forked from M-Labs/nalgebra
2235 lines
73 KiB
Rust
2235 lines
73 KiB
Rust
use num::{One, Zero};
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use approx::{AbsDiffEq, RelativeEq, UlpsEq};
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use std::any::TypeId;
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use std::cmp::Ordering;
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use std::fmt;
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use std::hash::{Hash, Hasher};
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use std::marker::PhantomData;
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use std::mem;
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#[cfg(feature = "serde-serialize-no-std")]
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use serde::{Deserialize, Deserializer, Serialize, Serializer};
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use simba::scalar::{ClosedAdd, ClosedMul, ClosedSub, Field, SupersetOf};
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use simba::simd::SimdPartialOrd;
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use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
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use crate::base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
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use crate::base::dimension::{Dim, DimAdd, DimSum, IsNotStaticOne, U1, U2, U3};
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use crate::base::iter::{
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ColumnIter, ColumnIterMut, MatrixIter, MatrixIterMut, RowIter, RowIterMut,
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};
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use crate::base::storage::{Owned, RawStorage, RawStorageMut, SameShapeStorage};
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use crate::base::{Const, DefaultAllocator, OMatrix, OVector, Scalar, Unit};
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use crate::{ArrayStorage, SMatrix, SimdComplexField, Storage, UninitMatrix};
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use crate::storage::IsContiguous;
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use crate::uninit::{Init, InitStatus, Uninit};
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#[cfg(any(feature = "std", feature = "alloc"))]
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use crate::{DMatrix, DVector, Dynamic, RowDVector, VecStorage};
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use std::mem::MaybeUninit;
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/// A square matrix.
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pub type SquareMatrix<T, D, S> = Matrix<T, D, D, S>;
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/// A matrix with one column and `D` rows.
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pub type Vector<T, D, S> = Matrix<T, D, U1, S>;
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/// A matrix with one row and `D` columns .
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pub type RowVector<T, D, S> = Matrix<T, U1, D, S>;
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/// The type of the result of a matrix sum.
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pub type MatrixSum<T, R1, C1, R2, C2> =
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Matrix<T, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<T, R1, C1, R2, C2>>;
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/// The type of the result of a matrix sum.
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pub type VectorSum<T, R1, R2> =
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Matrix<T, SameShapeR<R1, R2>, U1, SameShapeStorage<T, R1, U1, R2, U1>>;
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/// The type of the result of a matrix cross product.
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pub type MatrixCross<T, R1, C1, R2, C2> =
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Matrix<T, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<T, R1, C1, R2, C2>>;
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/// The most generic column-major matrix (and vector) type.
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///
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/// # Methods summary
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/// Because `Matrix` is the most generic types used as a common representation of all matrices and
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/// vectors of **nalgebra** this documentation page contains every single matrix/vector-related
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/// method. In order to make browsing this page simpler, the next subsections contain direct links
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/// to groups of methods related to a specific topic.
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///
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/// #### Vector and matrix construction
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/// - [Constructors of statically-sized vectors or statically-sized matrices](#constructors-of-statically-sized-vectors-or-statically-sized-matrices)
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/// (`Vector3`, `Matrix3x6`…)
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/// - [Constructors of fully dynamic matrices](#constructors-of-fully-dynamic-matrices) (`DMatrix`)
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/// - [Constructors of dynamic vectors and matrices with a dynamic number of rows](#constructors-of-dynamic-vectors-and-matrices-with-a-dynamic-number-of-rows)
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/// (`DVector`, `MatrixXx3`…)
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/// - [Constructors of matrices with a dynamic number of columns](#constructors-of-matrices-with-a-dynamic-number-of-columns)
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/// (`Matrix2xX`…)
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/// - [Generic constructors](#generic-constructors)
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/// (For code generic wrt. the vectors or matrices dimensions.)
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///
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/// #### Computer graphics utilities for transformations
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/// - [2D transformations as a Matrix3 <span style="float:right;">`new_rotation`…</span>](#2d-transformations-as-a-matrix3)
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/// - [3D transformations as a Matrix4 <span style="float:right;">`new_rotation`, `new_perspective`, `look_at_rh`…</span>](#3d-transformations-as-a-matrix4)
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/// - [Translation and scaling in any dimension <span style="float:right;">`new_scaling`, `new_translation`…</span>](#translation-and-scaling-in-any-dimension)
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/// - [Append/prepend translation and scaling <span style="float:right;">`append_scaling`, `prepend_translation_mut`…</span>](#appendprepend-translation-and-scaling)
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/// - [Transformation of vectors and points <span style="float:right;">`transform_vector`, `transform_point`…</span>](#transformation-of-vectors-and-points)
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///
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/// #### Common math operations
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/// - [Componentwise operations <span style="float:right;">`component_mul`, `component_div`, `inf`…</span>](#componentwise-operations)
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/// - [Special multiplications <span style="float:right;">`tr_mul`, `ad_mul`, `kronecker`…</span>](#special-multiplications)
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/// - [Dot/scalar product <span style="float:right;">`dot`, `dotc`, `tr_dot`…</span>](#dotscalar-product)
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/// - [Cross product <span style="float:right;">`cross`, `perp`…</span>](#cross-product)
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/// - [Magnitude and norms <span style="float:right;">`norm`, `normalize`, `metric_distance`…</span>](#magnitude-and-norms)
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/// - [In-place normalization <span style="float:right;">`normalize_mut`, `try_normalize_mut`…</span>](#in-place-normalization)
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/// - [Interpolation <span style="float:right;">`lerp`, `slerp`…</span>](#interpolation)
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/// - [BLAS functions <span style="float:right;">`gemv`, `gemm`, `syger`…</span>](#blas-functions)
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/// - [Swizzling <span style="float:right;">`xx`, `yxz`…</span>](#swizzling)
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/// - [Triangular matrix extraction <span style="float:right;">`upper_triangle`, `lower_triangle`</span>](#triangular-matrix-extraction)
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///
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/// #### Statistics
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/// - [Common operations <span style="float:right;">`row_sum`, `column_mean`, `variance`…</span>](#common-statistics-operations)
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/// - [Find the min and max components <span style="float:right;">`min`, `max`, `amin`, `amax`, `camin`, `cmax`…</span>](#find-the-min-and-max-components)
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/// - [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)
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///
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/// #### Iteration, map, and fold
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/// - [Iteration on components, rows, and columns <span style="float:right;">`iter`, `column_iter`…</span>](#iteration-on-components-rows-and-columns)
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/// - [Elementwise mapping and folding <span style="float:right;">`map`, `fold`, `zip_map`…</span>](#elementwise-mapping-and-folding)
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/// - [Folding or columns and rows <span style="float:right;">`compress_rows`, `compress_columns`…</span>](#folding-on-columns-and-rows)
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///
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/// #### Vector and matrix slicing
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/// - [Creating matrix slices from `&[T]` <span style="float:right;">`from_slice`, `from_slice_with_strides`…</span>](#creating-matrix-slices-from-t)
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/// - [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)
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/// - [Slicing based on index and length <span style="float:right;">`row`, `columns`, `slice`…</span>](#slicing-based-on-index-and-length)
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/// - [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)
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/// - [Slicing based on ranges <span style="float:right;">`rows_range`, `columns_range`…</span>](#slicing-based-on-ranges)
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/// - [Mutable slicing based on ranges <span style="float:right;">`rows_range_mut`, `columns_range_mut`…</span>](#mutable-slicing-based-on-ranges)
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///
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/// #### In-place modification of a single matrix or vector
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/// - [In-place filling <span style="float:right;">`fill`, `fill_diagonal`, `fill_with_identity`…</span>](#in-place-filling)
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/// - [In-place swapping <span style="float:right;">`swap`, `swap_columns`…</span>](#in-place-swapping)
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/// - [Set rows, columns, and diagonal <span style="float:right;">`set_column`, `set_diagonal`…</span>](#set-rows-columns-and-diagonal)
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///
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/// #### Vector and matrix size modification
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/// - [Rows and columns insertion <span style="float:right;">`insert_row`, `insert_column`…</span>](#rows-and-columns-insertion)
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/// - [Rows and columns removal <span style="float:right;">`remove_row`, `remove column`…</span>](#rows-and-columns-removal)
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/// - [Rows and columns extraction <span style="float:right;">`select_rows`, `select_columns`…</span>](#rows-and-columns-extraction)
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/// - [Resizing and reshaping <span style="float:right;">`resize`, `reshape_generic`…</span>](#resizing-and-reshaping)
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/// - [In-place resizing <span style="float:right;">`resize_mut`, `resize_vertically_mut`…</span>](#in-place-resizing)
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///
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/// #### Matrix decomposition
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/// - [Rectangular matrix decomposition <span style="float:right;">`qr`, `lu`, `svd`…</span>](#rectangular-matrix-decomposition)
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/// - [Square matrix decomposition <span style="float:right;">`cholesky`, `symmetric_eigen`…</span>](#square-matrix-decomposition)
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///
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/// #### Vector basis computation
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/// - [Basis and orthogonalization <span style="float:right;">`orthonormal_subspace_basis`, `orthonormalize`…</span>](#basis-and-orthogonalization)
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///
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/// # Type parameters
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/// The generic `Matrix` type has four type parameters:
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/// - `T`: for the matrix components scalar type.
