1 /*$Id: sbaijfact3.c,v 1.4 2001/06/21 21:17:00 bsmith Exp $*/ 2 #include "src/mat/impls/sbaij/seq/sbaij.h" 3 #include "src/inline/ilu.h" 4 5 /* Version for when blocks are 3 by 3 */ 6 #undef __FUNCT__ 7 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_3" 8 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B) 9 { 10 Mat C = *B; 11 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 12 IS perm = b->row; 13 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 14 int *ai,*aj,*a2anew,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 18 PetscFunctionBegin; 19 20 /* initialization */ 21 ierr = PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 22 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 23 ierr = PetscMalloc(2*mbs*sizeof(int),&il);CHKERRQ(ierr); 24 jl = il + mbs; 25 for (i=0; i<mbs; i++) { 26 jl[i] = mbs; il[0] = 0; 27 } 28 ierr = PetscMalloc(18*sizeof(MatScalar),&dk);CHKERRQ(ierr); 29 uik = dk + 9; 30 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 31 32 /* check permutation */ 33 if (!a->permute){ 34 ai = a->i; aj = a->j; aa = a->a; 35 } else { 36 ai = a->inew; aj = a->jnew; 37 ierr = PetscMalloc(9*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr); 38 ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 39 ierr = PetscMalloc(ai[mbs]*sizeof(int),&a2anew);CHKERRQ(ierr); 40 ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 41 42 for (i=0; i<mbs; i++){ 43 jmin = ai[i]; jmax = ai[i+1]; 44 for (j=jmin; j<jmax; j++){ 45 while (a2anew[j] != j){ 46 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 47 for (k1=0; k1<9; k1++){ 48 dk[k1] = aa[k*9+k1]; 49 aa[k*9+k1] = aa[j*9+k1]; 50 aa[j*9+k1] = dk[k1]; 51 } 52 } 53 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 54 if (i > aj[j]){ 55 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 56 ap = aa + j*9; /* ptr to the beginning of j-th block of aa */ 57 for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 58 for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */ 59 for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1]; 60 } 61 } 62 } 63 } 64 ierr = PetscFree(a2anew);CHKERRQ(ierr); 65 } 66 67 /* for each row k */ 68 for (k = 0; k<mbs; k++){ 69 70 /*initialize k-th row with elements nonzero in row perm(k) of A */ 71 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 72 if (jmin < jmax) { 73 ap = aa + jmin*9; 74 for (j = jmin; j < jmax; j++){ 75 vj = perm_ptr[aj[j]]; /* block col. index */ 76 rtmp_ptr = rtmp + vj*9; 77 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 78 } 79 } 80 81 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 82 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 83 i = jl[k]; /* first row to be added to k_th row */ 84 85 while (i < mbs){ 86 nexti = jl[i]; /* next row to be added to k_th row */ 87 88 /* compute multiplier */ 89 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 90 91 /* uik = -inv(Di)*U_bar(i,k) */ 92 diag = ba + i*9; 93 u = ba + ili*9; 94 95 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 96 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 97 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 98 99 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 100 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 101 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 102 103 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 104 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 105 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 106 107 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 108 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 109 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 110 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 111 112 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 113 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 114 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 115 116 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 117 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 118 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 119 120 /* update -U(i,k) */ 121 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 122 123 /* add multiple of row i to k-th row ... */ 124 jmin = ili + 1; jmax = bi[i+1]; 125 if (jmin < jmax){ 126 for (j=jmin; j<jmax; j++) { 127 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 128 rtmp_ptr = rtmp + bj[j]*9; 129 u = ba + j*9; 130 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 131 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 132 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 133 134 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 135 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 136 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 137 138 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 139 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 140 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 141 } 142 143 /* ... add i to row list for next nonzero entry */ 144 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 145 j = bj[jmin]; 146 jl[i] = jl[j]; jl[j] = i; /* update jl */ 147 } 148 i = nexti; 149 } 150 151 /* save nonzero entries in k-th row of U ... */ 152 153 /* invert diagonal block */ 154 diag = ba+k*9; 155 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 156 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 157 158 jmin = bi[k]; jmax = bi[k+1]; 159 if (jmin < jmax) { 160 for (j=jmin; j<jmax; j++){ 161 vj = bj[j]; /* block col. index of U */ 162 u = ba + j*9; 163 rtmp_ptr = rtmp + vj*9; 164 for (k1=0; k1<9; k1++){ 165 *u++ = *rtmp_ptr; 166 *rtmp_ptr++ = 0.0; 167 } 168 } 169 170 /* ... add k to row list for first nonzero entry in k-th row */ 171 il[k] = jmin; 172 i = bj[jmin]; 173 jl[k] = jl[i]; jl[i] = k; 174 } 175 } 176 177 ierr = PetscFree(rtmp);CHKERRQ(ierr); 178 ierr = PetscFree(il);CHKERRQ(ierr); 179 ierr = PetscFree(dk);CHKERRQ(ierr); 180 if (a->permute){ 181 ierr = PetscFree(aa);CHKERRQ(ierr); 182 } 183 184 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 185 C->factor = FACTOR_CHOLESKY; 186 C->assembled = PETSC_TRUE; 187 C->preallocated = PETSC_TRUE; 188 PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 189 PetscFunctionReturn(0); 190 } 191