Summary

This file contains a brief description of the main functions provided by the library. More details about these functions can be found here http://cristid9.github.io/libMatrix/files.html.

This is is a minimalist matrix library which provides support for basic mathematical operations like:

• addition of 2 matrices
• multiplication with a scalar
• multiplication of 2 matrices
• computing the trace
• computing the transpose
• computin the determinant
• computing the minorants of a matrix
• computing the inverse
• raising a matrix to a given power

It also provides some uility function that will make your life easier in with the data structures of the library:

• creating a matrix
• destroying a matrix
• printing a matrix(to the stdout)
• reading a matrix(from the stdin)
• copying a matrix
• comparing matrices

Building the library

To build the library you need to run the following commands:

sudo make
sudo make install

Creating a matrix

In order to create a matrix you need to include the matrix.h header file:

#include <matrix.h>

After you have done this you need to declare a pointer to a Matrix and assign to it the value returned by create_matrix. The function create_matrix takes 2 arguments: the number of rows and the number of columns. This is how you create a 2 by 2 matrix.

#include <matrix.h>

int main()
{
    Matrix *foo = create_matrix(2, 2);    
    destroy_matrix(foo);
    return 0;
}

The call to destroy_matrix is used to release the memory allocated for foo.

Compiling a source file

To compile a source file that uses the matrix library you need to dynamically link the library. This is how you will compile the file from the previous section:

gcc -Wall main.c -lMatrix -lm

Please remember to add -lm after -lMatrix.

Accessing properietes of a matrix

A matrix has some proprietes that you should care about:

• its elements
• trace
• inverse
• determinant

This is how you will access these proprites:

matrix->value[line][column];
matrix->trace;
matrix->determinant;
matrix->inverse->value[lineOfInverse][columnOfInverse];

Muliplication of a matrix with a scalar

In order to multiply a matrix with a scalar you will need to use the multiply_matrix_with_scalar function. This function takes 2 arguments: the matrix and the scalar to multiply that matrix with. The only issue of this function is that it modifies the value of the original matrix.

This is how you will do this:

#include <matrix.h>

int main()
{
    Matrix *foo = create_matrix(2, 2);
    multiply_matrix_with_scalar(foo, 2);
    print_matrix(foo);
    destroy_matrix(foo);

    return 0;
}

Computing the minorant of a matrix

You will use get_minor to do this job, which takes 3 arguments: the matrix, the line and the column that will be eliminated for the minorant. It returns a pointer to a Matrix which is the minorant. After you hae finished with the minorant and you do not need it anymore you need to destroy it.

#include <matrix.h>

int main()
{
    // let foo be a 3 by 3 not null matrix
    Matrix *minorantOfFoo = get_minor(foo, 1, 1);
    // do something with minorantOfFoo
    destroy_matrix(minorantOfFoo);
    
}

Computing the transpose of a matrix

The function that does this is called get_transpose and it takes 2 arguments the matrix, and a pointer to a matrix where the transpose will be initialized. This function returns an error status.

#include <matrix.h>

int main()
{
    // let foo be a 3 by 3 matrix
    Matrix *transpose;
    get_transpose(foo, &transpose);
    // do something with the transpose
    destroy_matrix(transpose);
}

Computing the inverse of a matrix

The function that does this is called compute_inverse and will just set the inverse member of the matrix you want to compute the inverse of.

This is how you will compute the inverse of a matrix called foo:

#include <matrix.h>

int main()
{
    // let foo be a 3 by 3 matrix
    compute_inverse(foo);
    destroy_matrix(foo);
}

You do not have to care about releasing the memory allocated to foo. destroy_matrix will do this for you.

Computing the determinant of a matrix

This operation is very simillar with the previous one. The function that does this is called get_determinant and takes only one argument, the matrix you want to compute the determinant of and it just sets the determinant member of that matrix.

This is how you will compute the determinant of a matrix:

#include <matrix.h>

int main()
{
    // let foo be a 3 by 3 matrix
    get_determinant(foo);
    // do something with the determinant of foo
    destroy_matrix(foo);    
}

Multiplying 2 matrices

In order to multiply 2 matrices you need to have a third variable where the result will be stored.

This is how you multiply 2 matrices a and b.

#include <matrix.h>

int main()
{
    // let a and b be 3 by 3 matrices
    Matrix *c; // the result
    // the result will be stored in c
    multiply_matrices(a, b, &c); 
    // destroy a and b
    destroy_matrix(c);

}

Adding 2 matrices

This is very simillar with the process of multiplying 2 matrices.

int main()
{
    // let a and b be 3 by 3 matrices
    Matrix *c; // the result
    // the result will be stored in c
    add_matrices(a, b, &c); 
    // destroy a and b
    destroy_matrix(c);

}

Copying a matrix

Say you want to copy the value of a matrix foo to a matrix bar. This is how you do it:

#include <matrix.h>

int main()
{
    // let foo be a 3 by 3 not empty matrix and bar newly created matrix.
    copy_matrix(foo, bar);
    // release the memory
}

Raising a matrix to a power

This is done with the function matrix_pow, which takes as arguments the matrix and the power to raise that matrix to. The function will return a pointer to the result.

#include <matrix.h>

int main()
{
    // let foo be a matrix
    Matrix *fooRaisedTo3 = matrix_pow(foo, 3);
    // do something with it
    destroy_matrix(fooRaisedTo3);
}

Comparing 2 matrices

In order to comper 2 matrices you will use the function compare_matrices which returns true if the matrices have the same elemnts and false otherwise. Boolean types are not suported in c89, we encourage you to use the c99 standard.

#include <matrix.h>

int main()
{
    // let foo and bar be 2 equal matrices
    if(compare_matrices(foo, bar)) {
        // they are equal
    }
    else {
        // they are not equal
    }
    
}