xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 84df9cb40eca90ea9b18a456fab7a4ecc7f6c1a4)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
4           C = A * B
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <petscbt.h>
10 #include <../src/mat/impls/dense/seq/dense.h> /*I "petscmat.h" I*/
11 
12 EXTERN_C_BEGIN
13 #undef __FUNCT__
14 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
15 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
16 {
17   PetscErrorCode ierr;
18 
19   PetscFunctionBegin;
20   if (scall == MAT_INITIAL_MATRIX){
21     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
22   }
23   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
24   PetscFunctionReturn(0);
25 }
26 EXTERN_C_END
27 
28 #undef __FUNCT__
29 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
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;
40   PetscReal          afill;
41 
42   PetscFunctionBegin;
43   /* Set up */
44   /* Allocate ci array, arrays for fill computation and */
45   /* free space for accumulating nonzero column info */
46   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
47   ci[0] = 0;
48 
49   /* create and initialize a linked list */
50   nlnk = bn+1;
51   ierr = PetscLLCreate(bn,bn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
52 
53   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
54   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
55   current_space = free_space;
56 
57   /* Determine symbolic info for each row of the product: */
58   for (i=0;i<am;i++) {
59     anzi = ai[i+1] - ai[i];
60     cnzi = 0;
61     j    = anzi;
62     aj   = a->j + ai[i];
63     while (j){/* assume cols are almost in increasing order, starting from its end saves computation */
64       j--;
65       brow = *(aj + j);
66       bnzj = bi[brow+1] - bi[brow];
67       bjj  = bj + bi[brow];
68       /* add non-zero cols of B into the sorted linked list lnk */
69       ierr = PetscLLAdd(bnzj,bjj,bn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
70       cnzi += nlnk;
71     }
72 
73     /* If free space is not available, make more free space */
74     /* Double the amount of total space in the list */
75     if (current_space->local_remaining<cnzi) {
76       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
77       nspacedouble++;
78     }
79 
80     /* Copy data into free space, then initialize lnk */
81     ierr = PetscLLClean(bn,bn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
82     current_space->array           += cnzi;
83     current_space->local_used      += cnzi;
84     current_space->local_remaining -= cnzi;
85 
86     ci[i+1] = ci[i] + cnzi;
87   }
88 
89   /* Column indices are in the list of free space */
90   /* Allocate space for cj, initialize cj, and */
91   /* destroy list of free space and other temporary array(s) */
92   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
93   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
94   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
95 
96   /* Allocate space for ca */
97   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
98   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
99 
100   /* put together the new symbolic matrix */
101   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
102 
103   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
104   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
105   c = (Mat_SeqAIJ *)((*C)->data);
106   c->free_a   = PETSC_TRUE;
107   c->free_ij  = PETSC_TRUE;
108   c->nonew    = 0;
109 
110   /* set MatInfo */
111   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
112   if (afill < 1.0) afill = 1.0;
113   c->maxnz                     = ci[am];
114   c->nz                        = ci[am];
115   (*C)->info.mallocs           = nspacedouble;
116   (*C)->info.fill_ratio_given  = fill;
117   (*C)->info.fill_ratio_needed = afill;
118 
119 #if defined(PETSC_USE_INFO)
120   if (ci[am]) {
121     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
122     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
123   } else {
124     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
125   }
126 #endif
127   PetscFunctionReturn(0);
128 }
129 
130 
131 #undef __FUNCT__
132 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
133 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
134 {
135   PetscErrorCode ierr;
136   PetscLogDouble flops=0.0;
137   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
138   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
139   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
140   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
141   PetscInt       am=A->rmap->N,cm=C->rmap->N;
142   PetscInt       i,j,k,anzi,bnzi,cnzi,brow,nextb;
143   MatScalar      *aa=a->a,*ba=b->a,*baj,*ca=c->a;
144 
145   PetscFunctionBegin;
146   /* clean old values in C */
147   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
148   /* Traverse A row-wise. */
149   /* Build the ith row in C by summing over nonzero columns in A, */
150   /* the rows of B corresponding to nonzeros of A. */
