nalgebra/src/lib.rs
2016-08-29 21:16:15 +02:00

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/*!
# nalgebra
**nalgebra** is a low-dimensional 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](http://www.rust-lang.org)
and the official package manager: [cargo](https://github.com/rust-lang/cargo).
Simply add the following to your `Cargo.toml` file:
```
[dependencies]
nalgebra = "0.10.*"
```
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`, `Unit<Quaternion>`.
* Unit-sized values (unit vectors, unit quaternions, etc.): `Unit<T>`, e.g., `Unit<Vector3<f32>>`.
* Isometries (translation rotation): `Isometry2`, `Isometry3`
* Similarity transformations (translation rotation uniform scale): `Similarity2`, `Similarity3`.
* 3D projections for computer graphics: `Persp3`, `PerspMatrix3`, `Ortho3`, `OrthoMatrix3`.
* 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.
*/
#![deny(non_camel_case_types)]
#![deny(unused_parens)]
#![deny(non_upper_case_globals)]
#![deny(unused_qualifications)]
#![deny(unused_results)]
#![warn(missing_docs)]
#![doc(html_root_url = "http://nalgebra.org/doc")]
extern crate rustc_serialize;
extern crate rand;
extern crate num;
#[cfg(feature="generic_sizes")]
extern crate generic_array;
#[cfg(feature="arbitrary")]
extern crate quickcheck;
#[cfg(feature="abstract_algebra")]
extern crate algebra;
use std::cmp;
use std::ops::{Neg, Mul};
use num::{Zero, One};
pub use traits::{
Absolute,
AbsoluteRotate,
ApproxEq,
Axpy,
Basis,
BaseFloat,
BaseNum,
Bounded,
Cast,
Column,
ColumnSlice, RowSlice,
Covariance,
Cross,
CrossMatrix,
Determinant,
Diagonal,
Dimension,
Dot,
EigenQR,
Eye,
FloatPoint,
FloatVector,
FromHomogeneous,
Indexable,
Inverse,
Iterable,
IterableMut,
Matrix,
Mean,
Norm,
NumPoint,
NumVector,
Origin,
Outer,
PartialOrder,
PartialOrdering,
PointAsVector,
Repeat,
Rotate, Rotation, RotationMatrix, RotationWithTranslation, RotationTo,
Row,
Shape,
SquareMatrix,
ToHomogeneous,
Transform, Transformation,
Translate, Translation,
Transpose,
UniformSphereSample
};
#[cfg(feature="generic_sizes")]
pub use structs::VectorN;
pub use structs::{
Identity,
DMatrix, DMatrix1, DMatrix2, DMatrix3, DMatrix4, DMatrix5, DMatrix6,
DVector, DVector1, DVector2, DVector3, DVector4, DVector5, DVector6,
Isometry2, Isometry3,
Similarity2, Similarity3,
Matrix1, Matrix2, Matrix3, Matrix4,
Matrix5, Matrix6,
Rotation2, Rotation3,
Vector1, Vector2, Vector3, Vector4, Vector5, Vector6,
Point1, Point2, Point3, Point4, Point5, Point6,
Perspective3, PerspectiveMatrix3,
Orthographic3, OrthographicMatrix3,
Quaternion, UnitQuaternion,
Unit
};
pub use linalg::{
qr,
householder_matrix,
cholesky,
hessenberg
};
mod structs;
mod traits;
mod linalg;
mod macros;
// mod lower_triangular;
// mod chol;
/// Change the input value to ensure it is on the range `[min, max]`.
#[inline]
pub fn clamp<T: PartialOrd>(val: T, min: T, max: T) -> T {
if val > min {
if val < max {
val
}
else {
max
}
}
else {
min
}
}
/// Same as `cmp::max`.
#[inline]
pub fn max<T: Ord>(a: T, b: T) -> T {
cmp::max(a, b)
}
/// Same as `cmp::min`.
#[inline]
pub fn min<T: Ord>(a: T, b: T) -> T {
cmp::min(a, b)
}
/// Returns the infimum of `a` and `b`.
