Move the `eigen_qr` function behind the `EigenQR` trait.

This simplifies generic programming.
This commit is contained in:
Sébastien Crozet 2014-10-26 17:24:33 +01:00
parent 27be1f0651
commit 171576e2a0
7 changed files with 47 additions and 17 deletions

View File

@ -129,6 +129,7 @@ pub use traits::{
Diag,
Dim,
Dot,
EigenQR,
Eye,
FloatPnt,
FloatVec,
@ -178,7 +179,6 @@ pub use structs::{
pub use linalg::{
qr,
eigen_qr,
householder_matrix
};
@ -875,6 +875,15 @@ pub fn mean<N, M: Mean<N>>(observations: &M) -> N {
Mean::mean(observations)
}
/*
* EigenQR<N, V>
*/
/// Computes the eigenvalues and eigenvectors of a square matrix usin the QR algorithm.
#[inline(always)]
pub fn eigen_qr<N, V, M: EigenQR<N, V>>(m: &M, eps: &N, niter: uint) -> (M, V) {
EigenQR::eigen_qr(m, eps, niter)
}
//
//
// Structure

View File

@ -76,12 +76,9 @@ pub fn qr<N, V, M>(m: &M) -> (M, M)
pub fn eigen_qr<N, V, VS, M>(m: &M, eps: &N, niter: uint) -> (M, V)
where N: Float,
VS: Indexable<uint, N> + Norm<N>,
M: Indexable<(uint, uint), N> + SquareMat<N, V> + ColSlice<VS> + ApproxEq<N> + Clone {
let (rows, cols) = m.shape();
assert!(rows == cols, "The matrix being decomposed must be square.");
let mut eigenvectors: M = Eye::new_identity(rows);
M: Indexable<(uint, uint), N> + SquareMat<N, V> + Add<M, M> + Sub<M, M> + ColSlice<VS> +
ApproxEq<N> + Clone {
let mut eigenvectors: M = ::one::<M>();
let mut eigenvalues = m.clone();
// let mut shifter: M = Eye::new_identity(rows);
@ -89,7 +86,7 @@ pub fn eigen_qr<N, V, VS, M>(m: &M, eps: &N, niter: uint) -> (M, V)
for _ in range(0, niter) {
let mut stop = true;
for j in range(0, cols) {
for j in range(0, ::dim::<M>()) {
for i in range(0, j) {
if unsafe { eigenvalues.unsafe_at((i, j)) }.abs() >= *eps {
stop = false;
@ -97,7 +94,7 @@ pub fn eigen_qr<N, V, VS, M>(m: &M, eps: &N, niter: uint) -> (M, V)
}
}
for i in range(j + 1, rows) {
for i in range(j + 1, ::dim::<M>()) {
if unsafe { eigenvalues.unsafe_at((i, j)) }.abs() >= *eps {
stop = false;
break;

View File

@ -13,8 +13,9 @@ use structs::dvec::{DVec1, DVec2, DVec3, DVec4, DVec5, DVec6};
use traits::structure::{Cast, Row, Col, Iterable, IterableMut, Dim, Indexable,
Eye, ColSlice, RowSlice, Diag, Shape};
use traits::operations::{Absolute, Transpose, Inv, Outer};
use traits::operations::{Absolute, Transpose, Inv, Outer, EigenQR};
use traits::geometry::{ToHomogeneous, FromHomogeneous, Orig};
use linalg;
/// Special identity matrix. All its operation are no-ops.
@ -128,6 +129,7 @@ diag_impl!(Mat1, Vec1, 1)
to_homogeneous_impl!(Mat1, Mat2, 1, 2)
from_homogeneous_impl!(Mat1, Mat2, 1, 2)
outer_impl!(Vec1, Mat1)
eigen_qr_impl!(Mat1, Vec1)
/// Square matrix of dimension 2.
#[deriving(Eq, PartialEq, Encodable, Decodable, Clone, Hash, Rand, Zero, Show)]
@ -231,6 +233,7 @@ diag_impl!(Mat2, Vec2, 2)
to_homogeneous_impl!(Mat2, Mat3, 2, 3)
from_homogeneous_impl!(Mat2, Mat3, 2, 3)
outer_impl!(Vec2, Mat2)
eigen_qr_impl!(Mat2, Vec2)
/// Square matrix of dimension 3.
#[deriving(Eq, PartialEq, Encodable, Decodable, Clone, Hash, Rand, Zero, Show)]
@ -348,6 +351,7 @@ diag_impl!(Mat3, Vec3, 3)
to_homogeneous_impl!(Mat3, Mat4, 3, 4)
from_homogeneous_impl!(Mat3, Mat4, 3, 4)
outer_impl!(Vec3, Mat3)
eigen_qr_impl!(Mat3, Vec3)
/// Square matrix of dimension 4.
#[deriving(Eq, PartialEq, Encodable, Decodable, Clone, Hash, Rand, Zero, Show)]
@ -519,6 +523,7 @@ diag_impl!(Mat4, Vec4, 4)
to_homogeneous_impl!(Mat4, Mat5, 4, 5)
from_homogeneous_impl!(Mat4, Mat5, 4, 5)
outer_impl!(Vec4, Mat4)
eigen_qr_impl!(Mat4, Vec4)
/// Square matrix of dimension 5.
#[deriving(Eq, PartialEq, Encodable, Decodable, Clone, Hash, Rand, Zero, Show)]
@ -706,6 +711,7 @@ diag_impl!(Mat5, Vec5, 5)
to_homogeneous_impl!(Mat5, Mat6, 5, 6)
from_homogeneous_impl!(Mat5, Mat6, 5, 6)
outer_impl!(Vec5, Mat5)
eigen_qr_impl!(Mat5, Vec5)
/// Square matrix of dimension 6.
#[deriving(Eq, PartialEq, Encodable, Decodable, Clone, Hash, Rand, Zero, Show)]
@ -943,3 +949,4 @@ col_slice_impl!(Mat6, Vec6, DVec6, 6)
row_slice_impl!(Mat6, Vec6, DVec6, 6)
diag_impl!(Mat6, Vec6, 6)
outer_impl!(Vec6, Mat6)
eigen_qr_impl!(Mat6, Vec6)