151   for (i=0;i<am;i++) {
152     anzi = ai[i+1] - ai[i];
153     for (j=0;j<anzi;j++) {
154       brow = *aj++;
155       bnzi = bi[brow+1] - bi[brow];
156       bjj  = bj + bi[brow];
157       baj  = ba + bi[brow];
158       nextb = 0;
159       for (k=0; nextb<bnzi; k++) {
160         if (cj[k] == bjj[nextb]){ /* ccol == bcol */
161           ca[k] += (*aa)*baj[nextb++];
162         }
163       }
164       flops += 2*bnzi;
165       aa++;
166     }
167     cnzi = ci[i+1] - ci[i];
168     ca += cnzi;
169     cj += cnzi;
170   }
171   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
172   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
173 
174   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
175   PetscFunctionReturn(0);
176 }
177 
178 
179 #undef __FUNCT__
180 #define __FUNCT__ "MatMatMultTranspose_SeqAIJ_SeqAIJ"
181 PetscErrorCode MatMatMultTranspose_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
182   PetscErrorCode ierr;
183 
184   PetscFunctionBegin;
185   if (scall == MAT_INITIAL_MATRIX){
186     ierr = MatMatMultTransposeSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
187   }
188   ierr = MatMatMultTransposeNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
189   PetscFunctionReturn(0);
190 }
191 
192 #undef __FUNCT__
193 #define __FUNCT__ "MatMatMultTransposeSymbolic_SeqAIJ_SeqAIJ"
194 PetscErrorCode MatMatMultTransposeSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
195 {
196   PetscErrorCode ierr;
197   Mat            At;
198   PetscInt       *ati,*atj;
199 
200   PetscFunctionBegin;
201   /* create symbolic At */
202   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
203   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
204 
205   /* get symbolic C=At*B */
206   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
207 
208   /* clean up */
209   ierr = MatDestroy(&At);CHKERRQ(ierr);
210   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
211   PetscFunctionReturn(0);
212 }
213 
214 #undef __FUNCT__
215 #define __FUNCT__ "MatMatMultTransposeNumeric_SeqAIJ_SeqAIJ"
216 PetscErrorCode MatMatMultTransposeNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
217 {
218   PetscErrorCode ierr;
219   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
220   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
221   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
222   PetscLogDouble flops=0.0;
223   MatScalar      *aa=a->a,*ba,*ca=c->a,*caj;
224 
225   PetscFunctionBegin;
226   /* clear old values in C */
227   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
228 
229   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
230   for (i=0;i<am;i++) {
231     bj   = b->j + bi[i];
232     ba   = b->a + bi[i];
233     bnzi = bi[i+1] - bi[i];
234     anzi = ai[i+1] - ai[i];
235     for (j=0; j<anzi; j++) {
236       nextb = 0;
237       crow  = *aj++;
238       cjj   = cj + ci[crow];
239       caj   = ca + ci[crow];
240       /* perform sparse axpy operation.  Note cjj includes bj. */
241       for (k=0; nextb<bnzi; k++) {
242         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
243           caj[k] += (*aa)*(*(ba+nextb));
244           nextb++;
245         }
246       }
247       flops += 2*bnzi;
248       aa++;
249     }
250   }
251 
252   /* Assemble the final matrix and clean up */
253   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
254   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
255   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
256   PetscFunctionReturn(0);
257 }
258 
259 EXTERN_C_BEGIN
260 #undef __FUNCT__
261 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
262 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
263 {
264   PetscErrorCode ierr;
265 
266   PetscFunctionBegin;
267   if (scall == MAT_INITIAL_MATRIX){
268     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
269   }
270   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
271   PetscFunctionReturn(0);
272 }
273 EXTERN_C_END
274 
275 #undef __FUNCT__
276 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
277 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
278 {
279   PetscErrorCode ierr;
280 
281   PetscFunctionBegin;
282   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
283   PetscFunctionReturn(0);
284 }
285 
286 #undef __FUNCT__
287 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
288 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
289 {
290   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
291   PetscErrorCode ierr;
292   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
293   MatScalar      *aa;
294   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
295   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
296 
297   PetscFunctionBegin;
298   if (!cm || !cn) PetscFunctionReturn(0);
299   if (bm != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap->n,bm);
300   if (A->rmap->n != C->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number rows in C %D not equal rows in A %D\n",C->rmap->n,A->rmap->n);
301   if (B->cmap->n != C->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in B %D not equal columns in C %D\n",B->cmap->n,C->cmap->n);
