arr-rs 0.6.0

arr-rs - rust arrays library
Documentation 
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

use crate::{
    core::prelude::*,
    errors::prelude::*,
    linalg::prelude::*,
    math::prelude::*,
    numeric::prelude::*,
    validators::prelude::*,
};

/// `ArrayTrait` - Array Linalg Norms functions
pub trait ArrayLinalgNorms<N: NumericOps> where Self: Sized + Clone {

    /// Calculates matrix or vector norm
    ///
    /// # Arguments
    ///
    /// * `ord` - order of the norm: {non-zero int, inf, -inf, `fro`, `nuc`}. optional
    /// * `axis` - axis along which vector norms are to be calculated. optional
    /// * `keepdims` - if true, the result will broadcast correctly against the input. optional
    ///
    /// # Examples
    ///
    /// ```
    /// use arr_rs::prelude::*;
    ///
    /// let array_a = Array::arange(-4., 4., None);
    /// let array_b = array_a.reshape(&[3, 3]);
    ///
    /// let expected = Array::single(7.745966692414834);
    /// assert_eq!(expected, array_a.norm(None::<NormOrd>, None, None));
    /// assert_eq!(expected, array_b.norm(None::<NormOrd>, None, None));
    /// ```
    ///
    /// # Errors
    ///
    /// may returns `ArrayError`
    fn norm(&self, ord: Option<impl NormOrdType>, axis: Option<Vec<isize>>, keepdims: Option<bool>) -> Result<Array<N>, ArrayError>;

    /// Compute the determinant of an array
    ///
    /// # Examples
    ///
    /// ```
    /// use arr_rs::prelude::*;
    ///
    /// assert_eq!(Array::single(-14), Array::new(vec![3, 8, 4, 6], vec![2, 2]).det());
    /// ```
    ///
    /// # Errors
    ///
    /// may returns `ArrayError`
    fn det(&self) -> Result<Array<N>, ArrayError>;
}

impl <N: NumericOps> ArrayLinalgNorms<N> for Array<N> {

    fn norm(&self, ord: Option<impl NormOrdType>, axis: Option<Vec<isize>>, keepdims: Option<bool>) -> Result<Self, ArrayError> {

        fn norm_simple<N: NumericOps>(array: &Array<N>, keepdims: Option<bool>) -> Result<Array<N>, ArrayError> {
            let ndim = array.ndim()?;
            let array = array.ravel()?;
            let result = array
                .dot(&array)
                .sqrt();
            if keepdims.unwrap_or(false) { result.reshape(&[ndim; 1]) }
            else { result }
        }

        let ndim = self.ndim()?;
        if axis.is_none() {
            match ord.clone() {
                Some(ord) => {
                    let ord = ord.to_ord()?;
                    if (ndim == 2 && ord == NormOrd::Fro) || (ndim == 1 && ord == NormOrd::Int(2)) {
                        return norm_simple(self, keepdims)
                    }
                },
                None => return norm_simple(self, keepdims)
            }
        }

        let axis = axis.unwrap_or_else(|| (0..ndim.to_isize()).collect());
        match axis.len() {
            1 => {
                let axis = Some(axis[0]);
                let ord = match ord {
                    Some(o) => o.to_ord()?,
                    None => NormOrd::Int(2),
                };
                match ord {
                    NormOrd::Inf => self.abs().max(axis),
                    NormOrd::NegInf => self.abs().min(axis),
                    NormOrd::Int(0) => self.map(|&i| if i == N::zero() { N::zero() } else { N::one() }).sum(axis),
                    NormOrd::Int(1) => self.abs().sum(axis),
                    NormOrd::Int(2) => self.multiply(self).abs()?.sum(axis).sqrt(),
                    NormOrd::Int(value) => self.abs()
                        .float_power(&Self::single(N::from(value))?)
                        .sum(axis)
                        .float_power(&Self::single(N::from(value)).reciprocal()?),
                    NormOrd::Fro | NormOrd::Nuc => {
                        Err(ArrayError::ParameterError { param: "`ord`", message: "invalid norm order for vectors." })
                    },
                }
            }
            2 => {
                let row_axis = self.normalize_axis(axis[0]).to_isize();
                let col_axis = self.normalize_axis(axis[1]).to_isize();
                if row_axis == col_axis {
                    return Err(ArrayError::ParameterError { param: "`axis`", message: "duplicate axes given." });
                }
                let ord = match ord {
                    Some(o) => o.to_ord()?,
                    None => NormOrd::Fro,
                };
                let result = match ord {
                    NormOrd::Int(1) => {
                        let col_axis = if col_axis > row_axis { -col_axis } else { col_axis };
                        self.abs().sum(Some(row_axis)).max(Some(col_axis))
                    },
                    NormOrd::Int(-1) => {
                        let col_axis = if col_axis > row_axis { -col_axis } else { col_axis };
                        self.abs().sum(Some(row_axis)).min(Some(col_axis))
                    },
                    NormOrd::Inf => {
                        let row_axis = if row_axis > col_axis { -row_axis } else { row_axis };
                        self.abs().sum(Some(col_axis)).max(Some(row_axis))
                    },
                    NormOrd::NegInf => {
                        let row_axis = if row_axis > col_axis { -row_axis } else { row_axis };
                        self.abs().sum(Some(col_axis)).min(Some(row_axis))
                    },
                    _ => {
                        Err(ArrayError::ParameterError { param: "`ord`", message: "invalid norm order for vectors." })
                    },
                };
                if keepdims.unwrap_or(false) {
                    let mut new_shape = result.get_shape()?;
                    new_shape.push(1);
                    result.reshape(&new_shape)
                } else {
                    result
                }
            }
            _ => Err(ArrayError::ParameterError { param: "`axis`", message: "improper number of dimensions to norm." })
        }
    }