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/// - `R`: for the matrix number of rows.
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/// - `C`: for the matrix number of columns.
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/// - `S`: for the matrix data storage, i.e., the buffer that actually contains the matrix
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/// components.
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///
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/// The matrix dimensions parameters `R` and `C` can either be:
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/// - type-level unsigned integer constants (e.g. `U1`, `U124`) from the `nalgebra::` root module.
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/// All numbers from 0 to 127 are defined that way.
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/// - type-level unsigned integer constants (e.g. `U1024`, `U10000`) from the `typenum::` crate.
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/// Using those, you will not get error messages as nice as for numbers smaller than 128 defined on
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/// the `nalgebra::` module.
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/// - the special value `Dynamic` from the `nalgebra::` root module. This indicates that the
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/// specified dimension is not known at compile-time. Note that this will generally imply that the
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/// matrix data storage `S` performs a dynamic allocation and contains extra metadata for the
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/// matrix shape.
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///
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/// Note that mixing `Dynamic` with type-level unsigned integers is allowed. Actually, a
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/// dynamically-sized column vector should be represented as a `Matrix<T, Dynamic, U1, S>` (given
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/// some concrete types for `T` and a compatible data storage type `S`).
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#[repr(C)]
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#[derive(Clone, Copy)]
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#[cfg_attr(
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feature = "rkyv-serialize-no-std",
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derive(rkyv::Archive, rkyv::Serialize, rkyv::Deserialize)
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)]
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#[cfg_attr(
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feature = "rkyv-serialize",
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archive_attr(derive(bytecheck::CheckBytes))
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)]
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#[cfg_attr(feature = "cuda", derive(cust_core::DeviceCopy))]
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pub struct Matrix<T, R, C, S> {
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/// The data storage that contains all the matrix components. Disappointed?
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///
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/// Well, if you came here to see how you can access the matrix components,
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/// you may be in luck: you can access the individual components of all vectors with compile-time
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/// dimensions <= 6 using field notation like this:
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/// `vec.x`, `vec.y`, `vec.z`, `vec.w`, `vec.a`, `vec.b`. Reference and assignation work too:
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/// ```
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/// # use nalgebra::Vector3;
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/// let mut vec = Vector3::new(1.0, 2.0, 3.0);
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/// vec.x = 10.0;
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/// vec.y += 30.0;
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/// assert_eq!(vec.x, 10.0);
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/// assert_eq!(vec.y + 100.0, 132.0);
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/// ```
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/// Similarly, for matrices with compile-time dimensions <= 6, you can use field notation
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/// like this: `mat.m11`, `mat.m42`, etc. The first digit identifies the row to address
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/// and the second digit identifies the column to address. So `mat.m13` identifies the component
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/// at the first row and third column (note that the count of rows and columns start at 1 instead
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/// of 0 here. This is so we match the mathematical notation).
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///
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/// For all matrices and vectors, independently from their size, individual components can
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/// be accessed and modified using indexing: `vec[20]`, `mat[(20, 19)]`. Here the indexing
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/// starts at 0 as you would expect.
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pub data: S,
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// NOTE: the fact that this field is private is important because
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// this prevents the user from constructing a matrix with
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// dimensions R, C that don't match the dimension of the
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// storage S. Instead they have to use the unsafe function
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// from_data_statically_unchecked.
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// Note that it would probably make sense to just have
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// the type `Matrix<S>`, and have `T, R, C` be associated-types
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// of the `RawStorage` trait. However, because we don't have
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// specialization, this is not possible because these `T, R, C`
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// allows us to desambiguate a lot of configurations.
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_phantoms: PhantomData<(T, R, C)>,
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}
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impl<T, R: Dim, C: Dim, S: fmt::Debug> fmt::Debug for Matrix<T, R, C, S> {
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fn fmt(&self, formatter: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
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self.data.fmt(formatter)
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}
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}
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impl<T, R, C, S> Default for Matrix<T, R, C, S>
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where
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T: Scalar,
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R: Dim,
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C: Dim,
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S: Default,
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{
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fn default() -> Self {
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Matrix {
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data: Default::default(),
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_phantoms: PhantomData,
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}
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}
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}
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#[cfg(feature = "serde-serialize-no-std")]
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impl<T, R, C, S> Serialize for Matrix<T, R, C, S>
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where
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T: Scalar,
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R: Dim,
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C: Dim,
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S: Serialize,
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{
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fn serialize<Ser>(&self, serializer: Ser) -> Result<Ser::Ok, Ser::Error>
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where
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Ser: Serializer,
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{
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self.data.serialize(serializer)
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}
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}
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#[cfg(feature = "serde-serialize-no-std")]
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impl<'de, T, R, C, S> Deserialize<'de> for Matrix<T, R, C, S>
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where
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T: Scalar,
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R: Dim,
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C: Dim,
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S: Deserialize<'de>,
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{
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fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
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where
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D: Deserializer<'de>,
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{
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S::deserialize(deserializer).map(|x| Matrix {
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data: x,
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_phantoms: PhantomData,
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})
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}
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}
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#[cfg(feature = "compare")]
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impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> matrixcompare_core::Matrix<T>
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for Matrix<T, R, C, S>
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{
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fn rows(&self) -> usize {
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self.nrows()
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}
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fn cols(&self) -> usize {
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self.ncols()
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}
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fn access(&self) -> matrixcompare_core::Access<'_, T> {
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matrixcompare_core::Access::Dense(self)
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}
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}
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#[cfg(feature = "compare")]
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impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> matrixcompare_core::DenseAccess<T>
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for Matrix<T, R, C, S>
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{
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fn fetch_single(&self, row: usize, col: usize) -> T {
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self.index((row, col)).clone()
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}
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}
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#[cfg(feature = "bytemuck")]
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unsafe impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> bytemuck::Zeroable
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for Matrix<T, R, C, S>
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where
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S: bytemuck::Zeroable,
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{
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}
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#[cfg(feature = "bytemuck")]
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unsafe impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> bytemuck::Pod for Matrix<T, R, C, S>
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where
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S: bytemuck::Pod,
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Self: Copy,
|
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{
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}
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impl<T, R, C, S> Matrix<T, R, C, S> {
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/// Creates a new matrix with the given data without statically checking that the matrix
|
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/// dimension matches the storage dimension.
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#[inline(always)]
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pub const unsafe fn from_data_statically_unchecked(data: S) -> Matrix<T, R, C, S> {
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Matrix {
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data,
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_phantoms: PhantomData,
|
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}
|
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}
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}
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impl<T, const R: usize, const C: usize> SMatrix<T, R, C> {
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/// Creates a new statically-allocated matrix from the given [`ArrayStorage`].
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///
|
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/// This method exists primarily as a workaround for the fact that `from_data` can not
|
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/// work in `const fn` contexts.
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#[inline(always)]
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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
|
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// storage, so there can be no mismatch
|
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unsafe { Self::from_data_statically_unchecked(storage) }
|
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}
|
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}
|
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|
||
// TODO: Consider removing/deprecating `from_vec_storage` once we are able to make
|
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// `from_data` const fn compatible
|
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#[cfg(any(feature = "std", feature = "alloc"))]
|
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impl<T> DMatrix<T> {
|
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/// Creates a new heap-allocated matrix from the given [`VecStorage`].
|
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///
|
||
/// This method exists primarily as a workaround for the fact that `from_data` can not
|
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/// work in `const fn` contexts.
|
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pub const fn from_vec_storage(storage: VecStorage<T, Dynamic, Dynamic>) -> Self {
|
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// This is sound because the dimensions of the matrix and the storage are guaranteed
|
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// to be the same
|
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unsafe { Self::from_data_statically_unchecked(storage) }
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}
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}
|
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|
||
// TODO: Consider removing/deprecating `from_vec_storage` once we are able to make
|
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// `from_data` const fn compatible
|
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#[cfg(any(feature = "std", feature = "alloc"))]
|
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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.
|
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pub const fn from_vec_storage(storage: VecStorage<T, Dynamic, U1>) -> Self {
|
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// This is sound because the dimensions of the matrix and the storage are guaranteed
|
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// to be the same
|
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unsafe { Self::from_data_statically_unchecked(storage) }
|
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}
|
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}
|
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|
||
// TODO: Consider removing/deprecating `from_vec_storage` once we are able to make
|
||
// `from_data` const fn compatible
|
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#[cfg(any(feature = "std", feature = "alloc"))]
|
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impl<T> RowDVector<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, U1, Dynamic>) -> Self {
|
||
// This is sound because the dimensions of the matrix and the storage are guaranteed
|
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// to be the same
|
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unsafe { Self::from_data_statically_unchecked(storage) }
|
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}
|
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}
|
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|
||
impl<T, R: Dim, C: Dim> UninitMatrix<T, R, C>
|
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where
|
||
DefaultAllocator: Allocator<T, R, C>,
|
||
{
|
||
/// Assumes a matrix's entries to be initialized. This operation should be near zero-cost.
|
||
///
|
||
/// # Safety
|
||
/// The user must make sure that every single entry of the buffer has been initialized,
|
||
/// or Undefined Behavior will immediately occur.
|
||
#[inline(always)]
|
||
pub unsafe fn assume_init(self) -> OMatrix<T, R, C> {
|
||
OMatrix::from_data(<DefaultAllocator as Allocator<T, R, C>>::assume_init(
|
||
self.data,
|
||
))
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S: RawStorage<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) }
|
||
}
|
||
|
||
/// The shape of this matrix returned as the tuple (number of rows, number of columns).
