svd.hpp File Reference

Destructive and value-producing exact dense singular value decompositions. More...

#include <uni20/linalg/backends/lapack/svd.hpp>
#include <uni20/linalg/blas/mdspan_matrix.hpp>
#include <uni20/linalg/decomposition_precision.hpp>
#include <uni20/linalg/dispatch.hpp>
#include <uni20/linalg/operation_tags.hpp>
#include <uni20/tensor/copy.hpp>
#include <uni20/tensor/output.hpp>
#include <uni20/tensor/tensor.hpp>
#include <algorithm>
#include <array>
#include <concepts>
#include <type_traits>
#include <utility>

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Classes
struct	uni20::linalg::SvdLeftResult< LeftTensor, SingularValueTensor >
	Owning left singular vectors and singular values returned by svd_left. More...
struct	uni20::linalg::SvdResult< LeftTensor, SingularValueTensor, RightAdjointTensor >
	Owning factors returned by svd. More...
struct	uni20::linalg::SvdRightResult< SingularValueTensor, RightAdjointTensor >
	Owning singular values and right singular vectors returned by svd_right. More...

Namespaces
namespace	uni20
namespace	uni20::linalg

Functions
template<KernelBackendSelector BackendSelector, uni20::MutableRankedTensorView< 1 > SingularValueTensor, uni20::MutableRankedTensorView< 2 > LeftTensor, uni20::MutableRankedTensorView< 2 > RightAdjointTensor, uni20::MutableRankedTensorView< 2 > MatrixTensor>
void	uni20::linalg::singular_value_decomposition (BackendSelector &&selector, SingularValueTensor &&singular_values, LeftTensor &&left_singular_vectors, RightAdjointTensor &&right_singular_vectors_adjoint, MatrixTensor &&matrix_work, SvdOptions options={}, std::optional< Precision > requested={})
	Compute a destructive exact SVD through an explicit selector.
template<KernelBackendSelector Selector, MutableRankedTensorView< 1 > V, MutableRankedTensorView< 2 > L, MutableRankedTensorView< 2 > R, MutableRankedTensorView< 2 > A>
void	uni20::linalg::singular_value_decomposition (Selector &&selector, V &&values, L &&left, R &&right, A &&matrix_work, Precision p, SvdOptions options={})
	Compute a destructive decomposition at explicit precision with optional output settings.
template<uni20::MutableRankedTensorView< 1 > SingularValueTensor, uni20::MutableRankedTensorView< 2 > LeftTensor, uni20::MutableRankedTensorView< 2 > RightAdjointTensor, uni20::MutableRankedTensorView< 2 > MatrixTensor>
void	uni20::linalg::singular_value_decomposition (SingularValueTensor &&singular_values, LeftTensor &&left_singular_vectors, RightAdjointTensor &&right_singular_vectors_adjoint, MatrixTensor &&matrix_work, SvdOptions options={}, std::optional< Precision > requested={})
	Compute a destructive exact SVD using tensor storage policy.
template<MutableRankedTensorView< 1 > V, MutableRankedTensorView< 2 > L, MutableRankedTensorView< 2 > R, MutableRankedTensorView< 2 > A>
void	uni20::linalg::singular_value_decomposition (V &&values, L &&left, R &&right, A &&matrix_work, Precision p, SvdOptions options={})
	Compute a destructive decomposition at explicit precision with optional output settings.
template<KernelBackendSelector BackendSelector, class MatrixTensor > requires uni20::OwningTensor<MatrixTensor> && uni20::MutableRankedImmediateTensorView<MatrixTensor, 2> && (!std::is_lvalue_reference_v<MatrixTensor>) && (!std::is_const_v<std::remove_reference_t<MatrixTensor>>)
auto	uni20::linalg::singular_values (BackendSelector &&selector, MatrixTensor &&matrix, std::optional< Precision > requested={})
	Consume an owning matrix and return its exact singular values through an explicit selector.
template<KernelBackendSelector BackendSelector, uni20::RankedTensorView< 2 > MatrixTensor>
