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]
// 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 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::*;

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.

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.
• vector
  Construct a fixed-size column vector directly from data.

Structs

• Complex
  A complex number in Cartesian form.

Traits

• ClosedAdd
  Trait alias for Add and AddAssign with result of type Self.
• ClosedDiv
  Trait alias for Div and DivAssign with result of type Self.
• ClosedMul
  Trait alias for Mul and MulAssign with result of type Self.
• ClosedSub
  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.