405 lines
12 KiB
Rust
405 lines
12 KiB
Rust
use num::{One, Zero};
|
||
use num_complex::Complex;
|
||
|
||
use na::allocator::Allocator;
|
||
use na::dimension::{Dim, DimMin, DimMinimum, U1};
|
||
use na::storage::Storage;
|
||
use na::{DefaultAllocator, Matrix, MatrixMN, MatrixN, Scalar, VectorN};
|
||
use ComplexHelper;
|
||
|
||
use lapack;
|
||
|
||
/// LU decomposition with partial pivoting.
|
||
///
|
||
/// This decomposes a matrix `M` with m rows and n columns into three parts:
|
||
/// * `L` which is a `m × min(m, n)` lower-triangular matrix.
|
||
/// * `U` which is a `min(m, n) × n` upper-triangular matrix.
|
||
/// * `P` which is a `m * m` permutation matrix.
|
||
///
|
||
/// Those are such that `M == P * L * U`.
|
||
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
|
||
#[cfg_attr(
|
||
feature = "serde-serialize",
|
||
serde(bound(
|
||
serialize = "DefaultAllocator: Allocator<N, R, C> +
|
||
Allocator<i32, DimMinimum<R, C>>,
|
||
MatrixMN<N, R, C>: Serialize,
|
||
PermutationSequence<DimMinimum<R, C>>: Serialize"
|
||
))
|
||
)]
|
||
#[cfg_attr(
|
||
feature = "serde-serialize",
|
||
serde(bound(
|
||
deserialize = "DefaultAllocator: Allocator<N, R, C> +
|
||
Allocator<i32, DimMinimum<R, C>>,
|
||
MatrixMN<N, R, C>: Deserialize<'de>,
|
||
PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>"
|
||
))
|
||
)]
|
||
#[derive(Clone, Debug)]
|
||
pub struct LU<N: Scalar, R: DimMin<C>, C: Dim>
|
||
where DefaultAllocator: Allocator<i32, DimMinimum<R, C>> + Allocator<N, R, C>
|
||
{
|
||
lu: MatrixMN<N, R, C>,
|
||
p: VectorN<i32, DimMinimum<R, C>>,
|
||
}
|
||
|
||
impl<N: Scalar, R: DimMin<C>, C: Dim> Copy for LU<N, R, C>
|
||
where
|
||
DefaultAllocator: Allocator<N, R, C> + Allocator<i32, DimMinimum<R, C>>,
|
||
MatrixMN<N, R, C>: Copy,
|
||
VectorN<i32, DimMinimum<R, C>>: Copy,
|
||
{}
|
||
|
||
impl<N: LUScalar, R: Dim, C: Dim> LU<N, R, C>
|
||
where
|
||
N: Zero + One,
|
||
R: DimMin<C>,
|
||
DefaultAllocator: Allocator<N, R, C>
|
||
+ Allocator<N, R, R>
|
||
+ Allocator<N, R, DimMinimum<R, C>>
|
||
+ Allocator<N, DimMinimum<R, C>, C>
|
||
+ Allocator<i32, DimMinimum<R, C>>,
|
||
{
|
||
/// Computes the LU decomposition with partial (row) pivoting of `matrix`.
|
||
pub fn new(mut m: MatrixMN<N, R, C>) -> Self {
|
||
let (nrows, ncols) = m.data.shape();
|
||
let min_nrows_ncols = nrows.min(ncols);
|
||
let nrows = nrows.value() as i32;
|
||
let ncols = ncols.value() as i32;
|
||
|
||
let mut ipiv: VectorN<i32, _> = Matrix::zeros_generic(min_nrows_ncols, U1);
|
||
|
||
let mut info = 0;
|
||
|
||
N::xgetrf(
|
||
nrows,
|
||
ncols,
|
||
m.as_mut_slice(),
|
||
nrows,
|
||
ipiv.as_mut_slice(),
|
||
&mut info,
|
||
);
|
||
lapack_panic!(info);
|
||
|
||
LU { lu: m, p: ipiv }
|
||
}
|
||
|
||
/// Gets the lower-triangular matrix part of the decomposition.
