Program:      GRADIENT

Purpose:      Calculates the gradients or the laplacian of a 
              map, using three by three sized templates.

Category:     CALCULATION

File:         gradient.c

Author:       Fred Lahuis

Keywords:

   INSET=     Set and subset(s) to be used.
              The maximum number of subsets is 50 and the maximun
              number of axis 10 (if desirable these values can be
              altered). The dimension of the subsets has to be 2.

   BOX=       Area to be used.  		        [whole subset]

   GRADIENT=  The kind of output wanted.                           [1]
			1 --> x and y gradient
			2 --> x gradient only
			3 --> y gradient only
			4 --> gradient and gradient-direction phi
                              (in radians anticlockwise from
                              positive x-axis)
			5 --> gradient only
			6 --> laplacian

   ASET=      First output set.
              If no name is entered <insetname>_xxx will be made,
              where xxx is gradx if gradient is 1 or 3, grady if
              gradient is 2, grad if gradient is 4 or 5.

   BSET=      Second output set, if GRAD= 1 or 4.
              If ASET is not entered <insetname>_xxx will be made,
              where xxx is grady if gradient is 1 and phi if gradient 
              is 4, else BSET is asked and a setname must be entered.

**BLANK=      Value used to substitute possible blanks             [0]
              in the map.

**CONSTANT=   Constant used in the gradient templates.       [sqrt(2)]
              Usually a value between 1 and 2 is used.

**FULL=       To determine the size of the output set(s).        [Y]/N
                    Y --> size of the input set
                    N --> size of the box

**SIGMA=      Value below which the gradient is                    [0]
              set to zero if its absolute value is less then this.

Comments:
              The values for BLANK, CONSTANT and SIGMA can be altered
              while the program is running, e.g. to enter a different 
              value for the next subset while the program is working
              on the present subset.

Description: 
              GRADIENT calculates the gradients in a map using three
              by three templates over the set and normalizing the
              result.

		             -1 0 1	                1  c  1
		(x templ.)   -c 0 c	   (y templ.)   0  0  0 
		       	     -1 0 1	               -1 -c -1

              The gradient (GRAD= 4 or 5) is taken as 

			grad = sqrt( sqr(buf_a) + sqr(buf_b) ).

              The laplacian is an approximation to the mathematical 
              laplacian. It is represented by a 'circular' template
              with a central value of -1 and four surrounding values
              of 0.25.

Comments:     Blank values in the map are treated as if being equal
              to zero, unless a value is given by BLANK, which is then
              used instead.

              If an existing set is overwritten the data outside
              the box is not removed.

              GRADIENT also updates the header item NOISE. This value is
              taken as the spread in data points, so to have a first
              guess of the true noise in the map.
              
Updates:      April 8 1991: FL Document created.
              Feb 25 1991:  FL Last update.