nalgebra/CHANGELOG.md

# Change Log
All notable changes to `nalgebra`, starting with the version 0.6.0 will be
documented here.

This project adheres to [Semantic Versioning](https://semver.org/).

## [0.27.0]
This removes the `convert-glam` and `convert-glam-unchecked` optional features.
Instead, this adds the `convert-glam013`, `convert-glam014`, and `convert-glam015` optional features for
conversions targeting the versions 0.13, 0.14, and 0.15 of `glam`.

### Added
- Add macros `matrix!`, `dmatrix!`, `vector!`, `dvector!`, `point!` for constructing matrices/vectors/points in a
  more convenient way. See [#886](https://github.com/dimforge/nalgebra/pull/886) and [#899](https://github.com/dimforge/nalgebra/pull/899).
- Add `CooMatrix::reserve` to `nalgebra-sparse`.  
- Add basic support for serialization using `rkyv`. Can be enabled with the features `rkyv-serialize` or
  `rkyv-serialize-no-std`.


### Fixed
- Fixed a potential unsoundness issue after deserializing an invalid `DVector` using `serde`.

## [0.26.2]
### Added
- Conversion from an array `[T; D]` to an isometry `Isometry<T, _, D>` (as a translation).
- Conversion from a static vector `SVector<T; D>` to an isometry `Isometry<T, _, D>` (as a translation).
- Conversion from a point `Point<T; D>` to an isometry `Isometry<T, _, D>` (as a translation).
- Conversion of an array `[T; D]` from/to a translation `Translation<T, D>`.
- Conversion of a point `Point<T, D>` to a translation `Translation<T, D>`.
- Conversion of the tuple of glam types `(Vec3, Quat)` from/to an `Isometry2` or `Isometry3`.
- Conversion of a glam type `Vec2/3/4` from/to a `Translation2/3/4`.

## [0.26.1]
Fix a regression introduced in 0.26.0 preventing `DVector` from being serialized with `serde`.

## [0.26.0]
This releases integrates `min-const-generics` to nalgebra. See
[our blog post](https://www.dimforge.com/blog/2021/04/12/integrating-const-generics-to-nalgebra)
for details about this release.

### Added
- Add type aliases for unit vector, e.g., `UnitVector3`.
- Add a `pow` and `pow_mut` function to square matrices.
- Add `Cholesky::determinant` to compute the determinant of a matrix decomposed
  with Cholesky.
- Add the `serde-serialize-no-std` feature to enable serialization of static matrices/vectors
  with serde, but without requiring `std`.
  

### Modified
- The `serde` crate isn't enabled by default now. Enable the `serde-serialize` or the
  `serde-serialize-no-std` features instead.
- The `Const<const D: usize>` type has been introduced to represent dimensions known
  at compile-time. This replaces the type-level integers from `typenum` as well as
  the `U1, U2, ..., U127` types from `nalgebra`. These `U1, U2, ..., U127` are now
  just aliases for `Const<D>`, e.g., `type U2 = Const<2>`.
- The `ArrayStorage` now uses a standard array `[[T; R]; C]` instead of a `GenericArray`.
- Many trait bounds were changed to accommodate const-generics. Most of these changes
  should be transparent wrt. non-generic code.
- The `MatrixMN` alias has been deprecated. Use `OMatrix` or `SMatrix` instead.
- The `MatrixN<T, D>` alias has been deprecated. Use `OMatrix<T, D, D>` or `SMatrix` instead.
- The `VectorN<T, D>` alias has been deprecated. Use `OVector` or `SVector` instead.
- The `Point`, `Translation`, `Isometry`, `Similarity`, and `Transformation` types now take an
  integer for their dimension (instead of a type-level integer).
- The type parameter order of `Isometry`, `Similarity`, `Transformation` changed to put
  the integer dimensions in the last position (this is required by the compiler).
- The `::new` constructors of translations, points, matrices, and vectors of dimensions `<= 6`
  are now `const fn`, making them usable to define constant globals. The `Quaternion::new`
  constructor is also a `const fn` now.

## [0.25.4]
### Fixed
- Fix a compilation error when only the `serde-serialize` feature is enabled.

## [0.25.3]
### Added
- The `Vector::simd_cap_magnitude` method to cap the magnitude of the a vector with
  SIMD components.

## [0.25.2]
### Added
- A `convert-glam` cargo feature to enable implementations of `From` traits to convert
  between `glam` types and `nalgebra` types.
- A `convert-glam-unchecked` cargo feature to enable some extra `glam`/`nalgebra` conversions that may
  lead to unexpected results if used improperly. For example, this enables the conversion from a
  `glam::Mat4` to a `na::Isometry3`. This conversion will be cheap (without any check) but willlead to
  unexpected results if the glam matrix contains non-isometric components (like scaling for example).
- A `cast` method has been added to most types. This can be used to change the
  type of the components of a given entity. Example: `vector.cast::<f32>()`.