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # 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.shape_generic();
|
||
(nrows.value(), ncols.value())
|
||
}
|
||
|
||
/// The shape of this matrix wrapped into their representative types (`Const` or `Dynamic`).
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn shape_generic(&self) -> (R, C) {
|
||
self.data.shape()
|
||
}
|
||
|
||
/// The number of rows of this matrix.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # 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.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # 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.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # 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: Clone,
|
||
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.clone(), max_relative.clone()))
|
||
}
|
||
|
||
/// 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: RawStorage<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
|
||
T: Scalar,
|
||
S: Storage<T, R, C>,
|
||
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
|
||
T: Scalar,
|
||
S: Storage<T, R, C>,
|
||
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
|
||
T: Scalar,
|
||
S: Storage<T, R, C>,
|
||
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
|
||
T: Scalar,
|
||
S: Storage<T, R, C>,
|
||
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 = Matrix::uninit(nrows, ncols);
|
||
|
||
unsafe {
|
||
// TODO: use copy_from?
|
||
for j in 0..res.ncols() {
|
||
for i in 0..res.nrows() {
|
||
*res.get_unchecked_mut((i, j)) =
|
||
MaybeUninit::new(self.get_unchecked((i, j)).clone());
|
||
}
|
||
}
|
||
|
||
// SAFETY: the output has been initialized above.
|
||
res.assume_init()
|
||
}
|
||
}
|
||
|
||
/// Transposes `self` and store the result into `out`.
|
||
#[inline]
|
||
fn transpose_to_uninit<Status, R2, C2, SB>(
|
||
&self,
|
||
_status: Status,
|
||
out: &mut Matrix<Status::Value, R2, C2, SB>,
|
||
) where
|
||
Status: InitStatus<T>,
|
||
T: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorageMut<Status::Value, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
|
||
{
|
||
let (nrows, ncols) = self.shape();
|
||
assert!(
|
||
(ncols, nrows) == out.shape(),
|
||
"Incompatible shape for transposition."
|
||
);
|
||
|
||
// TODO: optimize that.
|
||
for i in 0..nrows {
|
||
for j in 0..ncols {
|
||
// Safety: the indices are in range.
|
||
unsafe {
|
||
Status::init(
|
||
out.get_unchecked_mut((j, i)),
|
||
self.get_unchecked((i, j)).clone(),
|
||
);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// 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
|
||
T: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorageMut<T, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
|
||
{
|
||
self.transpose_to_uninit(Init, out)
|
||
}
|
||
|
||
/// Transposes `self`.
|
||
#[inline]
|
||
#[must_use = "Did you mean to use transpose_mut()?"]
|
||
pub fn transpose(&self) -> OMatrix<T, C, R>
|
||
where
|
||
T: Scalar,
|
||
DefaultAllocator: Allocator<T, C, R>,
|
||
{
|
||
let (nrows, ncols) = self.shape_generic();
|
||
|
||
let mut res = Matrix::uninit(ncols, nrows);
|
||
self.transpose_to_uninit(Uninit, &mut res);
|
||
// Safety: res is now fully initialized.
|
||
unsafe { res.assume_init() }
|
||
}
|
||
}
|
||
|
||
/// # Elementwise mapping and folding
|
||
impl<T, R: Dim, C: Dim, S: RawStorage<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
|
||
T: Scalar,
|
||
DefaultAllocator: Allocator<T2, R, C>,
|
||
{
|
||
let (nrows, ncols) = self.shape_generic();
|
||
let mut res = Matrix::uninit(nrows, ncols);
|
||
|
||
for j in 0..ncols.value() {
|
||
for i in 0..nrows.value() {
|
||
// Safety: all indices are in range.
|
||
unsafe {
|
||
let a = self.data.get_unchecked(i, j).clone();
|
||
*res.data.get_unchecked_mut(i, j) = MaybeUninit::new(f(a));
|
||
}
|
||
}
|
||
}
|
||
|
||
// Safety: res is now fully initialized.
|
||
unsafe { res.assume_init() }
|
||
}
|
||
|
||
/// 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
|
||
T: Scalar,
|
||
OMatrix<T2, R, C>: SupersetOf<Self>,
|
||
DefaultAllocator: Allocator<T2, R, C>,
|
||
{
|
||
crate::convert(self)
|
||
}
|
||
|
||
/// Attempts to 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.try_cast::<i32>();
|
||
/// assert_eq!(q2, Some(Vector3::new(1, 2, 3)));
|
||
/// ```
|
||
pub fn try_cast<T2: Scalar>(self) -> Option<OMatrix<T2, R, C>>
|
||
where
|
||
T: Scalar,
|
||
Self: SupersetOf<OMatrix<T2, R, C>>,
|
||
DefaultAllocator: Allocator<T2, R, C>,
|
||
{
|
||
crate::try_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
|
||
where
|
||
T: Scalar,
|
||
{
|
||
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
|
||
T: Scalar,
|
||
DefaultAllocator: Allocator<T2, R, C>,
|
||
{
|
||
let (nrows, ncols) = self.shape_generic();
|
||
let mut res = Matrix::uninit(nrows, ncols);
|
||
|
||
for j in 0..ncols.value() {
|
||
for i in 0..nrows.value() {
|
||
// Safety: all indices are in range.
|
||
unsafe {
|
||
let a = self.data.get_unchecked(i, j).clone();
|
||
*res.data.get_unchecked_mut(i, j) = MaybeUninit::new(f(i, j, a));
|
||
}
|
||
}
|
||
}
|
||
|
||
// Safety: res is now fully initialized.
|
||
unsafe { res.assume_init() }
|
||
}
|
||
|
||
/// 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
|
||
T: Scalar,
|
||
T2: Scalar,
|
||
N3: Scalar,
|
||
S2: RawStorage<T2, R, C>,
|
||
F: FnMut(T, T2) -> N3,
|
||
DefaultAllocator: Allocator<N3, R, C>,
|
||
{
|
||
let (nrows, ncols) = self.shape_generic();
|
||
let mut res = Matrix::uninit(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() {
|
||
// Safety: all indices are in range.
|
||
unsafe {
|
||
let a = self.data.get_unchecked(i, j).clone();
|
||
let b = rhs.data.get_unchecked(i, j).clone();
|
||
*res.data.get_unchecked_mut(i, j) = MaybeUninit::new(f(a, b))
|
||
}
|
||
}
|
||
}
|
||
|
||
// Safety: res is now fully initialized.
|
||
unsafe { res.assume_init() }
|
||
}
|
||
|
||
/// 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
|
||
T: Scalar,
|
||
T2: Scalar,
|
||
N3: Scalar,
|
||
N4: Scalar,
|
||
S2: RawStorage<T2, R, C>,
|
||
S3: RawStorage<N3, R, C>,
|
||
F: FnMut(T, T2, N3) -> N4,
|
||
DefaultAllocator: Allocator<N4, R, C>,
|
||
{
|
||
let (nrows, ncols) = self.shape_generic();
|
||
let mut res = Matrix::uninit(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() {
|
||
// Safety: all indices are in range.
|
||
unsafe {
|
||
let a = self.data.get_unchecked(i, j).clone();
|
||
let b = b.data.get_unchecked(i, j).clone();
|
||
let c = c.data.get_unchecked(i, j).clone();
|
||
*res.data.get_unchecked_mut(i, j) = MaybeUninit::new(f(a, b, c))
|
||
}
|
||
}
|
||
}
|
||
|
||
// Safety: res is now fully initialized.
|
||
unsafe { res.assume_init() }
|
||
}
|
||
|
||
/// 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
|
||
where
|
||
T: Scalar,
|
||
{
|
||
let (nrows, ncols) = self.shape_generic();
|
||
|
||
let mut res = init;
|
||
|
||
for j in 0..ncols.value() {
|
||
for i in 0..nrows.value() {
|
||
// Safety: all indices are in range.
