Elemental 0.78 documentation

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The prototypes for the following routines can be found at include/elemental/blas-like_decl.hpp, while the implementations are in include/elemental/blas-like/level2/.

Gemv

General matrix-vector multiply: \(y := \alpha \mbox{op}(A) x + \beta y\), where \(\mbox{op}(A)\) can be \(A\), \(A^T\), or \(A^H\). Whether or not \(x\) and \(y\) are stored as row vectors, they will be interpreted as column vectors.

void Gemv(Orientation orientation, T alpha, const Matrix<T>& A, const Matrix<T>& x, T beta, Matrix<T>& y)
void Gemv(Orientation orientation, T alpha, const DistMatrix<T>& A, const DistMatrix<T>& x, T beta, DistMatrix<T>& y)

Ger

General rank-one update: \(A := \alpha x y^H + A\). \(x\) and \(y\) are free to be stored as either row or column vectors, but they will be interpreted as column vectors.

void Ger(T alpha, const Matrix<T>& x, const Matrix<T>& y, Matrix<T>& A)
void Ger(T alpha, const DistMatrix<T>& x, const DistMatrix<T>& y, DistMatrix<T>& A)

Gerc

This is the same as Ger(), but the name is provided because it exists in the BLAS.

void Gerc(T alpha, const Matrix<T>& x, const Matrix<T>& y, Matrix<T>& A)
void Gerc(T alpha, const DistMatrix<T>& x, const DistMatrix<T>& y, DistMatrix<T>& A)

Geru

General rank-one update (unconjugated): \(A := \alpha x y^T + A\). \(x\) and \(y\) are free to be stored as either row or column vectors, but they will be interpreted as column vectors.

void Geru(T alpha, const Matrix<T>& x, const Matrix<T>& y, Matrix<T>& A)
void Geru(T alpha, const DistMatrix<T>& x, const DistMatrix<T>& y, DistMatrix<T>& A)

Hemv

Hermitian matrix-vector multiply: \(y := \alpha A x + \beta y\), where \(A\) is Hermitian.

void Hemv(UpperOrLower uplo, T alpha, const Matrix<T>& A, const Matrix<T>& x, T beta, Matrix<T>& y)
void Hemv(UpperOrLower uplo, T alpha, const DistMatrix<T>& A, const DistMatrix<T>& x, T beta, DistMatrix<T>& y)

Please see SetLocalSymvBlocksize<T>() and LocalSymvBlocksize<T>() in the Tuning parameters section for information on tuning the distributed Hemv().

Her

Hermitian rank-one update: implicitly performs \(A := \alpha x x^H + A\), where only the triangle of \(A\) specified by uplo is updated.

void Her(UpperOrLower uplo, T alpha, const Matrix<T>& x, Matrix<T>& A)
void Her(UpperOrLower uplo, T alpha, const DistMatrix<T>& x, DistMatrix<T>& A)

Her2

Hermitian rank-two update: implicitly performs \(A := \alpha ( x y^H + y x^H ) + A\), where only the triangle of \(A\) specified by uplo is updated.

void Her2(UpperOrLower uplo, T alpha, const Matrix<T>& x, const Matrix<T>& y, Matrix<T>& A)
void Her2(UpperOrLower uplo, T alpha, const DistMatrix<T>& x, const DistMatrix<T>& y, DistMatrix<T>& A)

Symv

Symmetric matrix-vector multiply: \(y := \alpha A x + \beta y\), where \(A\) is symmetric.

void Symv(UpperOrLower uplo, T alpha, const Matrix<T>& A, const Matrix<T>& x, T beta, Matrix<T>& y, bool conjugate=false )
void Symv(UpperOrLower uplo, T alpha, const DistMatrix<T>& A, const DistMatrix<T>& x, T beta, DistMatrix<T>& y, bool conjugate=false )

Please see SetLocalSymvBlocksize<T>() and LocalSymvBlocksize<T>() in the Tuning parameters section for information on tuning the distributed Symv().

Syr

Symmetric rank-one update: implicitly performs \(A := \alpha x x^T + A\), where only the triangle of \(A\) specified by uplo is updated.

void Syr(UpperOrLower uplo, T alpha, const Matrix<T>& x, Matrix<T>& A, bool conjugate=false )
void Syr(UpperOrLower uplo, T alpha, const DistMatrix<T>& x, DistMatrix<T>& A, bool conjugate=false )

Syr2

Symmetric rank-two update: implicitly performs \(A := \alpha ( x y^T + y x^T ) + A\), where only the triangle of \(A\) specified by uplo is updated.

void Syr2(UpperOrLower uplo, T alpha, const Matrix<T>& x, const Matrix<T>& y, Matrix<T>& A, bool conjugate=false )
void Syr2(UpperOrLower uplo, T alpha, const DistMatrix<T>& x, const DistMatrix<T>& y, DistMatrix<T>& A, bool conjugate=false )

Trmv

Not yet written. Please call Trmm() for now.

Trsv

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 triangular matrix, depending upon uplo. \(A\) can also be treated as implicitly having a unit-diagonal if diag is set to UNIT.

void Trsv(UpperOrLower uplo, Orientation orientation, UnitOrNonUnit diag, const Matrix<F>& A, Matrix<F>& x)
void Trsv(UpperOrLower uplo, Orientation orientation, UnitOrNonUnit diag, const DistMatrix<F>& A, DistMatrix<F>& x)

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