File: [local] / OpenXM_contrib2 / asir2000 / builtin / isolv.c (download)
Revision 1.1, Mon Oct 20 07:18:42 2003 UTC (20 years, 11 months ago) by saito
Branch: MAIN
add new function polynoimal equaiton solve.
return val is interval num.
solve( poly, limt); interval num.
nsolve( poly, limt); big num.
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/*
* $Id$
*/
#include "ca.h"
#include "parse.h"
#include "version.h"
#if defined(INTERVAL)
static void Solve(NODE, Obj *);
static void NSolve(NODE, Obj *);
void Solve1(P, Q, pointer *);
void Sturm(P, VECT *);
void boundbody(P, Q *);
void separate(Q, Q, VECT, Q, Q, int, int, MAT, int *);
void ueval(P, Q, Q *);
struct ftab isolv_tab[] = {
{"solve", Solve, 2},
{"nsolve", NSolve, 2},
{0,0,0},
};
static void
Solve(arg, rp)
NODE arg;
Obj *rp;
{
pointer p, Eps;
pointer root;
V v;
Q eps;
p = (pointer)ARG0(arg);
if ( !p ) {
*rp = 0;
return;
}
Eps = (pointer)ARG1(arg);
asir_assert(Eps, O_N, "solve");
if ( NID(Eps) != N_Q ) {
fprintf(stderr,"solve arg 2 is required a rational number");
error(" : invalid argument");
return;
}
DUPQ((Q)Eps, eps);
SGN(eps) = 1;
switch (OID(p)) {
case O_N:
*rp = 0;
break;
case O_P:
Pvars(arg, &root);
if (NEXT(BDY((LIST)root)) != 0) {
fprintf(stderr,"solve arg 1 is univariate polynormial");
error(" : invalid argument");
break;
}
Solve1((P)p, eps, &root);
*rp = (Obj)root;
break;
case O_LIST:
fprintf(stderr,"solve,");
error(" : Sorry, not yet implement of multivars");
break;
defaults:
*rp = 0;
}
}
static void
NSolve(arg, rp)
NODE arg;
Obj *rp;
{
pointer p, Eps;
LIST root, listp;
V v;
Q eps;
NODE n, n0, m0, m, ln0;
Num r;
Itv iv;
BF breal;
p = (pointer)ARG0(arg);
if ( !p ) {
*rp = 0;
return;
}
Eps = (pointer)ARG1(arg);
asir_assert(Eps, O_N, "solve");
if ( NID(Eps) != N_Q ) {
fprintf(stderr,"solve arg 2 is required a rational number");
error(" : invalid argument");
return;
}
DUPQ((Q)Eps, eps);
SGN(eps) = 1;
switch (OID(p)) {
case O_N:
*rp = 0;
break;
case O_P:
Pvars(arg, &root);
if (NEXT(BDY((LIST)root)) != 0) {
fprintf(stderr,"solve arg 1 is univariate polynormial");
error(" : invalid argument");
break;
}
Solve1((P)p, eps, &root);
for (m0 = BDY((LIST)root), n0 = 0; m0; m0 = NEXT(m0)) {
m = BDY((LIST)BDY(m0));
miditvp(BDY(m), &r);
ToBf(r, &breal);
NEXTNODE( n0, n );
MKNODE(ln0, breal, NEXT(m));
MKLIST(listp, ln0);
BDY(n) = (pointer)listp;
}
NEXT(n) = 0;
MKLIST(listp,n0);
*rp = (pointer)listp;
break;
case O_LIST:
fprintf(stderr,"solve,");
error(" : Sorry, not yet implement of multivars");
break;
defaults:
*rp = 0;
}
}
void
Solve1(inp, eps, rt)
P inp;
Q eps;
pointer *rt;
{
P p;
Q up, low, a;
DCP fctp, onedeg, zerodeg;
LIST listp;
VECT sseq;
MAT root;
int chvu, chvl, pad, tnumb, numb, i, j;
Itv iv;
NODE n0, n, ln0, ln;
boundbody(inp, &up);
if (!up) {
*rt = 0;
return;
}
Sturm(inp, &sseq);
DUPQ(up,low);
SGN(low) = -1;
chvu = stumq(sseq, up);
chvl = stumq(sseq, low);
tnumb = abs(chvu - chvl);
MKMAT(root, tnumb, 3);
pad = -1;
fctrp(CO,inp,&fctp);
for (fctp = NEXT(fctp), i = 0; fctp; fctp = NEXT(fctp)) {
p = COEF(fctp);
onedeg = DC(p);
if ( !cmpq(DEG(onedeg), ONE) ) {
pad++;
if ( !NEXT(onedeg) ) {
BDY(root)[pad][0] = 0;
BDY(root)[pad][1] = 0;
BDY(root)[pad][2] = DEG(fctp);
} else {
divq((Q)COEF(NEXT(onedeg)),(Q)COEF(onedeg),&a);
BDY(root)[pad][0] = a;
BDY(root)[pad][1] = BDY(root)[pad][0];
BDY(root)[pad][2] = DEG(fctp);
}
continue;
}
boundbody(p, &up);
Sturm(p, &sseq);
DUPQ(up,low);
SGN(low) = -1;
chvu = stumq(sseq, up);
chvl = stumq(sseq, low);
numb = abs(chvu - chvl);
separate(DEG(fctp), eps, sseq, up, low, chvu, chvl, root, &pad);
}
for (i = 0; i < pad; i++) {
for (j = i; j <= pad; j++) {
if (cmpq(BDY(root)[i][0], BDY(root)[j][0]) > 0) {
a = BDY(root)[i][0];
BDY(root)[i][0] = BDY(root)[j][0];
BDY(root)[j][0] = a;
a = BDY(root)[i][1];
BDY(root)[i][1] = BDY(root)[j][1];
BDY(root)[j][1] = a;
a = BDY(root)[i][2];
BDY(root)[i][2] = BDY(root)[j][2];
BDY(root)[j][2] = a;
}
}
}
for (i = 0, n0 = 0; i <= pad; i++) {
istoitv(BDY(root)[i][0], BDY(root)[i][1], &iv);
NEXTNODE(n0,n);
MKNODE(ln, BDY(root)[i][2], 0); MKNODE(ln0, iv, ln);
MKLIST(listp, ln0);BDY(n) = (pointer)listp;
}
NEXT(n) = 0;
MKLIST(listp,n0);
*rt = (pointer)listp;
}
void
separate(mult, eps, sseq, up, low, upn, lown, root, padp)
VECT sseq;
Q mult, eps, up, low;
int upn, lown;
MAT root;
int *padp;
{
int de, midn;
Q mid, a, b, c, d, e;
P p;
de = abs(lown - upn);
if (de == 0) return;
if (de == 1) {
(*padp)++;
BDY(root)[*padp][0] = up;
BDY(root)[*padp][1] = low;
subq( BDY(root)[*padp][1], BDY(root)[*padp][0], &e );
SGN(e) = 1;
p = (P *)sseq->body[0];
while (cmpq(e, eps) > 0) {
addq(BDY(root)[*padp][0], BDY(root)[*padp][1], &c);
divq(c, TWO, &d);
ueval(p, BDY(root)[*padp][1], &a);
ueval(p, d, &b);
if (SGN(a) == SGN(b))
BDY(root)[*padp][1] = d;
else BDY(root)[*padp][0] = d;
subq( BDY(root)[*padp][1], BDY(root)[*padp][0], &e);
SGN(e) = 1;
}
BDY(root)[*padp][2] = mult;