    fn det(&self) -> Result<Self<>, ArrayError> {
        if self.ndim()? == 0 {
            Err(ArrayError::MustBeAtLeast { value1: "`dimension`".to_string(), value2: "1".to_string() })
        } else if self.ndim()? == 1 {
            Ok(self.clone())
        } else if self.ndim()? == 2 {
            let shape = self.get_shape()?;
            self.is_square()?;
            if shape[0] == 2 {
                Self::single(N::from(self[0].to_f64().mul_add(self[3].to_f64(), -self[1].to_f64() * self[2].to_f64())))
            } else {
                let elems = (0..shape[0])
                    .map(|i| self[i * shape[0]].to_f64())
                    .collect::<Vec<f64>>();
                let dets = (0..shape[0])
                    .map(|i| Self::minor(self, i, 0).det())
                    .collect::<Vec<Result<Self, _>>>()
                    .has_error()?.into_iter()
                    .map(Result::unwrap)
                    .map(|i| i[0].to_f64())
                    .collect::<Vec<f64>>();
                let result = elems.iter().zip(&dets)
                    .enumerate()
                    .map(|(i, (&e, &d))| e * f64::powi(-1., i.to_i32() + 2) * d)
                    .sum::<f64>();
                Self::single(N::from(result))
            }
        } else {
            let shape = self.get_shape()?;
            shape.is_square()?;
            let sub_shape = shape[self.ndim()? - 2 ..].to_vec();
            let dets = self
                .ravel()?
                .split(self.len()? / sub_shape.iter().product::<usize>(), None)?
                .iter()
                .map(|arr| arr.reshape(&sub_shape).det())
                .collect::<Vec<Result<Self, _>>>()
                .has_error()?.into_iter()
                .flat_map(Result::unwrap)
                .collect::<Self>();
            Ok(dets)
        }
    }
}

impl <N: NumericOps> ArrayLinalgNorms<N> for Result<Array<N>, ArrayError> {

    fn norm(&self, ord: Option<impl NormOrdType>, axis: Option<Vec<isize>>, keepdims: Option<bool>) -> Self {
        self.clone()?.norm(ord, axis, keepdims)
    }

    fn det(&self) -> Self {
        self.clone()?.det()
    }
}

trait NormsHelper<N: NumericOps> {

    fn minor(arr: &Array<N>, row: usize, col: usize) -> Result<Array<N>, ArrayError> {
        arr.is_dim_supported(&[2])?;
        if row >= arr.get_shape()?[0] || col >= arr.get_shape()?[1] {
            return Err(ArrayError::OutOfBounds { value: "Row or column index out of bounds" })
        }

        let mut sub_shape = arr.get_shape()?;
        sub_shape[arr.ndim()? - 1] -= 1;
        sub_shape[arr.ndim()? - 2] -= 1;

        let mut sub_elements = Vec::new();
        for (i, &element) in arr.get_elements()?.iter().enumerate() {
            if i / arr.get_shape()?[1] != row && i % arr.get_shape()?[1] != col {
                sub_elements.push(element);
            }
        }

        Array::new(sub_elements, sub_shape)
    }
}

impl <N: NumericOps> NormsHelper<N> for Array<N> {}