Actual source code: sbaijfact7.c

petsc-3.12.2 2019-11-22
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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 5 by 5  */
  6: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(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,ipvt[5];
 13:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
 14:   MatScalar      *u,*d,*rtmp,*rtmp_ptr,work[25];
 15:   PetscReal      shift = info->shiftamount;
 16:   PetscBool      allowzeropivot,zeropivotdetected;

 19:   /* initialization */
 20:   allowzeropivot = PetscNot(A->erroriffailure);
 21:   PetscCalloc1(25*mbs,&rtmp);
 22:   PetscMalloc2(mbs,&il,mbs,&jl);
 23:   il[0] = 0;
 24:   for (i=0; i<mbs; i++) jl[i] = mbs;

 26:   PetscMalloc2(25,&dk,25,&uik);
 27:   ISGetIndices(perm,&perm_ptr);

 29:   /* check permutation */
 30:   if (!a->permute) {
 31:     ai = a->i; aj = a->j; aa = a->a;
 32:   } else {
 33:     ai   = a->inew; aj = a->jnew;
 34:     PetscMalloc1(25*ai[mbs],&aa);
 35:     PetscArraycpy(aa,a->a,25*ai[mbs]);
 36:     PetscMalloc1(ai[mbs],&a2anew);
 37:     PetscArraycpy(a2anew,a->a2anew,ai[mbs]);

 39:     for (i=0; i<mbs; i++) {
 40:       jmin = ai[i]; jmax = ai[i+1];
 41:       for (j=jmin; j<jmax; j++) {
 42:         while (a2anew[j] != j) {
 43:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
 44:           for (k1=0; k1<25; k1++) {
 45:             dk[k1]      = aa[k*25+k1];
 46:             aa[k*25+k1] = aa[j*25+k1];
 47:             aa[j*25+k1] = dk[k1];
 48:           }
 49:         }
 50:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
 51:         if (i > aj[j]) {
 52:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
 53:           ap = aa + j*25;                     /* ptr to the beginning of j-th block of aa */
 54:           for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 55:           for (k=0; k<5; k++) {               /* j-th block of aa <- dk^T */
 56:             for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
 57:           }
 58:         }
 59:       }
 60:     }
 61:     PetscFree(a2anew);
 62:   }

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

 67:     /*initialize k-th row with elements nonzero in row perm(k) of A */
 68:     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
 69:     if (jmin < jmax) {
 70:       ap = aa + jmin*25;
 71:       for (j = jmin; j < jmax; j++) {
 72:         vj       = perm_ptr[aj[j]];   /* block col. index */
 73:         rtmp_ptr = rtmp + vj*25;
 74:         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
 75:       }
 76:     }

 78:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 79:     PetscArraycpy(dk,rtmp+k*25,25);
 80:     i    = jl[k]; /* first row to be added to k_th row  */

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

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

 88:       /* uik = -inv(Di)*U_bar(i,k) */
 89:       d = ba + i*25;
 90:       u = ba + ili*25;

 92:       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
 93:       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
 94:       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
 95:       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
 96:       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);

 98:       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
 99:       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
100:       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
101:       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
102:       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);

104:       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
105:       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
106:       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
107:       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
108:       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);

110:       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
111:       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
112:       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
113:       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
114:       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);

116:       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
117:       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
118:       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
119:       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
120:       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);


123:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
124:       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
125:       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
126:       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
127:       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
128:       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];

130:       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
131:       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
132:       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
133:       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
134:       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];

136:       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
137:       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
138:       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
139:       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
140:       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];

142:       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
143:       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
144:       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
145:       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
146:       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];

148:       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
149:       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
150:       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
151:       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
152:       dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];

154:       PetscLogFlops(125.0*4.0);

156:       /* update -U(i,k) */
157:       PetscArraycpy(ba+ili*25,uik,25);

159:       /* add multiple of row i to k-th row ... */
160:       jmin = ili + 1; jmax = bi[i+1];
161:       if (jmin < jmax) {
162:         for (j=jmin; j<jmax; j++) {
163:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
164:           rtmp_ptr     = rtmp + bj[j]*25;
165:           u            = ba + j*25;
166:           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
167:           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
168:           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
169:           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
170:           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];

172:           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
173:           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
174:           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
175:           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
176:           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];

178:           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
179:           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
180:           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
181:           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
182:           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];

184:           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
185:           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
186:           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
187:           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
188:           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];

190:           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
191:           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
192:           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
193:           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
194:           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
195:         }
196:         PetscLogFlops(2.0*125.0*(jmax-jmin));

198:         /* ... add i to row list for next nonzero entry */
199:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
200:         j     = bj[jmin];
201:         jl[i] = jl[j]; jl[j] = i; /* update jl */
202:       }
203:       i = nexti;
204:     }

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

208:     /* invert diagonal block */
209:     d    = ba+k*25;
210:     PetscArraycpy(d,dk,25);
211:     PetscKernel_A_gets_inverse_A_5(d,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
212:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

214:     jmin = bi[k]; jmax = bi[k+1];
215:     if (jmin < jmax) {
216:       for (j=jmin; j<jmax; j++) {
217:         vj       = bj[j];      /* block col. index of U */
218:         u        = ba + j*25;
219:         rtmp_ptr = rtmp + vj*25;
220:         for (k1=0; k1<25; k1++) {
221:           *u++        = *rtmp_ptr;
222:           *rtmp_ptr++ = 0.0;
223:         }
224:       }

226:       /* ... add k to row list for first nonzero entry in k-th row */
227:       il[k] = jmin;
228:       i     = bj[jmin];
229:       jl[k] = jl[i]; jl[i] = k;
230:     }
231:   }

233:   PetscFree(rtmp);
234:   PetscFree2(il,jl);
235:   PetscFree2(dk,uik);
236:   if (a->permute) {
237:     PetscFree(aa);
238:   }

240:   ISRestoreIndices(perm,&perm_ptr);

242:   C->ops->solve          = MatSolve_SeqSBAIJ_5_inplace;
243:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_inplace;
244:   C->assembled           = PETSC_TRUE;
245:   C->preallocated        = PETSC_TRUE;

247:   PetscLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
248:   return(0);
249: }