1 #define PETSCMAT_DLL 2 3 #include "../src/mat/impls/sbaij/seq/sbaij.h" 4 #include "../src/inline/ilu.h" 5 6 /* Version for when blocks are 5 by 5 */ 7 #undef __FUNCT__ 8 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_5" 9 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat C,Mat A,const MatFactorInfo *info) 10 { 11 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 12 IS perm = b->row; 13 PetscErrorCode ierr; 14 const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j; 15 PetscInt i,j,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 16 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 17 MatScalar *u,*d,*rtmp,*rtmp_ptr; 18 PetscReal shift = info->shiftinblocks; 19 20 PetscFunctionBegin; 21 /* initialization */ 22 ierr = PetscMalloc(25*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 23 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 24 ierr = PetscMalloc(2*mbs*sizeof(PetscInt),&il);CHKERRQ(ierr); 25 jl = il + mbs; 26 for (i=0; i<mbs; i++) { 27 jl[i] = mbs; il[0] = 0; 28 } 29 ierr = PetscMalloc(50*sizeof(MatScalar),&dk);CHKERRQ(ierr); 30 uik = dk + 25; 31 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 32 33 /* check permutation */ 34 if (!a->permute){ 35 ai = a->i; aj = a->j; aa = a->a; 36 } else { 37 ai = a->inew; aj = a->jnew; 38 ierr = PetscMalloc(25*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr); 39 ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 40 ierr = PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);CHKERRQ(ierr); 41 ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));CHKERRQ(ierr); 42 43 for (i=0; i<mbs; i++){ 44 jmin = ai[i]; jmax = ai[i+1]; 45 for (j=jmin; j<jmax; j++){ 46 while (a2anew[j] != j){ 47 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 48 for (k1=0; k1<25; k1++){ 49 dk[k1] = aa[k*25+k1]; 50 aa[k*25+k1] = aa[j*25+k1]; 51 aa[j*25+k1] = dk[k1]; 52 } 53 } 54 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 55 if (i > aj[j]){ 56 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 57 ap = aa + j*25; /* ptr to the beginning of j-th block of aa */ 58 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 59 for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */ 60 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1]; 61 } 62 } 63 } 64 } 65 ierr = PetscFree(a2anew);CHKERRQ(ierr); 66 } 67 68 /* for each row k */ 69 for (k = 0; k<mbs; k++){ 70 71 /*initialize k-th row with elements nonzero in row perm(k) of A */ 72 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 73 if (jmin < jmax) { 74 ap = aa + jmin*25; 75 for (j = jmin; j < jmax; j++){ 76 vj = perm_ptr[aj[j]]; /* block col. index */ 77 rtmp_ptr = rtmp + vj*25; 78 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 79 } 80 } 81 82 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 83 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 84 i = jl[k]; /* first row to be added to k_th row */ 85 86 while (i < mbs){ 87 nexti = jl[i]; /* next row to be added to k_th row */ 88 89 /* compute multiplier */ 90 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 91 92 /* uik = -inv(Di)*U_bar(i,k) */ 93 d = ba + i*25; 94 u = ba + ili*25; 95 96 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 97 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 98 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 99 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 100 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 101 102 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 103 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 104 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 105 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 106 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 107 108 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 109 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 110 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 111 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 112 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 113 114 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 115 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 116 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 117 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 118 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 119 120 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 121 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 122 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 123 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 124 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 125 126 127 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 128 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 129 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 130 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 131 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 132 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 133 134 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 135 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 136 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 137 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 138 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 139 140 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 141 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 142 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 143 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 144 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 145 146 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 147 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 148 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 149 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 150 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 151 152 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 153 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 154 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 155 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 156 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 157 158 ierr = PetscLogFlops(125*4);CHKERRQ(ierr); 159 160 /* update -U(i,k) */ 161 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 162 163 /* add multiple of row i to k-th row ... */ 164 jmin = ili + 1; jmax = bi[i+1]; 165 if (jmin < jmax){ 166 for (j=jmin; j<jmax; j++) { 167 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 168 rtmp_ptr = rtmp + bj[j]*25; 169 u = ba + j*25; 170 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 171 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 172 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 173 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 174 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 175 176 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 177 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 178 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 179 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 180 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 181 182 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 183 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 184 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 185 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 186 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 187 188 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 189 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 190 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 191 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 192 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 193 194 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 195 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 196 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 197 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 198 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 199 } 200 ierr = PetscLogFlops(2*125*(jmax-jmin));CHKERRQ(ierr); 201 202 /* ... add i to row list for next nonzero entry */ 203 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 204 j = bj[jmin]; 205 jl[i] = jl[j]; jl[j] = i; /* update jl */ 206 } 207 i = nexti; 208 } 209 210 /* save nonzero entries in k-th row of U ... */ 211 212 /* invert diagonal block */ 213 d = ba+k*25; 214 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 215 ierr = Kernel_A_gets_inverse_A_5(d,shift);CHKERRQ(ierr); 216 217 jmin = bi[k]; jmax = bi[k+1]; 218 if (jmin < jmax) { 219 for (j=jmin; j<jmax; j++){ 220 vj = bj[j]; /* block col. index of U */ 221 u = ba + j*25; 222 rtmp_ptr = rtmp + vj*25; 223 for (k1=0; k1<25; k1++){ 224 *u++ = *rtmp_ptr; 225 *rtmp_ptr++ = 0.0; 226 } 227 } 228 229 /* ... add k to row list for first nonzero entry in k-th row */ 230 il[k] = jmin; 231 i = bj[jmin]; 232 jl[k] = jl[i]; jl[i] = k; 233 } 234 } 235 236 ierr = PetscFree(rtmp);CHKERRQ(ierr); 237 ierr = PetscFree(il);CHKERRQ(ierr); 238 ierr = PetscFree(dk);CHKERRQ(ierr); 239 if (a->permute){ 240 ierr = PetscFree(aa);CHKERRQ(ierr); 241 } 242 243 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 244 C->ops->solve = MatSolve_SeqSBAIJ_5; 245 C->ops->solvetranspose = MatSolve_SeqSBAIJ_5; 246 C->assembled = PETSC_TRUE; 247 C->preallocated = PETSC_TRUE; 248 ierr = PetscLogFlops(1.3333*125*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */ 249 PetscFunctionReturn(0); 250 } 251