namespace solver¶

// namespaces

namespace xf::solver::internal
namespace xf::solver::internalgetrf

geqrf¶

geqrf overload (1)¶

#include "MatrixDecomposition/geqrf.hpp"

template <
    typename T,
    int NRMAX,
    int NCMAX,
    int NCU
    >
int geqrf (
    int m,
    int n,
    T* A,
    int lda,
    T* tau
    )

This function computes QR decomposition of matrix \(A\)

\[\begin{equation*} {A = Q R}\end{equation*}\]

where \(A\) is a dense matrix of size \(m \times n\) , \(Q\) is a \(m \times n\) matrix with orthonormal columns, and \(R\) is an upper triangular matrix.

The maximum matrix size supported in FPGA is templated by NRMAX and NCMAX.

Parameters:

T	data type (support float and double)
NRMAX	maximum number of rows of input matrix
NCMAX	maximum number of columns of input matrix
NCU	number of computation unit
m	number of rows of matrix A
n	number of cols of matrix A
A	input matrix of size \(m \times lda\) , and overwritten by the output triangular R matrix and min(m,n) elementary reflectors
lda	leading dimension of matrix A
tau	scalar factors for elementary reflectors

gesvdj¶

#include "MatrixDecomposition/gesvdj.hpp"

template <
    typename T,
    int NMAX,
    int NCU
    >
void gesvdj (
    int m,
    T* A,
    int lda,
    T* S,
    T* U,
    int ldu,
    T* V,
    int ldv,
    int& info
    )

Symmetric Matrix Jacobi based Singular Value Decomposition (GESVDJ) .

\[\begin{equation*} {A = U \Sigma {V}^T}\end{equation*}\]

where \(A\) is a dense symmetric matrix of size \(m \times m\) , \(U\) and \(V\) are \(m \times m\) matrix with orthonormal columns, and \(\Sigma\) is diagonal matrix.

The maximum matrix size supported in FPGA is templated by NMAX.

Parameters:

T	data type (support float and double).
NMAX	maximum number of rows/columns of input matrix
NCU	number of computation unit
m	number of rows/cols of matrix A
A	input matrix of size \(m \times m\)
S	decomposed diagonal singular matrix of size \(m \times m\)
U	left U matrix of SVD
V	right V matrix of SVD
lda	leading dimension of matrix A
ldu	leading dimension of matrix U
ldv	leading dimension of matrix V
info	output info (unused)

gesvj¶

#include "MatrixDecomposition/gesvj.hpp"

template <
    typename T,
    int NRMAX,
    int NCMAX,
    int MCU,
    int NCU
    >
void gesvj (
    int m,
    int n,
    T* A,
    T* U,
    T* S,
    T* V
    )

This function implements singular value decomposition of matrix A using one-sided Jacobi algorihtm.

\[\begin{equation*} {A = U \Sigma {V}^T}\end{equation*}\]

where \(A\) is a dense matrix of size \(m \times n\) , \(U\) is \(m \times m\) matrix with orthonormal columns, \(V\) is \(n \times n\) matrix with orthonormal columns, and \(\Sigma\) is diagonal matrix.

The maximum matrix size supported in FPGA is templated by NCMAX, NRMAX.

Parameters:

T
:	the data type of gesvj
NRMAX	maximum number of rows of input matrix
NCMAX	maximum number of columns of input matrix
MCU	number of computation unit of M
NCU	number of computation unit of N
m	number of rows of matrix A
n	number of cols of matrix A
A	input matrix of size \(m \times n\)
S	decomposed diagonal singular matrix of size n
U	left U matrix of SVD of size \(m \times m\)
V	right V matrix of SVD \(n \times n\)

getrf¶

#include "MatrixDecomposition/getrf.hpp"

template <
    typename T,
    int NMAX,
    int NCU
    >
void getrf (
    int n,
    T* A,
    int lda,
    int* ipiv,
    int& info
    )

This function computes the LU decomposition (with partial pivoting) of matrix \(A\)

\[\begin{equation*} {P A = L U}\end{equation*}\]

where \(P\) is a permutation matrix, \(A\) is a dense matrix of size \(n \times n\) , \(L\) is a lower triangular matrix with unit diagonal, and \(U\) is an upper triangular matrix. This function does not implement pivoting.

The maximum matrix size supported in FPGA is templated by NMAX.

Parameters:

T	data type (support float and double)
NMAX	maximum number of rows/columns of input matrix
NCU	number of computation unit
n	number of rows/cols of matrix A
A	input matrix, and overwritten by the output upper and lower triangular matrix
lda	leading dimention of input matrix A
pivot	indices, row i of matrix A is stored in row[i]
info	output info (unused)

getrf_nopivot¶

#include "MatrixDecomposition/getrf_nopivot.hpp"

template <
    typename T,
    int NMAX,
    int NCU
    >
void getrf_nopivot (
    int n,
    T* A,
    int lda,
    int& info
    )

This function computes the LU decomposition (without pivoting) of matrix \(A\)

\[\begin{equation*} {A = L U}\end{equation*}\]

where \(A\) is a dense matrix of size \(n \times n\) , \(L\) is a lower triangular matrix with unit diagonal, and \(U\) is an upper triangular matrix. This function does not implement pivoting.

The maximum matrix size supported in FPGA is templated by NMAX.

Parameters:

T	data type (support float and double)
NMAX	maximum number of rows/cols of input matrix
NCU	number of computation unit
n	number of rows/cols of matrix A
A	input matrix
lda	leading dimention of input matrix A
info	output info (unused)

potrf¶

#include "MatrixDecomposition/potrf.hpp"

template <
    typename T,
    int NMAX,
    int NCU
    >
void potrf (
    int m,
    T* A,
    int lda,
    int& info
    )

This function computes the Cholesky decomposition of matrix \(A\)

\[\begin{equation*} {A = L {L}^T}\end{equation*}\]

where \(A\) is a dense symmetric positive-definite matrix of size \(m \times m\) , \(L\) is a lower triangular matrix, and \({L}^T\) is the transposed matrix of \(L\) .

The maximum matrix size supported in FPGA is templated by NMAX.

Parameters:

T	data type (support float and double)
NMAX	maximum number of rows/columns of input matrix
NCU	number of computation unit
m	number of rows/cols of matrix A
A	input matrix of size \(m \times m\)
lda	leading dimention of input matrix A
info	output info (unused)