forked from M-Labs/nalgebra
841 lines
27 KiB
Rust
841 lines
27 KiB
Rust
#[cfg(feature = "arbitrary")]
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use base::storage::Owned;
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#[cfg(feature = "arbitrary")]
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use quickcheck::{Arbitrary, Gen};
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use num::{Bounded, One, Zero};
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use rand::distributions::{Distribution, Standard};
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use rand::Rng;
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#[cfg(feature = "std")]
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use rand::{self, distributions::StandardNormal};
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use std::iter;
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use typenum::{self, Cmp, Greater};
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#[cfg(feature = "std")]
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use alga::general::Real;
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use alga::general::{ClosedAdd, ClosedMul};
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use base::allocator::Allocator;
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use base::dimension::{Dim, DimName, Dynamic, U1, U2, U3, U4, U5, U6};
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use base::storage::Storage;
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use base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, Scalar, Unit, Vector, VectorN};
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/*
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*
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* Generic constructors.
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*
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*/
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impl<N: Scalar, R: Dim, C: Dim> MatrixMN<N, R, C>
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where
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DefaultAllocator: Allocator<N, R, C>,
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{
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/// Creates a new uninitialized matrix. If the matrix has a compile-time dimension, this panics
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/// if `nrows != R::to_usize()` or `ncols != C::to_usize()`.
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#[inline]
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pub unsafe fn new_uninitialized_generic(nrows: R, ncols: C) -> Self {
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Self::from_data(DefaultAllocator::allocate_uninitialized(nrows, ncols))
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}
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/// Creates a matrix with all its elements set to `elem`.
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#[inline]
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pub fn from_element_generic(nrows: R, ncols: C, elem: N) -> Self {
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let len = nrows.value() * ncols.value();
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Self::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
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}
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/// Creates a matrix with all its elements set to `elem`.
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///
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/// Same as `from_element_generic`.
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#[inline]
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pub fn repeat_generic(nrows: R, ncols: C, elem: N) -> Self {
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let len = nrows.value() * ncols.value();
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Self::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
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}
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/// Creates a matrix with all its elements set to 0.
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#[inline]
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pub fn zeros_generic(nrows: R, ncols: C) -> Self
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where
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N: Zero,
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{
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Self::from_element_generic(nrows, ncols, N::zero())
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}
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/// Creates a matrix with all its elements filled by an iterator.
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#[inline]
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pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self
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where
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I: IntoIterator<Item = N>,
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{
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Self::from_data(DefaultAllocator::allocate_from_iterator(nrows, ncols, iter))
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}
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/// Creates a matrix with its elements filled with the components provided by a slice in
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/// row-major order.
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///
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/// The order of elements in the slice must follow the usual mathematic writing, i.e.,
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/// row-by-row.
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#[inline]
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pub fn from_row_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Self {
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assert!(
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slice.len() == nrows.value() * ncols.value(),
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"Matrix init. error: the slice did not contain the right number of elements."
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);
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let mut res = unsafe { Self::new_uninitialized_generic(nrows, ncols) };
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let mut iter = slice.iter();
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for i in 0..nrows.value() {
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for j in 0..ncols.value() {
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unsafe { *res.get_unchecked_mut(i, j) = *iter.next().unwrap() }
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}
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}
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res
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}
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/// Creates a matrix with its elements filled with the components provided by a slice. The
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/// components must have the same layout as the matrix data storage (i.e. column-major).
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#[inline]
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pub fn from_column_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Self {
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Self::from_iterator_generic(nrows, ncols, slice.iter().cloned())
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}
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/// Creates a matrix filled with the results of a function applied to each of its component
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/// coordinates.
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#[inline]
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pub fn from_fn_generic<F>(nrows: R, ncols: C, mut f: F) -> Self
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where
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F: FnMut(usize, usize) -> N,
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{
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let mut res = unsafe { Self::new_uninitialized_generic(nrows, ncols) };
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for j in 0..ncols.value() {
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for i in 0..nrows.value() {
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unsafe { *res.get_unchecked_mut(i, j) = f(i, j) }
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}
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}
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res
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}
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/// Creates a new identity matrix.
