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doraneko94doraneko94
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cargo fmt
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5 files changed

+211
-95
lines changed

5 files changed

+211
-95
lines changed

‎examples/tridiagonal.rs

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -27,4 +27,4 @@ fn factorize() -> Result<(), error::LinalgError> {
2727
fn main() {
2828
solve().unwrap();
2929
factorize().unwrap();
30-
}
30+
}

‎src/lapack/mod.rs

Lines changed: 11 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -31,7 +31,17 @@ pub type Pivot = Vec<i32>;
3131

3232
/// Trait for primitive types which implements LAPACK subroutines
3333
pub trait Lapack:
34-
OperatorNorm_ + QR_ + SVD_ + SVDDC_ + Solve_ + Solveh_ + Cholesky_ + Eig_ + Eigh_ + Triangular_ + TriDiagonal_
34+
OperatorNorm_
35+
+ QR_
36+
+ SVD_
37+
+ SVDDC_
38+
+ Solve_
39+
+ Solveh_
40+
+ Cholesky_
41+
+ Eig_
42+
+ Eigh_
43+
+ Triangular_
44+
+ TriDiagonal_
3545
{
3646
}
3747

‎src/lapack/tridiagonal.rs

Lines changed: 16 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -10,7 +10,7 @@ use super::{into_result, Pivot, Transpose};
1010

1111
use crate::error::*;
1212
use crate::layout::MatrixLayout;
13-
use crate::tridiagonal::{TriDiagonal, LUFactorizedTriDiagonal};
13+
use crate::tridiagonal::{LUFactorizedTriDiagonal, TriDiagonal};
1414
use crate::types::*;
1515

1616
/// Wraps `*gttrf`, `*gtcon` and `*gttrs`
@@ -24,28 +24,29 @@ pub trait TriDiagonal_: Scalar + Sized {
2424
lu: &LUFactorizedTriDiagonal<Self>,
2525
bl: MatrixLayout,
2626
t: Transpose,
27-
b: &mut [Self]) -> Result<()>;
27+
b: &mut [Self],
28+
) -> Result<()>;
2829
}
2930

3031
macro_rules! impl_tridiagonal {
3132
($scalar:ty, $gttrf:path, $gtcon:path, $gttrs:path) => {
3233
impl TriDiagonal_ for $scalar {
3334
unsafe fn lu_tridiagonal(a: &mut TriDiagonal<Self>) -> Result<(Array1<Self>, Pivot)> {
3435
let (n, _) = a.l.size();
35-
let dl = a.dl.as_slice_mut().unwrap();
36-
let d = a.d.as_slice_mut().unwrap();
37-
let du = a.du.as_slice_mut().unwrap();
38-
let mut du2 = vec![Zero::zero(); (n-2) as usize];
36+
let dl = a.dl.as_slice_mut().unwrap();
37+
let d = a.d.as_slice_mut().unwrap();
38+
let du = a.du.as_slice_mut().unwrap();
39+
let mut du2 = vec![Zero::zero(); (n - 2) as usize];
3940
let mut ipiv = vec![0; n as usize];
4041
let info = $gttrf(n, dl, d, du, &mut du2, &mut ipiv);
4142
into_result(info, (arr1(&du2), ipiv))
4243
}
43-
44+
4445
unsafe fn rcond_tridiagonal(lu: &LUFactorizedTriDiagonal<Self>) -> Result<Self::Real> {
4546
let (n, _) = lu.a.l.size();
46-
let dl = lu.a.dl.as_slice().unwrap();
47-
let d = lu.a.d.as_slice().unwrap();
48-
let du = lu.a.du.as_slice().unwrap();
47+
let dl = lu.a.dl.as_slice().unwrap();
48+
let d = lu.a.d.as_slice().unwrap();
49+
let du = lu.a.du.as_slice().unwrap();
4950
let du2 = lu.du2.as_slice().unwrap();
5051
let ipiv = &lu.ipiv;
5152
let anorm = lu.a.n1;
@@ -68,13 +69,13 @@ macro_rules! impl_tridiagonal {
6869
lu: &LUFactorizedTriDiagonal<Self>,
6970
bl: MatrixLayout,
7071
t: Transpose,
71-
b: &mut [Self]
72+
b: &mut [Self],
7273
) -> Result<()> {
7374
let (n, _) = lu.a.l.size();
7475
let (_, nrhs) = bl.size();
75-
let dl = lu.a.dl.as_slice().unwrap();
76-
let d = lu.a.d.as_slice().unwrap();
77-
let du = lu.a.du.as_slice().unwrap();
76+
let dl = lu.a.dl.as_slice().unwrap();
77+
let d = lu.a.d.as_slice().unwrap();
78+
let du = lu.a.du.as_slice().unwrap();
7879
let du2 = lu.du2.as_slice().unwrap();
7980
let ipiv = &lu.ipiv;
8081
let ldb = bl.lda();
@@ -100,4 +101,4 @@ macro_rules! impl_tridiagonal {
100101
impl_tridiagonal!(f64, lapacke::dgttrf, lapacke::dgtcon, lapacke::dgttrs);
101102
impl_tridiagonal!(f32, lapacke::sgttrf, lapacke::sgtcon, lapacke::sgttrs);
102103
impl_tridiagonal!(c64, lapacke::zgttrf, lapacke::zgtcon, lapacke::zgttrs);
103-
impl_tridiagonal!(c32, lapacke::cgttrf, lapacke::cgtcon, lapacke::cgttrs);
104+
impl_tridiagonal!(c32, lapacke::cgttrf, lapacke::cgtcon, lapacke::cgttrs);

