Modules
[Reexported at the root of this crate.] Data structures for vector and matrix computations.
[Reexported at the root of this crate.] Data structures for points and usual transformations
(rotations, isometries, etc.)
[Reexported at the root of this crate.] Factorization of real matrices.
Macros
Structs
The addition operator, commonly symbolized by
+.A array-based statically sized matrix data storage.
The bidiagonalization of a general matrix.
The Cholesky decomposition of a symmetric-definite-positive matrix.
An allocator based on
GenericArray and VecStorage for statically-sized and dynamically-sized
matrices respectively.Dim of dynamically-sized algebraic entities.
LU decomposition with full row and column pivoting.
Hessenberg decomposition of a general matrix.
The universal identity element wrt. a given operator, usually noted
Id with a
context-dependent subscript.A direct isometry, i.e., a rotation followed by a translation, aka. a rigid-body motion, aka. an element of a Special Euclidean (SE) group.
LU decomposition with partial (row) pivoting.
The most generic column-major matrix (and vector) type.
The multiplication operator, commonly symbolized by
×.A 3D orthographic projection stored as an homogeneous 4x4 matrix.
A sequence of row or column permutations.
A 3D perspective projection stored as an homogeneous 4x4 matrix.
A point in a n-dimensional euclidean space.
The QR decomposition of a general matrix.
A quaternion. See the type alias
UnitQuaternion = Unit<Quaternion> for a quaternion
that may be used as a rotation.Real Schur decomposition of a square matrix.
A reflection wrt. a plane.
A rotation matrix.
Singular Value Decomposition of a general matrix.
A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.
A matrix data storage for a matrix slice. Only contains an internal reference to another matrix data storage.
A mutable matrix data storage for mutable matrix slice. Only contains an internal mutable reference to another matrix data storage.
Eigendecomposition of a symmetric matrix.
Tridiagonalization of a symmetric matrix.
A transformation matrix in homogeneous coordinates.
A translation.
A type level dimension.
A type level dimension with a value of
1.A type level dimension.
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A wrapper that ensures the underlying algebraic entity has a unit norm.
A Vec-based matrix data storage. It may be dynamically-sized.
Enums
Tag representing an affine
Transform. Its bottom-row is equal to (0, 0 ... 0, 1).Tag representing the most general (not necessarily inversible)
Transform type.Tag representing the most general inversible
Transform type.Traits
Trait implemented by any type that can be used as a dimension. This includes type-level
integers and
Dynamic (for dimensions not known at compile-time).Trait implemented exclusively by type-level integers.
Trait of vector with components implementing the
BaseFloat trait.Trait of vector with components implementing the
BaseFloat trait.A type that is equipped with identity.
Trait implemented by
Dynamic.Trait implemented by
Dynamic and type-level integers different from U1.Trait grouping most common operations on vectors.
Trait grouping most common operations on vectors.
Trait shared by all reals.
The basic scalar type for all structures of
nalgebra.A range with a size that may be known at compile-time.
The trait shared by all matrix data storage.
Trait implemented by matrix data storage that can provide a mutable access to its elements.
Indicates that
Self is a more specific Transform category than Other.Indicates that
Self is a more general Transform category than Other.Trait implemented by phantom types identifying the projective transformation type.
Traits that gives the
Transform category that is compatible with the result of the
multiplication of transformations with categories Self and Other.Functions
absDeprecated
The absolute value of
a.angleDeprecated
Computes the smallest angle between two vectors.
The center of two points.
Returns a reference to the input value clamped to the interval
[min, max].Converts an object from one type to an equivalent or more general one.
Converts an object from one type to an equivalent or more general one.
Use with care! Same as
try_convert but
without any property checks.Use with care! Same as
try_convert but
without any property checks.The dimension of the given algebraic entity seen as a vector space.
The distance between two points.
The squared distance between two points.
dotDeprecated
Computes the dot product of two vectors.
Gets the ubiquitous multiplicative identity element.
Returns the infimum of
a and b.Returns simultaneously the infimum and supremum of
a and b.Computes the multiplicative inverse of an (always invertible) algebraic entity.
