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1.1 ! saito 1: /*
! 2: * $Id$
! 3: */
! 4:
! 5: #include "ca.h"
! 6: #include "parse.h"
! 7: #include "version.h"
! 8:
! 9: #if defined(INTERVAL)
! 10:
! 11: static void Solve(NODE, Obj *);
! 12: static void NSolve(NODE, Obj *);
! 13:
! 14: void Solve1(P, Q, pointer *);
! 15: void Sturm(P, VECT *);
! 16: void boundbody(P, Q *);
! 17: void separate(Q, Q, VECT, Q, Q, int, int, MAT, int *);
! 18: void ueval(P, Q, Q *);
! 19:
! 20: struct ftab isolv_tab[] = {
! 21: {"solve", Solve, 2},
! 22: {"nsolve", NSolve, 2},
! 23: {0,0,0},
! 24: };
! 25:
! 26: static void
! 27: Solve(arg, rp)
! 28: NODE arg;
! 29: Obj *rp;
! 30: {
! 31: pointer p, Eps;
! 32: pointer root;
! 33: V v;
! 34: Q eps;
! 35:
! 36: p = (pointer)ARG0(arg);
! 37: if ( !p ) {
! 38: *rp = 0;
! 39: return;
! 40: }
! 41: Eps = (pointer)ARG1(arg);
! 42: asir_assert(Eps, O_N, "solve");
! 43: if ( NID(Eps) != N_Q ) {
! 44: fprintf(stderr,"solve arg 2 is required a rational number");
! 45: error(" : invalid argument");
! 46: return;
! 47: }
! 48: DUPQ((Q)Eps, eps);
! 49: SGN(eps) = 1;
! 50: switch (OID(p)) {
! 51: case O_N:
! 52: *rp = 0;
! 53: break;
! 54: case O_P:
! 55: Pvars(arg, &root);
! 56: if (NEXT(BDY((LIST)root)) != 0) {
! 57: fprintf(stderr,"solve arg 1 is univariate polynormial");
! 58: error(" : invalid argument");
! 59: break;
! 60: }
! 61: Solve1((P)p, eps, &root);
! 62: *rp = (Obj)root;
! 63: break;
! 64: case O_LIST:
! 65: fprintf(stderr,"solve,");
! 66: error(" : Sorry, not yet implement of multivars");
! 67: break;
! 68: defaults:
! 69: *rp = 0;
! 70: }
! 71: }
! 72:
! 73: static void
! 74: NSolve(arg, rp)
! 75: NODE arg;
! 76: Obj *rp;
! 77: {
! 78: pointer p, Eps;
! 79: LIST root, listp;
! 80: V v;
! 81: Q eps;
! 82: NODE n, n0, m0, m, ln0;
! 83: Num r;
! 84: Itv iv;
! 85: BF breal;
! 86:
! 87: p = (pointer)ARG0(arg);
! 88: if ( !p ) {
! 89: *rp = 0;
! 90: return;
! 91: }
! 92: Eps = (pointer)ARG1(arg);
! 93: asir_assert(Eps, O_N, "solve");
! 94: if ( NID(Eps) != N_Q ) {
! 95: fprintf(stderr,"solve arg 2 is required a rational number");
! 96: error(" : invalid argument");
! 97: return;
! 98: }
! 99: DUPQ((Q)Eps, eps);
! 100: SGN(eps) = 1;
! 101: switch (OID(p)) {
! 102: case O_N:
! 103: *rp = 0;
! 104: break;
! 105: case O_P:
! 106: Pvars(arg, &root);
! 107: if (NEXT(BDY((LIST)root)) != 0) {
! 108: fprintf(stderr,"solve arg 1 is univariate polynormial");
