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1.2 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.3 noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.13 ! saito 48: * $OpenXM: OpenXM_contrib2/asir2000/engine/mat.c,v 1.12 2004/08/18 06:30:07 saito Exp $
1.2 noro 49: */
1.1 noro 50: #include "ca.h"
1.4 saito 51: #include "../parse/parse.h"
52:
53: extern int StrassenSize;
1.12 saito 54: void mulmatmat_miser();
1.1 noro 55:
56: void addmat(vl,a,b,c)
57: VL vl;
58: MAT a,b,*c;
59: {
60: int row,col,i,j;
1.4 saito 61: MAT t;
62: pointer *ab,*bb,*tb;
63:
64: if ( !a )
65: *c = b;
66: else if ( !b )
67: *c = a;
68: else if ( (a->row != b->row) || (a->col != b->col) ) {
69: *c = 0; error("addmat : size mismatch add");
70: } else {
71: row = a->row; col = a->col;
72: MKMAT(t,row,col);
73: for ( i = 0; i < row; i++ )
74: for ( j = 0, ab = BDY(a)[i], bb = BDY(b)[i], tb = BDY(t)[i];
75: j < col; j++ )
1.9 noro 76: arf_add(vl,(Obj)ab[j],(Obj)bb[j],(Obj *)&tb[j]);
1.4 saito 77: *c = t;
78: }
1.1 noro 79: }
80:
81: void submat(vl,a,b,c)
82: VL vl;
83: MAT a,b,*c;
84: {
85: int row,col,i,j;
1.4 saito 86: MAT t;
87: pointer *ab,*bb,*tb;
1.1 noro 88:
1.4 saito 89: if ( !a )
90: chsgnmat(b,c);
91: else if ( !b )
92: *c = a;
93: else if ( (a->row != b->row) || (a->col != b->col) ) {
94: *c = 0; error("submat : size mismatch sub");
95: } else {
96: row = a->row; col = a->col;
97: MKMAT(t,row,col);
98: for ( i = 0; i < row; i++ )
99: for ( j = 0, ab = BDY(a)[i], bb = BDY(b)[i], tb = BDY(t)[i];
100: j < col; j++ )
1.9 noro 101: arf_sub(vl,(Obj)ab[j],(Obj)bb[j],(Obj *)&tb[j]);
1.4 saito 102: *c = t;
103: }
1.1 noro 104: }
105:
1.11 saito 106: void addmat_miser(vl,a,b,c,ar0,ac0,ar1,ac1,br0,bc0,br1,bc1)
107: VL vl;
108: MAT a,b,*c;
109: int ar0,ac0,ar1,ac1,br0,bc0,br1,bc1;
110: {
111: int row,col,i,j;
112: MAT t;
113: pointer *ab,*bb,*tb;
114: row = ar1 - ar0 + 1; col = ac1 - ac0 + 1;
115:
116: if ( !a )
117: *c = b;
118: else if ( !b )
119: *c = a;
120: else if ( (row != br1 - br0 + 1) || (col != bc1 - bc0 + 1) ) {
121: *c = 0; error("addmat : size mismatch add");
122: } else {
123: MKMAT(t,row,col);
124: for ( i = 0; i < row; i++ ) {
125: if (i+ar0 > a->row-1) {
126: ab = NULL;
127: } else {
128: ab = BDY(a)[i+ar0];
129: }
130: if (i+br0 > b->row-1) {
131: bb = NULL;
132: } else {
133: bb = BDY(b)[i+br0];
134: }
135: tb = BDY(t)[i];
136: for ( j =0; j < col; j++ ) {
137: if ((ab == NULL || j+ac0 > a->col-1) && (bb == NULL || j+bc0 > b->col-1)) {
138: arf_add(vl,NULL,NULL,(Obj *)&tb[j]);
139: } else if ((ab != NULL && j+ac0 <= a->col-1) && (bb == NULL || j+bc0 > b->col-1)){
140: arf_add(vl,(Obj)ab[j+ac0],NULL,(Obj *)&tb[j]);
141: } else if ((ab == NULL || j+ac0 > a->col-1) && (bb != NULL && j+bc0 <= b->col-1)) {
