Matrix_Library

Author: Alessandro Conti - AlessandroConti11

License: MIT license.

Tags: #C, #cofactor, #determinant, #inverse_matrix, #matrix, #matrix_operation, #matrix_type, #minor, #pivot, #rank, #row_echelon_matrix, #transpose_matrix.

Specification

The project aims to create a library that contains all useful functions for handling matrices and their operations.

For all functions that require a result: you must provide the requested data structure (you can also use the one present as input).

Operation	Function	Description	Order of the Matrices	Example of Mathematical Representation
create a matrix	matrix *createMatrix(int n, int m);	create an empty matrix	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$	$\begin{align} &{[A]}=\begin{bmatrix} a_{(0;0)} & a_{(0;1)} & a_{(0;2)} & \cdots & a_{(0;m-1)} \\\ a_{(1;0)} & a_{(1;1)} & a_{(1;2)} & \cdots & a_{(1;m-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{(n-1;0)} & a_{(n-1;1)} & a_{(n-1;2)} & \cdots & a_{(n-1;m-1)} \end{bmatrix} \end{align}$
create identity matrix	matrix *createIdentityMatrix(int n);	create an identity matrix	$\begin{align} &{[Id]}:\;n\;x\;n \end{align}$	$\begin{align} &{[Id]}=\begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \\\ 0 & 1 & 0 & \cdots & 0 \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & 1 \end{bmatrix} \end{align}$
create a null matrix	matrix *createNullMatrix(int n, int m);	create a null matrix	$\begin{align} &{[0]}:\;n\;x\;m \end{align}$	$\begin{align} &{[0]}=\begin{bmatrix} 0 & 0 & 0 & \cdots & 0 \\\ 0 & 0 & 0 & \cdots & 0 \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & 0 \end{bmatrix} \end{align}$
initialize a matrix	void initializeMatrix(matrix *a, ...);	initialize an empty matrix by filling it by rows	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$
copy a matrix	void copyMatrix(matrix *a, matrix *b);	copy a matrix to another	$\begin{align} &{{[A]}:\;n\;x\;m} \\ &{{[B]}:\;p\;x\;q} \end{align}$
delete a matrix	void deleteMatrix(matrix *a);	delete a given matrix	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$
print a matrix	void printMatrix(matrix *a);	print a given matrix	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$
check if a matrix is an identity matrix	int isIdentityMatrix(matrix *a);	check whether the matrix only elements on the main diagonal equal 1 and the others equal	$\begin{align} &{[Id]}:\;n\;x\;n \end{align}$	$\begin{align} &{[Id]}=\begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \\\ 0 & 1 & 0 & \cdots & 0 \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & 1 \end{bmatrix} \end{align}$
check if a matrix is a null matrix	int isNullMatrix(matrix *a);	check whether the all matrix elements are equal to 0	$\begin{align} &{[0]}:\;n\;x\;m \end{align}$	$\begin{align} &{[0]}=\begin{bmatrix} 0 & 0 & 0 & \cdots & 0 \\\ 0 & 0 & 0 & \cdots & 0 \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & 0 \end{bmatrix} \end{align}$
check if a matrix is a diagonal matrix	int isDiagonalMatrix(matrix *a);	check whether the matrix has all elements not on the main diagonal equal to 0	$\begin{align} &{[D]}:\;n\;x\;n \end{align}$	$\begin{align} &{[D]}=\begin{bmatrix} a_{(0;0)} & 0 & 0 & \cdots & 0 \\\ 0 & a_{(1;1)} & 0 & \cdots & 0 \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & a_{(n-1;n-1)} \end{bmatrix} \end{align}$
check if a matrix is anti-diagonal matrix	int isAntidiagonalMatrix(matrix *a);	check whether the matrix has all elements not on the secondary diagonal equal to 0	$\begin{align} &{[AD]}:\;n\;x\;n \end{align}$	$\begin{align} &{[AD]}=\begin{bmatrix} 0 & \cdots & 0 & 0 & a_{(0;n-1)} \\\ 0 & \cdots & 0 & a_{(0;n-2)} & 0 \\\ \vdots & \ddots & \vdots & \vdots & \vdots \\\ a_{(n-1;0)} & \cdots & 0 & 0 & 0 \end{bmatrix} \end{align}$