‎src/tridiagonal.rs

Lines changed: 61 additions & 29 deletions
Original file line numberDiff line numberDiff line change
@@ -2,8 +2,8 @@
22
//! &
33
//! Methods for tridiagonal matrices
44
5-
use ndarray::*;
65
use cauchy::Scalar;
6+
use ndarray::*;
77
use num_traits::One;
88

99
use crate::opnorm::OperationNorm;
@@ -34,28 +34,30 @@ pub struct TriDiagonal<A: Scalar> {
3434
pub trait ToTriDiagonal<A: Scalar> {
3535
/// Extract tridiagonal elements and layout of the raw matrix.
3636
/// And also calculate 1-norm.
37-
///
37+
///
3838
/// If the raw matrix has some non-tridiagonal elements,
3939
/// they will be ignored.
40-
///
40+
///
4141
/// The shape of raw matrix should be equal to or larger than (2, 2).
4242
fn to_tridiagonal(&self) -> Result<TriDiagonal<A>>;
4343
}
4444

4545
impl<A, S> ToTriDiagonal<A> for ArrayBase<S, Ix2>
4646
where
4747
A: Scalar + Lapack,
48-
S: Data<Elem = A>
48+
S: Data<Elem = A>,
4949
{
5050
fn to_tridiagonal(&self) -> Result<TriDiagonal<A>> {
5151
let l = self.square_layout()?;
5252
let (n, _) = l.size();
53-
if n < 2 { panic!("Cannot make a tridiagonal matrix of shape=(1, 1)!"); }
53+
if n < 2 {
54+
panic!("Cannot make a tridiagonal matrix of shape=(1, 1)!");
55+
}
5456
let n1 = self.opnorm_one()?;
5557

