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Add more general norms and metrics. 

Fix #258.
This commit is contained in:
sebcrozet 2018-12-09 11:21:24 +01:00
parent cc2a70664d
commit 660b868603
2 changed files with 254 additions and 87 deletions
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138
src/base/matrix.rs
View File

@ -493,6 +493,57 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
res
}
/// Folds a function `f` on each entry of `self`.
#[inline]
pub fn fold<Acc>(&self, init: Acc, mut f: impl FnMut(Acc, N) -> Acc) -> Acc {
let (nrows, ncols) = self.data.shape();
let mut res = init;
for j in 0..ncols.value() {
for i in 0..nrows.value() {
unsafe {
let a = *self.data.get_unchecked(i, j);
res = f(res, a)
}
}
}
res
}
/// Folds a function `f` on each pairs of entries from `self` and `rhs`.
#[inline]
pub fn zip_fold<N2, R2, C2, S2, Acc>(&self, rhs: &Matrix<N2, R2, C2, S2>, init: Acc, mut f: impl FnMut(Acc, N, N2) -> Acc) -> Acc
where
N2: Scalar,
R2: Dim,
C2: Dim,
S2: Storage<N2, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>
{
let (nrows, ncols) = self.data.shape();
let mut res = init;
assert!(
(nrows.value(), ncols.value()) == rhs.shape(),
"Matrix simultaneous traversal error: dimension mismatch."
);
for j in 0..ncols.value() {
for i in 0..nrows.value() {
unsafe {
let a = *self.data.get_unchecked(i, j);
let b = *rhs.data.get_unchecked(i, j);
res = f(res, a, b)
}
}
}
res
}
/// Transposes `self` and store the result into `out`.
#[inline]
pub fn transpose_to<R2, C2, SB>(&self, out: &mut Matrix<N, R2, C2, SB>)
@ -1251,67 +1302,6 @@ impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
}
}
impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
/// The squared L2 norm of this vector.
#[inline]
pub fn norm_squared(&self) -> N {
let mut res = N::zero();
for i in 0..self.ncols() {
let col = self.column(i);
res += col.dot(&col)
}
res
}
/// The L2 norm of this matrix.
#[inline]
pub fn norm(&self) -> N {
self.norm_squared().sqrt()
}
/// A synonym for the norm of this matrix.
///
/// Aka the length.
///
/// This function is simply implemented as a call to `norm()`
#[inline]
pub fn magnitude(&self) -> N {
self.norm()
}
/// A synonym for the squared norm of this matrix.
///
/// Aka the squared length.
///
/// This function is simply implemented as a call to `norm_squared()`
#[inline]
pub fn magnitude_squared(&self) -> N {
self.norm_squared()
}
/// Returns a normalized version of this matrix.
#[inline]
pub fn normalize(&self) -> MatrixMN<N, R, C>
where DefaultAllocator: Allocator<N, R, C> {
self / self.norm()
}
/// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
#[inline]
pub fn try_normalize(&self, min_norm: N) -> Option<MatrixMN<N, R, C>>
where DefaultAllocator: Allocator<N, R, C> {
let n = self.norm();
if n <= min_norm {
None
} else {
Some(self / n)
}
}
}
impl<N: Scalar + Zero + One + ClosedAdd + ClosedSub + ClosedMul, D: Dim, S: Storage<N, D>>
Vector<N, D, S>
{
@ -1386,32 +1376,6 @@ impl<N: Real, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
}
}
impl<N: Real, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
/// Normalizes this matrix in-place and returns its norm.
#[inline]
pub fn normalize_mut(&mut self) -> N {
let n = self.norm();
*self /= n;
n
}
/// Normalizes this matrix in-place or does nothing if its norm is smaller or equal to `eps`.
///
/// If the normalization succeeded, returns the old normal of this matrix.
#[inline]
pub fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
let n = self.norm();
if n <= min_norm {
None
} else {
*self /= n;
Some(n)
}
}
}
impl<N, R: Dim, C: Dim, S> AbsDiffEq for Unit<Matrix<N, R, C, S>>
where
N: Scalar + AbsDiffEq,