check if a matrix is an upper diagonal matrix	int isUpperDiagonalMatrix(matrix *a);	check whether the matrix has all elements below the main diagonal equal to 0	$\begin{align} &{[UD]}:\;n\;x\;n \end{align}$	$\begin{align} &{[UD]}=\begin{bmatrix} a_{(0;0)} & a_{(0;1)} & a_{(0;1)} & \cdots & a_{(0;n-1)} \\\ 0 & a_{(1;1)} & a_{(1;2)} & \cdots & a_{(1;n-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & a_{(n-1;n-1)} \end{bmatrix} \end{align}$
check if a matrix is a lower diagonal matrix	int isLowerDiagonalMatrix(matrix *a);	check whether the matrix has all elements above the main diagonal equal to 0	$\begin{align} &{[LD]}:\;n\;x\;n \end{align}$	$\begin{align} &{[LD]}=\begin{bmatrix} a_{(0;0)} & 0 & 0 & \cdots & 0 \\\ a_{(1;0)} & a_{(1;1)} & 0 & \cdots & 0 \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{(n-1;0)} & a_{(n-1;1)} & a_{(n-1;2)} & \cdots & a_{(n-1;n-1)}) \end{bmatrix} \end{align}$
check if a matrix is a symmetric matrix	int isSymmetricMatrix(matrix *a);	check whether the matrix has all the element (i, j) equal to the element (j, i)	$\begin{align} &{[S]}:\;n\;x\;n \end{align}$	$\begin{align} &{[S]}=\begin{bmatrix} a_{(0;0)} & a_{(0;1)} & a_{(0;2)} & \cdots & a_{(0;n-1)} \\\ a_{(0;1)} & a_{(1;1)} & a_{(1;2)} & \cdots & a_{(1;n-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{(0;n-1)} & a_{(1;n-1)} & a_{(2;n-1)} & \cdots & a_{(n-1;n-1)} \end{bmatrix} \end{align}$
check if a matrix is an anti-symmetric matrix	int isAntisymmetricMatrix(matrix *a);	check whether the matrix has the elements (i, j) opposite to those (j, i)	$\begin{align} &{[AS]}:\;n\;x\;n \end{align}$	$\begin{align} &{[AS]}=\begin{bmatrix} a_{(0;0)} & a_{(0;1)} & a_{(0;2)} & \cdots & a_{(0;n-1)} \\\ -a_{(0;1)} & a_{(1;1)} & a_{(1;2)} & \cdots & a_{(1;n-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ -a_{(0;n-1)} & -a_{(1;n-1)} & -a_{(2;n-1)} & \cdots & a_{(n-1;n-1)} \end{bmatrix} \end{align}$
check if a matrix is invertible	int isInvertibleMatrix(matrix *a);	check whether the determinant is different from 0	$\begin{align} &{[A]}:\;n\;x\;n \end{align}$
check if a matrix is a row-echelon matrix	int isRowEchelonMatrix(matrix *a);	check whether the first nonzero element of each row is further to the right than the first nonzero element of the previous row.	$\begin{align} &{[RE]}:\;n\;x\;m \end{align}$	$\begin{align} &{[RE]}=\begin{bmatrix} a_{(0;0)} & a_{(0;1)} & a_{(0;2)} & \cdots & a_{(0;m-1)} \\\ 0 & 0 & a_{(1;2)} & \cdots & a_{(1;m-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & a_{(n-1;m-1)} \end{bmatrix} \end{align}$
check if a matrix is an Hankel matrix	int isHankelMatrix(matrix *a);	check whether the matrix has all the element (i, j) equal to the element (i-1, j+1)	$\begin{align} &{[H]}:\;n\;x\;n \end{align}$	$\begin{align} &{[H]}=\begin{bmatrix} a_0 & a_1 & a_2 & \cdots & a_{n-1} \\\ a_1 & a_2 & a_3 & \cdots & a_n \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{n-1} & a_n & a_{n+1} & \cdots & a_{n+n-2} \end{bmatrix} \end{align}$
check if a matrix is a Toeplitz matrix	int isToeplitzMatrix(matrix *a);	check whether the matrix has all the element (i, j) equal to the element (i-1, j-1)	$\begin{align} &{[T]}:\;n\;x\;n \end{align}$	$\begin{align} &{[T]}=\begin{bmatrix} a_0 & a_{-1} & a_{-2} & \cdots & a_{-n} \\\ a_1 & a_0 & a_{-1} & \cdots & a_{-n+1} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{n-2} & a_{n-3} & a_{n-4} & \cdots & a_0 \end{bmatrix} \end{align}$
transpose a matrix	void transposingMatrix(matrix *a, matrix *trans);	the transposed matrix is given by the elements (j, i)	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[A]^T}:\;m\;x\;n \end{align}$	$\begin{align} &{[A]}^T=\begin{bmatrix} a_{(0;0)} & a_{(1;0)} & a_{(2;0)} & \cdots & a_{(n-1;0)} \\\ a_{(0;1)} & a_{(1;1)} & a_{(2;1)} & \cdots & a_{(n-1;1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{(0;m-1)} & a_{(1;m-1)} & a_{(2;m-1)} & \cdots & a_{(n-1;m-1)} \end{bmatrix} \end{align}$
