1 /*$Id: sbaijfact4.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 /* 6 Version for when blocks are 3 by 3 Using natural ordering 7 */ 8 #undef __FUNCT__ 9 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering" 10 int 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 int ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 15 int *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 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 = PetscMalloc(2*mbs*sizeof(int),&il);CHKERRQ(ierr); 25 jl = il + mbs; 26 for (i=0; i<mbs; i++) { 27 jl[i] = mbs; il[0] = 0; 28 } 29 ierr = PetscMalloc(18*sizeof(MatScalar),&dk);CHKERRQ(ierr); 30 uik = dk + 9; 31 32 ai = a->i; aj = a->j; aa = a->a; 33 34 /* for each row k */ 35 for (k = 0; k<mbs; k++){ 36 37 /*initialize k-th row with elements nonzero in row k of A */ 38 jmin = ai[k]; jmax = ai[k+1]; 39 if (jmin < jmax) { 40 ap = aa + jmin*9; 41 for (j = jmin; j < jmax; j++){ 42 vj = aj[j]; /* block col. index */ 43 rtmp_ptr = rtmp + vj*9; 44 for (i=0; i<9; i++) *rtmp_ptr++ = *ap++; 45 } 46 } 47 48 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 49 ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr); 50 i = jl[k]; /* first row to be added to k_th row */ 51 52 while (i < mbs){ 53 nexti = jl[i]; /* next row to be added to k_th row */ 54 55 /* compute multiplier */ 56 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 57 58 /* uik = -inv(Di)*U_bar(i,k) */ 59 diag = ba + i*9; 60 u = ba + ili*9; 61 62 uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]); 63 uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]); 64 uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]); 65 66 uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]); 67 uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]); 68 uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]); 69 70 uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]); 71 uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]); 72 uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]); 73 74 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 75 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2]; 76 dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2]; 77 dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2]; 78 79 dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5]; 80 dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5]; 81 dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5]; 82 83 dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8]; 84 dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8]; 85 dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8]; 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 } 109 110 /* ... add i to row list for next nonzero entry */ 111 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 112 j = bj[jmin]; 113 jl[i] = jl[j]; jl[j] = i; /* update jl */ 114 } 115 i = nexti; 116 } 117 118 /* save nonzero entries in k-th row of U ... */ 119 120 /* invert diagonal block */ 121 diag = ba+k*9; 122 ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr); 123 ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr); 124 125 jmin = bi[k]; jmax = bi[k+1]; 126 if (jmin < jmax) { 127 for (j=jmin; j<jmax; j++){ 128 vj = bj[j]; /* block col. index of U */ 129 u = ba + j*9; 130 rtmp_ptr = rtmp + vj*9; 131 for (k1=0; k1<9; k1++){ 132 *u++ = *rtmp_ptr; 133 *rtmp_ptr++ = 0.0; 134 } 135 } 136 137 /* ... add k to row list for first nonzero entry in k-th row */ 138 il[k] = jmin; 139 i = bj[jmin]; 140 jl[k] = jl[i]; jl[i] = k; 141 } 142 } 143 144 ierr = PetscFree(rtmp);CHKERRQ(ierr); 145 ierr = PetscFree(il);CHKERRQ(ierr); 146 ierr = PetscFree(dk);CHKERRQ(ierr); 147 148 C->factor = FACTOR_CHOLESKY; 149 C->assembled = PETSC_TRUE; 150 C->preallocated = PETSC_TRUE; 151 PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */ 152 PetscFunctionReturn(0); 153 } 154