return;
}
addq(up, low, &mid);
divq(mid, TWO, &mid);
midn = stumq(sseq, mid);
separate(mult, eps, sseq, low, mid, lown, midn, root, padp);
separate(mult, eps, sseq, mid, up, midn, upn, root, padp);
}
void
Sturm(p, ret)
P p;
VECT *ret;
{
P g1,g2,q,r,s, *t;
Q a,b,c,d,h,l,m,x;
V v;
VECT seq;
int i,j;
v = VR(p);
t = (P *)ALLOCA((deg(v,p)+1)*sizeof(P));
g1 = t[0] = p; diffp(CO,p,v,(P *)&a); ptozp((P)a,1,&c,&g2); t[1] = g2;
for ( i = 1, h = ONE, x = ONE; ; ) {
if ( NUM(g2) ) break;
subq(DEG(DC(g1)),DEG(DC(g2)),&d);
l = (Q)LC(g2);
if ( SGN(l) < 0 ) {
chsgnq(l,&a); l = a;
}
addq(d,ONE,&a); pwrq(l,a,&b); mulp(CO,(P)b,g1,(P *)&a);
divsrp(CO,(P)a,g2,&q,&r);
if ( !r ) break;
chsgnp(r,&s); r = s; i++;
if ( NUM(r) ) {
t[i] = r; break;
}
pwrq(h,d,&m); g1 = g2;
mulq(m,x,&a); divsp(CO,r,(P)a,&g2); t[i] = g2;
x = (Q)LC(g1);
if ( SGN(x) < 0 ) {
chsgnq(x,&a); x = a;
}
pwrq(x,d,&a); mulq(a,h,&b); divq(b,m,&h);
}
MKVECT(seq,i+1);
for ( j = 0; j <= i; j++ ) seq->body[j] = (pointer)t[j];
*ret = seq;
}
int
stumq(s, val)
VECT s;
Q val;
{
int len, i, j, c;
P *ss;
Q a, a0;
len = s->len;
ss = (P *)s->body;
for ( j = 0; j < len; j++ ){
ueval(ss[j],val,&a0);
if (a0) break;
}
for ( i = j++, c =0; i < len; i++) {
ueval( ss[i], val, &a);
if ( a ) {
if( (SGN(a) > 0 && SGN(a0) < 0) || (SGN(a) < 0 && SGN(a0) > 0) ){
c++;
a0 = a;
}
}
}
return c;
}
void
boundbody(p, q)
P p;
Q *q;
{
Q t, max, tmp;
DCP dc;
if ( !p )
*q = 0;
else if ( p->id == O_N )
*q = 0;
else {
NEWQ(tmp);
SGN(tmp)=1;
for ( dc = DC(p), max=0; dc; dc = NEXT(dc) ) {
t = (Q)COEF(dc);
NM(tmp)=NM(t);
DN(tmp)=DN(t);
if ( cmpq(tmp, max) > 0 ) DUPQ(tmp, max);
}
addq(ONE, max, q);
}
}
void
ueval(p, q, rp)
P p;
Q q;
Q *rp;
{
Q d, d1, a, b, t;
Q deg, da;
Q nm, dn;
DCP dc;
if ( !p ) *rp = 0;
else if ( NUM(p) ) *rp = (Q)p;
else {
if ( q ) {
NTOQ( DN(q), 1, dn );
NTOQ( NM(q), SGN(q), nm );
} else {
dn = 0;
nm = 0;
}
if ( !dn ) {
dc = DC(p); t = (Q)COEF(dc);
for ( d = DEG(dc), dc = NEXT(dc); dc; d = DEG(dc), dc= NEXT(dc) ) {
subq(d, DEG(dc), &d1); pwrq(nm, d1, &a);
mulq(t,a,&b); addq(b,(Q)COEF(dc),&t);
}
if ( d ) {
pwrq(nm,d,&a); mulq(t,a,&b); t = b;
}
*rp = t;
} else {
dc = DC(p); t = (Q)COEF(dc);
for ( d=deg= DEG(dc), dc = NEXT(dc); dc; d = DEG(dc), dc= NEXT(dc) ) {
subq(d, DEG(dc), &d1); pwrq(nm, d1, &a);
mulq(t,a,&b);
subq(deg, DEG(dc), &d1); pwrq(dn, d1, &a);
mulq(a, (Q)COEF(dc), &da);
addq(b,da,&t);
}
if ( d ) {
pwrq(nm,d,&a); mulq(t,a,&b); t = b;
}
*rp = t;
}
}
}
#endif