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</pre><pre class='rust '>
<span class='doccomment'>/*!
# nalgebra
**nalgebra** is a low-dimensional linear algebra library written for Rust targeting:
* low-dimensional general-purpose linear algebra (still lacks a lot of features…).
* real time computer graphics.
* real time computer physics.
An on-line version of this documentation is available [here](http://nalgebra.org/doc/nalgebra).
## Using **nalgebra**
All the functionality of **nalgebra** is grouped in one place: the root module `nalgebra::`. This
module re-exports everything and includes free functions for all traits methods performing
out-of-place operations.
Thus, you can import the whole prelude using:
```.ignore
use nalgebra::*;
```
However, the recommended way to use **nalgebra** is to import types and traits explicitly, and call
free-functions using the `na::` prefix:
```.rust
extern crate nalgebra as na;
use na::{Vector3, Rotation3, Rotation};
fn main() {
let a = Vector3::new(1.0f64, 1.0, 1.0);
let mut b = Rotation3::new(na::zero());
b.append_rotation_mut(&a);
assert!(na::approx_eq(&na::rotation(&b), &a));
}
```
## 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:
* Vectors with predefined static sizes: `Vector1`, `Vector2`, `Vector3`, `Vector4`, `Vector5`, `Vector6`.
* Vector with a user-defined static size: `VectorN` (available only with the `generic_sizes` feature).
* Points with static sizes: `Point1`, `Point2`, `Point3`, `Point4`, `Point5`, `Point6`.
* Square matrices with static sizes: `Matrix1`, `Matrix2`, `Matrix3`, `Matrix4`, `Matrix5`, `Matrix6 `.
* Rotation matrices: `Rotation2`, `Rotation3`
* Quaternions: `Quaternion`, `UnitQuaternion`.
* Isometries (translation ⨯ rotation): `Isometry2`, `Isometry3`
* Similarity transformations (translation ⨯ rotation ⨯ uniform scale): `Similarity2`, `Similarity3`.
* 3D projections for computer graphics: `Perspective3`, `PerspectiveMatrix3`, `Orthographic3`, `OrthographicMatrix3`.
* Dynamically sized heap-allocated vector: `DVector`.
* Dynamically sized stack-allocated vectors with a maximum size: `DVector1` to `DVector6`.
* Dynamically sized heap-allocated (square or rectangular) matrix: `DMatrix`.
* Linear algebra and data analysis operators: `Covariance`, `Mean`, `qr`, `cholesky`.
* Almost one trait per functionality: useful for generic programming.
## **nalgebra** in use
Here are some projects using **nalgebra**.
Feel free to add your project to this list if you happen to use **nalgebra**!
* [nphysics](https://github.com/sebcrozet/nphysics): a real-time physics engine.
* [ncollide](https://github.com/sebcrozet/ncollide): a collision detection library.
* [kiss3d](https://github.com/sebcrozet/kiss3d): a minimalistic graphics engine.
* [nrays](https://github.com/sebcrozet/nrays): a ray tracer.
*/</span>
<span class='attribute'>#<span class='op'>!</span>[<span class='ident'>deny</span>(<span class='ident'>non_camel_case_types</span>)]</span>
<span class='attribute'>#<span class='op'>!</span>[<span class='ident'>deny</span>(<span class='ident'>unused_parens</span>)]</span>
<span class='attribute'>#<span class='op'>!</span>[<span class='ident'>deny</span>(<span class='ident'>non_upper_case_globals</span>)]</span>
<span class='attribute'>#<span class='op'>!</span>[<span class='ident'>deny</span>(<span class='ident'>unused_qualifications</span>)]</span>
<span class='attribute'>#<span class='op'>!</span>[<span class='ident'>deny</span>(<span class='ident'>unused_results</span>)]</span>
<span class='attribute'>#<span class='op'>!</span>[<span class='ident'>warn</span>(<span class='ident'>missing_docs</span>)]</span>
<span class='attribute'>#<span class='op'>!</span>[<span class='ident'>doc</span>(<span class='ident'>html_root_url</span> <span class='op'>=</span> <span class='string'>"http://nalgebra.org/doc"</span>)]</span>
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>rustc_serialize</span>;
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>rand</span>;
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>num</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span><span class='op'>=</span><span class='string'>"generic_sizes"</span>)]</span>
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>generic_array</span>;
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span><span class='op'>=</span><span class='string'>"arbitrary"</span>)]</span>
<span class='kw'>extern</span> <span class='kw'>crate</span> <span class='ident'>quickcheck</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>cmp</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::{<span class='ident'>Neg</span>, <span class='ident'>Mul</span>};
<span class='kw'>use</span> <span class='ident'>num</span>::{<span class='ident'>Zero</span>, <span class='ident'>One</span>};
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>traits</span>::{
<span class='ident'>Absolute</span>,
<span class='ident'>AbsoluteRotate</span>,
<span class='ident'>ApproxEq</span>,
<span class='ident'>Axpy</span>,
<span class='ident'>Basis</span>,
<span class='ident'>BaseFloat</span>,
<span class='ident'>BaseNum</span>,
<span class='ident'>Bounded</span>,
<span class='ident'>Cast</span>,
<span class='ident'>Column</span>,
<span class='ident'>ColumnSlice</span>, <span class='ident'>RowSlice</span>,
<span class='ident'>Covariance</span>,
<span class='ident'>Cross</span>,
<span class='ident'>CrossMatrix</span>,
<span class='ident'>Determinant</span>,
<span class='ident'>Diagonal</span>,
<span class='ident'>Dimension</span>,
<span class='ident'>Dot</span>,
<span class='ident'>EigenQR</span>,
<span class='ident'>Eye</span>,
<span class='ident'>FloatPoint</span>,
<span class='ident'>FloatVector</span>,
<span class='ident'>FromHomogeneous</span>,
<span class='ident'>Indexable</span>,
<span class='ident'>Inverse</span>,
<span class='ident'>Iterable</span>,
<span class='ident'>IterableMut</span>,
<span class='ident'>Matrix</span>,
<span class='ident'>Mean</span>,
<span class='ident'>Norm</span>,
<span class='ident'>NumPoint</span>,
<span class='ident'>NumVector</span>,
<span class='ident'>Origin</span>,
<span class='ident'>Outer</span>,
<span class='ident'>PartialOrder</span>,
<span class='ident'>PartialOrdering</span>,
<span class='ident'>PointAsVector</span>,
<span class='ident'>Repeat</span>,
<span class='ident'>Rotate</span>, <span class='ident'>Rotation</span>, <span class='ident'>RotationMatrix</span>, <span class='ident'>RotationWithTranslation</span>, <span class='ident'>RotationTo</span>,
