ndarray/tri.rs
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// Copyright 2014-2024 bluss and ndarray developers.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
use core::cmp::min;
use num_traits::Zero;
use crate::{
dimension::{is_layout_c, is_layout_f},
Array,
ArrayBase,
Axis,
Data,
Dimension,
Zip,
};
impl<S, A, D> ArrayBase<S, D>
where
S: Data<Elem = A>,
D: Dimension,
A: Clone + Zero,
{
/// Upper triangular of an array.
///
/// Return a copy of the array with elements below the *k*-th diagonal zeroed.
/// For arrays with `ndim` exceeding 2, `triu` will apply to the final two axes.
/// For 0D and 1D arrays, `triu` will return an unchanged clone.
///
/// See also [`ArrayBase::tril`]
///
/// ```
/// use ndarray::array;
///
/// let arr = array![
/// [1, 2, 3],
/// [4, 5, 6],
/// [7, 8, 9]
/// ];
/// assert_eq!(
/// arr.triu(0),
/// array![
/// [1, 2, 3],
/// [0, 5, 6],
/// [0, 0, 9]
/// ]
/// );
/// ```
pub fn triu(&self, k: isize) -> Array<A, D>
{
if self.ndim() <= 1 {
return self.to_owned();
}
// Performance optimization for F-order arrays.
// C-order array check prevents infinite recursion in edge cases like [[1]].
// k-size check prevents underflow when k == isize::MIN
let n = self.ndim();
if is_layout_f(&self.dim, &self.strides) && !is_layout_c(&self.dim, &self.strides) && k > isize::MIN {
let mut x = self.view();
x.swap_axes(n - 2, n - 1);
let mut tril = x.tril(-k);
tril.swap_axes(n - 2, n - 1);
return tril;
}
let mut res = Array::zeros(self.raw_dim());
let ncols = self.len_of(Axis(n - 1));
let nrows = self.len_of(Axis(n - 2));
let indices = Array::from_iter(0..nrows);
Zip::from(self.rows())
.and(res.rows_mut())
.and_broadcast(&indices)
.for_each(|src, mut dst, row_num| {
let mut lower = match k >= 0 {
true => row_num.saturating_add(k as usize), // Avoid overflow
false => row_num.saturating_sub(k.unsigned_abs()), // Avoid underflow, go to 0
};
lower = min(lower, ncols);
dst.slice_mut(s![lower..]).assign(&src.slice(s![lower..]));
});
res
}
/// Lower triangular of an array.
///
/// Return a copy of the array with elements above the *k*-th diagonal zeroed.
/// For arrays with `ndim` exceeding 2, `tril` will apply to the final two axes.
/// For 0D and 1D arrays, `tril` will return an unchanged clone.
///
/// See also [`ArrayBase::triu`]
///
/// ```
/// use ndarray::array;
///
/// let arr = array![
/// [1, 2, 3],
/// [4, 5, 6],
/// [7, 8, 9]
/// ];
/// assert_eq!(
/// arr.tril(0),
/// array![
/// [1, 0, 0],
/// [4, 5, 0],
/// [7, 8, 9]
/// ]
/// );
/// ```
pub fn tril(&self, k: isize) -> Array<A, D>
{
if self.ndim() <= 1 {
return self.to_owned();
}
// Performance optimization for F-order arrays.
// C-order array check prevents infinite recursion in edge cases like [[1]].
// k-size check prevents underflow when k == isize::MIN
let n = self.ndim();
if is_layout_f(&self.dim, &self.strides) && !is_layout_c(&self.dim, &self.strides) && k > isize::MIN {
let mut x = self.view();
x.swap_axes(n - 2, n - 1);
let mut tril = x.triu(-k);
tril.swap_axes(n - 2, n - 1);
return tril;
}
let mut res = Array::zeros(self.raw_dim());
let ncols = self.len_of(Axis(n - 1));
let nrows = self.len_of(Axis(n - 2));
let indices = Array::from_iter(0..nrows);
Zip::from(self.rows())
.and(res.rows_mut())
.and_broadcast(&indices)
.for_each(|src, mut dst, row_num| {
// let row_num = i.into_dimension().last_elem();
let mut upper = match k >= 0 {
true => row_num.saturating_add(k as usize).saturating_add(1), // Avoid overflow
false => row_num.saturating_sub((k + 1).unsigned_abs()), // Avoid underflow
};
upper = min(upper, ncols);
dst.slice_mut(s![..upper]).assign(&src.slice(s![..upper]));
});
res
}
}
#[cfg(test)]
mod tests
{
use core::isize;
use crate::{array, dimension, Array0, Array1, Array2, Array3, ShapeBuilder};