56-
let dl = self.slice(s![1..n, 0..n-1]).diag().to_owned();
57-
let d = self.diag().to_owned();
58-
let du = self.slice(s![0..n-1, 1..n]).diag().to_owned();
58+
let dl = self.slice(s![1..n, 0..n - 1]).diag().to_owned();
59+
let d = self.diag().to_owned();
60+
let du = self.slice(s![0..n - 1, 1..n]).diag().to_owned();
5961
Ok(TriDiagonal { l, n1, dl, d, du })
6062
}
6163
}
@@ -73,22 +75,22 @@ pub trait SolveTriDiagonal<A: Scalar, D: Dimension> {
7375
b: ArrayBase<S, D>,
7476
) -> Result<ArrayBase<S, D>>;
7577
/// Solves a system of linear equations `A^T * x = b` with tridiagonal
76-
/// matrix `A`, where `A` is `self`, `b` is the argument, and
78+
/// matrix `A`, where `A` is `self`, `b` is the argument, and
7779
/// `x` is the successful result.
7880
fn solve_t_tridiagonal<S: Data<Elem = A>>(&self, b: &ArrayBase<S, D>) -> Result<Array<A, D>>;
7981
/// Solves a system of linear equations `A^T * x = b` with tridiagonal
80-
/// matrix `A`, where `A` is `self`, `b` is the argument, and
82+
/// matrix `A`, where `A` is `self`, `b` is the argument, and
8183
/// `x` is the successful result.
8284
fn solve_t_tridiagonal_into<S: DataMut<Elem = A>>(
8385
&self,
8486
b: ArrayBase<S, D>,
8587
) -> Result<ArrayBase<S, D>>;
8688
/// Solves a system of linear equations `A^H * x = b` with tridiagonal
87-
/// matrix `A`, where `A` is `self`, `b` is the argument, and
89+
/// matrix `A`, where `A` is `self`, `b` is the argument, and
8890
/// `x` is the successful result.
8991
fn solve_h_tridiagonal<S: Data<Elem = A>>(&self, b: &ArrayBase<S, D>) -> Result<Array<A, D>>;
9092
/// Solves a system of linear equations `A^H * x = b` with tridiagonal
91-
/// matrix `A`, where `A` is `self`, `b` is the argument, and
93+
/// matrix `A`, where `A` is `self`, `b` is the argument, and
9294
/// `x` is the successful result.
9395
fn solve_h_tridiagonal_into<S: DataMut<Elem = A>>(
9496
&self,
@@ -155,7 +157,10 @@ where
155157
self.solve_tridiagonal_inplace(&mut b)?;
156158
Ok(b)
157159
}
158-
fn solve_t_tridiagonal<S: Data<Elem = A>>(&self, b: &ArrayBase<S, Ix2>) -> Result<Array<A, Ix2>> {
160+
fn solve_t_tridiagonal<S: Data<Elem = A>>(
161+
&self,
162+
b: &ArrayBase<S, Ix2>,
163+
) -> Result<Array<A, Ix2>> {
159164
let mut b = replicate(b);
160165
self.solve_t_tridiagonal_inplace(&mut b)?;
161166
Ok(b)
@@ -167,7 +172,10 @@ where
167172
self.solve_t_tridiagonal_inplace(&mut b)?;
168173
Ok(b)
169174
}
170-
fn solve_h_tridiagonal<S: Data<Elem = A>>(&self, b: &ArrayBase<S, Ix2>) -> Result<Array<A, Ix2>> {
175+
fn solve_h_tridiagonal<S: Data<Elem = A>>(
176+
&self,
177+
b: &ArrayBase<S, Ix2>,
178+
) -> Result<Array<A, Ix2>> {
171179
let mut b = replicate(b);
172180
self.solve_h_tridiagonal_inplace(&mut b)?;
173181
Ok(b)
@@ -186,7 +194,10 @@ where
186194
A: Scalar + Lapack,
187195
S: Data<Elem = A>,
188196
{
189-
fn solve_tridiagonal<Sb: Data<Elem = A>>(&self, b: &ArrayBase<Sb, Ix2>) -> Result<Array<A, Ix2>> {
197+
fn solve_tridiagonal<Sb: Data<Elem = A>>(
198+
&self,
199+
b: &ArrayBase<Sb, Ix2>,
200+
) -> Result<Array<A, Ix2>> {
190201
let mut b = replicate(b);
191202
self.solve_tridiagonal_inplace(&mut b)?;
192203
Ok(b)
@@ -198,7 +209,10 @@ where
198209
self.solve_tridiagonal_inplace(&mut b)?;
199210
Ok(b)
200211
}
201-
fn solve_t_tridiagonal<Sb: Data<Elem = A>>(&self, b: &ArrayBase<Sb, Ix2>) -> Result<Array<A, Ix2>> {
212+
fn solve_t_tridiagonal<Sb: Data<Elem = A>>(
213+
&self,
214+
b: &ArrayBase<Sb, Ix2>,
215+
) -> Result<Array<A, Ix2>> {
202216
let mut b = replicate(b);
203217
self.solve_t_tridiagonal_inplace(&mut b)?;
204218
Ok(b)
@@ -210,7 +224,10 @@ where
210224
self.solve_t_tridiagonal_inplace(&mut b)?;
211225
Ok(b)
212226
}
213-
fn solve_h_tridiagonal<Sb: Data<Elem = A>>(&self, b: &ArrayBase<Sb, Ix2>) -> Result<Array<A, Ix2>> {
227+
fn solve_h_tridiagonal<Sb: Data<Elem = A>>(
228+
&self,
229+
b: &ArrayBase<Sb, Ix2>,
230+
) -> Result<Array<A, Ix2>> {
214231
let mut b = replicate(b);
215232
self.solve_h_tridiagonal_inplace(&mut b)?;
216233
Ok(b)
@@ -334,7 +351,10 @@ where
