Actual source code: sbaijfact8.c

petsc-3.11.3 2019-06-26
Report Typos and Errors

  2:  #include <../src/mat/impls/sbaij/seq/sbaij.h>
  3:  #include <petsc/private/kernels/blockinvert.h>

  5: /*
  6:       Version for when blocks are 5 by 5 Using natural ordering
  7: */
  8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
  9: {
 10:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
 12:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 13:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili,ipvt[5];
 14:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
 15:   MatScalar      *u,*d,*rtmp,*rtmp_ptr,work[25];
 16:   PetscReal      shift = info->shiftamount;
 17:   PetscBool      allowzeropivot,zeropivotdetected;

 20:   /* initialization */
 21:   allowzeropivot = PetscNot(A->erroriffailure);
 22:   PetscCalloc1(25*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(25,&dk,25,&uik);
 28:   ai   = a->i; aj = a->j; aa = a->a;

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

 33:     /*initialize k-th row with elements nonzero in row k of A */
 34:     jmin = ai[k]; jmax = ai[k+1];
 35:     if (jmin < jmax) {
 36:       ap = aa + jmin*25;
 37:       for (j = jmin; j < jmax; j++) {
 38:         vj       = aj[j];   /* block col. index */
 39:         rtmp_ptr = rtmp + vj*25;
 40:         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
 41:       }
 42:     }

 44:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 45:     PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));
 46:     i    = jl[k]; /* first row to be added to k_th row  */

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

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

 54:       /* uik = -inv(Di)*U_bar(i,k) */
 55:       d = ba + i*25;
 56:       u = ba + ili*25;

 58:       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
 59:       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
 60:       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
 61:       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
 62:       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);

 64:       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
 65:       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
 66:       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
 67:       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
 68:       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);

 70:       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
 71:       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
 72:       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
 73:       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
 74:       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);

 76:       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
 77:       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
 78:       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
 79:       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
 80:       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);

 82:       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
 83:       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
 84:       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
 85:       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
 86:       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);


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

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

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

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

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

120:       PetscLogFlops(125.0*4.0);

122:       /* update -U(i,k) */
123:       PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));

125:       /* add multiple of row i to k-th row ... */
126:       jmin = ili + 1; jmax = bi[i+1];
127:       if (jmin < jmax) {
128:         for (j=jmin; j<jmax; j++) {
129:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
130:           rtmp_ptr     = rtmp + bj[j]*25;
131:           u            = ba + j*25;
132:           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
133:           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
134:           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
135:           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
136:           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];

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

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

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

156:           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
157:           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
158:           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
159:           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
160:           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
161:         }
162:         PetscLogFlops(2.0*125.0*(jmax-jmin));

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

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

174:     /* invert diagonal block */
175:     d    = ba+k*25;
176:     PetscMemcpy(d,dk,25*sizeof(MatScalar));
177:     PetscKernel_A_gets_inverse_A_5(d,ipvt,work,shift,allowzeropivot,&zeropivotdetected);
178:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

180:     jmin = bi[k]; jmax = bi[k+1];
181:     if (jmin < jmax) {
182:       for (j=jmin; j<jmax; j++) {
183:         vj       = bj[j];      /* block col. index of U */
184:         u        = ba + j*25;
185:         rtmp_ptr = rtmp + vj*25;
186:         for (k1=0; k1<25; k1++) {
187:           *u++        = *rtmp_ptr;
188:           *rtmp_ptr++ = 0.0;
189:         }
190:       }

192:       /* ... add k to row list for first nonzero entry in k-th row */
193:       il[k] = jmin;
194:       i     = bj[jmin];
195:       jl[k] = jl[i]; jl[i] = k;
196:     }
197:   }

199:   PetscFree(rtmp);
200:   PetscFree2(il,jl);
201:   PetscFree2(dk,uik);

203:   C->ops->solve          = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
204:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
205:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
206:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
207:   C->assembled           = PETSC_TRUE;
208:   C->preallocated        = PETSC_TRUE;

210:   PetscLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
211:   return(0);
212: }