## [0.25.1]
This release replaces the version 0.25.0 which has been yanked. The 0.25.0 version
added significant complication to build `nalgebra` targeting a `#[no-std]` platform
not supported by `rand`.

The `rand` dependency is now optional (and disabled by default). You may enable it with:
- The `rand-no-std` cargo feature when targeting a `#[no-std]` environment.
- The `rand` cargo feature when targeting a `std` environment.

## [0.25.0] - Yanked
This updates all the dependencies of nalgebra to their latest version, including:
- rand 0.8
- proptest 1.0
- simba 0.4

### New crate: nalgebra-sparse
Alongside this release of `nalgebra`, we are releasing `nalgebra-sparse`: a crate dedicated to sparse matrix
computation with `nalgebra`. The `sparse` module of `nalgebra`itself still exists for backward compatibility
but it will be deprecated soon in favor of the `nalgebra-sparse` crate.

### Added
* Add `UnitDualQuaternion`, a dual-quaternion with unit magnitude which can be used as an isometry transformation.
* Add `UDU::new()` and `matrix.udu()` to compute the UDU factorization of a matrix.
* Add `ColPivQR::new()` and `matrix.col_piv_qr()` to compute the QR decomposition with column pivoting of a matrix.
* Add `from_basis_unchecked` to all the rotation types. This builds a rotation from a set of basis vectors (representing the columns of the corresponding rotation matrix).
* Add `Matrix::cap_magnitude` to cap the magnitude of a vector.
* Add `UnitQuaternion::append_axisangle_linearized` to approximately append a rotation represented as an axis-angle to a rotation represented as an unit quaternion.
* Mark the iterators on matrix components as `DoubleEndedIter`.
* Re-export `simba::simd::SimdValue` at the root of the `nalgebra` crate.

## [0.24.0]

### Added
* The `DualQuaternion` type. It is still work-in-progress but the basics are here:
  creation from its real and dual part, multiplication of two dual quaternions,
  and normalization.
  
### Removed
* There is no blanket `impl<T> PartialEq for Unit<T>` any more. Instead, it is
  implemented specifically for `UnitComplex`, `UnitQuaternion` and `Unit<Vector>`.

## [0.23.2]
In this release, we improved the documentation of some of the geometric types
by applying changes similar to what we did in the version 0.23.1 for matrices.

### Added
* The `Isometry::inv_mul` method which is a more efficient way of doing
  `isometry1.inverse() * isometry2`.

## [0.23.1]
In this release we improved the documentation of the matrix and vector types by:
- Grouping `impl` bocks logically, adding a title comment to these impl blocks.
- Reference these impl blocks docs at the top of the documentation page for `Matrix`.
- Reduce the depth of type aliasing. Now all vector and matrix types are aliases of `Matrix`
  directly (instead of being aliases for other aliases).

## [0.23.0]

### Added
 * The `.inverse_transform_unit_vector(v)` was added to `Rotation2/3`, `Isometry2/3`, `UnitQuaternion`, and `UnitComplex`.
   It applies the corresponding rotation to a unit vector `Unit<Vector2/3>`.
 * The `Point.map(f)` and `Point.apply(f)` to apply a function to each component of the point, similarly to `Vector.map(f)`
   and `Vector.apply(f)`.
 * The `Quaternion::from([N; 4])` conversion to build a quaternion from an array of four elements.
 * The `Isometry::from(Translation)` conversion to build an isometry from a translation.
 * The `Vector::ith_axis(i)` which build a unit vector, e.g., `Unit<Vector3<f32>>` with its i-th component set to 1.0 and the
   others set to zero.
 * The `Isometry.lerp_slerp` and `Isometry.try_lerp_slerp` methods to interpolate between two isometries using linear
   interpolation for the translational part, and spherical interpolation for the rotational part.
 * The `Rotation2.slerp`, `Rotation3.slerp`, and `UnitQuaternion.slerp` method for 
   spherical interpolation.
   
## [0.22.0]
In this release, we are using the new version 0.2 of simba. One major change of that version is that the
use of `libm` is now opt-in when building targetting `no-std` environment. If you are using floating-point
operations with nalgebra in a `no-std` environment, you will need to enable the new `libm` feature
of nalgebra for your code to compile again.