Indicates if
try_convert will succeed without
actually performing the conversion.magnitude_squaredDeprecated
A synonym for
norm_squared,
aka length squared.Same as
cmp::max.Same as
cmp::min.normDeprecated
Computes the L2 (Euclidean) norm of a vector.
norm_squaredDeprecated
Computes the squared L2 (Euclidean) norm of the vector
v.normalizeDeprecated
Computes the normalized version of the vector
v.Gets the multiplicative identity element.
originDeprecated
Gets the origin of the given point.
Clamp
value between min and max. Returns None if value is not comparable to
min or max.Compare
a and b using a partial ordering relation.Returns
true iff a and b are comparable and a >= b.Returns
true iff a and b are comparable and a > b.Returns
true iff a and b are comparable and a <= b.Returns
true iff a and b are comparable and a < b.Return the maximum of
a and b if they are comparable.Return the minimum of
a and b if they are comparable.Sorts two values in increasing order using a partial ordering.
Returns the supremum of
a and b.Attempts to convert an object to a more specific one.
Attempts to convert an object to a more specific one.
Tries to gets an inverted copy of a square matrix.
Performs a LU decomposition to overwrite
out with the inverse of matrix.try_normalizeDeprecated
Computes the normalized version of the vector
v or returns None if its norm is smaller than min_norm.Computes the wilkinson shift, i.e., the 2x2 symmetric matrix eigenvalue to its tailing
component
tnn.Wraps
val into the range [min, max] using modular arithmetics.Gets the additive identity element.
Type Definitions
A 2D affine transformation. Stored as an homogeneous 3x3 matrix.
A 3D affine transformation. Stored as an homogeneous 4x4 matrix.
A dynamically sized column-major matrix.
A column-major matrix slice dynamic numbers of rows and columns.
A column-major mutable matrix slice dynamic numbers of rows and columns.
A dynamically sized column vector.
A column vector slice dynamic numbers of rows and columns.
A mutable column vector slice dynamic numbers of rows and columns.
A 2-dimensional direct isometry using a rotation matrix for its rotational part. Also known as a rigid-body motion, or as an element of SE(2).
A 3-dimensional direct isometry using a rotation matrix for its rotational part. Also known as a rigid-body motion, or as an element of SE(3).
A stack-allocated, column-major, 1x1 square matrix.
A stack-allocated, column-major, 1x2 matrix.
A stack-allocated, column-major, 1x3 matrix.
A stack-allocated, column-major, 1x4 matrix.
A stack-allocated, column-major, 1x5 matrix.
A stack-allocated, column-major, 1x6 matrix.
A stack-allocated, column-major, 2x2 square matrix.
A stack-allocated, column-major, 2x1 matrix.
A stack-allocated, column-major, 2x3 matrix.
A stack-allocated, column-major, 2x4 matrix.
A stack-allocated, column-major, 2x5 matrix.
A stack-allocated, column-major, 2x6 matrix.
A stack-allocated, column-major, 3x3 square matrix.
A stack-allocated, column-major, 3x1 matrix.
A stack-allocated, column-major, 3x2 matrix.
A stack-allocated, column-major, 3x4 matrix.
A stack-allocated, column-major, 3x5 matrix.
A stack-allocated, column-major, 3x6 matrix.
A stack-allocated, column-major, 4x4 square matrix.
A stack-allocated, column-major, 4x1 matrix.
A stack-allocated, column-major, 4x2 matrix.
A stack-allocated, column-major, 4x3 matrix.
A stack-allocated, column-major, 4x5 matrix.
A stack-allocated, column-major, 4x6 matrix.
A stack-allocated, column-major, 5x5 square matrix.
A stack-allocated, column-major, 5x1 matrix.
A stack-allocated, column-major, 5x2 matrix.
A stack-allocated, column-major, 5x3 matrix.
A stack-allocated, column-major, 5x4 matrix.
A stack-allocated, column-major, 5x6 matrix.
A stack-allocated, column-major, 6x6 square matrix.
A stack-allocated, column-major, 6x1 matrix.
A stack-allocated, column-major, 6x2 matrix.
