Merge pull request #342 from pascanur/jacobian_hessian

theano/tensor/__init__.py

@@ -51,4 +51,5 @@ def shared(*args, **kw):
 import nnet  # used for softmax, sigmoid, etc.
 
 
-from tensor_grad import Rop, Lop, grad, numeric_grad, verify_grad
+from tensor_grad import Rop, Lop, grad, numeric_grad, verify_grad, \
+        jacobian, hessian

theano/tensor/tests/test_2nd_order_grads.py

+"""
+Test for jacobian/hessian functions in Theano
+"""
+import unittest
+from theano.tests  import unittest_tools as utt
+from theano import function
+import theano
+from theano import tensor
+import numpy
+
+utt.seed_rng()
+
+
+def test001_jacobian_vector():
+    x = tensor.vector()
+    y = x * 2
+    rng = numpy.random.RandomState(seed=utt.fetch_seed())
+
+    # test when the jacobian is called with a tensor as wrt
+    Jx = tensor.jacobian(y, x)
+    f = theano.function([x], Jx)
+    vx = rng.uniform(size=(10,)).astype(theano.config.floatX)
+    assert numpy.allclose(f(vx), numpy.eye(10) * 2)
+
+    # test when the jacobian is called with a tuple as wrt
+    Jx = tensor.jacobian(y, (x,))
+    assert isinstance(Jx, tuple)
+    f = theano.function([x], Jx[0])
+    vx = rng.uniform(size=(10,)).astype(theano.config.floatX)
+    assert numpy.allclose(f(vx), numpy.eye(10) * 2)
+
+    # test when the jacobian is called with a list as wrt
+    Jx = tensor.jacobian(y, [x])
+    assert isinstance(Jx, list)
+    f = theano.function([x], Jx[0])
+    vx = rng.uniform(size=(10,)).astype(theano.config.floatX)
+    assert numpy.allclose(f(vx), numpy.eye(10) * 2)
+
+    # test when the jacobian is called with a list of two elements
+    z = tensor.vector()
+    y = x * z
+    Js = tensor.jacobian(y, [x, z])
+    f = theano.function([x, z], Js)
+    vx = rng.uniform(size=(10,)).astype(theano.config.floatX)
+    vz = rng.uniform(size=(10,)).astype(theano.config.floatX)
+    vJs = f(vx, vz)
+    evx = numpy.zeros((10, 10))
+    evz = numpy.zeros((10, 10))
+    numpy.fill_diagonal(evx, vx)
+    numpy.fill_diagonal(evz, vz)
+    assert numpy.allclose(vJs[0], evz)
+    assert numpy.allclose(vJs[1], evx)
+
+
+def test002_jacobian_matrix():
+    x = tensor.matrix()
+    y = 2 * x.sum(axis=0)
+    rng = numpy.random.RandomState(seed=utt.fetch_seed())
+    ev = numpy.zeros((10, 10, 10))
+    for dx in xrange(10):
+        ev[dx, :, dx] = 2.
+
+    # test when the jacobian is called with a tensor as wrt
+    Jx = tensor.jacobian(y, x)
+    f = theano.function([x], Jx)
+    vx = rng.uniform(size=(10, 10)).astype(theano.config.floatX)
+    assert numpy.allclose(f(vx), ev)
+
+    # test when the jacobian is called with a tuple as wrt
+    Jx = tensor.jacobian(y, (x,))
+    assert isinstance(Jx, tuple)
+    f = theano.function([x], Jx[0])
+    vx = rng.uniform(size=(10, 10)).astype(theano.config.floatX)
+    assert numpy.allclose(f(vx), ev)
+
+    # test when the jacobian is called with a list as wrt
+    Jx = tensor.jacobian(y, [x])
+    assert isinstance(Jx, list)
+    f = theano.function([x], Jx[0])
+    vx = rng.uniform(size=(10, 10)).astype(theano.config.floatX)
+    assert numpy.allclose(f(vx), ev)
+
+    # test when the jacobian is called with a list of two elements
+    z = tensor.matrix()
+    y = (x * z).sum(axis=1)
+    Js = tensor.jacobian(y, [x, z])
+    f = theano.function([x, z], Js)
+    vx = rng.uniform(size=(10, 10)).astype(theano.config.floatX)
+    vz = rng.uniform(size=(10, 10)).astype(theano.config.floatX)
+    vJs = f(vx, vz)
+    evx = numpy.zeros((10, 10, 10))
+    evz = numpy.zeros((10, 10, 10))
+    for dx in xrange(10):
+        evx[dx, dx, :] = vx[dx, :]
+        evz[dx, dx, :] = vz[dx, :]
+    assert numpy.allclose(vJs[0], evz)
+    assert numpy.allclose(vJs[1 ], evx)
+
+
+def test003_jacobian_scalar():
+    x = tensor.scalar()
+    y = x * 2
+    rng = numpy.random.RandomState(seed=utt.fetch_seed())
+
+    # test when the jacobian is called with a tensor as wrt
+    Jx = tensor.jacobian(y, x)
+    f = theano.function([x], Jx)
+    vx = numpy.cast[theano.config.floatX](rng.uniform())
+    assert numpy.allclose(f(vx), 2)
+
+    # test when the jacobian is called with a tuple as wrt
+    Jx = tensor.jacobian(y, (x,))
+    assert isinstance(Jx, tuple)
+    f = theano.function([x], Jx[0])
+    vx = numpy.cast[theano.config.floatX](rng.uniform())
+    assert numpy.allclose(f(vx), 2)
+
+    # test when the jacobian is called with a list as wrt
+    Jx = tensor.jacobian(y, [x])
+    assert isinstance(Jx,list)
+    f = theano.function([x], Jx[0])
+    vx = numpy.cast[theano.config.floatX](rng.uniform())
+    assert numpy.allclose(f(vx), 2)
+
+    # test when the jacobian is called with a list of two elements
+    z = tensor.scalar()
+    y = x * z
+    Jx = tensor.jacobian(y, [x, z])
+    f = theano.function([x, z], Jx)
+    vx = numpy.cast[theano.config.floatX](rng.uniform())
+    vz = numpy.cast[theano.config.floatX](rng.uniform())
+    vJx = f(vx, vz)
+
+    assert numpy.allclose(vJx[0], vz)
+    assert numpy.allclose(vJx[1], vx)
+
+
+def test004_hessian():
+    x = tensor.vector()
+    y = tensor.sum(x ** 2)
+    Hx = tensor.hessian(y, x)
+    f = theano.function([x], Hx)
+    vx = numpy.arange(10).astype(theano.config.floatX)
+    assert numpy.allclose(f(vx), numpy.eye(10) * 2)