28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.14 BLAS 2 algorithms [linalg.algs.blas2]

28.9.14.7 Symmetric or Hermitian Rank-1 (outer product) update of a matrix [linalg.algs.blas2.symherrank1]

[Note 1:
These functions correspond to the BLAS functions xSYR, xSPR, xHER, and xHPR[bib].
They have overloads taking a scaling factor alpha, because it would be impossible to express the update otherwise.
— end note]
The following elements apply to all functions in [linalg.algs.blas2.symherrank1].
Mandates:
• If InOutMat has layout_blas_packed layout, then the layout's Triangle template argument has the same type as the function's Triangle template argument;
• compatible-static-extents<decltype(A), decltype(A)>(0, 1) is true; and
• compatible-static-extents<decltype(A), decltype(x)>(0, 0) is true.
Preconditions:
• A.extent(0) equals A.extent(1), and
• A.extent(0) equals x.extent(0).
Complexity: .
```template<class Scalar, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle> void symmetric_matrix_rank_1_update(Scalar alpha, InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, class Scalar, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle> void symmetric_matrix_rank_1_update(ExecutionPolicy&& exec, Scalar alpha, InVec x, InOutMat A, Triangle t); ```
These functions perform a symmetric rank-1 update of the symmetric matrix A, taking into account the Triangle parameter that applies to A ([linalg.general]).
Effects: Computes a matrix such that , where the scalar α is alpha, and assigns each element of to the corresponding element of A.
```template<in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle> void symmetric_matrix_rank_1_update(InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle> void symmetric_matrix_rank_1_update(ExecutionPolicy&& exec, InVec x, InOutMat A, Triangle t); ```
These functions perform a symmetric rank-1 update of the symmetric matrix A, taking into account the Triangle parameter that applies to A ([linalg.general]).
Effects: Computes a matrix such that and assigns each element of to the corresponding element of A.
```template<class Scalar, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle> void hermitian_matrix_rank_1_update(Scalar alpha, InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, class Scalar, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle> void hermitian_matrix_rank_1_update(ExecutionPolicy&& exec, Scalar alpha, InVec x, InOutMat A, Triangle t); ```
These functions perform a Hermitian rank-1 update of the Hermitian matrix A, taking into account the Triangle parameter that applies to A ([linalg.general]).
Effects: Computes such that , where the scalar α is alpha, and assigns each element of to the corresponding element of A.
```template<in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle> void hermitian_matrix_rank_1_update(InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle> void hermitian_matrix_rank_1_update(ExecutionPolicy&& exec, InVec x, InOutMat A, Triangle t); ```
These functions perform a Hermitian rank-1 update of the Hermitian matrix A, taking into account the Triangle parameter that applies to A ([linalg.general]).
Effects: Computes a matrix such that and assigns each element of to the corresponding element of A.