1207 lines
36 KiB
Rust
1207 lines
36 KiB
Rust
use num::Zero;
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use num_complex::Complex;
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use std::cmp::Ordering;
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use std::marker::PhantomData;
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use std::fmt;
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use std::any::TypeId;
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use std::mem;
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use approx::ApproxEq;
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#[cfg(feature = "serde-serialize")]
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use serde::{Deserialize, Deserializer, Serialize, Serializer};
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#[cfg(feature = "abomonation-serialize")]
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use abomonation::Abomonation;
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use alga::general::{Real, Ring};
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use core::{DefaultAllocator, MatrixMN, MatrixN, Scalar, Unit, VectorN};
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use core::dimension::{Dim, DimAdd, DimSum, U1, U2, U3};
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use core::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
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use core::iter::{MatrixIter, MatrixIterMut};
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use core::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
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use core::storage::{ContiguousStorage, ContiguousStorageMut, Owned, SameShapeStorage, Storage,
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StorageMut};
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/// A square matrix.
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pub type SquareMatrix<N, D, S> = Matrix<N, D, D, S>;
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/// A matrix with one column and `D` rows.
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pub type Vector<N, D, S> = Matrix<N, D, U1, S>;
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/// A matrix with one row and `D` columns .
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pub type RowVector<N, D, S> = Matrix<N, U1, D, S>;
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/// The type of the result of a matrix sum.
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pub type MatrixSum<N, R1, C1, R2, C2> =
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Matrix<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<N, R1, C1, R2, C2>>;
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/// The type of the result of a matrix sum.
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pub type VectorSum<N, R1, R2> =
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Matrix<N, SameShapeR<R1, R2>, U1, SameShapeStorage<N, 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<N, R1, C1, R2, C2> =
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Matrix<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<N, 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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/// It combines four type parameters:
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/// - `N`: 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 contants (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<N, Dynamic, U1, S>` (given
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/// some concrete types for `N` and a compatible data storage type `S`).
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#[repr(C)]
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#[derive(Hash, Clone, Copy)]
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pub struct Matrix<N: Scalar, R: Dim, C: Dim, S> {
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/// The data storage that contains all the matrix components and informations about its number
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/// of rows and column (if needed).
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pub data: S,
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_phantoms: PhantomData<(N, R, C)>,
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}
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impl<N: Scalar, R: Dim, C: Dim, S: fmt::Debug> fmt::Debug for Matrix<N, R, C, S> {
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fn fmt(&self, formatter: &mut fmt::Formatter) -> Result<(), fmt::Error> {
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formatter.debug_struct("Matrix")
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.field("data", &self.data)
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.finish()
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}
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}
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#[cfg(feature = "serde-serialize")]
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impl<N, R, C, S> Serialize for Matrix<N, R, C, S>
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where
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N: 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<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
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where
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T: 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")]
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impl<'de, N, R, C, S> Deserialize<'de> for Matrix<N, R, C, S>
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where
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N: 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 = "abomonation-serialize")]
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impl<N: Scalar, R: Dim, C: Dim, S: Abomonation> Abomonation for Matrix<N, R, C, S> {
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unsafe fn entomb(&self, writer: &mut Vec<u8>) {
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self.data.entomb(writer)
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}
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unsafe fn embalm(&mut self) {
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self.data.embalm()
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}
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unsafe fn exhume<'a, 'b>(&'a mut self, bytes: &'b mut [u8]) -> Option<&'b mut [u8]> {
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self.data.exhume(bytes)
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}
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}
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impl<N: Scalar, R: Dim, C: Dim, S> Matrix<N, 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]
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pub unsafe fn from_data_statically_unchecked(data: S) -> Matrix<N, R, C, S> {
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Matrix {
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data: data,
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_phantoms: PhantomData,
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}
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}
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}
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impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
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/// Creates a new matrix with the given data.