A stack-allocated, column-major, 6x3 matrix.
A stack-allocated, column-major, 6x4 matrix.
A stack-allocated, column-major, 6x5 matrix.
MatrixArrayDeprecated
Renamed to ArrayStorage.
The type of the result of a matrix cross product.
A statically sized column-major matrix with
R rows and C columns.A statically sized column-major square matrix with
D rows and columns.MatrixNMDeprecated
A statically sized column-major matrix with
R rows and C columns.A matrix slice.
A column-major 1x1 matrix slice.
A column-major 1x2 matrix slice.
A column-major 1x3 matrix slice.
A column-major 1x4 matrix slice.
A column-major 1x5 matrix slice.
A column-major 1x6 matrix slice.
A column-major matrix slice with 1 row and a number of columns chosen at runtime.
A column-major 2x2 matrix slice.
A column-major 2x1 matrix slice.
A column-major 2x3 matrix slice.
A column-major 2x4 matrix slice.
A column-major 2x5 matrix slice.
A column-major 2x6 matrix slice.
A column-major matrix slice with 2 rows and a number of columns chosen at runtime.
A column-major 3x3 matrix slice.
A column-major 3x1 matrix slice.
A column-major 3x2 matrix slice.
A column-major 3x4 matrix slice.
A column-major 3x5 matrix slice.
A column-major 3x6 matrix slice.
A column-major matrix slice with 3 rows and a number of columns chosen at runtime.
A column-major 4x4 matrix slice.
A column-major 4x1 matrix slice.
A column-major 4x2 matrix slice.
A column-major 4x3 matrix slice.
A column-major 4x5 matrix slice.
A column-major 4x6 matrix slice.
A column-major matrix slice with 4 rows and a number of columns chosen at runtime.
A column-major 5x5 matrix slice.
A column-major 5x1 matrix slice.
A column-major 5x2 matrix slice.
A column-major 5x3 matrix slice.
A column-major 5x4 matrix slice.
A column-major 5x6 matrix slice.
A column-major matrix slice with 5 rows and a number of columns chosen at runtime.
A column-major 6x6 matrix slice.
A column-major 6x1 matrix slice.
A column-major 6x2 matrix slice.
A column-major 6x3 matrix slice.
A column-major 6x4 matrix slice.
A column-major 6x5 matrix slice.
A column-major matrix slice with 6 rows and a number of columns chosen at runtime.
A column-major matrix slice with
R rows and C columns.A matrix slice.
A column-major 1x1 mutable matrix slice.
A column-major 1x2 mutable matrix slice.
A column-major 1x3 mutable matrix slice.
A column-major 1x4 mutable matrix slice.
A column-major 1x5 mutable matrix slice.
A column-major 1x6 mutable matrix slice.
A column-major mutable matrix slice with 1 row and a number of columns chosen at runtime.
A column-major 2x2 mutable matrix slice.
A column-major 2x1 mutable matrix slice.
A column-major 2x3 mutable matrix slice.
A column-major 2x4 mutable matrix slice.
A column-major 2x5 mutable matrix slice.
A column-major 2x6 mutable matrix slice.
A column-major mutable matrix slice with 2 rows and a number of columns chosen at runtime.
A column-major 3x3 mutable matrix slice.
A column-major 3x1 mutable matrix slice.
A column-major 3x2 mutable matrix slice.
A column-major 3x4 mutable matrix slice.
A column-major 3x5 mutable matrix slice.
A column-major 3x6 mutable matrix slice.
A column-major mutable matrix slice with 3 rows and a number of columns chosen at runtime.
A column-major 4x4 mutable matrix slice.
A column-major 4x1 mutable matrix slice.
A column-major 4x2 mutable matrix slice.
A column-major 4x3 mutable matrix slice.
A column-major 4x5 mutable matrix slice.
A column-major 4x6 mutable matrix slice.
A column-major mutable matrix slice with 4 rows and a number of columns chosen at runtime.
A column-major 5x5 mutable matrix slice.
A column-major 5x1 mutable matrix slice.
A column-major 5x2 mutable matrix slice.
