ndarray_linalg/
generate.rs

1//! Generator functions for matrices
2
3use ndarray::*;
4use rand::prelude::*;
5
6use super::convert::*;
7use super::error::*;
8use super::qr::*;
9use super::types::*;
10
11/// Hermite conjugate matrix
12pub fn conjugate<A, S>(a: &ArrayRef<A, Ix2>) -> ArrayBase<S, Ix2>
13where
14    A: Scalar,
15    S: DataOwned<Elem = A> + DataMut,
16{
17    let mut a: ArrayBase<S, Ix2> = replicate(&a.t());
18    for val in a.iter_mut() {
19        *val = val.conj();
20    }
21    a
22}
23
24/// Generate random array with given shape
25///
26/// - This function uses [rand::thread_rng].
27///   See [random_using] for using another RNG
28pub fn random<A, S, Sh, D>(sh: Sh) -> ArrayBase<S, D>
29where
30    A: Scalar,
31    S: DataOwned<Elem = A>,
32    D: Dimension,
33    Sh: ShapeBuilder<Dim = D>,
34{
35    let mut rng = thread_rng();
36    random_using(sh, &mut rng)
37}
38
39/// Generate random array with given RNG
40///
41/// - See [random] for using default RNG
42pub fn random_using<A, S, Sh, D, R>(sh: Sh, rng: &mut R) -> ArrayBase<S, D>
43where
44    A: Scalar,
45    S: DataOwned<Elem = A>,
46    D: Dimension,
47    Sh: ShapeBuilder<Dim = D>,
48    R: Rng,
49{
50    ArrayBase::from_shape_fn(sh, |_| A::rand(rng))
51}
52
53/// Generate random unitary matrix using QR decomposition
54///
55/// - Be sure that this it **NOT** a uniform distribution.
56///   Use it only for test purpose.
57/// - This function uses [rand::thread_rng].
58///   See [random_unitary_using] for using another RNG.
59pub fn random_unitary<A>(n: usize) -> Array2<A>
60where
61    A: Scalar + Lapack,
62{
63    let mut rng = thread_rng();
64    random_unitary_using(n, &mut rng)
65}
66
67/// Generate random unitary matrix using QR decomposition with given RNG
68///
69/// - Be sure that this it **NOT** a uniform distribution.
70///   Use it only for test purpose.
71/// - See [random_unitary] for using default RNG.
72pub fn random_unitary_using<A, R>(n: usize, rng: &mut R) -> Array2<A>
73where
74    A: Scalar + Lapack,
75    R: Rng,
76{
77    let a: Array2<A> = random_using((n, n), rng);
78    let (q, _r) = a.qr_into().unwrap();
79    q
80}
81
82/// Generate random regular matrix
83///
84/// - Be sure that this it **NOT** a uniform distribution.
85///   Use it only for test purpose.
86/// - This function uses [rand::thread_rng].
87///   See [random_regular_using] for using another RNG.
88pub fn random_regular<A>(n: usize) -> Array2<A>
89where
90    A: Scalar + Lapack,
91{
92    let mut rng = rand::thread_rng();
93    random_regular_using(n, &mut rng)
94}
95
96/// Generate random regular matrix with given RNG
97///
98/// - Be sure that this it **NOT** a uniform distribution.
99///   Use it only for test purpose.
100/// - See [random_regular] for using default RNG.
101pub fn random_regular_using<A, R>(n: usize, rng: &mut R) -> Array2<A>
102where
103    A: Scalar + Lapack,
104    R: Rng,
105{
106    let a: Array2<A> = random_using((n, n), rng);
107    let (q, mut r) = a.qr_into().unwrap();
108    for i in 0..n {
109        r[(i, i)] = A::one() + A::from_real(r[(i, i)].abs());
110    }
111    q.dot(&r)
112}
113
114/// Random Hermite matrix
115///
116/// - This function uses [rand::thread_rng].
117///   See [random_hermite_using] for using another RNG.
118pub fn random_hermite<A, S>(n: usize) -> ArrayBase<S, Ix2>
119where
120    A: Scalar,
121    S: DataOwned<Elem = A> + DataMut,
122{
123    let mut rng = rand::thread_rng();
124    random_hermite_using(n, &mut rng)
125}
126
127/// Random Hermite matrix with given RNG
128///
129/// - See [random_hermite] for using default RNG.
130pub fn random_hermite_using<A, S, R>(n: usize, rng: &mut R) -> ArrayBase<S, Ix2>
131where
132    A: Scalar,
133    S: DataOwned<Elem = A> + DataMut,
134    R: Rng,
135{
136    let mut a: ArrayBase<S, Ix2> = random_using((n, n), rng);
137    for i in 0..n {
138        a[(i, i)] = a[(i, i)] + a[(i, i)].conj();
139        for j in (i + 1)..n {
140            a[(i, j)] = a[(j, i)].conj();
141        }
142    }
143    a
144}
145
146/// Random Hermite Positive-definite matrix
147///
148/// - Eigenvalue of matrix must be larger than 1 (thus non-singular)
149/// - This function uses [rand::thread_rng].
150///   See [random_hpd_using] for using another RNG.
151///
152pub fn random_hpd<A, S>(n: usize) -> ArrayBase<S, Ix2>
153where
154    A: Scalar,
155    S: DataOwned<Elem = A> + DataMut,
156{
157    let mut rng = rand::thread_rng();
158    random_hpd_using(n, &mut rng)
159}
160
161/// Random Hermite Positive-definite matrix with given RNG
162///
163/// - Eigenvalue of matrix must be larger than 1 (thus non-singular)
164/// - See [random_hpd] for using default RNG.
165///
166pub fn random_hpd_using<A, S, R>(n: usize, rng: &mut R) -> ArrayBase<S, Ix2>
167where
168    A: Scalar,
169    S: DataOwned<Elem = A> + DataMut,
170    R: Rng,
171{
172    let a: Array2<A> = random_using((n, n), rng);
173    let ah: Array2<A> = conjugate(&a);
174    ArrayBase::eye(n) + &ah.dot(&a)
175}
176
177/// construct matrix from diag
178pub fn from_diag<A>(d: &[A]) -> Array2<A>
179where
180    A: Scalar,
181{
182    let n = d.len();
183    let mut e = Array::zeros((n, n));
184    for i in 0..n {
185        e[(i, i)] = d[i];
186    }
187    e
188}
189
190/// stack vectors into matrix horizontally
191pub fn hstack<A, S>(xs: &[ArrayBase<S, Ix1>]) -> Result<Array<A, Ix2>>
192where
193    A: Scalar,
194    S: Data<Elem = A>,
195{
196    let views: Vec<_> = xs.iter().map(|x| x.view()).collect();
197    stack(Axis(1), &views).map_err(Into::into)
198}
199
200/// stack vectors into matrix vertically
201pub fn vstack<A, S>(xs: &[ArrayBase<S, Ix1>]) -> Result<Array<A, Ix2>>
202where
203    A: Scalar,
204    S: Data<Elem = A>,
205{
206    let views: Vec<_> = xs.iter().map(|x| x.view()).collect();
207    stack(Axis(0), &views).map_err(Into::into)
208}
ndarray_linalg/generate.rs

ndarray_linalg/
generate.rs
