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Manu — Nim Matrix Numeric library

Manu is a pure Nim library, no external dependencies to BLAS frameworks. Supports constructing and manipulating only real, dense matrices. It started as a port of JAMA library, and is adapted to Nim programming paradigm and specific performace considerations.

What is supported:

  • Compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions.
  • Generics allow matrices of SomeFloat only.
  • Arithmetic operators are overloaded to support matrices.
    • Broadcast scalars, column and row vectors to work with matrices.
  • Destructors, with sink annotations, copies can be avoided in some cases.

API documentation

Examples

In the examples directory you will find the following:

  1. two layer neural network
  2. stress state analysis script

showcasing what can already be done.

example2.nim

  import manu

  # Solve a linear system A x = b and compute the residual norm, ||b - A x||.
  let vals = @[@[1.0, 2, 3], @[4.0, 5, 6], @[7.0, 8, 10]]
  let A = matrix(vals)
  let b = randMatrix64(3, 1)
  let x = A.solve(b)
  let r = A * x - b
  let rnorm = r.normInf()
  echo("x =\n", x)
  echo("residual norm = ", rnorm)

Output:

x =
⎡-918.9217543597e-3⎤
⎢      2.1952979104⎥
⎣     -1.0796593055⎦
residual norm = 1.554312234475219e-15

Matrix decompositions

Five matrix decompositions are used to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. Theses are:

  • Cholesky Decomposition of symmetric, positive definite matrices
  • LU Decomposition (Gaussian elimination) of rectangular matrices
  • QR Decomposition of rectangular matrices
  • Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices
  • Singular Value Decomposition of rectangular matrices

Broadcasting

It is implemented with the help of two distinct types RowVector[T] and ColVector[T]. You can cast any compatible matrix to these and when performing matrix operations, it will be broadcasted to the correct dimensions:

var a = matrix(1, 5, 2.0)
let b = ones64(2, 1)
echo ColVector64(b) + RowVector64(a)
echo 2.0 + a # matrix-scalar ops are implicit

Results in:

⎡3  3  3  3  3⎤
⎣3  3  3  3  3⎦
⎡4  4  4  4  4⎤

If the matrices are not broadcastable an AssertionDefect will be thrown at runtime.

The correct paradigm of usage is to first initialize a matrix, i.e let a = ones64(1, 5) and cast it to RowVector64 where broadcasting is needed: RowVector64(a) + zeros64(5, 5). This system is designed to be more explicit, and since it is type-checked, work well with sink optimizations.

Feature improvements / contributions

License

This library is distributed under the MIT license.