A C library of numerical methods in computational science, designed to be fast, friendly, and accurate.

Some methods Gaisan implements or plans to implement:

• Finite difference
  • Forward difference
  • Backward difference
  • Central difference
• Rootfinding
  • Bisection
  • Fixed-point iteration
  • Newton's method
• Optimisation
  • Golden section search
  • Newton's method
• Linear systems
  • Gaussian elimination
• IVPs
  • Euler's method
• BVPs
  • Shooting method
  • Finite difference
• Monte Carlo methods
  • Integration

To build the library, simply

make

To generate documentation, run

make docs

To build the examples (in the examples/ directory), run

make examples

Gaisan contains full, working examples in the examples/ directory; however, here are some snippets:

Solving IVPs is easy in Gaisan. Here's a trivial example using Euler's method:

long double f(long double t, long double y) {return t;}

/* ... */

/* solve y'=t from 0 to 10, with y(0)=1 (taking 1/2 steps) */
long double** solution = euler(0, 10, 1, &f, 0.5);

That's it! Gaisan even provides convenient helper functions for working with numerical data. Let's print a table of values for our solution:

char* headings[3] = {"t", "y", NULL};
print_table(headings, solution, 20); /* print_table needs number of steps to print (i.e. 10*0.5=20) */    

This outputs:

|         t|      y(t)|
--------------------
|00.000000|01.000000|
|00.500000|01.250000|
|01.000000|01.750000|
|01.500000|02.500000|
|02.000000|03.500000|
|02.500000|04.750000|
|03.000000|06.250000|
|03.500000|08.000000|
|04.000000|10.000000|
|04.500000|12.250000|
|05.000000|14.750000|
|05.500000|17.500000|
|06.000000|20.500000|
|06.500000|23.750000|
|07.000000|27.250000|
|07.500000|31.000000|
|08.000000|35.000000|
|08.500000|39.250000|
|09.000000|43.750000|
|09.500000|48.500000|

Gaisan also makes solving linear systems a breeze. Once again, we use a naive method: Gaussian elimination.

Firstly, we need to allocate space for our matrices:

Matrix* A = matrix_init(3, 3);
Matrix* b = matrix_init(3, 1);

Note that this is equivalent to the following Matlab code:

A = zeros([3 3]);
b = zeros([3 1]);

Now we need to populate our matrices with our coefficients and RHS solutions. In practice, this can be done more gracefully, but we'll hard code our values for now:

/* coefficient matrix */
A->cells[0][0] = 1.0;
A->cells[0][1] = 2.0;
A->cells[0][2] = -1.0;
A->cells[1][0] = 2.0;
A->cells[1][1] = 1.0;
A->cells[1][2] = -2.0;
A->cells[2][0] = -3.0;
A->cells[2][1] = 1.0;
A->cells[2][2] = 1.0;

/* RHS vector */
b->cells[0][0] = 3.0;
b->cells[1][0] = 3.0;
b->cells[2][0] = -6.0;

Now for the actual solution:

Matrix* x = gauss_elim(A, b);

That's it!

Just like our last example, Gaisan also provides (an even nicer) helper method for printing our data:

print_matrix(x);

Which outputs:

 0.000000
 3.000000
-3.000000