29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.14 BLAS 2 algorithms [linalg.algs.blas2]

29.9.14.6 Rank-1 (outer product) update of a matrix [linalg.algs.blas2.rank1]

1
#
The following elements apply to all functions in [linalg.algs.blas2.rank1].
2
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Mandates:
  • (2.1)
    possibly-multipliable<OutMat, InVec2, InVec1>() is true, and
  • (2.2)
    possibly-addable<OutMat, InMat, OutMat>() is true for those overloads with an E parameter.
3
#
Preconditions:
  • (3.1)
    multipliable(A, y, x) is true, and
  • (3.2)
    addable(A, E, A) is true for those overloads with an E parameter.
4
#
Complexity: .
🔗
template<in-vector InVec1, in-vector InVec2, out-matrix OutMat> void matrix_rank_1_update(InVec1 x, InVec2 y, OutMat A); template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, out-matrix OutMat> void matrix_rank_1_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, OutMat A);
5
#
These functions perform an overwriting nonsymmetric nonconjugated rank-1 update.
[Note 1: 
These functions correspond to the BLAS functions xGER (for real element types) and xGERU (for complex element types)[bib].
— end note]
6
#
Effects: Computes .
🔗
template<in-vector InVec1, in-vector InVec2, in-matrix InMat, out-matrix OutMat> void matrix_rank_1_update(InVec1 x, InVec2 y, InMat E, OutMat A); template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, in-matrix InMat, out-matrix OutMat> void matrix_rank_1_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InMat E, OutMat A);
7
#
These functions perform an updating nonsymmetric nonconjugated rank-1 update.
[Note 2: 
These functions correspond to the BLAS functions xGER (for real element types) and xGERU (for complex element types)[bib].
— end note]
8
#
Effects: Computes .
9
#
Remarks: A may alias E.
🔗
template<in-vector InVec1, in-vector InVec2, out-matrix OutMat> void matrix_rank_1_update_c(InVec1 x, InVec2 y, OutMat A); template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, out-matrix OutMat> void matrix_rank_1_update_c(ExecutionPolicy&& exec, InVec1 x, InVec2 y, OutMat A);
10
#
These functions perform an overwriting nonsymmetric conjugated rank-1 update.
[Note 3: 
These functions correspond to the BLAS functions xGER (for real element types) and xGERC (for complex element types)[bib].
— end note]
11
#
Effects:
  • (11.1)
    For the overloads without an ExecutionPolicy argument, equivalent to: matrix_rank_1_update(x, conjugated(y), A);
  • (11.2)
    otherwise, equivalent to: matrix_rank_1_update(std::forward<ExecutionPolicy>(exec), x, conjugated(y), A);
🔗
template<in-vector InVec1, in-vector InVec2, in-matrix InMat, out-matrix OutMat> void matrix_rank_1_update_c(InVec1 x, InVec2 y, InMat E, OutMat A); template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, in-matrix InMat, out-matrix OutMat> void matrix_rank_1_update_c(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InMat E, OutMat A);
12
#
These functions perform an updating nonsymmetric conjugated rank-1 update.
[Note 4: 
These functions correspond to the BLAS functions xGER (for real element types) and xGERC (for complex element types)[bib].
— end note]
13
#
Effects:
  • (13.1)
    For the overloads without an ExecutionPolicy argument, equivalent to: matrix_rank_1_update(x, conjugated(y), A);
  • (13.2)
    otherwise, equivalent to: matrix_rank_1_update(std::forward<ExecutionPolicy>(exec), x, conjugated(y), E, A);