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 = "0.16"

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.