smmtl

The simple matrix manipulation template library (SMMTL) is a header-only C++ library implementing simple template definitions of matrix and vector objects.

Requirements

The use of the library requires a compiler capable of adopting the C++11 standard.

The variable type adopted in the template specialization, hereafter indicated with mytype, must implement a definition of the basic set of operators (+,-,+=,+=, *, <<) and must provide a definition of the abs and pow functions. Furthermore, the selected variable type should provide a way to explicitly cast the 0. double value according to mytype(0.).

The Mat class

The Mat class implements the basic functionality of a matrix object. The class supports both square and rectangular matrices. Element-wise sum and subtraction are invoked using the standard operators +, -, += and -=. The matrix product (multiplication of row by columns) between Mat objects or between Mat and Vec objects can be invoked using the operator *. The product of the matrix by a scalar value is also invoked using the * operator. The element-wise product is not implemented at the moment.

The matrix elements can be read and modified using the () operator by listing the row and column of the wanted element according to (row, col). The transposed of the matrix can be obtained by calling the .t() member function. If the user wants to transpose the object itself, the .transpose() method (void return) can be called.

The Mat class implements the is_square() function (bool return) that returns true when the matrix is squared or false otherwise. The class also implements the trace() function that, as the name implies, returns the trace of the matrix (only for square matrices).

Constructors

The user can initialize explicitly a matrix object specifying the number of rows and columns and a list of values ordered by rows:

Mat<mytype>(int nrows, int ncols)
Mat<mytype>(int nrows, int ncols, <mytype>* list)

If no list is provided all the elements will be initialized to the zero value according to the casting operation mytype(0.).

The class provides also a non-parametrized default constructor Mat<mytype>() that return non-initialized matrix objects. These can be initialized at a later time by using the provided copy assignment operator. An operation performed on non-initialized objects will result in an InitError exception.

The Vec class

The syntax and structure of the Vec class is essentially equivalent to the one described for the Mat class.

Element-wise sum and subtraction are invoked using the standard operators +, -, += and -=. The "matrix" product (multiplication of row by columns) between Mat and Vec objects or between Vec objects can be invoked using the operator *. Please notice how the scalar product between two vectors returns a variable of type mytype. The product of the vector by a scalar value is also invoked using the * operator. Also in this case, the element-wise product is, at the moment, not implemented.

The vector elements can be read and modified using the () operator by indicating the index of the wanted element according to (index). The transposed vector can be obtained by calling the .t() member function. If the user wants to transpose the object itself, the .transpose() method (void return) can be called.

The vector class can represent both column and row vectors. By default, the vector is initialized as a column vector but a row vector can be generated by invoking either the t() of transpose() functions. In order to verify the type of shape the Vec class implements the is_column() function that returns true if the vector is a column one or false otherwise.

The class also implements the p_norm(double p) function that computes the p-norm of the vector defined according to the equation:

The function norm() is also implemented and returns the euclidean norm of the vector (p-norm with p=2).

Exceptions

The smmtl.h header file defines also a set of custom exceptions. These are defined in the smmtl::exceptions namespace. A complete list of exceptions is provided in the following table:

Exception	Message	Description
BoundError	"Index out of bounds"	The exception is thrown whenever an invalid element index is called
InitError	"Operation performed on uninitialized object"	The exception is thrown whenever an operation is performed on a non-initialized object (e.g. object created with non-parametrized constructors)
ShapeError	""Mismatch between the objects shape"	The exception is thrown whenever a mismatch between expected shape values is encountered (e.g. product between matrices of non-compatible shapes)
OperationError	"The called function cannot be applied to the given object"	The exception is thrown whenever a defined operation is called improperly (e.g. calling the trace function for a rectangular matrix)
ValueError	"Invalid parameter value encountered"	The exception is thrown whenever a parameter assumes an invalid value (e.g. setting a negative or null integer as the matrix number of row or columns)

Example

The use of the SMMTL library is very simple. In what follows a sample code implementing a matrix-vector product is presented:

#include <iostream>
#include "smmtl.h"

int main(){

    double list_A[4] = {1., 2., 3., 4.};
    smmtl::Mat<double> A(2, 2, list_A);

    smmtl::Vec<double> v(2);
    v(0) = 1.;
    v(1) = -2.5;

    smmtl::Vec<double> w = A*v;

    std::cout << w.t();

    return 0;
}

The code can be compiled, using the GNU g++ compiler, using the command:

g++ -std=c++11 example.cpp -o example.x -I<location>

where <location> must represent the path to the folder containing the smmtl.h header file. When example.x is executed, the following output should be observed:

-4  -7