Actual source code: sbaijfact8.c

petsc-3.4.5 2014-06-29
  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: */
 10: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
 11: {
 12:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
 14:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 15:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili,ipvt[5];
 16:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
 17:   MatScalar      *u,*d,*rtmp,*rtmp_ptr,work[25];
 18:   PetscReal      shift = info->shiftamount;

 21:   /* initialization */
 22:   PetscMalloc(25*mbs*sizeof(MatScalar),&rtmp);
 23:   PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));
 24:   PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);
 25:   for (i=0; i<mbs; i++) {
 26:     jl[i] = mbs; il[0] = 0;
 27:   }
 28:   PetscMalloc2(25,MatScalar,&dk,25,MatScalar,&uik);
 29:   ai   = a->i; aj = a->j; aa = a->a;

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

 34:     /*initialize k-th row with elements nonzero in row k of A */
 35:     jmin = ai[k]; jmax = ai[k+1];
 36:     if (jmin < jmax) {
 37:       ap = aa + jmin*25;
 38:       for (j = jmin; j < jmax; j++) {
 39:         vj       = aj[j];   /* block col. index */
 40:         rtmp_ptr = rtmp + vj*25;
 41:         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
 42:       }
 43:     }

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

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

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

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

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

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

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

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

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


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

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

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

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

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

121:       PetscLogFlops(125.0*4.0);

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

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

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

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

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

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

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

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

175:     /* invert diagonal block */
176:     d    = ba+k*25;
177:     PetscMemcpy(d,dk,25*sizeof(MatScalar));
178:     PetscKernel_A_gets_inverse_A_5(d,ipvt,work,shift);

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: }