Name

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      QTRAP

Purpose

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      Integrate using trapezoidal rule to specified accuracy.

Explanation

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      Integrate a function to specified accuracy using the extended
      trapezoidal rule. Adapted from Numerical Recipes (1992, 2nd edition),
      Section 4.2.

Calling Sequence

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      QTRAP, func, A, B, S, [EPS = , MAX_ITER =, _EXTRA = ]

Inputs

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      func - scalar string giving name of function of one variable to
              be integrated
      A,B - numeric scalars giving the lower and upper bound of the
              integration

Outputs

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      S - Scalar giving the approximation to the integral of the specified
              function between A and B.
  OPTIONAL KEYWORD PARAMETERS:
      EPS - scalar specify the fractional accuracy before ending the
            iteration. Default = 1E-6
      MAX_ITER - Integer specifying the total number iterations at which
              QTRAP will terminate even if the specified accuracy has not yet
              been met. The maximum number of function evaluations will
              be 2^(MAX_ITER). Default value is MAX_ITER = 20
      Any other keywords are passed directly to the user-supplied function
      via the _EXTRA facility.

Notes

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      QTRAP is robust way of doing integrals that are not very smooth. If the
      function has a continuous 3rd derivative then the function QSIMP will
          likely be more efficient at performing the integral.

Example

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      Compute the integral of sin(x) from 0 to !PI/3.
   
      IDL> QTRAP, 'sin', 0, !PI/3, S & print,S
 
      The value obtained should be cos(!PI/3) = 0.5

Procedures Called

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      TRAPZD, ZPARCHECK

Revision History

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      W. Landsman ST Systems Co. August, 1991
      Continue after Max Iter warning message, W. Landsman March 1996
      Converted to IDL V5.0 W. Landsman September 1997
      Pass keyword to function via _EXTRA facility W. Landsman July 1999