203
src/base/norm.rs Normal file
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@ -0,0 +1,203 @@
use num::{Signed, Zero};
use std::cmp::PartialOrd;
use allocator::Allocator;
use ::{Real, Scalar};
use storage::{Storage, StorageMut};
use base::{DefaultAllocator, Matrix, Dim, MatrixMN};
use constraint::{SameNumberOfRows, SameNumberOfColumns, ShapeConstraint};
// FIXME: this should be be a trait on alga?
pub trait Norm<N: Scalar> {
fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N
where R: Dim, C: Dim, S: Storage<N, R, C>;
fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N
where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>;
}
/// Euclidean norm.
pub struct EuclideanNorm;
/// Lp norm.
pub struct LpNorm(pub i32);
/// L-infinite norm aka. Chebytchev norm aka. uniform norm aka. suppremum norm.
pub struct UniformNorm;
impl<N: Real> Norm<N> for EuclideanNorm {
#[inline]
fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N
where R: Dim, C: Dim, S: Storage<N, R, C> {
m.norm_squared().sqrt()
}
#[inline]
fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N
where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
m1.zip_fold(m2, N::zero(), |acc, a, b| {
let diff = a - b;
acc + diff * diff
}).sqrt()
}
}
impl<N: Real> Norm<N> for LpNorm {
#[inline]
fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N
where R: Dim, C: Dim, S: Storage<N, R, C> {
m.fold(N::zero(), |a, b| {
a + b.abs().powi(self.0)
}).powf(::convert(1.0 / (self.0 as f64)))
}
#[inline]
fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N
where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
m1.zip_fold(m2, N::zero(), |acc, a, b| {
let diff = a - b;
acc + diff.abs().powi(self.0)
}).powf(::convert(1.0 / (self.0 as f64)))
}
}
impl<N: Scalar + PartialOrd + Signed> Norm<N> for UniformNorm {
#[inline]
fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N
where R: Dim, C: Dim, S: Storage<N, R, C> {
m.amax()
}
#[inline]
fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N
where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
m1.zip_fold(m2, N::zero(), |acc, a, b| {
let val = (a - b).abs();
if val > acc {
val
} else {
acc
}
})
}
}
impl<N: Real, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
/// The squared L2 norm of this vector.
#[inline]
pub fn norm_squared(&self) -> N {
let mut res = N::zero();
for i in 0..self.ncols() {
let col = self.column(i);
res += col.dot(&col)
}
res
}
/// The L2 norm of this matrix.
#[inline]
pub fn norm(&self) -> N {
self.norm_squared().sqrt()
}
/// Computes the metric distance between `self` and `rhs` using the Euclidean metric.
#[inline]
pub fn metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>) -> N
where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
self.apply_metric_distance(rhs, &EuclideanNorm)
}
#[inline]
pub fn apply_norm(&self, norm: &impl Norm<N>) -> N {
norm.norm(self)
}
#[inline]
pub fn apply_metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>, norm: &impl Norm<N>) -> N
where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
norm.metric_distance(self,rhs)
}
/// The Lp norm of this matrix.
#[inline]
pub fn lp_norm(&self, p: i32) -> N {
self.apply_norm(&LpNorm(p))
}
/// A synonym for the norm of this matrix.
///
/// Aka the length.
///
/// This function is simply implemented as a call to `norm()`
#[inline]
pub fn magnitude(&self) -> N {
self.norm()
}
/// A synonym for the squared norm of this matrix.
///
/// Aka the squared length.
///
/// This function is simply implemented as a call to `norm_squared()`
#[inline]
pub fn magnitude_squared(&self) -> N {
self.norm_squared()
}
/// Returns a normalized version of this matrix.
#[inline]
pub fn normalize(&self) -> MatrixMN<N, R, C>
where DefaultAllocator: Allocator<N, R, C> {
self / self.norm()
}
/// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
#[inline]
pub fn try_normalize(&self, min_norm: N) -> Option<MatrixMN<N, R, C>>
where DefaultAllocator: Allocator<N, R, C> {
let n = self.norm();
if n <= min_norm {
None
} else {
Some(self / n)
}
}
}
impl<N: Real, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
/// Normalizes this matrix in-place and returns its norm.
#[inline]
pub fn normalize_mut(&mut self) -> N {
let n = self.norm();
*self /= n;
n
}
/// Normalizes this matrix in-place or does nothing if its norm is smaller or equal to `eps`.
///
/// If the normalization succeeded, returns the old normal of this matrix.
#[inline]
pub fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
let n = self.norm();
if n <= min_norm {
None
} else {
*self /= n;
Some(n)
}
}
}