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#[cfg(all(feature = "alloc", not(feature = "std")))]
use alloc::vec::Vec;
#[cfg(feature = "arbitrary")]
use crate::base::storage::Owned;
#[cfg(feature = "arbitrary")]
use quickcheck::{Arbitrary, Gen};
use num::{Bounded, One, Zero};
#[cfg(feature = "rand-no-std")]
use rand::{
distributions::{Distribution, Standard},
Rng,
};
use std::iter;
use typenum::{self, Cmp, Greater};
use simba::scalar::{ClosedAddAssign, ClosedMulAssign};
use crate::base::allocator::Allocator;
use crate::base::dimension::{Dim, DimName, Dyn, ToTypenum};
use crate::base::storage::RawStorage;
use crate::base::{
ArrayStorage, Const, DefaultAllocator, Matrix, OMatrix, OVector, Scalar, Unit, Vector,
};
use crate::UninitMatrix;
use std::mem::MaybeUninit;
impl<T: Scalar, R: Dim, C: Dim> UninitMatrix<T, R, C>
where
DefaultAllocator: Allocator<R, C>,
{
/// Builds a matrix with uninitialized elements of type `MaybeUninit<T>`.
#[inline(always)]
pub fn uninit(nrows: R, ncols: C) -> Self {
// SAFETY: this is OK because the dimension automatically match the storage
// because we are building an owned storage.
unsafe {
Self::from_data_statically_unchecked(DefaultAllocator::allocate_uninit(nrows, ncols))
}
}
}
/// # Generic constructors
/// This set of matrix and vector construction functions are all generic
/// with-regard to the matrix dimensions. They all expect to be given
/// the dimension as inputs.
///
/// These functions should only be used when working on dimension-generic code.
impl<T: Scalar, R: Dim, C: Dim> OMatrix<T, R, C>
where
DefaultAllocator: Allocator<R, C>,
{
/// Creates a matrix with all its elements set to `elem`.
#[inline]
pub fn from_element_generic(nrows: R, ncols: C, elem: T) -> Self {
let len = nrows.value() * ncols.value();
Self::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
}
/// Creates a matrix with all its elements set to `elem`.
///
/// Same as `from_element_generic`.
#[inline]
pub fn repeat_generic(nrows: R, ncols: C, elem: T) -> Self {
let len = nrows.value() * ncols.value();
Self::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
}
/// Creates a matrix with all its elements set to 0.
#[inline]
pub fn zeros_generic(nrows: R, ncols: C) -> Self
where
T: Zero,
{
Self::from_element_generic(nrows, ncols, T::zero())
}
/// Creates a matrix with all its elements filled by an iterator.
#[inline]
pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self
where
I: IntoIterator<Item = T>,
{
Self::from_data(DefaultAllocator::allocate_from_iterator(nrows, ncols, iter))
}
/// Creates a matrix with all its elements filled by an row-major order iterator.
#[inline]
pub fn from_row_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self
where
I: IntoIterator<Item = T>,
{
Self::from_data(DefaultAllocator::allocate_from_row_iterator(
nrows, ncols, iter,
))
}
/// Creates a matrix with its elements filled with the components provided by a slice in
/// row-major order.
///
/// The order of elements in the slice must follow the usual mathematic writing, i.e.,
/// row-by-row.
#[inline]
pub fn from_row_slice_generic(nrows: R, ncols: C, slice: &[T]) -> Self {
assert!(
slice.len() == nrows.value() * ncols.value(),
"Matrix init. error: the slice did not contain the right number of elements."
);
let mut res = Matrix::uninit(nrows, ncols);
let mut iter = slice.iter();
unsafe {
for i in 0..nrows.value() {
for j in 0..ncols.value() {
*res.get_unchecked_mut((i, j)) = MaybeUninit::new(iter.next().unwrap().clone())
}
}
// SAFETY: the result has been fully initialized above.
res.assume_init()
}
}
/// Creates a matrix with its elements filled with the components provided by a slice. The
/// components must have the same layout as the matrix data storage (i.e. column-major).
#[inline]
pub fn from_column_slice_generic(nrows: R, ncols: C, slice: &[T]) -> Self {
Self::from_iterator_generic(nrows, ncols, slice.iter().cloned())
}
/// Creates a matrix filled with the results of a function applied to each of its component
/// coordinates.
#[inline]
pub fn from_fn_generic<F>(nrows: R, ncols: C, mut f: F) -> Self
where
F: FnMut(usize, usize) -> T,
{
let mut res = Matrix::uninit(nrows, ncols);
unsafe {
for j in 0..ncols.value() {
for i in 0..nrows.value() {
*res.get_unchecked_mut((i, j)) = MaybeUninit::new(f(i, j));
}
}
// SAFETY: the result has been fully initialized above.
res.assume_init()
}
}
/// Creates a new identity matrix.
