Eigen

Eigen is a simple CLI that performs matrix and vector operations, modular arithmetic, and basic arithmetic.
Eigen is currently a work in progress, so feel free to report any bugs or let me know if you have any suggestions for the program!

Install

Install Go
$ git clone https://github.com/tbliu/Eigen
$ cd Eigen
$ go run Main.go

Documentation

Arithmetic

Use +,-,/,* to perform basic arithmetic in Eigen as you would normally.
- Eigen supports arithmetic for floating point digits as well as integers

Variable assignment

Use = to assign a variable to a value.
Valid value types are: int, float64, *Matrix
Variable names follow traditional rules:
- The first character cannot be a number
- All other characters can be either numbers or letters
- Variables are case sensitive
exit, clear, clean are all reserved key words and cannot be used as variables

Matrices

To declare a matrix:
1. Use [ to denote the beginning of the matrix.
2. Elements within a row are separated by a ,
3. Rows are separated by ;
4. Use ] to denote the end of the end of the matrix.
Example:
- [1, 2, 1; 4, 3, 1; 0, 2, 1] creates the matrix:
  
  ;
You can also assign matrices to variables:
- x = [1, 2, 1; 4, 3, 1; 0, 2, 1] creates the same matrix as above, and assigns it to the variable x.

Vectors

Vectors do not have a special definition in Eigen. They are simply defined as ℝ^Nx1 matrices. Any references to the word “Vector” or the parameter “*Vector” should just be understood as a matrix with one column.

Matrix Operations

Command	Description	Return type
`col(A *Matrix)`	Returns a matrix B whose columns span the column space of A	Matrix
`det(A *Matrix)`	Returns the determinant of a square matrix A	float64
`id(N int)`	Returns the NxN identity matrix	Matrix
`inv(A *Matrix)`	Returns the inverse of a square matrix A	Matrix
`Lnull(A *Matrix)`	Returns a matrix B whose columns span the left null space of A	Matrix
`null(A *Matrix)`	Returns a matrix B whose columns span the null space of A	Matrix
`nullity(A *Matrix)`	Returns the dimension of the null space of A	int
`rank(A *Matrix)`	Returns the dimension of the column space of A	int
`row(A *Matrix)`	Returns a matrix B whose columns span the row space of A	Matrix
`rref(A *Matrix)`	Returns the reduced row echelon form of a matrix A	Matrix
`solve(A Matrix, b Matrix)`	Returns the vector x that solves the system of equations Ax=b	Vector
`transpose(A *Matrix)`	Returns the transpose of a matrix A	Matrix
`zeros(N int)`	Returns the NxN zero matrix	Matrix
`zeros(N int, M int)`	Returns the NxM zero matrix	Matrix
`dot(v Vector, w Vector)`	Returns the dot products of vector v and vector w	float64
`orth(v Vector, w Vector)`	Returns 1 if v and w are orthogonal. 0 otherwise	int
`llse(A Matrix, b Vector)`	Returns the linear least squares estimate of `x` in `Ax=b`	Vector
`proj(v Vector, w Vector)`	Returns the projection of the vector w onto the vector v	Vector
`gs(A *Matrix)`	Orthonormalizes the columns of A	Matrix
`qr(A *Matrix, tag string)`	Performs QR decomposition on A. If tag == ‘q’, Q. If tag == ‘r’, return R. Quotes are not necessary.	Matrix
`norm(v *Vector)`	Returns a vector w, which is the normalized version of v	Vector
`roll(v *Vector, N int)`	Returns a vector w, whose values are the same as v’s, shifted by N places	Vector
`xcorr(v Vector, w Vector)`	Returns the cross-correlation of w with respect to v	Vector
`autocorr(v *Vector)`	Returns the auto-correlation of v	Vector

Modular Arithmetic Operations

Command	Description	Return type
`mod(x int, m int)`	Returns x modulo m	int
`modexp(x int, y int, m int)`	Returns x to the power of y modulo m. Uses repeated squaring, so this function works well with large ints.	int
`modinv(x int, m int)`	Returns the inverse of x modulo m.	int

Miscellaneous Operations

Command	Description	Return type
`gcd(x int, y int)`	Returns the greatest common divisor of x and y	int
`sqrt(x float64)`	Returns the square root of a number up to 3 decimal points	float64
`exit`	Exits the program	None
`clear`	Clears the terminal window	None
`clean`	Removes all variable assignments	None

List of Known Bugs

Incomplete arithmetic queries (ex: 3*) cause Eigen to panic (Index out of range error)
There are some bugs with matrix operations when not using variables (ex: [3,2] * [3,1;1,2] returns an ERROR message. But assigning A=[3,2] and B = [3,1;1,2] and doing A*B works).
Changing color to white after a red error message might make text invisible to people with white terminal backgrounds. Fix so it gets default terminal color
When subtracting with negative numbers, Eigen sometimes processes a negative number as a variable (ex: -3-4 returns “ERROR: Invalid variable ‘-3’”)