Crate algebra

Expand description

§nalgebra

nalgebra is a 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 and the official package manager: cargo.

Simply add the following to your Cargo.toml file:

[dependencies]
// TODO: replace the * by the latest version.
nalgebra = "*"

Most useful functionalities of nalgebra are grouped in the root module nalgebra::.

However, the recommended way to use nalgebra is to import types and traits explicitly, and call free-functions using the na:: prefix:

#[macro_use]
extern crate approx; // For the macro assert_relative_eq!
extern crate nalgebra as na;
use na::{Vector3, Rotation3};

fn main() {
    let axis  = Vector3::x_axis();
    let angle = 1.57;
    let b     = Rotation3::from_axis_angle(&axis, angle);

    assert_relative_eq!(b.axis().unwrap(), axis);
    assert_relative_eq!(b.angle(), angle);
}

§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:

A single parametrizable type Matrix for vectors, (square or rectangular) matrices, and slices with dimensions known either at compile-time (using type-level integers) or at runtime.
Matrices and vectors with compile-time sizes are statically allocated while dynamic ones are allocated on the heap.
Convenient aliases for low-dimensional matrices and vectors: Vector1 to Vector6 and Matrix1x1 to Matrix6x6, including rectangular matrices like Matrix2x5.
Points sizes known at compile time, and convenience aliases: Point1 to Point6.
Translation (seen as a transformation that composes by multiplication): Translation2, Translation3.
Rotation matrices: Rotation2, Rotation3.
Quaternions: Quaternion, UnitQuaternion (for 3D rotation).
Unit complex numbers can be used for 2D rotation: UnitComplex.
Algebraic entities with a norm equal to one: Unit<T>, e.g., Unit<Vector3<f32>>.
Isometries (translation ⨯ rotation): Isometry2, Isometry3
Similarity transformations (translation ⨯ rotation ⨯ uniform scale): Similarity2, Similarity3.
Affine transformations stored as a homogeneous matrix: Affine2, Affine3.
Projective (i.e. invertible) transformations stored as a homogeneous matrix: Projective2, Projective3.
General transformations that does not have to be invertible, stored as a homogeneous matrix: Transform2, Transform3.
3D projections for computer graphics: Perspective3, Orthographic3.
Matrix factorizations: Cholesky, QR, LU, FullPivLU, SVD, Schur, Hessenberg, SymmetricEigen.
Insertion and removal of rows of columns of a matrix.

Modules§

base: [Reexported at the root of this crate.] Data structures for vector and matrix computations.
geometry: [Reexported at the root of this crate.] Data structures for points and usual transformations (rotations, isometries, etc.)
linalg: [Reexported at the root of this crate.] Factorization of real matrices.

Macros§

dmatrix: Construct a dynamic matrix directly from data.
dvector: Construct a dynamic column vector directly from data.
matrix: Construct a fixed-size matrix directly from data.
point: Construct a fixed-size point directly from data.
stack: Construct a new matrix by stacking matrices in a block matrix.
vector: Construct a fixed-size column vector directly from data.

Structs§

ArrayStorage: An array-based statically sized matrix data storage.
Bidiagonal: The bidiagonalization of a general matrix.
Cholesky: The Cholesky decomposition of a symmetric-definite-positive matrix.
ColPivQR: The QR decomposition (with column pivoting) of a general matrix.
Complex: A complex number in Cartesian form.
Const
DefaultAllocator: An allocator based on ArrayStorage and VecStorage for statically-sized and dynamically-sized matrices respectively.
DualQuaternion: A dual quaternion.
Dyn: Dim of dynamically-sized algebraic entities.
EuclideanNorm: Euclidean norm.
FullPivLU: LU decomposition with full row and column pivoting.
Hessenberg: Hessenberg decomposition of a general matrix.
Isometry: A direct isometry, i.e., a rotation followed by a translation (aka. a rigid-body motion).
LU: LU decomposition with partial (row) pivoting.
LpNorm: Lp norm.
Matrix: The most generic column-major matrix (and vector) type.
OPoint: A point in an euclidean space.
Orthographic3: A 3D orthographic projection stored as a homogeneous 4x4 matrix.
PermutationSequence: A sequence of row or column permutations.
Perspective3: A 3D perspective projection stored as a homogeneous 4x4 matrix.
QR: The QR decomposition of a general matrix.
Quaternion: A quaternion. See the type alias UnitQuaternion = Unit<Quaternion> for a quaternion that may be used as a rotation.
Reflection: A reflection wrt. a plane.
Rotation: A rotation matrix.
SVD: Singular Value Decomposition of a general matrix.
Scale: A scale which supports non-uniform scaling.
Schur: Schur decomposition of a square matrix.
Similarity: A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.
SymmetricEigen: Eigendecomposition of a symmetric matrix.
SymmetricTridiagonal: Tridiagonalization of a symmetric matrix.
Transform: A transformation matrix in homogeneous coordinates.
Translation: A translation.
UDU: UDU factorization.
UniformNorm: L-infinite norm aka. Chebytchev norm aka. uniform norm aka. suppremum norm.
Unit: A wrapper that ensures the underlying algebraic entity has a unit norm.
VecStorage: A Vec-based matrix data storage. It may be dynamically-sized.
ViewStorage: A matrix data storage for a matrix view. Only contains an internal reference to another matrix data storage.
ViewStorageMut: A mutable matrix data storage for mutable matrix view. Only contains an internal mutable reference to another matrix data storage.

Enums§

TAffine: Tag representing an affine Transform. Its bottom-row is equal to (0, 0 ... 0, 1).
TGeneral: Tag representing the most general (not necessarily inversible) Transform type.
TProjective: Tag representing the most general inversible Transform type.

Constants§

U0: The constant dimension 0 .
U1: The constant dimension 1.
U2: The constant dimension 2 .
U3: The constant dimension 3 .
U4: The constant dimension 4 .
U5: The constant dimension 5 .
U6: The constant dimension 6 .
U7: The constant dimension 7 .
U8: The constant dimension 8 .
U9: The constant dimension 9 .
U10: The constant dimension 10 .
U11: The constant dimension 11 .
U12: The constant dimension 12 .
U13: The constant dimension 13 .
U14: The constant dimension 14 .
U15: The constant dimension 15 .
U16: The constant dimension 16 .
U17: The constant dimension 17 .
U18: The constant dimension 18 .
U19: The constant dimension 19 .
U20: The constant dimension 20 .
U21: The constant dimension 21 .
U22: The constant dimension 22 .
U23: The constant dimension 23 .
U24: The constant dimension 24 .
U25: The constant dimension 25 .
U26: The constant dimension 26 .
U27: The constant dimension 27 .
U28: The constant dimension 28 .
U29: The constant dimension 29 .
U30: The constant dimension 30 .
U31: The constant dimension 31 .
U32: The constant dimension 32 .
U33: The constant dimension 33 .
U34: The constant dimension 34 .
U35: The constant dimension 35 .
U36: The constant dimension 36 .
U37: The constant dimension 37 .
U38: The constant dimension 38 .
U39: The constant dimension 39 .
U40: The constant dimension 40 .
U41: The constant dimension 41 .
U42: The constant dimension 42 .
U43: The constant dimension 43 .
U44: The constant dimension 44 .
U45: The constant dimension 45 .
U46: The constant dimension 46 .
U47: The constant dimension 47 .
U48: The constant dimension 48 .
U49: The constant dimension 49 .
U50: The constant dimension 50 .
U51: The constant dimension 51 .
U52: The constant dimension 52 .
U53: The constant dimension 53 .
U54: The constant dimension 54 .
U55: The constant dimension 55 .
U56: The constant dimension 56 .
U57: The constant dimension 57 .
U58: The constant dimension 58 .
U59: The constant dimension 59 .
U60: The constant dimension 60 .
U61: The constant dimension 61 .
U62: The constant dimension 62 .
U63: The constant dimension 63 .
U64: The constant dimension 64 .
U65: The constant dimension 65 .
U66: The constant dimension 66 .
U67: The constant dimension 67 .
U68: The constant dimension 68 .
U69: The constant dimension 69 .
U70: The constant dimension 70 .
U71: The constant dimension 71 .
U72: The constant dimension 72 .
U73: The constant dimension 73 .
U74: The constant dimension 74 .
U75: The constant dimension 75 .
U76: The constant dimension 76 .
U77: The constant dimension 77 .
U78: The constant dimension 78 .
U79: The constant dimension 79 .
U80: The constant dimension 80 .
U81: The constant dimension 81 .
U82: The constant dimension 82 .
U83: The constant dimension 83 .
U84: The constant dimension 84 .
U85: The constant dimension 85 .
U86: The constant dimension 86 .
U87: The constant dimension 87 .
U88: The constant dimension 88 .
U89: The constant dimension 89 .
U90: The constant dimension 90 .
U91: The constant dimension 91 .
U92: The constant dimension 92 .
U93: The constant dimension 93 .
U94: The constant dimension 94 .
U95: The constant dimension 95 .
U96: The constant dimension 96 .
U97: The constant dimension 97 .
U98: The constant dimension 98 .
U99: The constant dimension 99 .
U100: The constant dimension 100 .
U101: The constant dimension 101 .
U102: The constant dimension 102 .
U103: The constant dimension 103 .
U104: The constant dimension 104 .
U105: The constant dimension 105 .
U106: The constant dimension 106 .
U107: The constant dimension 107 .
U108: The constant dimension 108 .
U109: The constant dimension 109 .
U110: The constant dimension 110 .
U111: The constant dimension 111 .
U112: The constant dimension 112 .
U113: The constant dimension 113 .
U114: The constant dimension 114 .
U115: The constant dimension 115 .
U116: The constant dimension 116 .
U117: The constant dimension 117 .
U118: The constant dimension 118 .
U119: The constant dimension 119 .
U120: The constant dimension 120 .
U121: The constant dimension 121 .
U122: The constant dimension 122 .
U123: The constant dimension 123 .
U124: The constant dimension 124 .
U125: The constant dimension 125 .
U126: The constant dimension 126 .
U127: The constant dimension 127 .

Traits§

AbstractRotation: Trait implemented by rotations that can be used inside of an Isometry or Similarity.
ClosedAddAssign: Trait alias for Add and AddAssign with result of type Self.
ClosedDivAssign: Trait alias for Div and DivAssign with result of type Self.
ClosedMulAssign: Trait alias for Mul and MulAssign with result of type Self.
ClosedSubAssign: Trait alias for Sub and SubAssign with result of type Self.
ComplexField: Trait shared by all complex fields and its subfields (like real numbers).
Dim: Trait implemented by any type that can be used as a dimension. This includes type-level integers and Dyn (for dimensions not known at compile-time).
DimAdd
DimDiv
DimMax
DimMin
DimMul
DimName: Trait implemented exclusively by type-level integers.
DimNameAdd
DimNameDiv
DimNameMax
DimNameMin
DimNameMul
DimNameSub
DimRange: A range with a size that may be known at compile-time.
DimSub
Field: Trait implemented by fields, i.e., complex numbers and floats.
IsContiguous: Marker trait indicating that a storage is stored contiguously in memory.
IsDynamic: Trait implemented by Dyn.
IsNotStaticOne: Trait implemented by Dyn and type-level integers different from U1.
Norm: A trait for abstract matrix norms.
Normed: Trait implemented by entities scan be be normalized and put in an Unit struct.
RawStorage: The trait shared by all matrix data storage.
RawStorageMut: Trait implemented by matrix data storage that can provide a mutable access to its elements.
RealField: Trait shared by all reals.
ReshapableStorage: A matrix storage that can be reshaped in-place.
Scalar: The basic scalar type for all structures of nalgebra.
SimdBool: Lane-wise generalization of bool for SIMD booleans.
SimdComplexField: Lane-wise generalisation of ComplexField for SIMD complex fields.
SimdPartialOrd: Lane-wise generalization of the standard PartialOrd for SIMD values.
SimdRealField: Lanewise generalization of RealField for SIMD reals.
SimdValue: Base trait for every SIMD types.
SliceRangeDeprecated: A range with a size that may be known at compile-time.
Storage: Trait shared by all matrix data storage that don’t contain any uninitialized elements.
StorageMut: Trait shared by all mutable matrix data storage that don’t contain any uninitialized elements.
SubTCategoryOf: Indicates that Self is a more specific Transform category than Other.
SuperTCategoryOf: Indicates that Self is a more general Transform category than Other.
TCategory: Trait implemented by phantom types identifying the projective transformation type.
TCategoryMul: Traits that gives the Transform category that is compatible with the result of the multiplication of transformations with categories Self and Other.
ToConst
ToTypenum

Functions§

absDeprecated: The absolute value of a.
center: The center of two points.
clamp: Returns a reference to the input value clamped to the interval [min, max].
convert: Converts an object from one type to an equivalent or more general one.
convert_ref: Converts an object from one type to an equivalent or more general one.
convert_ref_unchecked: Use with care! Same as try_convert() but without any property checks.
convert_unchecked: Use with care! Same as try_convert() but without any property checks.
distance: The distance between two points.
distance_squared: The squared distance between two points.
infDeprecated: Returns the infimum of a and b.
inf_supDeprecated: Returns simultaneously the infimum and supremum of a and b.
is_convertible: Indicates if try_convert() will succeed without actually performing the conversion.
max: Same as cmp::max.
min: Same as cmp::min.
one: Gets the multiplicative identity element.
partial_clamp: Clamp value between min and max. Returns None if value is not comparable to min or max.
partial_cmp: Compare a and b using a partial ordering relation.
partial_ge: Returns true iff a and b are comparable and a >= b.
partial_gt: Returns true iff a and b are comparable and a > b.
partial_le: Returns true iff a and b are comparable and a <= b.
partial_lt: Returns true iff a and b are comparable and a < b.
partial_max: Return the maximum of a and b if they are comparable.
partial_min: Return the minimum of a and b if they are comparable.
partial_sort2: Sorts two values in increasing order using a partial ordering.
supDeprecated: Returns the supremum of a and b.
try_convert: Attempts to convert an object to a more specific one.
try_convert_ref: Attempts to convert an object to a more specific one.
try_invert_to: Performs a LU decomposition to overwrite out with the inverse of matrix.
wilkinson_shift: Computes the wilkinson shift, i.e., the 2x2 symmetric matrix eigenvalue to its tailing component tnn.
wrap: Wraps val into the range [min, max] using modular arithmetics.
zero: Gets the additive identity element.

Type Aliases§

Affine2: A 2D affine transformation. Stored as a homogeneous 3x3 matrix.
Affine3: A 3D affine transformation. Stored as a homogeneous 4x4 matrix.
CStride: The column-stride of the owned data storage for a buffer of dimension (R, C).
DMatrix: A dynamically sized column-major matrix.
DMatrixSliceDeprecated: A column-major matrix slice dynamic numbers of rows and columns.
DMatrixSliceMutDeprecated: A column-major matrix slice dynamic numbers of rows and columns.
DMatrixView: An immutable column-major matrix view dynamic numbers of rows and columns.
DMatrixViewMut: A mutable column-major matrix view dynamic numbers of rows and columns.
DVector: A dynamically sized column vector.
DVectorSliceDeprecated: A column vector slice dynamic numbers of rows and columns.
DVectorSliceMutDeprecated: A column vector slice dynamic numbers of rows and columns.
DVectorView: An immutable column vector view dynamic numbers of rows and columns.
DVectorViewMut: A mutable column vector view dynamic numbers of rows and columns.
DimDiff
DimMaximum
DimMinimum
DimNameDiff
DimNameMaximum
DimNameMinimum
DimNameProd
DimNameQuot
DimNameSum
DimProd
DimQuot
DimSum
DynamicDeprecated
Isometry2: A 2-dimensional direct isometry using a unit complex number for its rotational part.
Isometry3: A 3-dimensional direct isometry using a unit quaternion for its rotational part.
IsometryMatrix2: A 2-dimensional direct isometry using a rotation matrix for its rotational part.
IsometryMatrix3: A 3-dimensional direct isometry using a rotation matrix for its rotational part.
Matrix1: A stack-allocated, column-major, 1x1 square matrix.
Matrix2: A stack-allocated, column-major, 2x2 square matrix.
Matrix3: A stack-allocated, column-major, 3x3 square matrix.
Matrix4: A stack-allocated, column-major, 4x4 square matrix.
Matrix5: A stack-allocated, column-major, 5x5 square matrix.
Matrix6: A stack-allocated, column-major, 6x6 square matrix.
Matrix1x2: A stack-allocated, column-major, 1x2 matrix.
Matrix1x3: A stack-allocated, column-major, 1x3 matrix.
Matrix1x4: A stack-allocated, column-major, 1x4 matrix.
Matrix1x5: A stack-allocated, column-major, 1x5 matrix.
Matrix1x6: A stack-allocated, column-major, 1x6 matrix.
Matrix1xX: A heap-allocated, column-major, matrix with 1 rows and a dynamic number of columns.
Matrix2x1: A stack-allocated, column-major, 2x1 matrix.
Matrix2x3: A stack-allocated, column-major, 2x3 matrix.
Matrix2x4: A stack-allocated, column-major, 2x4 matrix.
Matrix2x5: A stack-allocated, column-major, 2x5 matrix.
Matrix2x6: A stack-allocated, column-major, 2x6 matrix.
Matrix2xX: A heap-allocated, column-major, matrix with 2 rows and a dynamic number of columns.
Matrix3x1: A stack-allocated, column-major, 3x1 matrix.
Matrix3x2: A stack-allocated, column-major, 3x2 matrix.
Matrix3x4: A stack-allocated, column-major, 3x4 matrix.
Matrix3x5: A stack-allocated, column-major, 3x5 matrix.
Matrix3x6: A stack-allocated, column-major, 3x6 matrix.
Matrix3xX: A heap-allocated, column-major, matrix with 3 rows and a dynamic number of columns.
Matrix4x1: A stack-allocated, column-major, 4x1 matrix.
Matrix4x2: A stack-allocated, column-major, 4x2 matrix.
Matrix4x3: A stack-allocated, column-major, 4x3 matrix.
Matrix4x5: A stack-allocated, column-major, 4x5 matrix.
Matrix4x6: A stack-allocated, column-major, 4x6 matrix.
Matrix4xX: A heap-allocated, column-major, matrix with 4 rows and a dynamic number of columns.
Matrix5x1: A stack-allocated, column-major, 5x1 matrix.
Matrix5x2: A stack-allocated, column-major, 5x2 matrix.
Matrix5x3: A stack-allocated, column-major, 5x3 matrix.
Matrix5x4: A stack-allocated, column-major, 5x4 matrix.
Matrix5x6: A stack-allocated, column-major, 5x6 matrix.
Matrix5xX: A heap-allocated, column-major, matrix with 5 rows and a dynamic number of columns.
Matrix6x1: A stack-allocated, column-major, 6x1 matrix.
Matrix6x2: A stack-allocated, column-major, 6x2 matrix.
Matrix6x3: A stack-allocated, column-major, 6x3 matrix.
Matrix6x4: A stack-allocated, column-major, 6x4 matrix.
Matrix6x5: A stack-allocated, column-major, 6x5 matrix.
Matrix6xX: A heap-allocated, column-major, matrix with 6 rows and a dynamic number of columns.
MatrixCross: The type of the result of a matrix cross product.
MatrixMNDeprecated: An owned matrix column-major matrix with R rows and C columns.
MatrixNDeprecated: An owned matrix column-major matrix with D columns.
MatrixSliceDeprecated: A matrix slice.
MatrixSlice1Deprecated: A column-major 1x1 matrix slice.
MatrixSlice2Deprecated: A column-major 2x2 matrix slice.
MatrixSlice3Deprecated: A column-major 3x3 matrix slice.
MatrixSlice4Deprecated: A column-major 4x4 matrix slice.
MatrixSlice5Deprecated: A column-major 5x5 matrix slice.
MatrixSlice6Deprecated: A column-major 6x6 matrix slice.
MatrixSlice1x2Deprecated: A column-major 1x2 matrix slice.
MatrixSlice1x3Deprecated: A column-major 1x3 matrix slice.
MatrixSlice1x4Deprecated: A column-major 1x4 matrix slice.
MatrixSlice1x5Deprecated: A column-major 1x5 matrix slice.
MatrixSlice1x6Deprecated: A column-major 1x6 matrix slice.
MatrixSlice1xXDeprecated: A column-major matrix slice with 1 row and a number of columns chosen at runtime.
MatrixSlice2x1Deprecated: A column-major 2x1 matrix slice.
MatrixSlice2x3Deprecated: A column-major 2x3 matrix slice.
MatrixSlice2x4Deprecated: A column-major 2x4 matrix slice.
MatrixSlice2x5Deprecated: A column-major 2x5 matrix slice.
MatrixSlice2x6Deprecated: A column-major 2x6 matrix slice.
MatrixSlice2xXDeprecated: A column-major matrix slice with 2 rows and a number of columns chosen at runtime.
MatrixSlice3x1Deprecated: A column-major 3x1 matrix slice.
MatrixSlice3x2Deprecated: A column-major 3x2 matrix slice.
MatrixSlice3x4Deprecated: A column-major 3x4 matrix slice.
MatrixSlice3x5Deprecated: A column-major 3x5 matrix slice.
MatrixSlice3x6Deprecated: A column-major 3x6 matrix slice.
MatrixSlice3xXDeprecated: A column-major matrix slice with 3 rows and a number of columns chosen at runtime.
MatrixSlice4x1Deprecated: A column-major 4x1 matrix slice.
MatrixSlice4x2Deprecated: A column-major 4x2 matrix slice.
MatrixSlice4x3Deprecated: A column-major 4x3 matrix slice.
MatrixSlice4x5Deprecated: A column-major 4x5 matrix slice.
MatrixSlice4x6Deprecated: A column-major 4x6 matrix slice.
MatrixSlice4xXDeprecated: A column-major matrix slice with 4 rows and a number of columns chosen at runtime.
MatrixSlice5x1Deprecated: A column-major 5x1 matrix slice.
MatrixSlice5x2Deprecated: A column-major 5x2 matrix slice.
MatrixSlice5x3Deprecated: A column-major 5x3 matrix slice.
MatrixSlice5x4Deprecated: A column-major 5x4 matrix slice.
MatrixSlice5x6Deprecated: A column-major 5x6 matrix slice.
MatrixSlice5xXDeprecated: A column-major matrix slice with 5 rows and a number of columns chosen at runtime.
MatrixSlice6x1Deprecated: A column-major 6x1 matrix slice.
MatrixSlice6x2Deprecated: A column-major 6x2 matrix slice.
MatrixSlice6x3Deprecated: A column-major 6x3 matrix slice.
MatrixSlice6x4Deprecated: A column-major 6x4 matrix slice.
MatrixSlice6x5Deprecated: A column-major 6x5 matrix slice.
MatrixSlice6xXDeprecated: A column-major matrix slice with 6 rows and a number of columns chosen at runtime.
MatrixSliceMutDeprecated: A mutable matrix slice.
MatrixSliceMut1Deprecated: A column-major 1x1 matrix slice.
MatrixSliceMut2Deprecated: A column-major 2x2 matrix slice.
MatrixSliceMut3Deprecated: A column-major 3x3 matrix slice.
MatrixSliceMut4Deprecated: A column-major 4x4 matrix slice.
MatrixSliceMut5Deprecated: A column-major 5x5 matrix slice.
MatrixSliceMut6Deprecated: A column-major 6x6 matrix slice.
MatrixSliceMut1x2Deprecated: A column-major 1x2 matrix slice.
MatrixSliceMut1x3Deprecated: A column-major 1x3 matrix slice.
MatrixSliceMut1x4Deprecated: A column-major 1x4 matrix slice.
MatrixSliceMut1x5Deprecated: A column-major 1x5 matrix slice.
MatrixSliceMut1x6Deprecated: A column-major 1x6 matrix slice.
MatrixSliceMut1xXDeprecated: A column-major matrix slice with 1 row and a number of columns chosen at runtime.
MatrixSliceMut2x1Deprecated: A column-major 2x1 matrix slice.
MatrixSliceMut2x3Deprecated: A column-major 2x3 matrix slice.
MatrixSliceMut2x4Deprecated: A column-major 2x4 matrix slice.
MatrixSliceMut2x5Deprecated: A column-major 2x5 matrix slice.
MatrixSliceMut2x6Deprecated: A column-major 2x6 matrix slice.
MatrixSliceMut2xXDeprecated: A column-major matrix slice with 2 rows and a number of columns chosen at runtime.
MatrixSliceMut3x1Deprecated: A column-major 3x1 matrix slice.
MatrixSliceMut3x2Deprecated: A column-major 3x2 matrix slice.
MatrixSliceMut3x4Deprecated: A column-major 3x4 matrix slice.
MatrixSliceMut3x5Deprecated: A column-major 3x5 matrix slice.
MatrixSliceMut3x6Deprecated: A column-major 3x6 matrix slice.
MatrixSliceMut3xXDeprecated: A column-major matrix slice with 3 rows and a number of columns chosen at runtime.
MatrixSliceMut4x1Deprecated: A column-major 4x1 matrix slice.
MatrixSliceMut4x2Deprecated: A column-major 4x2 matrix slice.
MatrixSliceMut4x3Deprecated: A column-major 4x3 matrix slice.
MatrixSliceMut4x5Deprecated: A column-major 4x5 matrix slice.
MatrixSliceMut4x6Deprecated: A column-major 4x6 matrix slice.
MatrixSliceMut4xXDeprecated: A column-major matrix slice with 4 rows and a number of columns chosen at runtime.
MatrixSliceMut5x1Deprecated: A column-major 5x1 matrix slice.
MatrixSliceMut5x2Deprecated: A column-major 5x2 matrix slice.
MatrixSliceMut5x3Deprecated: A column-major 5x3 matrix slice.
MatrixSliceMut5x4Deprecated: A column-major 5x4 matrix slice.
MatrixSliceMut5x6Deprecated: A column-major 5x6 matrix slice.
MatrixSliceMut5xXDeprecated: A column-major matrix slice with 5 rows and a number of columns chosen at runtime.
MatrixSliceMut6x1Deprecated: A column-major 6x1 matrix slice.
MatrixSliceMut6x2Deprecated: A column-major 6x2 matrix slice.
MatrixSliceMut6x3Deprecated: A column-major 6x3 matrix slice.
MatrixSliceMut6x4Deprecated: A column-major 6x4 matrix slice.
MatrixSliceMut6x5Deprecated: A column-major 6x5 matrix slice.
MatrixSliceMut6xXDeprecated: A column-major matrix slice with 6 rows and a number of columns chosen at runtime.
MatrixSliceMutMNDeprecated: A column-major matrix slice with R rows and C columns.
MatrixSliceMutNDeprecated: A column-major matrix slice with D rows and columns.
MatrixSliceMutXx1Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 1 column.
MatrixSliceMutXx2Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 2 columns.
MatrixSliceMutXx3Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 3 columns.
MatrixSliceMutXx4Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 4 columns.
MatrixSliceMutXx5Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 5 columns.
MatrixSliceMutXx6Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 6 columns.
MatrixSliceXx1Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 1 column.
MatrixSliceXx2Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 2 columns.
MatrixSliceXx3Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 3 columns.
MatrixSliceXx4Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 4 columns.
MatrixSliceXx5Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 5 columns.
MatrixSliceXx6Deprecated: A column-major matrix slice with a number of rows chosen at runtime and 6 columns.
MatrixSum: The type of the result of a matrix sum.
MatrixVecDeprecated: Renamed to VecStorage.
MatrixView: A matrix view.
MatrixView1: An immutable column-major 1x1 matrix view.
MatrixView2: An immutable column-major 2x2 matrix view.
MatrixView3: An immutable column-major 3x3 matrix view.
MatrixView4: An immutable column-major 4x4 matrix view.
MatrixView5: An immutable column-major 5x5 matrix view.
MatrixView6: An immutable column-major 6x6 matrix view.
MatrixView1x2: An immutable column-major 1x2 matrix view.
MatrixView1x3: An immutable column-major 1x3 matrix view.
MatrixView1x4: An immutable column-major 1x4 matrix view.
MatrixView1x5: An immutable column-major 1x5 matrix view.
MatrixView1x6: An immutable column-major 1x6 matrix view.
MatrixView1xX: An immutable column-major matrix view with 1 row and a number of columns chosen at runtime.
MatrixView2x1: An immutable column-major 2x1 matrix view.
MatrixView2x3: An immutable column-major 2x3 matrix view.
MatrixView2x4: An immutable column-major 2x4 matrix view.
MatrixView2x5: An immutable column-major 2x5 matrix view.
MatrixView2x6: An immutable column-major 2x6 matrix view.
MatrixView2xX: An immutable column-major matrix view with 2 rows and a number of columns chosen at runtime.
MatrixView3x1: An immutable column-major 3x1 matrix view.
MatrixView3x2: An immutable column-major 3x2 matrix view.
MatrixView3x4: An immutable column-major 3x4 matrix view.
MatrixView3x5: An immutable column-major 3x5 matrix view.
MatrixView3x6: An immutable column-major 3x6 matrix view.
MatrixView3xX: An immutable column-major matrix view with 3 rows and a number of columns chosen at runtime.
MatrixView4x1: An immutable column-major 4x1 matrix view.
MatrixView4x2: An immutable column-major 4x2 matrix view.
MatrixView4x3: An immutable column-major 4x3 matrix view.
MatrixView4x5: An immutable column-major 4x5 matrix view.
MatrixView4x6: An immutable column-major 4x6 matrix view.
MatrixView4xX: An immutable column-major matrix view with 4 rows and a number of columns chosen at runtime.
MatrixView5x1: An immutable column-major 5x1 matrix view.
MatrixView5x2: An immutable column-major 5x2 matrix view.
MatrixView5x3: An immutable column-major 5x3 matrix view.
MatrixView5x4: An immutable column-major 5x4 matrix view.
MatrixView5x6: An immutable column-major 5x6 matrix view.
MatrixView5xX: An immutable column-major matrix view with 5 rows and a number of columns chosen at runtime.
MatrixView6x1: An immutable column-major 6x1 matrix view.
MatrixView6x2: An immutable column-major 6x2 matrix view.
MatrixView6x3: An immutable column-major 6x3 matrix view.
MatrixView6x4: An immutable column-major 6x4 matrix view.
MatrixView6x5: An immutable column-major 6x5 matrix view.
MatrixView6xX: An immutable column-major matrix view with 6 rows and a number of columns chosen at runtime.
MatrixViewMut: A mutable matrix view.
MatrixViewMut1: A mutable column-major 1x1 matrix view.
MatrixViewMut2: A mutable column-major 2x2 matrix view.
MatrixViewMut3: A mutable column-major 3x3 matrix view.
MatrixViewMut4: A mutable column-major 4x4 matrix view.
MatrixViewMut5: A mutable column-major 5x5 matrix view.
MatrixViewMut6: A mutable column-major 6x6 matrix view.
MatrixViewMut1x2: A mutable column-major 1x2 matrix view.
MatrixViewMut1x3: A mutable column-major 1x3 matrix view.
MatrixViewMut1x4: A mutable column-major 1x4 matrix view.
MatrixViewMut1x5: A mutable column-major 1x5 matrix view.
MatrixViewMut1x6: A mutable column-major 1x6 matrix view.
MatrixViewMut1xX: A mutable column-major matrix view with 1 row and a number of columns chosen at runtime.
MatrixViewMut2x1: A mutable column-major 2x1 matrix view.
MatrixViewMut2x3: A mutable column-major 2x3 matrix view.
MatrixViewMut2x4: A mutable column-major 2x4 matrix view.
MatrixViewMut2x5: A mutable column-major 2x5 matrix view.
MatrixViewMut2x6: A mutable column-major 2x6 matrix view.
MatrixViewMut2xX: A mutable column-major matrix view with 2 rows and a number of columns chosen at runtime.
MatrixViewMut3x1: A mutable column-major 3x1 matrix view.
MatrixViewMut3x2: A mutable column-major 3x2 matrix view.
MatrixViewMut3x4: A mutable column-major 3x4 matrix view.
MatrixViewMut3x5: A mutable column-major 3x5 matrix view.
MatrixViewMut3x6: A mutable column-major 3x6 matrix view.
MatrixViewMut3xX: A mutable column-major matrix view with 3 rows and a number of columns chosen at runtime.
MatrixViewMut4x1: A mutable column-major 4x1 matrix view.
MatrixViewMut4x2: A mutable column-major 4x2 matrix view.
MatrixViewMut4x3: A mutable column-major 4x3 matrix view.
MatrixViewMut4x5: A mutable column-major 4x5 matrix view.
MatrixViewMut4x6: A mutable column-major 4x6 matrix view.
MatrixViewMut4xX: A mutable column-major matrix view with 4 rows and a number of columns chosen at runtime.
MatrixViewMut5x1: A mutable column-major 5x1 matrix view.
MatrixViewMut5x2: A mutable column-major 5x2 matrix view.
MatrixViewMut5x3: A mutable column-major 5x3 matrix view.
MatrixViewMut5x4: A mutable column-major 5x4 matrix view.
MatrixViewMut5x6: A mutable column-major 5x6 matrix view.
MatrixViewMut5xX: A mutable column-major matrix view with 5 rows and a number of columns chosen at runtime.
MatrixViewMut6x1: A mutable column-major 6x1 matrix view.
MatrixViewMut6x2: A mutable column-major 6x2 matrix view.
MatrixViewMut6x3: A mutable column-major 6x3 matrix view.
MatrixViewMut6x4: A mutable column-major 6x4 matrix view.
MatrixViewMut6x5: A mutable column-major 6x5 matrix view.
MatrixViewMut6xX: A mutable column-major matrix view with 6 rows and a number of columns chosen at runtime.
MatrixViewMutXx1: A mutable column-major matrix view with a number of rows chosen at runtime and 1 column.
MatrixViewMutXx2: A mutable column-major matrix view with a number of rows chosen at runtime and 2 columns.
MatrixViewMutXx3: A mutable column-major matrix view with a number of rows chosen at runtime and 3 columns.
MatrixViewMutXx4: A mutable column-major matrix view with a number of rows chosen at runtime and 4 columns.
MatrixViewMutXx5: A mutable column-major matrix view with a number of rows chosen at runtime and 5 columns.
MatrixViewMutXx6: A mutable column-major matrix view with a number of rows chosen at runtime and 6 columns.
MatrixViewXx1: An immutable column-major matrix view with a number of rows chosen at runtime and 1 column.
MatrixViewXx2: An immutable column-major matrix view with a number of rows chosen at runtime and 2 columns.
MatrixViewXx3: An immutable column-major matrix view with a number of rows chosen at runtime and 3 columns.
MatrixViewXx4: An immutable column-major matrix view with a number of rows chosen at runtime and 4 columns.
MatrixViewXx5: An immutable column-major matrix view with a number of rows chosen at runtime and 5 columns.
MatrixViewXx6: An immutable column-major matrix view with a number of rows chosen at runtime and 6 columns.
MatrixXx1: A heap-allocated, column-major, matrix with a dynamic number of rows and 1 columns.
MatrixXx2: A heap-allocated, column-major, matrix with a dynamic number of rows and 2 columns.
MatrixXx3: A heap-allocated, column-major, matrix with a dynamic number of rows and 3 columns.
MatrixXx4: A heap-allocated, column-major, matrix with a dynamic number of rows and 4 columns.
MatrixXx5: A heap-allocated, column-major, matrix with a dynamic number of rows and 5 columns.
MatrixXx6: A heap-allocated, column-major, matrix with a dynamic number of rows and 6 columns.
OMatrix: An owned matrix column-major matrix with R rows and C columns.
OVector: An owned D-dimensional column vector.
Owned: The owned data storage that can be allocated from S.
OwnedUninit: The owned data storage that can be allocated from S.
Point: A point with D elements.
Point1: A statically sized 1-dimensional column point.
Point2: A statically sized 2-dimensional column point.
Point3: A statically sized 3-dimensional column point.
Point4: A statically sized 4-dimensional column point.
Point5: A statically sized 5-dimensional column point.
Point6: A statically sized 6-dimensional column point.
Projective2: An invertible 2D general transformation. Stored as a homogeneous 3x3 matrix.
Projective3: An invertible 3D general transformation. Stored as a homogeneous 4x4 matrix.
RStride: The row-stride of the owned data storage for a buffer of dimension (R, C).
Reflection1: A 1-dimensional reflection.
Reflection2: A 2-dimensional reflection.
Reflection3: A 3-dimensional reflection.
Reflection4: A 4-dimensional reflection.
Reflection5: A 5-dimensional reflection.
Reflection6: A 6-dimensional reflection.
Rotation2: A 2-dimensional rotation matrix.
Rotation3: A 3-dimensional rotation matrix.
RowDVector: A dynamically sized row vector.
RowOVector: An owned D-dimensional row vector.
RowSVector: A statically sized D-dimensional row vector.
RowVector: A matrix with one row and D columns .
RowVector1: A stack-allocated, 1-dimensional row vector.
RowVector2: A stack-allocated, 2-dimensional row vector.
RowVector3: A stack-allocated, 3-dimensional row vector.
RowVector4: A stack-allocated, 4-dimensional row vector.
RowVector5: A stack-allocated, 5-dimensional row vector.
RowVector6: A stack-allocated, 6-dimensional row vector.
SMatrix: A statically sized column-major matrix with R rows and C columns.
SMatrixSliceDeprecated: A column-major matrix slice with dimensions known at compile-time.
SMatrixSliceMutDeprecated: A column-major matrix slice with dimensions known at compile-time.
SMatrixView: An immutable column-major matrix view with dimensions known at compile-time.
SMatrixViewMut: A mutable column-major matrix view with dimensions known at compile-time.
SVector: A statically sized D-dimensional column vector.
SVectorSliceDeprecated: A column vector slice with dimensions known at compile-time.
SVectorSliceMutDeprecated: A column vector slice with dimensions known at compile-time.
SVectorView: An immutable column vector view with dimensions known at compile-time.
SVectorViewMut: A mutable column vector view with dimensions known at compile-time.
SameShapeStorage: The data storage for the sum of two matrices with dimensions (R1, C1) and (R2, C2).
Scale1: A 1-dimensional scale.
Scale2: A 2-dimensional scale.
Scale3: A 3-dimensional scale.
Scale4: A 4-dimensional scale.
Scale5: A 5-dimensional scale.
Scale6: A 6-dimensional scale.
Similarity2: A 2-dimensional similarity.
Similarity3: A 3-dimensional similarity.
SimilarityMatrix2: A 2-dimensional similarity using a rotation matrix for its rotation part.
SimilarityMatrix3: A 3-dimensional similarity using a rotation matrix for its rotation part.
SliceStorageDeprecated: A matrix data storage for a matrix view. Only contains an internal reference to another matrix data storage.
SliceStorageMutDeprecated: A mutable matrix data storage for mutable matrix view. Only contains an internal mutable reference to another matrix data storage.
SquareMatrix: A square matrix.
Transform2: A 2D general transformation that may not be invertible. Stored as a homogeneous 3x3 matrix.
Transform3: A 3D general transformation that may not be inversible. Stored as a homogeneous 4x4 matrix.
Translation1: A 1-dimensional translation.
Translation2: A 2-dimensional translation.
Translation3: A 3-dimensional translation.
Translation4: A 4-dimensional translation.
Translation5: A 5-dimensional translation.
Translation6: A 6-dimensional translation.
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UninitMatrix: An owned matrix with uninitialized data.
UninitVector: An owned matrix with uninitialized data.
UnitComplex: A 2D rotation represented as a complex number with magnitude 1.
UnitDualQuaternion: A unit dual quaternion. May be used to represent a rotation followed by a translation.
UnitQuaternion: A unit quaternions. May be used to represent a rotation.
UnitVector1: A stack-allocated, 1-dimensional unit vector.
UnitVector2: A stack-allocated, 2-dimensional unit vector.
UnitVector3: A stack-allocated, 3-dimensional unit vector.
UnitVector4: A stack-allocated, 4-dimensional unit vector.
UnitVector5: A stack-allocated, 5-dimensional unit vector.
UnitVector6: A stack-allocated, 6-dimensional unit vector.
Vector: A matrix with one column and D rows.
Vector1: A stack-allocated, 1-dimensional column vector.
Vector2: A stack-allocated, 2-dimensional column vector.
Vector3: A stack-allocated, 3-dimensional column vector.
Vector4: A stack-allocated, 4-dimensional column vector.
Vector5: A stack-allocated, 5-dimensional column vector.
Vector6: A stack-allocated, 6-dimensional column vector.
VectorNDeprecated: An owned matrix column-major matrix with R rows and C columns.
VectorSliceDeprecated: A column vector slice with dimensions known at compile-time.
VectorSlice1Deprecated: A 1D column vector slice.
VectorSlice2Deprecated: A 2D column vector slice.
VectorSlice3Deprecated: A 3D column vector slice.
VectorSlice4Deprecated: A 4D column vector slice.
VectorSlice5Deprecated: A 5D column vector slice.
VectorSlice6Deprecated: A 6D column vector slice.
VectorSliceMutDeprecated: A column vector slice with dimensions known at compile-time.
VectorSliceMut1Deprecated: A 1D column vector slice.
VectorSliceMut2Deprecated: A 2D column vector slice.
VectorSliceMut3Deprecated: A 3D column vector slice.
VectorSliceMut4Deprecated: A 4D column vector slice.
VectorSliceMut5Deprecated: A 5D column vector slice.
VectorSliceMut6Deprecated: A 6D column vector slice.
VectorSum: The type of the result of a matrix sum.
VectorView: An immutable column vector view with dimensions known at compile-time.
VectorView1: An immutable 1D column vector view.
VectorView2: An immutable 2D column vector view.
VectorView3: An immutable 3D column vector view.
VectorView4: An immutable 4D column vector view.
VectorView5: An immutable 5D column vector view.
VectorView6: An immutable 6D column vector view.
VectorViewMut: A mutable column vector view with dimensions known at compile-time.
VectorViewMut1: A mutable 1D column vector view.
VectorViewMut2: A mutable 2D column vector view.
VectorViewMut3: A mutable 3D column vector view.
VectorViewMut4: A mutable 4D column vector view.
VectorViewMut5: A mutable 5D column vector view.
VectorViewMut6: A mutable 6D column vector view.

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