///
/// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
/// to the identity matrix. All other entries are set to zero.
#[inline]
pub fn identity_generic(nrows: R, ncols: C) -> Self
where
T: Zero + One,
{
Self::from_diagonal_element_generic(nrows, ncols, T::one())
}
/// Creates a new matrix with its diagonal filled with copies of `elt`.
///
/// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
/// to the identity matrix. All other entries are set to zero.
#[inline]
pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: T) -> Self
where
T: Zero + One,
{
let mut res = Self::zeros_generic(nrows, ncols);
for i in 0..crate::min(nrows.value(), ncols.value()) {
unsafe { *res.get_unchecked_mut((i, i)) = elt.clone() }
}
res
}
/// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal elements are
/// filled with the content of `elts`. Others are set to 0.
///
/// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
#[inline]
pub fn from_partial_diagonal_generic(nrows: R, ncols: C, elts: &[T]) -> Self
where
T: Zero,
{
let mut res = Self::zeros_generic(nrows, ncols);
assert!(
elts.len() <= crate::min(nrows.value(), ncols.value()),
"Too many diagonal elements provided."
);
for (i, elt) in elts.iter().enumerate() {
unsafe { *res.get_unchecked_mut((i, i)) = elt.clone() }
}
res
}
/// Builds a new matrix from its rows.
///
/// Panics if not enough rows are provided (for statically-sized matrices), or if all rows do
/// not have the same dimensions.
///
/// # Example
/// ```
/// # use nalgebra::{RowVector3, Matrix3};
/// # use std::iter;
///
/// let m = Matrix3::from_rows(&[ RowVector3::new(1.0, 2.0, 3.0), RowVector3::new(4.0, 5.0, 6.0), RowVector3::new(7.0, 8.0, 9.0) ]);
///
/// assert!(m.m11 == 1.0 && m.m12 == 2.0 && m.m13 == 3.0 &&
/// m.m21 == 4.0 && m.m22 == 5.0 && m.m23 == 6.0 &&
/// m.m31 == 7.0 && m.m32 == 8.0 && m.m33 == 9.0);
/// ```
#[inline]
pub fn from_rows<SB>(rows: &[Matrix<T, Const<1>, C, SB>]) -> Self
where
SB: RawStorage<T, Const<1>, C>,
{
assert!(!rows.is_empty(), "At least one row must be given.");
let nrows = R::try_to_usize().unwrap_or(rows.len());
let ncols = rows[0].len();
assert!(
rows.len() == nrows,
"Invalid number of rows provided to build this matrix."
);
if C::try_to_usize().is_none() {
assert!(
rows.iter().all(|r| r.len() == ncols),
"The provided rows must all have the same dimension."
);
}
// TODO: optimize that.
Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |i, j| {
rows[i][(0, j)].clone()
})
}
/// Builds a new matrix from its columns.
///
/// Panics if not enough columns are provided (for statically-sized matrices), or if all
/// columns do not have the same dimensions.
///
/// # Example
/// ```
/// # use nalgebra::{Vector3, Matrix3};
/// # use std::iter;
///
/// let m = Matrix3::from_columns(&[ Vector3::new(1.0, 2.0, 3.0), Vector3::new(4.0, 5.0, 6.0), Vector3::new(7.0, 8.0, 9.0) ]);
///
/// assert!(m.m11 == 1.0 && m.m12 == 4.0 && m.m13 == 7.0 &&
/// m.m21 == 2.0 && m.m22 == 5.0 && m.m23 == 8.0 &&
/// m.m31 == 3.0 && m.m32 == 6.0 && m.m33 == 9.0);
/// ```
#[inline]
pub fn from_columns<SB>(columns: &[Vector<T, R, SB>]) -> Self
where
SB: RawStorage<T, R>,
{
assert!(!columns.is_empty(), "At least one column must be given.");
let ncols = C::try_to_usize().unwrap_or(columns.len());
let nrows = columns[0].len();
assert!(
columns.len() == ncols,
"Invalid number of columns provided to build this matrix."
);
if R::try_to_usize().is_none() {
assert!(
columns.iter().all(|r| r.len() == nrows),
"The columns provided must all have the same dimension."
);
}
// TODO: optimize that.
Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |i, j| {
columns[j][i].clone()
})
}
/// Creates a matrix filled with random values.
#[inline]
#[cfg(feature = "rand")]
pub fn new_random_generic(nrows: R, ncols: C) -> Self
where
Standard: Distribution<T>,
{
let mut rng = rand::thread_rng();
Self::from_fn_generic(nrows, ncols, |_, _| rng.gen())
}
/// Creates a matrix filled with random values from the given distribution.
