I confirmed that your proposed change provides for the correct output. Before merging, I want to understand where the wrapper generated by f2py fails when nr=0. I will study this before 22 Jan.

FWIW, this

       PROGRAM EMPTY
       REAL X(0) 
       END 

doesn't compile on my system (Ubuntu 14.04, compiler "fort77 Version 1.15" (from gcc)); error

Error on line 3: Declaration error for x: nonpositive dimension

Further, this fairly authentic looking Fortran 77 Standard says

          2.6  Array

          An array is a nonempty sequence of data that has a name
          and a type.  The name of an array is a symbolic name.

so it could just be invalid to have an empty array in Fortran 77.

The error that is addressed by this PR is thrown from the function array_from_pyobj of f2py, and in particular the message

ValueError: failed to create intent(cache|hide)|optional array-- must have defined dimensions but got...

is from line 684 in numpy/f2py/src/fortranobject.c. The conditional block is entered because count_nonpos (cf. code around line 595 of fortranobject.c detects that the number of columns of A or C is 0.

Regarding the case of no inputs (m=0), the same error occurs because the number of columns of D is m, as at line 239 of transform.pyf and as can be found in the code that is generated by f2py,

  /* Processing variable d */
  d_Dims[0]=max(1,p),d_Dims[1]=m;
  capi_d_intent |= F2PY_INTENT_HIDE|F2PY_INTENT_OUT;
  capi_d_tmp = array_from_pyobj(NPY_DOUBLE,d_Dims,d_Rank,capi_d_intent,Py_None);

Regarding the case of no outputs (p=0), it succeeds if m > 0.