#[inline]
pub fn inf<T: PartialOrder>(a: &T, b: &T) -> T {
PartialOrder::inf(a, b)
}
/// Returns the supremum of `a` and `b`.
#[inline]
pub fn sup<T: PartialOrder>(a: &T, b: &T) -> T {
PartialOrder::sup(a, b)
}
/// Compare `a` and `b` using a partial ordering relation.
#[inline]
pub fn partial_cmp<T: PartialOrder>(a: &T, b: &T) -> PartialOrdering {
PartialOrder::partial_cmp(a, b)
}
/// Returns `true` iff `a` and `b` are comparable and `a < b`.
#[inline]
pub fn partial_lt<T: PartialOrder>(a: &T, b: &T) -> bool {
PartialOrder::partial_lt(a, b)
}
/// Returns `true` iff `a` and `b` are comparable and `a <= b`.
#[inline]
pub fn partial_le<T: PartialOrder>(a: &T, b: &T) -> bool {
PartialOrder::partial_le(a, b)
}
/// Returns `true` iff `a` and `b` are comparable and `a > b`.
#[inline]
pub fn partial_gt<T: PartialOrder>(a: &T, b: &T) -> bool {
PartialOrder::partial_gt(a, b)
}
/// Returns `true` iff `a` and `b` are comparable and `a >= b`.
#[inline]
pub fn partial_ge<T: PartialOrder>(a: &T, b: &T) -> bool {
PartialOrder::partial_ge(a, b)
}
/// Return the minimum of `a` and `b` if they are comparable.
#[inline]
pub fn partial_min<'a, T: PartialOrder>(a: &'a T, b: &'a T) -> Option<&'a T> {
PartialOrder::partial_min(a, b)
}
/// Return the maximum of `a` and `b` if they are comparable.
#[inline]
pub fn partial_max<'a, T: PartialOrder>(a: &'a T, b: &'a T) -> Option<&'a T> {
PartialOrder::partial_max(a, b)
}
/// Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to
/// `min` or `max`.
#[inline]
pub fn partial_clamp<'a, T: PartialOrder>(value: &'a T, min: &'a T, max: &'a T) -> Option<&'a T> {
PartialOrder::partial_clamp(value, min, max)
}
//
//
// Constructors
//
//
/// Create a special identity object.
///
/// Same as `Identity::new()`.
#[inline]
pub fn identity() -> Identity {
Identity::new()
}
/// Create a zero-valued value.
///
/// This is the same as `std::num::zero()`.
#[inline]
pub fn zero<T: Zero>() -> T {
Zero::zero()
}
/// Tests is a value is iqual to zero.
#[inline]
pub fn is_zero<T: Zero>(val: &T) -> bool {
val.is_zero()
}
/// Create a one-valued value.
///
/// This is the same as `std::num::one()`.
#[inline]
pub fn one<T: One>() -> T {
One::one()
}
//
//
// Geometry
//
//
/// Returns the trivial origin of an affine space.
#[inline]
pub fn origin<P: Origin>() -> P {
Origin::origin()
}
/// Returns the center of two points.
#[inline]
pub fn center<N: BaseFloat, P: FloatPoint<N>>(a: &P, b: &P) -> P
where <P as PointAsVector>::Vector: Norm<NormType = N> {
(*a + b.to_vector()) / ::cast(2.0)
}
/*
* FloatPoint
*/
/// Returns the distance between two points.
#[inline]
pub fn distance<N: BaseFloat, P: FloatPoint<N>>(a: &P, b: &P) -> N where <P as PointAsVector>::Vector: Norm<NormType = N> {
a.distance(b)
}
/// Returns the squared distance between two points.