A column-major 5x3 mutable matrix slice.
A column-major 5x4 mutable matrix slice.
A column-major 5x6 mutable matrix slice.
A column-major mutable matrix slice with 5 rows and a number of columns chosen at runtime.
A column-major 6x6 mutable matrix slice.
A column-major 6x1 mutable matrix slice.
A column-major 6x2 mutable matrix slice.
A column-major 6x3 mutable matrix slice.
A column-major 6x4 mutable matrix slice.
A column-major 6x5 mutable matrix slice.
A column-major mutable matrix slice with 6 rows and a number of columns chosen at runtime.
A column-major mutable matrix slice with
R rows and C columns.A column-major mutable matrix slice with
D rows and columns.A column-major mutable matrix slice with a number of rows chosen at runtime and 1 column.
A column-major mutable matrix slice with a number of rows chosen at runtime and 2 columns.
A column-major mutable matrix slice with a number of rows chosen at runtime and 3 columns.
A column-major mutable matrix slice with a number of rows chosen at runtime and 4 columns.
A column-major mutable matrix slice with a number of rows chosen at runtime and 5 columns.
A column-major mutable matrix slice with a number of rows chosen at runtime and 6 columns.
A column-major matrix slice with
D rows and columns.A column-major matrix slice with a number of rows chosen at runtime and 1 column.
A column-major matrix slice with a number of rows chosen at runtime and 2 columns.
A column-major matrix slice with a number of rows chosen at runtime and 3 columns.
A column-major matrix slice with a number of rows chosen at runtime and 4 columns.
A column-major matrix slice with a number of rows chosen at runtime and 5 columns.
A column-major matrix slice with a number of rows chosen at runtime and 6 columns.
The type of the result of a matrix sum.
MatrixVecDeprecated
Renamed to VecStorage.
A statically sized 1-dimensional column point.
A statically sized 2-dimensional column point.
A statically sized 3-dimensional column point.
A statically sized 4-dimensional column point.
A statically sized 5-dimensional column point.
A statically sized 6-dimensional column point.
An invertible 2D general transformation. Stored as an homogeneous 3x3 matrix.
An invertible 3D general transformation. Stored as an homogeneous 4x4 matrix.
A dynamically sized row vector.
A matrix with one row and
D columns .A stack-allocated, 1-dimensional row vector.
A stack-allocated, 2-dimensional row vector.
A stack-allocated, 3-dimensional row vector.
A stack-allocated, 4-dimensional row vector.
A stack-allocated, 5-dimensional row vector.
A stack-allocated, 6-dimensional row vector.
A statically sized D-dimensional row vector.
A 2-dimensional similarity.
A 3-dimensional similarity.
A 2-dimensional similarity using a rotation matrix for its rotation part.
A 3-dimensional similarity using a rotation matrix for its rotation part.
A square matrix.
A 2D general transformation that may not be invertible. Stored as an homogeneous 3x3 matrix.
A 3D general transformation that may not be inversible. Stored as an homogeneous 4x4 matrix.
A 1-dimensional translation.
A 4-dimensional translation.
A 5-dimensional translation.
A 6-dimensional translation.
A complex number with a norm equal to 1.
A unit quaternions. May be used to represent a rotation.
A matrix with one column and
D rows.A stack-allocated, 1-dimensional column vector.
A stack-allocated, 2-dimensional column vector.
A stack-allocated, 3-dimensional column vector.
A stack-allocated, 4-dimensional column vector.
A stack-allocated, 5-dimensional column vector.
A stack-allocated, 6-dimensional column vector.
A statically sized D-dimensional column vector.
A 1D column vector slice.
A 2D column vector slice.
A 3D column vector slice.
A 4D column vector slice.
A 5D column vector slice.
A 6D column vector slice.
A 1D mutable column vector slice.
A 2D mutable column vector slice.
A 3D mutable column vector slice.
A 4D mutable column vector slice.
A 5D mutable column vector slice.
A 6D mutable column vector slice.
A mutable column vector slice with
D rows.A column vector slice with
D rows.The type of the result of a matrix sum.