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// Copyright 2014-2016 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 std::ops::{Add, Div, Mul};
use libnum::{self, One, Zero, Float};
use itertools::free::enumerate;
use imp_prelude::*;
use numeric_util;
use {FoldWhile, Zip};
/// # Numerical Methods for Arrays
impl<A, S, D> ArrayBase<S, D>
where S: Data<Elem=A>,
D: Dimension,
{
/// Return the sum of all elements in the array.
///
/// ```
/// use ndarray::arr2;
///
/// let a = arr2(&[[1., 2.],
/// [3., 4.]]);
/// assert_eq!(a.sum(), 10.);
/// ```
pub fn sum(&self) -> A
where A: Clone + Add<Output=A> + libnum::Zero,
{
if let Some(slc) = self.as_slice_memory_order() {
return numeric_util::unrolled_fold(slc, A::zero, A::add);
}
let mut sum = A::zero();
for row in self.inner_rows() {
if let Some(slc) = row.as_slice() {
sum = sum + numeric_util::unrolled_fold(slc, A::zero, A::add);
} else {
sum = sum + row.iter().fold(A::zero(), |acc, elt| acc + elt.clone());
}
}
sum
}
/// Return the sum of all elements in the array.
///
/// *This method has been renamed to `.sum()` and will be deprecated in the
/// next version.*
// #[deprecated(note="renamed to `sum`", since="0.13")]
pub fn scalar_sum(&self) -> A
where A: Clone + Add<Output=A> + libnum::Zero,
{
self.sum()
}
/// Return the product of all elements in the array.
///
/// ```
/// use ndarray::arr2;
///
/// let a = arr2(&[[1., 2.],
/// [3., 4.]]);
/// assert_eq!(a.product(), 24.);
/// ```
pub fn product(&self) -> A
where A: Clone + Mul<Output=A> + libnum::One,
{
if let Some(slc) = self.as_slice_memory_order() {
return numeric_util::unrolled_fold(slc, A::one, A::mul);
}
let mut sum = A::one();
for row in self.inner_rows() {
if let Some(slc) = row.as_slice() {
sum = sum * numeric_util::unrolled_fold(slc, A::one, A::mul);
} else {
sum = sum * row.iter().fold(A::one(), |acc, elt| acc * elt.clone());
}
}
sum
}
/// Return sum along `axis`.
///
/// ```
/// use ndarray::{aview0, aview1, arr2, Axis};
///
/// let a = arr2(&[[1., 2.],
/// [3., 4.]]);
/// assert!(
/// a.sum_axis(Axis(0)) == aview1(&[4., 6.]) &&
/// a.sum_axis(Axis(1)) == aview1(&[3., 7.]) &&
///
/// a.sum_axis(Axis(0)).sum_axis(Axis(0)) == aview0(&10.)
/// );
/// ```
///
/// **Panics** if `axis` is out of bounds.
pub fn sum_axis(&self, axis: Axis) -> Array<A, D::Smaller>
where A: Clone + Zero + Add<Output=A>,
D: RemoveAxis,
{
let n = self.len_of(axis);
let mut res = Array::zeros(self.raw_dim().remove_axis(axis));
let stride = self.strides()[axis.index()];
if self.ndim() == 2 && stride == 1 {
// contiguous along the axis we are summing
let ax = axis.index();
for (i, elt) in enumerate(&mut res) {
*elt = self.index_axis(Axis(1 - ax), i).sum();
}
} else {
for i in 0..n {
let view = self.index_axis(axis, i);
res = res + &view;
}
}
res
}
/// Return mean along `axis`.
///
/// **Panics** if `axis` is out of bounds or if the length of the axis is
/// zero and division by zero panics for type `A`.
///
/// ```
/// use ndarray::{aview1, arr2, Axis};
///
/// let a = arr2(&[[1., 2.],
/// [3., 4.]]);
/// assert!(
/// a.mean_axis(Axis(0)) == aview1(&[2.0, 3.0]) &&
/// a.mean_axis(Axis(1)) == aview1(&[1.5, 3.5])
/// );
/// ```
pub fn mean_axis(&self, axis: Axis) -> Array<A, D::Smaller>
where A: Clone + Zero + One + Add<Output=A> + Div<Output=A>,
D: RemoveAxis,
{
let n = self.len_of(axis);
let sum = self.sum_axis(axis);
let mut cnt = A::zero();
for _ in 0..n {
cnt = cnt + A::one();
}
sum / &aview0(&cnt)
}
/// Return variance along `axis`.