142: arf_add(vl,NULL, (Obj)bb[j+bc0],(Obj *)&tb[j]);
143: } else {
144: arf_add(vl,(Obj)ab[j+ac0],(Obj)bb[j+bc0],(Obj *)&tb[j]);
145: }
146:
147: }
148: }
149: *c = t;
150: }
151: }
152:
153: void submat_miser(vl,a,b,c,ar0,ac0,ar1,ac1,br0,bc0,br1,bc1)
154: VL vl;
155: MAT a,b,*c;
156: int ar0,ac0,ar1,ac1,br0,bc0,br1,bc1;
157: {
158: int row,col,i,j;
159: MAT t;
160: pointer *ab,*bb,*tb;
161:
162: row = ar1 - ar0 + 1; col = ac1 - ac0 + 1;
163:
164: if ( !a )
165: chsgnmat(b,c);
166: else if ( !b )
167: *c = a;
168: else if ( (row != br1 - br0 + 1) || (col != bc1 - bc0 + 1) ) {
169: *c = 0; error("submat : size mismatch sub");
170: } else {
171: MKMAT(t,row,col);
172: for ( i = 0; i < row; i++ ) {
173: if (i+ar0 > a->row-1) {
174: ab = NULL;
175: } else {
176: ab = BDY(a)[i+ar0];
177: }
178: if (i+br0 > b->row-1) {
179: bb = NULL;
180: } else {
181: bb = BDY(b)[i+br0];
182: }
183: tb = BDY(t)[i];
184: for ( j =0; j < col; j++ ) {
185: if ((ab == NULL || j+ac0 > a->col-1) && (bb == NULL || j+bc0 > b->col-1)) {
186: arf_sub(vl,NULL,NULL,(Obj *)&tb[j]);
187: } else if ((ab != NULL && j+ac0 <= a->col-1) && (bb == NULL || j+bc0 > b->col-1)){
188: arf_sub(vl,(Obj)ab[j+ac0],NULL,(Obj *)&tb[j]);
189: } else if ((ab == NULL || j+ac0 > a->col-1) && (bb != NULL && j+bc0 <= b->col-1)) {
190: arf_sub(vl,NULL, (Obj)bb[j+bc0],(Obj *)&tb[j]);
191: } else {
192: arf_sub(vl,(Obj)ab[j+ac0],(Obj)bb[j+bc0],(Obj *)&tb[j]);
193: }
194:
195: }
196: }
197: *c = t;
198: }
199: }
200:
1.1 noro 201: void mulmat(vl,a,b,c)
202: VL vl;
203: Obj a,b,*c;
204: {
1.8 noro 205: VECT vect;
206: MAT mat;
207:
208: if ( !a && !b )
1.1 noro 209: *c = 0;
1.8 noro 210: else if ( !a || !b ) {
211: if ( !a )
212: a = b;
213: switch ( OID(a) ) {
214: case O_VECT:
215: MKVECT(vect,((VECT)a)->len);
216: *c = (Obj)vect;
217: break;
218: case O_MAT:
219: MKMAT(mat,((MAT)a)->row,((MAT)a)->col);
220: *c = (Obj)mat;
221: break;
222: default:
223: *c = 0;
224: break;
225: }
1.10 noro 226: } else if ( OID(a) <= O_R || OID(a) == O_DP )
1.1 noro 227: mulrmat(vl,(Obj)a,(MAT)b,(MAT *)c);
1.10 noro 228: else if ( OID(b) <= O_R || OID(b) == O_DP )
1.1 noro 229: mulrmat(vl,(Obj)b,(MAT)a,(MAT *)c);
230: else
231: switch ( OID(a) ) {
232: case O_VECT:
233: switch ( OID(b) ) {
234: case O_MAT:
235: mulvectmat(vl,(VECT)a,(MAT)b,(VECT *)c); break;
236: case O_VECT: default:
237: notdef(vl,a,b,c); break;
238: }
239: break;
240: case O_MAT:
241: switch ( OID(b) ) {
242: case O_VECT:
243: mulmatvect(vl,(MAT)a,(VECT)b,(VECT *)c); break;
244: case O_MAT:
1.11 saito 245: mulmatmat_miser(vl,(MAT)a,(MAT)b,(MAT *)c, 0,0, ((MAT)a)->row-1, ((MAT)a)->col-1, 0,0,((MAT)b)->row-1, ((MAT)b)->col-1); break;
1.1 noro 246: default:
247: notdef(vl,a,b,c); break;
