Linear algebra library with transformations and statically-sized or dynamically-sized matrices.

```
# Change Log
All notable changes to `nalgebra`, starting with the version 0.6.0 will be
documented here.
This project adheres to [Semantic Versioning](http://semver.org/).
## [0.13.0]
The **nalgebra-lapack** crate has been updated. This now includes a broad range
matrix decompositions using LAPACK bindings.
This adds support for serialization using the
[abomonation](https://crates.io/crates/abomonation) crate.
### Breaking semantic change
* The implementation of slicing with steps now matches the documentation.
Before, step identified the number to add to pass from one column/row index
to the next one. This made 0 step invalid. Now (and on the documentation so
far), the step is the number of ignored row/columns between each
row/column. Thus, a step of 0 means that no row/column is ignored. For
example, a step of, say, 3 on previous versions should now bet set to 2.
### Modified
* The trait `Axpy` has been replaced by a metod `.axpy`.
* The alias `MatrixNM` is now deprecated. Use `MatrixMN` instead (we
reordered M and N to be in alphabetical order).
* In-place componentwise multiplication and division
`.component_mul_mut(...)` and `.component_div_mut(...)` have bee deprecated
for a future renaming. Use `.component_mul_assign(...)` and
`.component_div_assign(...)` instead.
### Added
* `alga::general::Real` is now re-exported by nalgebra.
elements.)
* `::zeros(...)` that creates a matrix filled with zeroes.
* `::from_partial_diagonal(...)` that creates a matrix from diagonal elements.
The matrix can be rectangular. If not enough elements are provided, the rest
of the diagonal is set to 0.
* `.conjugate_transpose()` computes the transposed conjugate of a
complex matrix.
* `.conjugate_transpose_to(...)` computes the transposed conjugate of a
complex matrix. The result written into a user-provided matrix.
* `.transpose_to(...)` is the same as `.transpose()` but stores the result in
the provided matrix.
* `.conjugate_transpose_to(...)` is the same as `.conjugate_transpose()` but
stores the result in the provided matrix.
* Implements `IntoIterator` for `&Matrix`, `&mut Matrix` and `Matrix`.
* `.mul_to(...)` multiplies two matrices and stores the result to the given buffer.
* `.tr_mul_to(...)` left-multiplies `self.transpose()` to another matrix and stores the result to the given buffer.
* `.add_scalar(...)` that adds a scalar to each component of a matrix.
* `.add_scalar_mut(...)` that adds in-place a scalar to each component of a matrix.
* `.kronecker(a, b)` computes the kronecker product (i.e. matrix tensor
product) of two matrices.
* `.apply(f)` replaces each component of a matrix with the results of the
closure `f` called on each of them.
Pure Rust implementation of some Blas operations:
* `.iamax()` retuns the index of the maximum value of a vector.
* `.axpy(...)` computes `self = a * x + b * self`.
* `.gemv(...)` computes `self = alpha * a * x + beta * self` with a matrix and vector `a` and `x`.
* `.ger(...)` computes `self = alpha * x^t * y + beta * self` where `x` and `y` are vectors.
* `.gemm(...)` computes `self = alpha * a * b + beta * self` where `a` and `b` are matrices.
* `.gemv_symm(...)` is the same as `.gemv` except that `self` is assumed symmetric.
* `.ger_symm(...)` is the same as `.ger` except that `self` is assumed symmetric.
New slicing methods:
* `.rows_range(...)` that retrieves a reference to a range of rows.
* `.rows_range_mut(...)` that retrieves a mutable reference to a range of rows.
* `.columns_range(...)` that retrieves a reference to a range of columns.
* `.columns_range_mut(...)` that retrieves a mutable reference to a range of columns.
Matrix decompositions implemented in pure Rust:
* Cholesky, SVD, LU, QR, Hessenberg, Schur, Symmetric eigendecompositions,
Bidiagonal, Symmetric tridiagonal
* Computation of householder reflectors and givens rotations.
