1 #define PETSCMAT_DLL 2 3 #include "src/mat/impls/sbaij/seq/sbaij.h" 4 #include "src/inline/ilu.h" 5 6 /* 7 Version for when blocks are 3 by 3 Using natural ordering 8 */ 9 #undef __FUNCT__ 10 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 11 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,MatFactorInfo *info,Mat *B) 12 { 13 Mat C = *B; 14 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 15 PetscErrorCode ierr; 16 PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 17 PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 18 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 19 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 20 PetscReal shift = info->shiftinblocks; 21 22 PetscFunctionBegin; 23 24 /* initialization */ 25 ierr = PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 26 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 27 ierr = PetscMalloc(2*mbs*sizeof(PetscInt),&il);CHKERRQ(ierr); 28 jl = il + mbs; 29 for (i=0; i<mbs; i++) { 30 jl[i] = mbs; il[0] = 0; 31 } 32 ierr = PetscMalloc(18*sizeof(MatScalar),&dk);CHKERRQ(ierr); 33 uik = dk + 9; 34 35 ai = a->i; aj = a->j; aa = a->a; 36 37 /* for each row k */ 38 for (k = 0; k<mbs; k++){ 39 40 /*initialize k-th row with elements nonzero in row k of A */ 41 jmin = ai[k]; jmax = ai[k+1]; 42 if (jmin < jmax) { 43 ap = aa + jmin*9; 44 for (j = jmin; j < jmax; j++){ 45 vj = aj[j]; /* block col. index */ 46 rtmp_ptr = rtmp + vj*9; 47 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 48 } 49 } 50 51 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 52 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 53 i = jl[k]; /* first row to be added to k_th row */ 54 55 while (i < mbs){ 56 nexti = jl[i]; /* next row to be added to k_th row */ 57 58 /* compute multiplier */ 59 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 60 61 /* uik = -inv(Di)*U_bar(i,k) */ 62 diag = ba + i*9; 63 u = ba + ili*9; 64 65 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 66 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 67 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 68 69 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 70 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 71 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 72 73 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 74 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 75 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 76 77 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 78 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 79 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 80 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 81 82 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 83 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 84 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 85 86 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 87 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 88 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 89 90 ierr = PetscLogFlops(27*4);CHKERRQ(ierr); 91 92 /* update -U(i,k) */ 93 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 94 95 /* add multiple of row i to k-th row ... */ 96 jmin = ili + 1; jmax = bi[i+1]; 97 if (jmin < jmax){ 98 for (j=jmin; j<jmax; j++) { 99 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 100 rtmp_ptr = rtmp + bj[j]*9; 101 u = ba + j*9; 102 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 103 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 104 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 105 106 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 107 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 108 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 109 110 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 111 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 112 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 113 } 114 ierr = PetscLogFlops(2*27*(jmax-jmin));CHKERRQ(ierr); 115 116 /* ... add i to row list for next nonzero entry */ 117 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 118 j = bj[jmin]; 119 jl[i] = jl[j]; jl[j] = i; /* update jl */ 120 } 121 i = nexti; 122 } 123 124 /* save nonzero entries in k-th row of U ... */ 125 126 /* invert diagonal block */ 127 diag = ba+k*9; 128 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 129 ierr = Kernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr); 130 131 jmin = bi[k]; jmax = bi[k+1]; 132 if (jmin < jmax) { 133 for (j=jmin; j<jmax; j++){ 134 vj = bj[j]; /* block col. index of U */ 135 u = ba + j*9; 136 rtmp_ptr = rtmp + vj*9; 137 for (k1=0; k1<9; k1++){ 138 *u++ = *rtmp_ptr; 139 *rtmp_ptr++ = 0.0; 140 } 141 } 142 143 /* ... add k to row list for first nonzero entry in k-th row */ 144 il[k] = jmin; 145 i = bj[jmin]; 146 jl[k] = jl[i]; jl[i] = k; 147 } 148 } 149 150 ierr = PetscFree(rtmp);CHKERRQ(ierr); 151 ierr = PetscFree(il);CHKERRQ(ierr); 152 ierr = PetscFree(dk);CHKERRQ(ierr); 153 154 C->ops->solve = MatSolve_SeqSBAIJ_3_NaturalOrdering; 155 C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering; 156 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering; 157 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering; 158 159 C->assembled = PETSC_TRUE; 160 C->preallocated = PETSC_TRUE; 161 ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */ 162 PetscFunctionReturn(0); 163 } 164