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/petsc/src/ksp/pc/impls/sor/
H A Dsor.tex18A_{ii}^{-1}( b_i - \sum_{j < i} A_{ij} x_j^{n+1/2} - \sum_{j \ge i} A_{ij} x_j^{n}) = (1 - \omega)…
22A_{ii}^{-1}( b_i - \sum_{j \le i} A_{ij} x_j^{n+1/2} - \sum_{j > i} A_{ij} x_j^{n+1}) = (1 - \ome…
28 x_i^{1/2} = \omega A_{ii}^{-1}( b_i - \sum_{j < i} A_{ij} x_j^{1/2})
32 x_i = (1 - \omega) x_i^{1/2} + \omega A_{ii}^{-1}( b_i - \sum_{j < i} A_{ij} x_j^{1/2} - \sum_{j > …
90 x_i = \omega D_{ii}^{-1}(b_i - \sum_{j<i} A_{ij} x_j)
93 x_i = (D_{ii}/\omega)^{-1}(b_i - \sum_{j<i} A_{ij} x_j)
/petsc/src/ksp/ksp/utils/lmvm/blas_cyclic/cupm/
H A Dblas_cyclic_cupm_impl.hpp93 const auto A_ = cupmScalarPtrCast(A); in dmv() local
110 PetscCallCUPMBLAS(cupmBlasXgbmv(handle, trans, m, m, 0, 0, calpha, A_, 1, x_, 1, cbeta, y_, 1)); in dmv()
114 …PetscCallCUPMBLAS(cupmBlasXgbmv(handle, trans, diff, diff, 0, 0, calpha, &A_[i_oldest], 1, &x_[i_o… in dmv()
118 …if (i_next) PetscCallCUPMBLAS(cupmBlasXgbmv(handle, trans, i_next, i_next, 0, 0, calpha, A_, 1, x_… in dmv()
119 …if (diff) PetscCallCUPMBLAS(cupmBlasXgbmv(handle, trans, diff, diff, 0, 0, calpha, &A_[i_oldest], … in dmv()
136 const auto A_ = cupmScalarPtrCast(A); in dsv() local
151 …upmBlasXtbsv(handle, CUPMBLAS_FILL_MODE_UPPER, trans, CUPMBLAS_DIAG_NON_UNIT, m, 0, A_, 1, y_, 1)); in dsv()
156 …handle, CUPMBLAS_FILL_MODE_UPPER, trans, CUPMBLAS_DIAG_NON_UNIT, diff, 0, &A_[i_oldest], 1, &y_[i_… in dsv()
162 …asXtbsv(handle, CUPMBLAS_FILL_MODE_UPPER, trans, CUPMBLAS_DIAG_NON_UNIT, i_next, 0, A_, 1, y_, 1)); in dsv()
166 …handle, CUPMBLAS_FILL_MODE_UPPER, trans, CUPMBLAS_DIAG_NON_UNIT, diff, 0, &A_[i_oldest], 1, &y_[i_… in dsv()
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/petsc/src/ksp/ksp/utils/lmvm/blas_cyclic/
H A Dblas_cyclic.c107 const PetscScalar *A_; in VecDMVCyclic() local
129 PetscCall(VecGetArrayReadAndMemType(A, &A_, &A_memtype)); in VecDMVCyclic()
134 …) PetscCall(DMVCyclic_CUPM_Private(hermitian_transpose, m, oldest, next, alpha, A_, x_, beta, y_)); in VecDMVCyclic()
141 PetscCall(VecRestoreArrayReadAndMemType(A, &A_)); in VecDMVCyclic()
143 PetscCall(VecGetArrayRead(A, &A_)); in VecDMVCyclic()
146 PetscCall(DMVCylic_Private(hermitian_transpose, m, oldest, next, alpha, A_, x_, beta, y_)); in VecDMVCyclic()
149 PetscCall(VecRestoreArrayRead(A, &A_)); in VecDMVCyclic()
191 const PetscScalar *A_; in VecDSVCyclic() local
213 PetscCall(VecGetArrayReadAndMemType(A, &A_, &A_memtype)); in VecDSVCyclic()