#[inline]
#[cfg(feature = "rand-no-std")]
pub fn from_distribution_generic<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>(
nrows: R,
ncols: C,
distribution: &Distr,
rng: &mut G,
) -> Self {
Self::from_fn_generic(nrows, ncols, |_, _| distribution.sample(rng))
}
/// Creates a matrix backed by a given `Vec`.
///
/// The output matrix is filled column-by-column.
///
/// # Example
/// ```
/// # use nalgebra::{Dyn, DMatrix, Matrix, Const};
///
/// let vec = vec![0, 1, 2, 3, 4, 5];
/// let vec_ptr = vec.as_ptr();
///
/// let matrix = Matrix::from_vec_generic(Dyn(vec.len()), Const::<1>, vec);
/// let matrix_storage_ptr = matrix.data.as_vec().as_ptr();
///
/// // `matrix` is backed by exactly the same `Vec` as it was constructed from.
/// assert_eq!(matrix_storage_ptr, vec_ptr);
/// ```
#[inline]
#[cfg(any(feature = "std", feature = "alloc"))]
pub fn from_vec_generic(nrows: R, ncols: C, data: Vec<T>) -> Self {
Self::from_iterator_generic(nrows, ncols, data)
}
}
impl<T, D: Dim> OMatrix<T, D, D>
where
T: Scalar,
DefaultAllocator: Allocator<D, D>,
{
/// Creates a square matrix with its diagonal set to `diag` and all other entries set to 0.
///
/// # Example
/// ```
/// # use nalgebra::{Vector3, DVector, Matrix3, DMatrix};
/// # use std::iter;
///
/// let m = Matrix3::from_diagonal(&Vector3::new(1.0, 2.0, 3.0));
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_diagonal(&DVector::from_row_slice(&[1.0, 2.0, 3.0]));
///
/// assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
/// m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
/// m.m31 == 0.0 && m.m32 == 0.0 && m.m33 == 3.0);
/// assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
/// dm[(1, 0)] == 0.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 0.0 &&
/// dm[(2, 0)] == 0.0 && dm[(2, 1)] == 0.0 && dm[(2, 2)] == 3.0);
/// ```
#[inline]
pub fn from_diagonal<SB: RawStorage<T, D>>(diag: &Vector<T, D, SB>) -> Self
where
T: Zero,
{
let (dim, _) = diag.shape_generic();
let mut res = Self::zeros_generic(dim, dim);
for i in 0..diag.len() {
unsafe {
*res.get_unchecked_mut((i, i)) = diag.vget_unchecked(i).clone();
}
}
res
}
}
/*
*
* Generate constructors with varying number of arguments, depending on the object type.
*
*/
macro_rules! impl_constructors(
($($Dims: ty),*; $(=> $DimIdent: ident: $DimBound: ident),*; $($gargs: expr),*; $($args: ident),*) => {
/// Creates a matrix or vector with all its elements set to `elem`.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
///
/// let v = Vector3::from_element(2.0);
/// // The additional argument represents the vector dimension.
/// let dv = DVector::from_element(3, 2.0);
/// let m = Matrix2x3::from_element(2.0);
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_element(2, 3, 2.0);
///
/// assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
/// assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
/// assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
/// m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
/// assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
/// dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);
/// ```
#[inline]
pub fn from_element($($args: usize,)* elem: T) -> Self {
Self::from_element_generic($($gargs, )* elem)
}
/// Creates a matrix or vector with all its elements set to `elem`.
///
/// Same as `.from_element`.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
///
/// let v = Vector3::repeat(2.0);
/// // The additional argument represents the vector dimension.
/// let dv = DVector::repeat(3, 2.0);
/// let m = Matrix2x3::repeat(2.0);
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::repeat(2, 3, 2.0);
///
/// assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
/// assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
/// assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
/// m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
/// assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
/// dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);
/// ```
#[inline]
pub fn repeat($($args: usize,)* elem: T) -> Self {
Self::repeat_generic($($gargs, )* elem)
}
/// Creates a matrix or vector with all its elements set to `0`.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
///
/// let v = Vector3::<f32>::zeros();
/// // The argument represents the vector dimension.
/// let dv = DVector::<f32>::zeros(3);
/// let m = Matrix2x3::<f32>::zeros();
/// // The two arguments represent the matrix dimensions.
/// let dm = DMatrix::<f32>::zeros(2, 3);
///
/// assert!(v.x == 0.0 && v.y == 0.0 && v.z == 0.0);
/// assert!(dv[0] == 0.0 && dv[1] == 0.0 && dv[2] == 0.0);
/// assert!(m.m11 == 0.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
/// m.m21 == 0.0 && m.m22 == 0.0 && m.m23 == 0.0);
/// assert!(dm[(0, 0)] == 0.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
/// dm[(1, 0)] == 0.0 && dm[(1, 1)] == 0.0 && dm[(1, 2)] == 0.0);
/// ```
#[inline]
pub fn zeros($($args: usize),*) -> Self
where T: Zero {
Self::zeros_generic($($gargs),*)
}
/// Creates a matrix or vector with all its elements filled by an iterator.