<span class='ident'>Row</span>,
<span class='ident'>Shape</span>,
<span class='ident'>SquareMatrix</span>,
<span class='ident'>ToHomogeneous</span>,
<span class='ident'>Transform</span>, <span class='ident'>Transformation</span>,
<span class='ident'>Translate</span>, <span class='ident'>Translation</span>,
<span class='ident'>Transpose</span>,
<span class='ident'>UniformSphereSample</span>
};
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span><span class='op'>=</span><span class='string'>"generic_sizes"</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>structs</span>::<span class='ident'>VectorN</span>;
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>structs</span>::{
<span class='ident'>Identity</span>,
<span class='ident'>DMatrix</span>, <span class='ident'>DMatrix1</span>, <span class='ident'>DMatrix2</span>, <span class='ident'>DMatrix3</span>, <span class='ident'>DMatrix4</span>, <span class='ident'>DMatrix5</span>, <span class='ident'>DMatrix6</span>,
<span class='ident'>DVector</span>, <span class='ident'>DVector1</span>, <span class='ident'>DVector2</span>, <span class='ident'>DVector3</span>, <span class='ident'>DVector4</span>, <span class='ident'>DVector5</span>, <span class='ident'>DVector6</span>,
<span class='ident'>Isometry2</span>, <span class='ident'>Isometry3</span>,
<span class='ident'>Similarity2</span>, <span class='ident'>Similarity3</span>,
<span class='ident'>Matrix1</span>, <span class='ident'>Matrix2</span>, <span class='ident'>Matrix3</span>, <span class='ident'>Matrix4</span>,
<span class='ident'>Matrix5</span>, <span class='ident'>Matrix6</span>,
<span class='ident'>Rotation2</span>, <span class='ident'>Rotation3</span>,
<span class='ident'>Vector1</span>, <span class='ident'>Vector2</span>, <span class='ident'>Vector3</span>, <span class='ident'>Vector4</span>, <span class='ident'>Vector5</span>, <span class='ident'>Vector6</span>,
<span class='ident'>Point1</span>, <span class='ident'>Point2</span>, <span class='ident'>Point3</span>, <span class='ident'>Point4</span>, <span class='ident'>Point5</span>, <span class='ident'>Point6</span>,
<span class='ident'>Perspective3</span>, <span class='ident'>PerspectiveMatrix3</span>,
<span class='ident'>Orthographic3</span>, <span class='ident'>OrthographicMatrix3</span>,
<span class='ident'>Quaternion</span>, <span class='ident'>UnitQuaternion</span>
};
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='ident'>linalg</span>::{
<span class='ident'>qr</span>,
<span class='ident'>householder_matrix</span>,
<span class='ident'>cholesky</span>,
<span class='ident'>hessenberg</span>
};
<span class='kw'>mod</span> <span class='ident'>structs</span>;
<span class='kw'>mod</span> <span class='ident'>traits</span>;
<span class='kw'>mod</span> <span class='ident'>linalg</span>;
<span class='kw'>mod</span> <span class='ident'>macros</span>;
<span class='comment'>// mod lower_triangular;</span>
<span class='comment'>// mod chol;</span>
<span class='doccomment'>/// Change the input value to ensure it is on the range `[min, max]`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>clamp</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>PartialOrd</span><span class='op'>></span>(<span class='ident'>val</span>: <span class='ident'>T</span>, <span class='ident'>min</span>: <span class='ident'>T</span>, <span class='ident'>max</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='kw'>if</span> <span class='ident'>val</span> <span class='op'>></span> <span class='ident'>min</span> {
<span class='kw'>if</span> <span class='ident'>val</span> <span class='op'><</span> <span class='ident'>max</span> {
<span class='ident'>val</span>
}
<span class='kw'>else</span> {
<span class='ident'>max</span>
}
}
<span class='kw'>else</span> {
<span class='ident'>min</span>
}
}
<span class='doccomment'>/// Same as `cmp::max`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>max</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Ord</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='ident'>T</span>, <span class='ident'>b</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>cmp</span>::<span class='ident'>max</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Same as `cmp::min`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>min</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Ord</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='ident'>T</span>, <span class='ident'>b</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>cmp</span>::<span class='ident'>min</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Returns the infimum of `a` and `b`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inf</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>inf</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Returns the supremum of `a` and `b`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>sup</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>sup</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Compare `a` and `b` using a partial ordering relation.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>partial_cmp</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>PartialOrdering</span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>partial_cmp</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Returns `true` iff `a` and `b` are comparable and `a < b`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>partial_lt</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>partial_lt</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Returns `true` iff `a` and `b` are comparable and `a <= b`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>partial_le</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>partial_le</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Returns `true` iff `a` and `b` are comparable and `a > b`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>partial_gt</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>partial_gt</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Returns `true` iff `a` and `b` are comparable and `a >= b`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>partial_ge</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>partial_ge</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Return the minimum of `a` and `b` if they are comparable.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>partial_min</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>partial_min</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Return the maximum of `a` and `b` if they are comparable.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>partial_max</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>partial_max</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to</span>
