LWG std::linalg (P1673) Review Plan

[crtrott]

Current Review Focus

We plan to get through matrix-vector-product and all the wording which is indirectly relevant for its full specification.

• 17.11.3.1 General matrix-vector-product
  • 17.2 General [linalg.general] Parts of this say what aliasing of mdspans means.
  • 17.3 Requirements [linalg.reqs] What can an implementer rely on for the arguments of the algorithm.
  • 17.10 Exposition-only concepts and traits [linalg.concepts] Concepts to constrain the arguments.
  • 17.11.1 Requirements based on template parameter name [linalg.algs.reqs]

We follow up with in place transformations of mdspans which can be used in conjunction with matrix-vector-product:

• 17.6 Scaled in-place transformation [linalg.scaled] scaled(alpha, A)
• 17.7 Conjugated in-place transformation [linalg.conj] conjugated(A)
• 17.8 Transpose in-place transformation [linalg.transp] transposed(A)
• 17.9 Conjugate transpose transform [linalg.conj_transp] conjugate_transposed(A)

Wording content list:

17 Wording

• 17.1 Add subsection 28.9 [linalg] with the following
• 17.2 General [linalg.general]
• 17.3 Requirements [linalg.reqs]
  • 17.3.1 Linear algebra value types [linalg.reqs.val]
  • 17.3.2 Algorithm and class requirements [linalg.reqs.alg]
  • 17.3.3 Requirements for functions on floating-point values [linalg.reqs.flpt]
• 17.4 Tag classes [linalg.tags]
  • 17.4.1 Storage order tags [linalg.tags.order]
  • 17.4.2 Triangle tags [linalg.tags.triangle]
  • 17.4.3 Diagonal tags [linalg.tags.diagonal]
• 17.5 Layouts for packed matrix types [linalg.layouts]
  • 17.5.1 layout_blas_packed [linalg.layouts.packed]
• 17.6 Scaled in-place transformation [linalg.scaled]
  • 17.6.1 Exposition-only function object abs-if-needed [linalg.scaled.abs]
  • 17.6.2 Exposition-only function object conj-if-needed [linalg.scaled.conj]
  • 17.6.3 Exposition-only function object real-if-needed [linalg.scaled.real]
  • 17.6.4 Exposition-only function object imag-if-needed [linalg.scaled.imag]
  • 17.6.5 Exposition-only class templates proxy-reference-base and proxy-reference [linalg.scaled.base]
  • 17.6.6 Exposition-only class template scaled-scalar
  • 17.6.7 Class template accessor_scaled [linalg.scaled.accessor_scaled]
  • 17.6.8 scaled [linalg.scaled.scaled]
• 17.7 Conjugated in-place transformation [linalg.conj]
  • 17.7.1 Exposition-only class template conjugated-scalar
  • 17.7.2 Class template accessor_conjugate [linalg.conj.accessor_conjugate]
  • 17.7.3 conjugated [linalg.conj.conjugated]
• 17.8 Transpose in-place transformation [linalg.transp]
  • 17.8.1 layout_transpose [linalg.transp.layout_transpose]
  • 17.8.2 transposed [linalg.transp.transposed]
• 17.9 Conjugate transpose transform [linalg.conj_transp]
• 17.10 Exposition-only concepts and traits [linalg.concepts]
• 17.11 Algorithms [linalg.algs]
  • 17.11.1 Requirements based on template parameter name [linalg.algs.reqs]
• 17.11.2 BLAS 1 functions [linalg.algs.blas1]
  • 17.11.2.1 Givens rotations [linalg.algs.blas1.givens]
    