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#[inline]
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pub fn from_data(data: S) -> Matrix<N, R, C, S> {
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unsafe { Self::from_data_statically_unchecked(data) }
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}
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/// The total number of elements of this matrix.
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#[inline]
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pub fn len(&self) -> usize {
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let (nrows, ncols) = self.shape();
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nrows * ncols
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}
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/// The shape of this matrix returned as the tuple (number of rows, number of columns).
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#[inline]
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pub fn shape(&self) -> (usize, usize) {
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let (nrows, ncols) = self.data.shape();
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(nrows.value(), ncols.value())
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}
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/// The number of rows of this matrix.
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#[inline]
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pub fn nrows(&self) -> usize {
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self.shape().0
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}
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/// The number of columns of this matrix.
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#[inline]
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pub fn ncols(&self) -> usize {
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self.shape().1
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}
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/// The strides (row stride, column stride) of this matrix.
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#[inline]
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pub fn strides(&self) -> (usize, usize) {
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let (srows, scols) = self.data.strides();
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(srows.value(), scols.value())
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}
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/// Iterates through this matrix coordinates.
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#[inline]
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pub fn iter(&self) -> MatrixIter<N, R, C, S> {
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MatrixIter::new(&self.data)
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}
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/// Computes the row and column coordinates of the i-th element of this matrix seen as a
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/// vector.
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#[inline]
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pub fn vector_to_matrix_index(&self, i: usize) -> (usize, usize) {
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let (nrows, ncols) = self.shape();
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// Two most common uses that should be optimized by the compiler for statically-sized
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// matrices.
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if nrows == 1 {
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(0, i)
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} else if ncols == 1 {
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(i, 0)
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} else {
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(i % nrows, i / nrows)
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}
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}
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/// Gets a reference to the element of this matrix at row `irow` and column `icol` without
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/// bound-checking.
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#[inline]
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pub unsafe fn get_unchecked(&self, irow: usize, icol: usize) -> &N {
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debug_assert!(
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irow < self.nrows() && icol < self.ncols(),
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"Matrix index out of bounds."
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);
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self.data.get_unchecked(irow, icol)
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}
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/// Tests whether `self` and `rhs` are equal up to a given epsilon.
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///
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/// See `relative_eq` from the `ApproxEq` trait for more details.
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#[inline]
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pub fn relative_eq<R2, C2, SB>(
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&self,
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other: &Matrix<N, R2, C2, SB>,
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eps: N::Epsilon,
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max_relative: N::Epsilon,
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) -> bool
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where
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N: ApproxEq,
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R2: Dim,
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C2: Dim,
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SB: Storage<N, R2, C2>,
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N::Epsilon: Copy,
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ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
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{
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assert!(self.shape() == other.shape());
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self.iter()
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.zip(other.iter())
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.all(|(a, b)| a.relative_eq(b, eps, max_relative))
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}
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/// Tests whether `self` and `rhs` are exactly equal.
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#[inline]
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pub fn eq<R2, C2, SB>(&self, other: &Matrix<N, R2, C2, SB>) -> bool
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where
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N: PartialEq,
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R2: Dim,
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C2: Dim,
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SB: Storage<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
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{
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assert!(self.shape() == other.shape());
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self.iter().zip(other.iter()).all(|(a, b)| *a == *b)
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}
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/// Moves this matrix into one that owns its data.
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#[inline]
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pub fn into_owned(self) -> MatrixMN<N, R, C>
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where
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DefaultAllocator: Allocator<N, R, C>,
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{
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Matrix::from_data(self.data.into_owned())
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}
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// FIXME: this could probably benefit from specialization.
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// XXX: bad name.
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/// Moves this matrix into one that owns its data. The actual type of the result depends on
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/// matrix storage combination rules for addition.
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#[inline]
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pub fn into_owned_sum<R2, C2>(self) -> MatrixSum<N, R, C, R2, C2>
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where
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R2: Dim,
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C2: Dim,
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DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
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{
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if TypeId::of::<SameShapeStorage<N, R, C, R2, C2>>() == TypeId::of::<Owned<N, R, C>>() {
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// We can just return `self.into_owned()`.