View File

@ -638,3 +638,14 @@ macro_rules! outer_impl(
}
)
)
macro_rules! eigen_qr_impl(
($t: ident, $v: ident) => (
impl<N> EigenQR<N, $v<N>> for $t<N>
where N: Float + ApproxEq<N> + Clone {
fn eigen_qr(m: &$t<N>, eps: &N, niter: uint) -> ($t<N>, $v<N>) {
linalg::eigen_qr(m, eps, niter)
}
}
)
)

View File

@ -9,7 +9,7 @@ pub use traits::structure::{FloatVec, FloatPnt, Basis, Cast, Col, Dim, Indexable
ColSlice, RowSlice, Diag, Eye, Shape};
pub use traits::operations::{Absolute, ApproxEq, Axpy, Cov, Det, Inv, LMul, Mean, Outer, POrd,
RMul, ScalarAdd, ScalarSub, ScalarMul, ScalarDiv, Transpose};
RMul, ScalarAdd, ScalarSub, ScalarMul, ScalarDiv, Transpose, EigenQR};
pub use traits::operations::{POrdering, PartialLess, PartialEqual, PartialGreater, NotComparable};
pub mod geometry;

View File

@ -1,6 +1,6 @@
//! Low level operations on vectors and matrices.
use traits::structure::SquareMat;
/// Result of a partial ordering.
#[deriving(Eq, PartialEq, Encodable, Decodable, Clone, Show)]
@ -250,6 +250,12 @@ pub trait Mean<N> {
fn mean(v: &Self) -> N;
}
/// Trait for computing the eigenvector and eigenvalues of a square matrix usin the QR algorithm.
pub trait EigenQR<N, V>: SquareMat<N, V> {
/// Computes the eigenvectors and eigenvalues of this matrix.
fn eigen_qr(m: &Self, eps: &N, niter: uint) -> (Self, V);
}
// /// Cholesky decomposition.
// pub trait Chol {

View File

@ -1,8 +1,8 @@
//! Traits giving structural informations on linear algebra objects or the space they live in.
use std::num::Zero;
use std::num::{Zero, One};
use std::slice::{Items, MutItems};
use traits::operations::{RMul, LMul, Axpy, Transpose};
use traits::operations::{RMul, LMul, Axpy, Transpose, Inv};
use traits::geometry::{Dot, Norm, Orig};
/// Traits of objects which can be created from an object of type `T`.
@ -21,12 +21,12 @@ impl<N, M, R, C> Mat<N, R, C> for M
}
/// Trait implemented by square matrices.
pub trait SquareMat<N, V>: Mat<N, V, V> + Mul<Self, Self> + Eye + Transpose + Add<Self, Self> +
Sub<Self, Self> + Diag<V> {
pub trait SquareMat<N, V>: Mat<N, V, V> + Mul<Self, Self> + Eye + Transpose + Diag<V> + Inv + Dim +
One {
}
impl<N, V, M> SquareMat<N, V> for M
where M: Mat<N, V, V> + Mul<M, M> + Eye + Transpose + Add<M, M> + Sub<M, M> + Diag<V> {
where M: Mat<N, V, V> + Mul<M, M> + Eye + Transpose + Diag<V> + Inv + Dim + One {
}
/// Trait for constructing the identity matrix