invert a matrix	void inverseMatrix(matrix *a, matrix *inv);	inverse the matrix using the method of cofactors	$\begin{align} &{[A]}:\;n\;x\;n \\ &{[A]^{-1}}:\;n\;x\;n \end{align}$	$\begin{align} &{[A]}^{-1}={\frac{1}{det(A)}}{\begin{bmatrix} Cof(0;0) & Cof(0;1) & Cof(0;2) & \cdots & Cof(0;n-1) \\\ Cof(1;0) & Cof(1;1) & Cof(1;2) & \cdots & Cof(1;n-1) \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ Cof(n-1;0) & Cof(n-1;1) & Cof(n-1;2) & \cdots & Cof(n-1;n-1) \end{bmatrix}}^T \end{align}$
transform a matrix to a row-echelon matrix	void rowEchelonMatrix(matrix *a, matrix *step);	transform the matrix using the Gaussian elimination method	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[A_{RE}]}:\;n\;x\;m \end{align}$	$\begin{align} &{[A_{RE}]}=\begin{bmatrix} {a'}_{(0;0)} & {a'}_{(0;1)} & {a'}_{(0;2)} & \cdots & {a'}_{(0;m-1)} \\\ 0 & 0 & {a'}_{(1;2)} & \cdots & {a'}_{(1;m-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & {a'}_{(n-1;m-1)} \end{bmatrix} \end{align}$
compute the absolute matrix	void absMatrix(matrix *a, matrix *abs);	compute the absolute value for each matrix element	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[A_{ABS}]}:\;n\;x\;m \end{align}$	$\begin{align} &{[A_{ABS}]}=\begin{bmatrix} \left\lvert a_{(0;0)} \right\rvert & \left\lvert a_{(0;1)} \right\rvert & \left\lvert a_{(0;2)} \right\rvert & \cdots & \left\lvert a_{(0;m-1)} \right\rvert \\\ \left\lvert a_{(1;0)} \right\rvert & \left\lvert a_{(1;1)} \right\rvert & \left\lvert a_{(1;2)} \right\rvert & \cdots & \left\lvert a_{(1;m-1)} \right\rvert \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ \left\lvert a_{(n-1;0)} \right\rvert & \left\lvert a_{(n-1;1)} \right\rvert & \left\lvert a_{(n-1;2)} \right\rvert & \cdots & \left\lvert a_{(n-1;m-1)} \right\rvert \end{bmatrix} \end{align}$
compute the minor of a matrix	double minor(matrix *a, int row, int column);	compute the minor (row, column)-th, the determinant of the matrix without the row and the column specified	$\begin{align} &{[A]}:\;n\;x\;n \end{align}$	$\begin{align} &{Min_{(0;0)}}={Det \left(\begin{bmatrix} a_{(1;1)} & a_{(1;2)} & a_{(1;3)} & \cdots & a_{(1;n-1)} \\\ a_{(2;1)} & a_{(2;1)} & a_{(2;3)} & \cdots & a_{(2;n-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{(n-1;1)} & a_{(n-1;2)} & a_{(n-1;3)} & \cdots & a_{(n-1;n-1)} \end{bmatrix}\right)} \end{align}$
compute the cofactor of a matrix	double cofactor(matrix *a, int row, int column);	compute the cofactor (row, column)-th, the (-1)^(row+column) determinant of the matrix without the row and the column specified	$\begin{align} &{[A]}:\;n\;x\;n \end{align}$	$\begin{align} &{Cof_{(i;j)}}={(-1)}^{(i+j)} \cdot \left\lvert Min_{(i;j)} \right\rvert \end{align}$
compute the determinant of a matrix	double determinantMatrix(matrix *a);	compute the determinant of the matrix	$\begin{align} &{[A]}:\;n\;x\;n \end{align}$	$\begin{align}Det([A])=\sum_{j=0}^{n-1}{\left(a_{(i;j)} \cdot Cof_{(i;j)}\right)} \end{align}$
compute the rank of a matrix	int rankMatrix(matrix *a);	compute the rank of the matrix using the minor method	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$	$\begin{align}\begin{cases} &{matrix\;order, \quad if\;Det([A])\neq 0} \\ \; \\ &{order\;of\;the\;maximum\;possible\;non\;zero\;minor\;of\;the\;matrix, \quad if\;Det([A])=0} \end{cases} \end{align}$
