Actual source code: sbaijfact6.c

petsc-3.11.3 2019-06-26
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  2:  #include <../src/mat/impls/sbaij/seq/sbaij.h>
  3:  #include <petsc/private/kernels/blockinvert.h>

  5: /* Version for when blocks are 4 by 4  */
  6: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat C,Mat A,const MatFactorInfo *info)
  7: {
  8:   Mat_SeqSBAIJ   *a   = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
  9:   IS             perm = b->row;
 11:   const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
 12:   PetscInt       i,j,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 13:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
 14:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
 15:   PetscBool      pivotinblocks = b->pivotinblocks;
 16:   PetscReal      shift         = info->shiftamount;
 17:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

 20:   /* initialization */
 21:   allowzeropivot = PetscNot(A->erroriffailure);
 22:   PetscCalloc1(16*mbs,&rtmp);
 23:   PetscMalloc2(mbs,&il,mbs,&jl);
 24:   il[0] = 0;
 25:   for (i=0; i<mbs; i++) jl[i] = mbs;
 26: 
 27:   PetscMalloc2(16,&dk,16,&uik);
 28:   ISGetIndices(perm,&perm_ptr);

 30:   /* check permutation */
 31:   if (!a->permute) {
 32:     ai = a->i; aj = a->j; aa = a->a;
 33:   } else {
 34:     ai   = a->inew; aj = a->jnew;
 35:     PetscMalloc1(16*ai[mbs],&aa);
 36:     PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));
 37:     PetscMalloc1(ai[mbs],&a2anew);
 38:     PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));

 40:     for (i=0; i<mbs; i++) {
 41:       jmin = ai[i]; jmax = ai[i+1];
 42:       for (j=jmin; j<jmax; j++) {
 43:         while (a2anew[j] != j) {
 44:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
 45:           for (k1=0; k1<16; k1++) {
 46:             dk[k1]      = aa[k*16+k1];
 47:             aa[k*16+k1] = aa[j*16+k1];
 48:             aa[j*16+k1] = dk[k1];
 49:           }
 50:         }
 51:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
 52:         if (i > aj[j]) {
 53:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
 54:           ap = aa + j*16;                     /* ptr to the beginning of j-th block of aa */
 55:           for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 56:           for (k=0; k<4; k++) {               /* j-th block of aa <- dk^T */
 57:             for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
 58:           }
 59:         }
 60:       }
 61:     }
 62:     PetscFree(a2anew);
 63:   }

 65:   /* for each row k */
 66:   for (k = 0; k<mbs; k++) {

 68:     /*initialize k-th row with elements nonzero in row perm(k) of A */
 69:     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
 70:     if (jmin < jmax) {
 71:       ap = aa + jmin*16;
 72:       for (j = jmin; j < jmax; j++) {
 73:         vj       = perm_ptr[aj[j]];   /* block col. index */
 74:         rtmp_ptr = rtmp + vj*16;
 75:         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
 76:       }
 77:     }

 79:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 80:     PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));
 81:     i    = jl[k]; /* first row to be added to k_th row  */

 83:     while (i < mbs) {
 84:       nexti = jl[i]; /* next row to be added to k_th row */

 86:       /* compute multiplier */
 87:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

 89:       /* uik = -inv(Di)*U_bar(i,k) */
 90:       diag = ba + i*16;
 91:       u    = ba + ili*16;

 93:       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
 94:       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
 95:       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
 96:       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);

 98:       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
 99:       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
100:       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
101:       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);

103:       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
104:       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
105:       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
106:       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);

108:       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
109:       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
110:       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
111:       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);

113:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
114:       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
115:       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
116:       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
117:       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];

119:       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
120:       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
121:       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
122:       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];

124:       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
125:       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
126:       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
127:       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];

129:       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
130:       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
131:       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
132:       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];

134:       PetscLogFlops(64.0*4.0);

136:       /* update -U(i,k) */
137:       PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));

139:       /* add multiple of row i to k-th row ... */
140:       jmin = ili + 1; jmax = bi[i+1];
141:       if (jmin < jmax) {
142:         for (j=jmin; j<jmax; j++) {
143:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
144:           rtmp_ptr     = rtmp + bj[j]*16;
145:           u            = ba + j*16;
146:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
147:           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
148:           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
149:           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];

151:           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
152:           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
153:           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
154:           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];

156:           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
157:           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
158:           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
159:           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];

161:           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
162:           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
163:           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
164:           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
165:         }
166:         PetscLogFlops(2.0*64.0*(jmax-jmin));

168:         /* ... add i to row list for next nonzero entry */
169:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
170:         j     = bj[jmin];
171:         jl[i] = jl[j]; jl[j] = i; /* update jl */
172:       }
173:       i = nexti;
174:     }

176:     /* save nonzero entries in k-th row of U ... */

178:     /* invert diagonal block */
179:     diag = ba+k*16;
180:     PetscMemcpy(diag,dk,16*sizeof(MatScalar));

182:     if (pivotinblocks) {
183:       PetscKernel_A_gets_inverse_A_4(diag,shift, allowzeropivot,&zeropivotdetected);
184:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
185:     } else {
186:       PetscKernel_A_gets_inverse_A_4_nopivot(diag);
187:     }

189:     jmin = bi[k]; jmax = bi[k+1];
190:     if (jmin < jmax) {
191:       for (j=jmin; j<jmax; j++) {
192:         vj       = bj[j];      /* block col. index of U */
193:         u        = ba + j*16;
194:         rtmp_ptr = rtmp + vj*16;
195:         for (k1=0; k1<16; k1++) {
196:           *u++        = *rtmp_ptr;
197:           *rtmp_ptr++ = 0.0;
198:         }
199:       }

201:       /* ... add k to row list for first nonzero entry in k-th row */
202:       il[k] = jmin;
203:       i     = bj[jmin];
204:       jl[k] = jl[i]; jl[i] = k;
205:     }
206:   }

208:   PetscFree(rtmp);
209:   PetscFree2(il,jl);
210:   PetscFree2(dk,uik);
211:   if (a->permute) {
212:     PetscFree(aa);
213:   }

215:   ISRestoreIndices(perm,&perm_ptr);

217:   C->ops->solve          = MatSolve_SeqSBAIJ_4_inplace;
218:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_inplace;
219:   C->assembled           = PETSC_TRUE;
220:   C->preallocated        = PETSC_TRUE;

222:   PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
223:   return(0);
224: }