|
||
unsafe {
|
||
let a = self.data.get_unchecked(i, j).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
|
||
T: Scalar,
|
||
T2: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
S2: RawStorage<T2, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
|
||
{
|
||
let (nrows, ncols) = self.shape_generic();
|
||
|
||
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).clone();
|
||
let b = rhs.data.get_unchecked(i, j).clone();
|
||
res = f(res, a, b)
|
||
}
|
||
}
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// Applies a closure `f` to modify each component of `self`.
|
||
#[inline]
|
||
pub fn apply<F: FnMut(&mut T)>(&mut self, mut f: F)
|
||
where
|
||
S: RawStorageMut<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);
|
||
f(e)
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// 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(&mut T, T2),
|
||
) where
|
||
S: RawStorageMut<T, R, C>,
|
||
T2: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
S2: RawStorage<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)).clone();
|
||
f(e, 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(&mut T, T2, N3),
|
||
) where
|
||
S: RawStorageMut<T, R, C>,
|
||
T2: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
S2: RawStorage<T2, R2, C2>,
|
||
N3: Scalar,
|
||
R3: Dim,
|
||
C3: Dim,
|
||
S3: RawStorage<N3, R3, C3>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
|
||
{
|
||
let (nrows, ncols) = self.shape();
|
||
|
||
assert_eq!(
|
||
(nrows, ncols),
|
||
b.shape(),
|
||
"Matrix simultaneous traversal error: dimension mismatch."
|
||
);
|
||
assert_eq!(
|
||
(nrows, ncols),
|
||
c.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 b = b.get_unchecked((i, j)).clone();
|
||
let c = c.get_unchecked((i, j)).clone();
|
||
f(e, b, c)
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// # Iteration on components, rows, and columns
|
||
impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
|
||
/// Iterates through this matrix coordinates in column-major order.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::Matrix2x3;
|
||
/// let mat = Matrix2x3::new(11, 12, 13,
|
||
/// 21, 22, 23);
|
||
/// let mut it = mat.iter();
|
||
/// assert_eq!(*it.next().unwrap(), 11);
|
||
/// assert_eq!(*it.next().unwrap(), 21);
|
||
/// assert_eq!(*it.next().unwrap(), 12);
|
||
/// assert_eq!(*it.next().unwrap(), 22);
|
||
/// assert_eq!(*it.next().unwrap(), 13);
|
||
/// assert_eq!(*it.next().unwrap(), 23);
|
||
/// assert!(it.next().is_none());
|
||
/// ```
|
||
#[inline]
|
||
pub fn iter(&self) -> MatrixIter<'_, T, R, C, S> {
|
||
MatrixIter::new(&self.data)
|
||
}
|
||
|
||
/// Iterate through the rows of this matrix.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::Matrix2x3;
|
||
/// let mut a = Matrix2x3::new(1, 2, 3,
|
||
/// 4, 5, 6);
|
||
/// for (i, row) in a.row_iter().enumerate() {
|
||
/// assert_eq!(row, a.row(i))
|
||
/// }
|
||
/// ```
|
||
#[inline]
|
||
pub fn row_iter(&self) -> RowIter<'_, T, R, C, S> {
|
||
RowIter::new(self)
|
||
}
|
||
|
||
/// Iterate through the columns of this matrix.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::Matrix2x3;
|
||
/// let mut a = Matrix2x3::new(1, 2, 3,
|
||
/// 4, 5, 6);
|
||
/// for (i, column) in a.column_iter().enumerate() {
|
||
/// assert_eq!(column, a.column(i))
|
||
/// }
|
||
/// ```
|
||
#[inline]
|
||
pub fn column_iter(&self) -> ColumnIter<'_, T, R, C, S> {
|
||
ColumnIter::new(self)
|
||
}
|
||
|
||
/// Mutably iterates through this matrix coordinates.
|
||
#[inline]
|
||
pub fn iter_mut(&mut self) -> MatrixIterMut<'_, T, R, C, S>
|
||
where
|
||
S: RawStorageMut<T, R, C>,
|
||
{
|
||
MatrixIterMut::new(&mut self.data)
|
||
}
|
||
|
||
/// Mutably iterates through this matrix rows.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::Matrix2x3;
|
||
/// let mut a = Matrix2x3::new(1, 2, 3,
|
||
/// 4, 5, 6);
|
||
/// for (i, mut row) in a.row_iter_mut().enumerate() {
|
||
/// row *= (i + 1) * 10;
|
||
/// }
|
||
///
|
||
/// let expected = Matrix2x3::new(10, 20, 30,
|
||
/// 80, 100, 120);
|
||
/// assert_eq!(a, expected);
|
||
/// ```
|
||
#[inline]
|
||
pub fn row_iter_mut(&mut self) -> RowIterMut<'_, T, R, C, S>
|
||
where
|
||
S: RawStorageMut<T, R, C>,
|
||
{
|
||
RowIterMut::new(self)
|
||
}
|
||
|
||
/// Mutably iterates through this matrix columns.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::Matrix2x3;
|
||
/// let mut a = Matrix2x3::new(1, 2, 3,
|
||
/// 4, 5, 6);
|
||
/// for (i, mut col) in a.column_iter_mut().enumerate() {
|
||
/// col *= (i + 1) * 10;
|
||
/// }
|
||
///
|
||
/// let expected = Matrix2x3::new(10, 40, 90,
|
||
/// 40, 100, 180);
|
||
/// assert_eq!(a, expected);
|
||
/// ```
|
||
#[inline]
|
||
pub fn column_iter_mut(&mut self) -> ColumnIterMut<'_, T, R, C, S>
|
||
where
|
||
S: RawStorageMut<T, R, C>,
|
||
{
|
||
ColumnIterMut::new(self)
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S> {
|
||
/// Returns a mutable pointer to the start of the matrix.
|
||
///
|
||
/// If the matrix is not empty, this pointer is guaranteed to be aligned
|
||
/// and non-null.
|
||
#[inline]
|
||
pub fn as_mut_ptr(&mut self) -> *mut T {
|
||
self.data.ptr_mut()
|
||
}
|
||
|
||
/// Swaps two entries without bound-checking.
|
||
#[inline]
|
||
pub unsafe fn swap_unchecked(&mut self, row_cols1: (usize, usize), row_cols2: (usize, usize)) {
|
||
debug_assert!(row_cols1.0 < self.nrows() && row_cols1.1 < self.ncols());
|
||
debug_assert!(row_cols2.0 < self.nrows() && row_cols2.1 < self.ncols());
|
||
self.data.swap_unchecked(row_cols1, row_cols2)
|
||
}
|
||
|
||
/// Swaps two entries.
|
||
#[inline]
|
||
pub fn swap(&mut self, row_cols1: (usize, usize), row_cols2: (usize, usize)) {
|
||
let (nrows, ncols) = self.shape();
|
||
assert!(
|
||
row_cols1.0 < nrows && row_cols1.1 < ncols,
|
||
"Matrix elements swap index out of bounds."
|
||
);
|
||
assert!(
|
||
row_cols2.0 < nrows && row_cols2.1 < ncols,
|
||
"Matrix elements swap index out of bounds."
|
||
);
|
||
unsafe { self.swap_unchecked(row_cols1, row_cols2) }
|
||
}
|
||
|
||
/// Fills this matrix with the content of a slice. Both must hold the same number of elements.
|
||
///
|
||
/// The components of the slice are assumed to be ordered in column-major order.
|
||
#[inline]
|
||
pub fn copy_from_slice(&mut self, slice: &[T])
|
||
where
|
||
T: Scalar,
|
||
{
|
||
let (nrows, ncols) = self.shape();
|
||
|
||
assert!(
|
||
nrows * ncols == slice.len(),
|
||
"The slice must contain the same number of elements as the matrix."
|
||
);
|
||
|
||
for j in 0..ncols {
|
||
for i in 0..nrows {
|
||
unsafe {
|
||
*self.get_unchecked_mut((i, j)) = slice.get_unchecked(i + j * nrows).clone();
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// Fills this matrix with the content of another one. Both must have the same shape.
|
||
#[inline]
|
||
pub fn copy_from<R2, C2, SB>(&mut self, other: &Matrix<T, R2, C2, SB>)
|
||
where
|
||
T: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorage<T, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
|
||
{
|
||
assert!(
|
||
self.shape() == other.shape(),
|
||
"Unable to copy from a matrix with a different shape."
|
||
);
|
||
|
||
for j in 0..self.ncols() {
|
||
for i in 0..self.nrows() {
|
||
unsafe {
|
||
*self.get_unchecked_mut((i, j)) = other.get_unchecked((i, j)).clone();
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// Fills this matrix with the content of the transpose another one.
