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use num::{One, Zero};
use num_complex::Complex;
#[cfg(feature = "abomonation-serialize")]
use std::io::{Result as IOResult, Write};
use approx::{AbsDiffEq, RelativeEq, UlpsEq};
use std::any::TypeId;
use std::cmp::Ordering;
use std::fmt;
use std::hash::{Hash, Hasher};
use std::marker::PhantomData;
use std::mem;
#[cfg(feature = "serde-serialize")]
use serde::{Deserialize, Deserializer, Serialize, Serializer};
#[cfg(feature = "abomonation-serialize")]
use abomonation::Abomonation;
use alga::general::{ClosedAdd, ClosedMul, ClosedSub, Real, Ring};
use base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
use base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
use base::dimension::{Dim, DimAdd, DimSum, IsNotStaticOne, U1, U2, U3};
use base::iter::{MatrixIter, MatrixIterMut};
use base::storage::{
ContiguousStorage, ContiguousStorageMut, Owned, SameShapeStorage, Storage, StorageMut,
};
use base::{DefaultAllocator, MatrixMN, MatrixN, Scalar, Unit, VectorN};
/// A square matrix.
pub type SquareMatrix<N, D, S> = Matrix<N, D, D, S>;
/// A matrix with one column and `D` rows.
pub type Vector<N, D, S> = Matrix<N, D, U1, S>;
/// A matrix with one row and `D` columns .
pub type RowVector<N, D, S> = Matrix<N, U1, D, S>;
/// The type of the result of a matrix sum.
pub type MatrixSum<N, R1, C1, R2, C2> =
Matrix<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<N, R1, C1, R2, C2>>;
/// The type of the result of a matrix sum.
pub type VectorSum<N, R1, R2> =
Matrix<N, SameShapeR<R1, R2>, U1, SameShapeStorage<N, R1, U1, R2, U1>>;
/// The type of the result of a matrix cross product.
pub type MatrixCross<N, R1, C1, R2, C2> =
Matrix<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>, SameShapeStorage<N, R1, C1, R2, C2>>;
/// The most generic column-major matrix (and vector) type.
///
/// It combines four type parameters:
/// - `N`: for the matrix components scalar type.
/// - `R`: for the matrix number of rows.
/// - `C`: for the matrix number of columns.
/// - `S`: for the matrix data storage, i.e., the buffer that actually contains the matrix
/// components.
///
/// The matrix dimensions parameters `R` and `C` can either be:
/// - type-level unsigned integer constants (e.g. `U1`, `U124`) from the `nalgebra::` root module.
/// All numbers from 0 to 127 are defined that way.
/// - type-level unsigned integer constants (e.g. `U1024`, `U10000`) from the `typenum::` crate.
/// Using those, you will not get error messages as nice as for numbers smaller than 128 defined on
/// the `nalgebra::` module.
/// - the special value `Dynamic` from the `nalgebra::` root module. This indicates that the
/// specified dimension is not known at compile-time. Note that this will generally imply that the
/// matrix data storage `S` performs a dynamic allocation and contains extra metadata for the
/// matrix shape.
///
/// Note that mixing `Dynamic` with type-level unsigned integers is allowed. Actually, a
/// dynamically-sized column vector should be represented as a `Matrix<N, Dynamic, U1, S>` (given
/// some concrete types for `N` and a compatible data storage type `S`).
#[repr(C)]
#[derive(Clone, Copy)]
pub struct Matrix<N: Scalar, R: Dim, C: Dim, S> {
/// The data storage that contains all the matrix components and informations about its number
/// of rows and column (if needed).