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///
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/// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
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/// to the identity matrix. All other entries are set to zero.
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#[inline]
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pub fn identity_generic(nrows: R, ncols: C) -> Self
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where
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N: Zero + One,
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{
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Self::from_diagonal_element_generic(nrows, ncols, N::one())
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}
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/// Creates a new matrix with its diagonal filled with copies of `elt`.
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///
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/// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
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/// to the identity matrix. All other entries are set to zero.
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#[inline]
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pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: N) -> Self
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where
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N: Zero + One,
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{
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let mut res = Self::zeros_generic(nrows, ncols);
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for i in 0..::min(nrows.value(), ncols.value()) {
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unsafe { *res.get_unchecked_mut(i, i) = elt }
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}
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res
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}
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/// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal elements are
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/// filled with the content of `elts`. Others are set to 0.
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///
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/// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
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#[inline]
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pub fn from_partial_diagonal_generic(nrows: R, ncols: C, elts: &[N]) -> Self
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where
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N: Zero,
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{
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let mut res = Self::zeros_generic(nrows, ncols);
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assert!(
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elts.len() <= ::min(nrows.value(), ncols.value()),
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"Too many diagonal elements provided."
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);
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for (i, elt) in elts.iter().enumerate() {
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unsafe { *res.get_unchecked_mut(i, i) = *elt }
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}
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res
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}
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/// Builds a new matrix from its rows.
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///
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/// Panics if not enough rows are provided (for statically-sized matrices), or if all rows do
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/// not have the same dimensions.
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#[inline]
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pub fn from_rows<SB>(rows: &[Matrix<N, U1, C, SB>]) -> Self
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where
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SB: Storage<N, U1, C>,
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{
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assert!(rows.len() > 0, "At least one row must be given.");
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let nrows = R::try_to_usize().unwrap_or(rows.len());
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let ncols = rows[0].len();
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assert!(
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rows.len() == nrows,
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"Invalid number of rows provided to build this matrix."
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);
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if C::try_to_usize().is_none() {
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assert!(
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rows.iter().all(|r| r.len() == ncols),
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"The provided rows must all have the same dimension."
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);
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}
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// FIXME: optimize that.
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Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |i, j| {
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rows[i][(0, j)]
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})
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}
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/// Builds a new matrix from its columns.
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///
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/// Panics if not enough columns are provided (for statically-sized matrices), or if all
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/// columns do not have the same dimensions.
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#[inline]
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pub fn from_columns<SB>(columns: &[Vector<N, R, SB>]) -> Self
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where
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SB: Storage<N, R>,
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{
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assert!(columns.len() > 0, "At least one column must be given.");
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let ncols = C::try_to_usize().unwrap_or(columns.len());
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let nrows = columns[0].len();
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assert!(
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columns.len() == ncols,
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"Invalid number of columns provided to build this matrix."
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);
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if R::try_to_usize().is_none() {
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assert!(
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columns.iter().all(|r| r.len() == nrows),
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"The columns provided must all have the same dimension."
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);
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}
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// FIXME: optimize that.
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Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |i, j| {
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columns[j][i]
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})
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}
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/// Creates a matrix filled with random values.
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#[inline]
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#[cfg(feature = "std")]
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pub fn new_random_generic(nrows: R, ncols: C) -> Self
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where
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Standard: Distribution<N>,
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{
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Self::from_fn_generic(nrows, ncols, |_, _| rand::random())
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}
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/// Creates a matrix filled with random values from the given distribution.
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#[inline]
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pub fn from_distribution_generic<Distr: Distribution<N> + ?Sized, G: Rng + ?Sized>(
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nrows: R,
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ncols: C,
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distribution: &mut Distr,
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rng: &mut G,
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) -> Self {
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Self::from_fn_generic(nrows, ncols, |_, _| distribution.sample(rng))
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}
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}
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impl<N, D: Dim> MatrixN<N, D>
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where
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N: Scalar,
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DefaultAllocator: Allocator<N, D, D>,
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{
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/// Creates a square matrix with its diagonal set to `diag` and all other entries set to 0.