|
||
#[inline]
|
||
pub fn tr_copy_from<R2, C2, SB>(&mut self, other: &Matrix<T, R2, C2, SB>)
|
||
where
|
||
T: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorage<T, R2, C2>,
|
||
ShapeConstraint: DimEq<R, C2> + SameNumberOfColumns<C, R2>,
|
||
{
|
||
let (nrows, ncols) = self.shape();
|
||
assert!(
|
||
(ncols, nrows) == other.shape(),
|
||
"Unable to copy from a matrix with incompatible shape."
|
||
);
|
||
|
||
for j in 0..ncols {
|
||
for i in 0..nrows {
|
||
unsafe {
|
||
*self.get_unchecked_mut((i, j)) = other.get_unchecked((j, i)).clone();
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
// TODO: rename `apply` to `apply_mut` and `apply_into` to `apply`?
|
||
/// Returns `self` with each of its components replaced by the result of a closure `f` applied on it.
|
||
#[inline]
|
||
pub fn apply_into<F: FnMut(&mut T)>(mut self, f: F) -> Self {
|
||
self.apply(f);
|
||
self
|
||
}
|
||
}
|
||
|
||
impl<T, D: Dim, S: RawStorage<T, D>> Vector<T, D, S> {
|
||
/// Gets a reference to the i-th element of this column vector without bound checking.
|
||
#[inline]
|
||
#[must_use]
|
||
pub unsafe fn vget_unchecked(&self, i: usize) -> &T {
|
||
debug_assert!(i < self.nrows(), "Vector index out of bounds.");
|
||
let i = i * self.strides().0;
|
||
self.data.get_unchecked_linear(i)
|
||
}
|
||
}
|
||
|
||
impl<T, D: Dim, S: RawStorageMut<T, D>> Vector<T, D, S> {
|
||
/// Gets a mutable reference to the i-th element of this column vector without bound checking.
|
||
#[inline]
|
||
#[must_use]
|
||
pub unsafe fn vget_unchecked_mut(&mut self, i: usize) -> &mut T {
|
||
debug_assert!(i < self.nrows(), "Vector index out of bounds.");
|
||
let i = i * self.strides().0;
|
||
self.data.get_unchecked_linear_mut(i)
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C> + IsContiguous> Matrix<T, R, C, S> {
|
||
/// Extracts a slice containing the entire matrix entries ordered column-by-columns.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn as_slice(&self) -> &[T] {
|
||
// Safety: this is OK thanks to the IsContiguous trait.
|
||
unsafe { self.data.as_slice_unchecked() }
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C> + IsContiguous> Matrix<T, R, C, S> {
|
||
/// Extracts a mutable slice containing the entire matrix entries ordered column-by-columns.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn as_mut_slice(&mut self) -> &mut [T] {
|
||
// Safety: this is OK thanks to the IsContiguous trait.
|
||
unsafe { self.data.as_mut_slice_unchecked() }
|
||
}
|
||
}
|
||
|
||
impl<T: Scalar, D: Dim, S: RawStorageMut<T, D, D>> Matrix<T, D, D, S> {
|
||
/// Transposes the square matrix `self` in-place.
|
||
pub fn transpose_mut(&mut self) {
|
||
assert!(
|
||
self.is_square(),
|
||
"Unable to transpose a non-square matrix in-place."
|
||
);
|
||
|
||
let dim = self.shape().0;
|
||
|
||
for i in 1..dim {
|
||
for j in 0..i {
|
||
unsafe { self.swap_unchecked((i, j), (j, i)) }
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<T: SimdComplexField, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S> {
|
||
/// Takes the adjoint (aka. conjugate-transpose) of `self` and store the result into `out`.
|
||
#[inline]
|
||
fn adjoint_to_uninit<Status, R2, C2, SB>(
|
||
&self,
|
||
_status: Status,
|
||
out: &mut Matrix<Status::Value, R2, C2, SB>,
|
||
) where
|
||
Status: InitStatus<T>,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorageMut<Status::Value, 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 {
|
||
// Safety: all indices are in range.
|
||
unsafe {
|
||
Status::init(
|
||
out.get_unchecked_mut((j, i)),
|
||
self.get_unchecked((i, j)).clone().simd_conjugate(),
|
||
);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// Takes the adjoint (aka. conjugate-transpose) of `self` and store the result into `out`.
|
||
#[inline]
|
||
pub fn adjoint_to<R2, C2, SB>(&self, out: &mut Matrix<T, R2, C2, SB>)
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorageMut<T, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
|
||
{
|
||
self.adjoint_to_uninit(Init, out)
|
||
}
|
||
|
||
/// The adjoint (aka. conjugate-transpose) of `self`.
|
||
#[inline]
|
||
#[must_use = "Did you mean to use adjoint_mut()?"]
|
||
pub fn adjoint(&self) -> OMatrix<T, C, R>
|
||
where
|
||
DefaultAllocator: Allocator<T, C, R>,
|
||
{
|
||
let (nrows, ncols) = self.shape_generic();
|
||
|
||
let mut res = Matrix::uninit(ncols, nrows);
|
||
self.adjoint_to_uninit(Uninit, &mut res);
|
||
|
||
// Safety: res is now fully initialized.
|
||
unsafe { res.assume_init() }
|
||
}
|
||
|
||
/// Takes the conjugate and transposes `self` and store the result into `out`.
|
||
#[deprecated(note = "Renamed `self.adjoint_to(out)`.")]
|
||
#[inline]
|
||
pub fn conjugate_transpose_to<R2, C2, SB>(&self, out: &mut Matrix<T, R2, C2, SB>)
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorageMut<T, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
|
||
{
|
||
self.adjoint_to(out)
|
||
}
|
||
|
||
/// The conjugate transposition of `self`.
|
||
#[deprecated(note = "Renamed `self.adjoint()`.")]
|
||
#[inline]
|
||
pub fn conjugate_transpose(&self) -> OMatrix<T, C, R>
|
||
where
|
||
DefaultAllocator: Allocator<T, C, R>,
|
||
{
|
||
self.adjoint()
|
||
}
|
||
|
||
/// The conjugate of `self`.
|
||
#[inline]
|
||
#[must_use = "Did you mean to use conjugate_mut()?"]
|
||
pub fn conjugate(&self) -> OMatrix<T, R, C>
|
||
where
|
||
DefaultAllocator: Allocator<T, R, C>,
|
||
{
|
||
self.map(|e| e.simd_conjugate())
|
||
}
|
||
|
||
/// Divides each component of the complex matrix `self` by the given real.
|
||
#[inline]
|
||
#[must_use = "Did you mean to use unscale_mut()?"]
|
||
pub fn unscale(&self, real: T::SimdRealField) -> OMatrix<T, R, C>
|
||
where
|
||
DefaultAllocator: Allocator<T, R, C>,
|
||
{
|
||
self.map(|e| e.simd_unscale(real.clone()))
|
||
}
|
||
|
||
/// Multiplies each component of the complex matrix `self` by the given real.
|
||
#[inline]
|
||
#[must_use = "Did you mean to use scale_mut()?"]
|
||
pub fn scale(&self, real: T::SimdRealField) -> OMatrix<T, R, C>
|
||
where
|
||
DefaultAllocator: Allocator<T, R, C>,
|
||
{
|
||
self.map(|e| e.simd_scale(real.clone()))
|
||
}
|
||
}
|
||
|
||
impl<T: SimdComplexField, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S> {
|
||
/// The conjugate of the complex matrix `self` computed in-place.
|
||
#[inline]
|
||
pub fn conjugate_mut(&mut self) {
|
||
self.apply(|e| *e = e.clone().simd_conjugate())
|
||
}
|
||
|
||
/// Divides each component of the complex matrix `self` by the given real.
|
||
#[inline]
|
||
pub fn unscale_mut(&mut self, real: T::SimdRealField) {
|
||
self.apply(|e| *e = e.clone().simd_unscale(real.clone()))
|
||
}
|
||
|
||
/// Multiplies each component of the complex matrix `self` by the given real.
|
||
#[inline]
|
||
pub fn scale_mut(&mut self, real: T::SimdRealField) {
|
||
self.apply(|e| *e = e.clone().simd_scale(real.clone()))
|
||
}
|
||
}
|
||
|
||
impl<T: SimdComplexField, D: Dim, S: RawStorageMut<T, D, D>> Matrix<T, D, D, S> {
|
||
/// Sets `self` to its adjoint.
|
||
#[deprecated(note = "Renamed to `self.adjoint_mut()`.")]
|
||
pub fn conjugate_transform_mut(&mut self) {
|
||
self.adjoint_mut()
|
||
}
|
||
|
||
/// Sets `self` to its adjoint (aka. conjugate-transpose).
|
||
pub fn adjoint_mut(&mut self) {
|
||
assert!(
|
||
self.is_square(),
|
||
"Unable to transpose a non-square matrix in-place."