<span class='doccomment'>/// `min` or `max`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>partial_clamp</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span>: <span class='ident'>PartialOrder</span><span class='op'>></span>(<span class='ident'>value</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span>, <span class='ident'>min</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span>, <span class='ident'>max</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='ident'>T</span><span class='op'>></span> {
<span class='ident'>PartialOrder</span>::<span class='ident'>partial_clamp</span>(<span class='ident'>value</span>, <span class='ident'>min</span>, <span class='ident'>max</span>)
}
<span class='comment'>//</span>
<span class='comment'>//</span>
<span class='comment'>// Constructors</span>
<span class='comment'>//</span>
<span class='comment'>//</span>
<span class='doccomment'>/// Create a special identity object.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Same as `Identity::new()`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>identity</span>() <span class='op'>-></span> <span class='ident'>Identity</span> {
<span class='ident'>Identity</span>::<span class='ident'>new</span>()
}
<span class='doccomment'>/// Create a zero-valued value.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This is the same as `std::num::zero()`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>zero</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Zero</span><span class='op'>></span>() <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>Zero</span>::<span class='ident'>zero</span>()
}
<span class='doccomment'>/// Tests is a value is iqual to zero.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>is_zero</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>Zero</span><span class='op'>></span>(<span class='ident'>val</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>val</span>.<span class='ident'>is_zero</span>()
}
<span class='doccomment'>/// Create a one-valued value.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This is the same as `std::num::one()`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>one</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>One</span><span class='op'>></span>() <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>One</span>::<span class='ident'>one</span>()
}
<span class='comment'>//</span>
<span class='comment'>//</span>
<span class='comment'>// Geometry</span>
<span class='comment'>//</span>
<span class='comment'>//</span>
<span class='doccomment'>/// Returns the trivial origin of an affine space.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>origin</span><span class='op'><</span><span class='ident'>P</span>: <span class='ident'>Origin</span><span class='op'>></span>() <span class='op'>-></span> <span class='ident'>P</span> {
<span class='ident'>Origin</span>::<span class='ident'>origin</span>()
}
<span class='doccomment'>/// Returns the center of two points.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>center</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span>, <span class='ident'>P</span>: <span class='ident'>FloatPoint</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>P</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>P</span>) <span class='op'>-></span> <span class='ident'>P</span>
<span class='kw'>where</span> <span class='op'><</span><span class='ident'>P</span> <span class='kw'>as</span> <span class='ident'>PointAsVector</span><span class='op'>></span>::<span class='ident'>Vector</span>: <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>
{
<span class='kw'>let</span> <span class='ident'>_2</span> <span class='op'>=</span> <span class='ident'>one</span>::<span class='op'><</span><span class='ident'>N</span><span class='op'>></span>() <span class='op'>+</span> <span class='ident'>one</span>();
(<span class='op'>*</span><span class='ident'>a</span> <span class='op'>+</span> <span class='ident'>b</span>.<span class='ident'>to_vector</span>()) <span class='op'>/</span> <span class='ident'>_2</span>
}
<span class='comment'>/*
* FloatPoint
*/</span>
<span class='doccomment'>/// Returns the distance between two points.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>distance</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span>, <span class='ident'>P</span>: <span class='ident'>FloatPoint</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>P</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>P</span>) <span class='op'>-></span> <span class='ident'>N</span> <span class='kw'>where</span> <span class='op'><</span><span class='ident'>P</span> <span class='kw'>as</span> <span class='ident'>PointAsVector</span><span class='op'>></span>::<span class='ident'>Vector</span>: <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='ident'>a</span>.<span class='ident'>distance</span>(<span class='ident'>b</span>)
}
<span class='doccomment'>/// Returns the squared distance between two points.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>distance_squared</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span>, <span class='ident'>P</span>: <span class='ident'>FloatPoint</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>P</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>P</span>) <span class='op'>-></span> <span class='ident'>N</span>
<span class='kw'>where</span> <span class='op'><</span><span class='ident'>P</span> <span class='kw'>as</span> <span class='ident'>PointAsVector</span><span class='op'>></span>::<span class='ident'>Vector</span>: <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>
{
<span class='ident'>a</span>.<span class='ident'>distance_squared</span>(<span class='ident'>b</span>)
}
<span class='comment'>/*
* Translation<V>
*/</span>
<span class='doccomment'>/// Gets the translation applicable by `m`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{Vector3, Isometry3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());</span>