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#[inline]
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pub fn from_diagonal<SB: Storage<N, D>>(diag: &Vector<N, D, SB>) -> Self
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where
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N: Zero,
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{
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let (dim, _) = diag.data.shape();
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let mut res = Self::zeros_generic(dim, dim);
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for i in 0..diag.len() {
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unsafe {
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*res.get_unchecked_mut(i, i) = *diag.vget_unchecked(i);
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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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/*
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*
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* Generate constructors with varying number of arguments, depending on the object type.
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*
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*/
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macro_rules! impl_constructors(
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($($Dims: ty),*; $(=> $DimIdent: ident: $DimBound: ident),*; $($gargs: expr),*; $($args: ident),*) => {
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impl<N: Scalar, $($DimIdent: $DimBound, )*> MatrixMN<N $(, $Dims)*>
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where DefaultAllocator: Allocator<N $(, $Dims)*> {
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/// Creates a new uninitialized matrix.
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#[inline]
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pub unsafe fn new_uninitialized($($args: usize),*) -> Self {
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Self::new_uninitialized_generic($($gargs),*)
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}
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/// Creates a matrix with all its elements set to `elem`.
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#[inline]
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pub fn from_element($($args: usize,)* elem: N) -> Self {
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Self::from_element_generic($($gargs, )* elem)
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}
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/// Creates a matrix with all its elements set to `elem`.
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///
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/// Same as `.from_element`.
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#[inline]
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pub fn repeat($($args: usize,)* elem: N) -> Self {
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Self::repeat_generic($($gargs, )* elem)
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}
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/// Creates a matrix with all its elements set to `0`.
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#[inline]
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pub fn zeros($($args: usize),*) -> Self
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where N: Zero {
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Self::zeros_generic($($gargs),*)
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}
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/// Creates a matrix with all its elements filled by an iterator.
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#[inline]
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pub fn from_iterator<I>($($args: usize,)* iter: I) -> Self
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where I: IntoIterator<Item = N> {
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Self::from_iterator_generic($($gargs, )* iter)
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}
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/// Creates a matrix with its elements filled with the components provided by a slice
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/// in row-major order.
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///
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/// The order of elements in the slice must follow the usual mathematic writing, i.e.,
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/// row-by-row.
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#[inline]
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pub fn from_row_slice($($args: usize,)* slice: &[N]) -> Self {
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Self::from_row_slice_generic($($gargs, )* slice)
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}
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/// Creates a matrix with its elements filled with the components provided by a slice
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/// in column-major order.
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#[inline]
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pub fn from_column_slice($($args: usize,)* slice: &[N]) -> Self {
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Self::from_column_slice_generic($($gargs, )* slice)
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}
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/// Creates a matrix filled with the results of a function applied to each of its
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/// component coordinates.
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// FIXME: don't take a dimension of the matrix is statically sized.
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#[inline]
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pub fn from_fn<F>($($args: usize,)* f: F) -> Self
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where F: FnMut(usize, usize) -> N {
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Self::from_fn_generic($($gargs, )* f)
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}
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/// Creates an identity matrix. If the matrix is not square, the largest square
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/// submatrix (starting at the first row and column) is set to the identity while all
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/// other entries are set to zero.
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#[inline]
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pub fn identity($($args: usize,)*) -> Self
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where N: Zero + One {
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Self::identity_generic($($gargs),* )
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}
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/// Creates a matrix filled with its diagonal filled with `elt` and all other
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/// components set to zero.
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#[inline]
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pub fn from_diagonal_element($($args: usize,)* elt: N) -> Self
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where N: Zero + One {
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Self::from_diagonal_element_generic($($gargs, )* elt)
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}
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/// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal
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/// elements are filled with the content of `elts`. Others are set to 0.