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unsafe {
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// FIXME: check that those copies are optimized away by the compiler.
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let owned = self.into_owned();
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let res = mem::transmute_copy(&owned);
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mem::forget(owned);
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res
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}
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} else {
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self.clone_owned_sum()
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}
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}
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/// Clones this matrix to one that owns its data.
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#[inline]
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pub fn clone_owned(&self) -> MatrixMN<N, R, C>
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where
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DefaultAllocator: Allocator<N, R, C>,
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{
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Matrix::from_data(self.data.clone_owned())
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}
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/// Clones this matrix into one that owns its data. The actual type of the result depends on
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/// matrix storage combination rules for addition.
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#[inline]
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pub fn clone_owned_sum<R2, C2>(&self) -> MatrixSum<N, R, C, R2, C2>
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where
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R2: Dim,
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C2: Dim,
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DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
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{
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let (nrows, ncols) = self.shape();
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let nrows: SameShapeR<R, R2> = Dim::from_usize(nrows);
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let ncols: SameShapeC<C, C2> = Dim::from_usize(ncols);
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let mut res: MatrixSum<N, R, C, R2, C2> =
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unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
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// FIXME: use copy_from
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for j in 0..res.ncols() {
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for i in 0..res.nrows() {
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unsafe {
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*res.get_unchecked_mut(i, j) = *self.get_unchecked(i, j);
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}
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}
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}
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res
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}
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/// Returns a matrix containing the result of `f` applied to each of its entries.
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#[inline]
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pub fn map<N2: Scalar, F: FnMut(N) -> N2>(&self, mut f: F) -> MatrixMN<N2, R, C>
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where
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DefaultAllocator: Allocator<N2, R, C>,
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{
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let (nrows, ncols) = self.data.shape();
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let mut res = unsafe { MatrixMN::new_uninitialized_generic(nrows, ncols) };
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for j in 0..ncols.value() {
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for i in 0..nrows.value() {
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unsafe {
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let a = *self.data.get_unchecked(i, j);
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*res.data.get_unchecked_mut(i, j) = f(a)
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}
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}
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}
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res
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}
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/// Returns a matrix containing the result of `f` applied to each entries of `self` and
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/// `rhs`.
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#[inline]
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pub fn zip_map<N2, N3, S2, F>(&self, rhs: &Matrix<N2, R, C, S2>, mut f: F) -> MatrixMN<N3, R, C>
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where
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N2: Scalar,
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N3: Scalar,
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S2: Storage<N2, R, C>,
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F: FnMut(N, N2) -> N3,
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DefaultAllocator: Allocator<N3, R, C>,
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{
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let (nrows, ncols) = self.data.shape();
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let mut res = unsafe { MatrixMN::new_uninitialized_generic(nrows, ncols) };
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assert!(
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(nrows.value(), ncols.value()) == rhs.shape(),
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"Matrix simultaneous traversal error: dimension mismatch."
|
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);
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|
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for j in 0..ncols.value() {
|
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for i in 0..nrows.value() {
|
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unsafe {
|
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let a = *self.data.get_unchecked(i, j);
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let b = *rhs.data.get_unchecked(i, j);
|
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*res.data.get_unchecked_mut(i, j) = f(a, b)
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}
|
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}
|
||
}
|
||
|
||
res
|
||
}
|
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|
||
/// Transposes `self` and store the result into `out`.
|
||
#[inline]
|
||
pub fn transpose_to<R2, C2, SB>(&self, out: &mut Matrix<N, R2, C2, SB>)
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: StorageMut<N, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
|
||
{
|
||
let (nrows, ncols) = self.shape();
|
||
assert!(
|
||
(ncols, nrows) == out.shape(),
|
||
"Incompatible shape for transpose-copy."
|
||
);
|
||
|
||
// FIXME: optimize that.
