README.md

MATCL - Matrix Computation Library

Matrix computation and linear algebra library written in C++.

Quick Start

#include "matcl-matrep/matcl_matrep.h"

using namespace matcl;

int main(int, const char* [])
{
    // generate random matrices
    Matrix A    = sprandn(5, 5, 0.1);
    Matrix B    = randn(5, 5);

    // some operations
    Matrix C    = cos(A * B) - 0.5;

    // change submatrix
    C(colon(2,3), colon(2,3)) = eye(2);

    disp(C);

    // change negative elements
    Matrix I    = find(C < 0);
    C(I)        = -2.0;

    disp(C);

    return 0;
}
output:
 dense real matrix, size: 5x5, type: general

   |        1 |       2 |       3 |        4 |       5
 -----------------------------------------------------
 1 |  0.37793 | 0.48910 | 0.41082 |  0.31894 | 0.47654
 2 | -0.20674 |  1.0000 |         | -0.48787 | 0.35069
 3 |  0.50000 |         |  1.0000 |  0.50000 | 0.50000
 4 |  0.50000 | 0.50000 | 0.50000 |  0.50000 | 0.50000
 5 |  0.50000 | 0.50000 | 0.50000 |  0.50000 | 0.50000

 dense real matrix, size: 5x5, type: general

   |       1 |       2 |       3 |       4 |       5
 ---------------------------------------------------
 1 | 0.37793 | 0.48910 | 0.41082 | 0.31894 | 0.47654
 2 | -2.0000 |  1.0000 |         | -2.0000 | 0.35069
 3 | 0.50000 |         |  1.0000 | 0.50000 | 0.50000
 4 | 0.50000 | 0.50000 | 0.50000 | 0.50000 | 0.50000
 5 | 0.50000 | 0.50000 | 0.50000 | 0.50000 | 0.50000

matcl-core

Library contains utility functions used by other libraries including memory allocators, input-output functions, pretty printing, option handling, error handling, management of global objects, definition of complex type, debugging utilities.

matcl-dynamic

Library defines the object type, which can store values of any type, and implements powerful multiple dispatching (or multimethods). Arbitrary function can be dynamically dispatched based on type info of supplied arguments (of object type).

Object of given type and functions defined on this object must be registered first, but can be registered in other libraries. Thanks to implicit conversion rules only a small set of overloads needs to be defined in order to call a function with arbitrary combination of object types.

Primary purpose of this library is ilustrated by the following example:

#include "matcl-dynamic/matcl_dynamic.h"
#include "matcl-scalar/matcl_scalar.h"

using namespace matcl;
using namespace matcl::dynamic;

// define function exp(x - y) for real values
static Real expm(Real x, Real y)
{
    return exp(x - y);
};

// define function exp(x - y) for complex values
static Complex expm(const Complex& x, const Complex& y)
{
    return exp(x - y);
};

// define function exp(x - y) for objects
object expm(const object& x, const object& y)
{
    static function_name f("expm");

    object ret;
    eval_function::eval(f, ret, x, y);
    return ret;
};

// register functions expm defined for real and complex values
MATCL_DEFINE_FUNCTION_NAME(expm)

MATCL_REGISTER_BIN_FUNC(tag1, expm, Real, Real, 
                MATCL_FUNCTION_NAME(expm))

MATCL_REGISTER_BIN_FUNC(tag2, expm, Complex, Complex,
                MATCL_FUNCTION_NAME(expm))

void example_object()
{
    object x = object(2.0f);
    object y = object(Integer(3));
    object z = object(Float_complex(1.0f, 2.0f));

    object ret1 = expm(x, y);
    object ret2 = expm(y, z);

    disp(ret1);
    disp(ret2);
};

Output:
 0.36788
 -3.0749 - 6.7188i

matcl-mp

Library defines multiprecision integer, rational, floating point and complex types as well as functions operating on these types.

For integer, rational, and floating point types this is just a wraper over MPFR and MPIR library with unified interface. Matcl-mp defines however functions for multiprecision complex type accurate up to 1 ulp.

matcl-mp-obj

Library defines objects storing multiprecision types from matcl-mp library. This library does not export new functions.

matcl-scalar

Library defines elementary functions operating on predefined scalar types (i.e. Integer, Float, Real, Float_complex, and Complex) and registers these functions for objects.

Library also defines new IO functions, timing functions, and random number generators.

matcl-simd

Higher level abstraction of single instruction, multiple data (SIMD) instructions for single and double precision floating point numbers and complex numbers.

Licence

This library is published under GPL licence.