|
||
);
|
||
|
||
let dim = self.shape().0;
|
||
|
||
for i in 0..dim {
|
||
for j in 0..i {
|
||
unsafe {
|
||
let ref_ij = self.get_unchecked((i, j)).clone();
|
||
let ref_ji = self.get_unchecked((j, i)).clone();
|
||
let conj_ij = ref_ij.simd_conjugate();
|
||
let conj_ji = ref_ji.simd_conjugate();
|
||
*self.get_unchecked_mut((i, j)) = conj_ji;
|
||
*self.get_unchecked_mut((j, i)) = conj_ij;
|
||
}
|
||
}
|
||
|
||
{
|
||
let diag = unsafe { self.get_unchecked_mut((i, i)) };
|
||
*diag = diag.clone().simd_conjugate();
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<T: Scalar, D: Dim, S: RawStorage<T, D, D>> SquareMatrix<T, D, S> {
|
||
/// The diagonal of this matrix.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn diagonal(&self) -> OVector<T, D>
|
||
where
|
||
DefaultAllocator: Allocator<T, D>,
|
||
{
|
||
self.map_diagonal(|e| e)
|
||
}
|
||
|
||
/// Apply the given function to this matrix's diagonal and returns it.
|
||
///
|
||
/// This is a more efficient version of `self.diagonal().map(f)` since this
|
||
/// allocates only once.
|
||
#[must_use]
|
||
pub fn map_diagonal<T2: Scalar>(&self, mut f: impl FnMut(T) -> T2) -> OVector<T2, D>
|
||
where
|
||
DefaultAllocator: Allocator<T2, D>,
|
||
{
|
||
assert!(
|
||
self.is_square(),
|
||
"Unable to get the diagonal of a non-square matrix."
|
||
);
|
||
|
||
let dim = self.shape_generic().0;
|
||
let mut res = Matrix::uninit(dim, Const::<1>);
|
||
|
||
for i in 0..dim.value() {
|
||
// Safety: all indices are in range.
|
||
unsafe {
|
||
*res.vget_unchecked_mut(i) =
|
||
MaybeUninit::new(f(self.get_unchecked((i, i)).clone()));
|
||
}
|
||
}
|
||
|
||
// Safety: res is now fully initialized.
|
||
unsafe { res.assume_init() }
|
||
}
|
||
|
||
/// Computes a trace of a square matrix, i.e., the sum of its diagonal elements.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn trace(&self) -> T
|
||
where
|
||
T: Scalar + Zero + ClosedAdd,
|
||
{
|
||
assert!(
|
||
self.is_square(),
|
||
"Cannot compute the trace of non-square matrix."
|
||
);
|
||
|
||
let dim = self.shape_generic().0;
|
||
let mut res = T::zero();
|
||
|
||
for i in 0..dim.value() {
|
||
res += unsafe { self.get_unchecked((i, i)).clone() };
|
||
}
|
||
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<T: SimdComplexField, D: Dim, S: Storage<T, D, D>> SquareMatrix<T, D, S> {
|
||
/// The symmetric part of `self`, i.e., `0.5 * (self + self.transpose())`.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn symmetric_part(&self) -> OMatrix<T, D, D>
|
||
where
|
||
DefaultAllocator: Allocator<T, D, D>,
|
||
{
|
||
assert!(
|
||
self.is_square(),
|
||
"Cannot compute the symmetric part of a non-square matrix."
|
||
);
|
||
let mut tr = self.transpose();
|
||
tr += self;
|
||
tr *= crate::convert::<_, T>(0.5);
|
||
tr
|
||
}
|
||
|
||
/// The hermitian part of `self`, i.e., `0.5 * (self + self.adjoint())`.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn hermitian_part(&self) -> OMatrix<T, D, D>
|
||
where
|
||
DefaultAllocator: Allocator<T, D, D>,
|
||
{
|
||
assert!(
|
||
self.is_square(),
|
||
"Cannot compute the hermitian part of a non-square matrix."
|
||
);
|
||
|
||
let mut tr = self.adjoint();
|
||
tr += self;
|
||
tr *= crate::convert::<_, T>(0.5);
|
||
tr
|
||
}
|
||
}
|
||
|
||
impl<T: Scalar + Zero + One, D: DimAdd<U1> + IsNotStaticOne, S: RawStorage<T, D, D>>
|
||
Matrix<T, D, D, S>
|
||
{
|
||
/// Yields the homogeneous matrix for this matrix, i.e., appending an additional dimension and
|
||
/// and setting the diagonal element to `1`.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn to_homogeneous(&self) -> OMatrix<T, DimSum<D, U1>, DimSum<D, U1>>
|
||
where
|
||
DefaultAllocator: Allocator<T, DimSum<D, U1>, DimSum<D, U1>>,
|
||
{
|
||
assert!(
|
||
self.is_square(),
|
||
"Only square matrices can currently be transformed to homogeneous coordinates."
|
||
);
|
||
let dim = DimSum::<D, U1>::from_usize(self.nrows() + 1);
|
||
let mut res = OMatrix::identity_generic(dim, dim);
|
||
res.generic_slice_mut::<D, D>((0, 0), self.shape_generic())
|
||
.copy_from(self);
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<T: Scalar + Zero, D: DimAdd<U1>, S: RawStorage<T, D>> Vector<T, D, S> {
|
||
/// Computes the coordinates in projective space of this vector, i.e., appends a `0` to its
|
||
/// coordinates.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn to_homogeneous(&self) -> OVector<T, DimSum<D, U1>>
|
||
where
|
||
DefaultAllocator: Allocator<T, DimSum<D, U1>>,
|
||
{
|
||
self.push(T::zero())
|
||
}
|
||
|
||
/// Constructs a vector from coordinates in projective space, i.e., removes a `0` at the end of
|
||
/// `self`. Returns `None` if this last component is not zero.
|
||
#[inline]
|
||
pub fn from_homogeneous<SB>(v: Vector<T, DimSum<D, U1>, SB>) -> Option<OVector<T, D>>
|
||
where
|
||
SB: RawStorage<T, DimSum<D, U1>>,
|
||
DefaultAllocator: Allocator<T, D>,
|
||
{
|
||
if v[v.len() - 1].is_zero() {
|
||
let nrows = D::from_usize(v.len() - 1);
|
||
Some(v.generic_slice((0, 0), (nrows, Const::<1>)).into_owned())
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<T: Scalar, D: DimAdd<U1>, S: RawStorage<T, D>> Vector<T, D, S> {
|
||
/// Constructs a new vector of higher dimension by appending `element` to the end of `self`.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn push(&self, element: T) -> OVector<T, DimSum<D, U1>>
|
||
where
|
||
DefaultAllocator: Allocator<T, DimSum<D, U1>>,
|
||
{
|
||
let len = self.len();
|
||
let hnrows = DimSum::<D, U1>::from_usize(len + 1);
|
||
let mut res = Matrix::uninit(hnrows, Const::<1>);
|
||
// This is basically a copy_from except that we warp the copied
|
||
// values into MaybeUninit.
|
||
res.generic_slice_mut((0, 0), self.shape_generic())
|
||
.zip_apply(self, |out, e| *out = MaybeUninit::new(e));
|
||
res[(len, 0)] = MaybeUninit::new(element);
|
||
|
||
// Safety: res has been fully initialized.
|
||
unsafe { res.assume_init() }
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S> AbsDiffEq for Matrix<T, R, C, S>
|
||
where
|
||
T: Scalar + AbsDiffEq,
|
||
S: RawStorage<T, R, C>,
|
||
T::Epsilon: Clone,
|
||
{
|
||
type Epsilon = T::Epsilon;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
T::default_epsilon()
|
||
}
|
||
|
||
#[inline]
|
||
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
|
||
self.iter()
|
||
.zip(other.iter())
|
||
.all(|(a, b)| a.abs_diff_eq(b, epsilon.clone()))
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S> RelativeEq for Matrix<T, R, C, S>
|
||
where
|
||
T: Scalar + RelativeEq,
|
||
S: Storage<T, R, C>,
|
||
T::Epsilon: Clone,
|
||
{
|
||
#[inline]
|
||
fn default_max_relative() -> Self::Epsilon {
|
||
T::default_max_relative()
|
||
}
|
||
|
||
#[inline]
|
||
fn relative_eq(
|
||
&self,
|
||
other: &Self,
|
||
epsilon: Self::Epsilon,
|
||
max_relative: Self::Epsilon,
|
||
) -> bool {
|
||
self.relative_eq(other, epsilon, max_relative)
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S> UlpsEq for Matrix<T, R, C, S>
|
||
where
|
||
T: Scalar + UlpsEq,
|
||
S: RawStorage<T, R, C>,
|
||
T::Epsilon: Clone,
|
||
{
|
||
#[inline]
|
||
fn default_max_ulps() -> u32 {
|
||
T::default_max_ulps()
|
||
}
|
||
|
||
#[inline]
|
||
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
|
||
assert!(self.shape() == other.shape());
|
||
self.iter()
|
||
.zip(other.iter())
|
||
.all(|(a, b)| a.ulps_eq(b, epsilon.clone(), max_ulps))
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S> PartialOrd for Matrix<T, R, C, S>
|
||
where
|
||
T: Scalar + PartialOrd,
|
||
S: RawStorage<T, R, C>,
|
||
{
|
||
#[inline]
|
||
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
|
||
if self.shape() != other.shape() {
|
||
return None;
|
||
}
|
||
|
||
if self.nrows() == 0 || self.ncols() == 0 {
|
||
return Some(Ordering::Equal);
|
||
}
|
||
|
||
let mut first_ord = unsafe {
|
||
self.data
|
||
.get_unchecked_linear(0)
|
||
.partial_cmp(other.data.get_unchecked_linear(0))
|
||
};
|
||
|
||
if let Some(first_ord) = first_ord.as_mut() {
|
||
let mut it = self.iter().zip(other.iter());
|
||
let _ = it.next(); // Drop the first elements (we already tested it).