|
||
for i in 0..nrows {
|
||
for j in 0..ncols {
|
||
unsafe {
|
||
*out.get_unchecked_mut(j, i) = *self.get_unchecked(i, j);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// Transposes `self`.
|
||
#[inline]
|
||
pub fn transpose(&self) -> MatrixMN<N, C, R>
|
||
where
|
||
DefaultAllocator: Allocator<N, C, R>,
|
||
{
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
unsafe {
|
||
let mut res = Matrix::new_uninitialized_generic(ncols, nrows);
|
||
self.transpose_to(&mut res);
|
||
|
||
res
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
|
||
/// Mutably iterates through this matrix coordinates.
|
||
#[inline]
|
||
pub fn iter_mut(&mut self) -> MatrixIterMut<N, R, C, S> {
|
||
MatrixIterMut::new(&mut self.data)
|
||
}
|
||
|
||
/// Gets a mutable reference to the i-th element of this matrix.
|
||
#[inline]
|
||
pub unsafe fn get_unchecked_mut(&mut self, irow: usize, icol: usize) -> &mut N {
|
||
debug_assert!(
|
||
irow < self.nrows() && icol < self.ncols(),
|
||
"Matrix index out of bounds."
|
||
);
|
||
self.data.get_unchecked_mut(irow, icol)
|
||
}
|
||
|
||
/// 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 another one. Both must have the same shape.
|
||
#[inline]
|
||
pub fn copy_from<R2, C2, SB>(&mut self, other: &Matrix<N, R2, C2, SB>)
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: Storage<N, 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);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// Fills this matrix with the content of the transpose another one.
|
||
#[inline]
|
||
pub fn tr_copy_from<R2, C2, SB>(&mut self, other: &Matrix<N, R2, C2, SB>)
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: Storage<N, 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);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// Replaces each component of `self` by the result of a closure `f` applied on it.
|
||
#[inline]
|
||
pub fn apply<F: FnMut(N) -> N>(&mut self, mut f: F)
|
||
where
|
||
DefaultAllocator: Allocator<N, 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)
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
|
||
/// Gets a reference to the i-th element of this column vector without bound checking.
|
||
#[inline]
|
||
pub unsafe fn vget_unchecked(&self, i: usize) -> &N {
|
||
debug_assert!(i < self.nrows(), "Vector index out of bounds.");
|
||
let i = i * self.strides().0;
|
||
self.data.get_unchecked_linear(i)
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, D: Dim, S: StorageMut<N, D>> Vector<N, D, S> {
|
||
/// Gets a mutable reference to the i-th element of this column vector without bound checking.
|
||
#[inline]
|
||
pub unsafe fn vget_unchecked_mut(&mut self, i: usize) -> &mut N {
|
||
debug_assert!(i < self.nrows(), "Vector index out of bounds.");
|
||
let i = i * self.strides().0;
|
||
self.data.get_unchecked_linear_mut(i)
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, R: Dim, C: Dim, S: ContiguousStorage<N, R, C>> Matrix<N, R, C, S> {
|
||
/// Extracts a slice containing the entire matrix entries ordered column-by-columns.
|
||
#[inline]
|
||
pub fn as_slice(&self) -> &[N] {
|
||
self.data.as_slice()
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, R: Dim, C: Dim, S: ContiguousStorageMut<N, R, C>> Matrix<N, R, C, S> {
|
||
/// Extracts a mutable slice containing the entire matrix entries ordered column-by-columns.
|
||
#[inline]
|
||
pub fn as_mut_slice(&mut self) -> &mut [N] {
|
||
self.data.as_mut_slice()
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, D: Dim, S: StorageMut<N, D, D>> Matrix<N, 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<N: Real, R: Dim, C: Dim, S: Storage<Complex<N>, R, C>> Matrix<Complex<N>, R, C, S> {
|
||
/// Takes the conjugate and transposes `self` and store the result into `out`.
