'''MakeConvolutionFormula.py
'''

def makeConvolutionFormula(kernel):
  nrows = len(kernel)
  ncols = len(kernel[0])
  midx = ncols / 2   # (midx, midy) is the origin of the kernel.
  midy = nrows / 2
  f = ""             # The formula starts out empty.
  dy = - midy        # Starting displacement for y
  for row in kernel: # Loop over rows.
    signdy = sign(dy)
    dx = - midx      # Starting displacement for x
    for elt in row:  # Loop over columns.
      signdx = sign(dx)
      if dx==0: dxExpression = ""
      else: dxExpression = signdx+str(abs(dx))
      if dy==0: dyExpression = ""
      else: dyExpression = signdy+str(abs(dy))
      if elt==0: continue  # if elt is 0, don't even 
                           # include the pixel expression.
      pixelExpression = "S1(x"+dxExpression+",y"+dyExpression+")"
      if elt==1:
        coefficientExpression = "+"
      elif elt == -1:
        coefficientExpression = "-"
      else:
        coefficientExpression = sign(elt)+str(abs(elt))+"*"
      f += coefficientExpression + pixelExpression
      dx += 1
    dy += 1
  if f[0]=='+': return f[1:]
  else: return f

def sign(n):
  if n < 0.0: return '-'
  else: return '+'

def test():
  sampleInput =\
  [[-1, -2, -1],\
   [ 0,  0,  0],\
   [ 1,  2,  1]]

  formula = makeConvolutionFormula(sampleInput)
  print "The formula is:"
  print formula

test()