Linear Algebra Solvers#

Eigen Decomposition#

#include <raft/linalg/eig.cuh>

namespace raft::linalg

template<typename ValueType, typename IndexType>
void eig_dc(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_matrix_view<ValueType, IndexType, raft::col_major> eig_vectors, raft::device_vector_view<ValueType, IndexType> eig_vals)#

eig decomp with divide and conquer method for the column-major symmetric matrices

Template Parameters:

  • ValueType – the data-type of input and output

  • IntegerType – Integer used for addressing

Parameters:
template<typename ValueType, typename IndexType>
void eig_dc_selective(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_matrix_view<ValueType, IndexType, raft::col_major> eig_vectors, raft::device_vector_view<ValueType, IndexType> eig_vals, std::size_t n_eig_vals, EigVecMemUsage memUsage)#

eig decomp to select top-n eigen values with divide and conquer method for the column-major symmetric matrices

Template Parameters:

  • ValueType – the data-type of input and output

  • IntegerType – Integer used for addressing

Parameters:

  • handle – [in] raft::resources

  • in – [in] input raft::device_matrix_view (symmetric matrix that has real eig values and vectors)

  • eig_vectors – [out] eigenvectors output of type raft::device_matrix_view

  • eig_vals – [out] eigen values output of type raft::device_vector_view

  • n_eig_vals – [in] number of eigenvectors to be generated

  • memUsage – [in] the memory selection for eig vector output

template<typename ValueType, typename IndexType>
void eig_jacobi(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_matrix_view<ValueType, IndexType, raft::col_major> eig_vectors, raft::device_vector_view<ValueType, IndexType> eig_vals, ValueType tol = 1.e-7, int sweeps = 15)#

overloaded function for eig decomp with Jacobi method for the column-major symmetric matrices (in parameter)

Template Parameters:

  • ValueType – the data-type of input and output

  • IntegerType – Integer used for addressing

Parameters:

  • handle – raft::resources

  • in – [in] input raft::device_matrix_view (symmetric matrix that has real eig values and vectors)

  • eig_vectors – [out] eigenvectors output of type raft::device_matrix_view

  • eig_vals – [out] eigen values output of type raft::device_vector_view

  • tol – [in] error tolerance for the jacobi method. Algorithm stops when the Frobenius norm of the absolute error is below tol

  • sweeps – [in] number of sweeps in the Jacobi algorithm. The more the better accuracy.

QR Decomposition#

#include <raft/linalg/qr.cuh>

namespace raft::linalg

template<typename ElementType, typename IndexType>
void qr_get_q(raft::resources const &handle, raft::device_matrix_view<const ElementType, IndexType, raft::col_major> M, raft::device_matrix_view<ElementType, IndexType, raft::col_major> Q)#

Compute the QR decomposition of matrix M and return only the Q matrix.

Parameters:
template<typename ElementType, typename IndexType>
void qr_get_qr(raft::resources const &handle, raft::device_matrix_view<const ElementType, IndexType, raft::col_major> M, raft::device_matrix_view<ElementType, IndexType, raft::col_major> Q, raft::device_matrix_view<ElementType, IndexType, raft::col_major> R)#

Compute the QR decomposition of matrix M and return both the Q and R matrices.

Parameters:

Randomized Singular-Value Decomposition#

#include <raft/linalg/rsvd.cuh>

namespace raft::linalg

template<typename ValueType, typename IndexType, typename UType, typename VType>
void rsvd_fixed_rank(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> M, raft::device_vector_view<ValueType, IndexType> S_vec, IndexType p, UType &&U_in, VType &&V_in)#

randomized singular value decomposition (RSVD) on a column major rectangular matrix using QR decomposition, by specifying no. of PCs and upsamples directly

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

  • UType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U_in

  • VType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V_in

Parameters:
template<typename ...Args, typename = std::enable_if_t<sizeof...(Args) == 4>>
void rsvd_fixed_rank(Args... args)#

Overload of rsvd_fixed_rank to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of rsvd_fixed_rank.

template<typename ValueType, typename IndexType, typename UType, typename VType>
void rsvd_fixed_rank_symmetric(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> M, raft::device_vector_view<ValueType, IndexType> S_vec, IndexType p, UType &&U_in, VType &&V_in)#

randomized singular value decomposition (RSVD) on a column major rectangular matrix using symmetric Eigen decomposition, by specifying no. of PCs and upsamples directly. The rectangular input matrix is made square and symmetric using B @ B^T

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

  • UType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U_in

  • VType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V_in

Parameters:
template<typename ...Args, typename = std::enable_if_t<sizeof...(Args) == 4>>
void rsvd_fixed_rank_symmetric(Args... args)#

Overload of rsvd_fixed_rank_symmetric to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of rsvd_fixed_rank_symmetric.

template<typename ValueType, typename IndexType, typename UType, typename VType>
void rsvd_fixed_rank_jacobi(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> M, raft::device_vector_view<ValueType, IndexType> S_vec, IndexType p, ValueType tol, int max_sweeps, UType &&U_in, VType &&V_in)#

randomized singular value decomposition (RSVD) on a column major rectangular matrix using Jacobi method, by specifying no. of PCs and upsamples directly