|
||
#[inline]
|
||
pub fn conjugate_transpose_to<R2, C2, SB>(&self, out: &mut Matrix<Complex<N>, R2, C2, SB>)
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: StorageMut<Complex<N>, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,
|
||
{
|
||
let (nrows, ncols) = self.shape();
|
||
assert!(
|
||
(ncols, nrows) == out.shape(),
|
||
"Incompatible shape for transpose-copy."
|
||
);
|
||
|
||
// FIXME: optimize that.
|
||
for i in 0..nrows {
|
||
for j in 0..ncols {
|
||
unsafe {
|
||
*out.get_unchecked_mut(j, i) = self.get_unchecked(i, j).conj();
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// The conjugate transposition of `self`.
|
||
#[inline]
|
||
pub fn conjugate_transpose(&self) -> MatrixMN<Complex<N>, C, R>
|
||
where
|
||
DefaultAllocator: Allocator<Complex<N>, C, R>,
|
||
{
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
unsafe {
|
||
let mut res: MatrixMN<_, C, R> = Matrix::new_uninitialized_generic(ncols, nrows);
|
||
self.conjugate_transpose_to(&mut res);
|
||
|
||
res
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Real, D: Dim, S: StorageMut<Complex<N>, D, D>> Matrix<Complex<N>, D, D, S> {
|
||
/// Sets `self` to its conjugate transpose.
|
||
pub fn conjugate_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 {
|
||
let ref_ij = self.get_unchecked_mut(i, j) as *mut Complex<N>;
|
||
let ref_ji = self.get_unchecked_mut(j, i) as *mut Complex<N>;
|
||
let conj_ij = (*ref_ij).conj();
|
||
let conj_ji = (*ref_ji).conj();
|
||
*ref_ij = conj_ji;
|
||
*ref_ji = conj_ij;
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
|
||
/// Creates a square matrix with its diagonal set to `diag` and all other entries set to 0.
|
||
#[inline]
|
||
pub fn diagonal(&self) -> VectorN<N, D>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
assert!(
|
||
self.is_square(),
|
||
"Unable to get the diagonal of a non-square matrix."
|
||
);
|
||
|
||
let dim = self.data.shape().0;
|
||
let mut res = unsafe { VectorN::new_uninitialized_generic(dim, U1) };
|
||
|
||
for i in 0..dim.value() {
|
||
unsafe {
|
||
*res.vget_unchecked_mut(i) = *self.get_unchecked(i, i);
|
||
}
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// Computes a trace of a square matrix, i.e., the sum of its diagonal elements.
|
||
#[inline]
|
||
pub fn trace(&self) -> N
|
||
where
|
||
N: Ring,
|
||
{
|
||
assert!(
|
||
self.is_square(),
|
||
"Cannot compute the trace of non-square matrix."
|
||
);
|
||
|
||
let dim = self.data.shape().0;
|
||
let mut res = N::zero();
|
||
|
||
for i in 0..dim.value() {
|
||
res += unsafe { *self.get_unchecked(i, i) };
|
||
}
|
||
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar + Zero, D: DimAdd<U1>, S: Storage<N, D>> Vector<N, D, S> {
|
||
/// Computes the coordinates in projective space of this vector, i.e., appends a `0` to its
|
||
/// coordinates.