### Added
 * The `libm` feature that enables `libm` when building for `no-std` environment.
 * The `libm-force` feature that enables `libm` even when building for a not `no-std` environment.
 * `Cholesky::new_unchecked` which build a Cholesky decomposition without checking that its input is
 positive-definite. It can be use with SIMD types.
 * The `Default` trait is now implemented for matrices, and quaternions. They are all filled with zeros,
 except for `UnitQuaternion` which is initialized with the identity.
 * Matrix exponential `matrix.exp()`.
 * The `Vector::ith(i, x)` that builds a vector filled with zeros except for the `i`-th component set to `x`.

## [0.21.0]
In this release, we are no longer relying on traits from the __alga__ crate for our generic code.
Instead, we use traits from the new [simba](https://crates.io/crates/simba) crate which are both
simpler, and allow for significant optimizations like AoSoA SIMD. 

Refer to the [monthly dimforge blogpost](https://www.dimforge.org/blog/2020/04/01/this-month-in-dimforge/)
for details about this switch and its benefits.

### Added
 * It is now possible to use SIMD types like `simba::f32x4` as scalar types for nalgebra's matrices and
   geometric types.
### Modified
 * Use of traits like `alga::general::{RealField, ComplexField}` have now been replaced by
  `simba::scalar::{RealField, ComplexField}`.
 * The implementation of traits from the __alga__ crate (and well as the dependency to _alga__) are now
   omitted unless the `alga` cargo feature is activated.
### Removed
 * The `Neg` unary operator is no longer implemented for `UnitComplex` and `UnitQuaternion`. This caused
   hard-to-track errors when we mistakenly write, e.g., `-q * v` instead of `-(q * v)`.
 * The `na::convert_unchecked` is no longer marked as unsafe.
 
## [0.20.0]
### Added
  * `cholesky.rank_one_update(...)` which performs a rank-one update on the cholesky decomposition of a matrix.
  * `From<&Matrix>` is now implemented for matrix slices.
  * `.try_set_magnitude(...)` which sets the magnitude of a vector, while keeping its direction.
  * Implementations of `From` and `Into` for the conversion between matrix slices and standard (`&[N]` `&mut [N]`) slices.
  
### Modified
  * We started some major changes in order to allow non-Copy types to be used as scalar types inside of matrices/vectors.

## [0.19.0]
### Added
  * `.remove_rows_at` and `remove_columns_at` which removes a set of rows or columns (specified by indices) from a matrix.
  * Several formatting traits have been implemented for all matrices/vectors: `LowerExp`, `UpperExp`, `Octal`, `LowerHex`,
  `UpperHex`, `Binary`, `Pointer`.
  * `UnitQuaternion::quaternions_mean(...)` which computes the mean rotation of a set of unit quaternions. This implements
  the algorithm from _Oshman, Yaakov, and Avishy Carmi, "Attitude estimation from vector observations using a genetic-algorithm-embedded quaternion particle filter."

### Modified
  * It is now possible to get the `min/max` element of unsigned integer matrices.

### Added to nalgebra-glm
  * Some infinite and reversed perspectives: `::infinite_perspective_rh_no`, `::infinite_perspective_rh_zo`,
  `::reversed_perspective_rh_zo`, and `::reversed_infinite_perspective_rh_zo`.

## [0.18.0]
This release adds full complex number support to nalgebra. This includes all common vector/matrix operations as well
as matrix decomposition. This excludes geometric type (like `Isometry`, `Rotation`, `Translation`, etc.) from the
`geometry` module.

### Added
#### Quaternion and geometric operations
  * Add trigonometric functions for quaternions: `.cos, .sin, .tan, .acos, .asin, .atan, .cosh, .sinh, .tanh, .acosh, .asinh, .atanh`.
  * Add geometric algebra operations for quaternions: `.inner, .outer, .project, .rejection`
  * Add `.left_div, .right_div` for quaternions.
  * Add `.renormalize` to `Unit<...>` and `Rotation3` to correct potential drift due to repeated operations.
    Those drifts could cause them not to be pure rotations anymore.
  
#### Convolution
  * `.convolve_full(kernel)` returns the convolution of `self` by `kernel`.
  * `.convolve_valid(kernel)` returns the convolution of `self` by `kernel` after removal of all the elements relying on zero-padding.
  * `.convolve_same(kernel)` returns the convolution of `self` by `kernel` with a result of the same size as `self`.
  