! 109: error(" : invalid argument");
! 110: break;
! 111: }
! 112: Solve1((P)p, eps, &root);
! 113: for (m0 = BDY((LIST)root), n0 = 0; m0; m0 = NEXT(m0)) {
! 114: m = BDY((LIST)BDY(m0));
! 115: miditvp(BDY(m), &r);
! 116: ToBf(r, &breal);
! 117: NEXTNODE( n0, n );
! 118: MKNODE(ln0, breal, NEXT(m));
! 119: MKLIST(listp, ln0);
! 120: BDY(n) = (pointer)listp;
! 121: }
! 122: NEXT(n) = 0;
! 123: MKLIST(listp,n0);
! 124: *rp = (pointer)listp;
! 125: break;
! 126: case O_LIST:
! 127: fprintf(stderr,"solve,");
! 128: error(" : Sorry, not yet implement of multivars");
! 129: break;
! 130: defaults:
! 131: *rp = 0;
! 132: }
! 133: }
! 134:
! 135: void
! 136: Solve1(inp, eps, rt)
! 137: P inp;
! 138: Q eps;
! 139: pointer *rt;
! 140: {
! 141: P p;
! 142: Q up, low, a;
! 143: DCP fctp, onedeg, zerodeg;
! 144: LIST listp;
! 145: VECT sseq;
! 146: MAT root;
! 147: int chvu, chvl, pad, tnumb, numb, i, j;
! 148: Itv iv;
! 149: NODE n0, n, ln0, ln;
! 150:
! 151: boundbody(inp, &up);
! 152: if (!up) {
! 153: *rt = 0;
! 154: return;
! 155: }
! 156: Sturm(inp, &sseq);
! 157: DUPQ(up,low);
! 158: SGN(low) = -1;
! 159: chvu = stumq(sseq, up);
! 160: chvl = stumq(sseq, low);
! 161: tnumb = abs(chvu - chvl);
! 162: MKMAT(root, tnumb, 3);
! 163: pad = -1;
! 164:
! 165: fctrp(CO,inp,&fctp);
! 166: for (fctp = NEXT(fctp), i = 0; fctp; fctp = NEXT(fctp)) {
! 167: p = COEF(fctp);
! 168: onedeg = DC(p);
! 169: if ( !cmpq(DEG(onedeg), ONE) ) {
! 170: pad++;
! 171: if ( !NEXT(onedeg) ) {
! 172: BDY(root)[pad][0] = 0;
! 173: BDY(root)[pad][1] = 0;
! 174: BDY(root)[pad][2] = DEG(fctp);
! 175: } else {
! 176: divq((Q)COEF(NEXT(onedeg)),(Q)COEF(onedeg),&a);
! 177: BDY(root)[pad][0] = a;
! 178: BDY(root)[pad][1] = BDY(root)[pad][0];
! 179: BDY(root)[pad][2] = DEG(fctp);
! 180: }
! 181: continue;
! 182: }
! 183: boundbody(p, &up);
! 184: Sturm(p, &sseq);
! 185: DUPQ(up,low);
! 186: SGN(low) = -1;
! 187: chvu = stumq(sseq, up);
! 188: chvl = stumq(sseq, low);
! 189: numb = abs(chvu - chvl);
! 190: separate(DEG(fctp), eps, sseq, up, low, chvu, chvl, root, &pad);
! 191: }
! 192: for (i = 0; i < pad; i++) {
! 193: for (j = i; j <= pad; j++) {
! 194: if (cmpq(BDY(root)[i][0], BDY(root)[j][0]) > 0) {
! 195: a = BDY(root)[i][0];
! 196: BDY(root)[i][0] = BDY(root)[j][0];
! 197: BDY(root)[j][0] = a;
! 198: a = BDY(root)[i][1];
! 199: BDY(root)[i][1] = BDY(root)[j][1];
! 200: BDY(root)[j][1] = a;
! 201: a = BDY(root)[i][2];