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

  • UType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U_in

  • VType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V_in

Parameters:
template<typename ...Args, typename = std::enable_if_t<sizeof...(Args) == 6>>
void rsvd_fixed_rank_jacobi(Args... args)#

Overload of rsvd_fixed_rank_jacobi to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of rsvd_fixed_rank_jacobi.

template<typename ValueType, typename IndexType, typename UType, typename VType>
void rsvd_fixed_rank_symmetric_jacobi(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> M, raft::device_vector_view<ValueType, IndexType> S_vec, IndexType p, ValueType tol, int max_sweeps, UType &&U_in, VType &&V_in)#

randomized singular value decomposition (RSVD) on a column major rectangular matrix using Jacobi method, by specifying no. of PCs and upsamples directly. The rectangular input matrix is made square and symmetric using B @ B^T

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

  • UType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U_in

  • VType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V_in

Parameters:
template<typename ...Args, typename = std::enable_if_t<sizeof...(Args) == 6>>
void rsvd_fixed_rank_symmetric_jacobi(Args... args)#

Overload of rsvd_fixed_rank_symmetric_jacobi to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of rsvd_fixed_rank_symmetric_jacobi.

template<typename ValueType, typename IndexType, typename UType, typename VType>
void rsvd_perc(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> M, raft::device_vector_view<ValueType, IndexType> S_vec, ValueType PC_perc, ValueType UpS_perc, UType &&U_in, VType &&V_in)#

randomized singular value decomposition (RSVD) on a column major rectangular matrix using QR decomposition, by specifying the PC and upsampling ratio

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

  • UType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U_in

  • VType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V_in

Parameters:
template<typename ...Args, typename = std::enable_if_t<sizeof...(Args) == 5>>
void rsvd_perc(Args... args)#

Overload of rsvd_perc to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of rsvd_perc.

template<typename ValueType, typename IndexType, typename UType, typename VType>
void rsvd_perc_symmetric(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> M, raft::device_vector_view<ValueType, IndexType> S_vec, ValueType PC_perc, ValueType UpS_perc, UType &&U_in, VType &&V_in)#

randomized singular value decomposition (RSVD) on a column major rectangular matrix using symmetric Eigen decomposition, by specifying the PC and upsampling ratio. The rectangular input matrix is made square and symmetric using B @ B^T

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

  • UType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U_in

  • VType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V_in

Parameters:
template<typename ...Args, typename = std::enable_if_t<sizeof...(Args) == 5>>
void rsvd_perc_symmetric(Args... args)#

Overload of rsvd_perc_symmetric to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of rsvd_perc_symmetric.

template<typename ValueType, typename IndexType, typename UType, typename VType>
void rsvd_perc_jacobi(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> M, raft::device_vector_view<ValueType, IndexType> S_vec, ValueType PC_perc, ValueType UpS_perc, ValueType tol, int max_sweeps, UType &&U_in, VType &&V_in)#

randomized singular value decomposition (RSVD) on a column major rectangular matrix using Jacobi method, by specifying the PC and upsampling ratio

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

  • UType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U_in

  • VType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V_in

Parameters:
template<typename ...Args, typename = std::enable_if_t<sizeof...(Args) == 7>>
void rsvd_perc_jacobi(Args... args)#

Overload of rsvd_perc_jacobi to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of rsvd_perc_jacobi.

template<typename ValueType, typename IndexType, typename UType, typename VType>
void rsvd_perc_symmetric_jacobi(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> M, raft::device_vector_view<ValueType, IndexType> S_vec, ValueType PC_perc, ValueType UpS_perc, ValueType tol, int max_sweeps, UType &&U_in, VType &&V_in)#

randomized singular value decomposition (RSVD) on a column major rectangular matrix using Jacobi method, by specifying the PC and upsampling ratio. The rectangular input matrix is made square and symmetric using B @ B^T

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

  • UType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U_in

  • VType – std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V_in

Parameters:
template<typename ...Args, typename = std::enable_if_t<sizeof...(Args) == 7>>
void rsvd_perc_symmetric_jacobi(Args... args)#

Overload of rsvd_perc_symmetric_jacobi to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of rsvd_perc_symmetric_jacobi.

template<typename math_t, typename idx_t>
void randomized_svd(const raft::resources &handle, raft::device_matrix_view<const math_t, idx_t, raft::col_major> in, raft::device_vector_view<math_t, idx_t> S, std::optional<raft::device_matrix_view<math_t, idx_t, raft::col_major>> U, std::optional<raft::device_matrix_view<math_t, idx_t, raft::col_major>> V, std::size_t p, std::size_t niters)#

randomized singular value decomposition (RSVD) using cusolver

Template Parameters:

  • math_t – the data type

  • idx_t – index type

Parameters:

  • handle – [in] raft handle

  • in – [in] input matrix in col-major format. Warning: the content of this matrix is modified by the cuSOLVER routines. [dim = n_rows * n_cols]

  • S – [out] array of singular values of input matrix. The rank k must be less than min(m,n). [dim = k]

  • U – [out] optional left singular values of input matrix. Use std::nullopt to not generate it. [dim = n_rows * k]

