Bubblesoft Maths Library: Demonstration Software

The Bubblesoft Maths library covers a wide range of operations. This demonstration software samples a tiny part, and is intended to give a feel for the quality and ease of use of the library, rather than to represent the full capabilities included.

If you are fortunate enough to be using the `LINUX' operating system on an x86 processor, you will be able to use the example executable programs (ELF format). Otherwise, you can still try out the software by compiling the source code extracts provided.

Solution of a matrix equation

Program matsol solves a matrix equation
A x = y
for x (a vector) given A (a matrix) and y (a vector). A may have more rows than columns (i.e. the problem may be overdetermined), in which case a least-squares solution is produced.

The program uses a library routine which solves the equation using Givens rotations to make A upper-triangular then back-substitution to find x.

Usage

At a command prompt, type

matsol < matsol.dat

to read data from file matsol.dat. The solution is written to standard output.

Input data

ASCII (text), free-format:

number_of_rows number_of_columns
For each row i in A:
   For each column j in A:
      A(i,j)
For each element i of y:
   y(i)

e.g.

2 2
1.5 2.3
-5.8 9.0
-1.2
7.3

Files

matsol.f: program source code
matsol.dat: example input data
matsol.out: output from example data
matsol.gz: gzipped executable (LINUX ELF format)

Fitting data with a polynomial

Program polyfit fits a set of (x,y) data points with a polynomial
y = sum_i=1ⁿ c_ix^i-1.
Each point has a weighting, which can reflect the uncertainty in the data (e.g. setting the weight w to 1/s where s is the standard deviation for the point).

The program uses a library routine which performs the fit by building an overdetermined matrix describing the problem, and solving to find a least-squares solution for the coefficients c_i.

The program can also plot the data and polynomial fit, using calls to the Bubblesoft Graphics Library. The executable provided calls the X-Windows version of this library.

If you're interested in details, the sample data was generated by taking the function
y = 0.56 - 2.8 x + 3.5 x²
of a set of x-values, and adding random noise with uniform distribution from 0 to 0.2.

Usage

At a command prompt, type

polyfit < polyfit.dat

to read data from file polyfit.dat. The coefficients c_i and residue are written to standard output, and a window opened to display the data and fit if X-Windows is running.

Input data

ASCII (text), free-format:

number_of_data_points
For each data point:
   x y weight
number_of_polynomial_coefficients
xmin xmax ymin ymax
number_of_line_segments

where

The number of polynomial coefficients is the order of the polynomial + 1, e.g. 3 for a quadratic.
xmin etc are the x and y limits for the graphical display.
The polynomial is drawn as a set of straight line segments. The number_of_line_segments tells the program how many to use. The higher the number, the smoother the curve.

e.g.

5
0.5 0.6
0.6 0.75
0.7 0.9
0.8 0.89
0.9 0.95
3
0.0 1.0 0.0 1.0
100

Files

polyfit.f: program source code
polyfit.dat: example input data
polyfit.out: output from example data
polyfit.gif: display from example data
polyfit.gz: gzipped executable (LINUX ELF format)

Additional source code

If you wish to compile the demonstration programs yourself, you may need the following files:

Makefile for UNIX systems.
mathslib.f: an extract of the library source code, allowing the demonstration programs to be compiled.

To compile the programs:

Put all source code in a single directory.
If you have access to the Bubblesoft maths and graphics libraries, make sure that the Makefile searches for them in the correct directory. Otherwise, you will only be able to build the `no library' versions, matsol_nolib and datafit_nolib.
Type make (or make program_name, where program_name is one or more of the program names).