pub data: S,
_phantoms: PhantomData<(N, R, C)>,
}
impl<N: Scalar, R: Dim, C: Dim, S: fmt::Debug> fmt::Debug for Matrix<N, R, C, S> {
fn fmt(&self, formatter: &mut fmt::Formatter) -> Result<(), fmt::Error> {
formatter
.debug_struct("Matrix")
.field("data", &self.data)
.finish()
}
}
#[cfg(feature = "serde-serialize")]
impl<N, R, C, S> Serialize for Matrix<N, R, C, S>
where
N: Scalar,
R: Dim,
C: Dim,
S: Serialize,
{
fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
where T: Serializer {
self.data.serialize(serializer)
}
}
#[cfg(feature = "serde-serialize")]
impl<'de, N, R, C, S> Deserialize<'de> for Matrix<N, R, C, S>
where
N: Scalar,
R: Dim,
C: Dim,
S: Deserialize<'de>,
{
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where D: Deserializer<'de> {
S::deserialize(deserializer).map(|x| Matrix {
data: x,
_phantoms: PhantomData,
})
}
}
#[cfg(feature = "abomonation-serialize")]
impl<N: Scalar, R: Dim, C: Dim, S: Abomonation> Abomonation for Matrix<N, R, C, S> {
unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
self.data.entomb(writer)
}
unsafe fn exhume<'a, 'b>(&'a mut self, bytes: &'b mut [u8]) -> Option<&'b mut [u8]> {
self.data.exhume(bytes)
}
fn extent(&self) -> usize {
self.data.extent()
}
}
impl<N: Scalar, R: Dim, C: Dim, S> Matrix<N, R, C, S> {
/// Creates a new matrix with the given data without statically checking that the matrix
/// dimension matches the storage dimension.
#[inline]
pub unsafe fn from_data_statically_unchecked(data: S) -> Matrix<N, R, C, S> {
Matrix {
data: data,
_phantoms: PhantomData,
}
}
}
impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
/// Creates a new matrix with the given data.
#[inline]
pub fn from_data(data: S) -> Matrix<N, R, C, S> {
unsafe { Self::from_data_statically_unchecked(data) }
}
/// The total number of elements of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.len(), 12);
#[inline]
pub fn len(&self) -> usize {
let (nrows, ncols) = self.shape();
nrows * ncols
}
/// The shape of this matrix returned as the tuple (number of rows, number of columns).
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.shape(), (3, 4));
#[inline]
pub fn shape(&self) -> (usize, usize) {
let (nrows, ncols) = self.data.shape();
(nrows.value(), ncols.value())
}
/// The number of rows of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.nrows(), 3);
#[inline]
pub fn nrows(&self) -> usize {
self.shape().0
}
/// The number of columns of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix3x4;
/// let mat = Matrix3x4::<f32>::zeros();
/// assert_eq!(mat.ncols(), 4);
#[inline]
pub fn ncols(&self) -> usize {
self.shape().1
}
/// The strides (row stride, column stride) of this matrix.
///
/// # Examples:
///
/// ```
/// # use nalgebra::DMatrix;
/// let mat = DMatrix::<f32>::zeros(10, 10);
/// let slice = mat.slice_with_steps((0, 0), (5, 3), (1, 2));
/// // The column strides is the number of steps (here 2) multiplied by the corresponding dimension.
/// assert_eq!(mat.strides(), (1, 10));
#[inline]
pub fn strides(&self) -> (usize, usize) {
let (srows, scols) = self.data.strides();
(srows.value(), scols.value())
}
/// Iterates through this matrix coordinates in column-major order.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix2x3;
/// let mat = Matrix2x3::new(11, 12, 13,
/// 21, 22, 23);
/// let mut it = mat.iter();
/// assert_eq!(*it.next().unwrap(), 11);
/// assert_eq!(*it.next().unwrap(), 21);
/// assert_eq!(*it.next().unwrap(), 12);
/// assert_eq!(*it.next().unwrap(), 22);
/// assert_eq!(*it.next().unwrap(), 13);
/// assert_eq!(*it.next().unwrap(), 23);
/// assert!(it.next().is_none());
#[inline]
pub fn iter(&self) -> MatrixIter<N, R, C, S> {
MatrixIter::new(&self.data)
}
/// Computes the row and column coordinates of the i-th element of this matrix seen as a
/// vector.
#[inline]
pub fn vector_to_matrix_index(&self, i: usize) -> (usize, usize) {
let (nrows, ncols) = self.shape();
// Two most common uses that should be optimized by the compiler for statically-sized
// matrices.
if nrows == 1 {
(0, i)
} else if ncols == 1 {
(i, 0)
} else {
(i % nrows, i / nrows)
}
}
/// Tests whether `self` and `rhs` are equal up to a given epsilon.