///
/// The variance is computed using the [Welford one-pass
/// algorithm](https://www.jstor.org/stable/1266577).
///
/// The parameter `ddof` specifies the "delta degrees of freedom". For
/// example, to calculate the population variance, use `ddof = 0`, or to
/// calculate the sample variance, use `ddof = 1`.
///
/// The variance is defined as:
///
/// ```text
/// 1 n
/// variance = ―――――――― ∑ (xᵢ - x̅)²
/// n - ddof i=1
/// ```
///
/// where
///
/// ```text
/// 1 n
/// x̅ = ― ∑ xᵢ
/// n i=1
/// ```
///
/// **Panics** if `ddof` is greater than or equal to the length of the
/// axis, if `axis` is out of bounds, or if the length of the axis is zero.
///
/// # Example
///
/// ```
/// use ndarray::{aview1, arr2, Axis};
///
/// let a = arr2(&[[1., 2.],
/// [3., 4.],
/// [5., 6.]]);
/// let var = a.var_axis(Axis(0), 1.);
/// assert_eq!(var, aview1(&[4., 4.]));
/// ```
pub fn var_axis(&self, axis: Axis, ddof: A) -> Array<A, D::Smaller>
where
A: Float,
D: RemoveAxis,
{
let mut count = A::zero();
let mut mean = Array::<A, _>::zeros(self.dim.remove_axis(axis));
let mut sum_sq = Array::<A, _>::zeros(self.dim.remove_axis(axis));
for subview in self.axis_iter(axis) {
count = count + A::one();
azip!(mut mean, mut sum_sq, x (subview) in {
let delta = x - *mean;
*mean = *mean + delta / count;
*sum_sq = (x - *mean).mul_add(delta, *sum_sq);
});
}
if ddof >= count {
panic!("`ddof` needs to be strictly smaller than the length \
of the axis you are computing the variance for!")
} else {
let dof = count - ddof;
sum_sq.mapv_into(|s| s / dof)
}
}
/// Return standard deviation along `axis`.
///
/// The standard deviation is computed from the variance using
/// the [Welford one-pass algorithm](https://www.jstor.org/stable/1266577).
///
/// The parameter `ddof` specifies the "delta degrees of freedom". For
/// example, to calculate the population standard deviation, use `ddof = 0`,
/// or to calculate the sample standard deviation, use `ddof = 1`.
///
/// The standard deviation is defined as:
///
/// ```text
/// 1 n
/// stddev = sqrt ( ―――――――― ∑ (xᵢ - x̅)² )
/// n - ddof i=1
/// ```
///
/// where
///
/// ```text
/// 1 n
/// x̅ = ― ∑ xᵢ
/// n i=1
/// ```
///
/// **Panics** if `ddof` is greater than or equal to the length of the
/// axis, if `axis` is out of bounds, or if the length of the axis is zero.
///
/// # Example
///
/// ```
/// use ndarray::{aview1, arr2, Axis};
///
/// let a = arr2(&[[1., 2.],
/// [3., 4.],
/// [5., 6.]]);
/// let stddev = a.std_axis(Axis(0), 1.);
/// assert_eq!(stddev, aview1(&[2., 2.]));
/// ```
pub fn std_axis(&self, axis: Axis, ddof: A) -> Array<A, D::Smaller>
where
A: Float,
D: RemoveAxis,
{
self.var_axis(axis, ddof).mapv_into(|x| x.sqrt())
}
/// Return `true` if the arrays' elementwise differences are all within
/// the given absolute tolerance, `false` otherwise.
///
/// If their shapes disagree, `rhs` is broadcast to the shape of `self`.
///
/// **Panics** if broadcasting to the same shape isn’t possible.
pub fn all_close<S2, E>(&self, rhs: &ArrayBase<S2, E>, tol: A) -> bool
where A: Float,
S2: Data<Elem=A>,
E: Dimension,
{
!Zip::from(self)
.and(rhs.broadcast_unwrap(self.raw_dim()))
.fold_while((), |_, x, y| {
if (*x - *y).abs() <= tol {
FoldWhile::Continue(())
} else {
FoldWhile::Done(())
}
}).is_done()
}
}