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

#[cfg(feature = "serde-serialize-no-std")]
use serde::{Deserialize, Serialize};

use num::One;
use simba::scalar::ClosedNeg;

use crate::allocator::Allocator;
use crate::base::{DefaultAllocator, Matrix, OVector, Scalar};
#[cfg(any(feature = "std", feature = "alloc"))]
use crate::dimension::Dyn;
use crate::dimension::{Const, Dim, DimName};
use crate::storage::StorageMut;

/// A sequence of row or column permutations.
#[cfg_attr(feature = "serde-serialize-no-std", derive(Serialize, Deserialize))]
#[cfg_attr(
    feature = "serde-serialize-no-std",
    serde(bound(serialize = "DefaultAllocator: Allocator<(usize, usize), D>,
         OVector<(usize, usize), D>: Serialize"))
)]
#[cfg_attr(
    feature = "serde-serialize-no-std",
    serde(bound(deserialize = "DefaultAllocator: Allocator<(usize, usize), D>,
         OVector<(usize, usize), D>: Deserialize<'de>"))
)]
#[derive(Clone, Debug)]
pub struct PermutationSequence<D: Dim>
where
    DefaultAllocator: Allocator<(usize, usize), D>,
{
    len: usize,
    ipiv: OVector<(usize, usize), D>,
}

impl<D: Dim> Copy for PermutationSequence<D>
where
    DefaultAllocator: Allocator<(usize, usize), D>,
    OVector<(usize, usize), D>: Copy,
{
}

impl<D: DimName> PermutationSequence<D>
where
    DefaultAllocator: Allocator<(usize, usize), D>,
{
    /// Creates a new statically-allocated sequence of `D` identity permutations.
    #[inline]
    pub fn identity() -> Self {
        Self::identity_generic(D::name())
    }
}

#[cfg(any(feature = "std", feature = "alloc"))]
impl PermutationSequence<Dyn>
where
    DefaultAllocator: Allocator<(usize, usize), Dyn>,
{
    /// Creates a new dynamically-allocated sequence of `n` identity permutations.
    #[inline]
    pub fn identity(n: usize) -> Self {
        Self::identity_generic(Dyn(n))
    }
}

impl<D: Dim> PermutationSequence<D>
where
    DefaultAllocator: Allocator<(usize, usize), D>,
{
    /// Creates a new sequence of D identity permutations.
    #[inline]
    pub fn identity_generic(dim: D) -> Self {
        Self {
            len: 0,
            // TODO: using a uninitialized matrix would save some computation, but
            //       that loos difficult to setup with MaybeUninit.
            ipiv: Matrix::repeat_generic(dim, Const::<1>, (0, 0)),
        }
    }

    /// Adds the interchange of the row (or column) `i` with the row (or column) `i2` to this
    /// sequence of permutations.
    #[inline]
    pub fn append_permutation(&mut self, i: usize, i2: usize) {
        if i != i2 {
            assert!(
                self.len < self.ipiv.len(),
                "Maximum number of permutations exceeded."
            );
            self.ipiv[self.len] = (i, i2);
            self.len += 1;
        }
    }

    /// Applies this sequence of permutations to the rows of `rhs`.
    #[inline]
    pub fn permute_rows<T: Scalar, R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<T, R2, C2, S2>)
    where
        S2: StorageMut<T, R2, C2>,
    {
        for i in self.ipiv.rows_range(..self.len).iter() {
            rhs.swap_rows(i.0, i.1)
        }
    }

    /// Applies this sequence of permutations in reverse to the rows of `rhs`.
    #[inline]
    pub fn inv_permute_rows<T: Scalar, R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<T, R2, C2, S2>)
    where
        S2: StorageMut<T, R2, C2>,
    {
        for i in 0..self.len {
            let (i1, i2) = self.ipiv[self.len - i - 1];
            rhs.swap_rows(i1, i2)
        }
    }

    /// Applies this sequence of permutations to the columns of `rhs`.
    #[inline]
    pub fn permute_columns<T: Scalar, R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<T, R2, C2, S2>)
    where
        S2: StorageMut<T, R2, C2>,
    {
        for i in self.ipiv.rows_range(..self.len).iter() {
            rhs.swap_columns(i.0, i.1)
        }
    }

    /// Applies this sequence of permutations in reverse to the columns of `rhs`.
    #[inline]
    pub fn inv_permute_columns<T: Scalar, R2: Dim, C2: Dim, S2>(
        &self,
        rhs: &mut Matrix<T, R2, C2, S2>,
    ) where
        S2: StorageMut<T, R2, C2>,
    {
        for i in 0..self.len {
            let (i1, i2) = self.ipiv[self.len - i - 1];
            rhs.swap_columns(i1, i2)
        }
    }

    /// The number of non-identity permutations applied by this sequence.
    #[must_use]
    pub fn len(&self) -> usize {
        self.len
    }

    /// Returns true if the permutation sequence contains no elements.
    #[must_use]
    pub fn is_empty(&self) -> bool {
        self.len() == 0
    }

    /// The determinant of the matrix corresponding to this permutation.
    #[inline]
    #[must_use]
    pub fn determinant<T: One + ClosedNeg>(&self) -> T {
        if self.len % 2 == 0 {
            T::one()
        } else {
            -T::one()
        }
    }
}