compute the sum between two matrices	void sumMatrix(matrix *a, matrix *b, matrix *res);	compute the sum between two given matrices	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[B]}:\;n\;x\;m \\ &{[A+B]}:\;n\;x\;m \end{align}$	$\begin{align} &{[A+B]}=\begin{bmatrix} {a_{(0;0)}+b_{(0;0)}} & {a_{(0;1)}+b_{(0;1)}} & {a_{(0;2)}+b_{(0;2)}} & \cdots & {a_{(0;m-1)}+b_{(0;m-1)}} \\\ {a_{(1;0)}+b_{(1;0)}} & {a_{(1;1)}+b_{(1;1)}} & {a_{(1;2)}+b_{(1;2)}} & \cdots & {a_{(1;m-1)}+b_{(1;m-1)}} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ {a_{(n-1;0)}+b_{(n-1;0)}} & {a_{(n-1;1)}+b_{(n-1;1)}} & {a_{(n-1;2)}+b_{(n-1;2)}} & \cdots & {a_{(n-1;m-1)}+b_{(n-1;m-1)}} \end{bmatrix} \end{align}$
compute the difference between two matrices	void subMatrix(matrix *a, matrix *b, matrix *res);	compute the difference between two given matrices	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[B]}:\;n\;x\;m \\ &{[A-B]}:\;n\;x\;m \end{align}$	$\begin{align} &{[A-B]}=\begin{bmatrix} {a_{(0;0)}-b_{(0;0)}} & {a_{(0;1)}-b_{(0;1)}} & {a_{(0;2)}-b_{(0;2)}} & \cdots & {a_{(0;m-1)}-b_{(0;m-1)}} \\\ {a_{(1;0)}-b_{(1;0)}} & {a_{(1;1)}-b_{(1;1)}} & {a_{(1;2)}-b_{(1;2)}} & \cdots & {a_{(1;m-1)}-b_{(1;m-1)}} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ {a_{(n-1;0)}-b_{(n-1;0)}} & {a_{(n-1;1)}-b_{(n-1;1)}} & {a_{(n-1;2)}-b_{(n-1;2)}} & \cdots & {a_{(n-1;m-1)}-b_{(n-1;m-1)}} \end{bmatrix} \end{align}$
compute the scalar product of a matrix	void scalarProductMatrix(double scalar, matrix *a, matrix *res);	compute the scalar product of the matrix	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[k \cdot A]}:\;n\;x\;m \end{align}$	$\begin{align} &{[k \cdot A]}=\begin{bmatrix} {k \cdot a_{(0;0)}} & {k \cdot a_{(0;1)}} & {k \cdot a_{(0;2)}} & \cdots & {k \cdot a_{(0;m-1)}} \\\ {k \cdot a_{(1;0)}} & {k \cdot a_{(1;1)}} & {k \cdot a_{(1;2)}} & \cdots & {k \cdot a_{(1;m-1)}} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ {k \cdot a_{(n-1;0)}} & {k \cdot a_{(n-1;1)}} & {k \cdot a_{(n-1;2)}} & \cdots & {k \cdot a_{(n-1;m-1)}} \end{bmatrix} \end{align}$
compute the product between two matrices	void productMatrix(matrix *a, matrix *b, matrix *res);	compute the product between two given matrices	$\begin{align} &{[A]}:\;n\;x\;p \\ &{[B]}:\;p\;x\;m \\ &{[A \cdot B]}:\;n\;x\;m \end{align}$	$\begin{align} &{[A \cdot B]}=\begin{bmatrix} {\sum_{k=1}^n{a_{(0;k)} \cdot b_{(k;0)}}} & {\sum_{k=1}^n{a_{(0;k)} \cdot b_{(k;1)}}} & {\sum_{k=1}^n{a_{(0;k)} \cdot b_{(k;2)}}} & \cdots & {\sum_{k=1}^n{a_{(0;k)} \cdot b_{(k;m-1)}}} \\\ {\sum_{k=1}^n{a_{(1;k)} \cdot b_{(k;0)}}} & {\sum_{k=1}^n{a_{(1;k)} \cdot b_{(k;1)}}} & {\sum_{k=1}^n{a_{(1;k)} \cdot b_{(k;2)}}} & \cdots & {\sum_{k=1}^n{a_{(1;k)} \cdot b_{(k;m-1)}}} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ {\sum_{k=1}^n{a_{(n-1;k)} \cdot b_{(k;0)}}} & {\sum_{k=1}^n{a_{(n-1;k)} \cdot b_{(k;1)}}} & {\sum_{k=1}^n{a_{(n-1;k)} \cdot b_{(k;2)}}} & \cdots & {\sum_{k=1}^n{a_{(n-1;k)} \cdot b_{(k;m-1)}}} \end{bmatrix} \end{align}$
compute the power elevation of a matrix	void powerMatrix(matrix *a, int k, matrix *res);	compute the power elevation of the matrix	$\begin{align} &{[A]}:\;n\;x\;n \\ &{[A]^k}:\;n\;x\;n \end{align}$	$\begin{align} &{[A]^k}=\prod^k{\begin{bmatrix} a_{(0;0)} & a_{(0;1)} & a_{(0;2)} & \cdots & a_{(0;n-1)} \\\ a_{(1;0)} & a_{(1;1)} & a_{(1;2)} & \cdots & a_{(1;n-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{(n-1;0)} & a_{(n-1;1)} & a_{(n-1;2)} & \cdots & a_{(n-1;n-1)} \end{bmatrix}} \end{align}$
compute the direct sum between two matrices	void directSumMatrix(matrix *a, matrix *b, matrix *res);	compute the direct sum between two matrices, the first matrix is placed in the upper-left corner and the second matrix in the bottom-right corner	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[B]}:\;p\;x\;q \\ &{[A \oplus B]}:\;(n+p)\;x\;(m+q) \end{align}$	$\begin{align} &{[A \oplus B]}=\begin{bmatrix} [A] & [0] \\\ [0] & [B] \end{bmatrix} \end{align}$
