forked from M-Labs/nalgebra
1547 lines
47 KiB
Rust
1547 lines
47 KiB
Rust
use num::{One, Zero};
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use num_complex::Complex;
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#[cfg(feature = "abomonation-serialize")]
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use std::io::{Result as IOResult, Write};
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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")]
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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::{ClosedAdd, ClosedMul, ClosedSub, Real, Ring};
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use base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
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use base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
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use base::dimension::{Dim, DimAdd, DimSum, IsNotStaticOne, U1, U2, U3};
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use base::iter::{MatrixIter, MatrixIterMut, RowIter, RowIterMut, ColumnIter, ColumnIterMut};
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use base::storage::{
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ContiguousStorage, ContiguousStorageMut, Owned, SameShapeStorage, Storage, StorageMut,
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};
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use base::{DefaultAllocator, MatrixMN, MatrixN, Scalar, Unit, VectorN};
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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 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<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(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
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.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 T: Serializer {
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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 D: Deserializer<'de> {
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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<W: Write>(&self, writer: &mut W) -> IOResult<()> {
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self.data.entomb(writer)
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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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fn extent(&self) -> usize {
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self.data.extent()
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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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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Matrix3x4;
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/// let mat = Matrix3x4::<f32>::zeros();
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/// assert_eq!(mat.len(), 12);
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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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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Matrix3x4;
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/// let mat = Matrix3x4::<f32>::zeros();
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/// assert_eq!(mat.shape(), (3, 4));
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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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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Matrix3x4;
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/// let mat = Matrix3x4::<f32>::zeros();
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/// assert_eq!(mat.nrows(), 3);
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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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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Matrix3x4;
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/// let mat = Matrix3x4::<f32>::zeros();
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/// assert_eq!(mat.ncols(), 4);
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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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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::DMatrix;
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/// let mat = DMatrix::<f32>::zeros(10, 10);
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/// let slice = mat.slice_with_steps((0, 0), (5, 3), (1, 2));
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/// // The column strides is the number of steps (here 2) multiplied by the corresponding dimension.
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/// assert_eq!(mat.strides(), (1, 10));
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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 in column-major order.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Matrix2x3;
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/// let mat = Matrix2x3::new(11, 12, 13,
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/// 21, 22, 23);
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/// let mut it = mat.iter();
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/// assert_eq!(*it.next().unwrap(), 11);
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/// assert_eq!(*it.next().unwrap(), 21);
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/// assert_eq!(*it.next().unwrap(), 12);
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/// assert_eq!(*it.next().unwrap(), 22);
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/// assert_eq!(*it.next().unwrap(), 13);
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/// assert_eq!(*it.next().unwrap(), 23);
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/// assert!(it.next().is_none());
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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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/// Iterate through the rows of this matrix.
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#[inline]
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pub fn row_iter(&self) -> RowIter<N, R, C, S> {
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RowIter::new(self)
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}
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/// Iterate through the columns of this matrix.
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#[inline]
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pub fn column_iter(&self) -> ColumnIter<N, R, C, S> {
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ColumnIter::new(self)
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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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/// 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 `RelativeEq` 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: RelativeEq,
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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 DefaultAllocator: Allocator<N, R, C> {
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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 DefaultAllocator: Allocator<N, R, C> {
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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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|
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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 DefaultAllocator: Allocator<N2, R, C> {
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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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|
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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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}
|
||
|
||
res
|
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}
|
||
|
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/// Returns a matrix containing the result of `f` applied to each of its entries. Unlike `map`,
|
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/// `f` also gets passed the row and column index, i.e. `f(row, col, value)`.
|
||
#[inline]
|
||
pub fn map_with_location<N2: Scalar, F: FnMut(usize, usize, N) -> N2>(
|
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&self,
|
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mut f: F,
|
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) -> MatrixMN<N2, R, C>
|
||
where
|
||
DefaultAllocator: Allocator<N2, R, C>,
|
||
{
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
let mut res = unsafe { MatrixMN::new_uninitialized_generic(nrows, ncols) };
|
||
|
||
for j in 0..ncols.value() {
|
||
for i in 0..nrows.value() {
|
||
unsafe {
|
||
let a = *self.data.get_unchecked(i, j);
|
||
*res.data.get_unchecked_mut(i, j) = f(i, j, a)
|
||
}
|
||
}
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// Returns a matrix containing the result of `f` applied to each entries of `self` and
|
||
/// `rhs`.