! 202: BDY(root)[i][2] = BDY(root)[j][2];
! 203: BDY(root)[j][2] = a;
! 204: }
! 205: }
! 206: }
! 207: for (i = 0, n0 = 0; i <= pad; i++) {
! 208: istoitv(BDY(root)[i][0], BDY(root)[i][1], &iv);
! 209: NEXTNODE(n0,n);
! 210: MKNODE(ln, BDY(root)[i][2], 0); MKNODE(ln0, iv, ln);
! 211: MKLIST(listp, ln0);BDY(n) = (pointer)listp;
! 212: }
! 213: NEXT(n) = 0;
! 214: MKLIST(listp,n0);
! 215: *rt = (pointer)listp;
! 216: }
! 217:
! 218: void
! 219: separate(mult, eps, sseq, up, low, upn, lown, root, padp)
! 220: VECT sseq;
! 221: Q mult, eps, up, low;
! 222: int upn, lown;
! 223: MAT root;
! 224: int *padp;
! 225: {
! 226: int de, midn;
! 227: Q mid, a, b, c, d, e;
! 228: P p;
! 229:
! 230: de = abs(lown - upn);
! 231: if (de == 0) return;
! 232: if (de == 1) {
! 233: (*padp)++;
! 234: BDY(root)[*padp][0] = up;
! 235: BDY(root)[*padp][1] = low;
! 236: subq( BDY(root)[*padp][1], BDY(root)[*padp][0], &e );
! 237: SGN(e) = 1;
! 238: p = (P *)sseq->body[0];
! 239: while (cmpq(e, eps) > 0) {
! 240: addq(BDY(root)[*padp][0], BDY(root)[*padp][1], &c);
! 241: divq(c, TWO, &d);
! 242: ueval(p, BDY(root)[*padp][1], &a);
! 243: ueval(p, d, &b);
! 244: if (SGN(a) == SGN(b))
! 245: BDY(root)[*padp][1] = d;
! 246: else BDY(root)[*padp][0] = d;
! 247: subq( BDY(root)[*padp][1], BDY(root)[*padp][0], &e);
! 248: SGN(e) = 1;
! 249: }
! 250: BDY(root)[*padp][2] = mult;
! 251: return;
! 252: }
! 253: addq(up, low, &mid);
! 254: divq(mid, TWO, &mid);
! 255: midn = stumq(sseq, mid);
! 256: separate(mult, eps, sseq, low, mid, lown, midn, root, padp);
! 257: separate(mult, eps, sseq, mid, up, midn, upn, root, padp);
! 258: }
! 259:
! 260: void
! 261: Sturm(p, ret)
! 262: P p;
! 263: VECT *ret;
! 264: {
! 265: P g1,g2,q,r,s, *t;
! 266: Q a,b,c,d,h,l,m,x;
! 267: V v;
! 268: VECT seq;
! 269: int i,j;
! 270:
! 271: v = VR(p);
! 272: t = (P *)ALLOCA((deg(v,p)+1)*sizeof(P));
! 273: g1 = t[0] = p; diffp(CO,p,v,(P *)&a); ptozp((P)a,1,&c,&g2); t[1] = g2;
! 274: for ( i = 1, h = ONE, x = ONE; ; ) {
! 275: if ( NUM(g2) ) break;
! 276: subq(DEG(DC(g1)),DEG(DC(g2)),&d);
! 277: l = (Q)LC(g2);
! 278: if ( SGN(l) < 0 ) {
! 279: chsgnq(l,&a); l = a;
! 280: }
! 281: addq(d,ONE,&a); pwrq(l,a,&b); mulp(CO,(P)b,g1,(P *)&a);
! 282: divsrp(CO,(P)a,g2,&q,&r);
! 283: if ( !r ) break;
! 284: chsgnp(r,&s); r = s; i++;
! 285: if ( NUM(r) ) {
! 286: t[i] = r; break;
! 287: }
! 288: pwrq(h,d,&m); g1 = g2;
! 289: mulq(m,x,&a); divsp(CO,r,(P)a,&g2); t[i] = g2;
