22 static constexpr std::string_view
name =
"least_squares";
28 static constexpr std::string_view
name =
"svd_least_squares";
34 static constexpr std::string_view
name =
"copy";
40 static constexpr std::string_view
name =
"conjugate_inplace";
49 static constexpr std::string_view
name =
"transform";
62 static constexpr std::string_view
name =
"transform_inplace";
76 static constexpr std::string_view
name =
"assign_product";
85 static constexpr std::string_view
name =
"gemm";
91 static constexpr std::string_view
name =
"gemv";
97template <std::
size_t LhsRank, std::
size_t RhsRank, std::
size_t ContractedRank>
struct contract_op
99 static constexpr std::string_view
name =
"contract";
106 static constexpr std::string_view
name =
"inner_product";
112 static constexpr std::string_view
name =
"norm";
136 static constexpr std::string_view
name =
"matrix_norm";
143 static constexpr std::string_view
name =
"lu_rcond";
156 static constexpr std::string_view
name =
"linear_solve";
166 static constexpr std::string_view
name =
"lu_factor";
172 static constexpr std::string_view
name =
"lu_solve";
180 static constexpr std::string_view
name =
"qr";
188 static constexpr std::string_view
name =
"lq";
196 static constexpr std::string_view
name =
"sum";
203 static constexpr std::string_view
name =
"matrix_exponential";
220 static constexpr std::string_view
name =
"matrix_set";
241 static constexpr std::string_view
name =
"self_adjoint_eigh";
271 static constexpr std::string_view
name =
"singular_values";
277 static constexpr std::string_view
name =
"svd_left";
285 static constexpr std::string_view
name =
"svd_right";
293 static constexpr std::string_view
name =
"svd";
302 static constexpr std::string_view
name =
"symmetric_tridiagonal_eigen";
309 static constexpr std::string_view
name =
"nonsymmetric_eigen";
316 static constexpr std::string_view
name =
"schur";
323 static constexpr std::string_view
name =
"hessenberg_schur";
330 static constexpr std::string_view
name =
"reorder_schur";
Normalized axis metadata for fixed-rank pairwise tensor contractions.
Definition linalg/async.hpp:28
MatrixTriangle
Triangle of a symmetric or Hermitian matrix supplied to an operation.
Definition operation_tags.hpp:226
SvdOverwrite
Input allocation overwritten by a singular-vector factor.
Definition operation_tags.hpp:262
SvdVectorExtent
Extent policy for one side of an exact singular value decomposition.
Definition operation_tags.hpp:248
MatrixNorm
Matrix norm selected by matrix_norm_op.
Definition operation_tags.hpp:119
@ One
Induced one-norm: largest column sum of entry magnitudes.
@ MaxAbs
Largest entry magnitude, max_ij abs(A[i,j]).
@ Frobenius
Frobenius norm: square root of the sum of squared entry magnitudes.
@ Infinity
Induced infinity-norm: largest row sum of entry magnitudes.
MatrixRegion
Matrix region selected by structured initialization operations.
Definition operation_tags.hpp:208
@ Upper
Entries with row <= column, including the diagonal.
@ All
All entries, including rectangular portions of the matrix.
@ Lower
Entries with row >= column, including the diagonal.
Normalized input and surviving axes for fixed-rank tensor reductions.
Canonical contracted and surviving axes for two fixed-rank operands.
Definition contraction_axes.hpp:26
Normalized axes for reducing a fixed-rank input.
Definition reduction_axes.hpp:30
Options for a dense symmetric or Hermitian eigensystem.
Definition operation_tags.hpp:233
bool compute_vectors
Definition operation_tags.hpp:234
MatrixTriangle triangle
Definition operation_tags.hpp:235
Output-shape options for an exact singular value decomposition.
Definition operation_tags.hpp:255
SvdVectorExtent right
Definition operation_tags.hpp:257
SvdVectorExtent left
Definition operation_tags.hpp:256
Replaceable-output dense matrix product operation tag.
Definition operation_tags.hpp:75
static constexpr std::string_view name
Definition operation_tags.hpp:76
Accessor-respecting in-place scalar conjugation operation tag.
Definition operation_tags.hpp:39
static constexpr std::string_view name
Definition operation_tags.hpp:40
Fixed-output pairwise tensor contraction operation.
Definition operation_tags.hpp:98
static constexpr std::string_view name
Definition operation_tags.hpp:99
ContractionAxes< LhsRank, RhsRank, ContractedRank > axes
Definition operation_tags.hpp:100
Accessor-respecting element copy operation tag.
Definition operation_tags.hpp:33
static constexpr std::string_view name
Definition operation_tags.hpp:34
Fixed-output dense matrix multiplication operation tag.
Definition operation_tags.hpp:84
static constexpr std::string_view name
Definition operation_tags.hpp:85
Dense matrix-vector multiplication operation tag.
Definition operation_tags.hpp:90
static constexpr std::string_view name
Definition operation_tags.hpp:91
Schur decomposition of an already upper-Hessenberg real matrix.