#[inline]
pub fn distance_squared<N: BaseFloat, P: FloatPoint<N>>(a: &P, b: &P) -> N
where <P as PointAsVector>::Vector: Norm<NormType = N> {
a.distance_squared(b)
}
/*
* Translation<V>
*/
/// Gets the translation applicable by `m`.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{Vector3, Isometry3};
///
/// fn main() {
/// let t = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());
/// let trans = na::translation(&t);
///
/// assert!(trans == Vector3::new(1.0, 1.0, 1.0));
/// }
/// ```
#[inline]
pub fn translation<V, M: Translation<V>>(m: &M) -> V {
m.translation()
}
/// Gets the inverse translation applicable by `m`.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{Vector3, Isometry3};
///
/// fn main() {
/// let t = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());
/// let itrans = na::inverse_translation(&t);
///
/// assert!(itrans == Vector3::new(-1.0, -1.0, -1.0));
/// }
/// ```
#[inline]
pub fn inverse_translation<V, M: Translation<V>>(m: &M) -> V {
m.inverse_translation()
}
/// Applies the translation `v` to a copy of `m`.
#[inline]
pub fn append_translation<V, M: Translation<V>>(m: &M, v: &V) -> M {
Translation::append_translation(m, v)
}
/*
* Translate<P>
*/
/// Applies a translation to a point.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{Point3, Vector3, Isometry3};
///
/// fn main() {
/// let t = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());
/// let p = Point3::new(2.0, 2.0, 2.0);
///
/// let tp = na::translate(&t, &p);
///
/// assert!(tp == Point3::new(3.0, 3.0, 3.0))
/// }
/// ```
#[inline]
pub fn translate<P, M: Translate<P>>(m: &M, p: &P) -> P {
m.translate(p)
}
/// Applies an inverse translation to a point.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{Point3, Vector3, Isometry3};
///
/// fn main() {
/// let t = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());
/// let p = Point3::new(2.0, 2.0, 2.0);
///
/// let tp = na::inverse_translate(&t, &p);
///
/// assert!(na::approx_eq(&tp, &Point3::new(1.0, 1.0, 1.0)))
/// }
#[inline]
pub fn inverse_translate<P, M: Translate<P>>(m: &M, p: &P) -> P {
m.inverse_translate(p)
}
/*
* Rotation<V>
*/
/// Gets the rotation applicable by `m`.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{Vector3, Rotation3};
///
/// fn main() {
/// let t = Rotation3::new(Vector3::new(1.0f64, 1.0, 1.0));
///
/// assert!(na::approx_eq(&na::rotation(&t), &Vector3::new(1.0, 1.0, 1.0)));
/// }
/// ```
#[inline]
pub fn rotation<V, M: Rotation<V>>(m: &M) -> V {
m.rotation()
}
/// Gets the inverse rotation applicable by `m`.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{Vector3, Rotation3};
///
/// fn main() {
/// let t = Rotation3::new(Vector3::new(1.0f64, 1.0, 1.0));
///
/// assert!(na::approx_eq(&na::inverse_rotation(&t), &Vector3::new(-1.0, -1.0, -1.0)));
/// }
/// ```
#[inline]
pub fn inverse_rotation<V, M: Rotation<V>>(m: &M) -> V {
m.inverse_rotation()
}
// FIXME: this example is a bit shity
/// Applies the rotation `v` to a copy of `m`.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{Vector3, Rotation3};
///
/// fn main() {
/// let t = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.0));
/// let v = Vector3::new(1.0, 1.0, 1.0);
/// let rt = na::append_rotation(&t, &v);
///
/// assert!(na::approx_eq(&na::rotation(&rt), &Vector3::new(1.0, 1.0, 1.0)))
/// }
/// ```
#[inline]
pub fn append_rotation<V, M: Rotation<V>>(m: &M, v: &V) -> M {
Rotation::append_rotation(m, v)
}
// FIXME: this example is a bit shity
/// Pre-applies the rotation `v` to a copy of `m`.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{Vector3, Rotation3};
///
/// fn main() {
/// let t = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.0));
/// let v = Vector3::new(1.0, 1.0, 1.0);
/// let rt = na::prepend_rotation(&t, &v);
///
/// assert!(na::approx_eq(&na::rotation(&rt), &Vector3::new(1.0, 1.0, 1.0)))
/// }
/// ```
#[inline]
pub fn prepend_rotation<V, M: Rotation<V>>(m: &M, v: &V) -> M {
Rotation::prepend_rotation(m, v)
}
/*
* Rotate<V>
*/
/// Applies a rotation to a vector.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{BaseFloat, Rotation3, Vector3};
///
/// fn main() {
/// let t = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));
/// let v = Vector3::new(1.0, 0.0, 0.0);
///
/// let tv = na::rotate(&t, &v);
///
/// assert!(na::approx_eq(&tv, &Vector3::new(0.0, 1.0, 0.0)))
/// }
/// ```
#[inline]
pub fn rotate<V, M: Rotate<V>>(m: &M, v: &V) -> V {
m.rotate(v)
}
/// Applies an inverse rotation to a vector.
