Extend README.rst with example

README.rst

@@ -29,3 +29,69 @@ or if you downloaded this `repository <https://github.com/theHamsta/pystencils_a
 .. code-block:: bash
 
    pip install -e .
+
+
+Usage
+-----
+
+Create a :class:`pystencils.AssignmentCollection` with pystencils:
+
+.. testcode::
+
+    import sympy
+    import pystencils
+
+    z, x, y = pystencils.fields("z, y, x: [20,30]")
+
+    forward_assignments = pystencils.AssignmentCollection({
+        z[0, 0]: x[0, 0] * sympy.log(x[0, 0] * y[0, 0])
+    })
+
+    print(forward_assignments)
+
+
+.. testoutput::
+    :options: -ELLIPSIS, +NORMALIZE_WHITESPACE
+
+    Subexpressions:
+    Main Assignments:
+         z[0,0] ← y_C*log(x_C*y_C)
+   
+You can then obtain the corresponding backward assignments:
+
+.. testcode::
+
+    from pystencils.autodiff import AutoDiffOp, create_backward_assignments
+    backward_assignments = create_backward_assignments(forward_assignments)
+
+    print(backward_assignments)
+
+You can see the derivatives with respective to the two inputs multiplied by the gradient diffz_C of the output z_C.
+
+.. testoutput::
+    :options: -ELLIPSIS, +NORMALIZE_WHITESPACE
+
+    Subexpressions:
+    Main Assignments:
+        \hat{y}[0,0] ← diffz_C*(log(x_C*y_C) + 1)
+        \hat{x}[0,0] ← diffz_C*y_C/x_C
+
+You can also use the class :class:`AutoDiffOp` to obtain both the assignments (if you are curious) and auto-differentiable operations for Tensorflow...
+
+.. testcode::
+
+    op = AutoDiffOp(forward_assignments)
+    backward_assignments = op.backward_assignments   
+
+    x_tensor = pystencils.autodiff.tf_variable_from_field(x)
+    y_tensor = pystencils.autodiff.tf_variable_from_field(y)
+    tensorflow_op = op.create_tensorflow_op({x: x_tensor, y: y_tensor}, backend='tensorflow')
+
+... or Torch:
+
+.. testcode::
+
+    x_tensor = pystencils.autodiff.torch_tensor_from_field(x, cuda=False, requires_grad=True)
+    y_tensor = pystencils.autodiff.torch_tensor_from_field(y, cuda=False, requires_grad=True)
+
+    z_tensor = op.create_tensorflow_op({x: x_tensor, y: y_tensor}, backend='torch')