Actual source code: matmatmult.c
1: #define PETSCMAT_DLL
3: /*
4: Defines matrix-matrix product routines for pairs of SeqAIJ matrices
5: C = A * B
6: */
8: #include src/mat/impls/aij/seq/aij.h
9: #include src/mat/utils/freespace.h
10: #include petscbt.h
11: #include src/mat/impls/dense/seq/dense.h
15: PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
16: {
20: if (scall == MAT_INITIAL_MATRIX){
21: MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
22: }
23: MatMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);
24: return(0);
25: }
30: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
31: {
32: PetscErrorCode ierr;
33: PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
34: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
35: PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci,*cj;
36: PetscInt am=A->rmap.N,bn=B->cmap.N,bm=B->rmap.N;
37: PetscInt i,j,anzi,brow,bnzj,cnzi,nlnk,*lnk,nspacedouble=0;
38: MatScalar *ca;
39: PetscBT lnkbt;
42: /* Set up */
43: /* Allocate ci array, arrays for fill computation and */
44: /* free space for accumulating nonzero column info */
45: PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);
46: ci[0] = 0;
47:
48: /* create and initialize a linked list */
49: nlnk = bn+1;
50: PetscLLCreate(bn,bn,nlnk,lnk,lnkbt);
52: /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
53: PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);
54: current_space = free_space;
56: /* Determine symbolic info for each row of the product: */
57: for (i=0;i<am;i++) {
58: anzi = ai[i+1] - ai[i];
59: cnzi = 0;
60: j = anzi;
61: aj = a->j + ai[i];
62: while (j){/* assume cols are almost in increasing order, starting from its end saves computation */
63: j--;
64: brow = *(aj + j);
65: bnzj = bi[brow+1] - bi[brow];
66: bjj = bj + bi[brow];
67: /* add non-zero cols of B into the sorted linked list lnk */
68: PetscLLAdd(bnzj,bjj,bn,nlnk,lnk,lnkbt);
69: cnzi += nlnk;
70: }
72: /* If free space is not available, make more free space */
73: /* Double the amount of total space in the list */
74: if (current_space->local_remaining<cnzi) {
75: PetscFreeSpaceGet(current_space->total_array_size,¤t_space);
76: nspacedouble++;
77: }
79: /* Copy data into free space, then initialize lnk */
80: PetscLLClean(bn,bn,cnzi,lnk,current_space->array,lnkbt);
81: current_space->array += cnzi;
82: current_space->local_used += cnzi;
83: current_space->local_remaining -= cnzi;
85: ci[i+1] = ci[i] + cnzi;
86: }
88: /* Column indices are in the list of free space */
89: /* Allocate space for cj, initialize cj, and */
90: /* destroy list of free space and other temporary array(s) */
91: PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);
92: PetscFreeSpaceContiguous(&free_space,cj);
93: PetscLLDestroy(lnk,lnkbt);
94:
95: /* Allocate space for ca */
96: PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);
97: PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));
98:
99: /* put together the new symbolic matrix */
100: MatCreateSeqAIJWithArrays(A->comm,am,bn,ci,cj,ca,C);
102: /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
103: /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
104: c = (Mat_SeqAIJ *)((*C)->data);
105: c->free_a = PETSC_TRUE;
106: c->free_ij = PETSC_TRUE;
107: c->nonew = 0;
109: if (nspacedouble){
110: PetscInfo5((*C),"nspacedouble:%D, nnz(A):%D, nnz(B):%D, fill:%G, nnz(C):%D\n",nspacedouble,ai[am],bi[bm],fill,ci[am]);
111: }
112: return(0);
113: }
118: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
119: {
121: PetscInt flops=0;
122: Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
123: Mat_SeqAIJ *b = (Mat_SeqAIJ *)B->data;
124: Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data;
125: PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
126: PetscInt am=A->rmap.N,cm=C->rmap.N;
127: PetscInt i,j,k,anzi,bnzi,cnzi,brow,nextb;
128: MatScalar *aa=a->a,*ba=b->a,*baj,*ca=c->a;
131: /* clean old values in C */
132: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
133: /* Traverse A row-wise. */
