1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <../src/mat/blockinvert.h> 4 5 /* Version for when blocks are 3 by 3 */ 6 #undef __FUNCT__ 7 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_3" 8 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat C,Mat A,const MatFactorInfo *info) 9 { 10 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 11 IS perm = b->row; 12 PetscErrorCode ierr; 13 const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j; 14 PetscInt *a2anew,i,j,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 15 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 16 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 17 PetscReal shift = info->shiftamount; 18 19 PetscFunctionBegin; 20 21 /* initialization */ 22 ierr = PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 23 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 24 ierr = PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 25 for (i=0; i<mbs; i++) { 26 jl[i] = mbs; il[0] = 0; 27 } 28 ierr = PetscMalloc2(9,MatScalar,&dk,9,MatScalar,&uik);CHKERRQ(ierr); 29 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 30 31 /* check permutation */ 32 if (!a->permute){ 33 ai = a->i; aj = a->j; aa = a->a; 34 } else { 35 ai = a->inew; aj = a->jnew; 36 ierr = PetscMalloc(9*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr); 37 ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 38 ierr = PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);CHKERRQ(ierr); 39 ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));CHKERRQ(ierr); 40 41 for (i=0; i<mbs; i++){ 42 jmin = ai[i]; jmax = ai[i+1]; 43 for (j=jmin; j<jmax; j++){ 44 while (a2anew[j] != j){ 45 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 46 for (k1=0; k1<9; k1++){ 47 dk[k1] = aa[k*9+k1]; 48 aa[k*9+k1] = aa[j*9+k1]; 49 aa[j*9+k1] = dk[k1]; 50 } 51 } 52 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 53 if (i > aj[j]){ 54 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 55 ap = aa + j*9; /* ptr to the beginning of j-th block of aa */ 56 for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 57 for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */ 58 for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1]; 59 } 60 } 61 } 62 } 63 ierr = PetscFree(a2anew);CHKERRQ(ierr); 64 } 65 66 /* for each row k */ 67 for (k = 0; k<mbs; k++){ 68 69 /*initialize k-th row with elements nonzero in row perm(k) of A */ 70 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 71 if (jmin < jmax) { 72 ap = aa + jmin*9; 73 for (j = jmin; j < jmax; j++){ 74 vj = perm_ptr[aj[j]]; /* block col. index */ 75 rtmp_ptr = rtmp + vj*9; 76 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 77 } 78 } 79 80 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 81 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 82 i = jl[k]; /* first row to be added to k_th row */ 83 84 while (i < mbs){ 85 nexti = jl[i]; /* next row to be added to k_th row */ 86 87 /* compute multiplier */ 88 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 89 90 /* uik = -inv(Di)*U_bar(i,k) */ 91 diag = ba + i*9; 92 u = ba + ili*9; 93 94 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 95 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 96 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 97 98 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 99 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 100 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 101 102 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 103 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 104 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 105 106 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 107 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 108 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 109 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 110 111 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 112 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 113 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 114 115 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 116 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 117 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 118 119 ierr = PetscLogFlops(27.0*4.0);CHKERRQ(ierr); 120 121 /* update -U(i,k) */ 122 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 123 124 /* add multiple of row i to k-th row ... */ 125 jmin = ili + 1; jmax = bi[i+1]; 126 if (jmin < jmax){ 127 for (j=jmin; j<jmax; j++) { 128 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 129 rtmp_ptr = rtmp + bj[j]*9; 130 u = ba + j*9; 131 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 132 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 133 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 134 135 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 136 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 137 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 138 139 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 140 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 141 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 142 } 143 ierr = PetscLogFlops(2.0*27.0*(jmax-jmin));CHKERRQ(ierr); 144 145 /* ... add i to row list for next nonzero entry */ 146 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 147 j = bj[jmin]; 148 jl[i] = jl[j]; jl[j] = i; /* update jl */ 149 } 150 i = nexti; 151 } 152 153 /* save nonzero entries in k-th row of U ... */ 154 155 /* invert diagonal block */ 156 diag = ba+k*9; 157 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 158 ierr = Kernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr); 159 160 jmin = bi[k]; jmax = bi[k+1]; 161 if (jmin < jmax) { 162 for (j=jmin; j<jmax; j++){ 163 vj = bj[j]; /* block col. index of U */ 164 u = ba + j*9; 165 rtmp_ptr = rtmp + vj*9; 166 for (k1=0; k1<9; k1++){ 167 *u++ = *rtmp_ptr; 168 *rtmp_ptr++ = 0.0; 169 } 170 } 171 172 /* ... add k to row list for first nonzero entry in k-th row */ 173 il[k] = jmin; 174 i = bj[jmin]; 175 jl[k] = jl[i]; jl[i] = k; 176 } 177 } 178 179 ierr = PetscFree(rtmp);CHKERRQ(ierr); 180 ierr = PetscFree2(il,jl);CHKERRQ(ierr); 181 ierr = PetscFree2(dk,uik);CHKERRQ(ierr); 182 if (a->permute){ 183 ierr = PetscFree(aa);CHKERRQ(ierr); 184 } 185 186 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 187 C->ops->solve = MatSolve_SeqSBAIJ_3_inplace; 188 C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace; 189 C->assembled = PETSC_TRUE; 190 C->preallocated = PETSC_TRUE; 191 ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */ 192 PetscFunctionReturn(0); 193 } 194