///
/// See `relative_eq` from the `RelativeEq` trait for more details.
#[inline]
pub fn relative_eq<R2, C2, SB>(
&self,
other: &Matrix<N, R2, C2, SB>,
eps: N::Epsilon,
max_relative: N::Epsilon,
) -> bool
where
N: RelativeEq,
R2: Dim,
C2: Dim,
SB: Storage<N, R2, C2>,
N::Epsilon: Copy,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
assert!(self.shape() == other.shape());
self.iter()
.zip(other.iter())
.all(|(a, b)| a.relative_eq(b, eps, max_relative))
}
/// Tests whether `self` and `rhs` are exactly equal.
#[inline]
pub fn eq<R2, C2, SB>(&self, other: &Matrix<N, R2, C2, SB>) -> bool
where
N: PartialEq,
R2: Dim,
C2: Dim,
SB: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
assert!(self.shape() == other.shape());
self.iter().zip(other.iter()).all(|(a, b)| *a == *b)
}
/// Moves this matrix into one that owns its data.
#[inline]
pub fn into_owned(self) -> MatrixMN<N, R, C>
where DefaultAllocator: Allocator<N, R, C> {
Matrix::from_data(self.data.into_owned())
}
// FIXME: this could probably benefit from specialization.
// XXX: bad name.
/// Moves this matrix into one that owns its data. The actual type of the result depends on
/// matrix storage combination rules for addition.
#[inline]
pub fn into_owned_sum<R2, C2>(self) -> MatrixSum<N, R, C, R2, C2>
where
R2: Dim,
C2: Dim,
DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
if TypeId::of::<SameShapeStorage<N, R, C, R2, C2>>() == TypeId::of::<Owned<N, R, C>>() {
// We can just return `self.into_owned()`.
unsafe {
// FIXME: check that those copies are optimized away by the compiler.
let owned = self.into_owned();
let res = mem::transmute_copy(&owned);
mem::forget(owned);
res
}
} else {
self.clone_owned_sum()
}
}
/// Clones this matrix to one that owns its data.
#[inline]
pub fn clone_owned(&self) -> MatrixMN<N, R, C>
where DefaultAllocator: Allocator<N, R, C> {
Matrix::from_data(self.data.clone_owned())
}
/// Clones this matrix into one that owns its data. The actual type of the result depends on
/// matrix storage combination rules for addition.
#[inline]
pub fn clone_owned_sum<R2, C2>(&self) -> MatrixSum<N, R, C, R2, C2>
where
R2: Dim,
C2: Dim,
DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
{
let (nrows, ncols) = self.shape();
let nrows: SameShapeR<R, R2> = Dim::from_usize(nrows);
let ncols: SameShapeC<C, C2> = Dim::from_usize(ncols);
let mut res: MatrixSum<N, R, C, R2, C2> =
unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
// FIXME: use copy_from
for j in 0..res.ncols() {
for i in 0..res.nrows() {
unsafe {
*res.get_unchecked_mut((i, j)) = *self.get_unchecked((i, j));
}
}
}
res
}
/// Returns a matrix containing the result of `f` applied to each of its entries.
#[inline]
pub fn map<N2: Scalar, F: FnMut(N) -> N2>(&self, mut f: F) -> 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(a)
}
}
}
res
}
/// Returns a matrix containing the result of `f` applied to each of its entries. Unlike `map`,
/// `f` also gets passed the row and column index, i.e. `f(value, row, col)`.
#[inline]
pub fn map_with_location<N2: Scalar, F: FnMut(usize, usize, N) -> N2>(
&self,
mut f: F,
) -> 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
}
/// 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)
}
/// 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)
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 + 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>> {
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> 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: 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()
}
/// A synonym for the norm of this matrix.
///
/// Aka the length.
///
/// This function is simply implemented as a call to `norm()`
#[inline]
pub fn magnitude(&self) -> N {
self.norm()
}
/// A synonym for the squared norm of this matrix.
///
/// Aka the squared length.
///
/// This function is simply implemented as a call to `norm_squared()`
#[inline]
pub fn magnitude_squared(&self) -> N {
self.norm_squared()
}
/// 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: 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: 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 succeeded, 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> 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);
}
}
}
}
}