auto	uni20::linalg::singular_values (BackendSelector &&selector, MatrixTensor const &matrix, std::optional< Precision > requested={})
	Preserve a matrix and return its exact singular values through an explicit selector.
template<class MatrixTensor > requires uni20::OwningTensor<MatrixTensor> && uni20::MutableRankedImmediateTensorView<MatrixTensor, 2> && (!std::is_lvalue_reference_v<MatrixTensor>) && (!std::is_const_v<std::remove_reference_t<MatrixTensor>>)
auto	uni20::linalg::singular_values (MatrixTensor &&matrix, std::optional< Precision > requested={})
	Consume an owning matrix and return its exact singular values.
template<uni20::RankedTensorView< 2 > MatrixTensor>
auto	uni20::linalg::singular_values (MatrixTensor const &matrix, std::optional< Precision > requested={})
	Preserve a matrix and return its exact singular values.
template<KernelBackendSelector BackendSelector, class MatrixTensor > requires uni20::OwningTensor<MatrixTensor> && uni20::MutableRankedImmediateTensorView<MatrixTensor, 2> && (!std::is_lvalue_reference_v<MatrixTensor>) && (!std::is_const_v<std::remove_reference_t<MatrixTensor>>)
auto	uni20::linalg::svd (BackendSelector &&selector, MatrixTensor &&matrix, SvdOptions options={}, std::optional< Precision > requested={})
	Consume an owning matrix and return its exact singular value decomposition.
template<KernelBackendSelector BackendSelector, uni20::RankedTensorView< 2 > MatrixTensor>
auto	uni20::linalg::svd (BackendSelector &&selector, MatrixTensor const &matrix, SvdOptions options={}, std::optional< Precision > requested={})
	Preserve a matrix and return its exact singular value decomposition through an explicit selector.
template<RankedTensorView< 2 > Matrix>
auto	uni20::linalg::svd (Matrix &&matrix, Precision p, SvdOptions options={})
	Compute SVD at explicit working precision with optional output settings.
template<class MatrixTensor > requires uni20::OwningTensor<MatrixTensor> && uni20::MutableRankedImmediateTensorView<MatrixTensor, 2> && (!std::is_lvalue_reference_v<MatrixTensor>) && (!std::is_const_v<std::remove_reference_t<MatrixTensor>>)
auto	uni20::linalg::svd (MatrixTensor &&matrix, SvdOptions options={}, std::optional< Precision > requested={})
	Consume an owning matrix and return its exact singular value decomposition.
template<uni20::RankedTensorView< 2 > MatrixTensor>
auto	uni20::linalg::svd (MatrixTensor const &matrix, SvdOptions options={}, std::optional< Precision > requested={})
	Preserve a matrix and return its exact singular value decomposition.
template<KernelBackendSelector Selector, RankedTensorView< 2 > Matrix>
auto	uni20::linalg::svd (Selector &&selector, Matrix &&matrix, Precision p, SvdOptions options={})
	Compute SVD at explicit working precision with optional output settings.
template<KernelBackendSelector BackendSelector, class MatrixTensor > requires uni20::OwningTensor<MatrixTensor> && uni20::MutableRankedImmediateTensorView<MatrixTensor, 2> && (!std::is_lvalue_reference_v<MatrixTensor>) && (!std::is_const_v<std::remove_reference_t<MatrixTensor>>)
auto	uni20::linalg::svd_left (BackendSelector &&selector, MatrixTensor &&matrix, SvdVectorExtent extent=SvdVectorExtent::Reduced, std::optional< Precision > requested={})
	Consume an owning matrix and return exact left singular vectors and singular values.
template<KernelBackendSelector BackendSelector, uni20::RankedTensorView< 2 > MatrixTensor>
auto	uni20::linalg::svd_left (BackendSelector &&selector, MatrixTensor const &matrix, SvdVectorExtent extent=SvdVectorExtent::Reduced, std::optional< Precision > requested={})
	Preserve a matrix and return exact left singular vectors and singular values.
template<RankedTensorView< 2 > Matrix>
