Python header: Add more 2D sym functions.

Add more 2D sym functions to abstract over the idea of 2D sym so that
we can choose to represent non-Matrix 2D sym to be something other
than an Array in the future. For example, we could use TableForm.

WIP: This is incomplete. More functions need to use these 2D sym
functions. Not sure if this is needed anymore as TableForm was shown
to be lacking various features such as indexing and taking
transpose. No other candidates are being considered at the moment.

* inst/private/{python_header.py,python_ipc_native.m}: Add new 2D sym
functions 'is_2d_sym', 'is_matrix', 'is_non_matrix_2d_sym',
'list_from_2d_sym' and 'shape_of_2d_sym'.
* inst/@sym/private/mat_rclist_{access,asgn}.m: Use them.
* inst/@sym/{transpose.m,vertcat.m}: Use them.

inst/@sym/private/mat_rclist_access.m

@@ -34,7 +34,7 @@
   end
 
   cmd = {'(A, rr, cc) = _ins'
-         'AA = A.tolist() if isinstance(A, (MatrixBase, NDimArray)) else [[A]]'
+         'AA = list_from_2d_sym(A) if is_2d_sym(A) else [[A]]'
          'MM = [[AA[i][j]] for i, j in zip(rr, cc)]'
          'M = make_2d_sym(MM)'
          'return M,'};

inst/@sym/private/mat_rclist_asgn.m

@@ -65,13 +65,13 @@
          'if A == []:'
          '    AA = []'
          '    (nrows_A, ncols_A) = (0, 0)'
-         'elif isinstance(A, (MatrixBase, NDimArray)):'
-         '    AA = A.tolist()'
-         '    (nrows_A, ncols_A) = A.shape'
+         'elif is_2d_sym(A):'
+         '    AA = list_from_2d_sym(A)'
+         '    (nrows_A, ncols_A) = shape_of_2d_sym(A)'
          'else:'
          '    AA = [[A]]'
          '    (nrows_A, ncols_A) = (1, 1)'
-         'bb = b.tolist() if isinstance(b, (MatrixBase, NDimArray)) else [[b]]'
+         'bb = list_from_2d_sym(b) if is_2d_sym(b) else [[b]]'
          'entries = dict(zip(zip(rr, cc), flatten(bb, levels=1)))'
          'def entry(i, j):'
          '    if (i, j) in entries:'

inst/@sym/transpose.m

@@ -66,10 +66,8 @@
     print_usage ();
   end
 
-  cmd = {'def is_matrix_or_array(x):'
-         '    return isinstance(x, (MatrixBase, NDimArray))'
-         'x, = _ins'
-         'return transpose(x) if is_matrix_or_array(x) else x'};
+  cmd = {'x, = _ins'
+         'return transpose(x) if is_2d_sym(x) else x'};
 
   z = pycall_sympy__ (cmd, x);
 

inst/@sym/vertcat.m

@@ -45,14 +45,12 @@
 
   % special case for 0x0 but other empties should be checked for
   % compatibilty
-  cmd = {'def is_matrix_or_array(x):'
-         '    return isinstance(x, (MatrixBase, NDimArray))'
-         'def number_of_columns(x):'
-         '    return x.shape[1] if is_matrix_or_array(x) else 1'
+  cmd = {'def number_of_columns(x):'
+         '    return shape_of_2d_sym(x)[1] if is_2d_sym(x) else 1'
          'def all_equal(*ls):'
          '    return True if ls == [] else all(ls[0] == x for x in ls[1:])'
          'def as_list_of_list(x):'
-         '    return x.tolist() if is_matrix_or_array(x) else [[x]]'
+         '    return list_from_2d_sym(x) if is_2d_sym(x) else [[x]]'
          'args = [x for x in _ins if x != zeros(0, 0)] # remove 0x0 matrices'
          'ncols = [number_of_columns(x) for x in args]'
          'if not all_equal(*ncols):'

inst/private/python_header.py

@@ -241,9 +241,10 @@ def octoutput(x, et):
 
 
 try:
+    # begin: 2D sym funcs
+    # 2D sym funcs defined in inst/private/python_ipc_native.m
+    # and inst/private/python_header.py should be kept in sync
     def make_2d_sym(it_of_it, dbg_matrix_only=False):
-        # should be kept in sync with the same function
-        # defined in inst/private/python_ipc_native.m
         # FIXME: dbg_matrix_only is used for debugging, remove
         # it once sympy drops non-Expr support in Matrix
         """
@@ -262,7 +263,26 @@ def make_2d_sym(it_of_it, dbg_matrix_only=False):
             return Matrix(ls_of_ls)
         else:
             dbout(f"make_2d_sym: constructing 2D sym...")
+            # FIXME: should we use Array or TableForm?
             return Array(ls_of_ls)
+    def is_2d_sym(x):
+        types = (MatrixBase, NDimArray, TableForm)
+        return isinstance(x, types)
+    def is_matrix(x):
+        return isinstance(x, MatrixBase)
+    def is_non_matrix_2d_sym(x):
+        return isinstance(x, (NDimArray, TableForm))
+    def list_from_2d_sym(X):
+        if isinstance(X, TableForm):
+            return [[x for x in tup] for tup in X._lines]
+        else:
+            return X.tolist()
+    def shape_of_2d_sym(X):
+        if isinstance(X, TableForm):
+            return (X._h, X._w)
+        else:
+            return X.shape
+    # end: 2D sym funcs
 except:
     echo_exception_stdout("in python_header defining fcns block 5")
     raise

inst/private/python_ipc_native.m

@@ -111,9 +111,10 @@
                     '    # should be kept in sync with the same function'
                     '    # defined in inst/private/python_header.py'
                     '    sys.stderr.write("pydebug: " + str(l) + "\n")'
+                    '# begin: 2D sym funcs'
+                    '# 2D sym funcs defined in inst/private/python_ipc_native.m'
+                    '# and inst/private/python_header.py should be kept in sync'
                     'def make_2d_sym(it_of_it, dbg_matrix_only=False):'
-                    '    # should be kept in sync with the same function'
-                    '    # defined in inst/private/python_header.py'
                     '    # FIXME: dbg_matrix_only is used for debugging, remove'
                     '    # it once sympy drops non-Expr support in Matrix'
                     '    """'
@@ -132,7 +133,26 @@
                     '        return Matrix(ls_of_ls)'
                     '    else:'
                     '        dbout(f"make_2d_sym: constructing 2D sym...")'
+                    '        # FIXME: should we use Array or TableForm?'
                     '        return Array(ls_of_ls)'
+                    'def is_2d_sym(x):'
+                    '    types = (MatrixBase, NDimArray, TableForm)'
+                    '    return isinstance(x, types)'
+                    'def is_matrix(x):'
+                    '    return isinstance(x, MatrixBase)'
+                    'def is_non_matrix_2d_sym(x):'
+                    '    return isinstance(x, (NDimArray, TableForm))'
+                    'def list_from_2d_sym(X):'
+                    '    if isinstance(X, TableForm):'
+                    '        return [[x for x in tup] for tup in X._lines]'
+                    '    else:'
+                    '        return X.tolist()'
+                    'def shape_of_2d_sym(X):'
+                    '    if isinstance(X, TableForm):'
+                    '        return (X._h, X._w)'
+                    '    else:'
+                    '        return X.shape'
+                    '# end: 2D sym funcs'
                   }, newl))
     have_headers = true;
   end