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; 29 aj = a->j; 30 aa = a->a; 31 32 /* for each row k */ 33 for (k = 0; k < mbs; k++) { 34 /*initialize k-th row with elements nonzero in row k of A */ 35 jmin = ai[k]; 36 jmax = ai[k + 1]; 37 if (jmin < jmax) { 38 ap = aa + jmin * 16; 39 for (j = jmin; j < jmax; j++) { 40 vj = aj[j]; /* block col. index */ 41 rtmp_ptr = rtmp + vj * 16; 42 for (i = 0; i < 16; i++) *rtmp_ptr++ = *ap++; 43 } 44 } 45 46 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 47 PetscCall(PetscArraycpy(dk, rtmp + k * 16, 16)); 48 i = jl[k]; /* first row to be added to k_th row */ 49 50 while (i < mbs) { 51 nexti = jl[i]; /* next row to be added to k_th row */ 52 53 /* compute multiplier */ 54 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 55 56 /* uik = -inv(Di)*U_bar(i,k) */ 57 diag = ba + i * 16; 58 u = ba + ili * 16; 59 60 uik[0] = -(diag[0] * u[0] + diag[4] * u[1] + diag[8] * u[2] + diag[12] * u[3]); 61 uik[1] = -(diag[1] * u[0] + diag[5] * u[1] + diag[9] * u[2] + diag[13] * u[3]); 62 uik[2] = -(diag[2] * u[0] + diag[6] * u[1] + diag[10] * u[2] + diag[14] * u[3]); 63 uik[3] = -(diag[3] * u[0] + diag[7] * u[1] + diag[11] * u[2] + diag[15] * u[3]); 64 65 uik[4] = -(diag[0] * u[4] + diag[4] * u[5] + diag[8] * u[6] + diag[12] * u[7]); 66 uik[5] = -(diag[1] * u[4] + diag[5] * u[5] + diag[9] * u[6] + diag[13] * u[7]); 67 uik[6] = -(diag[2] * u[4] + diag[6] * u[5] + diag[10] * u[6] + diag[14] * u[7]); 68 uik[7] = -(diag[3] * u[4] + diag[7] * u[5] + diag[11] * u[6] + diag[15] * u[7]); 69 70 uik[8] = -(diag[0] * u[8] + diag[4] * u[9] + diag[8] * u[10] + diag[12] * u[11]); 71 uik[9] = -(diag[1] * u[8] + diag[5] * u[9] + diag[9] * u[10] + diag[13] * u[11]); 72 uik[10] = -(diag[2] * u[8] + diag[6] * u[9] + diag[10] * u[10] + diag[14] * u[11]); 73 uik[11] = -(diag[3] * u[8] + diag[7] * u[9] + diag[11] * u[10] + diag[15] * u[11]); 74 75 uik[12] = -(diag[0] * u[12] + diag[4] * u[13] + diag[8] * u[14] + diag[12] * u[15]); 76 uik[13] = -(diag[1] * u[12] + diag[5] * u[13] + diag[9] * u[14] + diag[13] * u[15]); 77 uik[14] = -(diag[2] * u[12] + diag[6] * u[13] + diag[10] * u[14] + diag[14] * u[15]); 78 uik[15] = -(diag[3] * u[12] + diag[7] * u[13] + diag[11] * u[14] + diag[15] * u[15]); 79 80 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 81 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3]; 82 dk[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3]; 83 dk[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3]; 84 dk[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3]; 85 86 dk[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7]; 87 dk[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7]; 88 dk[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7]; 89 dk[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7]; 90 91 dk[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11]; 92 dk[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11]; 93 dk[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11]; 94 dk[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11]; 95 96 dk[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15]; 97 dk[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15]; 98 dk[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15]; 99 dk[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15]; 100 101 PetscCall(PetscLogFlops(64.0 * 4.0)); 102 103 /* update -U(i,k) */ 104 PetscCall(PetscArraycpy(ba + ili * 16, uik, 16)); 105 106 /* add multiple of row i to k-th row ... */ 107 jmin = ili + 1; 108 jmax = bi[i + 1]; 109 if (jmin < jmax) { 110 for (j = jmin; j < jmax; j++) { 111 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 112 rtmp_ptr = rtmp + bj[j] * 16; 113 u = ba + j * 16; 114 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3]; 115 rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3]; 116 rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3]; 117 rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3]; 118 119 rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7]; 120 rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7]; 121 rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7]; 122 rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7]; 123 124 rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11]; 125 rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11]; 126 rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11]; 127 rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11]; 128 129 rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15]; 130 rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15]; 131 rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15]; 132 rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15]; 133 } 134 PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin))); 135 136 /* ... add i to row list for next nonzero entry */ 137 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 138 j = bj[jmin]; 139 jl[i] = jl[j]; 140 jl[j] = i; /* update jl */ 141 } 142 i = nexti; 143 } 144 145 /* save nonzero entries in k-th row of U ... */ 146 147 /* invert diagonal block */ 148 diag = ba + k * 16; 149 PetscCall(PetscArraycpy(diag, dk, 16)); 150 if (pivotinblocks) { 151 PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected)); 152 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 153 } else { 154 PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag)); 155 } 156 157 jmin = bi[k]; 158 jmax = bi[k + 1]; 159 if (jmin < jmax) { 160 for (j = jmin; j < jmax; j++) { 161 vj = bj[j]; /* block col. index of U */ 162 u = ba + j * 16; 163 rtmp_ptr = rtmp + vj * 16; 164 for (k1 = 0; k1 < 16; k1++) { 165 *u++ = *rtmp_ptr; 166 *rtmp_ptr++ = 0.0; 167 } 168 } 169 170 /* ... add k to row list for first nonzero entry in k-th row */ 171 il[k] = jmin; 172 i = bj[jmin]; 173 jl[k] = jl[i]; 174 jl[i] = k; 175 } 176 } 177 178 PetscCall(PetscFree(rtmp)); 179 PetscCall(PetscFree2(il, jl)); 180 PetscCall(PetscFree2(dk, uik)); 181 182 C->ops->solve = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 183 C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 184 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 185 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 186 187 C->assembled = PETSC_TRUE; 188 C->preallocated = PETSC_TRUE; 189 190 PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */ 191 PetscFunctionReturn(PETSC_SUCCESS); 192 } 193