248: }
249: break;
250: default:
251: notdef(vl,a,b,c); break;
252: }
253: }
254:
255: void divmat(vl,a,b,c)
256: VL vl;
257: Obj a,b,*c;
258: {
259: Obj t;
260:
261: if ( !b )
262: error("divmat : division by 0");
263: else if ( !a )
264: *c = 0;
265: else if ( OID(b) > O_R )
266: notdef(vl,a,b,c);
267: else {
1.9 noro 268: arf_div(vl,(Obj)ONE,b,&t); mulrmat(vl,t,(MAT)a,(MAT *)c);
1.1 noro 269: }
270: }
271:
272: void chsgnmat(a,b)
273: MAT a,*b;
274: {
275: MAT t;
276: int row,col,i,j;
277: pointer *ab,*tb;
278:
279: if ( !a )
280: *b = 0;
281: else {
282: row = a->row; col = a->col;
283: MKMAT(t,row,col);
284: for ( i = 0; i < row; i++ )
285: for ( j = 0, ab = BDY(a)[i], tb = BDY(t)[i];
286: j < col; j++ )
1.9 noro 287: arf_chsgn((Obj)ab[j],(Obj *)&tb[j]);
1.1 noro 288: *b = t;
289: }
290: }
291:
292: void pwrmat(vl,a,r,c)
293: VL vl;
294: MAT a;
295: Obj r;
296: MAT *c;
297: {
1.8 noro 298: int n,i;
299: MAT t;
300:
1.1 noro 301: if ( !a )
302: *c = 0;
1.8 noro 303: else if ( !r ) {
304: if ( a->row != a->col ) {
305: *c = 0; error("pwrmat : non square matrix");
306: } else {
307: n = a->row;
308: MKMAT(t,n,n);
309: for ( i = 0; i < n; i++ )
310: t->body[i][i] = ONE;
311: *c = t;
312: }
313: } else if ( !NUM(r) || !RATN(r) ||
1.1 noro 314: !INT(r) || (SGN((Q)r)<0) || (PL(NM((Q)r))>1) ) {
315: *c = 0; error("pwrmat : invalid exponent");
316: } else if ( a->row != a->col ) {
317: *c = 0; error("pwrmat : non square matrix");
318: } else
319: pwrmatmain(vl,a,QTOS((Q)r),c);
320: }
321:
322: void pwrmatmain(vl,a,e,c)
323: VL vl;
324: MAT a;
325: int e;
326: MAT *c;
327: {
328: MAT t,s;
329:
330: if ( e == 1 ) {
331: *c = a;
332: return;
333: }
334:
335: pwrmatmain(vl,a,e/2,&t);
336: mulmat(vl,(Obj)t,(Obj)t,(Obj *)&s);
337: if ( e % 2 )
338: mulmat(vl,(Obj)s,(Obj)a,(Obj *)c);
339: else
340: *c = s;
341: }
342:
343: void mulrmat(vl,a,b,c)
344: VL vl;
345: Obj a;
346: MAT b,*c;
347: {
348: int row,col,i,j;
349: MAT t;
350: pointer *bb,*tb;
351:
352: if ( !a || !b )
353: *c = 0;
354: else {
355: row = b->row; col = b->col;
356: MKMAT(t,row,col);
357: for ( i = 0; i < row; i++ )
358: for ( j = 0, bb = BDY(b)[i], tb = BDY(t)[i];
359: j < col; j++ )
1.9 noro 360: arf_mul(vl,(Obj)a,(Obj)bb[j],(Obj *)&tb[j]);
1.1 noro 361: *c = t;
362: }
363: }
364:
365: void mulmatmat(vl,a,b,c)
366: VL vl;
367: MAT a,b,*c;
368: {
1.4 saito 369: int arow,bcol,i,j,k,m, h, arowh, bcolh;
370: MAT t, a11, a12, a21, a22;
371: MAT p, b11, b12, b21, b22;
372: MAT ans1, ans2, ans3, c11, c12, c21, c22;
373: MAT s1, s2, t1, t2, u1, v1, w1, aa, bb;
374: pointer s,u,v;
375: pointer *ab,*tb;
376: int a1row,a2row, a3row,a4row, a1col, a2col, a3col, a4col;
377: int b1row,b2row, b3row,b4row, b1col, b2col, b3col, b4col;
