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

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

Documentation

Arithmetic

1. Use +,-,/,* to perform basic arithmetic in Eigen as you would normally.

• Eigen supports arithmetic for floating point digits as well as integers

Variable assignment

1. Use = to assign a variable to a value.
2. Valid value types are: int, float64, *Matrix
3. 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

4. exit, clear, clean are all reserved key words and cannot be used as variables

Matrices

1. 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.
2. Example:
   • [1, 2, 1; 4, 3, 1; 0, 2, 1] creates the matrix:
     ;
3. 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

1. Incomplete arithmetic queries (ex: 3*) cause Eigen to panic (Index out of range error)
2. 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).
3. 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
4. When subtracting with negative numbers, Eigen sometimes processes a negative number as a variable (ex: -3-4 returns "ERROR: Invalid variable '-3'")