Numerical experiments, Tips, Tricks and Gotchas

## Fortran 90 to Python conversion

### 1. Introduction

All classical numerical algorithms were first implemented in FORTRAN and ALGOL [1-6] and later translated to many other languages. Numerous robust, efficient and reliable algorithms in FORTRAN still are freely available from various repositories [7-13].

The algorithms usually are well documented and include testing programs and data. Sometimes the old FORTRAN libraries are the only source of certain algorithms. If necessary, I borrowed and translated some algorithms to Pascal, C++, and C#.

There are many numerical packages in Python. However, the ability to convert the old good FORTRAN algorithm is still of interest (at least for me).

The developed conversion algorithm is focused on Fortran 90. This version is closer to modern languages, which makes it easier to convert using simple string manipulation. On the other hand, a lot of code was already converted to this (and later) versions. The earlier versions will be addressed in a separate project.

### 2. Algorithm

The algorithm includes the folliwing steps.

1. Replacement of Fortran statements with corresponding Python statements.
2. Replacement of math functions
3. Commenting out Fortan-specific statements
4. Conversion of 'do' loops to 'for' loops
5. Convertion of array access from '( )' to '[ ]'

#### 2.1. Replacement of Fortran statements with corresponding Python statements

Fortran Python Remark
'!'   '#'  Comment
'\t'   '    '  Tab → 2 spaces
'.d0'   '.0'
'd0'   '0'
'.eq.'   ' == '
'.ne.'   ' != '
'/='   ' != '
'.lt.'   ' < '
'.gt.'   ' > '
'.le.'   ' <= '
'.ge.'   ' >= '
'then'   ':'
'else if'   'elif'
'else'   'else:'
'&'   '\\'  Continuation
'.and.'   ' and '
'.or.'   ' or '
'.true.'   ' True '
'.false.'   ' False '
'end if'   ''
'do while'   'while'
'program'   'def'
'function'   'def'
'subroutine'   'def'

The replacements are stored as a list of pairs.

map_list=[('!','#'),
('\t','    '),
('.d0','.0'),
('d0','0'),
('.eq.',' == '),
. . . . . . . . .


The below case-insensitive replace function is used. It skips comments (from '#' to the rest of a line).

def ireplace(old, new, text):
''' Case Insensitive Replace excluding comments
based on
http://stackoverflow.com/questions/919056/python-case-insensitive-replace
'''
idx = 0
lim = text.find('#')
if lim < 0:
lim = len(text)
while idx < lim:
index_l = text.lower().find(old.lower(), idx)
if index_l == -1:
return text
text = text[:index_l] + new + text[index_l + len(old):]
idx = index_l + len(old)
return text


#### 2.2. Replacement of math functions

The list of double precision functions (incomplete).

Fortran Python Remark
'dabs'   'abs'
'dsqrt'   'math.sqrt'
'dlog'   'math.log'
'dexp'   'math.exp'

math_list=[
('dabs','abs'),
('dsqrt','math.sqrt'),
('dlog','math.log'),
('dexp','math.exp'),
]


#### 2.3. Commenting out Fortran-specific statements

Fortran Python Remark
'end do'   ''  Can be '# end do'
'end program'   '# end program'
'end function'   '# end function'
'end subroutine'   '# end subroutine'
'end'   '# end'
'integer'   '#integer'
'real'   '#real'
'allocate'   '#allocate'

There are two options:

1. Replace with an empty string (like with 'end do')
2. Keep as comments (like 'end program')

#### 2.4. Conversion of Fortran 'do' loops to Python 'for' loops

This function is called after statement and math function substitutions:

def process_do(line):
''' replaice Fortran do to Python for:
do i=1, N => for i in range(0, N):
do j=1, M, 2 => for j in range(0, M, 2):
do iq=ip+1, N => for iq in range(ip+1, N):
'''
if line.startswith('#'):
return line
if line.strip().startswith( 'do' ):
if '#' in line:
do_var_lims,comment = line.split('#')
comment = ' #'+''.join(comment)
else:
do_var_lims,comment = line, ''
do_var,lims = do_var_lims.split('=')
for_var = do_var.replace('do','for') + ' in range('
lims=lims.split(',')
lims=[i.strip() for i in lims]
if str(lims[0])=='1':    # heuristic correction for 0-based arrays
lims[0]='0'          # warning: this can be unnecessery sometimes.
result = for_var + ', '.join(lims) + '):'
if comment:
result += comment
return result
else:
return line


The loops in Fortran are usually used for processing arrays. The arrays in Fortran are 1-bsed and in Python are 0-based. Therefore, in addition to conversion from Fortran 'do' loops to Python 'for' loops, the indices are also shifted:  do i=1, N → for i in range(0, N). The indices are not shifted if a lower limit is a variable:  do i=j, N → for i in range(j, N). Note that this heurictic correction can be unnecessary sometimes.