Matrix edition:
* `.upper_triangle()` extracts the upper triangle of a matrix, including the diagonal.
* `.lower_triangle()` extracts the lower triangle of a matrix, including the diagonal.
* `.fill(...)` fills the matrix with a single value.
* `.fill_with_identity(...)` fills the matrix with the identity.
* `.fill_diagonal(...)` fills the matrix diagonal with a single value.
* `.fill_row(...)` fills a selected matrix row with a single value.
* `.fill_column(...)` fills a selected matrix column with a single value.
* `.set_diagonal(...)` sets the matrix diagonal.
* `.set_row(...)` sets a selected row.
* `.set_column(...)` sets a selected column.
* `.fill_lower_triangle(...)` fills some sub-diagonals bellow the main diagonal with a value.
* `.fill_upper_triangle(...)` fills some sub-diagonals above the main diagonal with a value.
* `.swap_rows(...)` swaps two rows.
* `.swap_columns(...)` swaps two columns.
Column removal:
* `.remove_column(...)` removes one column.
* `.remove_fixed_columns<D>(...)` removes `D` columns.
* `.remove_columns(...)` removes a number of columns known at run-time.
Row removal:
* `.remove_row(...)` removes one row.
* `.remove_fixed_rows<D>(...)` removes `D` rows.
* `.remove_rows(...)` removes a number of rows known at run-time.
Column insertion:
* `.insert_column(...)` adds one column at the given position.
* `.insert_fixed_columns<D>(...)` adds `D` columns at the given position.
* `.insert_columns(...)` adds at the given position a number of columns known at run-time.
Row insertion:
* `.insert_row(...)` adds one row at the given position.
* `.insert_fixed_rows<D>(...)` adds `D` rows at the given position.
* `.insert_rows(...)` adds at the given position a number of rows known at run-time.
## [0.12.0]
The main change of this release is the update of the dependency serde to 1.0.
### Added
* `.trace()` that computes the trace of a matrix (the sum of its diagonal
elements.)
## [0.11.0]
The [website](http://nalgebra.org) has been fully rewritten and gives a good
overview of all the added/modified features.
This version is a major rewrite of the library. Major changes are:
* Algebraic traits are now defined by the [alga](https://crates.io/crates/alga) crate.
All other mathematical traits, except `Axpy` have been removed from
**nalgebra**.
* Methods are now preferred to free functions because they do not require any
trait to be used any more.
* Most algebraic entities can be parametrized by type-level integers
to specify their dimensions. Using `Dynamic` instead of a type-level
integer indicates that the dimension known at run-time only.
* Statically-sized **rectangular** matrices.
* More transformation types have been added: unit-sized complex numbers (for
2D rotations), affine/projective/general transformations with `Affine2/3`,
`Projective2/3`, and `Transform2/3`.
* Serde serialization is now supported instead of `rustc_serialize`. Enable
it with the `serde-serialize` feature.
* Matrix **slices** are now implemented.
### Added
Lots of features including rectangular matrices, slices, and Serde
serialization. Refer to the brand new [website](http://nalgebra.org) for more
details. The following free-functions have been added as well:
* `::id()` that returns the universal [identity element](http://nalgebra.org/performance_tricks/#the-id-type)
of type `Id`.
* `::inf_sup()` that returns both the infimum and supremum of a value at the
same time.
* `::partial_sort2()` that attempts to sort two values in increasing order.
* `::wrap()` that moves a value to the given interval by adding or removing
the interval width to it.
### Modified
* `::cast` -> `::convert`
* `point.as_vector()` -> `point.coords`
* `na::origin` -> `P::origin()`
* `na::is_zero` -> `.is_zero()` (from num::Zero)
* `.transform` -> `.transform_point`/`.transform_vector`
* `.translate` -> `.translate_point`
* `::dimension::<P>` -> `::dimension::<P::Vector>`
* `::angle_between` -> `::angle`
Componentwise multiplication and division has been replaced by methods:
* multiplication -> `.componentwise_mul`, `.componentwise_mul_mut`.