|
||
#[inline]
|
||
pub fn l(&self) -> MatrixMN<N, R, DimMinimum<R, C>> {
|
||
let (nrows, ncols) = self.lu.data.shape();
|
||
let mut res = self.lu.columns_generic(0, nrows.min(ncols)).into_owned();
|
||
|
||
res.fill_upper_triangle(Zero::zero(), 1);
|
||
res.fill_diagonal(One::one());
|
||
|
||
res
|
||
}
|
||
|
||
/// Gets the upper-triangular matrix part of the decomposition.
|
||
#[inline]
|
||
pub fn u(&self) -> MatrixMN<N, DimMinimum<R, C>, C> {
|
||
let (nrows, ncols) = self.lu.data.shape();
|
||
let mut res = self.lu.rows_generic(0, nrows.min(ncols)).into_owned();
|
||
|
||
res.fill_lower_triangle(Zero::zero(), 1);
|
||
|
||
res
|
||
}
|
||
|
||
/// Gets the row permutation matrix of this decomposition.
|
||
///
|
||
/// Computing the permutation matrix explicitly is costly and usually not necessary.
|
||
/// To permute rows of a matrix or vector, use the method `self.permute(...)` instead.
|
||
#[inline]
|
||
pub fn p(&self) -> MatrixN<N, R> {
|
||
let (dim, _) = self.lu.data.shape();
|
||
let mut id = Matrix::identity_generic(dim, dim);
|
||
self.permute(&mut id);
|
||
|
||
id
|
||
}
|
||
|
||
// FIXME: when we support resizing a matrix, we could add unwrap_u/unwrap_l that would
|
||
// re-use the memory from the internal matrix!
|
||
|
||
/// Gets the LAPACK permutation indices.
|
||
#[inline]
|
||
pub fn permutation_indices(&self) -> &VectorN<i32, DimMinimum<R, C>> {
|
||
&self.p
|
||
}
|
||
|
||
/// Applies the permutation matrix to a given matrix or vector in-place.
|
||
#[inline]
|
||
pub fn permute<C2: Dim>(&self, rhs: &mut MatrixMN<N, R, C2>)
|
||
where DefaultAllocator: Allocator<N, R, C2> {
|
||
let (nrows, ncols) = rhs.shape();
|
||
|
||
N::xlaswp(
|
||
ncols as i32,
|
||
rhs.as_mut_slice(),
|
||
nrows as i32,
|
||
1,
|
||
self.p.len() as i32,
|
||
self.p.as_slice(),
|
||
-1,
|
||
);
|
||
}
|
||
|
||
fn generic_solve_mut<R2: Dim, C2: Dim>(&self, trans: u8, b: &mut MatrixMN<N, R2, C2>) -> bool
|
||
where DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2> {
|
||
let dim = self.lu.nrows();
|
||
|
||
assert!(
|
||
self.lu.is_square(),
|
||
"Unable to solve a set of under/over-determined equations."
|
||
);
|
||
assert!(
|
||
b.nrows() == dim,
|
||
"The number of rows of `b` must be equal to the dimension of the matrix `a`."
|
||
);
|
||
|
||
let nrhs = b.ncols() as i32;
|
||
let lda = dim as i32;
|
||
let ldb = dim as i32;
|
||
let mut info = 0;
|
||
|
||
N::xgetrs(
|
||
trans,
|
||
dim as i32,
|
||
nrhs,
|
||
self.lu.as_slice(),
|
||
lda,
|
||
self.p.as_slice(),
|
||
b.as_mut_slice(),
|
||
ldb,
|
||
&mut info,
|
||
);
|
||
lapack_test!(info)
|
||
}
|
||
|
||
/// Solves the linear system `self * x = b`, where `x` is the unknown to be determined.
|
||
pub fn solve<R2: Dim, C2: Dim, S2>(
|
||
&self,
|
||
b: &Matrix<N, R2, C2, S2>,
|
||
) -> Option<MatrixMN<N, R2, C2>>
|
||
where
|
||
S2: Storage<N, R2, C2>,
|
||
DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2>,
|
||
{
|
||
let mut res = b.clone_owned();
|
||
if self.generic_solve_mut(b'N', &mut res) {
|
||
Some(res)
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
|
||
/// Solves the linear system `self.transpose() * x = b`, where `x` is the unknown to be
|
||
/// determined.
