1 #include "sbaij.h" 2 #include "src/inline/ilu.h" 3 4 /* Version for when blocks are 5 by 5 */ 5 #undef __FUNC__ 6 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5" 7 int MatCholeskyFactorNumeric_SeqSBAIJ_5(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,*d,*rtmp,*rtmp_ptr; 16 17 PetscFunctionBegin; 18 /* initialization */ 19 ierr = PetscMalloc(25*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 20 ierr = PetscMemzero(rtmp,25*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(50*sizeof(MatScalar),&dk);CHKERRQ(ierr); 27 uik = dk + 25; 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(25*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr); 36 ierr = PetscMemcpy(aa,a->a,25*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<25; k1++){ 46 dk[k1] = aa[k*25+k1]; 47 aa[k*25+k1] = aa[j*25+k1]; 48 aa[j*25+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*25; /* ptr to the beginning of j-th block of aa */ 55 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 56 for (k=0; k<5; k++){ /* j-th block of aa <- dk^T */ 57 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*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*25; 72 for (j = jmin; j < jmax; j++){ 73 vj = perm_ptr[aj[j]]; /* block col. index */ 74 rtmp_ptr = rtmp + vj*25; 75 for (i=0; i<25; 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*25,25*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 d = ba + i*25; 91 u = ba + ili*25; 92 93 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 94 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 95 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 96 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 97 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 98 99 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 100 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 101 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 102 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 103 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 104 105 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 106 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 107 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 108 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 109 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 110 111 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 112 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 113 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 114 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 115 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 116 117 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 118 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 119 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 120 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 121 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 122 123 124 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 125 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 126 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 127 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 128 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 129 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 130 131 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 132 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 133 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 134 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 135 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 136 137 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 138 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 139 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 140 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 141 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 142 143 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 144 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 145 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 146 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 147 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 148 149 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 150 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 151 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 152 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 153 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 154 155 /* update -U(i,k) */ 156 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 157 158 /* add multiple of row i to k-th row ... */ 159 jmin = ili + 1; jmax = bi[i+1]; 160 if (jmin < jmax){ 161 for (j=jmin; j<jmax; j++) { 162 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 163 rtmp_ptr = rtmp + bj[j]*25; 164 u = ba + j*25; 165 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 166 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 167 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 168 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 169 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 170 171 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 172 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 173 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 174 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 175 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 176 177 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 178 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 179 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 180 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 181 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 182 183 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 184 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 185 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 186 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 187 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 188 189 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 190 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 191 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 192 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 193 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 194 } 195 196 /* ... add i to row list for next nonzero entry */ 197 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 198 j = bj[jmin]; 199 jl[i] = jl[j]; jl[j] = i; /* update jl */ 200 } 201 i = nexti; 202 } 203 204 /* save nonzero entries in k-th row of U ... */ 205 206 /* invert diagonal block */ 207 d = ba+k*25; 208 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 209 ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr); 210 211 jmin = bi[k]; jmax = bi[k+1]; 212 if (jmin < jmax) { 213 for (j=jmin; j<jmax; j++){ 214 vj = bj[j]; /* block col. index of U */ 215 u = ba + j*25; 216 rtmp_ptr = rtmp + vj*25; 217 for (k1=0; k1<25; k1++){ 218 *u++ = *rtmp_ptr; 219 *rtmp_ptr++ = 0.0; 220 } 221 } 222 223 /* ... add k to row list for first nonzero entry in k-th row */ 224 il[k] = jmin; 225 i = bj[jmin]; 226 jl[k] = jl[i]; jl[i] = k; 227 } 228 } 229 230 ierr = PetscFree(rtmp);CHKERRQ(ierr); 231 ierr = PetscFree(il);CHKERRQ(ierr); 232 ierr = PetscFree(dk);CHKERRQ(ierr); 233 if (a->permute){ 234 ierr = PetscFree(aa);CHKERRQ(ierr); 235 } 236 237 ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr); 238 C->factor = FACTOR_CHOLESKY; 239 C->assembled = PETSC_TRUE; 240 C->preallocated = PETSC_TRUE; 241 PetscLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */ 242 PetscFunctionReturn(0); 243 } 244