|
||
#[inline]
|
||
pub fn zip_map<N2, N3, S2, F>(&self, rhs: &Matrix<N2, R, C, S2>, mut f: F) -> MatrixMN<N3, R, C>
|
||
where
|
||
N2: Scalar,
|
||
N3: Scalar,
|
||
S2: Storage<N2, R, C>,
|
||
F: FnMut(N, N2) -> N3,
|
||
DefaultAllocator: Allocator<N3, R, C>,
|
||
{
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
let mut res = unsafe { MatrixMN::new_uninitialized_generic(nrows, ncols) };
|
||
|
||
assert!(
|
||
(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);
|
||
let b = *rhs.data.get_unchecked(i, j);
|
||
*res.data.get_unchecked_mut(i, j) = f(a, b)
|
||
}
|
||
}
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// Returns a matrix containing the result of `f` applied to each entries of `self` and
|
||
/// `b`, and `c`.
|
||
#[inline]
|
||
pub fn zip_zip_map<N2, N3, N4, S2, S3, F>(
|
||
&self,
|
||
b: &Matrix<N2, R, C, S2>,
|
||
c: &Matrix<N3, R, C, S3>,
|
||
mut f: F,
|
||
) -> MatrixMN<N4, R, C>
|
||
where
|
||
N2: Scalar,
|
||
N3: Scalar,
|
||
N4: Scalar,
|
||
S2: Storage<N2, R, C>,
|
||
S3: Storage<N3, R, C>,
|
||
F: FnMut(N, N2, N3) -> N4,
|
||
DefaultAllocator: Allocator<N4, R, C>,
|
||
{
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
let mut res = unsafe { MatrixMN::new_uninitialized_generic(nrows, ncols) };
|
||
|
||
assert!(
|
||
(nrows.value(), ncols.value()) == b.shape()
|
||
&& (nrows.value(), ncols.value()) == c.shape(),
|
||
"Matrix simultaneous traversal error: dimension mismatch."
|
||
);
|
||
|
||
for j in 0..ncols.value() {
|
||
for i in 0..nrows.value() {
|
||
unsafe {
|
||
let a = *self.data.get_unchecked(i, j);
|
||
let b = *b.data.get_unchecked(i, j);
|
||
let c = *c.data.get_unchecked(i, j);
|
||
*res.data.get_unchecked_mut(i, j) = f(a, b, c)
|
||
}
|
||
}
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// Folds a function `f` on each entry of `self`.
|
||
#[inline]
|
||
pub fn fold<Acc>(&self, init: Acc, mut f: impl FnMut(Acc, N) -> Acc) -> Acc {
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
let mut res = init;
|
||
|
||
for j in 0..ncols.value() {
|
||
for i in 0..nrows.value() {
|
||
unsafe {
|
||
let a = *self.data.get_unchecked(i, j);
|
||
res = f(res, a)
|
||
}
|
||
}
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// Folds a function `f` on each pairs of entries from `self` and `rhs`.
|
||
#[inline]
|
||
pub fn zip_fold<N2, R2, C2, S2, Acc>(&self, rhs: &Matrix<N2, R2, C2, S2>, init: Acc, mut f: impl FnMut(Acc, N, N2) -> Acc) -> Acc
|
||
where
|
||
N2: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
S2: Storage<N2, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>
|
||
{
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
let mut res = init;
|
||
|
||
assert!(
|
||
(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);
|
||
let b = *rhs.data.get_unchecked(i, j);
|
||
res = f(res, a, b)
|
||
}
|
||
}
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// 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)
|
||
}
|
||
|
||
/// Mutably iterates through this matrix rows.
|
||
#[inline]
|
||
pub fn row_iter_mut(&mut self) -> RowIterMut<N, R, C, S> {
|
||
RowIterMut::new(self)
|
||
}
|
||
|
||
/// Mutably iterates through this matrix columns.