378: int pflag1, pflag2;
1.5 saito 379: /* mismach col and row */
1.4 saito 380: if ( a->col != b->row ) {
381: *c = 0; error("mulmat : size mismatch");
382: }
383: else {
384: pflag1 = 0; pflag2 = 0;
385: arow = a->row; m = a->col; bcol = b->col;
386: MKMAT(t,arow,bcol);
387: /* StrassenSize == 0 or matrix size less then StrassenSize,
1.5 saito 388: then calc cannonical algorithm. */
389: if((StrassenSize == 0)||(a->row<=StrassenSize || a->col <= StrassenSize) || (b->row<=StrassenSize || b->col <= StrassenSize)) {
1.4 saito 390: for ( i = 0; i < arow; i++ )
391: for ( j = 0, ab = BDY(a)[i], tb = BDY(t)[i]; j < bcol; j++ ) {
392: for ( k = 0, s = 0; k < m; k++ ) {
1.9 noro 393: arf_mul(vl,(Obj)ab[k],(Obj)BDY(b)[k][j],(Obj *)&u);
394: arf_add(vl,(Obj)s,(Obj)u,(Obj *)&v);
1.4 saito 395: s = v;
396: }
397: tb[j] = s;
398: }
399: *c = t;
400: return;
401: }
1.5 saito 402: /* padding odd col and row to even number for zero */
1.4 saito 403: i = arow/2;
404: j = arow - i;
405: if (i != j) {
406: arow++;
407: pflag1 = 1;
408: }
409: i = m/2;
410: j = m - i;
411: if (i != j) {
412: m++;
413: pflag2 = 1;
414: }
415:
1.5 saito 416: /* split matrix A and B */
1.11 saito 417: a1row = arow/2; a1col = m/2;
1.4 saito 418: MKMAT(a11,a1row,a1col);
1.11 saito 419: MKMAT(a21,a1row,a1col);
420: MKMAT(a12,a1row,a1col);
421: MKMAT(a22,a1row,a1col);
1.4 saito 422:
1.11 saito 423: b1row = m/2; b1col = bcol/2;
1.4 saito 424: MKMAT(b11,b1row,b1col);
1.11 saito 425: MKMAT(b21,b1row,b1col);
426: MKMAT(b12,b1row,b1col);
427: MKMAT(b22,b1row,b1col);
1.4 saito 428:
1.5 saito 429: /* make a11 matrix */
1.4 saito 430: for (i = 0; i < a1row; i++) {
431: for (j = 0; j < a1col; j++) {
1.11 saito 432: a11->body[i][j] = a->body[i][j];
1.4 saito 433: }
434: }
435:
1.5 saito 436: /* make a21 matrix */
1.11 saito 437: for (i = a1row; i < a->row; i++) {
1.4 saito 438: for (j = 0; j < a1col; j++) {
1.11 saito 439: a21->body[i-a1row][j] = a->body[i][j];
1.4 saito 440: }
441: }
442:
1.5 saito 443: /* create a12 matrix */
1.4 saito 444: for (i = 0; i < a1row; i++) {
1.11 saito 445: for (j = a1col; j < a->col; j++) {
446: a12->body[i][j-a1col] = a->body[i][j];
1.4 saito 447: }
448: }
449:
1.5 saito 450: /* create a22 matrix */
1.11 saito 451: for (i = a1row; i < a->row; i++) {
452: for (j = a1col; j < a->col; j++) {
453: a22->body[i-a1row][j-a1col] = a->body[i][j];
1.4 saito 454: }
455: }
456:
457:
1.5 saito 458: /* create b11 submatrix */
1.4 saito 459: for (i = 0; i < b1row; i++) {
460: for (j = 0; j < b1col; j++) {
1.11 saito 461: b11->body[i][j] = b->body[i][j];
1.4 saito 462: }
463: }
464:
1.5 saito 465: /* create b21 submatrix */
1.11 saito 466: for (i = b1row; i < b->row; i++) {
1.4 saito 467: for (j = 0; j < b1col; j++) {
