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//! Functions to compute the distance between vectors.
extern crate libc;
use self::libc::{c_int, c_double, c_float};
use matrix::*;
use norm::{L2Norm, Norm};
use blas::{cblas_daxpy, cblas_saxpy};
use geometry::Point2D;
pub trait DistancePoint2D<T> {
fn euclid(&self, other: &Point2D<T>) -> T;
}
macro_rules! distance_point2d_impl {
($($t:ty)*) => ($(
impl DistancePoint2D<$t> for Point2D<$t> {
fn euclid(&self, other: &Point2D<$t>) -> $t {
((self.x - other.x).powi(2) + (self.y - other.y).powi(2)).sqrt()
}
}
)*)
}
distance_point2d_impl!{ f32 f64 }
// ----------------------------------------------------------------------------
/// Computes the distance between two vectors.
pub trait Distance<T> {
/// Computes the distance between vector `a` and `b` and returns `None`
/// on failure.
fn compute(a: &[T], b: &[T]) -> Option<T>;
}
pub struct Euclid;
impl Distance<f64> for Euclid {
/// Computes the euclidean distance between the vector `a` and `b`.
///
/// Returns `None` if the two vectors have a different length.
///
/// # Implementation details
///
/// First the BLAS function `cblas_daxpy` is used to compute the
/// difference between the vectors. This requires O(n) additional space
/// if `n` is the number of elements of each vector. Then, the result
/// of the L2 norm of the difference is returned.
fn compute(a: &[f64], b: &[f64]) -> Option<f64> {
// TODO handling of NaN and stuff like this
if a.len() != b.len() {
return None;
}
// c = b.clone() does not work here because cblas_daxpy
// modifies the content of c and cloned() on a slice does
// not create a copy.
let c: Vec<f64> = b.to_vec();
unsafe {
cblas_daxpy(
a.len() as c_int,
-1.0 as c_double,
a.as_ptr() as *const c_double,
1 as c_int,
c.as_ptr() as *mut c_double,
1 as c_int
);
}
Some(L2Norm::compute(&c))
}
}
impl Distance<f32> for Euclid {
/// Computes the euclidean distance between the vector `a` and `b`.
///
/// Returns `None` if the two vectors have a different length.
///
/// # Implementation details
///
/// First the BLAS function `cblas_daxpy` is used to compute the
/// difference between the vectors. This requires O(n) additional space
/// if `n` is the number of elements of each vector. Then, the result
/// of the L2 norm of the difference is returned.
fn compute(a: &[f32], b: &[f32]) -> Option<f32> {
// TODO handling of NaN and stuff like this
if a.len() != b.len() {
return None;
}
// c = b.clone() does not work here because cblas_daxpy
// modifies the content of c and cloned() on a slice does
// not create a copy.
let c: Vec<f32> = b.to_vec();
unsafe {
cblas_saxpy(
a.len() as c_int,
-1.0 as c_float,
a.as_ptr() as *const c_float,
1 as c_int,
c.as_ptr() as *mut c_float,
1 as c_int
);
}
Some(L2Norm::compute(&c))
}
}
pub fn all_pair_distances(m: &Matrix<f64>) -> Matrix<f64> {
let mut r = Matrix::fill(0.0, m.rows(), m.rows());
// TODO handling of NaN and stuff like this
for (i, row1) in m.row_iter().enumerate() {
for (j, row2) in m.row_iter_at(i + 1).enumerate() {
let p = j + i + 1;
let d = Euclid::compute(row1, row2).unwrap();
r.set(i, p, d);
r.set(p, i, d);
}
}
r
}
#[cfg(test)]
mod tests {
use matrix::*;
use super::*;
use geometry::Point2D;
#[test]
fn test_euclid() {
let a = vec![1.0, 2.0, 3.0];
let b = vec![2.0, 5.0, 13.0];
let c = vec![2.0, 5.0, 13.0];
let d = vec![1.0, 2.0, 3.0];
assert!(Euclid::compute(&a, &b).unwrap() - 10.488088 <= 0.000001);
assert_eq!(b, c);
assert_eq!(a, d);
}
#[test]
fn test_all_pair_distances() {
let m = mat![1.0, 2.0; 5.0, 12.0; 13.0, 27.0];
let r = all_pair_distances(&m);
assert_eq!(r.rows(), m.rows());
assert_eq!(r.cols(), m.rows());
assert_eq!(*r.get(0, 0).unwrap(), 0.0);
assert_eq!(*r.get(1, 1).unwrap(), 0.0);
assert_eq!(*r.get(2, 2).unwrap(), 0.0);
assert!(*r.get(0, 1).unwrap() - 10.770 <= 0.001);
assert!(*r.get(0, 2).unwrap() - 27.731 <= 0.001);
assert!(*r.get(1, 0).unwrap() - 10.770 <= 0.001);
assert!(*r.get(2, 0).unwrap() - 27.731 <= 0.001);
assert!(*r.get(1, 2).unwrap() - 17.0 <= 0.001);
assert!(*r.get(2, 1).unwrap() - 17.0 <= 0.001);
}
#[test]
fn test_euclid_point2d() {
let a = Point2D::new(2.0, 8.0);
let b = Point2D::new(5.0, 12.0);
assert!(a.euclid(&b) - 5.0 < 0.00001);
let d = Point2D::new(2.0, 8.0);
assert_eq!(a.euclid(&d), 0.0);
}
}