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 3 by 3 Using natural ordering 7 */ 8 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_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 PetscReal shift = info->shiftamount; 16 PetscBool allowzeropivot, zeropivotdetected; 17 18 PetscFunctionBegin; 19 /* initialization */ 20 allowzeropivot = PetscNot(A->erroriffailure); 21 PetscCall(PetscCalloc1(9 * 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(9, &dk, 9, &uik)); 27 ai = a->i; 28 aj = a->j; 29 aa = a->a; 30 31 /* for each row k */ 32 for (k = 0; k < mbs; k++) { 33 /*initialize k-th row with elements nonzero in row k of A */ 34 jmin = ai[k]; 35 jmax = ai[k + 1]; 36 if (jmin < jmax) { 37 ap = aa + jmin * 9; 38 for (j = jmin; j < jmax; j++) { 39 vj = aj[j]; /* block col. index */ 40 rtmp_ptr = rtmp + vj * 9; 41 for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++; 42 } 43 } 44 45 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 46 PetscCall(PetscArraycpy(dk, rtmp + k * 9, 9)); 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 * 9; 57 u = ba + ili * 9; 58 59 uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]); 60 uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]); 61 uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]); 62 63 uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]); 64 uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]); 65 uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]); 66 67 uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]); 68 uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]); 69 uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]); 70 71 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 72 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; 73 dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; 74 dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; 75 76 dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; 77 dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; 78 dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; 79 80 dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; 81 dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; 82 dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; 83 84 PetscCall(PetscLogFlops(27.0 * 4.0)); 85 86 /* update -U(i,k) */ 87 PetscCall(PetscArraycpy(ba + ili * 9, uik, 9)); 88 89 /* add multiple of row i to k-th row ... */ 90 jmin = ili + 1; 91 jmax = bi[i + 1]; 92 if (jmin < jmax) { 93 for (j = jmin; j < jmax; j++) { 94 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 95 rtmp_ptr = rtmp + bj[j] * 9; 96 u = ba + j * 9; 97 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; 98 rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; 99 rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; 100 101 rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; 102 rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; 103 rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; 104 105 rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; 106 rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; 107 rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; 108 } 109 PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin))); 110 111 /* ... add i to row list for next nonzero entry */ 112 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 113 j = bj[jmin]; 114 jl[i] = jl[j]; 115 jl[j] = i; /* update jl */ 116 } 117 i = nexti; 118 } 119 120 /* save nonzero entries in k-th row of U ... */ 121 122 /* invert diagonal block */ 123 diag = ba + k * 9; 124 PetscCall(PetscArraycpy(diag, dk, 9)); 125 PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected)); 126 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 127 128 jmin = bi[k]; 129 jmax = bi[k + 1]; 130 if (jmin < jmax) { 131 for (j = jmin; j < jmax; j++) { 132 vj = bj[j]; /* block col. index of U */ 133 u = ba + j * 9; 134 rtmp_ptr = rtmp + vj * 9; 135 for (k1 = 0; k1 < 9; k1++) { 136 *u++ = *rtmp_ptr; 137 *rtmp_ptr++ = 0.0; 138 } 139 } 140 141 /* ... add k to row list for first nonzero entry in k-th row */ 142 il[k] = jmin; 143 i = bj[jmin]; 144 jl[k] = jl[i]; 145 jl[i] = k; 146 } 147 } 148 149 PetscCall(PetscFree(rtmp)); 150 PetscCall(PetscFree2(il, jl)); 151 PetscCall(PetscFree2(dk, uik)); 152 153 C->ops->solve = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 154 C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 155 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 156 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace; 157 158 C->assembled = PETSC_TRUE; 159 C->preallocated = PETSC_TRUE; 160 161 PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */ 162 PetscFunctionReturn(PETSC_SUCCESS); 163 } 164