    • 17.11.2.1.1 Compute Givens rotation [linalg.algs.blas1.givens.lartg] (no hyperlink available)
    • 17.11.2.1.2 Apply a computed Givens rotation to vectors [linalg.algs.blas1.givens.rot] (no hyperlink available)
  • 17.11.2.2 Swap matrix or vector elements [linalg.algs.blas1.swap]
  • 17.11.2.3 Multiply the elements of an object in place by a scalar [linalg.algs.blas1.scal]
  • 17.11.2.4 Copy elements of one matrix or vector into another [linalg.algs.blas1.copy]
  • 17.11.2.5 Add vectors or matrices elementwise [linalg.algs.blas1.add]
  • 17.11.2.6 Dot product of two vectors [linalg.algs.blas1.dot]
    • 17.11.2.6.1 Nonconjugated dot product of two vectors [linalg.algs.blas1.dot.dotu] (no hyperlink available)
    • 17.11.2.6.2 Conjugated dot product of two vectors [linalg.algs.blas1.dot.dotc] (no hyperlink available)
  • 17.11.2.7 Scaled sum of squares of a vector’s elements [linalg.algs.blas1.ssq]
  • 17.11.2.8 Euclidean norm of a vector [linalg.algs.blas1.nrm2]
    • 17.11.2.8.1 Euclidean norm with specified result type (no hyperlink available)
    • 17.11.2.8.2 Euclidean norm with default result type (no hyperlink available)
  • 17.11.2.9 Sum of absolute values of vector elements [linalg.algs.blas1.asum]
    • 17.11.2.9.1 Sum of absolute values with specified result type (no hyperlink available)
    • 17.11.2.9.2 Sum of absolute values with default result type (no hyperlink available)
  • 17.11.2.10 Index of maximum absolute value of vector elements [linalg.algs.blas1.iamax]
  • 17.11.2.11 Frobenius norm of a matrix [linalg.algs.blas1.matfrobnorm]
    • 17.11.2.11.1 Frobenius norm with specified result type (no hyperlink available)
    • 17.11.2.11.2 Frobenius norm with default result type (no hyperlink available)
  • 17.11.2.12 One norm of a matrix [linalg.algs.blas1.matonenorm]
    • 17.11.2.12.1 One norm with specified result type (no hyperlink available)
    • 17.11.2.12.2 One norm with default result type (no hyperlink available)
  • 17.11.2.13 Infinity norm of a matrix [linalg.algs.blas1.matinfnorm]
    • 17.11.2.13.1 Infinity norm with specified result type (no hyperlink available)
    • 17.11.2.13.2 Infinity norm with default result type (no hyperlink available)
• 17.11.3 BLAS 2 functions [linalg.algs.blas2]
  • 17.11.3.1 General matrix-vector product [linalg.algs.blas2.gemv]
    • 17.11.3.1.1 Overwriting matrix-vector product (no hyperlink available)
    • 17.11.3.1.2 Updating matrix-vector product (no hyperlink available)
  • 17.11.3.2 Symmetric matrix-vector product [linalg.algs.blas2.symv]
    • 17.11.3.2.1 Overwriting symmetric matrix-vector product (no hyperlink available)
    • 17.11.3.2.2 Updating symmetric matrix-vector product (no hyperlink available)
  • 17.11.3.3 Hermitian matrix-vector product [linalg.algs.blas2.hemv]
    • 17.11.3.3.1 Overwriting Hermitian matrix-vector product (no hyperlink available)
    • 17.11.3.3.2 Updating Hermitian matrix-vector product (no hyperlink available)
  • 17.11.3.4 Triangular matrix-vector product [linalg.algs.blas2.trmv]
    • 17.11.3.4.1 Overwriting triangular matrix-vector product [linalg.algs.blas2.trmv.ov] (no hyperlink available)
    • 17.11.3.4.2 In-place triangular matrix-vector product [linalg.algs.blas2.trmv.in-place] (no hyperlink available)
    • 17.11.3.4.3 Updating triangular matrix-vector product [linalg.algs.blas2.trmv.up] (no hyperlink available)
  • 17.11.3.5 Solve a triangular linear system [linalg.algs.blas2.trsv]
    • 17.11.3.5.1 Not-in-place triangular solve [linalg.algs.blas2.trsv.not-in-place] (no hyperlink available)
    • 17.11.3.5.2 In-place triangular solve [linalg.algs.blas2.trsv.in-place]