134: /* Build the ith row in C by summing over nonzero columns in A, */
135: /* the rows of B corresponding to nonzeros of A. */
136: for (i=0;i<am;i++) {
137: anzi = ai[i+1] - ai[i];
138: for (j=0;j<anzi;j++) {
139: brow = *aj++;
140: bnzi = bi[brow+1] - bi[brow];
141: bjj = bj + bi[brow];
142: baj = ba + bi[brow];
143: nextb = 0;
144: for (k=0; nextb<bnzi; k++) {
145: if (cj[k] == bjj[nextb]){ /* ccol == bcol */
146: ca[k] += (*aa)*baj[nextb++];
147: }
148: }
149: flops += 2*bnzi;
150: aa++;
151: }
152: cnzi = ci[i+1] - ci[i];
153: ca += cnzi;
154: cj += cnzi;
155: }
156: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
157: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
159: PetscLogFlops(flops);
160: return(0);
161: }
166: PetscErrorCode MatMatMultTranspose_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
170: if (scall == MAT_INITIAL_MATRIX){
171: MatMatMultTransposeSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);
172: }
173: MatMatMultTransposeNumeric_SeqAIJ_SeqAIJ(A,B,*C);
174: return(0);
175: }
179: PetscErrorCode MatMatMultTransposeSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
180: {
182: Mat At;
183: PetscInt *ati,*atj;
186: /* create symbolic At */
187: MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);
188: MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap.n,A->rmap.n,ati,atj,PETSC_NULL,&At);
190: /* get symbolic C=At*B */
191: MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);
193: /* clean up */
194: MatDestroy(At);
195: MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);
196:
197: return(0);
198: }
202: PetscErrorCode MatMatMultTransposeNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
203: {
205: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
206: PetscInt am=A->rmap.n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
207: PetscInt cm=C->rmap.n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k,flops=0;
208: MatScalar *aa=a->a,*ba,*ca=c->a,*caj;
209:
211: /* clear old values in C */
212: PetscMemzero(ca,ci[cm]*sizeof(MatScalar));
214: /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
215: for (i=0;i<am;i++) {
216: bj = b->j + bi[i];
217: ba = b->a + bi[i];
218: bnzi = bi[i+1] - bi[i];
219: anzi = ai[i+1] - ai[i];
220: for (j=0; j<anzi; j++) {
221: nextb = 0;
222: crow = *aj++;
223: cjj = cj + ci[crow];
224: caj = ca + ci[crow];
225: /* perform sparse axpy operation. Note cjj includes bj. */
226: for (k=0; nextb<bnzi; k++) {
227: if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
228: caj[k] += (*aa)*(*(ba+nextb));
229: nextb++;
230: }
231: }
232: flops += 2*bnzi;
233: aa++;
234: }
235: }
237: /* Assemble the final matrix and clean up */
238: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
239: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
240: PetscLogFlops(flops);
241: return(0);
242: }
246: PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
247: {
251: if (scall == MAT_INITIAL_MATRIX){
252: MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);
253: }
254: MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);
255: return(0);
256: }
260: PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
261: {
265: MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);
266: return(0);
267: }
271: PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
272: {
273: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data;
275: PetscScalar *b,*c,r1,r2,r3,r4,*aa,*b1,*b2,*b3,*b4;
276: PetscInt cm=C->rmap.n, cn=B->cmap.n, bm=B->rmap.n, col, i,j,n,*aj, am = A->rmap.n;
277: PetscInt am2 = 2*am, am3 = 3*am, bm4 = 4*bm,colam;
280: if (!cm || !cn) return(0);
281: if (bm != A->cmap.n) SETERRQ2(PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap.n,bm);
282: if (A->rmap.n != C->rmap.n) SETERRQ2(PETSC_ERR_ARG_SIZ,"Number rows in C %D not equal rows in A %D\n",C->rmap.n,A->rmap.n);
283: if (B->cmap.n != C->cmap.n) SETERRQ2(PETSC_ERR_ARG_SIZ,"Number columns in B %D not equal columns in C %D\n",B->cmap.n,C->cmap.n);
284: MatGetArray(B,&b);
285: MatGetArray(C,&c);
286: b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