1.11 saito 468: b21->body[i-b1row][j] = b->body[i][j];
1.4 saito 469: }
470: }
471:
1.5 saito 472: /* create b12 submatrix */
1.4 saito 473: for (i = 0; i < b1row; i++) {
1.11 saito 474: for (j = b1col; j < b->col; j++) {
475: b12->body[i][j-b1col] = b->body[i][j];
1.4 saito 476: }
477: }
478:
1.5 saito 479: /* create b22 submatrix */
1.11 saito 480: for (i = b1row; i < b->row; i++) {
481: for (j = b1col; j < b->col; j++) {
482: b22->body[i-b1row][j-b1col] = b->body[i][j];
1.4 saito 483: }
484: }
1.5 saito 485: /* expand matrix by Strassen-Winograd algorithm */
1.4 saito 486: /* s1=A21+A22 */
487: addmat(vl,a21,a22,&s1);
488:
489: /* s2=s1-A11 */
490: submat(vl,s1,a11,&s2);
491:
492: /* t1=B12-B11 */
493: submat(vl, b12, b11, &t1);
494:
495: /* t2=B22-t1 */
496: submat(vl, b22, t1, &t2);
497:
498: /* u=(A11-A21)*(B22-B12) */
499: submat(vl, a11, a21, &ans1);
500: submat(vl, b22, b12, &ans2);
501: mulmatmat(vl, ans1, ans2, &u1);
502:
503: /* v=s1*t1 */
504: mulmatmat(vl, s1, t1, &v1);
505:
506: /* w=A11*B11+s2*t2 */
507: mulmatmat(vl, a11, b11, &ans1);
508: mulmatmat(vl, s2, t2, &ans2);
509: addmat(vl, ans1, ans2, &w1);
510:
511: /* C11 = A11*B11+A12*B21 */
512: mulmatmat(vl, a12, b21, &ans2);
513: addmat(vl, ans1, ans2, &c11);
514:
515: /* C12 = w1+v1+(A12-s2)*B22 */
516: submat(vl, a12, s2, &ans1);
517: mulmatmat(vl, ans1, b22, &ans2);
518: addmat(vl, w1, v1, &ans1);
519: addmat(vl, ans1, ans2, &c12);
520:
521: /* C21 = w1+u1+A22*(B21-t2) */
522: submat(vl, b21, t2, &ans1);
523: mulmatmat(vl, a22, ans1, &ans2);
1.6 saito 524: addmat(vl, w1, u1, &ans1);
525: addmat(vl, ans1, ans2, &c21);
526:
527: /* C22 = w1 + u1 + v1 */
528: addmat(vl, ans1, v1, &c22);
529: }
530:
531: for(i =0; i<c11->row; i++) {
532: for ( j=0; j < c11->col; j++) {
533: t->body[i][j] = c11->body[i][j];
534: }
535: }
536: if (pflag1 == 0) {
537: k = c21->row;
538: } else {
539: k = c21->row - 1;
540: }
541: for(i =0; i<k; i++) {
542: for ( j=0; j < c21->col; j++) {
543: t->body[i+c11->row][j] = c21->body[i][j];
544: }
545: }
546: if (pflag2 == 0) {
547: h = c12->col;
548: } else {
549: h = c12->col -1;
550: }
551: for(i =0; i<c12->row; i++) {
1.4 saito 552: for ( j=0; j < k; j++) {
553: t->body[i][j+c11->col] = c12->body[i][j];
554: }
555: }
556: if (pflag1 == 0) {
557: k = c22->row;
558: } else {
559: k = c22->row -1;
560: }
561: if (pflag2 == 0) {
562: h = c22->col;
563: } else {
564: h = c22->col - 1;
565: }
566: for(i =0; i<k; i++) {
567: for ( j=0; j < h; j++) {
568: t->body[i+c11->row][j+c11->col] = c22->body[i][j];
569: }
570: }
571: *c = t;
572: }
573:
1.11 saito 574: void mulmatmat_miser(vl,a,b,c,ar0,ac0,ar1,ac1,br0,bc0,br1,bc1)
575: VL vl;
576: MAT a,b,*c;
577: int ar0, ac0, ar1, ac1, br0, bc0, br1, bc1;
578: {
