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GAUSSIAN

GAUSSIAN

Name


      GAUSSIAN

Purpose


      Compute the 1-d Gaussian function and optionally the derivative

Explanation


      Compute the 1-D Gaussian function and optionally the derivative
      at an array of points.

Calling Sequence


      y = gaussian( xi, parms,[ pderiv ])

Inputs


      xi = array, independent variable of Gaussian function.
      parms = parameters of Gaussian, 2, 3 or 4 element array:
              parms[0] = maximum value (factor) of Gaussian,
              parms[1] = mean value (center) of Gaussian,
              parms[2] = standard deviation (sigma) of Gaussian.
              (if parms has only 2 elements then sigma taken from previous
              call to gaussian(), which is stored in a common block).
              parms[3] = optional, constant offset added to Gaussian.

Output


      y - Function returns array of Gaussian evaluated at xi. Values will
            be floating pt. (even if xi is double) unless the /DOUBLE keyword
            is set.

Optional Input


      /DOUBLE - set this keyword to return double precision for both
            the function values and (optionally) the partial derivatives.

Optional Output


      pderiv = [N,3] or [N,4] output array of partial derivatives,
              computed only if parameter is present in call.
              pderiv[*,i] = partial derivative at all xi absisca values
              with respect to parms[i], i=0,1,2,[3].

Example


      Evaulate a Gaussian centered at x=0, with sigma=1, and a peak value
      of 10 at the points 0.5 and 1.5. Also compute the derivative
      IDL> f = gaussian( [0.5,1.5], [10,0,1], DERIV )
      ==> f= [8.825,3.25]. DERIV will be a 2 x 3 array containing the
      numerical derivative at the two points with respect to the 3 parameters.
 

Common Blocks


      None

History


      Written, Frank Varosi NASA/GSFC 1992.
      Converted to IDL V5.0 W. Landsman September 1997
      Use machar() for machine precision, added /DOUBLE keyword,
      add optional constant 4th parameter W. Landsman November 2001



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