158 lines
2.1 KiB
C++
158 lines
2.1 KiB
C++
//-----------------------------------------------------------------------------
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//
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// Laguerre polynomial
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//
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// Input: tos-3 x (can be a symbol or expr)
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//
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// tos-2 n
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//
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// tos-1 k
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//
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// Output: Result on stack
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//
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// Uses the recurrence relation
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//
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// L(x,0,k) = 1
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//
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// L(x,1,k) = -x + k + 1
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//
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// n*L(x,n,k) = (2*(n-1)+1-x+k)*L(x,n-1,k) - (n-1+k)*L(x,n-2,k)
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//
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// In the "for" loop i = n-1 so the recurrence relation becomes
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//
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// (i+1)*L(x,n,k) = (2*i+1-x+k)*L(x,n-1,k) - (i+k)*L(x,n-2,k)
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//
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//-----------------------------------------------------------------------------
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#include "stdafx.h"
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#include "defs.h"
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#define X p1
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#define N p2
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#define K p3
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#define Y p4
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#define Y0 p5
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#define Y1 p6
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void
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laguerre(void)
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{
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save();
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yylaguerre();
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restore();
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}
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void
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yylaguerre(void)
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{
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int n;
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K = pop();
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N = pop();
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X = pop();
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push(N);
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n = pop_integer();
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if (n < 0) {
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push_symbol(LAGUERRE);
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push(X);
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push(N);
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push(K);
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list(4);
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return;
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}
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if (issymbol(X))
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yylaguerre2(n);
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else {
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Y = X; // do this when X is an expr
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X = symbol(SECRETX);
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yylaguerre2(n);
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X = Y;
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push(symbol(SECRETX));
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push(X);
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subst();
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eval();
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}
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}
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void
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yylaguerre2(int n)
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{
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int i;
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push_integer(1);
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push_integer(0);
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Y1 = pop();
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for (i = 0; i < n; i++) {
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Y0 = Y1;
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Y1 = pop();
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push_integer(2 * i + 1);
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push(X);
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subtract();
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push(K);
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add();
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push(Y1);
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multiply();
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push_integer(i);
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push(K);
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add();
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push(Y0);
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multiply();
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subtract();
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push_integer(i + 1);
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divide();
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}
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}
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static char *s[] = {
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"laguerre(x,n)",
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"laguerre(x,n,0)",
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"laguerre(x,n,k)",
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"laguerre(x,n,k)",
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"laguerre(x,0)-1",
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"0",
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"laguerre(x,1)-(-x+1)",
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"0",
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"laguerre(x,2)-1/2*(x^2-4*x+2)",
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"0",
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"laguerre(x,3)-1/6*(-x^3+9*x^2-18*x+6)",
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"0",
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"laguerre(x,0,k)-1",
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"0",
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"laguerre(x,1,k)-(-x+k+1)",
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"0",
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"laguerre(x,2,k)-1/2*(x^2-2*(k+2)*x+(k+1)*(k+2))",
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"0",
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"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))",
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"0",
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"laguerre(a-b,10)-eval(subst(a-b,x,laguerre(x,10)))",
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"0",
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};
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void
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test_laguerre(void)
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{
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test(__FILE__, s, sizeof s / sizeof (char *));
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}
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