28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.15 BLAS 3 algorithms [linalg.algs.blas3]

28.9.15.2 Symmetric, Hermitian, and triangular matrix-matrix product [linalg.algs.blas3.xxmm]

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[Note 1: 
These functions correspond to the BLAS functions xSYMM, xHEMM, and xTRMM[bib].
— end note]
2
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The following elements apply to all functions in [linalg.algs.blas3.xxmm] in addition to function-specific elements.
3
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Mandates:
  • (3.1)
    possibly-multipliable<decltype(A), decltype(B), decltype(C)>() is true, and
  • (3.2)
    possibly-addable<decltype(E), decltype(E), decltype(C)>() is true for those overloads that take an E parameter.
4
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Preconditions:
  • (4.1)
    multipliable(A, B, C) is true, and
  • (4.2)
    addable(E, E, C) is true for those overloads that take an E parameter.
5
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Complexity: .
🔗
template<in-matrix InMat1, class Triangle, in-matrix InMat2, out-matrix OutMat> void symmetric_matrix_product(InMat1 A, Triangle t, InMat2 B, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, class Triangle, in-matrix InMat2, out-matrix OutMat> void symmetric_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, InMat2 B, OutMat C); template<in-matrix InMat1, class Triangle, in-matrix InMat2, out-matrix OutMat> void hermitian_matrix_product(InMat1 A, Triangle t, InMat2 B, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, class Triangle, in-matrix InMat2, out-matrix OutMat> void hermitian_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, InMat2 B, OutMat C); template<in-matrix InMat1, class Triangle, class DiagonalStorage, in-matrix InMat2, out-matrix OutMat> void triangular_matrix_product(InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, class Triangle, class DiagonalStorage, in-matrix InMat2, out-matrix OutMat> void triangular_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, OutMat C);
6
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These functions perform a matrix-matrix multiply, taking into account the Triangle and DiagonalStorage (if applicable) parameters that apply to the symmetric, Hermitian, or triangular (respectively) matrix A ([linalg.general]).
7
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Mandates:
  • (7.1)
    If InMat1 has layout_blas_packed layout, then the layout's Triangle template argument has the same type as the function's Triangle template argument; and
  • (7.2)
    compatible-static-extents<InMat1, InMat1>(0, 1) is true.
8
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Preconditions: A.extent(0) == A.extent(1) is true.
9
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Effects: Computes .
🔗
template<in-matrix InMat1, in-matrix InMat2, class Triangle, out-matrix OutMat> void symmetric_matrix_product(InMat1 A, InMat2 B, Triangle t, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2, class Triangle, out-matrix OutMat> void symmetric_matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, Triangle t, OutMat C); template<in-matrix InMat1, in-matrix InMat2, class Triangle, out-matrix OutMat> void hermitian_matrix_product(InMat1 A, InMat2 B, Triangle t, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2, class Triangle, out-matrix OutMat> void hermitian_matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, Triangle t, OutMat C); template<in-matrix InMat1, in-matrix InMat2, class Triangle, class DiagonalStorage, out-matrix OutMat> void triangular_matrix_product(InMat1 A, InMat2 B, Triangle t, DiagonalStorage d, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2, class Triangle, class DiagonalStorage, out-matrix OutMat> void triangular_matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, Triangle t, DiagonalStorage d, OutMat C);
10
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These functions perform a matrix-matrix multiply, taking into account the Triangle and DiagonalStorage (if applicable) parameters that apply to the symmetric, Hermitian, or triangular (respectively) matrix B ([linalg.general]).
11
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Mandates:
  • (11.1)
    If InMat2 has layout_blas_packed layout, then the layout's Triangle template argument has the same type as the function's Triangle template argument; and
  • (11.2)
    compatible-static-extents<InMat2, InMat2>(0, 1) is true.
12
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Preconditions: B.extent(0) == B.extent(1) is true.
13
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Effects: Computes .
🔗
template<in-matrix InMat1, class Triangle, in-matrix InMat2, in-matrix InMat3, out-matrix OutMat> void symmetric_matrix_product(InMat1 A, Triangle t, InMat2 B, InMat3 E, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, class Triangle, in-matrix InMat2, in-matrix InMat3, out-matrix OutMat> void symmetric_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, InMat2 B, InMat3 E, OutMat C); template<in-matrix InMat1, class Triangle, in-matrix InMat2, in-matrix InMat3, out-matrix OutMat> void hermitian_matrix_product(InMat1 A, Triangle t, InMat2 B, InMat3 E, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, class Triangle, in-matrix InMat2, in-matrix InMat3, out-matrix OutMat> void hermitian_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, InMat2 B, InMat3 E, OutMat C); template<in-matrix InMat1, class Triangle, class DiagonalStorage, in-matrix InMat2, in-matrix InMat3, out-matrix OutMat> void triangular_matrix_product(InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, InMat3 E, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, class Triangle, class DiagonalStorage, in-matrix InMat2, in-matrix InMat3, out-matrix OutMat> void triangular_matrix_product(ExecutionPolicy&& exec, InMat1 A, Triangle t, DiagonalStorage d, InMat2 B, InMat3 E, OutMat C);
14
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These functions perform a potentially overwriting matrix-matrix multiply-add, taking into account the Triangle and DiagonalStorage (if applicable) parameters that apply to the symmetric, Hermitian, or triangular (respectively) matrix A ([linalg.general]).
15
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Mandates:
  • (15.1)
    If InMat1 has layout_blas_packed layout, then the layout's Triangle template argument has the same type as the function's Triangle template argument; and
  • (15.2)
    compatible-static-extents<InMat1, InMat1>(0, 1) is true.
16
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Preconditions: A.extent(0) == A.extent(1) is true.
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Effects: Computes .
18
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Remarks: C may alias E.
🔗
template<in-matrix InMat1, in-matrix InMat2, class Triangle, in-matrix InMat3, out-matrix OutMat> void symmetric_matrix_product(InMat1 A, InMat2 B, Triangle t, InMat3 E, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2, class Triangle, in-matrix InMat3, out-matrix OutMat> void symmetric_matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, Triangle t, InMat3 E, OutMat C); template<in-matrix InMat1, in-matrix InMat2, class Triangle, in-matrix InMat3, out-matrix OutMat> void hermitian_matrix_product(InMat1 A, InMat2 B, Triangle t, InMat3 E, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2, class Triangle, in-matrix InMat3, out-matrix OutMat> void hermitian_matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, Triangle t, InMat3 E, OutMat C); template<in-matrix InMat1, in-matrix InMat2, class Triangle, class DiagonalStorage, in-matrix InMat3, out-matrix OutMat> void triangular_matrix_product(InMat1 A, InMat2 B, Triangle t, DiagonalStorage d, InMat3 E, OutMat C); template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2, class Triangle, class DiagonalStorage, in-matrix InMat3, out-matrix OutMat> void triangular_matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, Triangle t, DiagonalStorage d, InMat3 E, OutMat C);
19
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These functions perform a potentially overwriting matrix-matrix multiply-add, taking into account the Triangle and DiagonalStorage (if applicable) parameters that apply to the symmetric, Hermitian, or triangular (respectively) matrix B ([linalg.general]).
20
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Mandates:
  • (20.1)
    If InMat2 has layout_blas_packed layout, then the layout's Triangle template argument has the same type as the function's Triangle template argument; and
  • (20.2)
    compatible-static-extents<InMat2, InMat2>(0, 1) is true.
21
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Preconditions: B.extent(0) == B.extent(1) is true.
22
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Effects: Computes .
23
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Remarks: C may alias E.