184 lines
2.1 KiB
C++
184 lines
2.1 KiB
C++
/* Laguerre function
|
|
|
|
Example
|
|
|
|
laguerre(x,3)
|
|
|
|
Result
|
|
|
|
1 3 3 2
|
|
- --- x + --- x - 3 x + 1
|
|
6 2
|
|
|
|
The computation uses the following recurrence relation.
|
|
|
|
L(x,0,k) = 1
|
|
|
|
L(x,1,k) = -x + k + 1
|
|
|
|
n*L(x,n,k) = (2*(n-1)+1-x+k)*L(x,n-1,k) - (n-1+k)*L(x,n-2,k)
|
|
|
|
In the "for" loop i = n-1 so the recurrence relation becomes
|
|
|
|
(i+1)*L(x,n,k) = (2*i+1-x+k)*L(x,n-1,k) - (i+k)*L(x,n-2,k)
|
|
*/
|
|
|
|
#include "stdafx.h"
|
|
#include "defs.h"
|
|
|
|
void
|
|
eval_laguerre(void)
|
|
{
|
|
// 1st arg
|
|
|
|
push(cadr(p1));
|
|
eval();
|
|
|
|
// 2nd arg
|
|
|
|
push(caddr(p1));
|
|
eval();
|
|
|
|
// 3rd arg
|
|
|
|
push(cadddr(p1));
|
|
eval();
|
|
|
|
p2 = pop();
|
|
if (p2 == symbol(NIL))
|
|
push_integer(0);
|
|
else
|
|
push(p2);
|
|
|
|
laguerre();
|
|
}
|
|
|
|
#define X p1
|
|
#define N p2
|
|
#define K p3
|
|
#define Y p4
|
|
#define Y0 p5
|
|
#define Y1 p6
|
|
|
|
void
|
|
laguerre(void)
|
|
{
|
|
int n;
|
|
save();
|
|
|
|
K = pop();
|
|
N = pop();
|
|
X = pop();
|
|
|
|
push(N);
|
|
n = pop_integer();
|
|
|
|
if (n < 0) {
|
|
push_symbol(LAGUERRE);
|
|
push(X);
|
|
push(N);
|
|
push(K);
|
|
list(4);
|
|
restore();
|
|
return;
|
|
}
|
|
|
|
if (issymbol(X))
|
|
laguerre2(n);
|
|
else {
|
|
Y = X; // do this when X is an expr
|
|
X = symbol(SECRETX);
|
|
laguerre2(n);
|
|
X = Y;
|
|
push(symbol(SECRETX));
|
|
push(X);
|
|
subst();
|
|
eval();
|
|
}
|
|
|
|
restore();
|
|
}
|
|
|
|
void
|
|
laguerre2(int n)
|
|
{
|
|
int i;
|
|
|
|
push_integer(1);
|
|
push_integer(0);
|
|
|
|
Y1 = pop();
|
|
|
|
for (i = 0; i < n; i++) {
|
|
|
|
Y0 = Y1;
|
|
|
|
Y1 = pop();
|
|
|
|
push_integer(2 * i + 1);
|
|
push(X);
|
|
subtract();
|
|
push(K);
|
|
add();
|
|
push(Y1);
|
|
multiply();
|
|
|
|
push_integer(i);
|
|
push(K);
|
|
add();
|
|
push(Y0);
|
|
multiply();
|
|
|
|
subtract();
|
|
|
|
push_integer(i + 1);
|
|
divide();
|
|
}
|
|
}
|
|
|
|
#if SELFTEST
|
|
|
|
static char *s[] = {
|
|
|
|
"laguerre(x,n)",
|
|
"laguerre(x,n,0)",
|
|
|
|
"laguerre(x,n,k)",
|
|
"laguerre(x,n,k)",
|
|
|
|
"laguerre(x,0)-1",
|
|
"0",
|
|
|
|
"laguerre(x,1)-(-x+1)",
|
|
"0",
|
|
|
|
"laguerre(x,2)-1/2*(x^2-4*x+2)",
|
|
"0",
|
|
|
|
"laguerre(x,3)-1/6*(-x^3+9*x^2-18*x+6)",
|
|
"0",
|
|
|
|
"laguerre(x,0,k)-1",
|
|
"0",
|
|
|
|
"laguerre(x,1,k)-(-x+k+1)",
|
|
"0",
|
|
|
|
"laguerre(x,2,k)-1/2*(x^2-2*(k+2)*x+(k+1)*(k+2))",
|
|
"0",
|
|
|
|
"laguerre(x,3,k)-1/6*(-x^3+3*(k+3)*x^2-3*(k+2)*(k+3)*x+(k+1)*(k+2)*(k+3))",
|
|
"0",
|
|
|
|
"laguerre(a-b,10)-eval(subst(a-b,x,laguerre(x,10)))",
|
|
"0",
|
|
};
|
|
|
|
void
|
|
test_laguerre(void)
|
|
{
|
|
test(__FILE__, s, sizeof s / sizeof (char *));
|
|
}
|
|
|
|
#endif
|