|
||
|
||
for (left, right) in it {
|
||
if let Some(ord) = left.partial_cmp(right) {
|
||
match ord {
|
||
Ordering::Equal => { /* Does not change anything. */ }
|
||
Ordering::Less => {
|
||
if *first_ord == Ordering::Greater {
|
||
return None;
|
||
}
|
||
*first_ord = ord
|
||
}
|
||
Ordering::Greater => {
|
||
if *first_ord == Ordering::Less {
|
||
return None;
|
||
}
|
||
*first_ord = ord
|
||
}
|
||
}
|
||
} else {
|
||
return None;
|
||
}
|
||
}
|
||
}
|
||
|
||
first_ord
|
||
}
|
||
|
||
#[inline]
|
||
fn lt(&self, right: &Self) -> bool {
|
||
assert_eq!(
|
||
self.shape(),
|
||
right.shape(),
|
||
"Matrix comparison error: dimensions mismatch."
|
||
);
|
||
self.iter().zip(right.iter()).all(|(a, b)| a.lt(b))
|
||
}
|
||
|
||
#[inline]
|
||
fn le(&self, right: &Self) -> bool {
|
||
assert_eq!(
|
||
self.shape(),
|
||
right.shape(),
|
||
"Matrix comparison error: dimensions mismatch."
|
||
);
|
||
self.iter().zip(right.iter()).all(|(a, b)| a.le(b))
|
||
}
|
||
|
||
#[inline]
|
||
fn gt(&self, right: &Self) -> bool {
|
||
assert_eq!(
|
||
self.shape(),
|
||
right.shape(),
|
||
"Matrix comparison error: dimensions mismatch."
|
||
);
|
||
self.iter().zip(right.iter()).all(|(a, b)| a.gt(b))
|
||
}
|
||
|
||
#[inline]
|
||
fn ge(&self, right: &Self) -> bool {
|
||
assert_eq!(
|
||
self.shape(),
|
||
right.shape(),
|
||
"Matrix comparison error: dimensions mismatch."
|
||
);
|
||
self.iter().zip(right.iter()).all(|(a, b)| a.ge(b))
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S> Eq for Matrix<T, R, C, S>
|
||
where
|
||
T: Scalar + Eq,
|
||
S: RawStorage<T, R, C>,
|
||
{
|
||
}
|
||
|
||
impl<T, R, R2, C, C2, S, S2> PartialEq<Matrix<T, R2, C2, S2>> for Matrix<T, R, C, S>
|
||
where
|
||
T: Scalar + PartialEq,
|
||
C: Dim,
|
||
C2: Dim,
|
||
R: Dim,
|
||
R2: Dim,
|
||
S: RawStorage<T, R, C>,
|
||
S2: RawStorage<T, R2, C2>,
|
||
{
|
||
#[inline]
|
||
fn eq(&self, right: &Matrix<T, R2, C2, S2>) -> bool {
|
||
self.shape() == right.shape() && self.iter().zip(right.iter()).all(|(l, r)| l == r)
|
||
}
|
||
}
|
||
|
||
macro_rules! impl_fmt {
|
||
($trait: path, $fmt_str_without_precision: expr, $fmt_str_with_precision: expr) => {
|
||
impl<T, R: Dim, C: Dim, S> $trait for Matrix<T, R, C, S>
|
||
where
|
||
T: Scalar + $trait,
|
||
S: RawStorage<T, R, C>,
|
||
{
|
||
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
|
||
#[cfg(feature = "std")]
|
||
fn val_width<T: Scalar + $trait>(val: &T, f: &mut fmt::Formatter<'_>) -> usize {
|
||
match f.precision() {
|
||
Some(precision) => format!($fmt_str_with_precision, val, precision)
|
||
.chars()
|
||
.count(),
|
||
None => format!($fmt_str_without_precision, val).chars().count(),
|
||
}
|
||
}
|
||
|
||
#[cfg(not(feature = "std"))]
|
||
fn val_width<T: Scalar + $trait>(_: &T, _: &mut fmt::Formatter<'_>) -> usize {
|
||
4
|
||
}
|
||
|
||
let (nrows, ncols) = self.shape();
|
||
|
||
if nrows == 0 || ncols == 0 {
|
||
return write!(f, "[ ]");
|
||
}
|
||
|
||
let mut max_length = 0;
|
||
|
||
for i in 0..nrows {
|
||
for j in 0..ncols {
|
||
max_length = crate::max(max_length, val_width(&self[(i, j)], f));
|
||
}
|
||
}
|
||
|
||
let max_length_with_space = max_length + 1;
|
||
|
||
writeln!(f)?;
|
||
writeln!(
|
||
f,
|
||
" ┌ {:>width$} ┐",
|
||
"",
|
||
width = max_length_with_space * ncols - 1
|
||
)?;
|
||
|
||
for i in 0..nrows {
|
||
write!(f, " │")?;
|
||
for j in 0..ncols {
|
||
let number_length = val_width(&self[(i, j)], f) + 1;
|
||
let pad = max_length_with_space - number_length;
|
||
write!(f, " {:>thepad$}", "", thepad = pad)?;
|
||
match f.precision() {
|
||
Some(precision) => {
|
||
write!(f, $fmt_str_with_precision, (*self)[(i, j)], precision)?
|
||
}
|
||
None => write!(f, $fmt_str_without_precision, (*self)[(i, j)])?,
|
||
}
|
||
}
|
||
writeln!(f, " │")?;
|
||
}
|
||
|
||
writeln!(
|
||
f,
|
||
" └ {:>width$} ┘",
|
||
"",
|
||
width = max_length_with_space * ncols - 1
|
||
)?;
|
||
writeln!(f)
|
||
}
|
||
}
|
||
};
|
||
}
|
||
impl_fmt!(fmt::Display, "{}", "{:.1$}");
|
||
impl_fmt!(fmt::LowerExp, "{:e}", "{:.1$e}");
|
||
impl_fmt!(fmt::UpperExp, "{:E}", "{:.1$E}");
|
||
impl_fmt!(fmt::Octal, "{:o}", "{:1$o}");
|
||
impl_fmt!(fmt::LowerHex, "{:x}", "{:1$x}");
|
||
impl_fmt!(fmt::UpperHex, "{:X}", "{:1$X}");
|
||
impl_fmt!(fmt::Binary, "{:b}", "{:.1$b}");
|
||
impl_fmt!(fmt::Pointer, "{:p}", "{:.1$p}");
|
||
|
||
#[cfg(test)]
|
||
mod tests {
|
||
#[test]
|
||
fn empty_display() {
|
||
let vec: Vec<f64> = Vec::new();
|
||
let dvector = crate::DVector::from_vec(vec);
|
||
assert_eq!(format!("{}", dvector), "[ ]")
|
||
}
|
||
|
||
#[test]
|
||
fn lower_exp() {
|
||
let test = crate::Matrix2::new(1e6, 2e5, 2e-5, 1.);
|
||
assert_eq!(
|
||
format!("{:e}", test),
|
||
r"
|
||
┌ ┐
|
||
│ 1e6 2e5 │
|
||
│ 2e-5 1e0 │
|
||
└ ┘
|
||
|
||
"
|
||
)
|
||
}
|
||
}
|
||
|
||
/// # Cross product
|
||
impl<T: Scalar + ClosedAdd + ClosedSub + ClosedMul, R: Dim, C: Dim, S: RawStorage<T, R, C>>
|
||
Matrix<T, R, C, S>
|
||
{
|
||
/// The perpendicular product between two 2D column vectors, i.e. `a.x * b.y - a.y * b.x`.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn perp<R2, C2, SB>(&self, b: &Matrix<T, R2, C2, SB>) -> T
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorage<T, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, U2>
|
||
+ SameNumberOfColumns<C, U1>
|
||
+ SameNumberOfRows<R2, U2>
|
||
+ SameNumberOfColumns<C2, U1>,
|
||
{
|
||
let shape = self.shape();
|
||
assert_eq!(
|
||
shape,
|
||
b.shape(),
|
||
"2D vector perpendicular product dimension mismatch."
