1 2 #include "src/mat/impls/sbaij/seq/sbaij.h" 3 #include "src/inline/ilu.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 A,Mat *B) 11 { 12 Mat C = *B; 13 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 14 PetscErrorCode ierr; 15 PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 16 PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 17 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 18 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 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 = PetscMalloc(2*mbs*sizeof(PetscInt),&il);CHKERRQ(ierr); 26 jl = il + mbs; 27 for (i=0; i<mbs; i++) { 28 jl[i] = mbs; il[0] = 0; 29 } 30 ierr = PetscMalloc(18*sizeof(MatScalar),&dk);CHKERRQ(ierr); 31 uik = dk + 9; 32 33 ai = a->i; aj = a->j; aa = a->a; 34 35 /* for each row k */ 36 for (k = 0; k<mbs; k++){ 37 38 /*initialize k-th row with elements nonzero in row k of A */ 39 jmin = ai[k]; jmax = ai[k+1]; 40 if (jmin < jmax) { 41 ap = aa + jmin*9; 42 for (j = jmin; j < jmax; j++){ 43 vj = aj[j]; /* block col. index */ 44 rtmp_ptr = rtmp + vj*9; 45 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 46 } 47 } 48 49 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 50 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 51 i = jl[k]; /* first row to be added to k_th row */ 52 53 while (i < mbs){ 54 nexti = jl[i]; /* next row to be added to k_th row */ 55 56 /* compute multiplier */ 57 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 58 59 /* uik = -inv(Di)*U_bar(i,k) */ 60 diag = ba + i*9; 61 u = ba + ili*9; 62 63 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 64 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 65 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 66 67 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 68 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 69 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 70 71 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 72 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 73 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 74 75 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 76 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 77 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 78 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 79 80 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 81 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 82 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 83 84 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 85 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 86 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 87 88 /* update -U(i,k) */ 89 ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr); 90 91 /* add multiple of row i to k-th row ... */ 92 jmin = ili + 1; jmax = bi[i+1]; 93 if (jmin < jmax){ 94 for (j=jmin; j<jmax; j++) { 95 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 96 rtmp_ptr = rtmp + bj[j]*9; 97 u = ba + j*9; 98 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 99 rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 100 rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 101 102 rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 103 rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 104 rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 105 106 rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 107 rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 108 rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 109 } 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);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 = PetscFree(il);CHKERRQ(ierr); 147 ierr = PetscFree(dk);CHKERRQ(ierr); 148 149 C->factor = FACTOR_CHOLESKY; 150 C->assembled = PETSC_TRUE; 151 C->preallocated = PETSC_TRUE; 152 PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 153 PetscFunctionReturn(0); 154 } 155