To focus the search input from anywhere on the page, press the 'S' key.
in-package search v0.1.0
Phantom-algebra — a strongly-typed tensor library à la GLSL
Phantom-algebra is a pure OCaml library implementing strongly-typed
small tensors with dimensions 0 ≤ 4, rank ≤ 2, and limited to square matrices.
It makes it possible to manipulate vector and matrix expressions with an
uniform notation while still catching non-sensical operations at compile time
For instance, this extract is valid
open Phantom_algebra.Core let v = vec3 1. 2. 3. let w = vec3 3. 2. 1. let u = scalar 2. + cross (v + w) (v - w) let rot = rotation u v 1. let r = w + rot * v
but adding a vector to a matrix is not, and yields a type error:
v + rot
Type errors tend to be quite long to say the least, but individual type
of scalars, vectors and matrices are much simpler. However, the size of the
type of higher order function may increase exponentially due to the exotic
type construction used internally.
Phantom-algebra is inspired by GLSL conventions:
addition is the usual vector addition, with scalar broadcasted
to tensors of any dimension and rank
let v = vec2 0. 1. + scalar 1. (* = (1. 2.) *)
x * yis interpreted as:
the external product if either
yis a scalar
the matrix product if either
yis a matrix
the component-wise (Hadamard) product otherwise
yare a vector)
the cross-product of two 2d vectors yields a scalar whereas
the cross-product of two 3d vectors yields a 3d pseudo-vectors.
(other cross-product are type errors), for instance
cross (vec2 1. 1.) (vec2 (-1.) 1.) + vec4 1 0. 0. 0. = vec4 3. 2. 2. 2.
Indices are also-strongly typed, trying to access a index beyond the
tensor dimension yields a type error.
let v = vec2 2. 3. let fine = v.%(x') let wrong = v.%(z') let m = mat2 v v let fine = m.%(xy') let also_wrong = m.%(zx') let wrong_rank_this_time = m.%(x')
Index names follows GLSL convention with a
'suffix to avoid shadowing:
Similarly, slicing a rank
ktensor with a rank
yields a rank
k-ntensor of the same dimension, e.g
let e1 = (vec2 1. 0.) let id = mat2 e1 (vec2 0. 1.) let e1' = id.%[x'] (* this is the first row of the id matrix *) let zero = id.%[xy']
Swizzling is supported:
dimindices can be combined with the
to yield an objet of
let v = vec4 0. 1. 2. 3. let w = v.%[w'&z'&'y&'x] (* slicing a vector yields a scalar, and 4 scalars grouped together become a vector *) ;; w = vec4 3. 2. 1. 0. let mat = eye d2 let s = mat.%[y'&x'] (* we are reversing the rows, and obtaining a new matrix*) ;; s = mat2 (vec2 0. 1.) (vec2 1. 0.)
the scalar product and usual norm are supported:
norm2 v = (v|*|v)
Usual mathematics functions have been extended to operates
element-wise on tensor, they are able in the
let v = Math.cos (vec2 1. 2.)
Some usual matrix and vector functions are predefined
let id = eye d2 let rxy t = rotation (vec3 1. 0. 0.) (vec3 0. 1. 0.) t let id = diag (vec3 1. 1. 1.)
The exponential function on matrices is the matrix exponentiation
;; exp (mat2 (0. 1.) (0. -1) ) = rxy 1.
Vectors can be concatened and stretched to a given dimension
let v = scalar 0. |+| vec2 1. 0. |+| scalar 1. let w = vec4' (scalar 1.)