Square to Hessenberg

Implementation

Subroutine header files

Test driver

Reduction

C++ API

void Hessenberg(UpperOrLower uplo, Matrix<F> &A, Matrix<F> &t)

void Hessenberg(UpperOrLower uplo, AbstractDistMatrix<F> &A, AbstractDistMatrix<F> &t)

Return the in-place reduction of the matrix A to lower-/upper-Hessenberg form. The vector t contains the scalings for the Householder reflectors, which are stored in the locations of the zeros that they introduced.

void hessenberg::ExplicitCondensed(UpperOrLower uplo, Matrix<F> &A)

void hessenberg::ExplicitCondensed(UpperOrLower uplo, AbstractDistMatrix<F> &A)

Return just the Hessenberg matrix.

C API

ElError ElHessenberg_s(ElUpperOrLower uplo, ElMatrix_s A, ElMatrix_s t)

ElError ElHessenberg_d(ElUpperOrLower uplo, ElMatrix_d A, ElMatrix_d t)

ElError ElHessenberg_c(ElUpperOrLower uplo, ElMatrix_c A, ElMatrix_c t)

ElError ElHessenberg_z(ElUpperOrLower uplo, ElMatrix_z A, ElMatrix_z t)

ElError ElHessenbergDist_s(ElUpperOrLower uplo, ElDistMatrix_s A, ElDistMatrix_s t)

ElError ElHessenbergDist_d(ElUpperOrLower uplo, ElDistMatrix_d A, ElDistMatrix_d t)

ElError ElHessenbergDist_c(ElUpperOrLower uplo, ElDistMatrix_c A, ElDistMatrix_c t)

ElError ElHessenbergDist_z(ElUpperOrLower uplo, ElDistMatrix_z A, ElDistMatrix_z t)

Return the in-place reduction of the matrix A to lower-/upper-Hessenberg form. The vector t contains the scalings for the Householder reflectors, which are stored in the locations of the zeros that they introduced.

ElError ElHessenbergExplicitCondensed_s(ElUpperOrLower uplo, ElMatrix_s A)

ElError ElHessenbergExplicitCondensed_d(ElUpperOrLower uplo, ElMatrix_d A)

ElError ElHessenbergExplicitCondensed_c(ElUpperOrLower uplo, ElMatrix_c A)

ElError ElHessenbergExplicitCondensed_z(ElUpperOrLower uplo, ElMatrix_z A)

ElError ElHessenbergExplicitCondensedDist_s(ElUpperOrLower uplo, ElDistMatrix_s A)

ElError ElHessenbergExplicitCondensedDist_d(ElUpperOrLower uplo, ElDistMatrix_d A)

ElError ElHessenbergExplicitCondensedDist_c(ElUpperOrLower uplo, ElDistMatrix_c A)

ElError ElHessenbergExplicitCondensedDist_z(ElUpperOrLower uplo, ElDistMatrix_z A)

Return just the Hessenberg matrix.

Applying the change of basis

C++ API

void hessenberg::ApplyQ(LeftOrRight side, UpperOrLower uplo, Orientation orientation, const Matrix<F> &A, const Matrix<F> &t, Matrix<F> &H)

void hessenberg::ApplyQ(LeftOrRight side, UpperOrLower uplo, Orientation orientation, const AbstractDistMatrix<F> &A, const AbstractDistMatrix<F> &t, AbstractDistMatrix<F> &H)

C API

ElError ElApplyQAfterHessenberg_s(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, ElConstMatrix_s A, ElConstMatrix_s t, ElMatrix_s H)

ElError ElApplyQAfterHessenberg_d(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, ElConstMatrix_d A, ElConstMatrix_d t, ElMatrix_d H)

ElError ElApplyQAfterHessenberg_c(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, ElConstMatrix_c A, ElConstMatrix_c t, ElMatrix_c H)

ElError ElApplyQAfterHessenberg_z(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, ElConstMatrix_z A, ElConstMatrix_z t, ElMatrix_z H)

ElError ElApplyQAfterHessenbergDist_s(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, ElConstDistMatrix_s A, ElConstDistMatrix_s t, ElDistMatrix_s H)

ElError ElApplyQAfterHessenbergDist_d(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, ElConstDistMatrix_d A, ElConstDistMatrix_d t, ElDistMatrix_d H)

ElError ElApplyQAfterHessenbergDist_c(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, ElConstDistMatrix_c A, ElConstDistMatrix_c t, ElDistMatrix_c H)

ElError ElApplyQAfterHessenbergDist_z(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, ElConstDistMatrix_z A, ElConstDistMatrix_z t, ElDistMatrix_z H)