cuSignm - Matrix Sign Function Approximation using CUDA

Copyright: Maximilian Behr

License: The software is licensed under under MIT. See LICENSE for details.

cuSignm is a CUDA library implementing Newton and Halley's method for the Sign Matrix Function Approximation of a square matrix $A$ with no eigenvalues on the imaginary axis.

cuSignm supports real and complex, single and double precision matrices.

Available Functions

Single Precision Functions

int cusignm_sNewtonBufferSize(const int n, size_t *d_bufferSize, size_t *h_bufferSize);
int cusignm_sNewton(const int n, const float *A, void *d_buffer, void *h_buffer, float *S);

int cusignm_sHalleyBufferSize(const int n, size_t *d_bufferSize, size_t *h_bufferSize);
int cusignm_sHalley(const int n, const float *A, void *d_buffer, void *h_buffer, float *S);

Double Precision Functions

int cusignm_dNewtonBufferSize(const int n, size_t *d_bufferSize, size_t *h_bufferSize);
int cusignm_dNewton(const int n, const double *A, void *d_buffer, void *h_buffer, double *S);

int cusignm_dHalleyBufferSize(const int n, size_t *d_bufferSize, size_t *h_bufferSize);
int cusignm_dHalley(const int n, const double *A, void *d_buffer, void *h_buffer, double *S);

Complex Single Precision Functions

int cusignm_cNewtonBufferSize(const int n, size_t *d_bufferSize, size_t *h_bufferSize);
int cusignm_cNewton(const int n, const cuComplex *A, void *d_buffer, void *h_buffer, cuComplex *S);

int cusignm_cHalleyBufferSize(const int n, size_t *d_bufferSize, size_t *h_bufferSize);
int cusignm_cHalley(const int n, const cuComplex *A, void *d_buffer, void *h_buffer, cuComplex *S);

Complex Double Precision Functions

int cusignm_zNewtonBufferSize(const int n, size_t *d_bufferSize, size_t *h_bufferSize);
int cusignm_zNewton(const int n, const cuDoubleComplex *A, void *d_buffer, void *h_buffer, cuDoubleComplex *S);

int cusignm_zHalleyBufferSize(const int n, size_t *d_bufferSize, size_t *h_bufferSize);
int cusignm_zHalley(const int n, const cuDoubleComplex *A, void *d_buffer, void *h_buffer, cuDoubleComplex *S);

Algorithm

cuSignm implements the Newton's method with scaling as well as Halley's method with scaling for the approximation of the matrix sign function. The matrix $A$ must be square and with no eigenvalues on the imaginary axis.

See also Algorithm 3.1

Chen, J., & Chow, E. (2014). A stable scaling of Newton-Schulz for improving the sign function computation of a Hermitian matrix. Preprint. ANL/MCS-P5059-0114.

Installation

Prerequisites:

• CMake >= 3.23
• CUDA >= 11.4.2

  mkdir build && cd build
  cmake ..
  make
  make install

Usage and Examples

We provide examples for all supported matrix formats:

File	Data
example_cusignm_sNewton.cu	real, single precision matrix
example_cusignm_dNewton.cu	real, double precision matrix
example_cusignm_cNewton.cu	complex, single precision matrix
example_cusignm_zNewton.cu	complex, double precision matrix
example_cusignm_sHalley.cu	real, single precision matrix
example_cusignm_dHalley.cu	real, double precision matrix
example_cusignm_cHalley.cu	complex, single precision matrix
example_cusignm_zHalley.cu	complex, double precision matrix