579: int arow,bcol,i,j,k,m, h;
580: MAT t, a11, a12, a21, a22;
581: MAT p, b11, b12, b21, b22;
582: MAT ans1, ans2, c11, c12, c21, c22;
583: MAT s1, s2, t1, t2, u1, v1, w1;
584: pointer s,u,v;
585: pointer *ab,*tb, *bb;
586: int a1row, a1col;
587: int b1row, b1col;
588: int pflag1, pflag2;
1.4 saito 589:
1.11 saito 590: arow = ar1-ar0 + 1; m = ac1-ac0 + 1; bcol = bc1 - bc0 + 1;
591: /* mismach col and row */
592: if ( m != br1-br0 + 1 ) {
593: *c = 0; error("mulmat : size mismatch");
594: }
595: else {
596: pflag1 = 0; pflag2 = 0;
597: MKMAT(t,arow,bcol);
598: /* StrassenSize == 0 or matrix size less then StrassenSize,
599: then calc cannonical algorithm. */
600: if((StrassenSize == 0)||(arow<=StrassenSize || m <= StrassenSize) || (m<=StrassenSize || bcol <= StrassenSize)) {
601: for ( i = 0; i < arow; i++ ) {
602: if (i+ar0 > a->row-1) {
603: ab = NULL;
604: } else {
605: ab = BDY(a)[i+ar0];
606: }
607: tb = BDY(t)[i];
608: for ( j = 0; j < bcol; j++ ) {
609: for ( k = 0, s = 0; k < m; k++ ) {
610: if (k+br0 > b->row-1) {
611: bb = NULL;
612: } else {
613: bb = BDY(b)[k+br0];
614: }
615: if ((ab == NULL || k+ac0 > a->col-1) && (bb == NULL || j+bc0 > b->col-1)) {
616: arf_mul(vl,NULL,NULL,(Obj *)&u);
617: } else if ((ab != NULL && k+ac0 <= a->col-1) && (bb == NULL || j+bc0 > b->col-1)){
618: arf_mul(vl,(Obj)ab[k+ac0],NULL,(Obj *)&u);
619: } else if ((ab == NULL || k+ac0 > a->col-1) && (bb != NULL && j+bc0 <= b->col-1)) {
620: arf_mul(vl,NULL,(Obj)bb[j+bc0],(Obj *)&u);
621: } else {
622: arf_mul(vl,(Obj)ab[k+ac0],(Obj)bb[j+bc0],(Obj *)&u);
623: }
624: arf_add(vl,(Obj)s,(Obj)u,(Obj *)&v);
625: s = v;
626: }
627: tb[j] = s;
628: }
629: }
630: *c = t;
631: return;
632:
633: }
634: /* padding odd col and row to even number for zero */
635: i = arow/2;
636: j = arow - i;
637: if (i != j) {
638: arow++;
639: pflag1 = 1;
640: }
641: i = m/2;
642: j = m - i;
643: if (i != j) {
644: m++;
645: pflag2 = 1;
646: }
647:
648: i = bcol/2;
649: j = bcol - i;
650: if (i != j) {
651: bcol++;
652: }
653:
654: /* split matrix A and B */
655: a1row = arow/2; a1col = m/2;
656: b1row = m/2; b1col = bcol/2;
657:
658: /* expand matrix by Strassen-Winograd algorithm */
659: /* s1=A21+A22 */
660: addmat_miser(vl,a,a,&s1, ar0 + a1row, ac0, ar0 + arow -1, ac0 + a1col-1, ar0 + a1row, ac0 + a1col, ar0 + arow -1, ac0 + m-1);
661:
662: /* s2=s1-A11 */
663: submat_miser(vl,s1,a,&s2, 0,0, s1->row-1, s1->col-1, ar0, ac0, ar0 + a1row-1, ac0 + a1col-1);
664:
665: /* t1=B12-B11 */
666: submat_miser(vl, b, b, &t1, br0, bc0 + b1col, br0 + b1row-1, bc0 + bcol - 1, br0,bc0,br0 + b1row-1, bc0 + b1col-1);
667:
668: /* t2=B22-t1 */
669: submat_miser(vl, b, t1, &t2, br0 + b1row, bc0 + b1col, br0 + m-1, bc0 + bcol-1, 0,0,t1->row-1, t1->col-1);