///
/// The output matrix is filled column-by-column.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
/// # use std::iter;
///
/// let v = Vector3::from_iterator((0..3).into_iter());
/// // The additional argument represents the vector dimension.
/// let dv = DVector::from_iterator(3, (0..3).into_iter());
/// let m = Matrix2x3::from_iterator((0..6).into_iter());
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_iterator(2, 3, (0..6).into_iter());
///
/// assert!(v.x == 0 && v.y == 1 && v.z == 2);
/// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
/// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
/// m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
/// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
/// dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
/// ```
#[inline]
pub fn from_iterator<I>($($args: usize,)* iter: I) -> Self
where I: IntoIterator<Item = T> {
Self::from_iterator_generic($($gargs, )* iter)
}
/// Creates a matrix or vector with all its elements filled by a row-major iterator.
///
/// The output matrix is filled row-by-row.
///
/// ## Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
/// # use std::iter;
///
/// let v = Vector3::from_row_iterator((0..3).into_iter());
/// // The additional argument represents the vector dimension.
/// let dv = DVector::from_row_iterator(3, (0..3).into_iter());
/// let m = Matrix2x3::from_row_iterator((0..6).into_iter());
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_row_iterator(2, 3, (0..6).into_iter());
///
/// // For Vectors from_row_iterator is identical to from_iterator
/// assert!(v.x == 0 && v.y == 1 && v.z == 2);
/// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
/// assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
/// m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
/// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
/// dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);
/// ```
#[inline]
pub fn from_row_iterator<I>($($args: usize,)* iter: I) -> Self
where I: IntoIterator<Item = T> {
Self::from_row_iterator_generic($($gargs, )* iter)
}
/// Creates a matrix or vector filled with the results of a function applied to each of its
/// component coordinates.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
/// # use std::iter;
///
/// let v = Vector3::from_fn(|i, _| i);
/// // The additional argument represents the vector dimension.
/// let dv = DVector::from_fn(3, |i, _| i);
/// let m = Matrix2x3::from_fn(|i, j| i * 3 + j);
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_fn(2, 3, |i, j| i * 3 + j);
///
/// assert!(v.x == 0 && v.y == 1 && v.z == 2);
/// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
/// assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
/// m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
/// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
/// dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);
/// ```
#[inline]
pub fn from_fn<F>($($args: usize,)* f: F) -> Self
where F: FnMut(usize, usize) -> T {
Self::from_fn_generic($($gargs, )* f)
}
/// Creates an identity matrix. If the matrix is not square, the largest square
/// submatrix (starting at the first row and column) is set to the identity while all
/// other entries are set to zero.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, DMatrix};
/// # use std::iter;
///
/// let m = Matrix2x3::<f32>::identity();
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::<f32>::identity(2, 3);
///
/// assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
/// m.m21 == 0.0 && m.m22 == 1.0 && m.m23 == 0.0);
/// assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
/// dm[(1, 0)] == 0.0 && dm[(1, 1)] == 1.0 && dm[(1, 2)] == 0.0);
/// ```
#[inline]
pub fn identity($($args: usize,)*) -> Self
where T: Zero + One {
Self::identity_generic($($gargs),* )
}
/// Creates a matrix filled with its diagonal filled with `elt` and all other
/// components set to zero.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, DMatrix};
/// # use std::iter;
///
/// let m = Matrix2x3::from_diagonal_element(5.0);
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_diagonal_element(2, 3, 5.0);
///
/// assert!(m.m11 == 5.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
/// m.m21 == 0.0 && m.m22 == 5.0 && m.m23 == 0.0);
/// assert!(dm[(0, 0)] == 5.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
/// dm[(1, 0)] == 0.0 && dm[(1, 1)] == 5.0 && dm[(1, 2)] == 0.0);
/// ```
#[inline]
pub fn from_diagonal_element($($args: usize,)* elt: T) -> Self
where T: Zero + One {
Self::from_diagonal_element_generic($($gargs, )* elt)
}
/// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal
/// elements are filled with the content of `elts`. Others are set to 0.
///
/// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix3, DMatrix};
/// # use std::iter;
///
/// let m = Matrix3::from_partial_diagonal(&[1.0, 2.0]);
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_partial_diagonal(3, 3, &[1.0, 2.0]);
///
/// assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
/// m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
/// m.m31 == 0.0 && m.m32 == 0.0 && m.m33 == 0.0);
/// assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
/// dm[(1, 0)] == 0.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 0.0 &&
/// dm[(2, 0)] == 0.0 && dm[(2, 1)] == 0.0 && dm[(2, 2)] == 0.0);
/// ```
#[inline]
pub fn from_partial_diagonal($($args: usize,)* elts: &[T]) -> Self
where T: Zero {
Self::from_partial_diagonal_generic($($gargs, )* elts)
}
/// Creates a matrix or vector filled with random values from the given distribution.