|
||
#[inline]
|
||
pub fn to_homogeneous(&self) -> VectorN<N, DimSum<D, U1>>
|
||
where
|
||
DefaultAllocator: Allocator<N, DimSum<D, U1>>,
|
||
{
|
||
let len = self.len();
|
||
let hnrows = DimSum::<D, U1>::from_usize(len + 1);
|
||
let mut res = unsafe { VectorN::<N, _>::new_uninitialized_generic(hnrows, U1) };
|
||
res.generic_slice_mut((0, 0), self.data.shape())
|
||
.copy_from(self);
|
||
res[(len, 0)] = N::zero();
|
||
|
||
res
|
||
}
|
||
|
||
/// 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<N, DimSum<D, U1>, SB>) -> Option<VectorN<N, D>>
|
||
where
|
||
SB: Storage<N, DimSum<D, U1>>,
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
if v[v.len() - 1].is_zero() {
|
||
let nrows = D::from_usize(v.len() - 1);
|
||
Some(v.generic_slice((0, 0), (nrows, U1)).into_owned())
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> ApproxEq for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar + ApproxEq,
|
||
S: Storage<N, R, C>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
type Epsilon = N::Epsilon;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
N::default_epsilon()
|
||
}
|
||
|
||
#[inline]
|
||
fn default_max_relative() -> Self::Epsilon {
|
||
N::default_max_relative()
|
||
}
|
||
|
||
#[inline]
|
||
fn default_max_ulps() -> u32 {
|
||
N::default_max_ulps()
|
||
}
|
||
|
||
#[inline]
|
||
fn relative_eq(
|
||
&self,
|
||
other: &Self,
|
||
epsilon: Self::Epsilon,
|
||
max_relative: Self::Epsilon,
|
||
) -> bool {
|
||
self.relative_eq(other, epsilon, max_relative)
|
||
}
|
||
|
||
#[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, max_ulps))
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> PartialOrd for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar + PartialOrd,
|
||
S: Storage<N, R, C>,
|
||
{
|
||
#[inline]
|
||
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
|
||
assert!(
|
||
self.shape() == other.shape(),
|
||
"Matrix comparison error: dimensions mismatch."
|
||
);
|
||
|
||
let first_ord = unsafe {
|
||
self.data
|
||
.get_unchecked_linear(0)
|
||
.partial_cmp(other.data.get_unchecked_linear(0))
|
||
};
|
||
|
||
if let Some(mut first_ord) = first_ord {
|
||
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;
|
||
}
|
||
}
|
||
}
|
||
|
||
None
|
||
}
|
||
|
||
#[inline]
|
||
fn lt(&self, right: &Self) -> bool {
|
||
assert!(
|
||
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!(
|
||
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!(
|
||
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!(
|
||
self.shape() == right.shape(),
|
||
"Matrix comparison error: dimensions mismatch."
|
||
);
|
||
self.iter().zip(right.iter()).all(|(a, b)| a.ge(b))
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> Eq for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar + Eq,
|
||
S: Storage<N, R, C>,
|
||
{
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> PartialEq for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar,
|
||
S: Storage<N, R, C>,
|
||
{
|
||
#[inline]
|
||
fn eq(&self, right: &Matrix<N, R, C, S>) -> bool {
|
||
assert!(
|
||
self.shape() == right.shape(),
|
||
"Matrix equality test dimension mismatch."
|
||
);
|
||
self.iter().zip(right.iter()).all(|(l, r)| l == r)
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> fmt::Display for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar + fmt::Display,
|
||
S: Storage<N, R, C>,
|
||
DefaultAllocator: Allocator<usize, R, C>,
|
||
{
|
||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||
fn val_width<N: Scalar + fmt::Display>(val: N, f: &mut fmt::Formatter) -> usize {
|
||
match f.precision() {
|
||
Some(precision) => format!("{:.1$}", val, precision).chars().count(),
|
||
None => format!("{}", val).chars().count(),
|