670:
671: /* u=(A11-A21)*(B22-B12) */
672: submat_miser(vl, a, a, &ans1, ar0, ac0, ar0 + a1row-1,ac0 + a1col-1, ar0 + a1row, ac0, ar0 + arow-1, ac0 + a1col-1);
673: submat_miser(vl, b, b, &ans2, br0 + b1row, bc0 + b1col, br0 + m-1, bc0 + bcol-1, br0, bc0 + b1col, br0 + b1row-1, bc0 + bcol-1);
674: mulmatmat_miser(vl, ans1, ans2, &u1, 0, 0, ans1->row -1, ans1->col-1, 0, 0, ans2->row -1, ans2->col-1);
675:
676: /* v=s1*t1 */
677: mulmatmat_miser(vl, s1, t1, &v1, 0, 0, s1->row -1, s1->col-1, 0, 0, t1->row -1, t1->col-1);
678:
679: /* w=A11*B11+s2*t2 */
680: mulmatmat_miser(vl, a, b, &ans1, ar0, ac0, ar0 + a1row-1,ac0 + a1col-1, br0, bc0, br0 + b1row-1,bc0 + b1col-1);
681: mulmatmat_miser(vl, s2, t2, &ans2, 0, 0, s2->row -1, s2->col-1, 0, 0, t2->row -1, t2->col-1);
682: addmat_miser(vl, ans1, ans2, &w1, 0, 0, ans1->row -1, ans1->col-1, 0, 0, ans2->row -1, ans2->col-1);
683:
684: /* C11 = A11*B11+A12*B21 */
685: mulmatmat_miser(vl, a, b, &ans2, ar0, ac0 + a1col, ar0 + a1row-1, ac0 + m-1, br0 + b1row, bc0 + 0, br0 + m-1, bc0 + b1col-1);
686: addmat_miser(vl, ans1, ans2, &c11, 0, 0, ans1->row -1, ans1->col -1, 0, 0, ans2->row -1, ans2->col-1);
687:
688: /* C12 = w1+v1+(A12-s2)*B22 */
689: submat_miser(vl, a, s2, &ans1, ar0, ac0 + a1col, ar0 + a1row-1, ac0 + m-1, 0, 0, s2->row -1, s2->col -1);
690: mulmatmat_miser(vl, ans1, b, &ans2, 0, 0, ans1->row -1, ans1->col -1, br0 + b1row, bc0 + b1col, br0 + m-1, bc0 + bcol-1);
691: addmat_miser(vl, w1, v1, &ans1, 0, 0, w1->row -1, w1->col -1, 0,0, v1->row-1, v1->col -1);
692: addmat_miser(vl, ans1, ans2, &c12, 0, 0, ans1->row -1, ans1->col -1, 0, 0, ans2->row -1, ans2->col-1);
693:
694: /* C21 = w1+u1+A22*(B21-t2) */
695: submat_miser(vl, b, t2, &ans1, br0 + b1row, bc0 + 0, br0 + m-1, bc0 + b1col-1, 0,0, t2->row-1, t2->col-1);
696: mulmatmat_miser(vl, a, ans1, &ans2, ar0 + a1row, ac0 + a1col, ar0 + arow-1, ac0 + m-1, 0, 0, ans1->row -1, ans1->col -1);
697: addmat_miser(vl, w1, u1, &ans1, 0,0,w1->row -1, w1->col-1, 0,0,u1->row -1, u1->col-1);
698: addmat_miser(vl, ans1, ans2, &c21, 0, 0, ans1->row -1, ans1->col -1, 0, 0, ans2->row -1, ans2->col-1);
699:
700: /* C22 = w1 + u1 + v1 */
701: addmat_miser(vl, ans1, v1, &c22, 0, 0, ans1->row -1, ans1->col -1, 0, 0, v1->row-1, v1->col-1);
702: }
703:
704: for(i =0; i<c11->row; i++) {
705: for ( j=0; j < c11->col; j++) {
706: t->body[i][j] = c11->body[i][j];
707: }
708: }
709: if (pflag1 == 0) {
710: k = c21->row;
711: } else {
712: k = c21->row - 1;
713: }
714: for(i =0; i<k; i++) {
715: for ( j=0; j < c21->col; j++) {
716: t->body[i+c11->row][j] = c21->body[i][j];
717: }
718: }
719: if (pflag2 == 0) {
720: h = c12->col;
721: } else {
722: h = c12->col -1;
723: }
724: for(i =0; i<c12->row; i++) {
