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Change Log

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

This project adheres to Semantic Versioning.

[0.17.0] - WIP


  • 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.


  • 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).


  • 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).


All dependencies have been updated to their latest versions.


  • Adjust UnitQuaternions, Rotation3s, and Rotation2s generated from the Standard distribution to be uniformly distributed.


  • 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.


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.


  • 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.


  • 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(...).



  • Allow the Isometry * Unit<Vector> multiplication.


  • 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 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.


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 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.


  • 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.


  • 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.


The main change of this release is the update of the dependency serde to 1.0.


  • .trace() that computes the trace of a matrix (the sum of its diagonal elements.)


The website 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 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.


Lots of features including rectangular matrices, slices, and Serde serialization. Refer to the brand new website for more details. The following free-functions have been added as well:

  • ::id() that returns the universal identity element 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.


  • ::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.


  • 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 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().



Binary operations are now allowed between references as well. For example Vector3<f32> + &Vector3<f32> is now possible.


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>).



  • 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


  • 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.



  • 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., becomes



  • Added implementation of assignment operators (+=, -=, etc.) for everything.


  • Points and vectors are now linked to each other with associated types (on the PointAsVector trait).


Announcement: a users forum has been created for nalgebra, ncollide, and nphysics. See you there!


  • Added a dependency to 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 zero-sized elements Vector0, Point0.
  • Removed 4-dimensional transformations Rotation4 and Isometry4 (which had an implementation to incomplete to be useful).


  • 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.