linalg

Import with:

import linalg

The module works with Vector and Matrix values and provides core numerical linear-algebra operations.

Constructors

linalg.vector(values)

Creates a numeric Vector from a List of Int or Float values.

let v = linalg.vector([3, 4])

linalg.matrix(rows)

Creates a numeric Matrix from a nested List:

let A = linalg.matrix([
    [1, 2],
    [3, 4]
])

Every row must be a list of numeric values and all rows must form a rectangular matrix.

Basic matrix functions

linalg.transpose(A)

Returns the transpose of a matrix.

linalg.transpose(A)

Matrices also expose a transpose() method:

A.transpose()

linalg.shape(A)

Returns a two-element List containing [rows, cols].

linalg.rows(A) / linalg.cols(A)

Return the matrix dimensions separately as Int values.

print(A.shape())
print(linalg.rows(A))
print(linalg.cols(A))

Matrix algebra

The matrix runtime supports the @ operator for matrix multiplication:

let C = A @ B

linalg.det(A)

Returns the determinant as a Float.

let d = linalg.det(A)

linalg.inverse(A)

Returns the inverse matrix. The operation fails when the matrix is not invertible or does not satisfy the requirements of the underlying algorithm.

let A_inv = linalg.inverse(A)

Solving systems

linalg.solve(A, b)

Solves the linear system A x = b.

The right-hand side b may be a Vector or a Matrix:

let A = linalg.matrix([
    [2, 1],
    [1, 3]
])

let b = linalg.vector([4, 5])
let x = linalg.solve(A, b)

The result has the same general container category as b: a Vector for a vector right-hand side or a Matrix for a matrix right-hand side.

linalg.solve_lstsq(A, b)

Computes a least-squares solution using the same Vector / Matrix right-hand-side conventions as solve().

let coefficients = linalg.solve_lstsq(X, y)

Linear regression

linalg.linear_regression(X, y)

Fits a least-squares linear model.

X must be a Matrix. y can be either a Vector or a one-column Matrix.

let X = linalg.matrix([
    [1, 10],
    [1, 12],
    [1, 15],
    [1, 20]
])

let y = linalg.vector([12, 14, 17, 22])

let fit = linalg.linear_regression(X, y)

The returned value is a Dict with these properties:

Property	Type	Meaning
coefficients	Matrix	Least-squares coefficient matrix
fitted	Matrix	Predicted values X @ coefficients
r_squared	Float	Coefficient of determination
residual_sum_of_squares	Float	Sum of squared residuals

Access a property with normal dictionary indexing:

print(fit["coefficients"])
print(fit["r_squared"])

Vector convenience methods

Vectors support numerical operations through the runtime and expose:

v.norm()

Returns the Euclidean norm of the vector.

let v = linalg.vector([3, 4])
print(v.norm())   // 5.0

Matrices similarly support common object-level helpers such as transpose() and shape(), while more specialized algorithms are provided by the linalg module.