///
/// ```rust
/// extern crate nalgebra as na;
/// use na::{BaseFloat, Rotation3, Vector3};
///
/// fn main() {
/// let t = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));
/// let v = Vector3::new(1.0, 0.0, 0.0);
///
/// let tv = na::inverse_rotate(&t, &v);
///
/// assert!(na::approx_eq(&tv, &Vector3::new(0.0, -1.0, 0.0)))
/// }
/// ```
#[inline]
pub fn inverse_rotate<V, M: Rotate<V>>(m: &M, v: &V) -> V {
m.inverse_rotate(v)
}
/*
* RotationWithTranslation<LV, AV>
*/
/// Rotates a copy of `m` by `amount` using `center` as the pivot point.
#[inline]
pub fn append_rotation_wrt_point<LV: Neg<Output = LV> + Copy,
AV,
M: RotationWithTranslation<LV, AV>>(
m: &M,
amount: &AV,
center: &LV) -> M {
RotationWithTranslation::append_rotation_wrt_point(m, amount, center)
}
/// Rotates a copy of `m` by `amount` using `m.translation()` as the pivot point.
#[inline]
pub fn append_rotation_wrt_center<LV: Neg<Output = LV> + Copy,
AV,
M: RotationWithTranslation<LV, AV>>(
m: &M,
amount: &AV) -> M {
RotationWithTranslation::append_rotation_wrt_center(m, amount)
}
/*
* RotationTo
*/
/// Computes the angle of the rotation needed to transfom `a` to `b`.
#[inline]
pub fn angle_between<V: RotationTo>(a: &V, b: &V) -> V::AngleType {
a.angle_to(b)
}
/// Computes the rotation needed to transform `a` to `b`.
#[inline]
pub fn rotation_between<V: RotationTo>(a: &V, b: &V) -> V::DeltaRotationType {
a.rotation_to(b)
}
/*
* RotationMatrix<LV, AV, R>
*/
/// Builds a rotation matrix from `r`.
#[inline]
pub fn to_rotation_matrix<N, LV, AV, R, M>(r: &R) -> M
where R: RotationMatrix<N, LV, AV, Output = M>,
M: SquareMatrix<N, LV> + Rotation<AV> + Copy,
LV: Mul<M, Output = LV>
{
// FIXME: rust-lang/rust#20413
r.to_rotation_matrix()
}
/*
* AbsoluteRotate<V>
*/
/// Applies a rotation using the absolute values of its components.
#[inline]
pub fn absolute_rotate<V, M: AbsoluteRotate<V>>(m: &M, v: &V) -> V {
m.absolute_rotate(v)
}
/*
* Transformation<T>
*/
/// Gets the transformation applicable by `m`.
#[inline]
pub fn transformation<T, M: Transformation<T>>(m: &M) -> T {
m.transformation()
}
/// Gets the inverse transformation applicable by `m`.
#[inline]
pub fn inverse_transformation<T, M: Transformation<T>>(m: &M) -> T {
m.inverse_transformation()
}
/// Gets a transformed copy of `m`.
#[inline]
pub fn append_transformation<T, M: Transformation<T>>(m: &M, t: &T) -> M {
Transformation::append_transformation(m, t)
}
/*
* Transform<V>
*/
/// Applies a transformation to a vector.
