Simple Matrix module for Nim

This module implements a linear algebra (matrix) class.

The algorithms in this module are not necessarily the fastest possible or memory efficient. Some optimizations have been made, hoever.

Limitations

• supports only dense matrices
• not the most memory efficient algorithms (returns new matrices rather than performing operations in place)
• no "inverse" function is provided at this point

Examples

Creation

A "constructor" for matrix types is provided via the generic newMatrix[T] function. Two flavors are provided, one which generates a zero-filled matrix of the requested size, and one that creates the matrix and populates it with th provided data.

import matrix
let x = newMatrix[float](2,3,[0.0, 1.0, 2.0, 3.0, 4.0, 5.0])
let y = newMatrix[float](3,2,[0.0, 1.0, 2.0, 3.0, 4.0, 5.0])
let z = newMatrix[float](2,3)
echo x
echo y
echo z

An overloaded "stringify" operator $ is provided to pretty-print a matrix allowing the easy use of echo. The output of the above code would be similar to:

|0.0, 1.0, 2.0|
|3.0, 4.0, 5.0|

|0.0, 1.0|
|2.0, 3.0|
|4.0, 5.0|

|0.0, 0.0, 0.0|
|0.0, 0.0, 0.0|

Note that the data provided in the creation of both x and y is identical but it is interpreted or reshaped differently. The number of elements in the supplied array must equal the total number of elements in the to-be-created matrix or an exception will be thrown.

Convenience functions are provided for common matrices include ones, zeros, and the identity:

import matrix
let x = ones[float](2,3)
let y = zeros[float](3,2)
let z = eye[float](3)
echo x
echo y
echo z

producing

|1.0, 1.0, 1.0|
|1.0, 1.0, 1.0|

|0.0, 0.0|
|0.0, 0.0|
|0.0, 0.0|

|1.0, 0.0, 0.0|
|0.0, 1.0, 0.0|
|0.0, 0.0, 1.0|

Of course a matrix of other types are supported:

import matrix, complex
let w = rand[float64](2,3,5)
let x = ones[float64](2,3)
let y = zeros[int](3,2)
let z = eye[Complex](3)
echo w
echo x
echo y
echo z

reulting in

|1.982323868801377, 4.202426847057126, 1.766680486226218|
|2.23291717398272, 1.593463861559403, 4.432142166115156|

|1.0, 1.0, 1.0|
|1.0, 1.0, 1.0|

|0, 0|
|0, 0|
|0, 0|

|(1.0, 0.0), (0.0, 0.0), (0.0, 0.0)|
|(0.0, 0.0), (1.0, 0.0), (0.0, 0.0)|
|(0.0, 0.0), (0.0, 0.0), (1.0, 0.0)|

of course, the random values of w may be different.

Math functions

The arithmetic operators are overloaded to support matrices. As such +, -, and * are available between matrices of identical types. Division of matrices is not (yet) supported. In addition to the linear algebra matrix multiply * and element-by-element multiply is provided via the new operator *. as seen below:

import matrix
let x = ones[float](3,3)
echo x
echo (x+x)
echo (x-x)
echo (x*x)
echo (x*.x)

resulting in

|1.0, 1.0, 1.0|
|1.0, 1.0, 1.0|
|1.0, 1.0, 1.0|

|2.0, 2.0, 2.0|
|2.0, 2.0, 2.0|
|2.0, 2.0, 2.0|

|0.0, 0.0, 0.0|
|0.0, 0.0, 0.0|
|0.0, 0.0, 0.0|

|3.0, 3.0, 3.0|
|3.0, 3.0, 3.0|
|3.0, 3.0, 3.0|

|1.0, 1.0, 1.0|
|1.0, 1.0, 1.0|
|1.0, 1.0, 1.0|

Scalar-matrix operations are supported:

import matrix
let x = ones[float](3,3)
echo x
echo x+10.0
echo 10.0+x
echo x-10.0
echo 10.0-x
echo 10.0*x
echo x*10.0

resulting in:

|1.0, 1.0, 1.0|
|1.0, 1.0, 1.0|
|1.0, 1.0, 1.0|

|11.0, 11.0, 11.0|
|11.0, 11.0, 11.0|
|11.0, 11.0, 11.0|

|11.0, 11.0, 11.0|
|11.0, 11.0, 11.0|
|11.0, 11.0, 11.0|

|-9.0, -9.0, -9.0|
|-9.0, -9.0, -9.0|
|-9.0, -9.0, -9.0|

|9.0, 9.0, 9.0|
|9.0, 9.0, 9.0|
|9.0, 9.0, 9.0|

|10.0, 10.0, 10.0|
|10.0, 10.0, 10.0|
|10.0, 10.0, 10.0|

|10.0, 10.0, 10.0|
|10.0, 10.0, 10.0|
|10.0, 10.0, 10.0|

Caveats and TODO

• At this point there is no matrix inversion nor is division by matrices supported.
• All types of floats, ints and complex have been tested. User defined types, obviously, have not been verified.