xref: /petsc/src/mat/impls/aij/seq/matptap.c (revision d736bfeb4d37a01fcbdf00fe73fb60d6f0ba2142) 
1 #define PETSCMAT_DLL
2 
3 /*
4   Defines projective product routines where A is a SeqAIJ matrix
5           C = P^T * A * P
6 */
7 
8 #include "../src/mat/impls/aij/seq/aij.h"   /*I "petscmat.h" I*/
9 #include "../src/mat/utils/freespace.h"
10 #include "petscbt.h"
11 
12 #undef __FUNCT__
13 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ"
14 PetscErrorCode MatPtAPSymbolic_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
15 {
16   PetscErrorCode ierr;
17 
18   PetscFunctionBegin;
19   if (!P->ops->ptapsymbolic_seqaij) SETERRQ2(((PetscObject)A)->comm,PETSC_ERR_SUP,"Not implemented for A=%s and P=%s",((PetscObject)A)->type_name,((PetscObject)P)->type_name);
20   ierr = (*P->ops->ptapsymbolic_seqaij)(A,P,fill,C);CHKERRQ(ierr);
21   PetscFunctionReturn(0);
22 }
23 
24 #undef __FUNCT__
25 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ"
26 PetscErrorCode MatPtAPNumeric_SeqAIJ(Mat A,Mat P,Mat C)
27 {
28   PetscErrorCode ierr;
29 
30   PetscFunctionBegin;
31   if (!P->ops->ptapnumeric_seqaij) SETERRQ2(((PetscObject)A)->comm,PETSC_ERR_SUP,"Not implemented for A=%s and P=%s",((PetscObject)A)->type_name,((PetscObject)P)->type_name);
32   ierr = (*P->ops->ptapnumeric_seqaij)(A,P,C);CHKERRQ(ierr);
33   PetscFunctionReturn(0);
34 }
35 
36 #undef __FUNCT__
37 #define __FUNCT__ "MatPtAPSymbolic_SeqAIJ_SeqAIJ"
38 PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
39 {
40   PetscErrorCode     ierr;
41   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
42   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
43   PetscInt           *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
44   PetscInt           *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
45   PetscInt           an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N;
46   PetscInt           i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
47   MatScalar          *ca;
48   PetscBT            lnkbt;
49 
50   PetscFunctionBegin;
51   /* Get ij structure of P^T */
52   ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
53   ptJ=ptj;
54 
55   /* Allocate ci array, arrays for fill computation and */
56   /* free space for accumulating nonzero column info */
57   ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
58   ci[0] = 0;
59 
60   ierr = PetscMalloc((2*an+1)*sizeof(PetscInt),&ptadenserow);CHKERRQ(ierr);
61   ierr = PetscMemzero(ptadenserow,(2*an+1)*sizeof(PetscInt));CHKERRQ(ierr);
62   ptasparserow = ptadenserow  + an;
63 
64   /* create and initialize a linked list */
65   nlnk = pn+1;
66   ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
67 
68   /* Set initial free space to be fill*nnz(A). */
69   /* This should be reasonable if sparsity of PtAP is similar to that of A. */
70   ierr          = PetscFreeSpaceGet((PetscInt)(fill*ai[am]),&free_space);
71   current_space = free_space;
72 
73   /* Determine symbolic info for each row of C: */
74   for (i=0;i<pn;i++) {
75     ptnzi  = pti[i+1] - pti[i];
76     ptanzi = 0;
77     /* Determine symbolic row of PtA: */
78     for (j=0;j<ptnzi;j++) {
79       arow = *ptJ++;
80       anzj = ai[arow+1] - ai[arow];
81       ajj  = aj + ai[arow];
82       for (k=0;k<anzj;k++) {
83         if (!ptadenserow[ajj[k]]) {
84           ptadenserow[ajj[k]]    = -1;
85           ptasparserow[ptanzi++] = ajj[k];
86         }
87       }
88     }
89     /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
90     ptaj = ptasparserow;
91     cnzi   = 0;
92     for (j=0;j<ptanzi;j++) {
93       prow = *ptaj++;
94       pnzj = pi[prow+1] - pi[prow];
95       pjj  = pj + pi[prow];
96       /* add non-zero cols of P into the sorted linked list lnk */
97       ierr = PetscLLAdd(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
98       cnzi += nlnk;
99     }
100 
101     /* If free space is not available, make more free space */
102     /* Double the amount of total space in the list */
103     if (current_space->local_remaining<cnzi) {
104       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
105       nspacedouble++;
106     }
107 
108     /* Copy data into free space, and zero out denserows */
109     ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
110     current_space->array           += cnzi;
111     current_space->local_used      += cnzi;
112     current_space->local_remaining -= cnzi;
113 
114     for (j=0;j<ptanzi;j++) {
115       ptadenserow[ptasparserow[j]] = 0;
116     }
117     /* Aside: Perhaps we should save the pta info for the numerical factorization. */
118     /*        For now, we will recompute what is needed. */
119     ci[i+1] = ci[i] + cnzi;
