Updates the akx computation spec file

The akx computation now uses a two dimensional data array (x) to store the
result of each iteration of the kernel rather than just storing the last and
final result.

examples/akx_comp.spec

@@ -1,12 +1,8 @@
 # ------------------------------------------------------------------------------
 #    for(iter=0; iter<k; iter++) {
-#      for(row=0; row<nrows; row++) {
-#S0:     y[row]=0.0;
-#      }
 #      for(nzid=0; nzid<nnz; i++) {
-#S1:     y[row[nzid]] += x[col[nzid]] * val[nzid];
+#S0:     x[iter][row[nzid]] += x[iter-1][col[nzid]] * val[nzid];
 #      }
-#S2:   temp=x; x=y; y=temp;
 #    }
 # ------------------------------------------------------------------------------
 
@@ -16,23 +12,11 @@ spec.add_symbolic(name='nnz',type='int %s',lower_bound=1)
 spec.add_symbolic(name='nrows',type='int %s',lower_bound=1)
 spec.add_symbolic(name='ncols',type='int %s',lower_bound=1)
 
-spec.add_data_array(
-        name='y',
-        type='double * %s',
-        elem_size='sizeof(double)',
-        bounds='{[k]: 0<=k and k<nrows}')
-
 spec.add_data_array(
         name='x',
-        type='double * %s',
+        type='double ** %s',
         elem_size='sizeof(double)',
-        bounds='{[k]: 0<=k and k<ncols}')
-
-spec.add_data_array(
-        name='temp',
-        type='double * %s',
-        elem_size='sizeof(double)',
-        bounds='{[k]: 0<=k and k<nrows}')
+        bounds='{[iter,c]: 0<=iter and iter<k and 0<=c and c<ncols}')
 
 spec.add_data_array(
         name='val',
@@ -52,50 +36,23 @@ spec.add_index_array(
         input_bounds='{[k]: 0<=k and k<nnz}',
         output_bounds='{[k]: 0<=k and k<ncols}')
 
-#    for(iter=0; iter<k; iter++) {
-#      for(nzid=0; nzid<nnz; i++) {
-#S0:     y[row[nzid]] += x[col[nzid]] * val[nzid];
-#      }
-#S1:   temp=x; x=y; y=temp;
-#      for(row=0; row<nrows; row++) {
-#S2:     y[row]=0.0;
-#      }
-#    }
-
-spec.add_statement(
-        name='zero_y',
-        text='y[%(a4)s]=0.0;',
-        iter_space='{[iter,row]: 0<=iter and iter<k and 0<=row and row<nrows}',
-        scatter='{[iter,row]->[c0,iter,c0,row,c0]: c0=0}')
-spec.add_access_relation(
-        statement_name='zero_y',
-        name='a4',
-        data_array='y',
-        iter_to_data='{[iter,row]->[ar]: ar=row}')
-
 spec.add_statement(
         name='mul_sum',
-        text='y[%(a1)s] += x[%(a2)s] * val[%(a3)s];',
+        text='x[%(a1)s] += x[%(a2)s] * val[%(a3)s];',
         iter_space='{[iter,nzid]: 0<=iter and iter<k and 0<=nzid and nzid<nnz}',
-        scatter='{[iter,nzid]->[c0,iter,c1,nzid,c0]: c0=0 and c1=1}')
+        scatter='{[iter,nzid]->[c0,iter,c0,nzid,c0]: c0=0}')
 spec.add_access_relation(
         statement_name='mul_sum',
         name='a1',
-        data_array='y',
-        iter_to_data='{[iter,nzid]->[ar]: ar=row(nzid)}')
+        data_array='x',
+        iter_to_data='{[iter,nzid]->[ar1,ar2]: ar1=iter and ar2=row(nzid)}')
 spec.add_access_relation(
         statement_name='mul_sum',
         name='a2',
         data_array='x',
-        iter_to_data='{[iter,nzid]->[ar]: ar=col(nzid)}')
+        iter_to_data='{[iter,nzid]->[ar1,ar2]: ar1=iter-1 and ar2=col(nzid)}')
 spec.add_access_relation(
         statement_name='mul_sum',
         name='a3',
         data_array='val',
         iter_to_data='{[iter,nzid]->[ar]: ar=nzid}')
-
-spec.add_statement(
-        name='swap_vecs',
-        text='temp=x; x=y; y=temp;',
-        iter_space='{[iter]: 0<=iter and iter<k}',
-        scatter='{[iter]->[c0,iter,c2,c0,c0]: c0=0 and c2=2}')