#[inline]
#[cfg(feature = "rand-no-std")]
pub fn from_distribution<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>(
$($args: usize,)*
distribution: &Distr,
rng: &mut G,
) -> Self {
Self::from_distribution_generic($($gargs, )* distribution, rng)
}
/// Creates a matrix filled with random values.
#[inline]
#[cfg(feature = "rand")]
pub fn new_random($($args: usize),*) -> Self
where Standard: Distribution<T> {
Self::new_random_generic($($gargs),*)
}
}
);
/// # Constructors of statically-sized vectors or statically-sized matrices
impl<T: Scalar, R: DimName, C: DimName> OMatrix<T, R, C>
where
DefaultAllocator: Allocator<R, C>,
{
// TODO: this is not very pretty. We could find a better call syntax.
impl_constructors!(R, C; // Arguments for Matrix<T, ..., S>
=> R: DimName, => C: DimName; // Type parameters for impl<T, ..., S>
R::name(), C::name(); // Arguments for `_generic` constructors.
); // Arguments for non-generic constructors.
}
/// # Constructors of matrices with a dynamic number of columns
impl<T: Scalar, R: DimName> OMatrix<T, R, Dyn>
where
DefaultAllocator: Allocator<R, Dyn>,
{
impl_constructors!(R, Dyn;
=> R: DimName;
R::name(), Dyn(ncols);
ncols);
}
/// # Constructors of dynamic vectors and matrices with a dynamic number of rows
impl<T: Scalar, C: DimName> OMatrix<T, Dyn, C>
where
DefaultAllocator: Allocator<Dyn, C>,
{
impl_constructors!(Dyn, C;
=> C: DimName;
Dyn(nrows), C::name();
nrows);
}
/// # Constructors of fully dynamic matrices
#[cfg(any(feature = "std", feature = "alloc"))]
impl<T: Scalar> OMatrix<T, Dyn, Dyn>
where
DefaultAllocator: Allocator<Dyn, Dyn>,
{
impl_constructors!(Dyn, Dyn;
;
Dyn(nrows), Dyn(ncols);
nrows, ncols);
}
/*
*
* Constructors that don't necessarily require all dimensions
* to be specified when one dimension is already known.
*
*/
macro_rules! impl_constructors_from_data(
($data: ident; $($Dims: ty),*; $(=> $DimIdent: ident: $DimBound: ident),*; $($gargs: expr),*; $($args: ident),*) => {
impl<T: Scalar, $($DimIdent: $DimBound, )*> OMatrix<T $(, $Dims)*>
where DefaultAllocator: Allocator<$($Dims),*> {
/// Creates a matrix with its elements filled with the components provided by a slice
/// in row-major order.
///
/// The order of elements in the slice must follow the usual mathematic writing, i.e.,
/// row-by-row.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
/// # use std::iter;
///
/// let v = Vector3::from_row_slice(&[0, 1, 2]);
/// // The additional argument represents the vector dimension.
/// let dv = DVector::from_row_slice(&[0, 1, 2]);
/// let m = Matrix2x3::from_row_slice(&[0, 1, 2, 3, 4, 5]);
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_row_slice(2, 3, &[0, 1, 2, 3, 4, 5]);
///
/// assert!(v.x == 0 && v.y == 1 && v.z == 2);
/// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
/// assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
/// m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
/// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
/// dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);
/// ```
#[inline]
pub fn from_row_slice($($args: usize,)* $data: &[T]) -> Self {
Self::from_row_slice_generic($($gargs, )* $data)
}
/// Creates a matrix with its elements filled with the components provided by a slice
/// in column-major order.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector3, DVector, DMatrix};
/// # use std::iter;
///
/// let v = Vector3::from_column_slice(&[0, 1, 2]);
/// // The additional argument represents the vector dimension.
/// let dv = DVector::from_column_slice(&[0, 1, 2]);
/// let m = Matrix2x3::from_column_slice(&[0, 1, 2, 3, 4, 5]);
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_column_slice(2, 3, &[0, 1, 2, 3, 4, 5]);
///
/// assert!(v.x == 0 && v.y == 1 && v.z == 2);
/// assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
/// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
/// m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
/// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
/// dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
/// ```
#[inline]
pub fn from_column_slice($($args: usize,)* $data: &[T]) -> Self {
Self::from_column_slice_generic($($gargs, )* $data)
}
/// Creates a matrix backed by a given `Vec`.
///
/// The output matrix is filled column-by-column.
///
/// # Example
/// ```
/// # use nalgebra::{DMatrix, Matrix2x3};
///
/// let m = Matrix2x3::from_vec(vec![0, 1, 2, 3, 4, 5]);
///
/// assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
/// m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
///
///
/// // The two additional arguments represent the matrix dimensions.