* division -> `.componentwise_div`, `.componentwise_div_mut`.
The following free-functions are now replaced by methods (with the same names)
only:
`::cross`, `::cholesky`, `::determinant`, `::diagonal`, `::eigen_qr` (becomes
`.eig`), `::hessenberg`, `::qr`, `::to_homogeneous`, `::to_rotation_matrix`,
`::transpose`, `::shape`.
The following free-functions are now replaced by static methods only:
* `::householder_matrix` under the name `::new_householder_generic`
* `::identity`
* `::new_identity` under the name `::identity`
* `::from_homogeneous`
* `::repeat` under the name `::from_element`
The following free-function are now replaced methods accessible through traits
only:
* `::transform` -> methods `.transform_point` and `.transform_vector` of the `alga::linear::Transformation` trait.
* `::inverse_transform` -> methods `.inverse_transform_point` and
`.inverse_transform_vector` of the `alga::linear::ProjectiveTransformation`
trait.
* `::translate`, `::inverse_translate`, `::rotate`, `::inverse_rotate` ->
methods from the `alga::linear::Similarity` trait instead. Those have the
same names but end with `_point` or `_vector`, e.g., `.translate_point` and
`.translate_vector`.
* `::orthonormal_subspace_basis` -> method with the same name from
`alga::linear::FiniteDimInnerSpace`.
* `::canonical_basis_element` and `::canonical_basis` -> methods with the
same names from `alga::linear::FiniteDimVectorSpace`.
* `::rotation_between` -> method with the same name from the
`alga::linear::Rotation` trait.
* `::is_zero` -> method with the same name from `num::Zero`.
### Removed
* The free functions `::prepend_rotation`, `::append_rotation`,
`::append_rotation_wrt_center`, `::append_rotation_wrt_point`,
`::append_transformation`, and `::append_translation ` have been removed.
Instead create the rotation or translation object explicitly and use
multiplication to compose it with anything else.
* The free function `::outer` has been removed. Use column-vector ×
row-vector multiplication instead.
* `::approx_eq`, `::approx_eq_eps` have been removed. Use the `relative_eq!`
macro from the [approx](https://crates.io/crates/approx) crate instead.
* `::covariance` has been removed. There is no replacement for now.
* `::mean` has been removed. There is no replacement for now.
* `::sample_sphere` has been removed. There is no replacement for now.
* `::cross_matrix` has been removed. There is no replacement for now.
* `::absolute_rotate` has been removed. There is no replacement for now.
* `::rotation`, `::transformation`, `::translation`, `::inverse_rotation`,
`::inverse_transformation`, `::inverse_translation` have been removed. Use
the appropriate methods/field of each transformation type, e.g.,
`rotation.angle()` and `rotation.axis()`.
## [0.10.0]
### Added
Binary operations are now allowed between references as well. For example
`Vector3<f32> + &Vector3<f32>` is now possible.
### Modified
Removed unused parameters to methods from the `ApproxEq` trait. Those were
required before rust 1.0 to help type inference. The are not needed any more
since it now allowed to write for a type `T` that implements `ApproxEq`:
`<T as ApproxEq>::approx_epsilon()`. This replaces the old form:
`ApproxEq::approx_epsilon(None::<T>)`.
## [0.9.0]
### Modified
* Renamed:
- `::from_col_vector` -> `::from_column_vector`
- `::from_col_iter` -> `::from_column_iter`
- `.col_slice` -> `.column_slice`
- `.set_col` -> `.set_column`
- `::canonical_basis_with_dim` -> `::canonical_basis_with_dimension`
- `::from_elem` -> `::from_element`
- `DiagMut` -> `DiagonalMut`
- `UnitQuaternion::new` becomes `UnitQuaternion::from_scaled_axis` or
`UnitQuaternion::from_axisangle`. The new `::new` method now requires a
not-normalized quaternion.
