# [−][src]Crate nalgebra

# nalgebra

**nalgebra** is a linear algebra library written for Rust targeting:

- General-purpose linear algebra (still lacks a lot of features…)
- RealField time computer graphics.
- RealField 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 = "0.18"

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`

,`Schur`

,`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 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. |

sparse | Sparse matrices. |

## Structs

Complex | A complex number in Cartesian form. |

Id | The universal identity element wrt. a given operator, usually noted |

## Traits

ComplexField | Trait shared by all complex fields and its subfields (like real numbers). |

Real | Deprecated The field of reals. This has been renamed to |

RealField | Trait shared by all reals. |

## Functions

abs | Deprecated The absolute value of |

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 |

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 |

convert_unchecked^{⚠} | Use with care! Same as |

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 | Deprecated Gets the ubiquitous multiplicative identity element. |

inf | Returns the infimum of |

inf_sup | Returns simultaneously the infimum and supremum of |

inverse | Deprecated Computes the multiplicative inverse of an (always invertible) algebraic entity. |

is_convertible | Indicates if |

magnitude | Deprecated A synonym for |

magnitude_squared | Deprecated A synonym for |

max | Same as |

min | Same as |

norm | Deprecated Computes the L2 (Euclidean) norm of a vector. |

norm_squared | Deprecated Computes the squared L2 (Euclidean) norm of the vector |

normalize | Deprecated Computes the normalized version of the vector |

one | Gets the multiplicative identity element. |

origin | Deprecated Gets the origin of the given point. |

partial_clamp | Clamp |

partial_cmp | Compare |

partial_ge | Returns |

partial_gt | Returns |

partial_le | Returns |

partial_lt | Returns |

partial_max | Return the maximum of |

partial_min | Return the minimum of |

partial_sort2 | Sorts two values in increasing order using a partial ordering. |

sup | Returns the supremum of |

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 | Deprecated Tries to gets an inverted copy of a square matrix. |

try_normalize | Deprecated Computes the normalized version of the vector |

wrap | Wraps |

zero | Gets the additive identity element. |