1 #include <../src/mat/impls/sbaij/seq/sbaij.h> 2 #include <petsc/private/kernels/blockinvert.h> 3 4 /* 5 Version for when blocks are 3 by 3 Using natural ordering 6 */ 7 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info) 8 { 9 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data; 10 PetscInt i, j, mbs = a->mbs, *bi = b->i, *bj = b->j; 11 PetscInt *ai, *aj, 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 PetscReal shift = info->shiftamount; 15 PetscBool allowzeropivot, zeropivotdetected; 16 17 PetscFunctionBegin; 18 /* initialization */ 19 allowzeropivot = PetscNot(A->erroriffailure); 20 PetscCall(PetscCalloc1(9 * 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(9, &dk, 9, &uik)); 26 ai = a->i; 27 aj = a->j; 28 aa = a->a; 29 30 /* for each row k */ 31 for (k = 0; k < mbs; k++) { 32 /*initialize k-th row with elements nonzero in row k of A */ 33 jmin = ai[k]; 34 jmax = ai[k + 1]; 35 if (jmin < jmax) { 36 ap = aa + jmin * 9; 37 for (j = jmin; j < jmax; j++) { 38 vj = aj[j]; /* block col. index */ 39 rtmp_ptr = rtmp + vj * 9; 40 for (i = 0; i < 9; 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 * 9, 9)); 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 * 9; 56 u = ba + ili * 9; 57 58 uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]); 59 uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]); 60 uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]); 61 62 uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]); 63 uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]); 64 uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]); 65 66 uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]); 67 uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]); 68 uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]); 69 70 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 71 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; 72 dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; 73 dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; 74 75 dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; 76 dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; 77 dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; 78 79 dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; 80 dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; 81 dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; 82 83 PetscCall(PetscLogFlops(27.0 * 4.0)); 84 85 /* update -U(i,k) */ 86 PetscCall(PetscArraycpy(ba + ili * 9, uik, 9)); 87 88 /* add multiple of row i to k-th row ... */ 89 jmin = ili + 1; 90 jmax = bi[i + 1]; 91 if (jmin < jmax) { 92 for (j = jmin; j < jmax; j++) { 93 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 94 rtmp_ptr = rtmp + bj[j] * 9; 95 u = ba + j * 9; 96 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; 97 rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; 98 rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; 99 100 rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; 101 rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; 102 rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; 103 104 rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; 105 rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; 106 rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; 107 } 108 PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin))); 109 110 /* ... add i to row list for next nonzero entry */ 111 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 112 j = bj[jmin]; 113 jl[i] = jl[j]; 114 jl[j] = i; /* update jl */ 115 } 116 i = nexti; 117 } 118 119 /* save nonzero entries in k-th row of U ... */ 120 121 /* invert diagonal block */ 122 diag = ba + k * 9; 123 PetscCall(PetscArraycpy(diag, dk, 9)); 124 PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected)); 125 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 126 127 jmin = bi[k]; 128 jmax = bi[k + 1]; 129 if (jmin < jmax) { 130 for (j = jmin; j < jmax; j++) { 131 vj = bj[j]; /* block col. index of U */ 132 u = ba + j * 9; 133 rtmp_ptr = rtmp + vj * 9; 134 for (k1 = 0; k1 < 9; k1++) { 135 *u++ = *rtmp_ptr; 136 *rtmp_ptr++ = 0.0; 137 } 138 } 139 140 /* ... add k to row list for first nonzero entry in k-th row */ 141 il[k] = jmin; 142 i = bj[jmin]; 143 jl[k] = jl[i]; 144 jl[i] = k; 145 } 146 } 147 148 PetscCall(PetscFree(rtmp)); 149 PetscCall(PetscFree2(il, jl)); 150 PetscCall(PetscFree2(dk, uik)); 151 152 C->ops->solve = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 153 C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 154 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 155 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 156 157 C->assembled = PETSC_TRUE; 158 C->preallocated = PETSC_TRUE; 159 160 PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */ 161 PetscFunctionReturn(PETSC_SUCCESS); 162 } 163