302   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
303   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
304   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
305   for (col=0; col<cn-4; col += 4){  /* over columns of C */
306     colam = col*am;
307     for (i=0; i<am; i++) {        /* over rows of C in those columns */
308       r1 = r2 = r3 = r4 = 0.0;
309       n   = a->i[i+1] - a->i[i];
310       aj  = a->j + a->i[i];
311       aa  = a->a + a->i[i];
312       for (j=0; j<n; j++) {
313         r1 += (*aa)*b1[*aj];
314         r2 += (*aa)*b2[*aj];
315         r3 += (*aa)*b3[*aj];
316         r4 += (*aa++)*b4[*aj++];
317       }
318       c[colam + i]       = r1;
319       c[colam + am + i]  = r2;
320       c[colam + am2 + i] = r3;
321       c[colam + am3 + i] = r4;
322     }
323     b1 += bm4;
324     b2 += bm4;
325     b3 += bm4;
326     b4 += bm4;
327   }
328   for (;col<cn; col++){     /* over extra columns of C */
329     for (i=0; i<am; i++) {  /* over rows of C in those columns */
330       r1 = 0.0;
331       n   = a->i[i+1] - a->i[i];
332       aj  = a->j + a->i[i];
333       aa  = a->a + a->i[i];
334 
335       for (j=0; j<n; j++) {
336         r1 += (*aa++)*b1[*aj++];
337       }
338       c[col*am + i]     = r1;
339     }
340     b1 += bm;
341   }
342   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
343   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
344   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
345   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
346   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
347   PetscFunctionReturn(0);
348 }
349 
350 /*
351    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
352 */
353 #undef __FUNCT__
354 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
355 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
356 {
357   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
358   PetscErrorCode ierr;
359   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
360   MatScalar      *aa;
361   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
362   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
363 
364   PetscFunctionBegin;
365   if (!cm || !cn) PetscFunctionReturn(0);
366   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
367   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
368   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
369 
370   if (a->compressedrow.use){ /* use compressed row format */
371     for (col=0; col<cn-4; col += 4){  /* over columns of C */
372       colam = col*am;
373       arm   = a->compressedrow.nrows;
374       ii    = a->compressedrow.i;
375       ridx  = a->compressedrow.rindex;
376       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
377 	r1 = r2 = r3 = r4 = 0.0;
378 	n   = ii[i+1] - ii[i];
379 	aj  = a->j + ii[i];
380 	aa  = a->a + ii[i];
381 	for (j=0; j<n; j++) {
382 	  r1 += (*aa)*b1[*aj];
383 	  r2 += (*aa)*b2[*aj];
384 	  r3 += (*aa)*b3[*aj];
385 	  r4 += (*aa++)*b4[*aj++];
386 	}
387 	c[colam       + ridx[i]] += r1;
388 	c[colam + am  + ridx[i]] += r2;
389 	c[colam + am2 + ridx[i]] += r3;
390 	c[colam + am3 + ridx[i]] += r4;
391       }
392       b1 += bm4;
393       b2 += bm4;
394       b3 += bm4;
395       b4 += bm4;
396     }
397     for (;col<cn; col++){     /* over extra columns of C */
398       colam = col*am;
399       arm   = a->compressedrow.nrows;
400       ii    = a->compressedrow.i;
401       ridx  = a->compressedrow.rindex;
402       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
403 	r1 = 0.0;
404 	n   = ii[i+1] - ii[i];
405 	aj  = a->j + ii[i];
406 	aa  = a->a + ii[i];
407 
408 	for (j=0; j<n; j++) {
409 	  r1 += (*aa++)*b1[*aj++];
410 	}
411 	c[col*am + ridx[i]] += r1;
412       }
413       b1 += bm;
414     }
415   } else {
416     for (col=0; col<cn-4; col += 4){  /* over columns of C */
417       colam = col*am;
418       for (i=0; i<am; i++) {        /* over rows of C in those columns */
419 	r1 = r2 = r3 = r4 = 0.0;
420 	n   = a->i[i+1] - a->i[i];
421 	aj  = a->j + a->i[i];
422 	aa  = a->a + a->i[i];
423 	for (j=0; j<n; j++) {
424 	  r1 += (*aa)*b1[*aj];
425 	  r2 += (*aa)*b2[*aj];
426 	  r3 += (*aa)*b3[*aj];
427 	  r4 += (*aa++)*b4[*aj++];
428 	}
429 	c[colam + i]       += r1;
430 	c[colam + am + i]  += r2;
431 	c[colam + am2 + i] += r3;
432 	c[colam + am3 + i] += r4;
433       }
434       b1 += bm4;
435       b2 += bm4;
436       b3 += bm4;
437       b4 += bm4;
438     }
439     for (;col<cn; col++){     /* over extra columns of C */
440       for (i=0; i<am; i++) {  /* over rows of C in those columns */
441 	r1 = 0.0;
442 	n   = a->i[i+1] - a->i[i];
443 	aj  = a->j + a->i[i];
444 	aa  = a->a + a->i[i];
445 
446 	for (j=0; j<n; j++) {
447 	  r1 += (*aa++)*b1[*aj++];
448 	}
449 	c[col*am + i]     += r1;
450       }
451       b1 += bm;
452     }
453   }
454   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
455   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
456   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
457   PetscFunctionReturn(0);
458 }
459