Definition operation_tags.hpp:322
static constexpr std::string_view name
Definition operation_tags.hpp:323
bool compute_vectors
Definition operation_tags.hpp:324
Conjugate-linear-left tensor inner-product operation tag.
Definition operation_tags.hpp:105
static constexpr std::string_view name
Definition operation_tags.hpp:106
Preserving full-column-rank least squares with fixed solution and diagnostic outputs.
Definition operation_tags.hpp:21
static constexpr std::string_view name
Definition operation_tags.hpp:22
Destructive dense general linear-system solve operation tag.
Definition operation_tags.hpp:155
static constexpr std::string_view name
Definition operation_tags.hpp:156
Reduced dense real LQ factorization operation tag.
Definition operation_tags.hpp:187
static constexpr std::string_view name
Definition operation_tags.hpp:188
Fixed-output packed LU factorization with zero-based row-swap pivots.
Definition operation_tags.hpp:165
static constexpr std::string_view name
Definition operation_tags.hpp:166
Reciprocal condition estimate from successful packed LU and an original matrix norm.
Definition operation_tags.hpp:142
static constexpr std::string_view name
Definition operation_tags.hpp:143
MatrixNorm norm
Definition operation_tags.hpp:144
Solve using read-only packed LU factors, overwriting an existing RHS.
Definition operation_tags.hpp:171
static constexpr std::string_view name
Definition operation_tags.hpp:172
Dense matrix exponential operation tag.
Definition operation_tags.hpp:202
static constexpr std::string_view name
Definition operation_tags.hpp:203
Dense rank-two matrix norm operation tag.
Definition operation_tags.hpp:135
static constexpr std::string_view name
Definition operation_tags.hpp:136
MatrixNorm kind
Definition operation_tags.hpp:137
Structured dense matrix initialization operation tag.
Definition operation_tags.hpp:219
MatrixRegion region
Definition operation_tags.hpp:221
static constexpr std::string_view name
Definition operation_tags.hpp:220
Dense nonsymmetric eigensystem operation tag.
Definition operation_tags.hpp:308
static constexpr std::string_view name
Definition operation_tags.hpp:309
bool compute_right_vectors
Definition operation_tags.hpp:310
Euclidean tensor norm operation tag.
Definition operation_tags.hpp:111
static constexpr std::string_view name
Definition operation_tags.hpp:112
Reduced dense real QR factorization operation tag.
Definition operation_tags.hpp:179
static constexpr std::string_view name
Definition operation_tags.hpp:180
Dense Schur decomposition operation tag.
Definition operation_tags.hpp:315
bool compute_vectors
Definition operation_tags.hpp:317
static constexpr std::string_view name
Definition operation_tags.hpp:316
Move one Schur block or entry to a requested position.
Definition operation_tags.hpp:329
static constexpr std::string_view name
Definition operation_tags.hpp:330
std::size_t to
Definition operation_tags.hpp:332
bool update_vectors
Definition operation_tags.hpp:333
std::size_t from
Definition operation_tags.hpp:331
Dense symmetric or Hermitian eigensystem operation tag.
Definition operation_tags.hpp:240
bool compute_vectors
Definition operation_tags.hpp:242
MatrixTriangle triangle
Definition operation_tags.hpp:243
static constexpr std::string_view name
Definition operation_tags.hpp:241
Exact dense singular-values-only operation tag.
Definition operation_tags.hpp:270
static constexpr std::string_view name
Definition operation_tags.hpp:271
Sum reduction over one or more fixed-rank input axes.
Definition operation_tags.hpp:195
ReductionAxes< InputRank, ReducedRank > axes
Definition operation_tags.hpp:197
static constexpr std::string_view name
Definition operation_tags.hpp:196
Preserving minimum-norm SVD least squares with explicit rank diagnostics.
Definition operation_tags.hpp:27
static constexpr std::string_view name
Definition operation_tags.hpp:28
Exact dense left singular-vector operation tag.
Definition operation_tags.hpp:276
SvdVectorExtent left
Definition operation_tags.hpp:278
static constexpr std::string_view name
Definition operation_tags.hpp:277
bool overwrite_input
Definition operation_tags.hpp:279
Exact dense singular value decomposition operation tag.
Definition operation_tags.hpp:292
SvdVectorExtent left
Definition operation_tags.hpp:294
SvdVectorExtent right
Definition operation_tags.hpp:295
SvdOverwrite overwrite
Definition operation_tags.hpp:296
static constexpr std::string_view name
Definition operation_tags.hpp:293
Exact dense right singular-vector operation tag.
Definition operation_tags.hpp:284
SvdVectorExtent right
Definition operation_tags.hpp:286
static constexpr std::string_view name
Definition operation_tags.hpp:285
bool overwrite_input
Definition operation_tags.hpp:287
Symmetric tridiagonal eigensystem operation tag.
Definition operation_tags.hpp:301
static constexpr std::string_view name
Definition operation_tags.hpp:302
bool compute_vectors
Definition operation_tags.hpp:303