1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <petsc/private/kernels/blockinvert.h> 4 5 /* Version for when blocks are 5 by 5 */ 6 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat C,Mat A,const MatFactorInfo *info) 7 { 8 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data; 9 IS perm = b->row; 10 const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j; 11 PetscInt i,j,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili,ipvt[5]; 12 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 13 MatScalar *u,*d,*rtmp,*rtmp_ptr,work[25]; 14 PetscReal shift = info->shiftamount; 15 PetscBool allowzeropivot,zeropivotdetected; 16 17 PetscFunctionBegin; 18 /* initialization */ 19 allowzeropivot = PetscNot(A->erroriffailure); 20 PetscCall(PetscCalloc1(25*mbs,&rtmp)); 21 PetscCall(PetscMalloc2(mbs,&il,mbs,&jl)); 22 il[0] = 0; 23 for (i=0; i<mbs; i++) jl[i] = mbs; 24 25 PetscCall(PetscMalloc2(25,&dk,25,&uik)); 26 PetscCall(ISGetIndices(perm,&perm_ptr)); 27 28 /* check permutation */ 29 if (!a->permute) { 30 ai = a->i; aj = a->j; aa = a->a; 31 } else { 32 ai = a->inew; aj = a->jnew; 33 PetscCall(PetscMalloc1(25*ai[mbs],&aa)); 34 PetscCall(PetscArraycpy(aa,a->a,25*ai[mbs])); 35 PetscCall(PetscMalloc1(ai[mbs],&a2anew)); 36 PetscCall(PetscArraycpy(a2anew,a->a2anew,ai[mbs])); 37 38 for (i=0; i<mbs; i++) { 39 jmin = ai[i]; jmax = ai[i+1]; 40 for (j=jmin; j<jmax; j++) { 41 while (a2anew[j] != j) { 42 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 43 for (k1=0; k1<25; k1++) { 44 dk[k1] = aa[k*25+k1]; 45 aa[k*25+k1] = aa[j*25+k1]; 46 aa[j*25+k1] = dk[k1]; 47 } 48 } 49 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 50 if (i > aj[j]) { 51 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 52 ap = aa + j*25; /* ptr to the beginning of j-th block of aa */ 53 for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 54 for (k=0; k<5; k++) { /* j-th block of aa <- dk^T */ 55 for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1]; 56 } 57 } 58 } 59 } 60 PetscCall(PetscFree(a2anew)); 61 } 62 63 /* for each row k */ 64 for (k = 0; k<mbs; k++) { 65 66 /*initialize k-th row with elements nonzero in row perm(k) of A */ 67 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 68 if (jmin < jmax) { 69 ap = aa + jmin*25; 70 for (j = jmin; j < jmax; j++) { 71 vj = perm_ptr[aj[j]]; /* block col. index */ 72 rtmp_ptr = rtmp + vj*25; 73 for (i=0; i<25; i++) *rtmp_ptr++ = *ap++; 74 } 75 } 76 77 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 78 PetscCall(PetscArraycpy(dk,rtmp+k*25,25)); 79 i = jl[k]; /* first row to be added to k_th row */ 80 81 while (i < mbs) { 82 nexti = jl[i]; /* next row to be added to k_th row */ 83 84 /* compute multiplier */ 85 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 86 87 /* uik = -inv(Di)*U_bar(i,k) */ 88 d = ba + i*25; 89 u = ba + ili*25; 90 91 uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]); 92 uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]); 93 uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]); 94 uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]); 95 uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]); 96 97 uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]); 98 uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]); 99 uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]); 100 uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]); 101 uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]); 102 103 uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]); 104 uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]); 105 uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]); 106 uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]); 107 uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]); 108 109 uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]); 110 uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]); 111 uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]); 112 uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]); 113 uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]); 114 115 uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]); 116 uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]); 117 uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]); 118 uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]); 119 uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]); 120 121 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 122 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 123 dk[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 124 dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 125 dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 126 dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 127 128 dk[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 129 dk[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 130 dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 131 dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 132 dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 133 134 dk[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 135 dk[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 136 dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 137 dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 138 dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 139 140 dk[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 141 dk[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 142 dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 143 dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 144 dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 145 146 dk[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 147 dk[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 148 dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 149 dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 150 dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 151 152 PetscCall(PetscLogFlops(125.0*4.0)); 153 154 /* update -U(i,k) */ 155 PetscCall(PetscArraycpy(ba+ili*25,uik,25)); 156 157 /* add multiple of row i to k-th row ... */ 158 jmin = ili + 1; jmax = bi[i+1]; 159 if (jmin < jmax) { 160 for (j=jmin; j<jmax; j++) { 161 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 162 rtmp_ptr = rtmp + bj[j]*25; 163 u = ba + j*25; 164 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4]; 165 rtmp_ptr[1] += uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4]; 166 rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4]; 167 rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4]; 168 rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4]; 169 170 rtmp_ptr[5] += uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9]; 171 rtmp_ptr[6] += uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]; 172 rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9]; 173 rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9]; 174 rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9]; 175 176 rtmp_ptr[10] += uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14]; 177 rtmp_ptr[11] += uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14]; 178 rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]; 179 rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14]; 180 rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14]; 181 182 rtmp_ptr[15] += uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19]; 183 rtmp_ptr[16] += uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19]; 184 rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19]; 185 rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]; 186 rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19]; 187 188 rtmp_ptr[20] += uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24]; 189 rtmp_ptr[21] += uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24]; 190 rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24]; 191 rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24]; 192 rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]; 193 } 194 PetscCall(PetscLogFlops(2.0*125.0*(jmax-jmin))); 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 PetscCall(PetscArraycpy(d,dk,25)); 209 PetscCall(PetscKernel_A_gets_inverse_A_5(d,ipvt,work,shift,allowzeropivot,&zeropivotdetected)); 210 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 211 212 jmin = bi[k]; jmax = bi[k+1]; 213 if (jmin < jmax) { 214 for (j=jmin; j<jmax; j++) { 215 vj = bj[j]; /* block col. index of U */ 216 u = ba + j*25; 217 rtmp_ptr = rtmp + vj*25; 218 for (k1=0; k1<25; k1++) { 219 *u++ = *rtmp_ptr; 220 *rtmp_ptr++ = 0.0; 221 } 222 } 223 224 /* ... add k to row list for first nonzero entry in k-th row */ 225 il[k] = jmin; 226 i = bj[jmin]; 227 jl[k] = jl[i]; jl[i] = k; 228 } 229 } 230 231 PetscCall(PetscFree(rtmp)); 232 PetscCall(PetscFree2(il,jl)); 233 PetscCall(PetscFree2(dk,uik)); 234 if (a->permute) { 235 PetscCall(PetscFree(aa)); 236 } 237 238 PetscCall(ISRestoreIndices(perm,&perm_ptr)); 239 240 C->ops->solve = MatSolve_SeqSBAIJ_5_inplace; 241 C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_inplace; 242 C->assembled = PETSC_TRUE; 243 C->preallocated = PETSC_TRUE; 244 245 PetscCall(PetscLogFlops(1.3333*125*b->mbs)); /* from inverting diagonal blocks */ 246 PetscFunctionReturn(0); 247 } 248