D = VL_ALLDIST2(X,Y) returns the pairwise distance matrix D of the columns of S1 and S2, yielding

  D(i,j) = sum (X(:,i) - Y(:,j)).^2


VL_ALLDIST2(X) returns the pairwise distance matrix fo the columns of S, yielding

  D(i,j) = sum (X(:,i) - X(:,j)).^2


VL_ALLDIST2(...,'METRIC') changes the computed distance. Supported values for METRIC are

 METRIC  D(i,j)
--------------------------------------------------------
LINF   max |X  - Y|
L2     sum (X  - Y).^2
L1     sum |X  - Y|
L0     sum (X ~= Y)
CHI2   sum (X  - Y).^2 ./ (X + Y)
HELL   sum (X^.5 - Y^.5) .^ 2


(Notice that the standard definition of chi2 is half of what is computed here).

VL_ALLDIST2(...,'KERNEL') computes the following 'kernels' K:

 KERNEL  K(i,j)
---------------------------------------------------------
KL2    sum X .* Y
KL1    sum min (X, Y)
KCHI2  2 * sum (X .* Y) ./ (X + Y)
KHELL  (X .* Y) .^ 0.5


The constant are chosen so that D(i,j) = K(i,i) + K(j,j) - 2 K(i,j) where D is the metric corresponding to the kenrel (if the arguments are non-negative vectors). Each kernel can be interpreted as the inner product inducing the corresponding metric in an embedding of the real space into an approrpiate reproducing Kenrel Hilbert space.

VL_ALLDIST2() supports several storage classes. X and Y must have the same storage class. The sotrage class of D is promoted to reduce the chance of overvlow, but this is not checked.

  X & Y class      D class
---------------------------
UINT8            UINT32
INT8             INT32
UINT16           UINT32
INT16            INT32
UINT32           UINT32
INT32            INT32
SINGLE           SINGLE
DOUBLE           DOUBLE


Warning: Both chi2 and kchi2 use integer math when presented with integer data types. This can easily result in zeros where you did not expect them.