https://github.com/jmcph4/gaisan
Fast numerical methods in computational science
https://github.com/jmcph4/gaisan
bisection computational-science euler finite-difference gaisan gauss-elimination gauss-jordan gauss-seidel golden-section-search horner ivp monte-carlo numerical-algorithms numerical-analysis numerical-integration numerical-methods numerical-optimization ode ode-solver root-finding
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Fast numerical methods in computational science
- Host: GitHub
- URL: https://github.com/jmcph4/gaisan
- Owner: jmcph4
- License: mit
- Created: 2017-10-26T10:35:19.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2019-01-01T04:56:44.000Z (over 6 years ago)
- Last Synced: 2025-02-16T00:44:44.770Z (3 months ago)
- Topics: bisection, computational-science, euler, finite-difference, gaisan, gauss-elimination, gauss-jordan, gauss-seidel, golden-section-search, horner, ivp, monte-carlo, numerical-algorithms, numerical-analysis, numerical-integration, numerical-methods, numerical-optimization, ode, ode-solver, root-finding
- Language: C
- Size: 62.5 KB
- Stars: 1
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Gaisan - fast numerical methods in computational science #
---
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
## Build ##
To build the library, simply
make
To generate documentation, run
make docs
To build the examples (in the `examples/` directory), run
make examples
## Examples ##
Gaisan contains full, working examples in the `examples/` directory; however, here are some snippets:
### Solve an IVP ###
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|
### Solve a linear system ###
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