1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <petsc/private/kernels/blockinvert.h> 4 5 /* Version for when blocks are 4 by 4 */ 6 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(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; 12 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 13 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 14 PetscBool pivotinblocks = b->pivotinblocks; 15 PetscReal shift = info->shiftamount; 16 PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE; 17 18 PetscFunctionBegin; 19 /* initialization */ 20 allowzeropivot = PetscNot(A->erroriffailure); 21 PetscCall(PetscCalloc1(16*mbs,&rtmp)); 22 PetscCall(PetscMalloc2(mbs,&il,mbs,&jl)); 23 il[0] = 0; 24 for (i=0; i<mbs; i++) jl[i] = mbs; 25 26 PetscCall(PetscMalloc2(16,&dk,16,&uik)); 27 PetscCall(ISGetIndices(perm,&perm_ptr)); 28 29 /* check permutation */ 30 if (!a->permute) { 31 ai = a->i; aj = a->j; aa = a->a; 32 } else { 33 ai = a->inew; aj = a->jnew; 34 PetscCall(PetscMalloc1(16*ai[mbs],&aa)); 35 PetscCall(PetscArraycpy(aa,a->a,16*ai[mbs])); 36 PetscCall(PetscMalloc1(ai[mbs],&a2anew)); 37 PetscCall(PetscArraycpy(a2anew,a->a2anew,ai[mbs])); 38 39 for (i=0; i<mbs; i++) { 40 jmin = ai[i]; jmax = ai[i+1]; 41 for (j=jmin; j<jmax; j++) { 42 while (a2anew[j] != j) { 43 k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; 44 for (k1=0; k1<16; k1++) { 45 dk[k1] = aa[k*16+k1]; 46 aa[k*16+k1] = aa[j*16+k1]; 47 aa[j*16+k1] = dk[k1]; 48 } 49 } 50 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 51 if (i > aj[j]) { 52 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 53 ap = aa + j*16; /* ptr to the beginning of j-th block of aa */ 54 for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 55 for (k=0; k<4; k++) { /* j-th block of aa <- dk^T */ 56 for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1]; 57 } 58 } 59 } 60 } 61 PetscCall(PetscFree(a2anew)); 62 } 63 64 /* for each row k */ 65 for (k = 0; k<mbs; k++) { 66 67 /*initialize k-th row with elements nonzero in row perm(k) of A */ 68 jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1]; 69 if (jmin < jmax) { 70 ap = aa + jmin*16; 71 for (j = jmin; j < jmax; j++) { 72 vj = perm_ptr[aj[j]]; /* block col. index */ 73 rtmp_ptr = rtmp + vj*16; 74 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 75 } 76 } 77 78 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 79 PetscCall(PetscArraycpy(dk,rtmp+k*16,16)); 80 i = jl[k]; /* first row to be added to k_th row */ 81 82 while (i < mbs) { 83 nexti = jl[i]; /* next row to be added to k_th row */ 84 85 /* compute multiplier */ 86 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 87 88 /* uik = -inv(Di)*U_bar(i,k) */ 89 diag = ba + i*16; 90 u = ba + ili*16; 91 92 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 93 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 94 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 95 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 96 97 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 98 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 99 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 100 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 101 102 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 103 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 104 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 105 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 106 107 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 108 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 109 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 110 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 111 112 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 113 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 114 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 115 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 116 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 117 118 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 119 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 120 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 121 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 122 123 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 124 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 125 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 126 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 127 128 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 129 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 130 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 131 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 132 133 PetscCall(PetscLogFlops(64.0*4.0)); 134 135 /* update -U(i,k) */ 136 PetscCall(PetscArraycpy(ba+ili*16,uik,16)); 137 138 /* add multiple of row i to k-th row ... */ 139 jmin = ili + 1; jmax = bi[i+1]; 140 if (jmin < jmax) { 141 for (j=jmin; j<jmax; j++) { 142 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 143 rtmp_ptr = rtmp + bj[j]*16; 144 u = ba + j*16; 145 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 146 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 147 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 148 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 149 150 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 151 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 152 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 153 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 154 155 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 156 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 157 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 158 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 159 160 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 161 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 162 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 163 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 164 } 165 PetscCall(PetscLogFlops(2.0*64.0*(jmax-jmin))); 166 167 /* ... add i to row list for next nonzero entry */ 168 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 169 j = bj[jmin]; 170 jl[i] = jl[j]; jl[j] = i; /* update jl */ 171 } 172 i = nexti; 173 } 174 175 /* save nonzero entries in k-th row of U ... */ 176 177 /* invert diagonal block */ 178 diag = ba+k*16; 179 PetscCall(PetscArraycpy(diag,dk,16)); 180 181 if (pivotinblocks) { 182 PetscCall(PetscKernel_A_gets_inverse_A_4(diag,shift, allowzeropivot,&zeropivotdetected)); 183 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 184 } else { 185 PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag)); 186 } 187 188 jmin = bi[k]; jmax = bi[k+1]; 189 if (jmin < jmax) { 190 for (j=jmin; j<jmax; j++) { 191 vj = bj[j]; /* block col. index of U */ 192 u = ba + j*16; 193 rtmp_ptr = rtmp + vj*16; 194 for (k1=0; k1<16; k1++) { 195 *u++ = *rtmp_ptr; 196 *rtmp_ptr++ = 0.0; 197 } 198 } 199 200 /* ... add k to row list for first nonzero entry in k-th row */ 201 il[k] = jmin; 202 i = bj[jmin]; 203 jl[k] = jl[i]; jl[i] = k; 204 } 205 } 206 207 PetscCall(PetscFree(rtmp)); 208 PetscCall(PetscFree2(il,jl)); 209 PetscCall(PetscFree2(dk,uik)); 210 if (a->permute) { 211 PetscCall(PetscFree(aa)); 212 } 213 214 PetscCall(ISRestoreIndices(perm,&perm_ptr)); 215 216 C->ops->solve = MatSolve_SeqSBAIJ_4_inplace; 217 C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_inplace; 218 C->assembled = PETSC_TRUE; 219 C->preallocated = PETSC_TRUE; 220 221 PetscCall(PetscLogFlops(1.3333*64*b->mbs)); /* from inverting diagonal blocks */ 222 PetscFunctionReturn(0); 223 } 224