|
||
#[inline]
|
||
pub fn column_iter_mut(&mut self) -> ColumnIterMut<N, R, C, S> {
|
||
ColumnIterMut::new(self)
|
||
}
|
||
|
||
/// 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: &[N]) {
|
||
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);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// 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) {
|
||
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)
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
/// 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<N2, R2, C2, S2>(&mut self, rhs: &Matrix<N2, R2, C2, S2>, mut f: impl FnMut(N, N2) -> N)
|
||
where N2: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
S2: Storage<N2, R2, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
|
||
let (nrows, ncols) = self.shape();
|
||
|
||
assert!(
|
||
(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));
|
||
*e = 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<N2, R2, C2, S2, N3, R3, C3, S3>(&mut self, b: &Matrix<N2, R2, C2, S2>, c: &Matrix<N3, R3, C3, S3>, mut f: impl FnMut(N, N2, N3) -> N)
|
||
where N2: Scalar,
|
||
R2: Dim,
|
||
C2: Dim,
|
||
S2: Storage<N2, R2, C2>,
|
||
N3: Scalar,
|
||
R3: Dim,
|
||
C3: Dim,
|
||
S3: Storage<N3, R3, C3>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
|
||
let (nrows, ncols) = self.shape();
|
||
|
||
assert!(
|
||
(nrows, ncols) == b.shape(),
|
||
"Matrix simultaneous traversal error: dimension mismatch."
|
||
);
|
||
assert!(
|
||
(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));
|
||
let c = c.get_unchecked((i, j));
|
||
*e = f(*e, *b, *c)
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
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 + One + Zero, D: DimAdd<U1> + IsNotStaticOne, S: Storage<N, D, D>> Matrix<N, 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]
|
||
pub fn to_homogeneous(&self) -> MatrixN<N, DimSum<D, U1>>
|
||
where DefaultAllocator: Allocator<N, 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 = MatrixN::identity_generic(dim, dim);
|
||
res.generic_slice_mut::<D, D>((0, 0), self.data.shape()).copy_from(&self);
|
||
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>> {
|
||
self.push(N::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<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: Scalar + Zero, D: DimAdd<U1>, S: Storage<N, D>> Vector<N, D, S> {
|
||
/// Constructs a new vector of higher dimension by appending `element` to the end of `self`.
|
||
#[inline]
|
||
pub fn push(&self, element: N) -> 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)] = element;
|
||
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> AbsDiffEq for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar + AbsDiffEq,
|
||
S: Storage<N, R, C>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
type Epsilon = N::Epsilon;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
N::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))
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> RelativeEq for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar + RelativeEq,
|
||
S: Storage<N, R, C>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
#[inline]
|
||
fn default_max_relative() -> Self::Epsilon {
|
||
N::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<N, R: Dim, C: Dim, S> UlpsEq for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar + UlpsEq,
|
||
S: Storage<N, R, C>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
#[inline]
|
||
fn default_max_ulps() -> u32 {
|
||
N::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, 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> {
|
||
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!(
|
||
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 {
|
||
#[cfg(feature = "std")]
|
||
fn val_width<N: Scalar + fmt::Display>(val: N, f: &mut fmt::Formatter) -> usize {
|
||
match f.precision() {
|
||
Some(precision) => format!("{:.1$}", val, precision).chars().count(),
|
||
None => format!("{}", val).chars().count(),
|
||
}
|
||
}
|
||
|
||
#[cfg(not(feature = "std"))]
|
||
fn val_width<N: Scalar + fmt::Display>(_: N, _: &mut fmt::Formatter) -> usize {
|
||
4
|
||
}
|
||
|
||
let (nrows, ncols) = self.data.shape();
|
||
|
||
if nrows.value() == 0 || ncols.value() == 0 {
|
||
return write!(f, "[ ]");
|
||
}
|
||
|
||
let mut max_length = 0;
|
||
let mut lengths: MatrixMN<usize, R, C> = Matrix::zeros_generic(nrows, ncols);
|
||
let (nrows, ncols) = self.shape();
|
||
|
||
for i in 0..nrows {
|
||
for j in 0..ncols {
|
||
lengths[(i, j)] = val_width(self[(i, j)], f);
|
||
max_length = ::max(max_length, lengths[(i, j)]);
|
||
}
|
||
}
|
||
|
||
let max_length_with_space = max_length + 1;
|
||
|
||
try!(writeln!(f));
|
||
try!(writeln!(
|
||
f,
|
||
" ┌ {:>width$} ┐",
|
||
"",
|
||
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: Scalar + Zero + One + ClosedAdd + ClosedSub + ClosedMul, D: Dim, S: Storage<N, D>>
|
||
Vector<N, D, S>
|
||
{
|
||
/// Returns `self * (1.0 - t) + rhs * t`, i.e., the linear blend of the vectors x and y using the scalar value a.