|
||
pub fn solve_transpose<R2: Dim, C2: Dim, S2>(
|
||
&self,
|
||
b: &Matrix<N, R2, C2, S2>,
|
||
) -> Option<MatrixMN<N, R2, C2>>
|
||
where
|
||
S2: Storage<N, R2, C2>,
|
||
DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2>,
|
||
{
|
||
let mut res = b.clone_owned();
|
||
if self.generic_solve_mut(b'T', &mut res) {
|
||
Some(res)
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
|
||
/// Solves the linear system `self.conjugate_transpose() * x = b`, where `x` is the unknown to
|
||
/// be determined.
|
||
pub fn solve_conjugate_transpose<R2: Dim, C2: Dim, S2>(
|
||
&self,
|
||
b: &Matrix<N, R2, C2, S2>,
|
||
) -> Option<MatrixMN<N, R2, C2>>
|
||
where
|
||
S2: Storage<N, R2, C2>,
|
||
DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2>,
|
||
{
|
||
let mut res = b.clone_owned();
|
||
if self.generic_solve_mut(b'T', &mut res) {
|
||
Some(res)
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
|
||
/// Solves in-place the linear system `self * x = b`, where `x` is the unknown to be determined.
|
||
///
|
||
/// Returns `false` if no solution was found (the decomposed matrix is singular).
|
||
pub fn solve_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
|
||
where DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2> {
|
||
self.generic_solve_mut(b'N', b)
|
||
}
|
||
|
||
/// Solves in-place the linear system `self.transpose() * x = b`, where `x` is the unknown to be
|
||
/// determined.
|
||
///
|
||
/// Returns `false` if no solution was found (the decomposed matrix is singular).
|
||
pub fn solve_transpose_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
|
||
where DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2> {
|
||
self.generic_solve_mut(b'T', b)
|
||
}
|
||
|
||
/// Solves in-place the linear system `self.conjugate_transpose() * x = b`, where `x` is the unknown to
|
||
/// be determined.
|
||
///
|
||
/// Returns `false` if no solution was found (the decomposed matrix is singular).
|
||
pub fn solve_conjugate_transpose_mut<R2: Dim, C2: Dim>(
|
||
&self,
|
||
b: &mut MatrixMN<N, R2, C2>,
|
||
) -> bool
|
||
where
|
||
DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2>,
|
||
{
|
||
self.generic_solve_mut(b'T', b)
|
||
}
|
||
}
|
||
|
||
impl<N: LUScalar, D: Dim> LU<N, D, D>
|
||
where
|
||
N: Zero + One,
|
||
D: DimMin<D, Output = D>,
|
||
DefaultAllocator: Allocator<N, D, D> + Allocator<i32, D>,
|
||
{
|
||
/// Computes the inverse of the decomposed matrix.
|
||
pub fn inverse(mut self) -> Option<MatrixN<N, D>> {
|
||
let dim = self.lu.nrows() as i32;
|
||
let mut info = 0;
|
||
let lwork = N::xgetri_work_size(
|
||
dim,
|
||
self.lu.as_mut_slice(),
|
||
dim,
|
||
self.p.as_mut_slice(),
|
||
&mut info,
|
||
);
|
||
lapack_check!(info);
|
||
|
||
let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
|
||
|
||
N::xgetri(
|
||
dim,
|
||
self.lu.as_mut_slice(),
|
||
dim,
|
||
self.p.as_mut_slice(),
|
||
&mut work,
|
||
lwork,
|
||
&mut info,
|
||
);
|
||
lapack_check!(info);
|
||
|
||
Some(self.lu)
|
||
}
|
||
}
|
||
|
||
/*
|
||
*
|
||
* Lapack functions dispatch.
|
||
*
|
||
*/
|
||
/// Trait implemented by scalars for which Lapack implements the LU decomposition.