Methods names starting with `new_with_` now start with `from_`. This is more
idiomatic in Rust.
The `Norm` trait now uses an associated type instead of a type parameter.
Other similar trait changes are to be expected in the future, e.g., for the
`Diagonal` trait.
Methods marked `unsafe` for reasons unrelated to memory safety are no
longer unsafe. Instead, their name end with `_unchecked`. In particular:
* `Rotation3::new_with_matrix` -> `Rotation3::from_matrix_unchecked`
* `PerspectiveMatrix3::new_with_matrix` -> `PerspectiveMatrix3::from_matrix_unchecked`
* `OrthographicMatrix3::new_with_matrix` -> `OrthographicMatrix3::from_matrix_unchecked`
### Added
- A `Unit<T>` type that wraps normalized values. In particular,
`UnitQuaternion<N>` is now an alias for `Unit<Quaternion<N>>`.
- `.ln()`, `.exp()` and `.powf(..)` for quaternions and unit quaternions.
- `::from_parts(...)` to build a quaternion from its scalar and vector
parts.
- The `Norm` trait now has a `try_normalize()` that returns `None` if the
norm is too small.
- The `BaseFloat` and `FloatVector` traits now inherit from `ApproxEq` as
well. It is clear that performing computations with floats requires
approximate equality.
Still WIP: add implementations of abstract algebra traits from the `algebra`
crate for vectors, rotations and points. To enable them, activate the
`abstract_algebra` feature.
## [0.8.0]
### Modified
* Almost everything (types, methods, and traits) now use full names instead
of abbreviations (e.g. `Vec3` becomes `Vector3`). Most changes are abvious.
Note however that:
- `::sqnorm` becomes `::norm_squared`.
- `::sqdist` becomes `::distance_squared`.
- `::abs`, `::min`, etc. did not change as this is a common name for
absolute values on, e.g., the libc.
- Dynamically sized structures keep the `D` prefix, e.g., `DMat` becomes
`DMatrix`.
* All files with abbreviated names have been renamed to their full version,
e.g., `vec.rs` becomes `vector.rs`.
## [0.7.0]
### Added
* Added implementation of assignement operators (+=, -=, etc.) for
everything.
### Modified
* Points and vectors are now linked to each other with associated types
(on the PointAsVector trait).
## [0.6.0]
**Announcement:** a users forum has been created for `nalgebra`, `ncollide`, and `nphysics`. See
you [there](http://users.nphysics.org)!
### Added
* Added a dependency to [generic-array](https://crates.io/crates/generic-array). Feature-gated:
requires `features="generic_sizes"`.
* Added statically sized vectors with user-defined sizes: `VectorN`. Feature-gated: requires
`features="generic_sizes"`.
* Added similarity transformations (an uniform scale followed by a rotation followed by a
translation): `Similarity2`, `Similarity3`.
### Removed
* Removed zero-sized elements `Vector0`, `Point0`.
* Removed 4-dimensional transformations `Rotation4` and `Isometry4` (which had an implementation to incomplete to be useful).
### Modified
* Vectors are now multipliable with isometries. This will result into a pure rotation (this is how
vectors differ from point semantically: they design directions so they are not translatable).
* `{Isometry3, Rotation3}::look_at` reimplemented and renamed to `::look_at_rh` and `::look_at_lh` to agree
with the computer graphics community (in particular, the GLM library). Use the `::look_at_rh`
variant to build a view matrix that
may be successfully used with `Persp` and `Ortho`.
* The old `{Isometry3, Rotation3}::look_at` implementations are now called `::new_observer_frame`.
* Rename every `fov` on `Persp` to `fovy`.
* Fixed the perspective and orthographic projection matrices.
```