|
||
///
|
||
/// The value for a is not restricted to the range `[0, 1]`.
|
||
///
|
||
/// # Examples:
|
||
///
|
||
/// ```
|
||
/// # use nalgebra::Vector3;
|
||
/// let x = Vector3::new(1.0, 2.0, 3.0);
|
||
/// let y = Vector3::new(10.0, 20.0, 30.0);
|
||
/// assert_eq!(x.lerp(&y, 0.1), Vector3::new(1.9, 3.8, 5.7));
|
||
/// ```
|
||
pub fn lerp<S2: Storage<N, D>>(&self, rhs: &Vector<N, D, S2>, t: N) -> VectorN<N, D>
|
||
where DefaultAllocator: Allocator<N, D> {
|
||
let mut res = self.clone_owned();
|
||
res.axpy(t, rhs, N::one() - t);
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<N: Real, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
|
||
/// Computes the spherical linear interpolation between two unit vectors.
|
||
pub fn slerp<S2: Storage<N, D>>(
|
||
&self,
|
||
rhs: &Unit<Vector<N, D, S2>>,
|
||
t: N,
|
||
) -> Unit<VectorN<N, D>>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
// FIXME: the result is wrong when self and rhs are collinear with opposite direction.
|
||
self.try_slerp(rhs, t, N::default_epsilon())
|
||
.unwrap_or(Unit::new_unchecked(self.clone_owned()))
|
||
}
|
||
|
||
/// Computes the spherical linear interpolation between two unit vectors.
|
||
///
|
||
/// Returns `None` if the two vectors are almost collinear and with opposite direction
|
||
/// (in this case, there is an infinity of possible results).
|
||
pub fn try_slerp<S2: Storage<N, D>>(
|
||
&self,
|
||
rhs: &Unit<Vector<N, D, S2>>,
|
||
t: N,
|
||
epsilon: N,
|
||
) -> Option<Unit<VectorN<N, D>>>
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
{
|
||
let c_hang = self.dot(rhs);
|
||
|
||
// self == other
|
||
if c_hang.abs() >= N::one() {
|
||
return Some(Unit::new_unchecked(self.clone_owned()));
|
||
}
|
||
|
||
let hang = c_hang.acos();
|
||
let s_hang = (N::one() - c_hang * c_hang).sqrt();
|
||
|
||
// FIXME: what if s_hang is 0.0 ? The result is not well-defined.
|
||
if relative_eq!(s_hang, N::zero(), epsilon = epsilon) {
|
||
None
|
||
} else {
|
||
let ta = ((N::one() - t) * hang).sin() / s_hang;
|
||
let tb = (t * hang).sin() / s_hang;
|
||
let res = &**self * ta + &**rhs * tb;
|
||
|
||
Some(Unit::new_unchecked(res))
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> AbsDiffEq for Unit<Matrix<N, R, C, S>>
|
||
where
|
||
N: Scalar + AbsDiffEq,
|
||
S: Storage<N, R, C>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
type Epsilon = N::Epsilon;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
N::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<N, R: Dim, C: Dim, S> RelativeEq for Unit<Matrix<N, R, C, S>>
|
||
where
|
||
N: Scalar + RelativeEq,
|
||
S: Storage<N, R, C>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
#[inline]
|
||
fn default_max_relative() -> Self::Epsilon {
|
||
N::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<N, R: Dim, C: Dim, S> UlpsEq for Unit<Matrix<N, R, C, S>>
|
||
where
|
||
N: Scalar + UlpsEq,
|
||
S: Storage<N, R, C>,
|
||
N::Epsilon: Copy,
|
||
{
|
||
#[inline]
|
||
fn default_max_ulps() -> u32 {
|
||
N::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<N, R, C, S> Hash for Matrix<N, R, C, S>
|
||
where
|
||
N: Scalar + Hash,
|
||
R: Dim,
|
||
C: Dim,
|
||
S: Storage<N, 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);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|