function to compute hessian

theano/tensor/tensor_grad.py

@@ -770,3 +770,59 @@ def jacobian(expression, wrt, consider_constant=None, warn_type=False,
     if not use_list:
         jacobs = jacobs[0]
     return jacobs
+
+
+def hessian(cost, wrt, consider_constant=None, warn_type=False,
+             disconnected_inputs='raise'):
+    """
+    :type cost: Scalar (0-dimensional) `Variable`
+    :type wrt: 'Variable' or list of `Variables`s
+
+    :param consider_constant: a list of expressions not to backpropagate
+        through
+
+    :param warn_type: a value of True will cause warnings to be logged for any
+        Op that emits a gradient that does not match its input type.
+
+    :type disconnected_inputs: string
+    :param disconnected_inputs: Defines the behaviour if some of the variables
+        in ``wrt`` are not part of the computational graph computing ``cost``
+        (or if all links are non-differentiable). The possible values are:
+        - 'ignore': considers that the gradient on these parameters is zero.
+        - 'warn': consider the gradient zero, and print a warning.
+        - 'raise': raise an exception.
+
+    :return: either a instance of `Variable` or list/tuple of `Variable`s
+            (depending upon `wrt`). If an element of `wrt` is not
+            differentiable with respect to the output, then a zero
+            variable is returned. The return value is of same type
+            as `wrt`: a list/tuple or TensorVariable in all cases.
+    """
+    # Check inputs have the right format
+    assert isisntance(cost, TensorVariable), \
+            "tensor.hessian expects a Tensor Variable as `cost`"
+    assert cost.ndim == 0, \
+            "tensor.hessian expects a 0 dimensional variable as `cost`"
+
+    if isintance(wrt, (list, tuple)):
+        use_list = True
+        wrt = list(wrt)
+    else:
+        use_list = False
+        wrt = [wrt]
+
+    hessians = []
+    for input in wrt:
+        assert isisntance(cost, TensorVariable), \
+                "tensor.hessian expects a (list of) Tensor Variable as `wrt`"
+        assert cost.ndim == 0, \
+                "tensor.hessian expects a (list of) 1 dimensional variable"\
+                "as `wrt`"
+        expr = grad(cost, input)
+        hess, _ = scan(lambda i, y, x: grad(y[i], x),
+                       sequences=arange(expr.shape[0]),
+                       non_sequences=[expr, input])
+        hessians.append(hess)
+    if not use_list:
+        hessians = hessians[0]
+    return hessians