Crate nalgebra

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 assert_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);

    assert_relative_eq!(b.axis().unwrap(), axis);
    assert_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 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 base as core;
pub use crate::base::*;
pub use crate::geometry::*;
pub use crate::linalg::*;
pub use crate::sparse::*;

Modules§

base: [Reexported at the root of this crate.] Data structures for vector and matrix computations.
debug: Various tools useful for testing/debugging/benchmarking.
geometry: [Reexported at the root of this crate.] Data structures for points and usual transformations (rotations, isometries, etc.)
io: Parsers for various matrix formats.
linalg: [Reexported at the root of this crate.] Factorization of real matrices.
proptest: proptest-related features for nalgebra data structures.
sparse: Sparse matrices.

Macros§

dmatrix: Construct a dynamic matrix directly from data.
dvector: Construct a dynamic column vector directly from data.
matrix: Construct a fixed-size matrix directly from data.
point: Construct a fixed-size point directly from data.
stack: Construct a new matrix by stacking matrices in a block matrix.
vector: Construct a fixed-size column vector directly from data.

Structs§

Complex: A complex number in Cartesian form.

Traits§

ClosedAddAssign: Trait alias for Add and AddAssign with result of type Self.
ClosedDivAssign: Trait alias for Div and DivAssign with result of type Self.
ClosedMulAssign: Trait alias for Mul and MulAssign with result of type Self.
ClosedSubAssign: Trait alias for Sub and SubAssign with result of type Self.
ComplexField: Trait shared by all complex fields and its subfields (like real numbers).
Field: Trait implemented by fields, i.e., complex numbers and floats.
RealField: Trait shared by all reals.
SimdBool: Lane-wise generalization of bool for SIMD booleans.
SimdComplexField: Lane-wise generalisation of ComplexField for SIMD complex fields.
SimdPartialOrd: Lane-wise generalization of the standard PartialOrd for SIMD values.
SimdRealField: Lanewise generalization of RealField for SIMD reals.
SimdValue: Base trait for every SIMD types.

Functions§

absDeprecated: The absolute value of a.
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.
distance: The distance between two points.
distance_squared: The squared distance between two points.
infDeprecated: Returns the infimum of a and b.
inf_supDeprecated: Returns simultaneously the infimum and supremum of a and b.
is_convertible: Indicates if try_convert() will succeed without actually performing the conversion.
max: Same as cmp::max.
min: Same as cmp::min.
one: Gets the multiplicative identity element.
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.
supDeprecated: 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.
wrap: Wraps val into the range [min, max] using modular arithmetics.
zero: Gets the additive identity element.

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