Math and Statistics

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

Integration

Solving Equations

Minimization

Linear Regression

Polynomial Fit

Surface Fit

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

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 Recipes 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.

IDL Demo Online Help (October 11, 2006)