libhades is a small wrapper around LAPACK and BLAS. While LAPACK and BLAS are very fast and reliable, the API is from the 70ies. For example, zgeev, the routine to compute eigenvalues and left and/or right eigenvectors of a generic complex matrix, has 14 arguments!

libhades tries to make things easier for you. It defines a simple matrix type for complex and real matrices and gives you simple functions to add or multiply matrices, to find eigenvalues and eigenvectors, calculate the matrix exponential for arbitrary matrices, to solve differential equations, to invert matrices or to calculate a LU decomposition and much more. While in the background still LAPACK or BLAS do all the job, you have a simple and clean API. And in case you really need to call a LAPACK function yourself, you can still do so.

• low-level operations on matrices like addition, multiplication...
• calculation of trace, determinant and norm of matrices
• LU decomposition and inverting of matrices
• Kronecker product
• eigenvalue problems
• matrix exponential using squaring and scaling algorithm with Padé-approximation
• integration of ordinary differential equations
• symplectic implicit integrator

Allocate a real 3x3 matrix:

matrix_t *M = matrix_alloc(3,3);

Create a complex 4x4 identity matrix:

matrix_t *M = matrix_complex_eye(4,4);

Multiply two complex matrices and create a new matrix C=A*B:

matrix_complex_t *C = matrix_complex_mult(A,B,NULL)

Calculate eigenvalues and right eigenvectors of a generic complex matrix M:

eig_complex_generic(M, w, NULL, vr);

A full example to invert a real matrix (this is an example in the examples/ directory):

#include <stdio.h>
#include <libhades.h>

int main(int argc, char *argv[])
{
    matrix_t *M = matrix_alloc(2,2);

    matrix_set(M, 0,0, 1);
    matrix_set(M, 0,1, 2);
    matrix_set(M, 1,0, 3);
    matrix_set(M, 1,1, 4);

    printf("Inverse of\n");
    matrix_fprintf(stdout, M, "%+4g", "  ", "\n");

    matrix_invert(M);

    printf("is:\n");
    matrix_fprintf(stdout, M, "%+4g", "  ", "\n");

    return 0;
}

You can compile this file using:

gcc -O2 -Wall invert.c -o invert -lm -lhades -llapack -lblas

There are more examples available in the examples/ directory. Just have a look!

It's easy to access LAPACK functions. The matrix type is just a struct with some information on the matrix, for example matrix_t is defined as:

typedef struct {
    int rows;    /**< rows of matrix */
    int columns; /**< columns of matrix */
    int min;     /**< MIN(rows,columns) */
    int size;    /**< size = rows*columns */
    int type;    /**< type of matrix */
    int view;    /**< matrix is a view */
    double *M;   /**< data in column major order */
} matrix_t;

M is a pointer the memory. The matrix is saved in column-major order (or Fortran order). For this reason you don't have to transpose matrices. We store the matrix just like LAPACK. To access matrix elements, use the macros matrix_get and matrix set:

M10 = matrix_get(M, 1,0); /* get matrix element in 2nd row, 1st column /*
matrix_set(M, 2,3, 5);    /* set matrix element in 2nd row, 3rd column to 5 */

To call LAPACK function, just call the function name of the LAPACK function and add an underscore at the end. So, if you want to call dgetrf, call dgetrf_. There is one example available, so have a look at examples/lu_lapack.c.

You need the development version of LAPACK and BLAS installed on your computer. On Ubuntu/Debian you can install the dependencies using:

$ apt-get install gcc libc6-dev make libblas-dev liblapack-dev

At the moment there is no build system. To compile the library change to the directory libhades/ and run:

make
make install

This will compile the library and copy the shared object file libhades.so to /usr/lib. You might need to run ldconfig afterwards.

Documentation is available using Doxygen at https://michael-hartmann.github.io/libhades/html/.

Send bug reports, feature requests and merge requests! libhades is still in development and there are probably a lot of bugs. I'm also happy for unit tests.

The code is in the public domain, see the LICENSE file.

• Moler, Loan, "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later", SIAM Review, 2005
• Awad H. Al-Mohy and Nicholas J. Higham (2009) "A New Scaling and Squaring Algorithm for the Matrix Exponential." SIAM Journal on Matrix Analysis and Applications. 31 (3). pp. 970-989. ISSN 1095-7162
• Higham, "Functions of Matrices: Theory and Computation", Society for Industrial and Applied Mathematics, 2008
• Markiewicz, "Survey On Symplectic Integrators"