334351
let b = self.solve_tridiagonal_into(b)?;
335352
Ok(flatten(b))
336353
}
337-
fn solve_t_tridiagonal<S: Data<Elem = A>>(&self, b: &ArrayBase<S, Ix1>) -> Result<Array<A, Ix1>> {
354+
fn solve_t_tridiagonal<S: Data<Elem = A>>(
355+
&self,
356+
b: &ArrayBase<S, Ix1>,
357+
) -> Result<Array<A, Ix1>> {
338358
let b = b.to_owned();
339359
self.solve_t_tridiagonal_into(b)
340360
}
@@ -346,7 +366,10 @@ where
346366
let b = self.solve_t_tridiagonal_into(b)?;
347367
Ok(flatten(b))
348368
}
349-
fn solve_h_tridiagonal<S: Data<Elem = A>>(&self, b: &ArrayBase<S, Ix1>) -> Result<Array<A, Ix1>> {
369+
fn solve_h_tridiagonal<S: Data<Elem = A>>(
370+
&self,
371+
b: &ArrayBase<S, Ix1>,
372+
) -> Result<Array<A, Ix1>> {
350373
let b = b.to_owned();
351374
self.solve_h_tridiagonal_into(b)
352375
}
@@ -365,7 +388,10 @@ where
365388
A: Scalar + Lapack,
366389
S: Data<Elem = A>,
367390
{
368-
fn solve_tridiagonal<Sb: Data<Elem = A>>(&self, b: &ArrayBase<Sb, Ix1>) -> Result<Array<A, Ix1>> {
391+
fn solve_tridiagonal<Sb: Data<Elem = A>>(
392+
&self,
393+
b: &ArrayBase<Sb, Ix1>,
394+
) -> Result<Array<A, Ix1>> {
369395
let b = b.to_owned();
370396
self.solve_tridiagonal_into(b)
371397
}
@@ -378,7 +404,10 @@ where
378404
let b = f.solve_tridiagonal_into(b)?;
379405
Ok(flatten(b))
380406
}
381-
fn solve_t_tridiagonal<Sb: Data<Elem = A>>(&self, b: &ArrayBase<Sb, Ix1>) -> Result<Array<A, Ix1>> {
407+
fn solve_t_tridiagonal<Sb: Data<Elem = A>>(
408+
&self,
409+
b: &ArrayBase<Sb, Ix1>,
410+
) -> Result<Array<A, Ix1>> {
382411
let b = b.to_owned();
383412
self.solve_t_tridiagonal_into(b)
384413
}
@@ -391,7 +420,10 @@ where
391420
let b = f.solve_t_tridiagonal_into(b)?;
392421
Ok(flatten(b))
393422
}
394-
fn solve_h_tridiagonal<Sb: Data<Elem = A>>(&self, b: &ArrayBase<Sb, Ix1>) -> Result<Array<A, Ix1>> {
423+
fn solve_h_tridiagonal<Sb: Data<Elem = A>>(
424+
&self,
425+
b: &ArrayBase<Sb, Ix1>,
426+
) -> Result<Array<A, Ix1>> {
395427
let b = b.to_owned();
396428
self.solve_h_tridiagonal_into(b)
397429
}
@@ -429,7 +461,7 @@ where
429461
Ok(LUFactorizedTriDiagonal {
430462
a: self,
431463
du2: du2,
432-
ipiv: ipiv
464+
ipiv: ipiv,
433465
})
434466
}
435467
}
@@ -448,7 +480,7 @@ where
448480
impl<A, S> FactorizeTriDiagonal<A> for ArrayBase<S, Ix2>
449481
where
450482
A: Scalar + Lapack,
451-
S: Data<Elem = A>
483+
S: Data<Elem = A>,
452484
{
453485
fn factorize_tridiagonal(&self) -> Result<LUFactorizedTriDiagonal<A>> {
454486
let mut a = self.to_tridiagonal()?;
@@ -462,19 +494,19 @@ where
462494
/// where {a_1, a_2, ..., a_n} are diagonal elements,
463495
/// {b_1, b_2, ..., b_{n-1}} are super-diagonal elements, and
464496
/// {c_1, c_2, ..., c_{n-1}} are sub-diagonal elements of matrix.
465-
///
497+
///
466498
/// f[n] is used to calculate the determinant.
467499
/// (https://en.wikipedia.org/wiki/Tridiagonal_matrix#Determinant)
468-
///
500+
///
469501
/// In the future, the vector `f` can be used to calculate the inverce matrix.
470502
/// (https://en.wikipedia.org/wiki/Tridiagonal_matrix#Inversion)
471503
fn rec_rel<A: Scalar>(tridiag: &TriDiagonal<A>) -> Vec<A> {
472504
let n = tridiag.d.shape()[0];
473-
let mut f = Vec::with_capacity(n+1);
505+
let mut f = Vec::with_capacity(n + 1);
474506
f.push(One::one());
475507
f.push(tridiag.d[0]);
476508
for i in 1..n {
477-
f.push(tridiag.d[i] * f[i] - tridiag.dl[i-1] * tridiag.du[i-1] * f[i-1]);
509+
f.push(tridiag.d[i] * f[i] - tridiag.dl[i - 1] * tridiag.du[i - 1] * f[i - 1]);
478510
}
479511
f
480512
}
@@ -483,7 +515,7 @@ fn rec_rel<A: Scalar>(tridiag: &TriDiagonal<A>) -> Vec<A> {
483515
pub trait DeterminantTriDiagonal<A: Scalar> {
484516
/// Computes the determinant of the matrix.
485517
/// Unlike `.det()` of Determinant trait, this method
486-
/// doesn't returns the natural logarithm of the determinant
518+
/// doesn't returns the natural logarithm of the determinant
487519
/// but the determinant itself.
488520
fn det_tridiagonal(&self) -> Result<A>;
489521
}

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