#[inline]
pub fn transform<V, M: Transform<V>>(m: &M, v: &V) -> V {
m.transform(v)
}
/// Applies an inverse transformation to a vector.
#[inline]
pub fn inverse_transform<V, M: Transform<V>>(m: &M, v: &V) -> V {
m.inverse_transform(v)
}
/*
* Dot<N>
*/
/// Computes the dot product of two vectors.
#[inline]
pub fn dot<V: Dot<N>, N>(a: &V, b: &V) -> N {
Dot::dot(a, b)
}
/*
* Norm<N>
*/
/// Computes the L2 norm of a vector.
#[inline]
pub fn norm<V: Norm>(v: &V) -> V::NormType {
Norm::norm(v)
}
/// Computes the squared L2 norm of a vector.
#[inline]
pub fn norm_squared<V: Norm>(v: &V) -> V::NormType {
Norm::norm_squared(v)
}
/// Gets the normalized version of a vector.
#[inline]
pub fn normalize<V: Norm>(v: &V) -> V {
Norm::normalize(v)
}
/// Gets the normalized version of a vector or `None` if its norm is smaller than `min_norm`.
#[inline]
pub fn try_normalize<V: Norm>(v: &V, min_norm: V::NormType) -> Option<V> {
Norm::try_normalize(v, min_norm)
}
/*
* Determinant<N>
*/
/// Computes the determinant of a square matrix.
#[inline]
pub fn determinant<M: Determinant<N>, N>(m: &M) -> N {
Determinant::determinant(m)
}
/*
* Cross<V>
*/
/// Computes the cross product of two vectors.
#[inline]
pub fn cross<LV: Cross>(a: &LV, b: &LV) -> LV::CrossProductType {
Cross::cross(a, b)
}
/*
* CrossMatrix<M>
*/
/// Given a vector, computes the matrix which, when multiplied by another vector, computes a cross
/// product.
#[inline]
pub fn cross_matrix<V: CrossMatrix<M>, M>(v: &V) -> M {
CrossMatrix::cross_matrix(v)
}
/*
* ToHomogeneous<U>
*/
/// Converts a matrix or vector to homogeneous coordinates.
#[inline]
pub fn to_homogeneous<M: ToHomogeneous<Res>, Res>(m: &M) -> Res {
ToHomogeneous::to_homogeneous(m)
}
/*
* FromHomogeneous<U>
*/
/// Converts a matrix or vector from homogeneous coordinates.
///
/// w-normalization is appied.
#[inline]
pub fn from_homogeneous<M, Res: FromHomogeneous<M>>(m: &M) -> Res {
FromHomogeneous::from(m)
}
/*
* UniformSphereSample
*/
/// Samples the unit sphere living on the dimension as the samples types.
///
/// The number of sampling point is implementation-specific. It is always uniform.
#[inline]
pub fn sample_sphere<V: UniformSphereSample, F: FnMut(V)>(f: F) {
UniformSphereSample::sample(f)
}
//
//
// Operations
//
//
/*
* AproxEq<N>
*/
/// Tests approximate equality.
#[inline]
pub fn approx_eq<T: ApproxEq<N>, N>(a: &T, b: &T) -> bool {
ApproxEq::approx_eq(a, b)
}
/// Tests approximate equality using a custom epsilon.
#[inline]
pub fn approx_eq_eps<T: ApproxEq<N>, N>(a: &T, b: &T, eps: &N) -> bool {
ApproxEq::approx_eq_eps(a, b, eps)
}
/*
* Absolute<A>
*/
/// Computes a component-wise absolute value.
#[inline]
pub fn abs<M: Absolute<Res>, Res>(m: &M) -> Res {
Absolute::abs(m)
}
/*
* Inverse
*/
/// Gets an inverted copy of a matrix.
#[inline]
pub fn inverse<M: Inverse>(m: &M) -> Option<M> {
Inverse::inverse(m)
}
/*
* Transpose
*/
/// Gets a transposed copy of a matrix.