compute the Kronecker product between two matrices	void kroneckerProductMatrix(matrix *a, matrix *b, matrix *res);	compute the Kronecker product between two matrices	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[B]}:\;p\;x\;q \\ &{[A \otimes B]}:\;(n \cdot p)\;x\;(m \cdot q) \end{align}$	$\begin{align} &{[A \otimes B]}=\begin{bmatrix} {a_{(0;0)} \cdot [B]} & {a_{(0;1)} \cdot [B]} & {a_{(0;2)} \cdot [B]} & \cdots & {a_{(0;m-1)} \cdot [B]} \\\ {a_{(1;0)} \cdot [B]} & {a_{(1;1)} \cdot [B]} & {a_{(1;2)} \cdot [B]} & \cdots & {a_{(1;m-1)} \cdot [B]} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ {a_{(n-1;0)} \cdot [B]} & {a_{(n-1;1)} \cdot [B]} & {a_{(n-1;2)} \cdot [B]} & \cdots & {a_{(n-1;m-1)} \cdot [B]} \end{bmatrix} \end{align}$
swap two rows of a matrix	void swapRowMatrix(matrix *a, int row1, int row2, matrix *swap);	swap two rows of given matrix	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[SR_{(i;j)}]}:\;n\;x\;m \end{align}$	$\begin{align} &{[SR_{(0;n)}]}=\begin{bmatrix} a_{(n-1;0)} & a_{(n-1;1)} & a_{(n-1;2)} & \cdots & a_{(n-1;m-1)} \\\ a_{(1;0)} & a_{(1;1)} & a_{(1;2)} & \cdots & a_{(1;m-1)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{(0;0)} & a_{(0;1)} & a_{(0;2)} & \cdots & a_{(0;m-1)} \end{bmatrix} \end{align}$
swap two column of a matrix	void swapColumnMatrix(matrix *a, int col1, int col2, matrix *swap);	swap two column of given matrix	$\begin{align} &{[A]}:\;n\;x\;m \\ &{[SC_{(i;j)}]}:\;n\;x\;m \end{align}$	$\begin{align} &{[SC_{(0;n)}]}=\begin{bmatrix} a_{(0;n-1)} & a_{(0;1)} & a_{(0;2)} & \cdots & a_{(0;0)} \\\ a_{(1;n-1)} & a_{(1;1)} & a_{(1;2)} & \cdots & a_{(1;0)} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ a_{(n-1;n-1)} & a_{(n-1;1)} & a_{(n-1;2)} & \cdots & a_{(n-1;0)} \end{bmatrix} \end{align}$
find the maximum value in a matrix	double findMaxMatrix(matrix *a, int *rowPos, int *colPos);	find the maximum value in the matrix and return its position	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$
find the minimum value in a matrix	double findMinMatrix(matrix *a, int *rowPos, int *colPos);	find the minimum value in the matrix and return its position	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$
find the elements on the diagonal of a matrix	double *diagonalMatrix(matrix *a, int *numberOfElements);	find the elements on the diagonal of the matrix	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$	$\begin{align}\overrightarrow{Diagonal}=\begin{bmatrix} a_{(0;0)} & a_{(1;1)} & \cdots & a_{(n-1;n-1)} \end{bmatrix} \end{align}$
find the pivot in a matrix	double *pivot(matrix *a, int *pivotsNumber);	find the pivots in the matrix transforming it in a row-echelon matrix	$\begin{align} &{[A]}:\;n\;x\;m \end{align}$
decompose a matrix using Lower-Upper decomposition	void luDecomposition(matrix *a, matrix *l, matrix *u);	decompose a matrix using Lower-Upper decomposition, the matrix is decomposed in a lower triangular matrix and an upper triangular matrix	$\begin{align} &{[A]}:\;n\;x\;n \\ &{[L]}:\;n\;x\;n \\ &{[U]}:\;n\;x\;n \end{align}$	$\begin{align} &{[A]=[L] \cdot [U]} \\ &{\begin{cases} &{{[L]}={\begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \\\ l_{(1;0)} & 1 & 0 & \cdots & 0 \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ l_{(n-1;0)} & l_{(n-1;1)} & l_{(n-1;2)} & \cdots & l_{(n-1;n-1)} \end{bmatrix}}} \\ \; \\ &{{[U]}={\begin{bmatrix} u_{(0;0)} & u_{(0;1)} & u_{(0;2)} & \cdots & u_{(0;n-1)} \\\ 0 & u_{(1;1)} & u_{(1;2)} & \cdots & u_{1;n-1} \\\ \vdots & \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & 0 & \cdots & u_{(n-1;n-1)} \end{bmatrix}}} \end{cases}} \end{align}$