120   }
121   /* nnz is now stored in ci[ptm], column indices are in the list of free space */
122   /* Allocate space for cj, initialize cj, and */
123   /* destroy list of free space and other temporary array(s) */
124   ierr = PetscMalloc((ci[pn]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
125   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
126   ierr = PetscFree(ptadenserow);CHKERRQ(ierr);
127   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
128 
129   /* Allocate space for ca */
130   ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
131   ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr);
132 
133   /* put together the new matrix */
134   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,pn,pn,ci,cj,ca,C);CHKERRQ(ierr);
135 
136   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
137   /* Since these are PETSc arrays, change flags to free them as necessary. */
138   c = (Mat_SeqAIJ *)((*C)->data);
139   c->free_a  = PETSC_TRUE;
140   c->free_ij = PETSC_TRUE;
141   c->nonew   = 0;
142 
143   /* Clean up. */
144   ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
145 #if defined(PETSC_USE_INFO)
146   if (ci[pn] != 0) {
147     PetscReal afill = ((PetscReal)ci[pn])/ai[am];
148     if (afill < 1.0) afill = 1.0;
149     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
150     ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr);
151   } else {
152     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
153   }
154 #endif
155   PetscFunctionReturn(0);
156 }
157 
158 #undef __FUNCT__
159 #define __FUNCT__ "MatPtAPNumeric_SeqAIJ_SeqAIJ"
160 PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
161 {
162   PetscErrorCode ierr;
163   PetscLogDouble flops=0.0;
164   Mat_SeqAIJ     *a  = (Mat_SeqAIJ *) A->data;
165   Mat_SeqAIJ     *p  = (Mat_SeqAIJ *) P->data;
166   Mat_SeqAIJ     *c  = (Mat_SeqAIJ *) C->data;
167   PetscInt       *ai=a->i,*aj=a->j,*apj,*apjdense,*pi=p->i,*pj=p->j,*pJ=p->j,*pjj;
168   PetscInt       *ci=c->i,*cj=c->j,*cjj;
169   PetscInt       am=A->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
170   PetscInt       i,j,k,anzi,pnzi,apnzj,nextap,pnzj,prow,crow;
171   MatScalar      *aa=a->a,*apa,*pa=p->a,*pA=p->a,*paj,*ca=c->a,*caj;
172 
173   PetscFunctionBegin;
174   /* Allocate temporary array for storage of one row of A*P */
175   ierr = PetscMalloc(cn*(sizeof(MatScalar)+2*sizeof(PetscInt)),&apa);CHKERRQ(ierr);
176   ierr = PetscMemzero(apa,cn*(sizeof(MatScalar)+2*sizeof(PetscInt)));CHKERRQ(ierr);
177 
178   apj      = (PetscInt *)(apa + cn);
179   apjdense = apj + cn;
180 
181   /* Clear old values in C */
182   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
183 
184   for (i=0;i<am;i++) {
185     /* Form sparse row of A*P */
186     anzi  = ai[i+1] - ai[i];
187     apnzj = 0;
188     for (j=0;j<anzi;j++) {
189       prow = *aj++;
190       pnzj = pi[prow+1] - pi[prow];
191       pjj  = pj + pi[prow];
192       paj  = pa + pi[prow];
193       for (k=0;k<pnzj;k++) {
194         if (!apjdense[pjj[k]]) {
195           apjdense[pjj[k]] = -1;
196           apj[apnzj++]     = pjj[k];
197         }
198         apa[pjj[k]] += (*aa)*paj[k];
199       }
200       flops += 2.0*pnzj;
201       aa++;
202     }
203 
204     /* Sort the j index array for quick sparse axpy. */
205     /* Note: a array does not need sorting as it is in dense storage locations. */
206     ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr);
207 
208     /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
209     pnzi = pi[i+1] - pi[i];
210     for (j=0;j<pnzi;j++) {
211       nextap = 0;
212       crow   = *pJ++;
213       cjj    = cj + ci[crow];
214       caj    = ca + ci[crow];
215       /* Perform sparse axpy operation.  Note cjj includes apj. */
216       for (k=0;nextap<apnzj;k++) {
217 #if defined(PETSC_USE_DEBUG)
218         if (k >= ci[crow+1] - ci[crow]) {
219           SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"k too large k %d, crow %d",k,crow);
220         }
221 #endif
222         if (cjj[k]==apj[nextap]) {
223           caj[k] += (*pA)*apa[apj[nextap++]];
224         }
225       }
226       flops += 2.0*apnzj;
227       pA++;
228     }
229 
230     /* Zero the current row info for A*P */
231     for (j=0;j<apnzj;j++) {
232       apa[apj[j]]      = 0.;
233       apjdense[apj[j]] = 0;
234     }
235   }
236 
237   /* Assemble the final matrix and clean up */
238   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
239   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
240   ierr = PetscFree(apa);CHKERRQ(ierr);
241   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
242 
243   PetscFunctionReturn(0);
244 }
245