||
}
|
||
}
|
||
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
if nrows.value() == 0 || ncols.value() == 0 {
|
||
return write!(f, "[ ]");
|
||
}
|
||
|
||
let mut max_length = 0;
|
||
let mut lengths: MatrixMN<usize, R, C> = Matrix::zeros_generic(nrows, ncols);
|
||
let (nrows, ncols) = self.shape();
|
||
|
||
for i in 0..nrows {
|
||
for j in 0..ncols {
|
||
lengths[(i, j)] = val_width(self[(i, j)], f);
|
||
max_length = ::max(max_length, lengths[(i, j)]);
|
||
}
|
||
}
|
||
|
||
let max_length_with_space = max_length + 1;
|
||
|
||
try!(writeln!(f, ""));
|
||
try!(writeln!(
|
||
f,
|
||
" ┌ {:>width$} ┐",
|
||
"",
|
||
width = max_length_with_space * ncols - 1
|
||
));
|
||
|
||
for i in 0..nrows {
|
||
try!(write!(f, " │"));
|
||
for j in 0..ncols {
|
||
let number_length = lengths[(i, j)] + 1;
|
||
let pad = max_length_with_space - number_length;
|
||
try!(write!(f, " {:>thepad$}", "", thepad = pad));
|
||
match f.precision() {
|
||
Some(precision) => try!(write!(f, "{:.1$}", (*self)[(i, j)], precision)),
|
||
None => try!(write!(f, "{}", (*self)[(i, j)])),
|
||
}
|
||
}
|
||
try!(writeln!(f, " │"));
|
||
}
|
||
|
||
try!(writeln!(
|
||
f,
|
||
" └ {:>width$} ┘",
|
||
"",
|
||
width = max_length_with_space * ncols - 1
|
||
));
|
||
writeln!(f, "")
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar + Ring, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
|
||
/// The perpendicular product between two 2D column vectors, i.e. `a.x * b.y - a.y * b.x`.
|
||
#[inline]
|
||
pub fn perp<R2, C2, SB>(&self, b: &Matrix<N, R2, C2, SB>) -> N
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: Storage<N, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, U2>
|
||
+ SameNumberOfColumns<C, U1>
|
||
+ SameNumberOfRows<R2, U2>
|
||
+ SameNumberOfColumns<C2, U1>,
|
||
{
|
||
assert!(self.shape() == (2, 1), "2D perpendicular product ");
|
||
|
||
unsafe {
|
||
*self.get_unchecked(0, 0) * *b.get_unchecked(1, 0)
|
||
- *self.get_unchecked(1, 0) * *b.get_unchecked(0, 0)
|
||
}
|
||
}
|
||
|
||
// FIXME: 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]
|
||
pub fn cross<R2, C2, SB>(&self, b: &Matrix<N, R2, C2, SB>) -> MatrixCross<N, R, C, R2, C2>
|
||
where
|
||
R2: Dim,
|
||
C2: Dim,
|
||
SB: Storage<N, R2, C2>,
|
||
DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
|
||
{
|
||
let shape = self.shape();
|
||
assert!(
|
||
shape == b.shape(),
|
||
"Vector cross product dimension mismatch."
|
||
);
|
||
assert!(
|
||
(shape.0 == 3 && shape.1 == 1) || (shape.0 == 1 && shape.1 == 3),
|
||
"Vector cross product dimension mismatch."
|
||
);
|
||
|
||
if shape.0 == 3 {
|
||
unsafe {
|
||
// FIXME: soooo ugly!
|
||
let nrows = SameShapeR::<R, R2>::from_usize(3);
|
||
let ncols = SameShapeC::<C, C2>::from_usize(1);
|
||
let mut res = Matrix::new_uninitialized_generic(nrows, ncols);
|
||
|
||
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) = ay * bz - az * by;
|
||
*res.get_unchecked_mut(1, 0) = az * bx - ax * bz;
|
||
*res.get_unchecked_mut(2, 0) = ax * by - ay * bx;
|
||
|
||
res
|
||
}
|
||
} else {
|
||
unsafe {
|
||
// FIXME: ugly!
|
||
let nrows = SameShapeR::<R, R2>::from_usize(1);
|
||
let ncols = SameShapeC::<C, C2>::from_usize(3);
|
||
let mut res = Matrix::new_uninitialized_generic(nrows, ncols);
|
||
|
||
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) = ay * bz - az * by;
|
||
*res.get_unchecked_mut(0, 1) = az * bx - ax * bz;
|
||
*res.get_unchecked_mut(0, 2) = ax * by - ay * bx;
|
||
|
||
res
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Real, S: Storage<N, U3>> Vector<N, U3, S>
|
||
where
|
||
DefaultAllocator: Allocator<N, U3>,
|
||
{
|
||
/// Computes the matrix `M` such that for all vector `v` we have `M * v == self.cross(&v)`.