#### Complex number support
  * Add the `::from_matrix` constructor too all rotation types to extract a rotation from a raw matrix.
  * Add the `::from_matrix_eps` constructor too all rotation types to extract a rotation from a raw matrix. This takes
    more argument than `::from_matrix` to control the convergence of the underlying optimization algorithm.
  * Add `.camax()` which returns the matrix component with the greatest L1-norm.
  * Add `.camin()` which returns the matrix component with the smallest L1-norm.
  * Add `.ad_mul(b)` for matrix-multiplication of `self.adjoint() * b`.
  * Add `.ad_mul_to(b)` which is the same as `.ad_mul` but with a provided matrix to be filled with the result of the multiplication.
  * Add BLAS operations involving complex conjugation (following similar names as the original BLAS spec):
      * `.dotc(rhs)` equal to  `self.adjoint() * rhs`.
      * `.gerc(alpha, x, y, beta)` equivalent to `self = alpha * x * y.adjoint() + beta * self`
      * `.hegerc` which is like `gerc` but for Hermitian matrices.
      * `.syger` which is the new name of `.ger_symm` which is equivalent to `self = alpha * x * y.transpose() + beta * self`.
      * `.sygemv` which is the new name of `.gemv_symm` which is equivalent to `self = alpha * a * x + beta * self` with `a` symmetric.
      * `.hegemv(alpha, a, x, beta)` which is like `.sygemv` but with `a` Hermitian.
      * `.gemv_ad(alpha, a, x, beta)` which is equivalent to `self = alpha * a.adjoint() * x + beta * self`.
      * `.gemm_ad(alpha, a, b, beta)` which is equivalent to `self = alpha * a.adjoint() * b + beta * self`.
      * `.icamax()` which returns the index of the complex vector component with the greatest L1-norm.

Note that all the other BLAS operation will continue to work for all fields, including floats and complex numbers.

### Renamed
  * `RealSchur` has been renamed `Schur` because it can now work with complex matrices.


## [0.17.0]

### Added
  * Add swizzling up to dimension 3 for vectors. For example, you can do `v.zxy()` as an equivalent to `Vector3::new(v.z, v.x, v.y)`.
  * Add swizzling up to dimension 3 for points. For example, you can do `p.zxy()` as an equivalent to `Point3::new(p.z, p.x, p.y)`.
  * Add `.copy_from_slice` to copy matrix components from a slice in column-major order.
  * Add `.dot` to quaternions.
  * Add `.zip_zip_map` for iterating on three matrices simultaneously, and applying a closure to them.
  * Add `.slerp` and `.try_slerp` to unit vectors.
  * Add `.lerp` to vectors.
  * Add `.to_projective` and `.as_projective` to `Perspective3` and `Orthographic3` in order to
  use them as `Projective3` structures.
  * Add `From/Into` impls to allow the conversion of any transformation type to a matrix.
  * Add `Into` impls to convert a matrix slice into an owned matrix.
  * Add `Point*::from_slice` to create a point from a slice.
  * Add `.map_with_location` to matrices to apply a map which passes the component indices to the user-defined closure alongside
  the component itself.
  * Add impl `From<Vector>` for `Point`.
  * Add impl `From<Vector4>` for `Quaternion`.
  * Add impl `From<Vector>` for `Translation`.
  * Add the `::from_vec` constructor to construct a matrix from a `Vec` (a `DMatrix` will reuse the original `Vec`
  as-is for its storage).
  * Add `.to_homogeneous` to square matrices (and with dimensions higher than 1x1). This will increase their number of row
  and columns by 1. The new column and row are filled with 0, except for the diagonal element which is set to 1.
  * Implement `Extend<Vec>` for matrices with a dynamic storage. The provided `Vec` is assumed to represent a column-major
  matrix with the same number of rows as the one being extended. This will effectively append new columns on the right of
  the matrix being extended.
  * Implement `Extend<Vec>` for vectors with a dynamic storage. This will concatenate the vector with the given `Vec`.
  * Implement `Extend<Matrix<...>>` for matrices with dynamic storage. This will concatenate the columns of both matrices.
  * Implement `Into<Vec>` for the `MatrixVec` storage.
  * Implement `Hash` for all matrices.
  * Add a `.len()` method to retrieve the size of a `MatrixVec`.

### Modified
  * The orthographic projection no longer require that `bottom < top`, that `left < right`, and that `znear < zfar`. The
  only restriction now ith that they must not be equal (in which case the projection would be singular).
  * The `Point::from_coordinates` methods is deprecated. Use `Point::from` instead.
  * The `.transform_point` and `.transform_vector` methods are now inherent methods for matrices so that the user does not have to
  explicitly import the `Transform` trait from the alga crate.
  * Renamed the matrix storage types: `MatrixArray` -> `ArrayStorage` and `MatrixVec` -> `VecStorage`.
  * Renamed `.unwrap()` to `.into_inner()` for geometric types that wrap another type.
    This is for the case of `Unit`, `Transform`, `Orthographic3`, `Perspective3`, `Rotation`.
  * Deprecate several functions at the root of the crate (replaced by methods).