/// let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 5]);
///
/// assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
/// dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);
/// ```
#[inline]
#[cfg(any(feature = "std", feature = "alloc"))]
pub fn from_vec($($args: usize,)* $data: Vec<T>) -> Self {
Self::from_vec_generic($($gargs, )* $data)
}
}
}
);
// TODO: this is not very pretty. We could find a better call syntax.
impl_constructors_from_data!(data; R, C; // Arguments for Matrix<T, ..., S>
=> R: DimName, => C: DimName; // Type parameters for impl<T, ..., S>
R::name(), C::name(); // Arguments for `_generic` constructors.
); // Arguments for non-generic constructors.
impl_constructors_from_data!(data; R, Dyn;
=> R: DimName;
R::name(), Dyn(data.len() / R::dim());
);
impl_constructors_from_data!(data; Dyn, C;
=> C: DimName;
Dyn(data.len() / C::dim()), C::name();
);
#[cfg(any(feature = "std", feature = "alloc"))]
impl_constructors_from_data!(data; Dyn, Dyn;
;
Dyn(nrows), Dyn(ncols);
nrows, ncols);
/*
*
* Zero, One, Rand traits.
*
*/
impl<T, R: DimName, C: DimName> Zero for OMatrix<T, R, C>
where
T: Scalar + Zero + ClosedAddAssign,
DefaultAllocator: Allocator<R, C>,
{
#[inline]
fn zero() -> Self {
Self::from_element(T::zero())
}
#[inline]
fn is_zero(&self) -> bool {
self.iter().all(|e| e.is_zero())
}
}
impl<T, D: DimName> One for OMatrix<T, D, D>
where
T: Scalar + Zero + One + ClosedMulAssign + ClosedAddAssign,
DefaultAllocator: Allocator<D, D>,
{
#[inline]
fn one() -> Self {
Self::identity()
}
}
impl<T, R: DimName, C: DimName> Bounded for OMatrix<T, R, C>
where
T: Scalar + Bounded,
DefaultAllocator: Allocator<R, C>,
{
#[inline]
fn max_value() -> Self {
Self::from_element(T::max_value())
}
#[inline]
fn min_value() -> Self {
Self::from_element(T::min_value())
}
}
#[cfg(feature = "rand-no-std")]
impl<T: Scalar, R: Dim, C: Dim> Distribution<OMatrix<T, R, C>> for Standard
where
DefaultAllocator: Allocator<R, C>,
Standard: Distribution<T>,
{
#[inline]
fn sample<G: Rng + ?Sized>(&self, rng: &mut G) -> OMatrix<T, R, C> {
let nrows = R::try_to_usize().unwrap_or_else(|| rng.gen_range(0..10));
let ncols = C::try_to_usize().unwrap_or_else(|| rng.gen_range(0..10));
OMatrix::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |_, _| rng.gen())
}
}
#[cfg(feature = "arbitrary")]
impl<T, R, C> Arbitrary for OMatrix<T, R, C>
where
R: Dim,
C: Dim,
T: Scalar + Arbitrary + Send,
DefaultAllocator: Allocator<R, C>,
Owned<T, R, C>: Clone + Send,
{
#[inline]
fn arbitrary(g: &mut Gen) -> Self {
let nrows = R::try_to_usize().unwrap_or(usize::arbitrary(g) % 10);
let ncols = C::try_to_usize().unwrap_or(usize::arbitrary(g) % 10);
Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |_, _| {
T::arbitrary(g)
})
}
}
// TODO(specialization): faster impls possible for D≤4 (see rand_distr::{UnitCircle, UnitSphere})
#[cfg(feature = "rand")]
impl<T: crate::RealField, D: DimName> Distribution<Unit<OVector<T, D>>> for Standard
where
DefaultAllocator: Allocator<D>,
rand_distr::StandardNormal: Distribution<T>,
{
/// Generate a uniformly distributed random unit vector.
#[inline]
fn sample<G: Rng + ?Sized>(&self, rng: &mut G) -> Unit<OVector<T, D>> {
Unit::new_normalize(OVector::from_distribution_generic(
D::name(),
Const::<1>,
&rand_distr::StandardNormal,
rng,
))
}
}
/*
*
* Constructors for small matrices and vectors.