! 290: x = (Q)LC(g1);
! 291: if ( SGN(x) < 0 ) {
! 292: chsgnq(x,&a); x = a;
! 293: }
! 294: pwrq(x,d,&a); mulq(a,h,&b); divq(b,m,&h);
! 295: }
! 296: MKVECT(seq,i+1);
! 297: for ( j = 0; j <= i; j++ ) seq->body[j] = (pointer)t[j];
! 298: *ret = seq;
! 299: }
! 300:
! 301: int
! 302: stumq(s, val)
! 303: VECT s;
! 304: Q val;
! 305: {
! 306: int len, i, j, c;
! 307: P *ss;
! 308: Q a, a0;
! 309:
! 310: len = s->len;
! 311: ss = (P *)s->body;
! 312: for ( j = 0; j < len; j++ ){
! 313: ueval(ss[j],val,&a0);
! 314: if (a0) break;
! 315: }
! 316: for ( i = j++, c =0; i < len; i++) {
! 317: ueval( ss[i], val, &a);
! 318: if ( a ) {
! 319: if( (SGN(a) > 0 && SGN(a0) < 0) || (SGN(a) < 0 && SGN(a0) > 0) ){
! 320: c++;
! 321: a0 = a;
! 322: }
! 323: }
! 324: }
! 325: return c;
! 326: }
! 327:
! 328: void
! 329: boundbody(p, q)
! 330: P p;
! 331: Q *q;
! 332: {
! 333: Q t, max, tmp;
! 334: DCP dc;
! 335:
! 336: if ( !p )
! 337: *q = 0;
! 338: else if ( p->id == O_N )
! 339: *q = 0;
! 340: else {
! 341: NEWQ(tmp);
! 342: SGN(tmp)=1;
! 343: for ( dc = DC(p), max=0; dc; dc = NEXT(dc) ) {
! 344: t = (Q)COEF(dc);
! 345: NM(tmp)=NM(t);
! 346: DN(tmp)=DN(t);
! 347: if ( cmpq(tmp, max) > 0 ) DUPQ(tmp, max);
! 348: }
! 349: addq(ONE, max, q);
! 350: }
! 351: }
! 352:
! 353: void
! 354: ueval(p, q, rp)
! 355: P p;
! 356: Q q;
! 357: Q *rp;
! 358: {
! 359: Q d, d1, a, b, t;
! 360: Q deg, da;
! 361: Q nm, dn;
! 362: DCP dc;
! 363:
! 364: if ( !p ) *rp = 0;
! 365: else if ( NUM(p) ) *rp = (Q)p;
! 366: else {
! 367: if ( q ) {
! 368: NTOQ( DN(q), 1, dn );
! 369: NTOQ( NM(q), SGN(q), nm );
! 370: } else {
! 371: dn = 0;
! 372: nm = 0;
! 373: }
! 374: if ( !dn ) {
! 375: dc = DC(p); t = (Q)COEF(dc);
! 376: for ( d = DEG(dc), dc = NEXT(dc); dc; d = DEG(dc), dc= NEXT(dc) ) {
! 377: subq(d, DEG(dc), &d1); pwrq(nm, d1, &a);
! 378: mulq(t,a,&b); addq(b,(Q)COEF(dc),&t);
! 379: }
! 380: if ( d ) {
! 381: pwrq(nm,d,&a); mulq(t,a,&b); t = b;
! 382: }
! 383: *rp = t;
! 384: } else {
! 385: dc = DC(p); t = (Q)COEF(dc);
! 386: for ( d=deg= DEG(dc), dc = NEXT(dc); dc; d = DEG(dc), dc= NEXT(dc) ) {
! 387: subq(d, DEG(dc), &d1); pwrq(nm, d1, &a);
! 388: mulq(t,a,&b);
! 389: subq(deg, DEG(dc), &d1); pwrq(dn, d1, &a);
! 390: mulq(a, (Q)COEF(dc), &da);
! 391: addq(b,da,&t);
! 392: }
! 393: if ( d ) {
! 394: pwrq(nm,d,&a); mulq(t,a,&b); t = b;
! 395: }
! 396: *rp = t;
! 397: }
! 398: }
! 399: }
! 400: #endif