  • 17.11.3.6 Rank-1 (outer product) update of a matrix [linalg.algs.blas2.rank1]
    • 17.11.3.6.1 Nonsymmetric nonconjugated rank-1 update [linalg.algs.blas2.rank1.geru] (no hyperlink available)
    • 17.11.3.6.2 Nonsymmetric conjugated rank-1 update [linalg.algs.blas2.rank1.gerc] (no hyperlink available)
    • 17.11.3.6.3 Rank-1 update of a Symmetric matrix [linalg.algs.blas2.rank1.syr] (no hyperlink available)
    • 17.11.3.6.4 Rank-1 update of a Hermitian matrix [linalg.algs.blas2.rank1.her] (no hyperlink available)
  • 17.11.3.7 Rank-2 update of a symmetric matrix [linalg.algs.blas2.rank2.syr2]
  • 17.11.3.8 Rank-2 update of a Hermitian matrix [linalg.algs.blas2.rank2.her2]
• 17.11.4 BLAS 3 functions [linalg.algs.blas3]
  • 17.11.4.1 General matrix-matrix product [linalg.algs.blas3.gemm]
    • 17.11.4.1.1 Overwriting general matrix-matrix product (no hyperlink available)
    • 17.11.4.1.2 Updating general matrix-matrix product (no hyperlink available)
  • 17.11.4.2 Symmetric matrix-matrix product [linalg.algs.blas3.symm]
    • 17.11.4.2.1 Overwriting symmetric matrix-matrix left product [linalg.algs.blas3.symm.ov.left] (no hyperlink available)
    • 17.11.4.2.2 Overwriting symmetric matrix-matrix right product [linalg.algs.blas3.symm.ov.right] (no hyperlink available)
    • 17.11.4.2.3 Updating symmetric matrix-matrix left product [linalg.algs.blas3.symm.up.left] (no hyperlink available)
    • 17.11.4.2.4 Updating symmetric matrix-matrix right product [linalg.algs.blas3.symm.up.right] (no hyperlink available)
  • 17.11.4.3 Hermitian matrix-matrix product [linalg.algs.blas3.hemm]
    • 17.11.4.3.1 Overwriting Hermitian matrix-matrix left product [linalg.algs.blas3.hemm.ov.left] (no hyperlink available)
    • 17.11.4.3.2 Overwriting Hermitian matrix-matrix right product [linalg.algs.blas3.hemm.ov.right] (no hyperlink available)
    • 17.11.4.3.3 Updating Hermitian matrix-matrix left product [linalg.algs.blas3.hemm.up.left] (no hyperlink available)
    • 17.11.4.3.4 Updating Hermitian matrix-matrix right product [linalg.algs.blas3.hemm.up.right] (no hyperlink available)
  • 17.11.4.4 Triangular matrix-matrix product [linalg.algs.blas3.trmm]
    • 17.11.4.4.1 Overwriting triangular matrix-matrix left product [linalg.algs.blas3.trmm.ov.left] (no hyperlink available)
    • 17.11.4.4.2 Overwriting triangular matrix-matrix right product [linalg.algs.blas3.trmm.ov.right] (no hyperlink available)
    • 17.11.4.4.3 Updating triangular matrix-matrix left product [linalg.algs.blas3.trmm.up.left] (no hyperlink available)
    • 17.11.4.4.4 Updating triangular matrix-matrix right product [linalg.algs.blas3.trmm.up.right] (no hyperlink available)
  • 17.11.4.5 Rank-k update of a symmetric or Hermitian matrix [linalg.alg.blas3.rank-k]
    • 17.11.4.5.1 Rank-k symmetric matrix update [linalg.alg.blas3.rank-k.syrk] (no hyperlink available)
    • 17.11.4.5.2 Rank-k Hermitian matrix update [linalg.alg.blas3.rank-k.herk] (no hyperlink available)
  • 17.11.4.6 Rank-2k update of a symmetric or Hermitian matrix [linalg.alg.blas3.rank2k]
    • 17.11.4.6.1 Rank-2k symmetric matrix update [linalg.alg.blas3.rank2k.syr2k] (no hyperlink available)
    • 17.11.4.6.2 Rank-2k Hermitian matrix update [linalg.alg.blas3.rank2k.her2k] (no hyperlink available)
  • 17.11.4.7 Solve multiple triangular linear systems [linalg.alg.blas3.trsm]
    • 17.11.4.7.1 Solve multiple triangular linear systems with triangular matrix on the left [linalg.alg.blas3.trsm.left] (no hyperlink available)
    • 17.11.4.7.2 Solve multiple triangular linear systems with triangular matrix on the right [linalg.alg.blas3.trsm.right] (no hyperlink available)