There is nothing to distinguish between arrays and functions in Mathematica. Array and function arguments may therefore not be handled appropriately when translating expressions.
On an alternative note, the internal representation of a symbolic expression is often translated verbatim and this can lead to inefficiencies. An example is negation. Mathematica stores the expression -x internally as Times[-1,x]. The following expression is translated into appropriate form in FORTRAN.
In[4]:= FortranForm[ -x ] Out[4]//FortranForm= -xHowever, the function N is often applied to obtain numerical approximants, and convert constants, often simplifies results. This is not accounted for by Mathematica's formatting functions.
In[5]:= FortranForm[ N[a[1] - b[1]] ] Out[5]//FortranForm= a(1.) - 1.*b(1.)Two issues are raised here. There is a need for some method of protecting array or function arguments from numerical approximation. We also have to overcome the display of N[-x] as -1.*x, which results in unnecessary multiplication. A partial fix is to explicitly use NProtectedAll to protect specified arguments from N.
In[6]:= SetAttributes[{a,b},NProtectedAll];
In[7]:= FortranForm[a[1] - b[1]] //N
Out[7]//FortranForm= a(1) - 1.*b(1)
These attributes remain unless they are cleared.
In[8]:= Attributes[{a,b}]
Out[8]= {{NProtectedAll}, {NProtectedAll}}
Array conversion in the Assign functions is handled using the
option AssignToArray. Conversion to the negative sign is accomplished
by using a pattern matching rule to recover expressions of the form
Times[-1.,
In[9]:= ClearAttributes[{a,b},NProtectedAll];
In[10]:= FortranAssign[a[1] - b[1], AssignToArray->{a,b},
AssignIndent->""]
Out[10]//OutputForm= a(1)-b(1)
Any attributes assigned by Assign functions are removed when
execution is complete.
In[11]:= Attributes[{a,b}]
Out[11]= {{}, {}}
As illustrated above, when an array is specified explicitly using AssignToArray,
it is exempt from the test for ANSI compatible functions.