1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <../src/mat/blockinvert.h> 4 5 /* 6 Version for when blocks are 3 by 3 Using natural ordering 7 */ 8 #undef __FUNCT__ 9 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 10 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info) 11 { 12 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 13 PetscErrorCode ierr; 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; 16 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 17 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 18 PetscReal shift = info->shiftamount; 19 20 PetscFunctionBegin; 21 22 /* initialization */ 23 ierr = PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 24 ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr); 25 ierr = PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr); 26 for (i=0; i<mbs; i++) { 27 jl[i] = mbs; il[0] = 0; 28 } 29 ierr = PetscMalloc2(9,MatScalar,&dk,9,MatScalar,&uik);CHKERRQ(ierr); 30 ai = a->i; aj = a->j; aa = a->a; 31 32 /* for each row k */ 33 for (k = 0; k<mbs; k++){ 34 35 /*initialize k-th row with elements nonzero in row k of A */ 36 jmin = ai[k]; jmax = ai[k+1]; 37 if (jmin < jmax) { 38 ap = aa + jmin*9; 39 for (j = jmin; j < jmax; j++){ 40 vj = aj[j]; /* block col. index */ 41 rtmp_ptr = rtmp + vj*9; 42 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 43 } 44 } 45 46 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 47 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 48 i = jl[k]; /* first row to be added to k_th row */ 49 50 while (i < mbs){ 51 nexti = jl[i]; /* next row to be added to k_th row */ 52 53 /* compute multiplier */ 54 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 55 56 /* uik = -inv(Di)*U_bar(i,k) */ 57 diag = ba + i*9; 58 u = ba + ili*9; 59 60 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 61 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 62 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 63 64 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 65 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 66 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 67 68 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 69 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 70 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 71 72 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 73 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 74 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 75 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 76 77 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 78 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 79 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 80 81 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 82 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 83 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 84 85 ierr = PetscLogFlops(27.0*4.0);CHKERRQ(ierr); 86 87 /* update -U(i,k) */ 88 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 89 90 /* add multiple of row i to k-th row ... */ 91 jmin = ili + 1; jmax = bi[i+1]; 92 if (jmin < jmax){ 93 for (j=jmin; j<jmax; j++) { 94 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 95 rtmp_ptr = rtmp + bj[j]*9; 96 u = ba + j*9; 97 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 98 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 99 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 100 101 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 102 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 103 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 104 105 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 106 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 107 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 108 } 109 ierr = PetscLogFlops(2.0*27.0*(jmax-jmin));CHKERRQ(ierr); 110 111 /* ... add i to row list for next nonzero entry */ 112 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 113 j = bj[jmin]; 114 jl[i] = jl[j]; jl[j] = i; /* update jl */ 115 } 116 i = nexti; 117 } 118 119 /* save nonzero entries in k-th row of U ... */ 120 121 /* invert diagonal block */ 122 diag = ba+k*9; 123 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 124 ierr = Kernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr); 125 126 jmin = bi[k]; jmax = bi[k+1]; 127 if (jmin < jmax) { 128 for (j=jmin; j<jmax; j++){ 129 vj = bj[j]; /* block col. index of U */ 130 u = ba + j*9; 131 rtmp_ptr = rtmp + vj*9; 132 for (k1=0; k1<9; k1++){ 133 *u++ = *rtmp_ptr; 134 *rtmp_ptr++ = 0.0; 135 } 136 } 137 138 /* ... add k to row list for first nonzero entry in k-th row */ 139 il[k] = jmin; 140 i = bj[jmin]; 141 jl[k] = jl[i]; jl[i] = k; 142 } 143 } 144 145 ierr = PetscFree(rtmp);CHKERRQ(ierr); 146 ierr = PetscFree2(il,jl);CHKERRQ(ierr); 147 ierr = PetscFree2(dk,uik);CHKERRQ(ierr); 148 149 C->ops->solve = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 150 C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 151 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 152 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 153 154 C->assembled = PETSC_TRUE; 155 C->preallocated = PETSC_TRUE; 156 ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */ 157 PetscFunctionReturn(0); 158 } 159