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 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info) 9 { 10 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data; 11 PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j; 12 PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili; 13 MatScalar *ba = b->a,*aa,*ap,*dk,*uik; 14 MatScalar *u,*diag,*rtmp,*rtmp_ptr; 15 PetscBool pivotinblocks = b->pivotinblocks; 16 PetscReal shift = info->shiftamount; 17 PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE; 18 19 PetscFunctionBegin; 20 /* initialization */ 21 allowzeropivot = PetscNot(A->erroriffailure); 22 PetscCall(PetscCalloc1(16*mbs,&rtmp)); 23 PetscCall(PetscMalloc2(mbs,&il,mbs,&jl)); 24 il[0] = 0; 25 for (i=0; i<mbs; i++) jl[i] = mbs; 26 27 PetscCall(PetscMalloc2(16,&dk,16,&uik)); 28 ai = a->i; aj = a->j; aa = a->a; 29 30 /* for each row k */ 31 for (k = 0; k<mbs; k++) { 32 33 /*initialize k-th row with elements nonzero in row k of A */ 34 jmin = ai[k]; jmax = ai[k+1]; 35 if (jmin < jmax) { 36 ap = aa + jmin*16; 37 for (j = jmin; j < jmax; j++) { 38 vj = aj[j]; /* block col. index */ 39 rtmp_ptr = rtmp + vj*16; 40 for (i=0; i<16; i++) *rtmp_ptr++ = *ap++; 41 } 42 } 43 44 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 45 PetscCall(PetscArraycpy(dk,rtmp+k*16,16)); 46 i = jl[k]; /* first row to be added to k_th row */ 47 48 while (i < mbs) { 49 nexti = jl[i]; /* next row to be added to k_th row */ 50 51 /* compute multiplier */ 52 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 53 54 /* uik = -inv(Di)*U_bar(i,k) */ 55 diag = ba + i*16; 56 u = ba + ili*16; 57 58 uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]); 59 uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]); 60 uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]); 61 uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]); 62 63 uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]); 64 uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]); 65 uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]); 66 uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]); 67 68 uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]); 69 uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]); 70 uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]); 71 uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]); 72 73 uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]); 74 uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]); 75 uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]); 76 uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]); 77 78 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 79 dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 80 dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 81 dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 82 dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 83 84 dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 85 dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 86 dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 87 dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 88 89 dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 90 dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 91 dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 92 dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 93 94 dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 95 dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 96 dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 97 dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 98 99 PetscCall(PetscLogFlops(64.0*4.0)); 100 101 /* update -U(i,k) */ 102 PetscCall(PetscArraycpy(ba+ili*16,uik,16)); 103 104 /* add multiple of row i to k-th row ... */ 105 jmin = ili + 1; jmax = bi[i+1]; 106 if (jmin < jmax) { 107 for (j=jmin; j<jmax; j++) { 108 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 109 rtmp_ptr = rtmp + bj[j]*16; 110 u = ba + j*16; 111 rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3]; 112 rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3]; 113 rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3]; 114 rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]; 115 116 rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7]; 117 rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7]; 118 rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7]; 119 rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7]; 120 121 rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11]; 122 rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11]; 123 rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11]; 124 rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11]; 125 126 rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15]; 127 rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15]; 128 rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15]; 129 rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]; 130 } 131 PetscCall(PetscLogFlops(2.0*64.0*(jmax-jmin))); 132 133 /* ... add i to row list for next nonzero entry */ 134 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 135 j = bj[jmin]; 136 jl[i] = jl[j]; jl[j] = i; /* update jl */ 137 } 138 i = nexti; 139 } 140 141 /* save nonzero entries in k-th row of U ... */ 142 143 /* invert diagonal block */ 144 diag = ba+k*16; 145 PetscCall(PetscArraycpy(diag,dk,16)); 146 if (pivotinblocks) { 147 PetscCall(PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected)); 148 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 149 } else { 150 PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag)); 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 PetscCall(PetscFree(rtmp)); 173 PetscCall(PetscFree2(il,jl)); 174 PetscCall(PetscFree2(dk,uik)); 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 PetscCall(PetscLogFlops(1.3333*64*b->mbs)); /* from inverting diagonal blocks */ 185 PetscFunctionReturn(0); 186 } 187