<span class='doccomment'>/// let trans = na::translation(&t);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(trans == Vector3::new(1.0, 1.0, 1.0));</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>translation</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Translation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>translation</span>()
}
<span class='doccomment'>/// Gets the inverse translation applicable by `m`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{Vector3, Isometry3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());</span>
<span class='doccomment'>/// let itrans = na::inverse_translation(&t);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(itrans == Vector3::new(-1.0, -1.0, -1.0));</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse_translation</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Translation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>inverse_translation</span>()
}
<span class='doccomment'>/// Applies the translation `v` to a copy of `m`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>append_translation</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Translation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>Translation</span>::<span class='ident'>append_translation</span>(<span class='ident'>m</span>, <span class='ident'>v</span>)
}
<span class='comment'>/*
* Translate<P>
*/</span>
<span class='doccomment'>/// Applies a translation to a point.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{Point3, Vector3, Isometry3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());</span>
<span class='doccomment'>/// let p = Point3::new(2.0, 2.0, 2.0);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// let tp = na::translate(&t, &p);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(tp == Point3::new(3.0, 3.0, 3.0))</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>translate</span><span class='op'><</span><span class='ident'>P</span>, <span class='ident'>M</span>: <span class='ident'>Translate</span><span class='op'><</span><span class='ident'>P</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>p</span>: <span class='kw-2'>&</span><span class='ident'>P</span>) <span class='op'>-></span> <span class='ident'>P</span> {
<span class='ident'>m</span>.<span class='ident'>translate</span>(<span class='ident'>p</span>)
}
<span class='doccomment'>/// Applies an inverse translation to a point.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{Point3, Vector3, Isometry3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());</span>
<span class='doccomment'>/// let p = Point3::new(2.0, 2.0, 2.0);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// let tp = na::inverse_translate(&t, &p);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(na::approx_eq(&tp, &Point3::new(1.0, 1.0, 1.0)))</span>
<span class='doccomment'>/// }</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse_translate</span><span class='op'><</span><span class='ident'>P</span>, <span class='ident'>M</span>: <span class='ident'>Translate</span><span class='op'><</span><span class='ident'>P</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>p</span>: <span class='kw-2'>&</span><span class='ident'>P</span>) <span class='op'>-></span> <span class='ident'>P</span> {
<span class='ident'>m</span>.<span class='ident'>inverse_translate</span>(<span class='ident'>p</span>)
}
<span class='comment'>/*
* Rotation<V>
*/</span>
<span class='doccomment'>/// Gets the rotation applicable by `m`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{Vector3, Rotation3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Rotation3::new(Vector3::new(1.0f64, 1.0, 1.0));</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(na::approx_eq(&na::rotation(&t), &Vector3::new(1.0, 1.0, 1.0)));</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>rotation</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>rotation</span>()
}
<span class='doccomment'>/// Gets the inverse rotation applicable by `m`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{Vector3, Rotation3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Rotation3::new(Vector3::new(1.0f64, 1.0, 1.0));</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(na::approx_eq(&na::inverse_rotation(&t), &Vector3::new(-1.0, -1.0, -1.0)));</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse_rotation</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>inverse_rotation</span>()
}
<span class='comment'>// FIXME:Â this example is a bit shity</span>
<span class='doccomment'>/// Applies the rotation `v` to a copy of `m`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{Vector3, Rotation3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.0));</span>
<span class='doccomment'>/// let v = Vector3::new(1.0, 1.0, 1.0);</span>
<span class='doccomment'>/// let rt = na::append_rotation(&t, &v);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(na::approx_eq(&na::rotation(&rt), &Vector3::new(1.0, 1.0, 1.0)))</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>append_rotation</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>Rotation</span>::<span class='ident'>append_rotation</span>(<span class='ident'>m</span>, <span class='ident'>v</span>)
}
<span class='comment'>// FIXME:Â this example is a bit shity</span>
<span class='doccomment'>/// Pre-applies the rotation `v` to a copy of `m`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{Vector3, Rotation3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.0));</span>
<span class='doccomment'>/// let v = Vector3::new(1.0, 1.0, 1.0);</span>
<span class='doccomment'>/// let rt = na::prepend_rotation(&t, &v);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(na::approx_eq(&na::rotation(&rt), &Vector3::new(1.0, 1.0, 1.0)))</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>prepend_rotation</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>Rotation</span>::<span class='ident'>prepend_rotation</span>(<span class='ident'>m</span>, <span class='ident'>v</span>)
}
<span class='comment'>/*
* Rotate<V>
*/</span>
<span class='doccomment'>/// Applies a rotation to a vector.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{BaseFloat, Rotation3, Vector3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));</span>