*
*/
macro_rules! transpose_array(
[$($a: ident),*;] => {
[$([$a]),*]
};
[$($a: ident),*; $($b: ident),*;] => {
[$([$a, $b]),*]
};
[$($a: ident),*; $($b: ident),*; $($c: ident),*;] => {
[$([$a, $b, $c]),*]
};
[$($a: ident),*; $($b: ident),*; $($c: ident),*; $($d: ident),*;] => {
[$([$a, $b, $c, $d]),*]
};
[$($a: ident),*; $($b: ident),*; $($c: ident),*; $($d: ident),*; $($e: ident),*;] => {
[$([$a, $b, $c, $d, $e]),*]
};
[$($a: ident),*; $($b: ident),*; $($c: ident),*; $($d: ident),*; $($e: ident),*; $($f: ident),*;] => {
[$([$a, $b, $c, $d, $e, $f]),*]
};
);
macro_rules! componentwise_constructors_impl(
($($R: expr, $C: expr, [$($($args: ident),*);*] $(;)*)*) => {$(
impl<T> Matrix<T, Const<$R>, Const<$C>, ArrayStorage<T, $R, $C>> {
/// Initializes this matrix from its components.
#[inline]
#[allow(clippy::too_many_arguments)]
pub const fn new($($($args: T),*),*) -> Self {
unsafe {
Self::from_data_statically_unchecked(
ArrayStorage(
transpose_array![
$(
$($args),*
;)*
]
)
)
}
}
}
)*}
);
componentwise_constructors_impl!(
/*
* Square matrices 1 .. 6.
*/
2, 2, [m11, m12;
m21, m22];
3, 3, [m11, m12, m13;
m21, m22, m23;
m31, m32, m33];
4, 4, [m11, m12, m13, m14;
m21, m22, m23, m24;
m31, m32, m33, m34;
m41, m42, m43, m44];
5, 5, [m11, m12, m13, m14, m15;
m21, m22, m23, m24, m25;
m31, m32, m33, m34, m35;
m41, m42, m43, m44, m45;
m51, m52, m53, m54, m55];
6, 6, [m11, m12, m13, m14, m15, m16;
m21, m22, m23, m24, m25, m26;
m31, m32, m33, m34, m35, m36;
m41, m42, m43, m44, m45, m46;
m51, m52, m53, m54, m55, m56;
m61, m62, m63, m64, m65, m66];
/*
* Rectangular matrices with 2 rows.
*/
2, 3, [m11, m12, m13;
m21, m22, m23];
2, 4, [m11, m12, m13, m14;
m21, m22, m23, m24];
2, 5, [m11, m12, m13, m14, m15;
m21, m22, m23, m24, m25];
2, 6, [m11, m12, m13, m14, m15, m16;
m21, m22, m23, m24, m25, m26];
/*
* Rectangular matrices with 3 rows.
*/
3, 2, [m11, m12;
m21, m22;
m31, m32];
3, 4, [m11, m12, m13, m14;
m21, m22, m23, m24;
m31, m32, m33, m34];
3, 5, [m11, m12, m13, m14, m15;
m21, m22, m23, m24, m25;
m31, m32, m33, m34, m35];
3, 6, [m11, m12, m13, m14, m15, m16;
m21, m22, m23, m24, m25, m26;
m31, m32, m33, m34, m35, m36];
/*
* Rectangular matrices with 4 rows.
*/
4, 2, [m11, m12;
m21, m22;
m31, m32;
m41, m42];
4, 3, [m11, m12, m13;
m21, m22, m23;
m31, m32, m33;
m41, m42, m43];
4, 5, [m11, m12, m13, m14, m15;
m21, m22, m23, m24, m25;
m31, m32, m33, m34, m35;
m41, m42, m43, m44, m45];
4, 6, [m11, m12, m13, m14, m15, m16;
m21, m22, m23, m24, m25, m26;
m31, m32, m33, m34, m35, m36;
m41, m42, m43, m44, m45, m46];
/*
* Rectangular matrices with 5 rows.
*/
5, 2, [m11, m12;
m21, m22;
m31, m32;
m41, m42;
m51, m52];
5, 3, [m11, m12, m13;
m21, m22, m23;
m31, m32, m33;
m41, m42, m43;
m51, m52, m53];
5, 4, [m11, m12, m13, m14;
m21, m22, m23, m24;
m31, m32, m33, m34;
m41, m42, m43, m44;
m51, m52, m53, m54];
5, 6, [m11, m12, m13, m14, m15, m16;
m21, m22, m23, m24, m25, m26;
m31, m32, m33, m34, m35, m36;
m41, m42, m43, m44, m45, m46;
m51, m52, m53, m54, m55, m56];
/*
* Rectangular matrices with 6 rows.
*/
6, 2, [m11, m12;
m21, m22;
m31, m32;
m41, m42;
m51, m52;
m61, m62];
6, 3, [m11, m12, m13;
m21, m22, m23;
m31, m32, m33;
m41, m42, m43;
m51, m52, m53;
m61, m62, m63];
6, 4, [m11, m12, m13, m14;
m21, m22, m23, m24;
m31, m32, m33, m34;
m41, m42, m43, m44;
m51, m52, m53, m54;
m61, m62, m63, m64];
6, 5, [m11, m12, m13, m14, m15;
m21, m22, m23, m24, m25;
m31, m32, m33, m34, m35;
m41, m42, m43, m44, m45;
m51, m52, m53, m54, m55;
m61, m62, m63, m64, m65];
/*
* Row vectors 1 .. 6.
