## Delta functions and related

## Dirac Delta ``function'' (actually a distribution)
## Defined by Intergral_I(f*DiracDelta) = f(0) for I=[a,b], where
## a<0<=b.

## Discrete Delta
## Takes a vector v and returns 1 if any entry is non-zero, 0 otherwise
## FIXME: Is this right?
## FIXME: this works fine for vectors, but I need to cast matrices
# as vectors to get it to work for matrices.
function DiscreteDelta(v) = KroneckerDelta([0,v])
protect("DiscreteDelta");
SetHelp("DiscreteDelta","functions","Returns 1 iff all elements are zero");

## Kronecker Delta
## Takes a vector v and returns 1 if all entries are equal,
## 0 otherwise
function KroneckerDelta(v) = 
 (
  test_value=v@(1);
  for i in v do (
    if i != test_value then return 0
  );
  1
 )
protect("KroneckerDelta");
SetHelp("KroneckerDelta","functions","Returns 1 iff all elements are equal");

## Unit Step Function
## The integral of the Dirac Delta function
## FIXME: should have option to make UnitStep(0) be undefined
function UnitStep(x) = if (x<0) then 0 else 1
protect("UnitStep");
SetHelp("UnitStep","functions","The unit step function = 0 for x<0, 1 otherwise.  This is the integral of the Dirac Delta function.");