Crate nalgebra

nalgebra

nalgebra is a linear algebra library written for Rust targeting:

• General-purpose linear algebra (still lacks a lot of features…)
• Real time computer graphics.
• Real time computer physics.

Using nalgebra

You will need the last stable build of the rust compiler and the official package manager: cargo.

Simply add the following to your Cargo.toml file:

[dependencies]
nalgebra = "0.17"

Most useful functionalities of nalgebra are grouped in the root module nalgebra::.

However, the recommended way to use nalgebra is to import types and traits explicitly, and call free-functions using the na:: prefix:

#[macro_use]
extern crate approx; // For the macro relative_eq!
extern crate nalgebra as na;
use na::{Vector3, Rotation3};

fn main() {
    let axis  = Vector3::x_axis();
    let angle = 1.57;
    let b     = Rotation3::from_axis_angle(&axis, angle);

    relative_eq!(b.axis().unwrap(), axis);
    relative_eq!(b.angle(), angle);
}

Features

nalgebra is meant to be a general-purpose, low-dimensional, linear algebra library, with an optimized set of tools for computer graphics and physics. Those features include:

• A single parametrizable type Matrix for vectors, (square or rectangular) matrices, and slices with dimensions known either at compile-time (using type-level integers) or at runtime.
• Matrices and vectors with compile-time sizes are statically allocated while dynamic ones are allocated on the heap.
• Convenient aliases for low-dimensional matrices and vectors: Vector1 to Vector6 and Matrix1x1 to Matrix6x6, including rectangular matrices like Matrix2x5.
• Points sizes known at compile time, and convenience aliases: Point1 to Point6.
• Translation (seen as a transformation that composes by multiplication): Translation2, Translation3.
• Rotation matrices: Rotation2, Rotation3.
• Quaternions: Quaternion, UnitQuaternion (for 3D rotation).
• Unit complex numbers can be used for 2D rotation: UnitComplex.
• Algebraic entities with a norm equal to one: Unit<T>, e.g., Unit<Vector3<f32>>.
• Isometries (translation ⨯ rotation): Isometry2, Isometry3
• Similarity transformations (translation ⨯ rotation ⨯ uniform scale): Similarity2, Similarity3.
• Affine transformations stored as an homogeneous matrix: Affine2, Affine3.
• Projective (i.e. invertible) transformations stored as an homogeneous matrix: Projective2, Projective3.
• General transformations that does not have to be invertible, stored as an homogeneous matrix: Transform2, Transform3.
• 3D projections for computer graphics: Perspective3, Orthographic3.
• Matrix factorizations: Cholesky, QR, LU, FullPivLU, SVD, RealSchur, Hessenberg, SymmetricEigen.
• Insertion and removal of rows of columns of a matrix.
• Implements traits from the alga crate for generic programming.

Re-exports

pub use base as core;

pub use base::*;

pub use geometry::*;

pub use linalg::*;

Modules

base	[Reexported at the root of this crate.] Data structures for vector and matrix computations.
geometry	[Reexported at the root of this crate.] Data structures for points and usual transformations (rotations, isometries, etc.)
linalg	[Reexported at the root of this crate.] Factorization of real matrices.

Structs

Id	The universal identity element wrt. a given operator, usually noted Id with a context-dependent subscript.

Traits

Real	Trait shared by all reals.

Functions

abs	[ Deprecated ] The absolute value of a.
angle	[ Deprecated ] Computes the smallest angle between two vectors.
center	The center of two points.
clamp	Returns a reference to the input value clamped to the interval [min, max].
convert	Converts an object from one type to an equivalent or more general one.
convert_ref	Converts an object from one type to an equivalent or more general one.
convert_ref_unchecked⚠	Use with care! Same as try_convert but without any property checks.
convert_unchecked⚠	Use with care! Same as try_convert but without any property checks.
dimension	The dimension of the given algebraic entity seen as a vector space.
distance	The distance between two points.
distance_squared	The squared distance between two points.
dot	[ Deprecated ] Computes the dot product of two vectors.
id	Gets the ubiquitous multiplicative identity element.
inf	Returns the infimum of a and b.
inf_sup	Returns simultaneously the infimum and supremum of a and b.
inverse	Computes the multiplicative inverse of an (always invertible) algebraic entity.
is_convertible	Indicates if try_convert will succeed without actually performing the conversion.
magnitude	[ Deprecated ] A synonym for norm, aka length.
magnitude_squared	[ Deprecated ] A synonym for norm_squared, aka length squared.
max	Same as cmp::max.
min	Same as cmp::min.
norm	[ Deprecated ] Computes the L2 (Euclidean) norm of a vector.
norm_squared	[ Deprecated ] Computes the squared L2 (Euclidean) norm of the vector v.
normalize	[ Deprecated ] Computes the normalized version of the vector v.
one	Gets the multiplicative identity element.
origin	[ Deprecated ] Gets the origin of the given point.
partial_clamp	Clamp value between min and max. Returns None if value is not comparable to min or max.
partial_cmp	Compare a and b using a partial ordering relation.
partial_ge	Returns true iff a and b are comparable and a >= b.
partial_gt	Returns true iff a and b are comparable and a > b.
partial_le	Returns true iff a and b are comparable and a <= b.
partial_lt	Returns true iff a and b are comparable and a < b.
partial_max	Return the maximum of a and b if they are comparable.
partial_min	Return the minimum of a and b if they are comparable.
partial_sort2	Sorts two values in increasing order using a partial ordering.
sup	Returns the supremum of a and b.
try_convert	Attempts to convert an object to a more specific one.
try_convert_ref	Attempts to convert an object to a more specific one.
try_inverse	Tries to gets an inverted copy of a square matrix.
try_normalize	[ Deprecated ] Computes the normalized version of the vector v or returns None if its norm is smaller than min_norm.
wrap	Wraps val into the range [min, max] using modular arithmetics.
zero	Gets the additive identity element.