##### Example
  do i=1, 50
sm=0.d0
do ip=1, N-1     !sum off-diagonal elements
do iq=ip+1, N
sm=sm+DABS(A(ip,iq))
end do
end do
. . . . .


The above Fortran code is converted to

  for i in range(0, 50):
sm=0.0
for ip in range(0, N-1): #sum off-diagonal elements
for iq in range(ip+1, N):
sm=sm+abs(A[ip,iq])
. . . . . . .


#### 2.5. Convertion of array access from '( )' to '[ ]'

This function replaces parentheses with square brackets.

def adjust_array(line, arr):
line = 'A(i,j) = A(m,A(k,l))'
arr = 'A'
result = 'A[i,j] = A[m,A[k,l]]'
'''
if line.startswith('#'):
return line
i = line.find(arr+'(')
while i >= 0:
j = line.find('(',i)
line = line[:j] + '[' + line[j+1:]
c = 1
for k in range(j+1,len(line)):
if line[k] == '(':
c += 1
if line[k] == ')':
c -= 1
if c == 0:
line = line[:k] + ']' + line[k+1:]
#                 i = line.find(arr+'(', k+1) # does not process nested arrays
i = line.find(arr+'(')
break
return line


#### 2.6. Conversion of function headers

This function transforms Fortran function/subroutine declarations to Python ones.

def adjust_functions(content):
""" Adds ':' after ')' """
for n,line in enumerate(content):
count = 0
if line.strip().startswith('def'):
i = line.find('(')
if i >= 0:
count = 1
for k in range(i,len(line)):
#print(k, line[k])
if line[k] == '#':
break
if line[k] == ')':
count = 0
content[n] = line[:k+1] + ':' + line[k+1:]
break
else:
count = 0
i = line.find('#')
if i >= 0:
content[n] =  line[:i] + ':' + line[i:]
else:
content[n] =  line + ':'
else:
if count > 0:
i = 0
for k in range(i,len(line)):
if line[k] == '#':
break
if line[k] == ')':
count = 0
content[n] = line[:k+1] + ':' + line[k+1:]
break
return content


##### Example
  Subroutine Jacobi(A,N,D,V,NROT)
. . . . .


def Jacobi(A,N,D,V,NROT):
. . . . .


### 3. Results and discussion

The algorithm was implemented as IPython HTML notebook. The notebook can be viewed or downloaded.

#### Example/Test

The project started when I needed the Jacobi diagonalization algorithm. I found this Fortran 90 implementation ujacobi.f90.

The initial file with syntax highlighting: ujacobi.f90.

The resulting Python file: ujacobi.py.

Obviously, the generated Python file requires some additional manual adjustment and formatting. It also requires some refactoring.

In particular, the loop limits at lines 35, 73, 79 must be adjusted. The line 107 must be commented out. The allocations should be replaced with array creation.The working version and the test (based on [15]) are available at Downloads below.

### 4. TO DO List

• Automatic detection of arrays.
• Convert the notebook to a command-line tool - Done
• Extension to pre-Fortran 90 versions.
The module f90_to_py.py can be used as a command-line tool.

### References

1. John Hawgood, Numerical methods in Algol. McGraw-Hill, New York, 1965.
2. D. D. McCracken and W. S. Dorn, Numerical methods and FORTRAN programming. John Wiley, New York, 1966
3. Hans Paul Kunzi, Numerical methods of mathematical optimization with ALGOL and FORTRAN programs. Academic Press, 1968.
4. J.H. Wilkinson and C. Reinsch, Handbook for Automatic Computation (Vol II, Linear Algebra), Springer-Verlag, 1971.
5. George E. Forsythe, Michael A. Malcolm, Cleve B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, 1977.
6. D. Kahaner, C. Moler, and S. Nash, Numerical Methods and Software, Prentice Hall, 1989.
7. The Netlib.
8. Fortran Software repositories.
9. Alan Miller's Fortran Software
10. Free Software/Patches.
11. Fortran Tools, Libraries, and Application Software.
12. Fortran Wiki Libraries.
13. Fortran Wiki Jean-Pierre Moreau Website.
14. ujacobi.f90.
15. tjacobi.f90.