*/
1, 1, [x];
1, 2, [x, y];
1, 3, [x, y, z];
1, 4, [x, y, z, w];
1, 5, [x, y, z, w, a];
1, 6, [x, y, z, w, a, b];
/*
* Column vectors 1 .. 6.
*/
2, 1, [x; y];
3, 1, [x; y; z];
4, 1, [x; y; z; w];
5, 1, [x; y; z; w; a];
6, 1, [x; y; z; w; a; b];
);
/*
*
* Axis constructors.
*
*/
impl<T, R: DimName> OVector<T, R>
where
R: ToTypenum,
T: Scalar + Zero + One,
DefaultAllocator: Allocator<R>,
{
/// The column vector with `val` as its i-th component.
#[inline]
pub fn ith(i: usize, val: T) -> Self {
let mut res = Self::zeros();
res[i] = val;
res
}
/// The column unit vector with `T::one()` as its i-th component.
#[inline]
pub fn ith_axis(i: usize) -> Unit<Self> {
Unit::new_unchecked(Self::ith(i, T::one()))
}
/// The column vector with a 1 as its first component, and zero elsewhere.
#[inline]
pub fn x() -> Self
where
R::Typenum: Cmp<typenum::U0, Output = Greater>,
{
let mut res = Self::zeros();
unsafe {
*res.vget_unchecked_mut(0) = T::one();
}
res
}
/// The column vector with a 1 as its second component, and zero elsewhere.
#[inline]
pub fn y() -> Self
where
R::Typenum: Cmp<typenum::U1, Output = Greater>,
{
let mut res = Self::zeros();
unsafe {
*res.vget_unchecked_mut(1) = T::one();
}
res
}
/// The column vector with a 1 as its third component, and zero elsewhere.
#[inline]
pub fn z() -> Self
where
R::Typenum: Cmp<typenum::U2, Output = Greater>,
{
let mut res = Self::zeros();
unsafe {
*res.vget_unchecked_mut(2) = T::one();
}
res
}
/// The column vector with a 1 as its fourth component, and zero elsewhere.
#[inline]
pub fn w() -> Self
where
R::Typenum: Cmp<typenum::U3, Output = Greater>,
{
let mut res = Self::zeros();
unsafe {
*res.vget_unchecked_mut(3) = T::one();
}
res
}
/// The column vector with a 1 as its fifth component, and zero elsewhere.
#[inline]
pub fn a() -> Self
where
R::Typenum: Cmp<typenum::U4, Output = Greater>,
{
let mut res = Self::zeros();
unsafe {
*res.vget_unchecked_mut(4) = T::one();
}
res
}
/// The column vector with a 1 as its sixth component, and zero elsewhere.
#[inline]
pub fn b() -> Self
where
R::Typenum: Cmp<typenum::U5, Output = Greater>,
{
let mut res = Self::zeros();
unsafe {
*res.vget_unchecked_mut(5) = T::one();
}
res
}
/// The unit column vector with a 1 as its first component, and zero elsewhere.
#[inline]
pub fn x_axis() -> Unit<Self>
where
R::Typenum: Cmp<typenum::U0, Output = Greater>,
{
Unit::new_unchecked(Self::x())
}
/// The unit column vector with a 1 as its second component, and zero elsewhere.
#[inline]
pub fn y_axis() -> Unit<Self>
where
R::Typenum: Cmp<typenum::U1, Output = Greater>,
{
Unit::new_unchecked(Self::y())
}
/// The unit column vector with a 1 as its third component, and zero elsewhere.
#[inline]
pub fn z_axis() -> Unit<Self>
where
R::Typenum: Cmp<typenum::U2, Output = Greater>,
{
Unit::new_unchecked(Self::z())
}
/// The unit column vector with a 1 as its fourth component, and zero elsewhere.
#[inline]
pub fn w_axis() -> Unit<Self>
where
R::Typenum: Cmp<typenum::U3, Output = Greater>,
{
Unit::new_unchecked(Self::w())
}
/// The unit column vector with a 1 as its fifth component, and zero elsewhere.
#[inline]
pub fn a_axis() -> Unit<Self>
where
R::Typenum: Cmp<typenum::U4, Output = Greater>,
{
Unit::new_unchecked(Self::a())
}
/// The unit column vector with a 1 as its sixth component, and zero elsewhere.
#[inline]
pub fn b_axis() -> Unit<Self>
where
R::Typenum: Cmp<typenum::U5, Output = Greater>,
{
Unit::new_unchecked(Self::b())
}
}