QuasiTrsv

Quasi-triangular solve with a vector: computes \(x := \mbox{op}(A)^{-1} x\), where \(\mbox{op}(A)\) is either \(A\), \(A^T\), or \(A^H\), and \(A\) is treated an either a lower or upper quasi-triangular matrix, depending upon uplo.

Note that the term quasi-triangular is in the context of real Schur decompositions, which produce triangular matrices with mixes of \(1 \times 1\) and \(2 \times 2\) diagonal blocks.

Note

There is no corresponding BLAS routine, but it is a natural extension of Trsv.

Note

For the best performance, both A and x should be in [MC,MR] distributions.

C++ API

void QuasiTrsv(UpperOrLower uplo, Orientation orientation, const Matrix<F> &A, Matrix<F> &x, bool checkIfSingular = false)

void QuasiTrsv(UpperOrLower uplo, Orientation orientation, const AbstractDistMatrix<F> &A, AbstractDistMatrix<F> &x, bool checkIfSingular = false)

C API

ElError ElQuasiTrsv_s(ElUpperOrLower uplo, ElOrientation orientation, ElConstMatrix_s A, ElMatrix_s x)

ElError ElQuasiTrsv_d(ElUpperOrLower uplo, ElOrientation orientation, ElConstMatrix_d A, ElMatrix_d x)

ElError ElQuasiTrsv_c(ElUpperOrLower uplo, ElOrientation orientation, ElConstMatrix_c A, ElMatrix_c x)

ElError ElQuasiTrsv_z(ElUpperOrLower uplo, ElOrientation orientation, ElConstMatrix_z A, ElMatrix_z x)

ElError ElQuasiTrsvDist_s(ElUpperOrLower uplo, ElOrientation orientation, ElConstDistMatrix_s A, ElDistMatrix_s x)

ElError ElQuasiTrsvDist_d(ElUpperOrLower uplo, ElOrientation orientation, ElConstDistMatrix_d A, ElDistMatrix_d x)

ElError ElQuasiTrsvDist_c(ElUpperOrLower uplo, ElOrientation orientation, ElConstDistMatrix_c A, ElDistMatrix_c x)

ElError ElQuasiTrsvDist_z(ElUpperOrLower uplo, ElOrientation orientation, ElConstDistMatrix_z A, ElDistMatrix_z x)