lyng/docs/Matrix.md

Matrix (lyng.matrix)

lyng.matrix adds dense immutable Matrix and Vector types for linear algebra.

Import it when you need matrix or vector arithmetic:

import lyng.matrix

Construction

Create vectors from a flat list and matrices from nested row lists:

import lyng.matrix

val v: Vector = vector([1, 2, 3])
val m: Matrix = matrix([[1, 2, 3], [4, 5, 6]])

assertEquals([1.0, 2.0, 3.0], v.toList())
assertEquals([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]], m.toList())

Factory methods are also available:

import lyng.matrix

val z: Vector = Vector.zeros(3)
val i: Matrix = Matrix.identity(3)
val m: Matrix = Matrix.zeros(2, 4)

All elements are standard double-precision numeric values internally.

Shapes

Matrices may have any rectangular geometry:

import lyng.matrix

val a: Matrix = matrix([[1, 2, 3], [4, 5, 6]])

assertEquals(2, a.rows)
assertEquals(3, a.cols)
assertEquals([2, 3], a.shape)
assertEquals(false, a.isSquare)

Vectors expose:

• size
• length as an alias of size

Matrix Operations

Supported matrix operations:

• + and - for element-wise matrix arithmetic
• * for matrix-matrix product
• * and / by a scalar
• transpose()
• trace()
• rank()
• determinant()
• inverse()
• solve(rhs) for Vector or Matrix right-hand sides

Example:

import lyng.matrix

val a: Matrix = matrix([[1, 2, 3], [4, 5, 6]])
val b: Matrix = matrix([[7, 8], [9, 10], [11, 12]])
val product: Matrix = a * b
assertEquals([[58.0, 64.0], [139.0, 154.0]], product.toList())
assertEquals([[1.0, 4.0], [2.0, 5.0], [3.0, 6.0]], a.transpose().toList())

Inverse and solve:

import lyng.matrix

val a: Matrix = matrix([[4, 7], [2, 6]])
val rhs: Vector = vector([1, 0])

val inv: Matrix = a.inverse()
val x: Vector = a.solve(rhs)

assert(abs(a.determinant() - 10.0) < 1e-9)
assert(abs(inv.get(0, 0) - 0.6) < 1e-9)
assert(abs(x.get(0) - 0.6) < 1e-9)

Vector Operations

Supported vector operations:

• + and -
• scalar * and /
• dot(other)
• norm()
• normalize()
• cross(other) for 3D vectors
• outer(other) producing a matrix

import lyng.matrix

val a: Vector = vector([1, 2, 3])
val b: Vector = vector([2, 0, 0])

assertEquals(2.0, a.dot(b))
assertEquals([0.2672612419124244, 0.5345224838248488, 0.8017837257372732], a.normalize().toList())

Indexing and Slicing

Matrix supports both method-style indexing and bracket syntax.

Scalar access:

import lyng.matrix

val m: Matrix = matrix([[1, 2, 3], [4, 5, 6]])

assertEquals(6.0, m.get(1, 2))
assertEquals(6.0, m[1, 2])

Bracket indexing accepts two selectors: [row, col]. Each selector may be either:

• an Int
• a Range

Examples:

import lyng.matrix

val m: Matrix = matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

assertEquals(7.0, m[1, 2])
val columnSlice: Matrix = m[0..2, 2]
val topLeft: Matrix = m[0..1, 0..1]
val tail: Matrix = m[1.., 1..]
assertEquals([[3.0], [7.0], [11.0]], columnSlice.toList())
assertEquals([[1.0, 2.0], [5.0, 6.0]], topLeft.toList())
assertEquals([[6.0, 7.0, 8.0], [10.0, 11.0, 12.0]], tail.toList())

Shape rules:

• m[Int, Int] returns a Real
• m[Range, Int] returns an Nx1 Matrix
• m[Int, Range] returns a 1xM Matrix
• m[Range, Range] returns a submatrix

Open-ended ranges are supported:

• m[..1, ..1]
• m[1.., 1..]
• m[.., 2]

Stepped ranges are not supported in matrix slicing.

Slices currently return new matrices, not views.

Rows and Columns

If you want plain lists instead of a sliced matrix:

import lyng.matrix

val a: Matrix = matrix([[1, 2, 3], [4, 5, 6]])

assertEquals([4.0, 5.0, 6.0], a.row(1))
assertEquals([2.0, 5.0], a.column(1))

Backend Notes

The matrix module uses a platform-specific backend where available and falls back to pure Kotlin where needed.

The public Lyng API stays the same across platforms.