Fortran 90 Implementation

The implementation of this method in Fortran algorithms when a Fortran 90 compiler is available is facilitated by the fact that the intrinsic functions and operators can be redefined and overloaded. The implementation has been mostly automated with the help of a script and a module and the procedure is as follows:

• Download the complexify1.3.py script and the complexify.f90 module. To run the script you need Python, which is available for all platforms at www.python.org.
• Run the script on all the subroutines you want to complexify, e.g. type: python complexify1.3.py *.f.
• Run the script on all the subroutines you want to complexify, e.g. type: python complexify1.3.py *.f.
• For each file that is processed a new one is created with c_ added to the beginning of each file name.
• Add complexify.f90 to your makefile and change the original Fortran file names by adding c_ to the beginning of each name.
• Make sure you compile in double precision (use the -r8 flag for Intel compilers, -fdefault-real-8 for gfortran).
• Use a flag to extend the maximum source code line width, since the complexified code might expand certain lines.
• Cast the complex variables on ‘read’ and ‘write’ statements to real. You can also change these statements such that you can read and write the whole complex numbers, rather than just the real parts. Unfortunately, this must be done by hand
• In the code, you can now add a small complex-step h to the variable of interest, e.g.:
  x = cmplx(x, h)
  Before the end of * code you can calculate the derivative of another variable with respect to the first one by using the complex-step approximation, e.g.: * dfdx = aimag(f) / h
• Compile the new code and run it.

Note for SGI compilers: unlike most Fortran 90 compilers the SGI compiler does not allow the re-definition of the .eq. and .ge. operators and the complexify.f90 module will not compile. I am currently trying to convince SGI to change their compilers as I see not good reason for this restriction.

Fortran 77 Implementation

When a Fortran 90 compiler is not available, and since Fortran 77 does not support intrinsic operator or function redefinition, there is no automatic way of implementing the method.

It is, however, still possible to implement the method by writing the new function definitions under different names and changing the function calls to those names. For example, you would write a function called complex_abs() and substitute all the calls to abs() with this one. You also need to change the comparison operations to compare only the real parts of the arguments. The correct function definitions can be found in the complexify.f90 module.