#[inline]
pub fn transpose<M: Transpose>(m: &M) -> M {
Transpose::transpose(m)
}
/*
* Outer<M>
*/
/// Computes the outer product of two vectors.
#[inline]
pub fn outer<V: Outer>(a: &V, b: &V) -> V::OuterProductType {
Outer::outer(a, b)
}
/*
* Covariance<M>
*/
/// Computes the covariance of a set of observations.
#[inline]
pub fn covariance<M: Covariance<Res>, Res>(observations: &M) -> Res {
Covariance::covariance(observations)
}
/*
* Mean<N>
*/
/// Computes the mean of a set of observations.
#[inline]
pub fn mean<N, M: Mean<N>>(observations: &M) -> N {
Mean::mean(observations)
}
/*
* EigenQR<N, V>
*/
/// Computes the eigenvalues and eigenvectors of a square matrix usin the QR algorithm.
#[inline]
pub fn eigen_qr<N, V, M>(m: &M, eps: &N, niter: usize) -> (M, V)
where V: Mul<M, Output = V>,
M: EigenQR<N, V> {
EigenQR::eigen_qr(m, eps, niter)
}
//
//
// Structure
//
//
/*
* Eye
*/
/// Construct the identity matrix for a given dimension
#[inline]
pub fn new_identity<M: Eye>(dimension: usize) -> M {
Eye::new_identity(dimension)
}
/*
* Repeat
*/
/// Create an object by repeating a value.
///
/// Same as `Identity::new()`.
#[inline]
pub fn repeat<N, T: Repeat<N>>(val: N) -> T {
Repeat::repeat(val)
}
/*
* Basis
*/
/// Computes the canonical basis for a given dimension.
#[inline]
pub fn canonical_basis<V: Basis, F: FnMut(V) -> bool>(f: F) {
Basis::canonical_basis(f)
}
/// Computes the basis of the orthonormal subspace of a given vector.
#[inline]
pub fn orthonormal_subspace_basis<V: Basis, F: FnMut(V) -> bool>(v: &V, f: F) {
Basis::orthonormal_subspace_basis(v, f)
}
/// Gets the (0-based) i-th element of the canonical basis of V.
#[inline]
pub fn canonical_basis_element<V: Basis>(i: usize) -> Option<V> {
Basis::canonical_basis_element(i)
}
/*
* Row<R>
*/
/*
* Column<C>
*/
/*
* Diagonal<V>
*/
/// Gets the diagonal of a square matrix.
#[inline]
pub fn diagonal<M: Diagonal<V>, V>(m: &M) -> V {
m.diagonal()
}
/*
* Dimension
*/
/// Gets the dimension an object lives in.
///
/// Same as `Dimension::dimension::(None::<V>)`.
#[inline]
pub fn dimension<V: Dimension>() -> usize {
Dimension::dimension(None::<V>)
}
/// Gets the indexable range of an object.
#[inline]
pub fn shape<V: Shape<I>, I>(v: &V) -> I {
v.shape()
}
/*
* Cast<T>
*/
/// Converts an object from one type to another.
///
/// For primitive types, this is the same as the `as` keywords.
/// The following properties are preserved by a cast:
///
/// * Type-level geometric invariants cannot be broken (eg. a cast from Rotation3<f64> to Rotation3<i64> is
/// not possible)
/// * A cast to a type with more type-level invariants cannot be done (eg. a cast from Matrix<f64> to
/// Rotation3<f64> is not possible)
/// * For primitive types an unbounded cast is done using the `as` keyword (this is different from
/// the standard library which makes bound-checking to ensure eg. that a i64 is not out of the
/// range of an i32 when a cast from i64 to i32 is done).
/// * A cast does not affect the dimension of an algebraic object. Note that this prevents an
/// isometric transform to be cast to a raw matrix. Use `to_homogeneous` for that special purpose.
#[inline]
pub fn cast<T, U: Cast<T>>(t: T) -> U {
Cast::from(t)
}
/*
* Indexable
*/