1 #include "sbaij.h" 2 #include "src/inline/ilu.h" 3 4 /* Version for when blocks are 4 by 4 */ 5 #undef __FUNC__ 6 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4" 7 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B) 8 { 9 Mat C = *B; 10 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 11 IS perm = b->row; 12 int *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 13 int *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 14 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 15 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 16 17 PetscFunctionBegin; 18 /* initialization */ 19 ierr = PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 20 ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr); 21 ierr = PetscMalloc(2*mbs*sizeof(int),&il);CHKERRQ(ierr); 22 jl = il + mbs; 23 for (i=0; i<mbs; i++) { 24 jl[i] = mbs; il[0] = 0; 25 } 26 ierr = PetscMalloc(32*sizeof(MatScalar),&dk);CHKERRQ(ierr); 27 uik = dk + 16; 28 ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr); 29 30 /* check permutation */ 31 if (!a->permute){ 32 ai = a->i; aj = a->j; aa = a->a; 33 } else { 34 ai = a->inew; aj = a->jnew; 35 ierr = PetscMalloc(16*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr); 36 ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr); 37 ierr = PetscMalloc(ai[mbs]*sizeof(int),&a2anew);CHKERRQ(ierr); 38 ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr); 39 40 for (i=0; i<mbs; i++){ 41 jmin = ai[i]; jmax = ai[i+1]; 42 for (j=jmin; j<jmax; j++){ 43 while (a2anew[j] != j){ 44 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 45 for (k1=0; k1<16; k1++){ 46 dk[k1] = aa[k*16+k1]; 47 aa[k*16+k1] = aa[j*16+k1]; 48 aa[j*16+k1] = dk[k1]; 49 } 50 } 51 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 52 if (i > aj[j]){ 53 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 54 ap = aa + j*16; /* ptr to the beginning of j-th block of aa */ 55 for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 56 for (k=0; k<4; k++){ /* j-th block of aa <- dk^T */ 57 for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1]; 58 } 59 } 60 } 61 } 62 ierr = PetscFree(a2anew);CHKERRQ(ierr); 63 } 64 65 /* for each row k */ 66 for (k = 0; k<mbs; k++){ 67 68 /*initialize k-th row with elements nonzero in row perm(k) of A */ 69 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 70 if (jmin < jmax) { 71 ap = aa + jmin*16; 72 for (j = jmin; j < jmax; j++){ 73 vj = perm_ptr[aj[j]]; /* block col. index */ 74 rtmp_ptr = rtmp + vj*16; 75 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 76 } 77 } 78 79 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 80 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 81 i = jl[k]; /* first row to be added to k_th row */ 82 83 while (i < mbs){ 84 nexti = jl[i]; /* next row to be added to k_th row */ 85 86 /* compute multiplier */ 87 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 88 89 /* uik = -inv(Di)*U_bar(i,k) */ 90 diag = ba + i*16; 91 u = ba + ili*16; 92 93 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 94 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 95 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 96 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 97 98 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 99 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 100 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 101 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 102 103 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 104 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 105 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 106 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 107 108 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 109 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 110 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 111 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 112 113 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 114 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 115 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 116 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 117 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 118 119 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 120 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 121 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 122 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 123 124 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 125 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 126 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 127 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 128 129 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 130 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 131 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 132 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 133 134 /* update -U(i,k) */ 135 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 136 137 /* add multiple of row i to k-th row ... */ 138 jmin = ili + 1; jmax = bi[i+1]; 139 if (jmin < jmax){ 140 for (j=jmin; j<jmax; j++) { 141 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 142 rtmp_ptr = rtmp + bj[j]*16; 143 u = ba + j*16; 144 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 145 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 146 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 147 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 148 149 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 150 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 151 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 152 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 153 154 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 155 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 156 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 157 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 158 159 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 160 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 161 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 162 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 163 } 164 165 /* ... add i to row list for next nonzero entry */ 166 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 167 j = bj[jmin]; 168 jl[i] = jl[j]; jl[j] = i; /* update jl */ 169 } 170 i = nexti; 171 } 172 173 /* save nonzero entries in k-th row of U ... */ 174 175 /* invert diagonal block */ 176 diag = ba+k*16; 177 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 178 ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr); 179 180 jmin = bi[k]; jmax = bi[k+1]; 181 if (jmin < jmax) { 182 for (j=jmin; j<jmax; j++){ 183 vj = bj[j]; /* block col. index of U */ 184 u = ba + j*16; 185 rtmp_ptr = rtmp + vj*16; 186 for (k1=0; k1<16; k1++){ 187 *u++ = *rtmp_ptr; 188 *rtmp_ptr++ = 0.0; 189 } 190 } 191 192 /* ... add k to row list for first nonzero entry in k-th row */ 193 il[k] = jmin; 194 i = bj[jmin]; 195 jl[k] = jl[i]; jl[i] = k; 196 } 197 } 198 199 ierr = PetscFree(rtmp);CHKERRQ(ierr); 200 ierr = PetscFree(il);CHKERRQ(ierr); 201 ierr = PetscFree(dk);CHKERRQ(ierr); 202 if (a->permute){ 203 ierr = PetscFree(aa);CHKERRQ(ierr); 204 } 205 206 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 207 C->factor = FACTOR_CHOLESKY; 208 C->assembled = PETSC_TRUE; 209 C->preallocated = PETSC_TRUE; 210 PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */ 211 PetscFunctionReturn(0); 212 } 213