How to run

0. install gcc

   sudo apt-get install gcc 

1. compile the project

   gcc -Wall -Werror -O2 -g3 main.c -o EXECUTABLE 

2. run the project

   ./EXECUTABLE

The Makefile in the repository can also be used to compile the code.

• this option allows you to compile with the following tags: -Wall -Werror -O2 -g3

  make compile

• if you want to specify different tags, you can set them

  make compile CFLAGS=YOUR_FLAGS

• if you want to use Address SANitizer

  make asan

• if you want to delete some file - default is the executable file

  make clean

Contribute

• If you find a security vulnerability, do NOT open an issue. Email Alessandro Conti instead.
• If you find a bug or error or want to add some other function that is not implemented yet
  1. FORK the repo
  2. CLONE the project to your own machine
  3. COMMIT to your own branch
  4. PUSH your work back up to your fork
  5. submit a PULL REQUEST so that I can review your changes

  NOTE: Be sure to merge the latest from "upstream" before making a pull request!

Code Style

Each new function must be documented using the following style:

• Short function description: A brief description explaining what the function does.
• @details: A detailed section describing how the function works, explaining the algorithms and logic used.
• @warning: A section listing all the assumptions made by the function, such as the preconditions that the parameters must fulfil.
• Blank line: Add a blank line to separate the documentation sections.
• @param: A list of the parameters required by the function, each accompanied by a brief description of its role and type.
• @return: A description of what the function returns, including the data type.

Within the function, each variable must be commented out to explain its purpose. In general, any additional comments that might improve understanding of the code are welcome. 😃