WELCOME TO THE MATHEMATICS AND STATISTICS DEMO 


   IDL's mathematics and statistics tools are designed
   for use in a wide variety of disciplines. This demo
   introduces 6 features.


   MENU OPTIONS
   ------------

   File Menu:
      Select "Quit" to exit the Mathematics and 
      Statistics Demo and return to the IDL Demo
      main screen.

   About Menu:
      Select "About mathematics and statistics" for
      information about the Mathematics and Statistics
      Demo.


   FEATURES
   --------

   <<Integration>> radio button

      The INT_TABULATED function uses a fifth-order 
      Newton-Cotes integration formula and 
      neighborhood spline curve-fitting to produce 
      integrations of tabulated data (discrete 
      points). This is one of the most accurate 
      integration techniques available.

      area = INT_TABULATED(time, amplitude)

      You can also use IDL to integrate functions 
      that have algebraic singularities and asymptotic
      behavior.

      <<Generate new data>> button
         Creates a new set of data.

   <<Solving Equations>> radio button

      Dozens of "Numerical Recipes" library routines 
      for performing complex mathematical computations
      are integrated into IDL.

      For example, the NR_NEWT function solves systems
      of non-linear equations. Multiple solutions can
      be found by starting the NR_NEWT algorithm at 
      different initial values. The black markers show
      the locations of the initial guesses. The white 
      markers show the solutions to the non-linear
      system of equations.  The solutions lie on the 
      intersection of the three surfaces:

      z = -(x*x - y - 4) (Bottom surface - blue)
      z = 0              (Middle surface - green)
      z = x*x + y*y - 8  (Top surface - red)

      The Numerical Recipes algorithms are used by 
      permission and are taken from the book 
      "Numerical Recipes in C, The Art of Scientific
      Computing" (second edition) by: William H. Press,
      Saul A. Teukolsky, William T. Vetterling, and
      Brian P. Flannery.


   <<Minimization>> radio button

      The IDL Numerical Recipies routine NR_POWELL can 
      be used to find the local minimum of a function 
      of 'n' variables. In this demo, clicking on the 
      plot identifies the nearest local minimum of the 
      function:

      y=SIN(SIN(x^2)-COS(x))+COS(SIN(x)+SIN(x)^2)']


   <<Linear regression>> radio button

      The "Method of Least Absolute Deviation" (the 
      plot on the right) is used to accurately fit a 
      curve through data. This curve fitting method, 
      unlike "least-square" fitting (the plot on the 
      left) is not adversely affected by outlying 
      points.

      <<Number of Points Above>> slider
         Sets the number of outliers above the 
         main cluster.

      <<Number of Points Below>> slider
         Sets the number of outliers below the
         main cluster.
 
   <<Polynomial Fit>> radio button

      The "POLY_FIT" function fits a least-square 
      polynomial curve through scattered data points.

      <<Number of points>> slider
         Sets the number of data points.

      <<Degree>> slider
         Sets the polynomial degree.

   <<Surface Fit>> radio button
       The MIN_CURVE_SURF function can be used to fit a
       minimum curvature surface through irregularly-
       gridded 3D data.

       <<Number of Points>>
          Sets the number of data points.