Fortran90 implementation of the RKHS method

1. Compile the source code by opening a terminal and writing

make

NOTE: You might change the Fortran compiler specified in the first line of the Makefile.

2. Run the code by typing

./example.x

3. The code should produce the following output

Slow evaluation at point 1.5000000000000000 0.50000000000000000 gives 1.6807426393791589
Slow evaluation at point 1.5000000000000000 0.50000000000000000 gives derivative of f with respect to x(1): -1.7620891821210760
Slow evaluation at point 1.5000000000000000 0.50000000000000000 gives derivative of f with respect to x(2): 2.9379071414204212
Slow evaluation at point 1.5000000000000000 0.50000000000000000 gives the Hessian: 2.0514523884667937 0.0000000000000000
-2.9275790292041037 5.5628495784683452
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives 1.6807426363836484
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives derivative of f with respect to x(1): -1.7620891821013807
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives derivative of f with respect to x(2): 2.9379071414564648
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives the Hessian: 2.0514523888919172 -2.9275790292041037
-2.9275790292507025 5.5628495784669223
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives 1.6807426363836484
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives derivative of f with respect to x(1): -1.7620891821013807
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives derivative of f with respect to x(2): 2.9379071414564648
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives the Hessian: 2.0514523888919172 -2.9275790292507025
-2.9275790292507025 5.5628495784669223

Evaluation with supplied mask: Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives 1.6807426363836484
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives derivative of f with respect to x(1): -1.7620891821013807
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives derivative of f with respect to x(2): 0.0000000000000000
Fast evaluation at point 1.5000000000000000 0.50000000000000000 gives the Hessian: 2.0514523888919172 0.0000000000000000
0.0000000000000000 5.5628495784669223

and should generate a binary file called "test.kernel" and a .csv file called "multidimensional-grid-RECOVERED.csv".

TROUBLESHOOTING: If the code produces a different output, the most likely problem is that "multidimensional-grid.csv" could not be read properly. If available, check the contents of "multidimensional-grid-RECOVERED.csv" and see whether it matches to the contents of "multidimensional-grid.csv". Most often the issue can be resolved by converting the line endings in "multidimensional-grid.csv" to the control character that is appropriate for your system.

4. For a tutorial on how to incorporate the RKHS module into your own code, go to src/example.f90. There you will find a step by step tutorial how kernels are initialized and evaluated. It also gives details on the format required for training data.

5. For a detailed step-by-step tutorial on how to use the RKHS module to construct PES, download PES_Tutorial.zip and execute the example codes.