### Removed
    * Remove the `Deref` impl for `MatrixVec` as it could cause hard-to-understand compilation errors.

### nalgebra-glm
  * Add several alternative projection computations, e.g., `ortho_lh`, `ortho_lh_no`, `perspective_lh`, etc.
  * Add features matching those of nalgebra, in particular: `serde-serialize`, `abmonation-serialize`, std` (enabled by default).

## [0.16.0]
All dependencies have been updated to their latest versions.

## Modified
  * Adjust `UnitQuaternion`s, `Rotation3`s, and `Rotation2`s generated from the `Standard` distribution to be uniformly distributed.
### Added
  * Add a feature `stdweb` to activate the dependency feature `rand/stdweb`.
  * Add blas-like methods `.imin()` and `.imax()` that return the index of the minimum and maximum entry of a vector.
  * Add construction of a `Point` from an array by implementing the `From` trait.
  * Add support for generating uniformly distributed random unit column vectors using the `Standard` distribution.

## [0.15.0]
The most notable change of this release is the support for using part of the library without the rust standard
library (i.e. it supports `#![no_std]`). See the corresponding [documentation](https://nalgebra.org/wasm_and_embedded_programming/).
### Modified
  * Rename the `core` module to `base` to avoid conflicts with the `core` crate implicitly imported when
    `#![no_std]` is enabled.
  * Constructors of the `MatrixSlice*` types have been renamed from `new_*` to `from_slice_*`. This was
    necessary to avoid the `incoherent_fundamental_impls` lint that is going to become a hard error.
### Added
  * Add `UnitQuaternion` constructor `::new_eps(...)` and `::from_scaled_axis_eps(...)` that return the
    identity if the magnitude of the input axisangle is smaller than the epsilon provided.
  * Add methods `.rotation_between_axis(...)` and `.scaled_rotation_between_axis(...)` to `UnitComplex`
    to compute the rotation matrix between two 2D **unit** vectors.
  * Add methods `.axis_angle()` to `UnitComplex` and `UnitQuaternion` in order to retrieve both the
    unit rotation axis and the rotation angle simultaneously.
  * Add functions to construct a random matrix with a user-defined distribution: `::from_distribution(...)`.

## [0.14.0]
### Modified
  * Allow the `Isometry * Unit<Vector>` multiplication.
### Added
  * Add blas-like operations: `.quadform(...)` and `.quadform_tr(...)` to compute respectively
    the quadratic forms `self = alpha * A.transpose() * B * A + beta * self` and
    `alpha * A * B * A.transpose() + beta * self`. Here, `A, B` are matrices with
    `B` square, and `alpha, beta` are reals.
  * Add blas-like operations: `.gemv_tr(...)` that behaves like `.gemv` except that the
    provided matrix is assumed to be transposed.
  * Add blas-like operations: `cmpy, cdpy` for component-wise multiplications and
    division with scalar factors:
        - `self <- alpha * self + beta * a * b`
        - `self <- alpha * self + beta * a / b`
  * `.cross_matrix()` returns the cross-product matrix of a given 3D vector, i.e.,
    the matrix `M` such that for all vector `v` we have
    `M * v == self.cross(&v)`.
  * `.iamin()` that returns the index of the vector entry with
    smallest absolute value.
  * The `mint` feature that can be enabled in order to allow conversions from
    and to types of the [mint](https://crates.io/crates/mint) crate.
  * Aliases for matrix and vector slices. Their are named by adding `Slice`
    before the dimension numbers, i.e., a 3x5 matrix slice with dimensions known
    at compile-time is called `MatrixSlice3x5`. A vector slice with dimensions
    unknown at compile-time is called `DVectorSlice`.
  * Add functions for constructing matrix slices from a slice `&[N]`, e.g.,
    `MatrixSlice2::new(...)` and `MatrixSlice2::new_with_strides(...)`.
  * The `::repeat(...)` constructor that is an alternative name to
    `::from_element(...)`.
  * `UnitQuaternion::scaled_rotation_between_axis(...)` and
    `UnitQuaternion::rotation_between_axis(...)` that take Unit vectors instead of
    Vector as arguments.



## [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 method `.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()` returns 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 below 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](https://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](https://nalgebra.org) for more
details. The following free-functions have been added as well:
  * `::id()` that returns the universal [identity element](https://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 assignment 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](https://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.