287: for (col=0; col<cn-4; col += 4){ /* over columns of C */
288: colam = col*am;
289: for (i=0; i<am; i++) { /* over rows of C in those columns */
290: r1 = r2 = r3 = r4 = 0.0;
291: n = a->i[i+1] - a->i[i];
292: aj = a->j + a->i[i];
293: aa = a->a + a->i[i];
294: for (j=0; j<n; j++) {
295: r1 += (*aa)*b1[*aj];
296: r2 += (*aa)*b2[*aj];
297: r3 += (*aa)*b3[*aj];
298: r4 += (*aa++)*b4[*aj++];
299: }
300: c[colam + i] = r1;
301: c[colam + am + i] = r2;
302: c[colam + am2 + i] = r3;
303: c[colam + am3 + i] = r4;
304: }
305: b1 += bm4;
306: b2 += bm4;
307: b3 += bm4;
308: b4 += bm4;
309: }
310: for (;col<cn; col++){ /* over extra columns of C */
311: for (i=0; i<am; i++) { /* over rows of C in those columns */
312: r1 = 0.0;
313: n = a->i[i+1] - a->i[i];
314: aj = a->j + a->i[i];
315: aa = a->a + a->i[i];
317: for (j=0; j<n; j++) {
318: r1 += (*aa++)*b1[*aj++];
319: }
320: c[col*am + i] = r1;
321: }
322: b1 += bm;
323: }
324: PetscLogFlops(cn*(2*a->nz - A->rmap.n));
325: MatRestoreArray(B,&b);
326: MatRestoreArray(C,&c);
327: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
328: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
329: return(0);
330: }
332: /*
333: Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
334: */
337: PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
338: {
339: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data;
341: PetscScalar *b,*c,r1,r2,r3,r4,*aa,*b1,*b2,*b3,*b4;
342: PetscInt cm=C->rmap.n, cn=B->cmap.n, bm=B->rmap.n, col, i,j,n,*aj, am = A->rmap.n,*ii,arm;
343: PetscInt am2 = 2*am, am3 = 3*am, bm4 = 4*bm,colam,*ridx;
346: if (!cm || !cn) return(0);
347: MatGetArray(B,&b);
348: MatGetArray(C,&c);
349: b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
351: if (a->compressedrow.use){ /* use compressed row format */
352: for (col=0; col<cn-4; col += 4){ /* over columns of C */
353: colam = col*am;
354: arm = a->compressedrow.nrows;
355: ii = a->compressedrow.i;
356: ridx = a->compressedrow.rindex;
357: for (i=0; i<arm; i++) { /* over rows of C in those columns */
358: r1 = r2 = r3 = r4 = 0.0;
359: n = ii[i+1] - ii[i];
360: aj = a->j + ii[i];
361: aa = a->a + ii[i];
362: for (j=0; j<n; j++) {
363: r1 += (*aa)*b1[*aj];
364: r2 += (*aa)*b2[*aj];
365: r3 += (*aa)*b3[*aj];
366: r4 += (*aa++)*b4[*aj++];
367: }
368: c[colam + ridx[i]] += r1;
369: c[colam + am + ridx[i]] += r2;
370: c[colam + am2 + ridx[i]] += r3;
371: c[colam + am3 + ridx[i]] += r4;
372: }
373: b1 += bm4;
374: b2 += bm4;
375: b3 += bm4;
376: b4 += bm4;
377: }
378: for (;col<cn; col++){ /* over extra columns of C */
379: colam = col*am;
380: arm = a->compressedrow.nrows;
381: ii = a->compressedrow.i;
382: ridx = a->compressedrow.rindex;
383: for (i=0; i<arm; i++) { /* over rows of C in those columns */
384: r1 = 0.0;
385: n = ii[i+1] - ii[i];
386: aj = a->j + ii[i];
387: aa = a->a + ii[i];
389: for (j=0; j<n; j++) {
390: r1 += (*aa++)*b1[*aj++];
391: }
392: c[col*am + ridx[i]] += r1;
393: }
394: b1 += bm;
395: }
396: } else {
397: for (col=0; col<cn-4; col += 4){ /* over columns of C */
398: colam = col*am;
399: for (i=0; i<am; i++) { /* over rows of C in those columns */
400: r1 = r2 = r3 = r4 = 0.0;
401: n = a->i[i+1] - a->i[i];
402: aj = a->j + a->i[i];
403: aa = a->a + a->i[i];
404: for (j=0; j<n; j++) {
405: r1 += (*aa)*b1[*aj];
406: r2 += (*aa)*b2[*aj];
407: r3 += (*aa)*b3[*aj];
408: r4 += (*aa++)*b4[*aj++];
409: }
410: c[colam + i] += r1;
411: c[colam + am + i] += r2;
412: c[colam + am2 + i] += r3;
413: c[colam + am3 + i] += r4;
414: }
415: b1 += bm4;
416: b2 += bm4;
417: b3 += bm4;
418: b4 += bm4;
419: }
420: for (;col<cn; col++){ /* over extra columns of C */
421: for (i=0; i<am; i++) { /* over rows of C in those columns */
422: r1 = 0.0;
423: n = a->i[i+1] - a->i[i];
424: aj = a->j + a->i[i];
425: aa = a->a + a->i[i];
427: for (j=0; j<n; j++) {
428: r1 += (*aa++)*b1[*aj++];
429: }
430: c[col*am + i] += r1;
431: }
432: b1 += bm;
433: }
434: }
435: PetscLogFlops(cn*2*a->nz);
436: MatRestoreArray(B,&b);
437: MatRestoreArray(C,&c);
438: return(0);
439: }