Lanczos-Lib

Lanczos-Lib is a high-performance library implementing classical and block Lanczos algorithms on both CPU and GPU in C and Fortran, optimized for Intel CPU and NVIDIA GPU.

Features

• MATLAB Prototypes: Provided for deeper insight into the Lanczos algorithm.
• Intel CPU Implementation: Utilizes Intel MKL for high-performance numerical routines.
• Reproducibility Control: Implements Intel Conditional Numerical Reproducibility (CNR) for bitwise-consistent results across runs. Automatically detect and set to the optimal reproducibility.
• NVIDIA GPU Implementation: Utilizes NVIDIA cuBLAS for high-performance numerical routines.
• [fortran] (TBC)
• [eigen-system and solver]??? (TBC)

Prerequisites

• Make
• Intel MKL (implemented with intel-oneapi-hpc-toolkit-2025.1.0.666)
• Intel C and Fortran compilers (tested with intel-oneapi-hpc-toolkit-2025.1.0.666)
• NVIDIA HPC SDK (tested with nvhpc_2025_253_Linux_x86_64_cuda_12.8, Driver 570.133.07)
• NVIDIA cuBLAS library (implemented with nvhpc_2025_253_Linux_x86_64_cuda_12.8)

Quick Start

1. Clone the repository

git clone https://github.com/taiwan-jjl/Lanczos-Lib.git
cd Lanczos-Lib

2. Configure (edit makefile if needed)

# Compile and output object files and executables
make

# Clean build artifacts
make clean

3. main.c is the tutorial for initializing and using the following Lanczos functions.

Matrix storage scheme

If the input A matrix is stored in "full-matrix" scheme, switch to "GEXX" BLAS operation.
If the input A matrix is stored in "uppler or lower triangular" scheme, switch to "SYXX" BLAS operation.

Function specification

basic_lanczos_cpu :

void basic_lanczos_cpu(
    const double* A,
    double* nu,
    double* omega,
    double* alpha,
    double* beta,
    const int A_dim,
    const double Lanczos_stop_crit,
    const int Lanczos_stop_check_freq,
    int* Lanczos_iter
)

Output: none.

Input:

• A: "A" matrix in Lanczos algorithm. A pointer to a 1d array of double in heap memory.
• nu: "nu" vector in Lanczos algorithm. A pointer to a 1d array of double in heap memory.
• omega: "omega" vector in Lanczos algorithm. A pointer to a 1d array of double in heap memory.
• alpha: "alpha" scalar in Lanczos algorithm. A pointer to a 1d array of double in heap memory.
• beta: "beta" scalar in Lanczos algorithm. A pointer to a 1d array of double in heap memory.
• A_dim: The dimension n of a n by n A matrix. An integer in stack memory.
• Lanczos_stop_crit: The Lanczos stop crition of a truncation method for checking the "beta" value to avoid the numerical break down. Default value is 10 times of DBL_EPSILON. DBL_EPSILON is the minimum precision the system guarantees for "double" on host meachine. A double float-point in stack memory.
• Lanczos_stop_check_freq: How many Lanczos iterations the "Lanczos_stop_crit" would be checked in. Default value is 0 which means every iteration. It is a trade off between performance and correctness. An integer in stack memory.
• Lanczos_iter: A retuen value from "basic_lanczos_cpu" function. It means how many full Lanczos iterations are executed. An integer in stack memory.

basic_lanczos_gpu :

void basic_lanczos_cpu(
    const double* A,
    double* nu,
    double* omega,
    double* alpha,
    double* beta,
    const int A_dim,
    const double Lanczos_stop_crit,
    const int Lanczos_stop_check_freq,
    int* Lanczos_iter
)

Output: none.

Input:

• A: "A" matrix in Lanczos algorithm. A pointer to a 1d array of double in device memory.
• nu: "nu" vector in Lanczos algorithm. A pointer to a 1d array of double in device memory.
• omega: "omega" vector in Lanczos algorithm. A pointer to a 1d array of double in device memory.
• alpha: "alpha" scalar in Lanczos algorithm. A pointer to a 1d array of double in device memory.
• beta: "beta" scalar in Lanczos algorithm. A pointer to a 1d array of double in device memory.
• A_dim: The dimension n of a n by n A matrix. An integer in host memory.
• Lanczos_stop_crit: The Lanczos stop crition of a truncation method for checking the "beta" value to avoid the numerical break down. Default value is 10 times of DBL_EPSILON. DBL_EPSILON is the minimum precision the system guarantees for "double" on host meachine. A double float-point in host memory.
• Lanczos_stop_check_freq: How many Lanczos iterations the "Lanczos_stop_crit" would be checked in. Default value is 0 which means every iteration. It is a trade off between performance and correctness. An integer in host memory.
• Lanczos_iter: A retuen value from "basic_lanczos_cpu" function. It means how many full Lanczos iterations are executed. An integer in host memory.

Future Work

• More error detect and handing code.

  Currently, it is omitted for code readability and simplicity.

• SYMV (symmetric matrix-vector product) issue on GPU:

  • https://icl.utk.edu/files/publications/2012/icl-utk-530-2012.pdf
  • https://www.researchgate.net/publication/220782116_Optimizing_symmetric_dense_matrix-vector_multiplication_on_GPUS
  • https://arxiv.org/abs/1410.1726
  • https://siboehm.com/articles/22/CUDA-MMM

• More initial vector (nu) methods.

• Advanced memory allocation method in GPU version.