A Custom linear algebra library

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Motivation

The reason for building this project was to implement the common linear algebra algorithms that were introduced during the introductory linear algebra course during my freshman year

Demo

$$2x+5y+z=20$$

$$4x+5y+z=10$$

$$6x+5y=0$$

$$A = \begin{pmatrix} 2 & 5 & 1 \\ 4 & 5 & 1 \\ 6 & 5 & 0 \\ \end{pmatrix} $$

$$B = \begin{pmatrix} 20 \\ 10 \\ 0\\ \end{pmatrix}$$

$$Solution => x=-5,y=6,z=0$$

What can it do?

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API:

• Create a new matrix:
  • mat* mat_new(unsigned int num_rows,unsigned int num_cols)
  • Assigning values: mat->data[row][col] = desired_value
• Free a created matrix:
  • void mat_free(mat* matrix)
• Create a matrix with random numbers
  • mat *mat_rnd(unsigned int num_rows, unsigned int num_cols, int min, int max)
• Generate a square matrix
  • mat *mat_sqr(unsigned int rowCol)
  • Assigning values: mat->data[row][col] = desired_value
• Generate a square random matrix
  • mat *mat_sqr_rnd(unsigned int rowCol, int min, int max
• Matrix addition
  • mat* mat_add(mat* a,mat* b)
• Matrix subtraction
  • mat* mat_subtract(mat* a,mat* b)
• Matrix multiplication
  • mat* mat_mul_naive(mat* a,mat* b)
• Finding Row Echelon Form of a Matrix
  • mat* mat_ref(mat* a)
• Finding Reduced Row Echelon Form of a Matrix
  • mat* mat_rref(mat* a)
• LU decomposition
  • mat_lup* mat_LU(mat* a)
• Solving linear equations
  • mat* solve_linear_LU(mat* a,mat* b)
• Finding the inverse
  • Using LU method
    • mat* mat_inverse(mat* a)
• Finding the determinant
  • double mat_determinant(mat* a)

Background and References

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• I was completely new to C when I started with this project.
• I had done a freshmen introduction to linear algebra so I was kind of familiar with the mathematical concepts.
• References:
  • 3b1b Linear Algebra playlist
  • Linear Algebra playlist from Khan Academy
  • Linear Algebra playlist from MathTheBeautiful
  • The C programming language(Dennis Ritchie and Brian Kernighan)

Can this be used in production?

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Definitely not. This project was build for educational purposes only and this is definitely not a library that one should use for their projects.

Future of this project

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• This project is far from complete.
• Some new features to be implemented:
  • A CLI interface for users
  • Replacing current makefile with CMake
  • Computing eigenvalues and eignevectors
  • Adding faster algorithms and better data structures
    • Addition of strassen's algorithm for matrix multiplicaton
    • Dense and sparse matrices
    • More...