1 #include <../src/mat/impls/sbaij/seq/sbaij.h> 2 #include <petsc/private/kernels/blockinvert.h> 3 4 /* 5 Version for when blocks are 4 by 4 Using natural ordering 6 */ 7 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_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 PetscBool pivotinblocks = b->pivotinblocks; 15 PetscReal shift = info->shiftamount; 16 PetscBool allowzeropivot, zeropivotdetected = PETSC_FALSE; 17 18 PetscFunctionBegin; 19 /* initialization */ 20 allowzeropivot = PetscNot(A->erroriffailure); 21 PetscCall(PetscCalloc1(16 * 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(16, &dk, 16, &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 * 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 PetscCall(PetscArraycpy(dk, rtmp + k * 16, 16)); 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 PetscCall(PetscLogFlops(64.0 * 4.0)); 101 102 /* update -U(i,k) */ 103 PetscCall(PetscArraycpy(ba + ili * 16, uik, 16)); 104 105 /* add multiple of row i to k-th row ... */ 106 jmin = ili + 1; 107 jmax = bi[i + 1]; 108 if (jmin < jmax) { 109 for (j = jmin; j < jmax; j++) { 110 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 111 rtmp_ptr = rtmp + bj[j] * 16; 112 u = ba + j * 16; 113 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3]; 114 rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3]; 115 rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3]; 116 rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3]; 117 118 rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7]; 119 rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7]; 120 rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7]; 121 rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7]; 122 123 rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11]; 124 rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11]; 125 rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11]; 126 rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11]; 127 128 rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15]; 129 rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15]; 130 rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15]; 131 rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15]; 132 } 133 PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin))); 134 135 /* ... add i to row list for next nonzero entry */ 136 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 137 j = bj[jmin]; 138 jl[i] = jl[j]; 139 jl[j] = i; /* update jl */ 140 } 141 i = nexti; 142 } 143 144 /* save nonzero entries in k-th row of U ... */ 145 146 /* invert diagonal block */ 147 diag = ba + k * 16; 148 PetscCall(PetscArraycpy(diag, dk, 16)); 149 if (pivotinblocks) { 150 PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected)); 151 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 152 } else { 153 PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag)); 154 } 155 156 jmin = bi[k]; 157 jmax = bi[k + 1]; 158 if (jmin < jmax) { 159 for (j = jmin; j < jmax; j++) { 160 vj = bj[j]; /* block col. index of U */ 161 u = ba + j * 16; 162 rtmp_ptr = rtmp + vj * 16; 163 for (k1 = 0; k1 < 16; k1++) { 164 *u++ = *rtmp_ptr; 165 *rtmp_ptr++ = 0.0; 166 } 167 } 168 169 /* ... add k to row list for first nonzero entry in k-th row */ 170 il[k] = jmin; 171 i = bj[jmin]; 172 jl[k] = jl[i]; 173 jl[i] = k; 174 } 175 } 176 177 PetscCall(PetscFree(rtmp)); 178 PetscCall(PetscFree2(il, jl)); 179 PetscCall(PetscFree2(dk, uik)); 180 181 C->ops->solve = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 182 C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 183 C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 184 C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace; 185 186 C->assembled = PETSC_TRUE; 187 C->preallocated = PETSC_TRUE; 188 189 PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */ 190 PetscFunctionReturn(PETSC_SUCCESS); 191 } 192