|
||
);
|
||
assert_eq!(
|
||
shape,
|
||
(2, 1),
|
||
"2D perpendicular product requires (2, 1) vectors {:?}",
|
||
shape
|
||
);
|
||
|
||
// SAFETY: assertion above ensures correct shape
|
||
let ax = unsafe { self.get_unchecked((0, 0)).clone() };
|
||
let ay = unsafe { self.get_unchecked((1, 0)).clone() };
|
||
let bx = unsafe { b.get_unchecked((0, 0)).clone() };
|
||
let by = unsafe { b.get_unchecked((1, 0)).clone() };
|
||
|
||
ax * by - ay * bx
|
||
}
|
||
|
||
// TODO: use specialization instead of an assertion.
|
||
/// The 3D cross product between two vectors.
|
||
///
|
||
/// Panics if the shape is not 3D vector. In the future, this will be implemented only for
|
||
/// dynamically-sized matrices and statically-sized 3D matrices.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn cross<R2, C2, SB>(&self, b: &Matrix<T, R2, C2, SB>) -> MatrixCross<T, R, C, R2, C2>
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: RawStorage<T, R2, C2>,
|
||
DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
|
||
{
|
||
let shape = self.shape();
|
||
assert_eq!(shape, b.shape(), "Vector cross product dimension mismatch.");
|
||
assert!(
|
||
shape == (3, 1) || shape == (1, 3),
|
||
"Vector cross product dimension mismatch: must be (3, 1) or (1, 3) but found {:?}.",
|
||
shape
|
||
);
|
||
|
||
if shape.0 == 3 {
|
||
unsafe {
|
||
let mut res = Matrix::uninit(Dim::from_usize(3), Dim::from_usize(1));
|
||
|
||
let ax = self.get_unchecked((0, 0));
|
||
let ay = self.get_unchecked((1, 0));
|
||
let az = self.get_unchecked((2, 0));
|
||
|
||
let bx = b.get_unchecked((0, 0));
|
||
let by = b.get_unchecked((1, 0));
|
||
let bz = b.get_unchecked((2, 0));
|
||
|
||
*res.get_unchecked_mut((0, 0)) =
|
||
MaybeUninit::new(ay.clone() * bz.clone() - az.clone() * by.clone());
|
||
*res.get_unchecked_mut((1, 0)) =
|
||
MaybeUninit::new(az.clone() * bx.clone() - ax.clone() * bz.clone());
|
||
*res.get_unchecked_mut((2, 0)) =
|
||
MaybeUninit::new(ax.clone() * by.clone() - ay.clone() * bx.clone());
|
||
|
||
// Safety: res is now fully initialized.
|
||
res.assume_init()
|
||
}
|
||
} else {
|
||
unsafe {
|
||
let mut res = Matrix::uninit(Dim::from_usize(1), Dim::from_usize(3));
|
||
|
||
let ax = self.get_unchecked((0, 0));
|
||
let ay = self.get_unchecked((0, 1));
|
||
let az = self.get_unchecked((0, 2));
|
||
|
||
let bx = b.get_unchecked((0, 0));
|
||
let by = b.get_unchecked((0, 1));
|
||
let bz = b.get_unchecked((0, 2));
|
||
|
||
*res.get_unchecked_mut((0, 0)) =
|
||
MaybeUninit::new(ay.clone() * bz.clone() - az.clone() * by.clone());
|
||
*res.get_unchecked_mut((0, 1)) =
|
||
MaybeUninit::new(az.clone() * bx.clone() - ax.clone() * bz.clone());
|
||
*res.get_unchecked_mut((0, 2)) =
|
||
MaybeUninit::new(ax.clone() * by.clone() - ay.clone() * bx.clone());
|
||
|
||
// Safety: res is now fully initialized.
|
||
res.assume_init()
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<T: Scalar + Field, S: RawStorage<T, U3>> Vector<T, U3, S> {
|
||
/// Computes the matrix `M` such that for all vector `v` we have `M * v == self.cross(&v)`.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn cross_matrix(&self) -> OMatrix<T, U3, U3> {
|
||
OMatrix::<T, U3, U3>::new(
|
||
T::zero(),
|
||
-self[2].clone(),
|
||
self[1].clone(),
|
||
self[2].clone(),
|
||
T::zero(),
|
||
-self[0].clone(),
|
||
-self[1].clone(),
|
||
self[0].clone(),
|
||
T::zero(),
|
||
)
|
||
}
|
||
}
|
||
|
||
impl<T: SimdComplexField, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S> {
|
||
/// The smallest angle between two vectors.
|
||
#[inline]
|
||
#[must_use]
|
||
pub fn angle<R2: Dim, C2: Dim, SB>(&self, other: &Matrix<T, R2, C2, SB>) -> T::SimdRealField
|
||
where
|
||
SB: Storage<T, R2, C2>,
|
||
ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
|
||
{
|
||
let prod = self.dotc(other);
|
||
let n1 = self.norm();
|
||
let n2 = other.norm();
|
||
|
||
if n1.is_zero() || n2.is_zero() {
|
||
T::SimdRealField::zero()
|
||
} else {
|
||
let cang = prod.simd_real() / (n1 * n2);
|
||
cang.simd_clamp(-T::SimdRealField::one(), T::SimdRealField::one())
|
||
.simd_acos()
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S> AbsDiffEq for Unit<Matrix<T, R, C, S>>
|
||
where
|
||
T: Scalar + AbsDiffEq,
|
||
S: RawStorage<T, R, C>,
|
||
T::Epsilon: Clone,
|
||
{
|
||
type Epsilon = T::Epsilon;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
T::default_epsilon()
|
||
}
|
||
|
||
#[inline]
|
||
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
|
||
self.as_ref().abs_diff_eq(other.as_ref(), epsilon)
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S> RelativeEq for Unit<Matrix<T, R, C, S>>
|
||
where
|
||
T: Scalar + RelativeEq,
|
||
S: Storage<T, R, C>,
|
||
T::Epsilon: Clone,
|
||
{
|
||
#[inline]
|
||
fn default_max_relative() -> Self::Epsilon {
|
||
T::default_max_relative()
|
||
}
|
||
|
||
#[inline]
|
||
fn relative_eq(
|
||
&self,
|
||
other: &Self,
|
||
epsilon: Self::Epsilon,
|
||
max_relative: Self::Epsilon,
|
||
) -> bool {
|
||
self.as_ref()
|
||
.relative_eq(other.as_ref(), epsilon, max_relative)
|
||
}
|
||
}
|
||
|
||
impl<T, R: Dim, C: Dim, S> UlpsEq for Unit<Matrix<T, R, C, S>>
|
||
where
|
||
T: Scalar + UlpsEq,
|
||
S: RawStorage<T, R, C>,
|
||
T::Epsilon: Clone,
|
||
{
|
||
#[inline]
|
||
fn default_max_ulps() -> u32 {
|
||
T::default_max_ulps()
|
||
}
|
||
|
||
#[inline]
|
||
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
|
||
self.as_ref().ulps_eq(other.as_ref(), epsilon, max_ulps)
|
||
}
|
||
}
|
||
|
||
impl<T, R, C, S> Hash for Matrix<T, R, C, S>
|
||
where
|
||
T: Scalar + Hash,
|
||
R: Dim,
|
||
C: Dim,
|
||
S: RawStorage<T, R, C>,
|
||
{
|
||
fn hash<H: Hasher>(&self, state: &mut H) {
|
||
let (nrows, ncols) = self.shape();
|
||
(nrows, ncols).hash(state);
|
||
|
||
for j in 0..ncols {
|
||
for i in 0..nrows {
|
||
unsafe {
|
||
self.get_unchecked((i, j)).hash(state);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<T, D, S> Unit<Vector<T, D, S>>
|
||
where
|
||
T: Scalar,
|
||
D: Dim,
|
||
S: RawStorage<T, D, U1>,
|
||
{
|
||
/// Cast the components of `self` to another type.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::Vector3;
|
||
/// let v = Vector3::<f64>::y_axis();
|
||
/// let v2 = v.cast::<f32>();
|
||
/// assert_eq!(v2, Vector3::<f32>::y_axis());
|
||
/// ```
|
||
pub fn cast<T2: Scalar>(self) -> Unit<OVector<T2, D>>
|
||
where
|
||
T: Scalar,
|
||
OVector<T2, D>: SupersetOf<Vector<T, D, S>>,
|
||
DefaultAllocator: Allocator<T2, D, U1>,
|
||
{
|
||
Unit::new_unchecked(crate::convert_ref(self.as_ref()))
|
||
}
|
||
}
|