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
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
// 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 num_traits::{self, Float, FromPrimitive, Zero};
use std::ops::{Add, Div, Mul};

use crate::imp_prelude::*;
use crate::itertools::enumerate;
use crate::numeric_util;

use crate::{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> + num_traits::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
    }

    /// Returns the [arithmetic mean] x̅ of all elements in the array:
    ///
    /// ```text
    ///     1   n
    /// x̅ = ―   ∑ xᵢ
    ///     n  i=1
    /// ```
    ///
    /// If the array is empty, `None` is returned.
    ///
    /// **Panics** if `A::from_usize()` fails to convert the number of elements in the array.
    ///
    /// [arithmetic mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
    pub fn mean(&self) -> Option<A>
    where
        A: Clone + FromPrimitive + Add<Output = A> + Div<Output = A> + Zero,
    {
        let n_elements = self.len();
        if n_elements == 0 {
            None
        } else {
            let n_elements = A::from_usize(n_elements)
                .expect("Converting number of elements to `A` must not fail.");
            Some(self.sum() / n_elements)
        }
    }

    /// 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> + num_traits::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> + num_traits::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., 5., 6.]]);
    /// assert!(
    ///     a.sum_axis(Axis(0)) == aview1(&[5., 7., 9.]) &&
    ///     a.sum_axis(Axis(1)) == aview1(&[6., 15.]) &&
    ///
    ///     a.sum_axis(Axis(0)).sum_axis(Axis(0)) == aview0(&21.)
    /// );
    /// ```
    ///
    /// **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`.
    ///
    /// Return `None` if the length of the axis is zero.
    ///
    /// **Panics** if `axis` is out of bounds or if `A::from_usize()`
    /// fails for the axis length.
    ///
    /// ```
    /// use ndarray::{aview0, aview1, arr2, Axis};
    ///
    /// let a = arr2(&[[1., 2., 3.],
    ///                [4., 5., 6.]]);
    /// assert!(
    ///     a.mean_axis(Axis(0)).unwrap() == aview1(&[2.5, 3.5, 4.5]) &&
    ///     a.mean_axis(Axis(1)).unwrap() == aview1(&[2., 5.]) &&
    ///
    ///     a.mean_axis(Axis(0)).unwrap().mean_axis(Axis(0)).unwrap() == aview0(&3.5)
    /// );
    /// ```
    pub fn mean_axis(&self, axis: Axis) -> Option<Array<A, D::Smaller>>
    where
        A: Clone + Zero + FromPrimitive + Add<Output = A> + Div<Output = A>,
        D: RemoveAxis,
    {
        let axis_length = self.len_of(axis);
        if axis_length == 0 {
            None
        } else {
            let axis_length =
                A::from_usize(axis_length).expect("Converting axis length to `A` must not fail.");
            let sum = self.sum_axis(axis);
            Some(sum / aview0(&axis_length))
        }
    }

    /// 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
    /// ```
    ///
    /// and `n` is the length of the axis.
    ///
    /// **Panics** if `ddof` is less than zero or greater than `n`, if `axis`
    /// is out of bounds, or if `A::from_usize()` fails for any any of the
    /// numbers in the range `0..=n`.
    ///
    /// # 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 + FromPrimitive,
        D: RemoveAxis,
    {
        let zero = A::from_usize(0).expect("Converting 0 to `A` must not fail.");
        let n = A::from_usize(self.len_of(axis)).expect("Converting length to `A` must not fail.");
        assert!(
            !(ddof < zero || ddof > n),
            "`ddof` must not be less than zero or greater than the length of \
             the axis",
        );
        let dof = n - ddof;
        let mut mean = Array::<A, _>::zeros(self.dim.remove_axis(axis));
        let mut sum_sq = Array::<A, _>::zeros(self.dim.remove_axis(axis));
        for (i, subview) in self.axis_iter(axis).enumerate() {
            let count = A::from_usize(i + 1).expect("Converting index to `A` must not fail.");
            azip!((mean in &mut mean, sum_sq in &mut sum_sq, &x in &subview) {
                let delta = x - *mean;
                *mean = *mean + delta / count;
                *sum_sq = (x - *mean).mul_add(delta, *sum_sq);
            });
        }
        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
    /// ```
    ///
    /// and `n` is the length of the axis.
    ///
    /// **Panics** if `ddof` is less than zero or greater than `n`, if `axis`
    /// is out of bounds, or if `A::from_usize()` fails for any any of the
    /// numbers in the range `0..=n`.
    ///
    /// # 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 + FromPrimitive,
        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.
    #[deprecated(
        note = "Use `abs_diff_eq` - it requires the `approx` crate feature",
        since = "0.13.0"
    )]
    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()
    }
}