Expand description
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]
// TODO: replace the * by the latest version.
nalgebra = "*"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
Matrixfor 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:
Vector1toVector6andMatrix1x1toMatrix6x6, including rectangular matrices likeMatrix2x5. - Points sizes known at compile time, and convenience aliases:
Point1toPoint6. - 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 a homogeneous matrix:
Affine2,Affine3. - Projective (i.e. invertible) transformations stored as a homogeneous matrix:
Projective2,Projective3. - General transformations that does not have to be invertible, stored as a homogeneous matrix:
Transform2,Transform3. - 3D projections for computer graphics:
Perspective3,Orthographic3. - Matrix factorizations:
Cholesky,QR,LU,FullPivLU,SVD,Schur,Hessenberg,SymmetricEigen. - Insertion and removal of rows of columns of a matrix.
Re-exports
pub use crate::base::*;pub use crate::geometry::*;pub use crate::linalg::*;pub use crate::sparse::*;pub use base as core;Modules
[Reexported at the root of this crate.] Data structures for vector and matrix computations.
Various tools useful for testing/debugging/benchmarking.
[Reexported at the root of this crate.] Data structures for points and usual transformations (rotations, isometries, etc.)
Parsers for various matrix formats.
[Reexported at the root of this crate.] Factorization of real matrices.
proptest-related features for nalgebra data structures.
Sparse matrices.
Macros
Construct a dynamic matrix directly from data.
Construct a dynamic column vector directly from data.
Construct a fixed-size matrix directly from data.
Construct a fixed-size point directly from data.
Construct a fixed-size column vector directly from data.
Structs
A complex number in Cartesian form.
Traits
Trait alias for Add and AddAssign with result of type Self.
Trait alias for Div and DivAssign with result of type Self.
Trait alias for Mul and MulAssign with result of type Self.
Trait alias for Sub and SubAssign with result of type Self.
Trait shared by all complex fields and its subfields (like real numbers).
Trait implemented by fields, i.e., complex numbers and floats.
Trait shared by all reals.
Lane-wise generalization of bool for SIMD booleans.
Lane-wise generalisation of ComplexField for SIMD complex fields.
Lane-wise generalization of the standard PartialOrd for SIMD values.
Lanewise generalization of RealField for SIMD reals.
Base trait for every SIMD types.
Functions
The absolute value of a.
The center of two points.
Returns a reference to the input value clamped to the interval [min, max].
Converts an object from one type to an equivalent or more general one.
Converts an object from one type to an equivalent or more general one.
Use with care! Same as try_convert but
without any property checks.
Use with care! Same as try_convert but
without any property checks.
The distance between two points.
The squared distance between two points.
Returns the infimum of a and b.
Returns simultaneously the infimum and supremum of a and b.
Indicates if try_convert will succeed without
actually performing the conversion.
Same as cmp::max.
Same as cmp::min.
Gets the multiplicative identity element.
Clamp value between min and max. Returns None if value is not comparable to
min or max.
Compare a and b using a partial ordering relation.
Returns true iff a and b are comparable and a >= b.
Returns true iff a and b are comparable and a > b.
Returns true iff a and b are comparable and a <= b.
Returns true iff a and b are comparable and a < b.
Return the maximum of a and b if they are comparable.
Return the minimum of a and b if they are comparable.
Sorts two values in increasing order using a partial ordering.
Returns the supremum of a and b.
Attempts to convert an object to a more specific one.
Attempts to convert an object to a more specific one.
Wraps val into the range [min, max] using modular arithmetics.
Gets the additive identity element.