223 …if (m_local == m) PetscCall(DSVCyclic_CUPM_Private(hermitian_transpose, m, oldest, next, A_, x_, y… in VecDSVCyclic()
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/petsc/src/ksp/ksp/utils/lmvm/dense/cd_cupm/
H A Dcd_cupm.cxx30 auto A_ = cupmScalarPtrCast(A); in SolveInPlace() local
38 …mitian_transpose ? CUPMBLAS_OP_C : CUPMBLAS_OP_N, CUPMBLAS_DIAG_NON_UNIT, n, A_, lda, x_, stride)); in SolveInPlace()
56 auto A_ = cupmScalarPtrCast(A); in SolveInPlaceCyclic() local
68 …dle, CUPMBLAS_FILL_MODE_UPPER, CUPMBLAS_OP_N, CUPMBLAS_DIAG_NON_UNIT, n_new, A_, lda, x_, stride)); in SolveInPlaceCyclic()
69 …llCUPMBLAS(cupmBlasXgemv(handle, CUPMBLAS_OP_N, n_old, n_new, &minus_one, &A_[oldest_index], lda, … in SolveInPlaceCyclic()
70 …, CUPMBLAS_FILL_MODE_UPPER, CUPMBLAS_OP_N, CUPMBLAS_DIAG_NON_UNIT, n_old, &A_[oldest_index * (lda … in SolveInPlaceCyclic()
72 …, CUPMBLAS_FILL_MODE_UPPER, CUPMBLAS_OP_C, CUPMBLAS_DIAG_NON_UNIT, n_old, &A_[oldest_index * (lda … in SolveInPlaceCyclic()
73 …llCUPMBLAS(cupmBlasXgemv(handle, CUPMBLAS_OP_C, n_old, n_new, &minus_one, &A_[oldest_index], lda, … in SolveInPlaceCyclic()
74 …dle, CUPMBLAS_FILL_MODE_UPPER, CUPMBLAS_OP_C, CUPMBLAS_DIAG_NON_UNIT, n_new, A_, lda, x_, stride)); in SolveInPlaceCyclic()
/petsc/doc/manual/
H A Dksp.md1952 A_{00} & A_{01} & A_{02} & A_{03} \\
1953 A_{10} & A_{11} & A_{12} & A_{13} \\
1954 A_{20} & A_{21} & A_{22} & A_{23} \\
1955 A_{30} & A_{31} & A_{32} & A_{33} \\
1959 where each $A_{ij}$ is an entire block. The matrices on a parallel computer are not explicitly stor…
1960 own some rows of $A_{0*}$, $A_{1*}$ etc. On a
1965 A_{{00}_{00}} & A_{{00}_{01}} & A_{{00}_{02}} & ... & A_{{01}_{00}} & A_{{01}_{01}} & ... \\
1966 A_{{00}_{10}} & A_{{00}_{11}} & A_{{00}_{12}} & ... & A_{{01}_{10}} & A_{{01}_{11}} & ... \\
1967 A_{{00}_{20}} & A_{{00}_{21}} & A_{{00}_{22}} & ... & A_{{01}_{20}} & A_{{01}_{21}} & ...\\
1969 A_{{10}_{00}} & A_{{10}_{01}} & A_{{10}_{02}} & ... & A_{{11}_{00}} & A_{{11}_{01}} & ... \\
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H A Dmat.md726 A_{aa} & A_{ab} & A_{ac} \\
727 A_{ba} & A_{bb} & A_{bc} \\
728 A_{ca} & A_{cb} & A_{cc}
894 - :math:`r = A_{type}`
/petsc/share/petsc/matlab/
H A DUFgetPetscMat.m8 % each matrix named as A_{id}
29 % converts to PETSc binary format and writes into ~mat/A_{id}
/petsc/src/mat/tests/output/
H A Dex161.out1 Mat Object: (A_) 1 MPI process
H A Dex93_2.out1 Mat Object: (A_) 2 MPI processes
/petsc/doc/changes/
H A D322.md96 - Reuse the result of $T = A_{00}^-1 A_{01}$ in `PCApply_FieldSplit_Schur` with `-pc_fieldsplit_sch…