|
||
pub trait LUScalar: Scalar {
|
||
#[allow(missing_docs)]
|
||
fn xgetrf(m: i32, n: i32, a: &mut [Self], lda: i32, ipiv: &mut [i32], info: &mut i32);
|
||
#[allow(missing_docs)]
|
||
fn xlaswp(n: i32, a: &mut [Self], lda: i32, k1: i32, k2: i32, ipiv: &[i32], incx: i32);
|
||
#[allow(missing_docs)]
|
||
fn xgetrs(
|
||
trans: u8,
|
||
n: i32,
|
||
nrhs: i32,
|
||
a: &[Self],
|
||
lda: i32,
|
||
ipiv: &[i32],
|
||
b: &mut [Self],
|
||
ldb: i32,
|
||
info: &mut i32,
|
||
);
|
||
#[allow(missing_docs)]
|
||
fn xgetri(
|
||
n: i32,
|
||
a: &mut [Self],
|
||
lda: i32,
|
||
ipiv: &[i32],
|
||
work: &mut [Self],
|
||
lwork: i32,
|
||
info: &mut i32,
|
||
);
|
||
#[allow(missing_docs)]
|
||
fn xgetri_work_size(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32], info: &mut i32) -> i32;
|
||
}
|
||
|
||
macro_rules! lup_scalar_impl(
|
||
($N: ty, $xgetrf: path, $xlaswp: path, $xgetrs: path, $xgetri: path) => (
|
||
impl LUScalar for $N {
|
||
#[inline]
|
||
fn xgetrf(m: i32, n: i32, a: &mut [Self], lda: i32, ipiv: &mut [i32], info: &mut i32) {
|
||
unsafe { $xgetrf(m, n, a, lda, ipiv, info) }
|
||
}
|
||
|
||
#[inline]
|
||
fn xlaswp(n: i32, a: &mut [Self], lda: i32, k1: i32, k2: i32, ipiv: &[i32], incx: i32) {
|
||
unsafe { $xlaswp(n, a, lda, k1, k2, ipiv, incx) }
|
||
}
|
||
|
||
#[inline]
|
||
fn xgetrs(trans: u8, n: i32, nrhs: i32, a: &[Self], lda: i32, ipiv: &[i32],
|
||
b: &mut [Self], ldb: i32, info: &mut i32) {
|
||
unsafe { $xgetrs(trans, n, nrhs, a, lda, ipiv, b, ldb, info) }
|
||
}
|
||
|
||
#[inline]
|
||
fn xgetri(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32],
|
||
work: &mut [Self], lwork: i32, info: &mut i32) {
|
||
unsafe { $xgetri(n, a, lda, ipiv, work, lwork, info) }
|
||
}
|
||
|
||
#[inline]
|
||
fn xgetri_work_size(n: i32, a: &mut [Self], lda: i32, ipiv: &[i32], info: &mut i32) -> i32 {
|
||
let mut work = [ Zero::zero() ];
|
||
let lwork = -1 as i32;
|
||
|
||
unsafe { $xgetri(n, a, lda, ipiv, &mut work, lwork, info); }
|
||
ComplexHelper::real_part(work[0]) as i32
|
||
}
|
||
}
|
||
)
|
||
);
|
||
|
||
lup_scalar_impl!(
|
||
f32,
|
||
lapack::sgetrf,
|
||
lapack::slaswp,
|
||
lapack::sgetrs,
|
||
lapack::sgetri
|
||
);
|
||
lup_scalar_impl!(
|
||
f64,
|
||
lapack::dgetrf,
|
||
lapack::dlaswp,
|
||
lapack::dgetrs,
|
||
lapack::dgetri
|
||
);
|
||
lup_scalar_impl!(
|
||
Complex<f32>,
|
||
lapack::cgetrf,
|
||
lapack::claswp,
|
||
lapack::cgetrs,
|
||
lapack::cgetri
|
||
);
|
||
lup_scalar_impl!(
|
||
Complex<f64>,
|
||
lapack::zgetrf,
|
||
lapack::zlaswp,
|
||
lapack::zgetrs,
|
||
lapack::zgetri
|
||
);
|