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///
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/// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
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#[inline]
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pub fn from_partial_diagonal($($args: usize,)* elts: &[N]) -> Self
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where N: Zero {
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Self::from_partial_diagonal_generic($($gargs, )* elts)
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}
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/// Creates a matrix filled with random values from the given distribution.
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#[inline]
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pub fn from_distribution<Distr: Distribution<N> + ?Sized, G: Rng + ?Sized>(
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$($args: usize,)*
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distribution: &mut Distr,
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rng: &mut G,
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) -> Self {
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Self::from_distribution_generic($($gargs, )* distribution, rng)
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}
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}
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impl<N: Scalar, $($DimIdent: $DimBound, )*> MatrixMN<N $(, $Dims)*>
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where
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DefaultAllocator: Allocator<N $(, $Dims)*>,
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Standard: Distribution<N> {
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/// Creates a matrix filled with random values.
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#[inline]
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#[cfg(feature = "std")]
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pub fn new_random($($args: usize),*) -> Self {
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Self::new_random_generic($($gargs),*)
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}
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}
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}
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);
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// FIXME: this is not very pretty. We could find a better call syntax.
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impl_constructors!(R, C; // Arguments for Matrix<N, ..., S>
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=> R: DimName, => C: DimName; // Type parameters for impl<N, ..., S>
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R::name(), C::name(); // Arguments for `_generic` constructors.
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); // Arguments for non-generic constructors.
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impl_constructors!(R, Dynamic;
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=> R: DimName;
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R::name(), Dynamic::new(ncols);
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ncols);
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impl_constructors!(Dynamic, C;
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=> C: DimName;
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Dynamic::new(nrows), C::name();
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nrows);
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impl_constructors!(Dynamic, Dynamic;
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;
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Dynamic::new(nrows), Dynamic::new(ncols);
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nrows, ncols);
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/*
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*
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* Zero, One, Rand traits.
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*
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*/
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impl<N, R: DimName, C: DimName> Zero for MatrixMN<N, R, C>
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where
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N: Scalar + Zero + ClosedAdd,
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DefaultAllocator: Allocator<N, R, C>,
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{
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#[inline]
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fn zero() -> Self {
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Self::from_element(N::zero())
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}
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#[inline]
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fn is_zero(&self) -> bool {
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self.iter().all(|e| e.is_zero())
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}
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}
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impl<N, D: DimName> One for MatrixN<N, D>
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where
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N: Scalar + Zero + One + ClosedMul + ClosedAdd,
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DefaultAllocator: Allocator<N, D, D>,
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{
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#[inline]
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fn one() -> Self {
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Self::identity()
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}
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}
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impl<N, R: DimName, C: DimName> Bounded for MatrixMN<N, R, C>
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where
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N: Scalar + Bounded,
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DefaultAllocator: Allocator<N, R, C>,
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{
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#[inline]
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fn max_value() -> Self {
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Self::from_element(N::max_value())
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}
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#[inline]
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fn min_value() -> Self {
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Self::from_element(N::min_value())
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}
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}
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impl<N: Scalar, R: Dim, C: Dim> Distribution<MatrixMN<N, R, C>> for Standard
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where
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DefaultAllocator: Allocator<N, R, C>,
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Standard: Distribution<N>,
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{
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#[inline]
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fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> MatrixMN<N, R, C> {
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let nrows = R::try_to_usize().unwrap_or(rng.gen_range(0, 10));
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let ncols = C::try_to_usize().unwrap_or(rng.gen_range(0, 10));
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MatrixMN::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |_, _| rng.gen())
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}
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}
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#[cfg(feature = "arbitrary")]
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impl<N, R, C> Arbitrary for MatrixMN<N, R, C>
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where
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R: Dim,
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C: Dim,
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N: Scalar + Arbitrary + Send,
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DefaultAllocator: Allocator<N, R, C>,
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Owned<N, R, C>: Clone + Send,
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{
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#[inline]
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fn arbitrary<G: Gen>(g: &mut G) -> Self {
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let nrows = R::try_to_usize().unwrap_or(g.gen_range(0, 10));
|
||
let ncols = C::try_to_usize().unwrap_or(g.gen_range(0, 10));
|
||
|
||
Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |_, _| {
|
||
N::arbitrary(g)
|
||
})
|
||
}
|
||
}
|
||
|
||
#[cfg(feature = "std")]
|
||
impl<N: Real, D: DimName> Distribution<Unit<VectorN<N, D>>> for Standard
|
||
where
|
||
DefaultAllocator: Allocator<N, D>,
|
||
StandardNormal: Distribution<N>,
|
||
{
|
||
/// Generate a uniformly distributed random unit vector.