|
||
#[inline]
|
||
pub fn cross_matrix(&self) -> MatrixN<N, U3> {
|
||
MatrixN::<N, U3>::new(
|
||
N::zero(),
|
||
-self[2],
|
||
self[1],
|
||
self[2],
|
||
N::zero(),
|
||
-self[0],
|
||
-self[1],
|
||
self[0],
|
||
N::zero(),
|
||
)
|
||
}
|
||
}
|
||
|
||
impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
|
||
/// The smallest angle between two vectors.
|
||
#[inline]
|
||
pub fn angle<R2: Dim, C2: Dim, SB>(&self, other: &Matrix<N, R2, C2, SB>) -> N
|
||
where
|
||
SB: Storage<N, R2, C2>,
|
||
ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
|
||
{
|
||
let prod = self.dot(other);
|
||
let n1 = self.norm();
|
||
let n2 = other.norm();
|
||
|
||
if n1.is_zero() || n2.is_zero() {
|
||
N::zero()
|
||
} else {
|
||
let cang = prod / (n1 * n2);
|
||
|
||
if cang > N::one() {
|
||
N::zero()
|
||
} else if cang < -N::one() {
|
||
N::pi()
|
||
} else {
|
||
cang.acos()
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
|
||
/// The squared L2 norm of this vector.
|
||
#[inline]
|
||
pub fn norm_squared(&self) -> N {
|
||
let mut res = N::zero();
|
||
|
||
for i in 0..self.ncols() {
|
||
let col = self.column(i);
|
||
res += col.dot(&col)
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// The L2 norm of this matrix.
|
||
#[inline]
|
||
pub fn norm(&self) -> N {
|
||
self.norm_squared().sqrt()
|
||
}
|
||
|
||
/// Returns a normalized version of this matrix.
|
||
#[inline]
|
||
pub fn normalize(&self) -> MatrixMN<N, R, C>
|
||
where
|
||
DefaultAllocator: Allocator<N, R, C>,
|
||
{
|
||
self / self.norm()
|
||
}
|
||
|
||
/// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
|
||
#[inline]
|
||
pub fn try_normalize(&self, min_norm: N) -> Option<MatrixMN<N, R, C>>
|
||
where
|
||
DefaultAllocator: Allocator<N, R, C>,
|
||
{
|
||
let n = self.norm();
|
||
|
||
if n <= min_norm {
|
||
None
|
||
} else {
|
||
Some(self / n)
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Real, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
|
||
/// Normalizes this matrix in-place and returns its norm.
|
||
#[inline]
|
||
pub fn normalize_mut(&mut self) -> N {
|
||
let n = self.norm();
|
||
*self /= n;
|
||
|
||
n
|
||
}
|
||
|
||
/// Normalizes this matrix in-place or does nothing if its norm is smaller or equal to `eps`.
|
||
///
|
||
/// If the normalization succeded, returns the old normal of this matrix.
|
||
#[inline]
|
||
pub fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
|
||
let n = self.norm();
|
||
|
||
if n <= min_norm {
|
||
None
|
||
} else {
|
||
*self /= n;
|
||
Some(n)
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> ApproxEq for Unit<Matrix<N, R, C, S>>
|
||
where
|
||
N: Scalar + ApproxEq,
|
||
S: Storage<N, R, C>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
type Epsilon = N::Epsilon;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
N::default_epsilon()
|
||
}
|
||
|
||
#[inline]
|
||
fn default_max_relative() -> Self::Epsilon {
|
||
N::default_max_relative()
|
||
}
|
||
|
||
#[inline]
|
||
fn default_max_ulps() -> u32 {
|
||
N::default_max_ulps()
|
||
}
|
||
|
||
#[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)
|
||
}
|
||
|
||
#[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)
|
||
}
|
||
}
|