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Utilities¶

Householder reflectors¶

TODO: Describe major difference from LAPACK’s conventions (i.e., we do not treat the identity matrix as a Householder transform since it requires the \(u\) in \(H=I-2uu'\) to have norm zero rather than one).

F LeftReflector(F &chi, Matrix<F> &x)¶

F LeftReflector(Matrix<F> &chi, Matrix<F> &x)¶

F LeftReflector(F &chi, DistMatrix<F> &x)¶

F LeftReflector(DistMatrix<F> &chi, DistMatrix<F> &x)¶

F reflector::Col(F &chi, DistMatrix<F> &x)¶

F reflector::Col(DistMatrix<F> &chi, DistMatrix<F> &x)¶

F RightReflector(F &chi, Matrix<F> &x)¶

F RightReflector(Matrix<F> &chi, Matrix<F> &x)¶

F RightReflector(F &chi, DistMatrix<F> &x)¶

F RightReflector(DistMatrix<F> &chi, DistMatrix<F> &x)¶

F reflector::Row(F &chi, DistMatrix<F> &x)¶

F reflector::Row(DistMatrix<F> &chi, DistMatrix<F> &x)¶

F LeftHyperbolicReflector(F &chi, Matrix<F> &x)¶

F LeftHyperbolicReflector(Matrix<F> &chi, Matrix<F> &x)¶

F LeftHyperbolicReflector(F &chi, DistMatrix<F> &x)¶

F LeftHyperbolicReflector(DistMatrix<F> &chi, DistMatrix<F> &x)¶

F hyp_reflector::Col(F &chi, DistMatrix<F> &x)¶

F hyp_reflector::Col(DistMatrix<F> &chi, DistMatrix<F> &x)¶

F RightHyperbolicReflector(F &chi, Matrix<F> &x)¶

F RightHyperbolicReflector(Matrix<F> &chi, Matrix<F> &x)¶

F RightHyperbolicReflector(F &chi, DistMatrix<F> &x)¶

F RightHyperbolicReflector(DistMatrix<F> &chi, DistMatrix<F> &x)¶

F hyp_reflector::Row(F &chi, DistMatrix<F> &x)¶

F hyp_reflector::Row(DistMatrix<F> &chi, DistMatrix<F> &x)¶

void ApplyPackedReflectors(LeftOrRight side, UpperOrLower uplo, VerticalOrHorizontal dir, ForwardOrBackward order, Conjugation conjugation, int offset, const Matrix<F> &H, const Matrix<F> &t, Matrix<F> &A)¶

void ApplyPackedReflectors(LeftOrRight side, UpperOrLower uplo, VerticalOrHorizontal dir, ForwardOrBackward order, Conjugation conjugation, int offset, const DistMatrix<F> &H, const DistMatrix<F, MD, STAR> &t, DistMatrix<F> &A)¶

void ApplyPackedReflectors(LeftOrRight side, UpperOrLower uplo, VerticalOrHorizontal dir, ForwardOrBackward order, Conjugation conjugation, int offset, const DistMatrix<F> &H, const DistMatrix<F, STAR, STAR> &t, DistMatrix<F> &A)¶

void ExpandPackedReflectors(UpperOrLower uplo, VerticalOrHorizontal dir, Conjugation conjugation, int offset, Matrix<F> &H, const Matrix<F> &t)¶

void ExpandPackedReflectors(UpperOrLower uplo, VerticalOrHorizontal dir, Conjugation conjugation, int offset, DistMatrix<F> &H, const DistMatrix<F, MD, STAR> &t)¶

void ExpandPackedReflectors(UpperOrLower uplo, VerticalOrHorizontal dir, Conjugation conjugation, int offset, DistMatrix<F> &H, const DistMatrix<F, STAR, STAR> &t)¶

Sorting¶

void Sort(Matrix<Real> &X, SortType sort = ASCENDING)¶

void Sort(DistMatrix<Real, U, V> &X, SortType sort = ASCENDING)¶

std::vector<ValueInt<Real>> TaggedSort(const Matrix<Real> &X, SortType sort = ASCENDING)¶

std::vector<ValueInt<Real>> TaggedSort(const DistMatrix<Real, U, V> &X, SortType sort = ASCENDING)¶

ValueInt<Real> Median(const Matrix<Real> &x)¶

ValueInt<Real> Median(const DistMatrix<Real, U, V> &x)¶