|
||
#[inline]
|
||
fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Unit<VectorN<N, D>> {
|
||
Unit::new_normalize(VectorN::from_distribution_generic(
|
||
D::name(),
|
||
U1,
|
||
&mut StandardNormal,
|
||
rng,
|
||
))
|
||
}
|
||
}
|
||
|
||
/*
|
||
*
|
||
* Constructors for small matrices and vectors.
|
||
*
|
||
*/
|
||
macro_rules! componentwise_constructors_impl(
|
||
($($R: ty, $C: ty, $($args: ident:($irow: expr,$icol: expr)),*);* $(;)*) => {$(
|
||
impl<N> MatrixMN<N, $R, $C>
|
||
where N: Scalar,
|
||
DefaultAllocator: Allocator<N, $R, $C> {
|
||
/// Initializes this matrix from its components.
|
||
#[inline]
|
||
pub fn new($($args: N),*) -> Self {
|
||
unsafe {
|
||
let mut res = Self::new_uninitialized();
|
||
$( *res.get_unchecked_mut($irow, $icol) = $args; )*
|
||
|
||
res
|
||
}
|
||
}
|
||
}
|
||
)*}
|
||
);
|
||
|
||
componentwise_constructors_impl!(
|
||
/*
|
||
* Square matrices 1 .. 6.
|
||
*/
|
||
U2, U2, m11:(0,0), m12:(0,1),
|
||
m21:(1,0), m22:(1,1);
|
||
U3, U3, m11:(0,0), m12:(0,1), m13:(0,2),
|
||
m21:(1,0), m22:(1,1), m23:(1,2),
|
||
m31:(2,0), m32:(2,1), m33:(2,2);
|
||
U4, U4, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3);
|
||
U5, U5, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3), m35:(2,4),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3), m45:(3,4),
|
||
m51:(4,0), m52:(4,1), m53:(4,2), m54:(4,3), m55:(4,4);
|
||
U6, U6, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4), m16:(0,5),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4), m26:(1,5),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3), m35:(2,4), m36:(2,5),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3), m45:(3,4), m46:(3,5),
|
||
m51:(4,0), m52:(4,1), m53:(4,2), m54:(4,3), m55:(4,4), m56:(4,5),
|
||
m61:(5,0), m62:(5,1), m63:(5,2), m64:(5,3), m65:(5,4), m66:(5,5);
|
||
|
||
/*
|
||
* Rectangular matrices with 2 rows.
|
||
*/
|
||
U2, U3, m11:(0,0), m12:(0,1), m13:(0,2),
|
||
m21:(1,0), m22:(1,1), m23:(1,2);
|
||
U2, U4, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3);
|
||
U2, U5, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4);
|
||
U2, U6, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4), m16:(0,5),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4), m26:(1,5);
|
||
|
||
/*
|
||
* Rectangular matrices with 3 rows.
|
||
*/
|
||
U3, U2, m11:(0,0), m12:(0,1),
|
||
m21:(1,0), m22:(1,1),
|
||
m31:(2,0), m32:(2,1);
|
||
U3, U4, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3);
|
||
U3, U5, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3), m35:(2,4);
|
||
U3, U6, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4), m16:(0,5),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4), m26:(1,5),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3), m35:(2,4), m36:(2,5);
|
||
|
||
/*
|
||
* Rectangular matrices with 4 rows.
