added gif

README.md

@@ -1,76 +1,104 @@
 ## A Custom linear algebra library
-***
-
-### About
-<p>This project is an attempt to implement whatever I learned during my introductory linear algebra course during my first year of engineering. </p>
 
-<h3>Problem</h3>
+---
 
-
-<h4>Input for solving a linear system of equations </h4>
+### Motivation
+<p>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</p>
 
 <br>
 
+### Demo
+<br>
 
-<img src="./images/Math_white.svg" id="math" style="filter:invert(1)">
+$$2*x+5*y+z=20$$
+$$4*x+5*y+z=10$$
+$$6x+5y=0$$
+$$A = \begin{pmatrix} 2 & 5 & 1\\ 4 & 5 & 1\\ 6 & 5 & 0\end{pmatrix}$$
+$$B = \begin{pmatrix} 20 \\ 10 \\ 0\end{pmatrix}$$
 
-> If you have difficulty viewing this image, checkout the image [here](/images/Math_black.svg)
+Solution => $ x=-5,y=6,z=0$
 
 
 <br/>
 <br/>
 
-<h4>Main function</h4>
-
-![img.png](images/input.png)
-
-
-<h4>Output</h4>
-
-![Output.png](images/Output.png)
-
-
-### What can it do? 
-***
-- Matrix multiplication 
- - Currently,this is done using the naive O(n^3) algorithm (```mat_mul_naive``` function in the code)
- - The plan is to shift this to strassen's algorithm(```mat_mul_strassen`` function in the code)
+![./images/gif.gif](./images/gif.gif)
+
+### What can it do?
+
+---
+
+**Data structures**:
+ - Matrix(```mat```)
+ - ```c
+ {
+  unsigned int num_rows;
+  unsigned int num_cols;
+  double **data;
+  int isSquare;
+ }
+ ```
+ -LUP Matrix(```mat_lup```)
+ - ```c
+ {
+  mat *L;
+  mat *U;
+  mat *P;
+  unsigned int num_permutations;
+ }
+ ```
+
+**API**:
+
+- 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
- - Multiple Implementations of the same
- - ```solve_linear_forward``` using the forward substitution method
- - ```solve_linear_backward``` using the backward substitution method
+ - ```mat* solve_linear_LU(mat* a,mat* b)```
 - Finding the inverse
  - Using LU method
+ - ```mat* mat_inverse(mat* a)```
 - Finding the determinant
-- QR decomposition
-
+ - ```double mat_determinant(mat* a)```
+
+
 ### Background and References
-***
 
-- 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 
+---
+
+- 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
+ - [3b1b Linear Algebra playlist](https://www.youtube.com/watch?v=kjBOesZCoqc&list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B)
+ - [Linear Algebra playlist from Khan Academy](https://www.khanacademy.org/math/linear-algebra)
+ - [Linear Algebra playlist from MathTheBeautiful](https://www.youtube.com/watch?v=odV3oJOpE8s&list=PLlXfTHzgMRUIqYrutsFXCOmiqKUgOgGJ5)
  - The C programming language(Dennis Ritchie and Brian Kernighan)
 
 ### Can this be used in production?
-***
-<p>Definitely not, this project was build for educational purposes only and this is definitely not a library that one should use for their projects</p>
+
+---
+
+<p>Definitely not. This project was build for educational purposes only and this is definitely not a library that one should use for their projects.</p>
 
 ### Future of this project
-***
-- This project is far from complete
-- Some new features to be implemented
- - A CLI interface for users 
+
+---
+
+- 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...
-
-

matrix.h

@@ -149,7 +149,7 @@ mat *solve_linear_LU(mat *A, mat *b);
 mat *mat_inverse();
 
 // determinant of matrix using LU(P)
-mat *mat_determinant();
+double *mat_determinant();
 
 // QR decomposition
 mat *mat_QR();

test.c

@@ -17,11 +17,13 @@ int main(int argc, char *argv[])
  A->data[2][1] = 5;
  A->data[2][2] = 0;
 
+
+
  B->data[0][0] = 20;
  B->data[1][0] = 10;
  B->data[2][0] = 0;
 
- mat *x = solve_linear_LU(A, B);
+ mat *x =solve_linear_LU(A, B);
 // mat *x = mat_mul_naive(A,B);
  mat_print(x);
  mat_free(x);