matrix

A Javascript Library to perform basic matrix operations using the functional nature of Javascript

Usage

var a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
var A = matrix(a);

Operations

1. Identity

A(); //returns [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

2. Row

A(0); // returns [1, 2, 3]

3. Column

A([], 0); // returns [[1], [4], [7]]

4. Element

A(1, 2); // returns 6

5. Range

A([1,2]); // returns [[4, 5, 6], [7, 8, 9]]
A([],[1,2]); // returns [[2, 3], [5, 6], [8, 9]]
A([1,2],[1,2]); // returns [[5, 6], [8, 9]]
A([2,1],[]); // returns [[7, 8, 9], [4, 5 ,6]]
A([],[2,1]); // returns [[3, 2], [6, 5], [9, 8]]
A([2,1],[2,1]); // returns [[9, 8], [6, 5]]

6. Size

A.size(); //returns [3, 3]

7. Set

A.set(0).to(0); // returns [[0, 0, 0], [4, 5, 6], [7, 8, 9]]
A.set(1,2).to(10); // returns [[1, 2, 3], [4, 5, 10], [7, 8, 9]]
A.set([], 0).to(0); // returns [[0, 2, 3], [0, 5, 6], [0, 8, 9]]
A.set([1,2]).to(4); // returns [[1, 2, 3], [4, 4, 4], [4, 4, 4]]
A.set([], [1,2]).to(1); // returns [[1, 1, 1], [4, 1, 1], [7, 1, 1]]

8. Addition

var B = matrix([[3, 4, 5], [6, 7, 8], [9, 10, 11]]);
A.add(B); // returns [[4, 6, 8], [10, 12, 14], [16, 18, 20]]

9. Subtraction

B.sub(A); // returns [[2, 2, 2], [2, 2, 2], [2, 2, 2]]

10. Multiplication

A.mul(B); // returns [[3, 8, 15], [24, 35, 48], [56, 80, 99]]

NOTE: This is not classical matrix multiplication (which is implemented using the prod() method). This simply multiplies together each element in matrix A with the corresponding element in matrix B. If A and B are not the same size, it will produce some NaN results.

11. Division

A.div(B); // returns [[0.33, 0.5, 0.6], [0.66, 0.71, 0.75], [0.77, 0.8, 0.81]]

12. Product

A.prod(B); // returns [[42, 48, 54], [96, 111, 126], [150, 174, 198]]

13. Transpose

A.trans(); // returns [[1, 4, 7], [2, 5, 8], [3, 6, 9]]

14. Determinant

var C = matrix([[5, 4, 7], [4, 8, 2], [9, 0, 4]]);
C.det(); // returns -336

15. Inverse

Should be invertible

M = matrix([[1, 3, 3], [1, 4, 3], [1, 3 ,4]]);
M.inv(); // returns [[7, -3, -3], [-1, 1, 0], [-1, 0 ,1]]

16. Merge

Merges two matrices in all directions

• Left

M = matrix([[3, 4], [7, 8]]);
M.merge.left([[1, 2], [5, 6]]); // returns [[1, 2, 3, 4], [5, 6, 7, 8]]

• Right

M = matrix([[1, 2], [5, 6]]);
M.merge.right([[3, 4], [7, 8]]); // returns [[1, 2, 3, 4], [5, 6, 7, 8]]

• Top

M = matrix([5, 6, 7, 8]);
M.merge.top([1, 2, 3, 4]); // returns [[1, 2, 3, 4], [5, 6, 7, 8]]

• Bottom

M = matrix([1, 2, 3 ,4]);
M.merge.bottom([5, 6, 7, 8]); // returns [[1, 2, 3, 4], [5, 6, 7, 8]]

17. Map

Applies a given function over the matrix, elementwise. Similar to Array.map()

M = matrix([1, 2, 3]);
M.map(x => x*x); // returns [1, 4, 9]

This example shows the arguments provided to the function

M = matrix([[1, 2], [3, 4]]);
M.map((value, pos, mat) => value * pos[1]);
// returns [[0, 2], [0, 4]]

18. Equals

Checks the equality of two matrices and returns a boolean. A matrix is equal to itself.

A = matrix([[1,2],[3,4]]);
A.equals(A);
// returns true
B = matrix([[3,4], [1,2]]);
A.equals(B);
// returns false

19. Generate

Generates a matrix with the value passed across the entire matrix or just the diagonal.

matrix.gen(4).size(2,3); // returns [[4,4,4],[4,4,4]]
matrix.gen(2).size(2); // returns [[2,2],[2,2]]
matrix.gen(1).diag(3); // return [[1,0,0],[0,1,0],[0,0,1]], identity matrix
// Diagonal matrices are normally square. Here, only diagonal elements are filled where row and column indices are same. 
matrix.gen(1).diag(3,2); // returns [[1,0],[0,1],[0,0]]
matrix.gen(2).diag(3,4); // returns [[2,0,0,0],[0,2,0,0],[0,0,2,0]