#include <../src/mat/impls/sbaij/seq/sbaij.h> #include /* Version for when blocks are 3 by 3 */ PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat C, Mat A, const MatFactorInfo *info) { Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data; IS perm = b->row; const PetscInt *ai, *aj, *perm_ptr, mbs = a->mbs, *bi = b->i, *bj = b->j; PetscInt *a2anew, i, j, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili; MatScalar *ba = b->a, *aa, *ap, *dk, *uik; MatScalar *u, *diag, *rtmp, *rtmp_ptr; PetscReal shift = info->shiftamount; PetscBool allowzeropivot, zeropivotdetected; PetscFunctionBegin; /* initialization */ allowzeropivot = PetscNot(A->erroriffailure); PetscCall(PetscCalloc1(9 * mbs, &rtmp)); PetscCall(PetscMalloc2(mbs, &il, mbs, &jl)); il[0] = 0; for (i = 0; i < mbs; i++) jl[i] = mbs; PetscCall(PetscMalloc2(9, &dk, 9, &uik)); PetscCall(ISGetIndices(perm, &perm_ptr)); /* check permutation */ if (!a->permute) { ai = a->i; aj = a->j; aa = a->a; } else { ai = a->inew; aj = a->jnew; PetscCall(PetscMalloc1(9 * ai[mbs], &aa)); PetscCall(PetscArraycpy(aa, a->a, 9 * ai[mbs])); PetscCall(PetscMalloc1(ai[mbs], &a2anew)); PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs])); for (i = 0; i < mbs; i++) { jmin = ai[i]; jmax = ai[i + 1]; for (j = jmin; j < jmax; j++) { while (a2anew[j] != j) { k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k; for (k1 = 0; k1 < 9; k1++) { dk[k1] = aa[k * 9 + k1]; aa[k * 9 + k1] = aa[j * 9 + k1]; aa[j * 9 + k1] = dk[k1]; } } /* transform column-oriented blocks that lie in the lower triangle to row-oriented blocks */ if (i > aj[j]) { /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ ap = aa + j * 9; /* ptr to the beginning of j-th block of aa */ for (k = 0; k < 9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ for (k = 0; k < 3; k++) { /* j-th block of aa <- dk^T */ for (k1 = 0; k1 < 3; k1++) *ap++ = dk[k + 3 * k1]; } } } } PetscCall(PetscFree(a2anew)); } /* for each row k */ for (k = 0; k < mbs; k++) { /*initialize k-th row with elements nonzero in row perm(k) of A */ jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k] + 1]; if (jmin < jmax) { ap = aa + jmin * 9; for (j = jmin; j < jmax; j++) { vj = perm_ptr[aj[j]]; /* block col. index */ rtmp_ptr = rtmp + vj * 9; for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++; } } /* modify k-th row by adding in those rows i with U(i,k) != 0 */ PetscCall(PetscArraycpy(dk, rtmp + k * 9, 9)); i = jl[k]; /* first row to be added to k_th row */ while (i < mbs) { nexti = jl[i]; /* next row to be added to k_th row */ /* compute multiplier */ ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ /* uik = -inv(Di)*U_bar(i,k) */ diag = ba + i * 9; u = ba + ili * 9; uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]); uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]); uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]); uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]); uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]); uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]); uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]); uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]); uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]); /* update D(k) += -U(i,k)^T * U_bar(i,k) */ dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; PetscCall(PetscLogFlops(27.0 * 4.0)); /* update -U(i,k) */ PetscCall(PetscArraycpy(ba + ili * 9, uik, 9)); /* add multiple of row i to k-th row ... */ jmin = ili + 1; jmax = bi[i + 1]; if (jmin < jmax) { for (j = jmin; j < jmax; j++) { /* rtmp += -U(i,k)^T * U_bar(i,j) */ rtmp_ptr = rtmp + bj[j] * 9; u = ba + j * 9; rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; } PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin))); /* ... add i to row list for next nonzero entry */ il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ j = bj[jmin]; jl[i] = jl[j]; jl[j] = i; /* update jl */ } i = nexti; } /* save nonzero entries in k-th row of U ... */ /* invert diagonal block */ diag = ba + k * 9; PetscCall(PetscArraycpy(diag, dk, 9)); PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected)); if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; jmin = bi[k]; jmax = bi[k + 1]; if (jmin < jmax) { for (j = jmin; j < jmax; j++) { vj = bj[j]; /* block col. index of U */ u = ba + j * 9; rtmp_ptr = rtmp + vj * 9; for (k1 = 0; k1 < 9; k1++) { *u++ = *rtmp_ptr; *rtmp_ptr++ = 0.0; } } /* ... add k to row list for first nonzero entry in k-th row */ il[k] = jmin; i = bj[jmin]; jl[k] = jl[i]; jl[i] = k; } } PetscCall(PetscFree(rtmp)); PetscCall(PetscFree2(il, jl)); PetscCall(PetscFree2(dk, uik)); if (a->permute) PetscCall(PetscFree(aa)); PetscCall(ISRestoreIndices(perm, &perm_ptr)); C->ops->solve = MatSolve_SeqSBAIJ_3_inplace; C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace; C->assembled = PETSC_TRUE; C->preallocated = PETSC_TRUE; PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */ PetscFunctionReturn(PETSC_SUCCESS); }