Add pairwise distance computation in condensed form for symmetric metrics.

Author: lucabrivio

README.md

@@ -93,7 +93,13 @@ R = pairwise(dist, X)
 ```
 
 This statement will result in an ``m-by-m`` matrix, where ``R[i,j]`` is the distance between ``X[:,i]`` and ``X[:,j]``.
-``pairwise(dist, X)`` is typically more efficient than ``pairwise(dist, X, X)``, as the former will take advantage of the symmetry when ``dist`` is a semi-metric (including metric).
+``pairwise(dist, X)`` is typically more efficient than ``pairwise(dist, X, X)``, as the former will take advantage of the symmetry when ``dist`` is a semi-metric (including metric). You can also compute symmetric distances in a condensed vector representation:
+
+```julia
+r = cond_pairwise(dist, X)
+```
+
+This will return a vector ``r`` of length ``n * (n - 1) / 2``, containing the corresponding matrix elements arranged in the order ``(2,1), (3,1), ..., (m,1), (3,2), ..., (m,2), ..., (m,m–1)``.
 
 #### Computing column-wise and pairwise distances inplace
 
@@ -103,9 +109,10 @@ If the vector/matrix to store the results are pre-allocated, you may use the sto
 colwise!(r, dist, X, Y)
 pairwise!(R, dist, X, Y)
 pairwise!(R, dist, X)
+pairwise!(r, dist, X)
 ```
 
-Please pay attention to the difference, the functions for inplace computation are ``colwise!`` and ``pairwise!`` (instead of ``colwise`` and ``pairwise``).
+Please pay attention to the difference, the functions for inplace computation are ``colwise!`` and ``pairwise!`` (instead of ``colwise`` and ``pairwise``/``cond_pairwise``).
 
 
 ## Distance type hierarchy

src/Distances.jl

@@ -12,6 +12,7 @@ export
     result_type,
     colwise,
     pairwise,
+    cond_pairwise,
     colwise!,
     pairwise!,
     evaluate,

src/generic.jl

@@ -126,3 +126,25 @@ function pairwise(metric::PreMetric, a::AbstractMatrix)
     r = Matrix{result_type(metric, a, a)}(n, n)
     pairwise!(r, metric, a)
 end
+
+# Generic pairwise evaluation to a condensed form, for symmetrical distances
+
+function pairwise!(r::AbstractVector, metric::SemiMetric, a::AbstractMatrix)
+    n = size(a, 2)
+    length(r) == div((n * (n - 1)), 2) || throw(DimensionMismatch("Incorrect size of r."))
+    k = 1
+    for j = 1:n
+        aj = view(a, :, j)
+        for i = (j + 1):n
+            @inbounds r[k] = evaluate(metric, view(a, :, i), aj)
+            k += 1
+        end
+    end
+    r
+end
+
+function cond_pairwise(metric::SemiMetric, a::AbstractMatrix)
+    n = size(a, 2)
+    r = Vector{result_type(metric, a, a)}(div(n * (n - 1), 2))
+    pairwise!(r, metric, a)
+end