use alloc::vec;
#[test]
fn test_keep_order()
{
let x = Array2::<f64>::ones((3, 3).f());
let res = x.triu(0);
assert!(dimension::is_layout_f(&res.dim, &res.strides));
let res = x.tril(0);
assert!(dimension::is_layout_f(&res.dim, &res.strides));
}
#[test]
fn test_0d()
{
let x = Array0::<f64>::ones(());
let res = x.triu(0);
assert_eq!(res, x);
let res = x.tril(0);
assert_eq!(res, x);
let x = Array0::<f64>::ones(().f());
let res = x.triu(0);
assert_eq!(res, x);
let res = x.tril(0);
assert_eq!(res, x);
}
#[test]
fn test_1d()
{
let x = array![1, 2, 3];
let res = x.triu(0);
assert_eq!(res, x);
let res = x.triu(0);
assert_eq!(res, x);
let x = Array1::<f64>::ones(3.f());
let res = x.triu(0);
assert_eq!(res, x);
let res = x.triu(0);
assert_eq!(res, x);
}
#[test]
fn test_2d()
{
let x = array![[1, 2, 3], [4, 5, 6], [7, 8, 9]];
// Upper
let res = x.triu(0);
assert_eq!(res, array![[1, 2, 3], [0, 5, 6], [0, 0, 9]]);
// Lower
let res = x.tril(0);
assert_eq!(res, array![[1, 0, 0], [4, 5, 0], [7, 8, 9]]);
let x = Array2::from_shape_vec((3, 3).f(), vec![1, 4, 7, 2, 5, 8, 3, 6, 9]).unwrap();
// Upper
let res = x.triu(0);
assert_eq!(res, array![[1, 2, 3], [0, 5, 6], [0, 0, 9]]);
// Lower
let res = x.tril(0);
assert_eq!(res, array![[1, 0, 0], [4, 5, 0], [7, 8, 9]]);
}
#[test]
fn test_2d_single()
{
let x = array![[1]];
assert_eq!(x.triu(0), array![[1]]);
assert_eq!(x.tril(0), array![[1]]);
assert_eq!(x.triu(1), array![[0]]);
assert_eq!(x.tril(1), array![[1]]);
assert_eq!(x.triu(-1), array![[1]]);
assert_eq!(x.tril(-1), array![[0]]);
}
#[test]
fn test_3d()
{
let x = array![
[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
[[10, 11, 12], [13, 14, 15], [16, 17, 18]],
[[19, 20, 21], [22, 23, 24], [25, 26, 27]]
];
// Upper
let res = x.triu(0);
assert_eq!(
res,
array![
[[1, 2, 3], [0, 5, 6], [0, 0, 9]],
[[10, 11, 12], [0, 14, 15], [0, 0, 18]],
[[19, 20, 21], [0, 23, 24], [0, 0, 27]]
]
);
// Lower
let res = x.tril(0);
assert_eq!(
res,
array![
[[1, 0, 0], [4, 5, 0], [7, 8, 9]],
[[10, 0, 0], [13, 14, 0], [16, 17, 18]],
[[19, 0, 0], [22, 23, 0], [25, 26, 27]]
]
);
let x = Array3::from_shape_vec(
(3, 3, 3).f(),
vec![1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 3, 12, 21, 6, 15, 24, 9, 18, 27],
)
.unwrap();
// Upper
let res = x.triu(0);
assert_eq!(
res,
array![
[[1, 2, 3], [0, 5, 6], [0, 0, 9]],
[[10, 11, 12], [0, 14, 15], [0, 0, 18]],
[[19, 20, 21], [0, 23, 24], [0, 0, 27]]
]
);
// Lower
let res = x.tril(0);
assert_eq!(
res,
array![
[[1, 0, 0], [4, 5, 0], [7, 8, 9]],
[[10, 0, 0], [13, 14, 0], [16, 17, 18]],
[[19, 0, 0], [22, 23, 0], [25, 26, 27]]
]
);
}
#[test]
fn test_off_axis()
{
let x = array![
[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
[[10, 11, 12], [13, 14, 15], [16, 17, 18]],
[[19, 20, 21], [22, 23, 24], [25, 26, 27]]
];
let res = x.triu(1);
assert_eq!(
res,
array![
[[0, 2, 3], [0, 0, 6], [0, 0, 0]],
[[0, 11, 12], [0, 0, 15], [0, 0, 0]],
[[0, 20, 21], [0, 0, 24], [0, 0, 0]]
]
);
let res = x.triu(-1);
assert_eq!(
res,
array![
[[1, 2, 3], [4, 5, 6], [0, 8, 9]],
[[10, 11, 12], [13, 14, 15], [0, 17, 18]],
[[19, 20, 21], [22, 23, 24], [0, 26, 27]]
]
);
}
#[test]
fn test_odd_shape()
{
let x = array![[1, 2, 3], [4, 5, 6]];
let res = x.triu(0);
assert_eq!(res, array![[1, 2, 3], [0, 5, 6]]);
let res = x.tril(0);
assert_eq!(res, array![[1, 0, 0], [4, 5, 0]]);
let x = array![[1, 2], [3, 4], [5, 6]];
let res = x.triu(0);
assert_eq!(res, array![[1, 2], [0, 4], [0, 0]]);
let res = x.tril(0);
assert_eq!(res, array![[1, 0], [3, 4], [5, 6]]);
}
#[test]
fn test_odd_k()
{
let x = array![[1, 2, 3], [4, 5, 6], [7, 8, 9]];
let z = Array2::zeros([3, 3]);
assert_eq!(x.triu(isize::MIN), x);
assert_eq!(x.tril(isize::MIN), z);
assert_eq!(x.triu(isize::MAX), z);
assert_eq!(x.tril(isize::MAX), x);
}
}