1 #define PETSCMAT_DLL 2 3 #include "src/mat/impls/sbaij/seq/sbaij.h" 4 #include "src/inline/ilu.h" 5 6 /* 7 Version for when blocks are 5 by 5 Using natural ordering 8 */ 9 #undef __FUNCT__ 10 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering" 11 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,MatFactorInfo *info,Mat *B) 12 { 13 Mat C = *B; 14 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data; 15 PetscErrorCode ierr; 16 PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 17 PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 18 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 19 MatScalar *u,*d,*rtmp,*rtmp_ptr; 20 PetscReal shift = info->shiftinblocks; 21 22 PetscFunctionBegin; 23 /* initialization */ 24 ierr = PetscMalloc(25*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr); 25 ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr); 26 ierr = PetscMalloc(2*mbs*sizeof(PetscInt),&il);CHKERRQ(ierr); 27 jl = il + mbs; 28 for (i=0; i<mbs; i++) { 29 jl[i] = mbs; il[0] = 0; 30 } 31 ierr = PetscMalloc(50*sizeof(MatScalar),&dk);CHKERRQ(ierr); 32 uik = dk + 25; 33 34 ai = a->i; aj = a->j; aa = a->a; 35 36 /* for each row k */ 37 for (k = 0; k<mbs; k++){ 38 39 /*initialize k-th row with elements nonzero in row k of A */ 40 jmin = ai[k]; jmax = ai[k+1]; 41 if (jmin < jmax) { 42 ap = aa + jmin*25; 43 for (j = jmin; j < jmax; j++){ 44 vj = aj[j]; /* block col. index */ 45 rtmp_ptr = rtmp + vj*25; 46 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 47 } 48 } 49 50 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 51 ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr); 52 i = jl[k]; /* first row to be added to k_th row */ 53 54 while (i < mbs){ 55 nexti = jl[i]; /* next row to be added to k_th row */ 56 57 /* compute multiplier */ 58 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 59 60 /* uik = -inv(Di)*U_bar(i,k) */ 61 d = ba + i*25; 62 u = ba + ili*25; 63 64 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 65 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 66 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 67 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 68 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 69 70 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 71 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 72 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 73 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 74 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 75 76 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 77 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 78 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 79 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 80 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 81 82 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 83 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 84 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 85 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 86 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 87 88 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 89 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 90 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 91 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 92 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 93 94 95 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 96 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 97 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 98 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 99 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 100 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 101 102 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 103 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 104 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 105 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 106 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 107 108 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 109 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 110 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 111 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 112 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 113 114 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 115 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 116 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 117 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 118 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 119 120 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 121 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 122 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 123 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 124 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 125 126 ierr = PetscLogFlops(125*4);CHKERRQ(ierr); 127 128 /* update -U(i,k) */ 129 ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr); 130 131 /* add multiple of row i to k-th row ... */ 132 jmin = ili + 1; jmax = bi[i+1]; 133 if (jmin < jmax){ 134 for (j=jmin; j<jmax; j++) { 135 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 136 rtmp_ptr = rtmp + bj[j]*25; 137 u = ba + j*25; 138 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 139 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 140 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 141 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 142 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 143 144 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 145 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 146 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 147 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 148 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 149 150 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 151 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 152 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 153 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 154 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 155 156 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 157 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 158 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 159 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 160 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 161 162 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 163 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 164 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 165 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 166 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 167 } 168 ierr = PetscLogFlops(2*125*(jmax-jmin));CHKERRQ(ierr); 169 170 /* ... add i to row list for next nonzero entry */ 171 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 172 j = bj[jmin]; 173 jl[i] = jl[j]; jl[j] = i; /* update jl */ 174 } 175 i = nexti; 176 } 177 178 /* save nonzero entries in k-th row of U ... */ 179 180 /* invert diagonal block */ 181 d = ba+k*25; 182 ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr); 183 ierr = Kernel_A_gets_inverse_A_5(d,shift);CHKERRQ(ierr); 184 185 jmin = bi[k]; jmax = bi[k+1]; 186 if (jmin < jmax) { 187 for (j=jmin; j<jmax; j++){ 188 vj = bj[j]; /* block col. index of U */ 189 u = ba + j*25; 190 rtmp_ptr = rtmp + vj*25; 191 for (k1=0; k1<25; k1++){ 192 *u++ = *rtmp_ptr; 193 *rtmp_ptr++ = 0.0; 194 } 195 } 196 197 /* ... add k to row list for first nonzero entry in k-th row */ 198 il[k] = jmin; 199 i = bj[jmin]; 200 jl[k] = jl[i]; jl[i] = k; 201 } 202 } 203 204 ierr = PetscFree(rtmp);CHKERRQ(ierr); 205 ierr = PetscFree(il);CHKERRQ(ierr); 206 ierr = PetscFree(dk);CHKERRQ(ierr); 207 208 C->ops->solve = MatSolve_SeqSBAIJ_5_NaturalOrdering; 209 C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_NaturalOrdering; 210 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_5_NaturalOrdering; 211 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_5_NaturalOrdering; 212 C->assembled = PETSC_TRUE; 213 C->preallocated = PETSC_TRUE; 214 ierr = PetscLogFlops(1.3333*125*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */ 215 PetscFunctionReturn(0); 216 } 217