Attention

The vector search and clustering algorithms in RAFT are being migrated to a new library dedicated to vector search called cuVS. We will continue to support the vector search algorithms in RAFT during this move, but will no longer update them after the RAPIDS 24.06 (June) release. We plan to complete the migration by RAPIDS 24.08 (August) release.

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:
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