<span class='doccomment'>/// let v = Vector3::new(1.0, 0.0, 0.0);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// let tv = na::rotate(&t, &v);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(na::approx_eq(&tv, &Vector3::new(0.0, 1.0, 0.0)))</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>rotate</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Rotate</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>rotate</span>(<span class='ident'>v</span>)
}
<span class='doccomment'>/// Applies an inverse rotation to a vector.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// extern crate nalgebra as na;</span>
<span class='doccomment'>/// use na::{BaseFloat, Rotation3, Vector3};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// fn main() {</span>
<span class='doccomment'>/// let t = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));</span>
<span class='doccomment'>/// let v = Vector3::new(1.0, 0.0, 0.0);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// let tv = na::inverse_rotate(&t, &v);</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// assert!(na::approx_eq(&tv, &Vector3::new(0.0, -1.0, 0.0)))</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse_rotate</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Rotate</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>inverse_rotate</span>(<span class='ident'>v</span>)
}
<span class='comment'>/*
* RotationWithTranslation<LV, AV>
*/</span>
<span class='doccomment'>/// Rotates a copy of `m` by `amount` using `center` as the pivot point.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>append_rotation_wrt_point</span><span class='op'><</span><span class='ident'>LV</span>: <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>LV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Copy</span>,
<span class='ident'>AV</span>,
<span class='ident'>M</span>: <span class='ident'>RotationWithTranslation</span><span class='op'><</span><span class='ident'>LV</span>, <span class='ident'>AV</span><span class='op'>>></span>(
<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>,
<span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>AV</span>,
<span class='ident'>center</span>: <span class='kw-2'>&</span><span class='ident'>LV</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>RotationWithTranslation</span>::<span class='ident'>append_rotation_wrt_point</span>(<span class='ident'>m</span>, <span class='ident'>amount</span>, <span class='ident'>center</span>)
}
<span class='doccomment'>/// Rotates a copy of `m` by `amount` using `m.translation()` as the pivot point.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>append_rotation_wrt_center</span><span class='op'><</span><span class='ident'>LV</span>: <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>LV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Copy</span>,
<span class='ident'>AV</span>,
<span class='ident'>M</span>: <span class='ident'>RotationWithTranslation</span><span class='op'><</span><span class='ident'>LV</span>, <span class='ident'>AV</span><span class='op'>>></span>(
<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>,
<span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>AV</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>RotationWithTranslation</span>::<span class='ident'>append_rotation_wrt_center</span>(<span class='ident'>m</span>, <span class='ident'>amount</span>)
}
<span class='comment'>/*
* RotationTo
*/</span>
<span class='doccomment'>/// Computes the angle of the rotation needed to transfom `a` to `b`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>angle_between</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>RotationTo</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>V</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>::<span class='ident'>AngleType</span> {
<span class='ident'>a</span>.<span class='ident'>angle_to</span>(<span class='ident'>b</span>)
}
<span class='doccomment'>/// Computes the rotation needed to transform `a` to `b`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>rotation_between</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>RotationTo</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>V</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>::<span class='ident'>DeltaRotationType</span> {
<span class='ident'>a</span>.<span class='ident'>rotation_to</span>(<span class='ident'>b</span>)
}
<span class='comment'>/*
* RotationMatrix<LV, AV, R>
*/</span>
<span class='doccomment'>/// Builds a rotation matrix from `r`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>to_rotation_matrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>LV</span>, <span class='ident'>AV</span>, <span class='ident'>R</span>, <span class='ident'>M</span><span class='op'>></span>(<span class='ident'>r</span>: <span class='kw-2'>&</span><span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>M</span>
<span class='kw'>where</span> <span class='ident'>R</span>: <span class='ident'>RotationMatrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>LV</span>, <span class='ident'>AV</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>M</span><span class='op'>></span>,
<span class='ident'>M</span>: <span class='ident'>SquareMatrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>LV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>AV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Copy</span>,
<span class='ident'>LV</span>: <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>M</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>LV</span><span class='op'>></span>
{
<span class='comment'>// FIXME: rust-lang/rust#20413</span>
<span class='ident'>r</span>.<span class='ident'>to_rotation_matrix</span>()
}
<span class='comment'>/*
* AbsoluteRotate<V>
*/</span>
<span class='doccomment'>/// Applies a rotation using the absolute values of its components.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>absolute_rotate</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>AbsoluteRotate</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>absolute_rotate</span>(<span class='ident'>v</span>)
}
<span class='comment'>/*
* Transformation<T>
*/</span>
<span class='doccomment'>/// Gets the transformation applicable by `m`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>transformation</span><span class='op'><</span><span class='ident'>T</span>, <span class='ident'>M</span>: <span class='ident'>Transformation</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>m</span>.<span class='ident'>transformation</span>()
}
<span class='doccomment'>/// Gets the inverse transformation applicable by `m`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse_transformation</span><span class='op'><</span><span class='ident'>T</span>, <span class='ident'>M</span>: <span class='ident'>Transformation</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>m</span>.<span class='ident'>inverse_transformation</span>()
}
<span class='doccomment'>/// Gets a transformed copy of `m`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>append_transformation</span><span class='op'><</span><span class='ident'>T</span>, <span class='ident'>M</span>: <span class='ident'>Transformation</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>t</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>Transformation</span>::<span class='ident'>append_transformation</span>(<span class='ident'>m</span>, <span class='ident'>t</span>)
}
<span class='comment'>/*
* Transform<V>
*/</span>
<span class='doccomment'>/// Applies a transformation to a vector.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>transform</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Transform</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>transform</span>(<span class='ident'>v</span>)
}
<span class='doccomment'>/// Applies an inverse transformation to a vector.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse_transform</span><span class='op'><</span><span class='ident'>V</span>, <span class='ident'>M</span>: <span class='ident'>Transform</span><span class='op'><</span><span class='ident'>V</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>inverse_transform</span>(<span class='ident'>v</span>)
}
<span class='comment'>/*
* Dot<N>
*/</span>
<span class='doccomment'>/// Computes the dot product of two vectors.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>dot</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Dot</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>N</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>V</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='ident'>Dot</span>::<span class='ident'>dot</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='comment'>/*
* Norm<N>
*/</span>
<span class='doccomment'>/// Computes the L2 norm of a vector.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>norm</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span>(<span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='ident'>Norm</span>::<span class='ident'>norm</span>(<span class='ident'>v</span>)
}
<span class='doccomment'>/// Computes the squared L2 norm of a vector.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>norm_squared</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span>(<span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='ident'>Norm</span>::<span class='ident'>norm_squared</span>(<span class='ident'>v</span>)
}
<span class='doccomment'>/// Gets the normalized version of a vector.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>normalize</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span>(<span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>Norm</span>::<span class='ident'>normalize</span>(<span class='ident'>v</span>)
}
<span class='comment'>/*
* Determinant<N>
*/</span>
<span class='doccomment'>/// Computes the determinant of a square matrix.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>determinant</span><span class='op'><</span><span class='ident'>M</span>: <span class='ident'>Determinant</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>N</span><span class='op'>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='ident'>Determinant</span>::<span class='ident'>determinant</span>(<span class='ident'>m</span>)
}
<span class='comment'>/*
* Cross<V>
*/</span>
<span class='doccomment'>/// Computes the cross product of two vectors.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>cross</span><span class='op'><</span><span class='ident'>LV</span>: <span class='ident'>Cross</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>LV</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>LV</span>) <span class='op'>-></span> <span class='ident'>LV</span>::<span class='ident'>CrossProductType</span> {
<span class='ident'>Cross</span>::<span class='ident'>cross</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='comment'>/*
* CrossMatrix<M>
*/</span>
<span class='doccomment'>/// Given a vector, computes the matrix which, when multiplied by another vector, computes a cross</span>
<span class='doccomment'>/// product.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>cross_matrix</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>CrossMatrix</span><span class='op'><</span><span class='ident'>M</span><span class='op'>></span>, <span class='ident'>M</span><span class='op'>></span>(<span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>CrossMatrix</span>::<span class='ident'>cross_matrix</span>(<span class='ident'>v</span>)
}
<span class='comment'>/*
* ToHomogeneous<U>
*/</span>
<span class='doccomment'>/// Converts a matrix or vector to homogeneous coordinates.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>to_homogeneous</span><span class='op'><</span><span class='ident'>M</span>: <span class='ident'>ToHomogeneous</span><span class='op'><</span><span class='ident'>Res</span><span class='op'>></span>, <span class='ident'>Res</span><span class='op'>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>Res</span> {
<span class='ident'>ToHomogeneous</span>::<span class='ident'>to_homogeneous</span>(<span class='ident'>m</span>)
}
<span class='comment'>/*
* FromHomogeneous<U>
*/</span>
<span class='doccomment'>/// Converts a matrix or vector from homogeneous coordinates.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// w-normalization is appied.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>from_homogeneous</span><span class='op'><</span><span class='ident'>M</span>, <span class='ident'>Res</span>: <span class='ident'>FromHomogeneous</span><span class='op'><</span><span class='ident'>M</span><span class='op'>>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>Res</span> {
<span class='ident'>FromHomogeneous</span>::<span class='ident'>from</span>(<span class='ident'>m</span>)
}
<span class='comment'>/*
* UniformSphereSample
*/</span>
<span class='doccomment'>/// Samples the unit sphere living on the dimension as the samples types.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The number of sampling point is implementation-specific. It is always uniform.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>sample_sphere</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>UniformSphereSample</span>, <span class='ident'>F</span>: <span class='ident'>FnMut</span>(<span class='ident'>V</span>)<span class='op'>></span>(<span class='ident'>f</span>: <span class='ident'>F</span>) {
<span class='ident'>UniformSphereSample</span>::<span class='ident'>sample</span>(<span class='ident'>f</span>)
}
<span class='comment'>//</span>
<span class='comment'>//</span>
<span class='comment'>// Operations</span>
<span class='comment'>//</span>
<span class='comment'>//</span>
<span class='comment'>/*
* AproxEq<N>
*/</span>
<span class='doccomment'>/// Tests approximate equality.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>approx_eq</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>N</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>ApproxEq</span>::<span class='ident'>approx_eq</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='doccomment'>/// Tests approximate equality using a custom epsilon.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>approx_eq_eps</span><span class='op'><</span><span class='ident'>T</span>: <span class='ident'>ApproxEq</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>N</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>T</span>, <span class='ident'>eps</span>: <span class='kw-2'>&</span><span class='ident'>N</span>) <span class='op'>-></span> <span class='ident'>bool</span> {
<span class='ident'>ApproxEq</span>::<span class='ident'>approx_eq_eps</span>(<span class='ident'>a</span>, <span class='ident'>b</span>, <span class='ident'>eps</span>)
}
<span class='comment'>/*
* Absolute<A>
*/</span>
<span class='doccomment'>/// Computes a component-wise absolute value.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>abs</span><span class='op'><</span><span class='ident'>M</span>: <span class='ident'>Absolute</span><span class='op'><</span><span class='ident'>Res</span><span class='op'>></span>, <span class='ident'>Res</span><span class='op'>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>Res</span> {
<span class='ident'>Absolute</span>::<span class='ident'>abs</span>(<span class='ident'>m</span>)
}
<span class='comment'>/*
* Inverse
*/</span>
<span class='doccomment'>/// Gets an inverted copy of a matrix.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>inverse</span><span class='op'><</span><span class='ident'>M</span>: <span class='ident'>Inverse</span><span class='op'>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>M</span><span class='op'>></span> {
<span class='ident'>Inverse</span>::<span class='ident'>inverse</span>(<span class='ident'>m</span>)
}
<span class='comment'>/*
* Transpose
*/</span>
<span class='doccomment'>/// Gets a transposed copy of a matrix.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>transpose</span><span class='op'><</span><span class='ident'>M</span>: <span class='ident'>Transpose</span><span class='op'>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>Transpose</span>::<span class='ident'>transpose</span>(<span class='ident'>m</span>)
}
<span class='comment'>/*
* Outer<M>
*/</span>
<span class='doccomment'>/// Computes the outer product of two vectors.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>outer</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Outer</span><span class='op'>></span>(<span class='ident'>a</span>: <span class='kw-2'>&</span><span class='ident'>V</span>, <span class='ident'>b</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>::<span class='ident'>OuterProductType</span> {
<span class='ident'>Outer</span>::<span class='ident'>outer</span>(<span class='ident'>a</span>, <span class='ident'>b</span>)
}
<span class='comment'>/*
* Covariance<M>
*/</span>
<span class='doccomment'>/// Computes the covariance of a set of observations.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>covariance</span><span class='op'><</span><span class='ident'>M</span>: <span class='ident'>Covariance</span><span class='op'><</span><span class='ident'>Res</span><span class='op'>></span>, <span class='ident'>Res</span><span class='op'>></span>(<span class='ident'>observations</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>Res</span> {
<span class='ident'>Covariance</span>::<span class='ident'>covariance</span>(<span class='ident'>observations</span>)
}
<span class='comment'>/*
* Mean<N>
*/</span>
<span class='doccomment'>/// Computes the mean of a set of observations.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>mean</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>M</span>: <span class='ident'>Mean</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>(<span class='ident'>observations</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='ident'>Mean</span>::<span class='ident'>mean</span>(<span class='ident'>observations</span>)
}
<span class='comment'>/*
* EigenQR<N, V>
*/</span>
<span class='doccomment'>/// Computes the eigenvalues and eigenvectors of a square matrix usin the QR algorithm.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>eigen_qr</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>V</span>, <span class='ident'>M</span><span class='op'>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>, <span class='ident'>eps</span>: <span class='kw-2'>&</span><span class='ident'>N</span>, <span class='ident'>niter</span>: <span class='ident'>usize</span>) <span class='op'>-></span> (<span class='ident'>M</span>, <span class='ident'>V</span>)
<span class='kw'>where</span> <span class='ident'>V</span>: <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>M</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>V</span><span class='op'>></span>,
<span class='ident'>M</span>: <span class='ident'>EigenQR</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>V</span><span class='op'>></span> {
<span class='ident'>EigenQR</span>::<span class='ident'>eigen_qr</span>(<span class='ident'>m</span>, <span class='ident'>eps</span>, <span class='ident'>niter</span>)
}
<span class='comment'>//</span>
<span class='comment'>//</span>
<span class='comment'>// Structure</span>
<span class='comment'>//</span>
<span class='comment'>//</span>
<span class='comment'>/*
* Eye
*/</span>
<span class='doccomment'>/// Construct the identity matrix for a given dimension</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new_identity</span><span class='op'><</span><span class='ident'>M</span>: <span class='ident'>Eye</span><span class='op'>></span>(<span class='ident'>dimension</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='ident'>M</span> {
<span class='ident'>Eye</span>::<span class='ident'>new_identity</span>(<span class='ident'>dimension</span>)
}
<span class='comment'>/*
* Repeat
*/</span>
<span class='doccomment'>/// Create an object by repeating a value.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Same as `Identity::new()`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>repeat</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>T</span>: <span class='ident'>Repeat</span><span class='op'><</span><span class='ident'>N</span><span class='op'>>></span>(<span class='ident'>val</span>: <span class='ident'>N</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='ident'>Repeat</span>::<span class='ident'>repeat</span>(<span class='ident'>val</span>)
}
<span class='comment'>/*
* Basis
*/</span>
<span class='doccomment'>/// Computes the canonical basis for a given dimension.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>canonical_basis</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Basis</span>, <span class='ident'>F</span>: <span class='ident'>FnMut</span>(<span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>bool</span><span class='op'>></span>(<span class='ident'>f</span>: <span class='ident'>F</span>) {
<span class='ident'>Basis</span>::<span class='ident'>canonical_basis</span>(<span class='ident'>f</span>)
}
<span class='doccomment'>/// Computes the basis of the orthonormal subspace of a given vector.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>orthonormal_subspace_basis</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Basis</span>, <span class='ident'>F</span>: <span class='ident'>FnMut</span>(<span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>bool</span><span class='op'>></span>(<span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>, <span class='ident'>f</span>: <span class='ident'>F</span>) {
<span class='ident'>Basis</span>::<span class='ident'>orthonormal_subspace_basis</span>(<span class='ident'>v</span>, <span class='ident'>f</span>)
}
<span class='doccomment'>/// Gets the (0-based) i-th element of the canonical basis of V.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>canonical_basis_element</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Basis</span><span class='op'>></span>(<span class='ident'>i</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='ident'>Basis</span>::<span class='ident'>canonical_basis_element</span>(<span class='ident'>i</span>)
}
<span class='comment'>/*
* Row<R>
*/</span>
<span class='comment'>/*
* Column<C>
*/</span>
<span class='comment'>/*
* Diagonal<V>
*/</span>
<span class='doccomment'>/// Gets the diagonal of a square matrix.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>diagonal</span><span class='op'><</span><span class='ident'>M</span>: <span class='ident'>Diagonal</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span>, <span class='ident'>V</span><span class='op'>></span>(<span class='ident'>m</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='ident'>V</span> {
<span class='ident'>m</span>.<span class='ident'>diagonal</span>()
}
<span class='comment'>/*
* Dimension
*/</span>
<span class='doccomment'>/// Gets the dimension an object lives in.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Same as `Dimension::dimension::(None::<V>)`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>dimension</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Dimension</span><span class='op'>></span>() <span class='op'>-></span> <span class='ident'>usize</span> {
<span class='ident'>Dimension</span>::<span class='ident'>dimension</span>(<span class='prelude-val'>None</span>::<span class='op'><</span><span class='ident'>V</span><span class='op'>></span>)
}
<span class='doccomment'>/// Gets the indexable range of an object.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>shape</span><span class='op'><</span><span class='ident'>V</span>: <span class='ident'>Shape</span><span class='op'><</span><span class='ident'>I</span><span class='op'>></span>, <span class='ident'>I</span><span class='op'>></span>(<span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>I</span> {
<span class='ident'>v</span>.<span class='ident'>shape</span>()
}
<span class='comment'>/*
* Cast<T>
*/</span>
<span class='doccomment'>/// Converts an object from one type to another.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// For primitive types, this is the same as the `as` keywords.</span>
<span class='doccomment'>/// The following properties are preserved by a cast:</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// * Type-level geometric invariants cannot be broken (eg. a cast from Rotation3<f64> to Rotation3<i64> is</span>
<span class='doccomment'>/// not possible)</span>
<span class='doccomment'>/// * A cast to a type with more type-level invariants cannot be done (eg. a cast from Matrix<f64> to</span>
<span class='doccomment'>/// Rotation3<f64> is not possible)</span>
<span class='doccomment'>/// * For primitive types an unbounded cast is done using the `as` keyword (this is different from</span>
<span class='doccomment'>/// the standard library which makes bound-checking to ensure eg. that a i64 is not out of the</span>
<span class='doccomment'>/// range of an i32 when a cast from i64 to i32 is done).</span>
<span class='doccomment'>/// * A cast does not affect the dimension of an algebraic object. Note that this prevents an</span>
<span class='doccomment'>/// isometric transform to be cast to a raw matrix. Use `to_homogeneous` for that special purpose.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>cast</span><span class='op'><</span><span class='ident'>T</span>, <span class='ident'>U</span>: <span class='ident'>Cast</span><span class='op'><</span><span class='ident'>T</span><span class='op'>>></span>(<span class='ident'>t</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='ident'>U</span> {
<span class='ident'>Cast</span>::<span class='ident'>from</span>(<span class='ident'>t</span>)
}
<span class='comment'>/*
* Indexable
*/</span>
</pre>
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