auto	uni20::linalg::svd_left (Matrix &&matrix, Precision p, SvdVectorExtent extent=SvdVectorExtent::Reduced)
	Compute left SVD factors at explicit working precision with optional output settings.
template<class MatrixTensor > requires uni20::OwningTensor<MatrixTensor> && uni20::MutableRankedImmediateTensorView<MatrixTensor, 2> && (!std::is_lvalue_reference_v<MatrixTensor>) && (!std::is_const_v<std::remove_reference_t<MatrixTensor>>)
auto	uni20::linalg::svd_left (MatrixTensor &&matrix, SvdVectorExtent extent=SvdVectorExtent::Reduced, std::optional< Precision > requested={})
	Consume an owning matrix and return exact left singular vectors and singular values.
template<uni20::RankedTensorView< 2 > MatrixTensor>
auto	uni20::linalg::svd_left (MatrixTensor const &matrix, SvdVectorExtent extent=SvdVectorExtent::Reduced, std::optional< Precision > requested={})
	Preserve a matrix and return exact left singular vectors and singular values.
template<KernelBackendSelector Selector, RankedTensorView< 2 > Matrix>
auto	uni20::linalg::svd_left (Selector &&selector, Matrix &&matrix, Precision p, SvdVectorExtent extent=SvdVectorExtent::Reduced)
	Compute left SVD factors at explicit working precision with optional output settings.
template<KernelBackendSelector BackendSelector, class MatrixTensor > requires uni20::OwningTensor<MatrixTensor> && uni20::MutableRankedImmediateTensorView<MatrixTensor, 2> && (!std::is_lvalue_reference_v<MatrixTensor>) && (!std::is_const_v<std::remove_reference_t<MatrixTensor>>)
auto	uni20::linalg::svd_right (BackendSelector &&selector, MatrixTensor &&matrix, SvdVectorExtent extent=SvdVectorExtent::Reduced, std::optional< Precision > requested={})
	Consume an owning matrix and return exact singular values and right singular vectors.
template<KernelBackendSelector BackendSelector, uni20::RankedTensorView< 2 > MatrixTensor>
auto	uni20::linalg::svd_right (BackendSelector &&selector, MatrixTensor const &matrix, SvdVectorExtent extent=SvdVectorExtent::Reduced, std::optional< Precision > requested={})
	Preserve a matrix and return exact singular values and right singular vectors.
template<RankedTensorView< 2 > Matrix>
auto	uni20::linalg::svd_right (Matrix &&matrix, Precision p, SvdVectorExtent extent=SvdVectorExtent::Reduced)
	Compute right SVD factors at explicit working precision with optional output settings.
template<class MatrixTensor > requires uni20::OwningTensor<MatrixTensor> && uni20::MutableRankedImmediateTensorView<MatrixTensor, 2> && (!std::is_lvalue_reference_v<MatrixTensor>) && (!std::is_const_v<std::remove_reference_t<MatrixTensor>>)
auto	uni20::linalg::svd_right (MatrixTensor &&matrix, SvdVectorExtent extent=SvdVectorExtent::Reduced, std::optional< Precision > requested={})
	Consume an owning matrix and return exact singular values and right singular vectors.
template<uni20::RankedTensorView< 2 > MatrixTensor>
auto	uni20::linalg::svd_right (MatrixTensor const &matrix, SvdVectorExtent extent=SvdVectorExtent::Reduced, std::optional< Precision > requested={})
	Preserve a matrix and return exact singular values and right singular vectors.
template<KernelBackendSelector Selector, RankedTensorView< 2 > Matrix>
auto	uni20::linalg::svd_right (Selector &&selector, Matrix &&matrix, Precision p, SvdVectorExtent extent=SvdVectorExtent::Reduced)
	Compute right SVD factors at explicit working precision with optional output settings.

Detailed Description

Destructive and value-producing exact dense singular value decompositions.

Precision may be inferred from the input matrix or supplied explicitly. Fixed results require their native precision; runtime decompositions require finite precision. Owning results record the selected default.