725: for ( j=0; j < k; j++) {
726: t->body[i][j+c11->col] = c12->body[i][j];
727: }
728: }
729: if (pflag1 == 0) {
730: k = c22->row;
731: } else {
732: k = c22->row -1;
733: }
734: if (pflag2 == 0) {
735: h = c22->col;
736: } else {
737: h = c22->col - 1;
738: }
739: for(i =0; i<k; i++) {
740: for ( j=0; j < h; j++) {
741: t->body[i+c11->row][j+c11->col] = c22->body[i][j];
742: }
743: }
744: *c = t;
745: }
1.1 noro 746:
747: void mulmatvect(vl,a,b,c)
748: VL vl;
749: MAT a;
750: VECT b;
751: VECT *c;
752: {
753: int arow,i,j,m;
754: VECT t;
755: pointer s,u,v;
756: pointer *ab;
757:
758: if ( !a || !b )
759: *c = 0;
760: else if ( a->col != b->len ) {
761: *c = 0; error("mulmatvect : size mismatch");
762: } else {
1.7 noro 763: for ( i = 0; i < b->len; i++ )
764: if ( BDY(b)[i] && OID((Obj)BDY(b)[i]) > O_R )
765: error("mulmatvect : invalid argument");
1.1 noro 766: arow = a->row; m = a->col;
767: MKVECT(t,arow);
768: for ( i = 0; i < arow; i++ ) {
769: for ( j = 0, s = 0, ab = BDY(a)[i]; j < m; j++ ) {
1.9 noro 770: arf_mul(vl,(Obj)ab[j],(Obj)BDY(b)[j],(Obj *)&u); arf_add(vl,(Obj)s,(Obj)u,(Obj *)&v); s = v;
1.1 noro 771: }
772: BDY(t)[i] = s;
773: }
774: *c = t;
775: }
776: }
777:
778: void mulvectmat(vl,a,b,c)
779: VL vl;
780: VECT a;
781: MAT b;
782: VECT *c;
783: {
784: int bcol,i,j,m;
785: VECT t;
786: pointer s,u,v;
787:
788: if ( !a || !b )
789: *c = 0;
790: else if ( a->len != b->row ) {
791: *c = 0; error("mulvectmat : size mismatch");
792: } else {
1.7 noro 793: for ( i = 0; i < a->len; i++ )
794: if ( BDY(a)[i] && OID((Obj)BDY(a)[i]) > O_R )
795: error("mulvectmat : invalid argument");
1.1 noro 796: bcol = b->col; m = a->len;
797: MKVECT(t,bcol);
798: for ( j = 0; j < bcol; j++ ) {
799: for ( i = 0, s = 0; i < m; i++ ) {
1.9 noro 800: arf_mul(vl,(Obj)BDY(a)[i],(Obj)BDY(b)[i][j],(Obj *)&u); arf_add(vl,(Obj)s,(Obj)u,(Obj *)&v); s = v;
1.1 noro 801: }
802: BDY(t)[j] = s;
803: }
804: *c = t;
805: }
806: }
807:
808: int compmat(vl,a,b)
809: VL vl;
810: MAT a,b;
811: {
812: int i,j,t,row,col;
813:
814: if ( !a )
815: return b?-1:0;
816: else if ( !b )
817: return 1;
818: else if ( a->row != b->row )
819: return a->row>b->row ? 1 : -1;
820: else if (a->col != b->col )
821: return a->col > b->col ? 1 : -1;
822: else {
823: row = a->row; col = a->col;
824: for ( i = 0; i < row; i++ )
825: for ( j = 0; j < col; j++ )
1.9 noro 826: if ( t = arf_comp(vl,(Obj)BDY(a)[i][j],(Obj)BDY(b)[i][j]) )
1.1 noro 827: return t;
828: return 0;
829: }
830: }
831:
832: pointer **almat_pointer(n,m)
833: int n,m;
834: {
835: pointer **mat;
836: int i;
837:
838: mat = (pointer **)MALLOC(n*sizeof(pointer *));
839: for ( i = 0; i < n; i++ )
840: mat[i] = (pointer *)CALLOC(m,sizeof(pointer));
841: return mat;
842: }