Linear Algebra Solvers

Linear Algebra Solvers#

2025-10-17

22 min read time

Applies to Linux

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:
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:
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:
Parameters:

  • handle – [in] raft::resources

  • M – [in] input raft::device_matrix_view with layout raft::col_major of shape (M, N)

  • S_vec – [out] singular values raft::device_vector_view of shape (K)

  • p – [in] no. of upsamples

  • tol – [in] tolerance for Jacobi-based solvers

  • max_sweeps – [in] maximum number of sweeps for Jacobi-based solvers

  • U_in – [out] std::optional left singular values of raft::device_matrix_view with layout raft::col_major

  • V_in – [out] std::optional right singular values of raft::device_matrix_view with layout raft::col_major

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:
Parameters:

  • handle – [in] raft::resources

  • M – [in] input raft::device_matrix_view with layout raft::col_major of shape (M, N)

  • S_vec – [out] singular values raft::device_vector_view of shape (K)

  • p – [in] no. of upsamples

  • tol – [in] tolerance for Jacobi-based solvers

  • max_sweeps – [in] maximum number of sweeps for Jacobi-based solvers

  • U_in – [out] std::optional left singular values of raft::device_matrix_view with layout raft::col_major

  • V_in – [out] std::optional right singular values of raft::device_matrix_view with layout raft::col_major

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:
Parameters:

  • handle – [in] raft::resources

  • M – [in] input raft::device_matrix_view with layout raft::col_major of shape (M, N)

  • S_vec – [out] singular values raft::device_vector_view of shape (K)

  • PC_perc – [in] percentage of singular values to be computed

  • UpS_perc – [in] upsampling percentage

  • U_in – [out] std::optional left singular values of raft::device_matrix_view with layout raft::col_major

  • V_in – [out] std::optional right singular values of raft::device_matrix_view with layout raft::col_major

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:
Parameters:

  • handle – [in] raft::resources

  • M – [in] input raft::device_matrix_view with layout raft::col_major of shape (M, N)

  • S_vec – [out] singular values raft::device_vector_view of shape (K)

  • PC_perc – [in] percentage of singular values to be computed

  • UpS_perc – [in] upsampling percentage

  • U_in – [out] std::optional left singular values of raft::device_matrix_view with layout raft::col_major

  • V_in – [out] std::optional right singular values of raft::device_matrix_view with layout raft::col_major

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:
Parameters:

  • handle – [in] raft::resources

  • M – [in] input raft::device_matrix_view with layout raft::col_major of shape (M, N)

  • S_vec – [out] singular values raft::device_vector_view of shape (K)

  • PC_perc – [in] percentage of singular values to be computed

  • UpS_perc – [in] upsampling percentage

  • tol – [in] tolerance for Jacobi-based solvers

  • max_sweeps – [in] maximum number of sweeps for Jacobi-based solvers

  • U_in – [out] std::optional left singular values of raft::device_matrix_view with layout raft::col_major

  • V_in – [out] std::optional right singular values of raft::device_matrix_view with layout raft::col_major

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:
Parameters:

  • handle – [in] raft::resources

  • M – [in] input raft::device_matrix_view with layout raft::col_major of shape (M, N)

  • S_vec – [out] singular values raft::device_vector_view of shape (K)

  • PC_perc – [in] percentage of singular values to be computed

  • UpS_perc – [in] upsampling percentage

  • tol – [in] tolerance for Jacobi-based solvers

  • max_sweeps – [in] maximum number of sweeps for Jacobi-based solvers

  • U_in – [out] std::optional left singular values of raft::device_matrix_view with layout raft::col_major

  • V_in – [out] std::optional right singular values of raft::device_matrix_view with layout raft::col_major

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 T>
cusolverStatus_t cusolverDngesvd_bufferSize(
cusolverDnHandle_t handle,
int m,
int n,
int *lwork
)#
template<typename T>
cusolverStatus_t cusolverDngesvd(
cusolverDnHandle_t handle,
signed char jobu,
signed char jobvt,
int m,
int n,
T *A,
int lda,
T *S,
T *U,
int ldu,
T *VT,
int ldvt,
T *work,
int lwork,
T *rwork,
int *devInfo,
cudaStream_t stream
)#
template<>
inline cusolverStatus_t cusolverDngesvd(
cusolverDnHandle_t handle,
signed char jobu,
signed char jobvt,
int m,
int n,
float *A,
int lda,
float *S,
float *U,
int ldu,
float *VT,
int ldvt,
float *work,
int lwork,
float *rwork,
int *devInfo,
cudaStream_t stream
)#
template<>
inline cusolverStatus_t cusolverDngesvd(
cusolverDnHandle_t handle,
signed char jobu,
signed char jobvt,
int m,
int n,
double *A,
int lda,
double *S,
double *U,
int ldu,
double *VT,
int ldvt,
double *work,
int lwork,
double *rwork,
int *devInfo,
cudaStream_t stream
)#
template<typename T> inline cusolverStatus_t CUSOLVERAPI cusolverDngesvdj_bufferSize (cusolverDnHandle_t handle, cusolverEigMode_t jobz, int econ, int m, int n, const T *A, int lda, const T *S, const T *U, int ldu, const T *V, int ldv, int *lwork, gesvdjInfo_t params)
template<> inline cusolverStatus_t CUSOLVERAPI cusolverDngesvdj_bufferSize (cusolverDnHandle_t handle, cusolverEigMode_t jobz, int econ, int m, int n, const float *A, int lda, const float *S, const float *U, int ldu, const float *V, int ldv, int *lwork, gesvdjInfo_t params)
template<> inline cusolverStatus_t CUSOLVERAPI cusolverDngesvdj_bufferSize (cusolverDnHandle_t handle, cusolverEigMode_t jobz, int econ, int m, int n, const double *A, int lda, const double *S, const double *U, int ldu, const double *V, int ldv, int *lwork, gesvdjInfo_t params)
template<typename T> inline cusolverStatus_t CUSOLVERAPI cusolverDngesvdj (cusolverDnHandle_t handle, cusolverEigMode_t jobz, int econ, int m, int n, T *A, int lda, T *S, T *U, int ldu, T *V, int ldv, T *work, int lwork, int *info, gesvdjInfo_t params, cudaStream_t stream)
template<> inline cusolverStatus_t CUSOLVERAPI cusolverDngesvdj (cusolverDnHandle_t handle, cusolverEigMode_t jobz, int econ, int m, int n, float *A, int lda, float *S, float *U, int ldu, float *V, int ldv, float *work, int lwork, int *info, gesvdjInfo_t params, cudaStream_t stream)
template<> inline cusolverStatus_t CUSOLVERAPI cusolverDngesvdj (cusolverDnHandle_t handle, cusolverEigMode_t jobz, int econ, int m, int n, double *A, int lda, double *S, double *U, int ldu, double *V, int ldv, double *work, int lwork, int *info, gesvdjInfo_t params, cudaStream_t stream)
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:

  • handle – [in] raft::resources

  • U – [in] left singular values of raft::device_matrix_view with layout raft::col_major and dimensions (m, k)

  • S – [in] square matrix with singular values on its diagonal of shape (k, k)

  • V – [in] right singular values of raft::device_matrix_view with layout raft::col_major and dimensions (k, n)

  • out – [out] output raft::device_matrix_view with layout raft::col_major of shape (m, n)

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: