/
matrix.rs
2151 lines (1939 loc) · 70.8 KB
/
matrix.rs
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use num::{One, Zero};
#[cfg(feature = "abomonation-serialize")]
use std::io::{Result as IOResult, Write};
use approx::{AbsDiffEq, RelativeEq, UlpsEq};
use std::any::TypeId;
use std::cmp::Ordering;
use std::fmt;
use std::hash::{Hash, Hasher};
use std::marker::PhantomData;
use std::mem;
#[cfg(feature = "serde-serialize-no-std")]
use serde::{Deserialize, Deserializer, Serialize, Serializer};
#[cfg(feature = "abomonation-serialize")]
use abomonation::Abomonation;
use simba::scalar::{ClosedAdd, ClosedMul, ClosedSub, Field, SupersetOf};
use simba::simd::SimdPartialOrd;
use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
use crate::base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
use crate::base::dimension::{Dim, DimAdd, DimSum, IsNotStaticOne, U1, U2, U3};
use crate::base::iter::{
ColumnIter, ColumnIterMut, MatrixIter, MatrixIterMut, RowIter, RowIterMut,
};
use crate::base::storage::{
ContiguousStorage, ContiguousStorageMut, Owned, SameShapeStorage, Storage, StorageMut,
};
use crate::base::{Const, DefaultAllocator, OMatrix, OVector, Scalar, Unit};
use crate::{ArrayStorage, SMatrix, SimdComplexField};
#[cfg(any(feature = "std", feature = "alloc"))]
use crate::{DMatrix, DVector, Dynamic, VecStorage};
/// A square matrix.
pub type SquareMatrix<T, D, S> = Matrix<T, D, D, S>;
/// A matrix with one column and `D` rows.
pub type Vector<T, D, S> = Matrix<T, D, U1, S>;
/// A matrix with one row and `D` columns .
pub type RowVector<T, D, S> = Matrix<T, U1, D, S>;
/// The type of the result of a matrix sum.
pub type MatrixSum<T, R1, C1, R2, C2> =
Matrix<T, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<T, R1, C1, R2, C2>>;
/// The type of the result of a matrix sum.
pub type VectorSum<T, R1, R2> =
Matrix<T, SameShapeR<R1, R2>, U1, SameShapeStorage<T, R1, U1, R2, U1>>;
/// The type of the result of a matrix cross product.
pub type MatrixCross<T, R1, C1, R2, C2> =
Matrix<T, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<T, R1, C1, R2, C2>>;
/// The most generic column-major matrix (and vector) type.
///
/// # Methods summary
/// Because `Matrix` is the most generic types used as a common representation of all matrices and
/// vectors of **nalgebra** this documentation page contains every single matrix/vector-related
/// method. In order to make browsing this page simpler, the next subsections contain direct links
/// to groups of methods related to a specific topic.
///
/// #### Vector and matrix construction
/// - [Constructors of statically-sized vectors or statically-sized matrices](#constructors-of-statically-sized-vectors-or-statically-sized-matrices)
/// (`Vector3`, `Matrix3x6`…)
/// - [Constructors of fully dynamic matrices](#constructors-of-fully-dynamic-matrices) (`DMatrix`)
/// - [Constructors of dynamic vectors and matrices with a dynamic number of rows](#constructors-of-dynamic-vectors-and-matrices-with-a-dynamic-number-of-rows)
/// (`DVector`, `MatrixXx3`…)
/// - [Constructors of matrices with a dynamic number of columns](#constructors-of-matrices-with-a-dynamic-number-of-columns)
/// (`Matrix2xX`…)
/// - [Generic constructors](#generic-constructors)
/// (For code generic wrt. the vectors or matrices dimensions.)
///
/// #### Computer graphics utilities for transformations
/// - [2D transformations as a Matrix3 <span style="float:right;">`new_rotation`…</span>](#2d-transformations-as-a-matrix3)
/// - [3D transformations as a Matrix4 <span style="float:right;">`new_rotation`, `new_perspective`, `look_at_rh`…</span>](#3d-transformations-as-a-matrix4)
/// - [Translation and scaling in any dimension <span style="float:right;">`new_scaling`, `new_translation`…</span>](#translation-and-scaling-in-any-dimension)
/// - [Append/prepend translation and scaling <span style="float:right;">`append_scaling`, `prepend_translation_mut`…</span>](#appendprepend-translation-and-scaling)
/// - [Transformation of vectors and points <span style="float:right;">`transform_vector`, `transform_point`…</span>](#transformation-of-vectors-and-points)
///
/// #### Common math operations
/// - [Componentwise operations <span style="float:right;">`component_mul`, `component_div`, `inf`…</span>](#componentwise-operations)
/// - [Special multiplications <span style="float:right;">`tr_mul`, `ad_mul`, `kronecker`…</span>](#special-multiplications)
/// - [Dot/scalar product <span style="float:right;">`dot`, `dotc`, `tr_dot`…</span>](#dotscalar-product)
/// - [Cross product <span style="float:right;">`cross`, `perp`…</span>](#cross-product)
/// - [Magnitude and norms <span style="float:right;">`norm`, `normalize`, `metric_distance`…</span>](#magnitude-and-norms)
/// - [In-place normalization <span style="float:right;">`normalize_mut`, `try_normalize_mut`…</span>](#in-place-normalization)
/// - [Interpolation <span style="float:right;">`lerp`, `slerp`…</span>](#interpolation)
/// - [BLAS functions <span style="float:right;">`gemv`, `gemm`, `syger`…</span>](#blas-functions)
/// - [Swizzling <span style="float:right;">`xx`, `yxz`…</span>](#swizzling)
///
/// #### Statistics
/// - [Common operations <span style="float:right;">`row_sum`, `column_mean`, `variance`…</span>](#common-statistics-operations)
/// - [Find the min and max components <span style="float:right;">`min`, `max`, `amin`, `amax`, `camin`, `cmax`…</span>](#find-the-min-and-max-components)
/// - [Find the min and max components (vector-specific methods) <span style="float:right;">`argmin`, `argmax`, `icamin`, `icamax`…</span>](#find-the-min-and-max-components-vector-specific-methods)
///
/// #### Iteration, map, and fold
/// - [Iteration on components, rows, and columns <span style="float:right;">`iter`, `column_iter`…</span>](#iteration-on-components-rows-and-columns)
/// - [Elementwise mapping and folding <span style="float:right;">`map`, `fold`, `zip_map`…</span>](#elementwise-mapping-and-folding)
/// - [Folding or columns and rows <span style="float:right;">`compress_rows`, `compress_columns`…</span>](#folding-on-columns-and-rows)
///
/// #### Vector and matrix slicing
/// - [Creating matrix slices from `&[T]` <span style="float:right;">`from_slice`, `from_slice_with_strides`…</span>](#creating-matrix-slices-from-t)
/// - [Creating mutable matrix slices from `&mut [T]` <span style="float:right;">`from_slice_mut`, `from_slice_with_strides_mut`…</span>](#creating-mutable-matrix-slices-from-mut-t)
/// - [Slicing based on index and length <span style="float:right;">`row`, `columns`, `slice`…</span>](#slicing-based-on-index-and-length)
/// - [Mutable slicing based on index and length <span style="float:right;">`row_mut`, `columns_mut`, `slice_mut`…</span>](#mutable-slicing-based-on-index-and-length)
/// - [Slicing based on ranges <span style="float:right;">`rows_range`, `columns_range`…</span>](#slicing-based-on-ranges)
/// - [Mutable slicing based on ranges <span style="float:right;">`rows_range_mut`, `columns_range_mut`…</span>](#mutable-slicing-based-on-ranges)
///
/// #### In-place modification of a single matrix or vector
/// - [In-place filling <span style="float:right;">`fill`, `fill_diagonal`, `fill_with_identity`…</span>](#in-place-filling)
/// - [In-place swapping <span style="float:right;">`swap`, `swap_columns`…</span>](#in-place-swapping)
/// - [Set rows, columns, and diagonal <span style="float:right;">`set_column`, `set_diagonal`…</span>](#set-rows-columns-and-diagonal)
///
/// #### Vector and matrix size modification
/// - [Rows and columns insertion <span style="float:right;">`insert_row`, `insert_column`…</span>](#rows-and-columns-insertion)
/// - [Rows and columns removal <span style="float:right;">`remove_row`, `remove column`…</span>](#rows-and-columns-removal)
/// - [Rows and columns extraction <span style="float:right;">`select_rows`, `select_columns`…</span>](#rows-and-columns-extraction)
/// - [Resizing and reshaping <span style="float:right;">`resize`, `reshape_generic`…</span>](#resizing-and-reshaping)
/// - [In-place resizing <span style="float:right;">`resize_mut`, `resize_vertically_mut`…</span>](#in-place-resizing)
///
/// #### Matrix decomposition
/// - [Rectangular matrix decomposition <span style="float:right;">`qr`, `lu`, `svd`…</span>](#rectangular-matrix-decomposition)
/// - [Square matrix decomposition <span style="float:right;">`cholesky`, `symmetric_eigen`…</span>](#square-matrix-decomposition)
///
/// #### Vector basis computation
/// - [Basis and orthogonalization <span style="float:right;">`orthonormal_subspace_basis`, `orthonormalize`…</span>](#basis-and-orthogonalization)
///
/// # Type parameters
/// The generic `Matrix` type has four type parameters:
/// - `T`: for the matrix components scalar type.
/// - `R`: for the matrix number of rows.
/// - `C`: for the matrix number of columns.
/// - `S`: for the matrix data storage, i.e., the buffer that actually contains the matrix
/// components.
///
/// The matrix dimensions parameters `R` and `C` can either be:
/// - type-level unsigned integer constants (e.g. `U1`, `U124`) from the `nalgebra::` root module.
/// All numbers from 0 to 127 are defined that way.
/// - type-level unsigned integer constants (e.g. `U1024`, `U10000`) from the `typenum::` crate.
/// Using those, you will not get error messages as nice as for numbers smaller than 128 defined on
/// the `nalgebra::` module.
/// - the special value `Dynamic` from the `nalgebra::` root module. This indicates that the
/// specified dimension is not known at compile-time. Note that this will generally imply that the
/// matrix data storage `S` performs a dynamic allocation and contains extra metadata for the
/// matrix shape.
///
/// Note that mixing `Dynamic` with type-level unsigned integers is allowed. Actually, a
/// dynamically-sized column vector should be represented as a `Matrix<T, Dynamic, U1, S>` (given
/// some concrete types for `T` and a compatible data storage type `S`).
#[repr(C)]
#[derive(Clone, Copy)]
pub struct Matrix<T, R, C, S> {
/// The data storage that contains all the matrix components. Disappointed?
///
/// Well, if you came here to see how you can access the matrix components,
/// you may be in luck: you can access the individual components of all vectors with compile-time
/// dimensions <= 6 using field notation like this:
/// `vec.x`, `vec.y`, `vec.z`, `vec.w`, `vec.a`, `vec.b`. Reference and assignation work too:
/// ```
/// # use nalgebra::Vector3;
/// let mut vec = Vector3::new(1.0, 2.0, 3.0);
/// vec.x = 10.0;
/// vec.y += 30.0;
/// assert_eq!(vec.x, 10.0);
/// assert_eq!(vec.y + 100.0, 132.0);
/// ```
/// Similarly, for matrices with compile-time dimensions <= 6, you can use field notation
/// like this: `mat.m11`, `mat.m42`, etc. The first digit identifies the row to address
/// and the second digit identifies the column to address. So `mat.m13` identifies the component
/// at the first row and third column (note that the count of rows and columns start at 1 instead
/// of 0 here. This is so we match the mathematical notation).
///
/// For all matrices and vectors, independently from their size, individual components can
/// be accessed and modified using indexing: `vec[20]`, `mat[(20, 19)]`. Here the indexing
/// starts at 0 as you would expect.
pub data: S,
// NOTE: the fact that this field is private is important because
// this prevents the user from constructing a matrix with
// dimensions R, C that don't match the dimension of the
// storage S. Instead they have to use the unsafe function
// from_data_statically_unchecked.
// Note that it would probably make sense to just have
// the type `Matrix<S>`, and have `T, R, C` be associated-types
// of the `Storage` trait. However, because we don't have
// specialization, this is not bossible because these `T, R, C`
// allows us to desambiguate a lot of configurations.
_phantoms: PhantomData<(T, R, C)>,
}
impl<T, R: Dim, C: Dim, S: fmt::Debug> fmt::Debug for Matrix<T, R, C, S> {
fn fmt(&self, formatter: &mut fmt::Formatter) -> Result<(), fmt::Error> {
formatter
.debug_struct("Matrix")
.field("data", &self.data)
.finish()
}
}
impl<T, R, C, S> Default for Matrix<T, R, C, S>
where
T: Scalar,
R: Dim,
C: Dim,
S: Default,
{
fn default() -> Self {
Matrix {
data: Default::default(),
_phantoms: PhantomData,
}
}
}
#[cfg(feature = "serde-serialize-no-std")]
impl<T, R, C, S> Serialize for Matrix<T, R, C, S>
where
T: Scalar,
R: Dim,
C: Dim,
S: Serialize,
{
fn serialize<Ser>(&self, serializer: Ser) -> Result<Ser::Ok, Ser::Error>
where
Ser: Serializer,
{
self.data.serialize(serializer)
}
}
#[cfg(feature = "serde-serialize-no-std")]
impl<'de, T, R, C, S> Deserialize<'de> for Matrix<T, R, C, S>
where
T: Scalar,
R: Dim,
C: Dim,
S: Deserialize<'de>,
{
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where
D: Deserializer<'de>,
{
S::deserialize(deserializer).map(|x| Matrix {
data: x,
_phantoms: PhantomData,
})
}
}
#[cfg(feature = "abomonation-serialize")]
impl<T: Scalar, R: Dim, C: Dim, S: Abomonation> Abomonation for Matrix<T, R, C, S> {
unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
self.data.entomb(writer)
}
unsafe fn exhume<'a, 'b>(&'a mut self, bytes: &'b mut [u8]) -> Option<&'b mut [u8]> {
self.data.exhume(bytes)
}
fn extent(&self) -> usize {
self.data.extent()
}
}
#[cfg(feature = "compare")]
impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> matrixcompare_core::Matrix<T>
for Matrix<T, R, C, S>
{
fn rows(&self) -> usize {
self.nrows()
}
fn cols(&self) -> usize {
self.ncols()
}
fn access(&self) -> matrixcompare_core::Access<T> {
matrixcompare_core::Access::Dense(self)
}
}
#[cfg(feature = "compare")]
impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> matrixcompare_core::DenseAccess<T>
for Matrix<T, R, C, S>
{
fn fetch_single(&self, row: usize, col: usize) -> T {
self.index((row, col)).clone()
}
}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> bytemuck::Zeroable
for Matrix<T, R, C, S>
where
S: bytemuck::Zeroable,
{
}
#[cfg(feature = "bytemuck")]
unsafe impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> bytemuck::Pod for Matrix<T, R, C, S>
where
S: bytemuck::Pod,
Self: Copy,
{
}
#[cfg(feature = "rkyv-serialize-no-std")]
mod rkyv_impl {
use super::Matrix;
use core::marker::PhantomData;
use rkyv::{offset_of, project_struct, Archive, Deserialize, Fallible, Serialize};
impl<T: Archive, R: Archive, C: Archive, S: Archive> Archive for Matrix<T, R, C, S> {
type Archived = Matrix<T::Archived, R::Archived, C::Archived, S::Archived>;
type Resolver = S::Resolver;
fn resolve(
&self,
pos: usize,
resolver: Self::Resolver,
out: &mut core::mem::MaybeUninit<Self::Archived>,
) {
self.data.resolve(
pos + offset_of!(Self::Archived, data),
resolver,
project_struct!(out: Self::Archived => data),
);
}
}
impl<T: Archive, R: Archive, C: Archive, S: Serialize<_S>, _S: Fallible + ?Sized> Serialize<_S>
for Matrix<T, R, C, S>
{
fn serialize(&self, serializer: &mut _S) -> Result<Self::Resolver, _S::Error> {
self.data.serialize(serializer)
}
}
impl<T: Archive, R: Archive, C: Archive, S: Archive, D: Fallible + ?Sized>
Deserialize<Matrix<T, R, C, S>, D>
for Matrix<T::Archived, R::Archived, C::Archived, S::Archived>
where
S::Archived: Deserialize<S, D>,
{
fn deserialize(&self, deserializer: &mut D) -> Result<Matrix<T, R, C, S>, D::Error> {
Ok(Matrix {
data: self.data.deserialize(deserializer)?,
_phantoms: PhantomData,
})
}
}
}
impl<T, R, C, S> Matrix<T, R, C, S> {
/// Creates a new matrix with the given data without statically checking that the matrix
/// dimension matches the storage dimension.
#[inline(always)]
pub const unsafe fn from_data_statically_unchecked(data: S) -> Matrix<T, R, C, S> {
Matrix {
data,
_phantoms: PhantomData,
}
}
}
impl<T, const R: usize, const C: usize> SMatrix<T, R, C> {
/// Creates a new statically-allocated matrix from the given [ArrayStorage].
///
/// This method exists primarily as a workaround for the fact that `from_data` can not
/// work in `const fn` contexts.
#[inline(always)]
pub const fn from_array_storage(storage: ArrayStorage<T, R, C>) -> Self {
// This is sound because the row and column types are exactly the same as that of the
// storage, so there can be no mismatch
unsafe { Self::from_data_statically_unchecked(storage) }
}
}
// TODO: Consider removing/deprecating `from_vec_storage` once we are able to make
// `from_data` const fn compatible
#[cfg(any(feature = "std", feature = "alloc"))]
impl<T> DMatrix<T> {
/// Creates a new heap-allocated matrix from the given [VecStorage].
///
/// This method exists primarily as a workaround for the fact that `from_data` can not
/// work in `const fn` contexts.
pub const fn from_vec_storage(storage: VecStorage<T, Dynamic, Dynamic>) -> Self {
// This is sound because the dimensions of the matrix and the storage are guaranteed
// to be the same
unsafe { Self::from_data_statically_unchecked(storage) }
}
}
// TODO: Consider removing/deprecating `from_vec_storage` once we are able to make
// `from_data` const fn compatible
#[cfg(any(feature = "std", feature = "alloc"))]
impl<T> DVector<T> {
/// Creates a new heap-allocated matrix from the given [VecStorage].
///
/// This method exists primarily as a workaround for the fact that `from_data` can not
/// work in `const fn` contexts.
pub const fn from_vec_storage(storage: VecStorage<T, Dynamic, U1>) -> Self {
// This is sound because the dimensions of the matrix and the storage are guaranteed
// to be the same
unsafe { Self::from_data_statically_unchecked(storage) }
}
}
impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S> {
/// Creates a new matrix with the given data.
#[inline(always)]
pub fn from_data(data: S) -> Self {
unsafe { Self::from_data_statically_unchecked(data) }
}
/// Creates a new uninitialized matrix with the given uninitialized data
pub unsafe fn from_uninitialized_data(data: mem::MaybeUninit<S>) -> mem::MaybeUninit<Self> {
let res: Matrix<T, R, C, mem::MaybeUninit<S>> = Matrix {
data,
_phantoms: PhantomData,
};
let res: mem::MaybeUninit<Matrix<T, R, C, mem::MaybeUninit<S>>> =
mem::MaybeUninit::new(res);
// safety: since we wrap the inner MaybeUninit in an outer MaybeUninit above, the fact that the `data` field is partially-uninitialized is still opaque.
// with s/transmute_copy/transmute/, rustc claims that `MaybeUninit<Matrix<T, R, C, MaybeUninit<S>>>` may be of a different size from `MaybeUninit<Matrix<T, R, C, S>>`
// but MaybeUninit's documentation says "MaybeUninit<T> is guaranteed to have the same size, alignment, and ABI as T", which implies those types should be the same size
let res: mem::MaybeUninit<Matrix<T, R, C, S>> = mem::transmute_copy(&res);
res
}
/// The shape of this matrix returned as the tuple (number of rows, number of columns).
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.shape(), (3, 4));
#[inline]
#[must_use]
pub fn shape(&self) -> (usize, usize) {
let (nrows, ncols) = self.data.shape();
(nrows.value(), ncols.value())
}
/// The number of rows of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.nrows(), 3);
#[inline]
#[must_use]
pub fn nrows(&self) -> usize {
self.shape().0
}
/// The number of columns of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.ncols(), 4);
#[inline]
#[must_use]
pub fn ncols(&self) -> usize {
self.shape().1
}
/// The strides (row stride, column stride) of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::DMatrix;
/// let mat = DMatrix::<f32>::zeros(10, 10);
/// let slice = mat.slice_with_steps((0, 0), (5, 3), (1, 2));
/// // The column strides is the number of steps (here 2) multiplied by the corresponding dimension.
/// assert_eq!(mat.strides(), (1, 10));
#[inline]
#[must_use]
pub fn strides(&self) -> (usize, usize) {
let (srows, scols) = self.data.strides();
(srows.value(), scols.value())
}
/// Computes the row and column coordinates of the i-th element of this matrix seen as a
/// vector.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2;
/// let m = Matrix2::new(1, 2,
/// 3, 4);
/// let i = m.vector_to_matrix_index(3);
/// assert_eq!(i, (1, 1));
/// assert_eq!(m[i], m[3]);
/// ```
#[inline]
#[must_use]
pub fn vector_to_matrix_index(&self, i: usize) -> (usize, usize) {
let (nrows, ncols) = self.shape();
// Two most common uses that should be optimized by the compiler for statically-sized
// matrices.
if nrows == 1 {
(0, i)
} else if ncols == 1 {
(i, 0)
} else {
(i % nrows, i / nrows)
}
}
/// Returns a pointer to the start of the matrix.
///
/// If the matrix is not empty, this pointer is guaranteed to be aligned
/// and non-null.
///
/// # Example
/// ```
/// # use nalgebra::Matrix2;
/// let m = Matrix2::new(1, 2,
/// 3, 4);
/// let ptr = m.as_ptr();
/// assert_eq!(unsafe { *ptr }, m[0]);
/// ```
#[inline]
#[must_use]
pub fn as_ptr(&self) -> *const T {
self.data.ptr()
}
/// Tests whether `self` and `rhs` are equal up to a given epsilon.
///
/// See `relative_eq` from the `RelativeEq` trait for more details.
#[inline]
#[must_use]
pub fn relative_eq<R2, C2, SB>(
&self,
other: &Matrix<T, R2, C2, SB>,
eps: T::Epsilon,
max_relative: T::Epsilon,
) -> bool
where
T: RelativeEq,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
T::Epsilon: Copy,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
assert!(self.shape() == other.shape());
self.iter()
.zip(other.iter())
.all(|(a, b)| a.relative_eq(b, eps, max_relative))
}
/// Tests whether `self` and `rhs` are exactly equal.
#[inline]
#[must_use]
#[allow(clippy::should_implement_trait)]
pub fn eq<R2, C2, SB>(&self, other: &Matrix<T, R2, C2, SB>) -> bool
where
T: PartialEq,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
assert!(self.shape() == other.shape());
self.iter().zip(other.iter()).all(|(a, b)| *a == *b)
}
/// Moves this matrix into one that owns its data.
#[inline]
pub fn into_owned(self) -> OMatrix<T, R, C>
where
DefaultAllocator: Allocator<T, R, C>,
{
Matrix::from_data(self.data.into_owned())
}
// TODO: this could probably benefit from specialization.
// XXX: bad name.
/// Moves this matrix into one that owns its data. The actual type of the result depends on
/// matrix storage combination rules for addition.
#[inline]
pub fn into_owned_sum<R2, C2>(self) -> MatrixSum<T, R, C, R2, C2>
where
R2: Dim,
C2: Dim,
DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
if TypeId::of::<SameShapeStorage<T, R, C, R2, C2>>() == TypeId::of::<Owned<T, R, C>>() {
// We can just return `self.into_owned()`.
unsafe {
// TODO: check that those copies are optimized away by the compiler.
let owned = self.into_owned();
let res = mem::transmute_copy(&owned);
mem::forget(owned);
res
}
} else {
self.clone_owned_sum()
}
}
/// Clones this matrix to one that owns its data.
#[inline]
#[must_use]
pub fn clone_owned(&self) -> OMatrix<T, R, C>
where
DefaultAllocator: Allocator<T, R, C>,
{
Matrix::from_data(self.data.clone_owned())
}
/// Clones this matrix into one that owns its data. The actual type of the result depends on
/// matrix storage combination rules for addition.
#[inline]
#[must_use]
pub fn clone_owned_sum<R2, C2>(&self) -> MatrixSum<T, R, C, R2, C2>
where
R2: Dim,
C2: Dim,
DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
let (nrows, ncols) = self.shape();
let nrows: SameShapeR<R, R2> = Dim::from_usize(nrows);
let ncols: SameShapeC<C, C2> = Dim::from_usize(ncols);
let mut res: MatrixSum<T, R, C, R2, C2> =
unsafe { crate::unimplemented_or_uninitialized_generic!(nrows, ncols) };
// TODO: use copy_from
for j in 0..res.ncols() {
for i in 0..res.nrows() {
unsafe {
*res.get_unchecked_mut((i, j)) = self.get_unchecked((i, j)).inlined_clone();
}
}
}
res
}
/// Transposes `self` and store the result into `out`.
#[inline]
pub fn transpose_to<R2, C2, SB>(&self, out: &mut Matrix<T, R2, C2, SB>)
where
R2: Dim,
C2: Dim,
SB: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
{
let (nrows, ncols) = self.shape();
assert!(
(ncols, nrows) == out.shape(),
"Incompatible shape for transpose-copy."
);
// TODO: optimize that.
for i in 0..nrows {
for j in 0..ncols {
unsafe {
*out.get_unchecked_mut((j, i)) = self.get_unchecked((i, j)).inlined_clone();
}
}
}
}
/// Transposes `self`.
#[inline]
#[must_use = "Did you mean to use transpose_mut()?"]
pub fn transpose(&self) -> OMatrix<T, C, R>
where
DefaultAllocator: Allocator<T, C, R>,
{
let (nrows, ncols) = self.data.shape();
unsafe {
let mut res = crate::unimplemented_or_uninitialized_generic!(ncols, nrows);
self.transpose_to(&mut res);
res
}
}
}
/// # Elementwise mapping and folding
impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S> {
/// Returns a matrix containing the result of `f` applied to each of its entries.
#[inline]
#[must_use]
pub fn map<T2: Scalar, F: FnMut(T) -> T2>(&self, mut f: F) -> OMatrix<T2, R, C>
where
DefaultAllocator: Allocator<T2, R, C>,
{
let (nrows, ncols) = self.data.shape();
let mut res: OMatrix<T2, R, C> =
unsafe { crate::unimplemented_or_uninitialized_generic!(nrows, ncols) };
for j in 0..ncols.value() {
for i in 0..nrows.value() {
unsafe {
let a = self.data.get_unchecked(i, j).inlined_clone();
*res.data.get_unchecked_mut(i, j) = f(a)
}
}
}
res
}
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// let q = Vector3::new(1.0f64, 2.0, 3.0);
/// let q2 = q.cast::<f32>();
/// assert_eq!(q2, Vector3::new(1.0f32, 2.0, 3.0));
/// ```
pub fn cast<T2: Scalar>(self) -> OMatrix<T2, R, C>
where
OMatrix<T2, R, C>: SupersetOf<Self>,
DefaultAllocator: Allocator<T2, R, C>,
{
crate::convert(self)
}
/// Similar to `self.iter().fold(init, f)` except that `init` is replaced by a closure.
///
/// The initialization closure is given the first component of this matrix:
/// - If the matrix has no component (0 rows or 0 columns) then `init_f` is called with `None`
/// and its return value is the value returned by this method.
/// - If the matrix has has least one component, then `init_f` is called with the first component
/// to compute the initial value. Folding then continues on all the remaining components of the matrix.
#[inline]
#[must_use]
pub fn fold_with<T2>(
&self,
init_f: impl FnOnce(Option<&T>) -> T2,
f: impl FnMut(T2, &T) -> T2,
) -> T2 {
let mut it = self.iter();
let init = init_f(it.next());
it.fold(init, f)
}
/// Returns a matrix containing the result of `f` applied to each of its entries. Unlike `map`,
/// `f` also gets passed the row and column index, i.e. `f(row, col, value)`.
#[inline]
#[must_use]
pub fn map_with_location<T2: Scalar, F: FnMut(usize, usize, T) -> T2>(
&self,
mut f: F,
) -> OMatrix<T2, R, C>
where
DefaultAllocator: Allocator<T2, R, C>,
{
let (nrows, ncols) = self.data.shape();
let mut res: OMatrix<T2, R, C> =
unsafe { crate::unimplemented_or_uninitialized_generic!(nrows, ncols) };
for j in 0..ncols.value() {
for i in 0..nrows.value() {
unsafe {
let a = self.data.get_unchecked(i, j).inlined_clone();
*res.data.get_unchecked_mut(i, j) = f(i, j, a)
}
}
}
res
}
/// Returns a matrix containing the result of `f` applied to each entries of `self` and
/// `rhs`.
#[inline]
#[must_use]
pub fn zip_map<T2, N3, S2, F>(&self, rhs: &Matrix<T2, R, C, S2>, mut f: F) -> OMatrix<N3, R, C>
where
T2: Scalar,
N3: Scalar,
S2: Storage<T2, R, C>,
F: FnMut(T, T2) -> N3,
DefaultAllocator: Allocator<N3, R, C>,
{
let (nrows, ncols) = self.data.shape();
let mut res: OMatrix<N3, R, C> =
unsafe { crate::unimplemented_or_uninitialized_generic!(nrows, ncols) };
assert_eq!(
(nrows.value(), ncols.value()),
rhs.shape(),
"Matrix simultaneous traversal error: dimension mismatch."
);
for j in 0..ncols.value() {
for i in 0..nrows.value() {
unsafe {
let a = self.data.get_unchecked(i, j).inlined_clone();
let b = rhs.data.get_unchecked(i, j).inlined_clone();
*res.data.get_unchecked_mut(i, j) = f(a, b)
}
}
}
res
}
/// Returns a matrix containing the result of `f` applied to each entries of `self` and
/// `b`, and `c`.
#[inline]
#[must_use]
pub fn zip_zip_map<T2, N3, N4, S2, S3, F>(
&self,
b: &Matrix<T2, R, C, S2>,
c: &Matrix<N3, R, C, S3>,
mut f: F,
) -> OMatrix<N4, R, C>
where
T2: Scalar,
N3: Scalar,
N4: Scalar,
S2: Storage<T2, R, C>,
S3: Storage<N3, R, C>,
F: FnMut(T, T2, N3) -> N4,
DefaultAllocator: Allocator<N4, R, C>,
{
let (nrows, ncols) = self.data.shape();
let mut res: OMatrix<N4, R, C> =
unsafe { crate::unimplemented_or_uninitialized_generic!(nrows, ncols) };
assert_eq!(
(nrows.value(), ncols.value()),
b.shape(),
"Matrix simultaneous traversal error: dimension mismatch."
);
assert_eq!(
(nrows.value(), ncols.value()),
c.shape(),
"Matrix simultaneous traversal error: dimension mismatch."
);
for j in 0..ncols.value() {
for i in 0..nrows.value() {
unsafe {
let a = self.data.get_unchecked(i, j).inlined_clone();
let b = b.data.get_unchecked(i, j).inlined_clone();
let c = c.data.get_unchecked(i, j).inlined_clone();
*res.data.get_unchecked_mut(i, j) = f(a, b, c)
}
}
}
res
}
/// Folds a function `f` on each entry of `self`.
#[inline]
#[must_use]
pub fn fold<Acc>(&self, init: Acc, mut f: impl FnMut(Acc, T) -> Acc) -> Acc {
let (nrows, ncols) = self.data.shape();
let mut res = init;
for j in 0..ncols.value() {
for i in 0..nrows.value() {
unsafe {
let a = self.data.get_unchecked(i, j).inlined_clone();
res = f(res, a)
}
}
}
res
}
/// Folds a function `f` on each pairs of entries from `self` and `rhs`.
#[inline]
#[must_use]
pub fn zip_fold<T2, R2, C2, S2, Acc>(
&self,
rhs: &Matrix<T2, R2, C2, S2>,
init: Acc,
mut f: impl FnMut(Acc, T, T2) -> Acc,
) -> Acc
where
T2: Scalar,
R2: Dim,
C2: Dim,
S2: Storage<T2, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
let (nrows, ncols) = self.data.shape();
let mut res = init;
assert_eq!(
(nrows.value(), ncols.value()),
rhs.shape(),
"Matrix simultaneous traversal error: dimension mismatch."
);
for j in 0..ncols.value() {
for i in 0..nrows.value() {
unsafe {
let a = self.data.get_unchecked(i, j).inlined_clone();
let b = rhs.data.get_unchecked(i, j).inlined_clone();
res = f(res, a, b)
}
}
}
res
}
/// Replaces each component of `self` by the result of a closure `f` applied on it.
#[inline]
pub fn apply<F: FnMut(T) -> T>(&mut self, mut f: F)
where
S: StorageMut<T, R, C>,
{
let (nrows, ncols) = self.shape();
for j in 0..ncols {
for i in 0..nrows {
unsafe {
let e = self.data.get_unchecked_mut(i, j);
*e = f(e.inlined_clone())
}
}
}
}
/// Replaces each component of `self` by the result of a closure `f` applied on its components
/// joined with the components from `rhs`.
#[inline]
pub fn zip_apply<T2, R2, C2, S2>(
&mut self,
rhs: &Matrix<T2, R2, C2, S2>,
mut f: impl FnMut(T, T2) -> T,
) where
S: StorageMut<T, R, C>,
T2: Scalar,
R2: Dim,
C2: Dim,
S2: Storage<T2, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
let (nrows, ncols) = self.shape();
assert_eq!(
(nrows, ncols),
rhs.shape(),
"Matrix simultaneous traversal error: dimension mismatch."
);
for j in 0..ncols {
for i in 0..nrows {
unsafe {
let e = self.data.get_unchecked_mut(i, j);
let rhs = rhs.get_unchecked((i, j)).inlined_clone();
*e = f(e.inlined_clone(), rhs)
}
}
}
}
/// Replaces each component of `self` by the result of a closure `f` applied on its components
/// joined with the components from `b` and `c`.
#[inline]
pub fn zip_zip_apply<T2, R2, C2, S2, N3, R3, C3, S3>(
&mut self,
b: &Matrix<T2, R2, C2, S2>,
c: &Matrix<N3, R3, C3, S3>,
mut f: impl FnMut(T, T2, N3) -> T,
) where
S: StorageMut<T, R, C>,
T2: Scalar,
R2: Dim,
C2: Dim,