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

//! Methods for triangular matrices

use lax::*;
use ndarray::*;
use num_traits::Zero;

use super::convert::*;
use super::error::*;
use super::layout::*;
use super::types::*;

pub use lax::Diag;

/// solve a triangular system with upper triangular matrix
pub trait SolveTriangular<A, S, D>
where
    A: Scalar + Lapack,
    S: Data<Elem = A>,
    D: Dimension,
{
    fn solve_triangular(&self, uplo: UPLO, diag: Diag, b: &ArrayBase<S, D>) -> Result<Array<A, D>>;
}

/// solve a triangular system with upper triangular matrix
pub trait SolveTriangularInto<S, D>
where
    S: DataMut,
    D: Dimension,
{
    fn solve_triangular_into(
        &self,
        uplo: UPLO,
        diag: Diag,
        b: ArrayBase<S, D>,
    ) -> Result<ArrayBase<S, D>>;
}

/// solve a triangular system with upper triangular matrix
pub trait SolveTriangularInplace<S, D>
where
    S: DataMut,
    D: Dimension,
{
    fn solve_triangular_inplace<'a>(
        &self,
        uplo: UPLO,
        diag: Diag,
        b: &'a mut ArrayBase<S, D>,
    ) -> Result<&'a mut ArrayBase<S, D>>;
}

impl<A, Si, So> SolveTriangularInto<So, Ix2> for ArrayBase<Si, Ix2>
where
    A: Scalar + Lapack,
    Si: Data<Elem = A>,
    So: DataMut<Elem = A> + DataOwned,
{
    fn solve_triangular_into(
        &self,
        uplo: UPLO,
        diag: Diag,
        mut b: ArrayBase<So, Ix2>,
    ) -> Result<ArrayBase<So, Ix2>> {
        self.solve_triangular_inplace(uplo, diag, &mut b)?;
        Ok(b)
    }
}

impl<A, Si, So> SolveTriangularInplace<So, Ix2> for ArrayBase<Si, Ix2>
where
    A: Scalar + Lapack,
    Si: Data<Elem = A>,
    So: DataMut<Elem = A> + DataOwned,
{
    fn solve_triangular_inplace<'a>(
        &self,
        uplo: UPLO,
        diag: Diag,
        b: &'a mut ArrayBase<So, Ix2>,
    ) -> Result<&'a mut ArrayBase<So, Ix2>> {
        let la = self.layout()?;
        let a_ = self.as_allocated()?;
        let lb = b.layout()?;
        if !la.same_order(&lb) {
            transpose_data(b)?;
        }
        let lb = b.layout()?;
        A::solve_triangular(la, lb, uplo, diag, a_, b.as_allocated_mut()?)?;
        Ok(b)
    }
}

impl<A, Si, So> SolveTriangular<A, So, Ix2> for ArrayBase<Si, Ix2>
where
    A: Scalar + Lapack,
    Si: Data<Elem = A>,
    So: DataMut<Elem = A> + DataOwned,
{
    fn solve_triangular(
        &self,
        uplo: UPLO,
        diag: Diag,
        b: &ArrayBase<So, Ix2>,
    ) -> Result<Array2<A>> {
        let b = replicate(b);
        self.solve_triangular_into(uplo, diag, b)
    }
}

impl<A, Si, So> SolveTriangularInto<So, Ix1> for ArrayBase<Si, Ix2>
where
    A: Scalar + Lapack,
    Si: Data<Elem = A>,
    So: DataMut<Elem = A> + DataOwned,
{
    fn solve_triangular_into(
        &self,
        uplo: UPLO,
        diag: Diag,
        b: ArrayBase<So, Ix1>,
    ) -> Result<ArrayBase<So, Ix1>> {
        let b = into_col(b);
        let b = self.solve_triangular_into(uplo, diag, b)?;
        Ok(flatten(b))
    }
}

impl<A, Si, So> SolveTriangular<A, So, Ix1> for ArrayBase<Si, Ix2>
where
    A: Scalar + Lapack,
    Si: Data<Elem = A>,
    So: DataMut<Elem = A> + DataOwned,
{
    fn solve_triangular(
        &self,
        uplo: UPLO,
        diag: Diag,
        b: &ArrayBase<So, Ix1>,
    ) -> Result<Array1<A>> {
        let b = b.to_owned();
        self.solve_triangular_into(uplo, diag, b)
    }
}

pub trait IntoTriangular<T> {
    fn into_triangular(self, uplo: UPLO) -> T;
}

impl<'a, A, S> IntoTriangular<&'a mut ArrayBase<S, Ix2>> for &'a mut ArrayBase<S, Ix2>
where
    A: Zero,
    S: DataMut<Elem = A>,
{
    fn into_triangular(self, uplo: UPLO) -> &'a mut ArrayBase<S, Ix2> {
        match uplo {
            UPLO::Upper => {
                for ((i, j), val) in self.indexed_iter_mut() {
                    if i > j {
                        *val = A::zero();
                    }
                }
            }
            UPLO::Lower => {
                for ((i, j), val) in self.indexed_iter_mut() {
                    if i < j {
                        *val = A::zero();
                    }
                }
            }
        }
        self
    }
}

impl<A, S> IntoTriangular<ArrayBase<S, Ix2>> for ArrayBase<S, Ix2>
where
    A: Zero,
    S: DataMut<Elem = A>,
{
    fn into_triangular(mut self, uplo: UPLO) -> ArrayBase<S, Ix2> {
        (&mut self).into_triangular(uplo);
        self
    }
}