|
||
*/
|
||
U4, U2, m11:(0,0), m12:(0,1),
|
||
m21:(1,0), m22:(1,1),
|
||
m31:(2,0), m32:(2,1),
|
||
m41:(3,0), m42:(3,1);
|
||
U4, U3, m11:(0,0), m12:(0,1), m13:(0,2),
|
||
m21:(1,0), m22:(1,1), m23:(1,2),
|
||
m31:(2,0), m32:(2,1), m33:(2,2),
|
||
m41:(3,0), m42:(3,1), m43:(3,2);
|
||
U4, U5, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3), m35:(2,4),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3), m45:(3,4);
|
||
U4, U6, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4), m16:(0,5),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4), m26:(1,5),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3), m35:(2,4), m36:(2,5),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3), m45:(3,4), m46:(3,5);
|
||
|
||
/*
|
||
* Rectangular matrices with 5 rows.
|
||
*/
|
||
U5, U2, m11:(0,0), m12:(0,1),
|
||
m21:(1,0), m22:(1,1),
|
||
m31:(2,0), m32:(2,1),
|
||
m41:(3,0), m42:(3,1),
|
||
m51:(4,0), m52:(4,1);
|
||
U5, U3, m11:(0,0), m12:(0,1), m13:(0,2),
|
||
m21:(1,0), m22:(1,1), m23:(1,2),
|
||
m31:(2,0), m32:(2,1), m33:(2,2),
|
||
m41:(3,0), m42:(3,1), m43:(3,2),
|
||
m51:(4,0), m52:(4,1), m53:(4,2);
|
||
U5, U4, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3),
|
||
m51:(4,0), m52:(4,1), m53:(4,2), m54:(4,3);
|
||
U5, U6, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4), m16:(0,5),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4), m26:(1,5),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3), m35:(2,4), m36:(2,5),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3), m45:(3,4), m46:(3,5),
|
||
m51:(4,0), m52:(4,1), m53:(4,2), m54:(4,3), m55:(4,4), m56:(4,5);
|
||
|
||
/*
|
||
* Rectangular matrices with 6 rows.
|
||
*/
|
||
U6, U2, m11:(0,0), m12:(0,1),
|
||
m21:(1,0), m22:(1,1),
|
||
m31:(2,0), m32:(2,1),
|
||
m41:(3,0), m42:(3,1),
|
||
m51:(4,0), m52:(4,1),
|
||
m61:(5,0), m62:(5,1);
|
||
U6, U3, m11:(0,0), m12:(0,1), m13:(0,2),
|
||
m21:(1,0), m22:(1,1), m23:(1,2),
|
||
m31:(2,0), m32:(2,1), m33:(2,2),
|
||
m41:(3,0), m42:(3,1), m43:(3,2),
|
||
m51:(4,0), m52:(4,1), m53:(4,2),
|
||
m61:(5,0), m62:(5,1), m63:(5,2);
|
||
U6, U4, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3),
|
||
m51:(4,0), m52:(4,1), m53:(4,2), m54:(4,3),
|
||
m61:(5,0), m62:(5,1), m63:(5,2), m64:(5,3);
|
||
U6, U5, m11:(0,0), m12:(0,1), m13:(0,2), m14:(0,3), m15:(0,4),
|
||
m21:(1,0), m22:(1,1), m23:(1,2), m24:(1,3), m25:(1,4),
|
||
m31:(2,0), m32:(2,1), m33:(2,2), m34:(2,3), m35:(2,4),
|
||
m41:(3,0), m42:(3,1), m43:(3,2), m44:(3,3), m45:(3,4),
|
||
m51:(4,0), m52:(4,1), m53:(4,2), m54:(4,3), m55:(4,4),
|
||
m61:(5,0), m62:(5,1), m63:(5,2), m64:(5,3), m65:(5,4);
|
||
|
||
/*
|
||
* Row vectors 1 .. 6.
