1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <petsc/private/kernels/blockinvert.h> 4 5 /* 6 Version for when blocks are 4 by 4 Using natural ordering 7 */ 8 #undef __FUNCT__ 9 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering" 10 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info) 11 { 12 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data; 13 PetscErrorCode ierr; 14 PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 15 PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 16 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 17 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 18 PetscBool pivotinblocks = b->pivotinblocks; 19 PetscReal shift = info->shiftamount; 20 21 PetscFunctionBegin; 22 /* initialization */ 23 ierr = PetscCalloc1(16*mbs,&rtmp);CHKERRQ(ierr); 24 ierr = PetscMalloc2(mbs,&il,mbs,&jl);CHKERRQ(ierr); 25 for (i=0; i<mbs; i++) { 26 jl[i] = mbs; il[0] = 0; 27 } 28 ierr = PetscMalloc2(16,&dk,16,&uik);CHKERRQ(ierr); 29 ai = a->i; aj = a->j; aa = a->a; 30 31 /* for each row k */ 32 for (k = 0; k<mbs; k++) { 33 34 /*initialize k-th row with elements nonzero in row k of A */ 35 jmin = ai[k]; jmax = ai[k+1]; 36 if (jmin < jmax) { 37 ap = aa + jmin*16; 38 for (j = jmin; j < jmax; j++) { 39 vj = aj[j]; /* block col. index */ 40 rtmp_ptr = rtmp + vj*16; 41 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 42 } 43 } 44 45 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 46 ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr); 47 i = jl[k]; /* first row to be added to k_th row */ 48 49 while (i < mbs) { 50 nexti = jl[i]; /* next row to be added to k_th row */ 51 52 /* compute multiplier */ 53 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 54 55 /* uik = -inv(Di)*U_bar(i,k) */ 56 diag = ba + i*16; 57 u = ba + ili*16; 58 59 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 60 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 61 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 62 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 63 64 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 65 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 66 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 67 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 68 69 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 70 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 71 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 72 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 73 74 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 75 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 76 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 77 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 78 79 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 80 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 81 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 82 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 83 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 84 85 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 86 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 87 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 88 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 89 90 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 91 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 92 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 93 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 94 95 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 96 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 97 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 98 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 99 100 ierr = PetscLogFlops(64.0*4.0);CHKERRQ(ierr); 101 102 /* update -U(i,k) */ 103 ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr); 104 105 /* add multiple of row i to k-th row ... */ 106 jmin = ili + 1; jmax = bi[i+1]; 107 if (jmin < jmax) { 108 for (j=jmin; j<jmax; j++) { 109 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 110 rtmp_ptr = rtmp + bj[j]*16; 111 u = ba + j*16; 112 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 113 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 114 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 115 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 116 117 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 118 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 119 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 120 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 121 122 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 123 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 124 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 125 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 126 127 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 128 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 129 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 130 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 131 } 132 ierr = PetscLogFlops(2.0*64.0*(jmax-jmin));CHKERRQ(ierr); 133 134 /* ... add i to row list for next nonzero entry */ 135 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 136 j = bj[jmin]; 137 jl[i] = jl[j]; jl[j] = i; /* update jl */ 138 } 139 i = nexti; 140 } 141 142 /* save nonzero entries in k-th row of U ... */ 143 144 /* invert diagonal block */ 145 diag = ba+k*16; 146 ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr); 147 if (pivotinblocks) { 148 ierr = PetscKernel_A_gets_inverse_A_4(diag,shift);CHKERRQ(ierr); 149 } else { 150 ierr = PetscKernel_A_gets_inverse_A_4_nopivot(diag);CHKERRQ(ierr); 151 } 152 153 jmin = bi[k]; jmax = bi[k+1]; 154 if (jmin < jmax) { 155 for (j=jmin; j<jmax; j++) { 156 vj = bj[j]; /* block col. index of U */ 157 u = ba + j*16; 158 rtmp_ptr = rtmp + vj*16; 159 for (k1=0; k1<16; k1++) { 160 *u++ = *rtmp_ptr; 161 *rtmp_ptr++ = 0.0; 162 } 163 } 164 165 /* ... add k to row list for first nonzero entry in k-th row */ 166 il[k] = jmin; 167 i = bj[jmin]; 168 jl[k] = jl[i]; jl[i] = k; 169 } 170 } 171 172 ierr = PetscFree(rtmp);CHKERRQ(ierr); 173 ierr = PetscFree2(il,jl);CHKERRQ(ierr); 174 ierr = PetscFree2(dk,uik);CHKERRQ(ierr); 175 176 C->ops->solve = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 177 C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 178 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 179 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 180 181 C->assembled = PETSC_TRUE; 182 C->preallocated = PETSC_TRUE; 183 184 ierr = PetscLogFlops(1.3333*64*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */ 185 PetscFunctionReturn(0); 186 } 187