
eval();
push_integer(1);
C = pop();
for (i = 1; i <= k; i++) {
push(F); // f = f'
push(X);
derivative();
F = pop();
if (iszero(F))
break;
push(C); // c = c * (x - a)
push(X);
push(A);
subtract();
multiply();
C = pop();
push(F); // f(a)
push(X);
push(A);
subst();
eval();
push(C);
multiply();
push_integer(i);
factorial();
divide();
add();
}
restore();
}
#if SELFTEST
static char *s[] = {
"taylor(1/(5+4*cos(x)),x,6,0)-(1/9+2/81*x^2+5/1458*x^4+49/131220*x^6)",
"0",
"taylor(1/(5+4*cos(x)),x,6)-(1/9+2/81*x^2+5/1458*x^4+49/131220*x^6)",
"0",
};
void
test_taylor(void)
{
test(__FILE__, s, sizeof s / sizeof (char *));
}
#endif