|
||
*/
|
||
U1, U1, x:(0,0);
|
||
U1, U2, x:(0,0), y:(0,1);
|
||
U1, U3, x:(0,0), y:(0,1), z:(0,2);
|
||
U1, U4, x:(0,0), y:(0,1), z:(0,2), w:(0,3);
|
||
U1, U5, x:(0,0), y:(0,1), z:(0,2), w:(0,3), a:(0,4);
|
||
U1, U6, x:(0,0), y:(0,1), z:(0,2), w:(0,3), a:(0,4), b:(0,5);
|
||
|
||
/*
|
||
* Column vectors 1 .. 6.
|
||
*/
|
||
U2, U1, x:(0,0), y:(1,0);
|
||
U3, U1, x:(0,0), y:(1,0), z:(2,0);
|
||
U4, U1, x:(0,0), y:(1,0), z:(2,0), w:(3,0);
|
||
U5, U1, x:(0,0), y:(1,0), z:(2,0), w:(3,0), a:(4,0);
|
||
U6, U1, x:(0,0), y:(1,0), z:(2,0), w:(3,0), a:(4,0), b:(5,0);
|
||
);
|
||
|
||
/*
|
||
*
|
||
* Axis constructors.
|
||
*
|
||
*/
|
||
impl<N, R: DimName> VectorN<N, R>
|
||
where
|
||
N: Scalar + Zero + One,
|
||
DefaultAllocator: Allocator<N, R>,
|
||
{
|
||
/// The column vector with a 1 as its first component, and zero elsewhere.
|
||
#[inline]
|
||
pub fn x() -> Self
|
||
where
|
||
R::Value: Cmp<typenum::U0, Output = Greater>,
|
||
{
|
||
let mut res = Self::zeros();
|
||
unsafe {
|
||
*res.vget_unchecked_mut(0) = N::one();
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// The column vector with a 1 as its second component, and zero elsewhere.
|
||
#[inline]
|
||
pub fn y() -> Self
|
||
where
|
||
R::Value: Cmp<typenum::U1, Output = Greater>,
|
||
{
|
||
let mut res = Self::zeros();
|
||
unsafe {
|
||
*res.vget_unchecked_mut(1) = N::one();
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// The column vector with a 1 as its third component, and zero elsewhere.
|
||
#[inline]
|
||
pub fn z() -> Self
|
||
where
|
||
R::Value: Cmp<typenum::U2, Output = Greater>,
|
||
{
|
||
let mut res = Self::zeros();
|
||
unsafe {
|
||
*res.vget_unchecked_mut(2) = N::one();
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// The column vector with a 1 as its fourth component, and zero elsewhere.
|
||
#[inline]
|
||
pub fn w() -> Self
|
||
where
|
||
R::Value: Cmp<typenum::U3, Output = Greater>,
|
||
{
|
||
let mut res = Self::zeros();
|
||
unsafe {
|
||
*res.vget_unchecked_mut(3) = N::one();
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// The column vector with a 1 as its fifth component, and zero elsewhere.
|
||
#[inline]
|
||
pub fn a() -> Self
|
||
where
|
||
R::Value: Cmp<typenum::U4, Output = Greater>,
|
||
{
|
||
let mut res = Self::zeros();
|
||
unsafe {
|
||
*res.vget_unchecked_mut(4) = N::one();
|
||
}
|
||
|
||
res
|
||
}
|
||
|
||
/// The column vector with a 1 as its sixth component, and zero elsewhere.
|
||
#[inline]
|
||
pub fn b() -> Self
|
||
where
|
||
R::Value: Cmp<typenum::U5, Output = Greater>,
|
||
{
|
||
let mut res = Self::zeros();
|
||
unsafe {
|
||
*res.vget_unchecked_mut(5) = N::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::Value: 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::Value: 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::Value: 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::Value: 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::Value: 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::Value: Cmp<typenum::U5, Output = Greater>,
|
||
{
|
||
Unit::new_unchecked(Self::b())
|
||
}
|
||
}
|