  • V – [out] optional right singular values of input matrix. Use std::nullopt to not generate it. [dim = k * n_cols]

  • p – [in] Oversampling. The size of the subspace will be (k + p). (k+p) is less than min(m,n). (Recommended to be at least 2*k)

  • niters – [in] Number of iteration of power method. (2 is recommended)

template<typename math_t, typename idx_t, typename opt_u_vec_t, typename opt_v_vec_t>
void randomized_svd(const raft::resources &handle, raft::device_matrix_view<const math_t, idx_t, raft::col_major> in, raft::device_vector_view<math_t, idx_t> S, opt_u_vec_t &&U, opt_v_vec_t &&V, std::size_t p, std::size_t niters)#

Overload of randomized_svd to help the compiler find the above overload, in case users pass in std::nullopt for the optional arguments.

Please see above for documentation of randomized_svd.

Singular-Value Decomposition#

#include <raft/linalg/svd.cuh>

namespace raft::linalg

template<typename ValueType, typename IndexType>
void svd_qr(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_vector_view<ValueType, IndexType> sing_vals, std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U = std::nullopt, std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V = std::nullopt)#

singular value decomposition (SVD) on a column major matrix using QR decomposition

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

Parameters:
template<typename ValueType, typename IndexType, typename UType, typename VType>
void svd_qr(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_vector_view<ValueType, IndexType> sing_vals, UType &&U_in = std::nullopt, VType &&V_in = std::nullopt)#

Overload of svd_qr to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of svd_qr.

template<typename ValueType, typename IndexType>
void svd_qr_transpose_right_vec(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_vector_view<ValueType, IndexType> sing_vals, std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U = std::nullopt, std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> V = std::nullopt)#

singular value decomposition (SVD) on a column major matrix using QR decomposition. Right singular vector matrix is transposed before returning

Template Parameters:

  • ValueType – value type of parameters

  • IndexType – index type of parameters

Parameters:
template<typename ValueType, typename IndexType, typename UType, typename VType>
void svd_qr_transpose_right_vec(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_vector_view<ValueType, IndexType> sing_vals, UType &&U_in = std::nullopt, VType &&V_in = std::nullopt)#

Overload of svd_qr_transpose_right_vec to help the compiler find the above overload, in case users pass in std::nullopt for one or both of the optional arguments.

Please see above for documentation of svd_qr_transpose_right_vec.

template<typename ValueType, typename IndexType>
void svd_eig(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_vector_view<ValueType, IndexType> S, raft::device_matrix_view<ValueType, IndexType, raft::col_major> V, std::optional<raft::device_matrix_view<ValueType, IndexType, raft::col_major>> U = std::nullopt)#

singular value decomposition (SVD) on a column major matrix using Eigen decomposition. A square symmetric covariance matrix is constructed for the SVD

Parameters:
template<typename ValueType, typename IndexType, typename UType>
void svd_eig(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> in, raft::device_vector_view<ValueType, IndexType> S, raft::device_matrix_view<ValueType, IndexType, raft::col_major> V, UType &&U = std::nullopt)#
template<typename ValueType, typename IndexType>
void svd_reconstruction(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> U, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> S, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> V, raft::device_matrix_view<ValueType, IndexType, raft::col_major> out)#

reconstruct a matrix use left and right singular vectors and singular values

Parameters:

Least Squares#

#include <raft/linalg/lstsq.cuh>

namespace raft::linalg

template<typename ValueType, typename IndexType>
void lstsq_svd_qr(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> A, raft::device_vector_view<const ValueType, IndexType> b, raft::device_vector_view<ValueType, IndexType> w)#

Solves the linear ordinary least squares problem Aw = b Via SVD decomposition of A = U S Vt.

Template Parameters:

ValueType – the data-type of input/output

Parameters:
template<typename ValueType, typename IndexType>
void lstsq_svd_jacobi(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> A, raft::device_vector_view<const ValueType, IndexType> b, raft::device_vector_view<ValueType, IndexType> w)#

Solves the linear ordinary least squares problem Aw = b Via SVD decomposition of A = U S V^T using Jacobi iterations.

Template Parameters:

ValueType – the data-type of input/output

Parameters:
template<typename ValueType, typename IndexType>
void lstsq_eig(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> A, raft::device_vector_view<const ValueType, IndexType> b, raft::device_vector_view<ValueType, IndexType> w)#

Solves the linear ordinary least squares problem Aw = b via eigenvalue decomposition of A^T * A (covariance matrix for dataset A). (w = (A^T A)^-1 A^T b)

Template Parameters:

ValueType – the data-type of input/output

Parameters:
template<typename ValueType, typename IndexType>
void lstsq_qr(raft::resources const &handle, raft::device_matrix_view<const ValueType, IndexType, raft::col_major> A, raft::device_vector_view<const ValueType, IndexType> b, raft::device_vector_view<ValueType, IndexType> w)#

Solves the linear ordinary least squares problem Aw = b via QR decomposition of A = QR. (triangular system of equations Rw = Q^T b)

Template Parameters:

ValueType – the data-type of input/output

Parameters: