Move the exercies from the basic tutorial to a ipython notebook.

Author: abergeron

ipnb/01_scalar_soln.py

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+import numpy as np
+from theano import function
+import theano.tensor as T
+
+
+def make_scalar():
+    """
+    Returns a new Theano scalar.
+    """
+
+    return T.scalar()
+
+
+def log(x):
+    """
+    Returns the logarithm of a Theano scalar x.
+    """
+
+    return T.log(x)
+
+
+def add(x, y):
+    """
+    Adds two theano scalars together and returns the result.
+    """
+
+    return x + y
+
+a = make_scalar()
+b = make_scalar()
+c = log(b)
+d = add(a, c)
+f = function([a, b], d)
+a = np.cast[a.dtype](1.)
+b = np.cast[b.dtype](2.)
+actual = f(a, b)
+expected = 1. + np.log(2.)
+assert np.allclose(actual, expected)
+print "SUCCESS!"

ipnb/02_vector_mat_soln.py

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+import numpy as np
+from theano import function
+import theano.tensor as T
+
+
+def make_vector():
+    """
+    Returns a new Theano vector.
+    """
+
+    return T.vector()
+
+
+def make_matrix():
+    """
+    Returns a new Theano matrix.
+    """
+
+    return T.matrix()
+
+
+def elemwise_mul(a, b):
+    """
+    a: A theano matrix
+    b: A theano matrix
+    Returns the elementwise product of a and b
+    """
+
+    return a * b
+
+
+def matrix_vector_mul(a, b):
+    """
+    a: A theano matrix
+    b: A theano vector
+    Returns the matrix-vector product of a and b
+    """
+
+    return T.dot(a, b)
+
+a = make_vector()
+b = make_vector()
+c = elemwise_mul(a, b)
+d = make_matrix()
+e = matrix_vector_mul(d, c)
+
+f = function([a, b, d], e)
+
+rng = np.random.RandomState([1, 2, 3])
+a_value = rng.randn(5).astype(a.dtype)
+b_value = rng.rand(5).astype(b.dtype)
+c_value = a_value * b_value
+d_value = rng.randn(5, 5).astype(d.dtype)
+expected = np.dot(d_value, c_value)
+
+actual = f(a_value, b_value, d_value)
+
+assert np.allclose(actual, expected)
+print "SUCCESS!"

ipnb/03_tensor_soln.py

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+import numpy as np
+from theano import function
+import theano.tensor as T
+
+
+def make_tensor(dim):
+    """
+    Returns a new Theano tensor with no broadcastable dimensions.
+    dim: the total number of dimensions of the tensor.
+    """
+
+    return T.TensorType(broadcastable=tuple([False] * dim), dtype='float32')()
+
+
+def broadcasted_add(a, b):
+    """
+    a: a 3D theano tensor
+    b: a 4D theano tensor
+    Returns c, a 4D theano tensor, where
+
+    c[i, j, k, l] = a[l, k, i] + b[i, j, k, l]
+
+    for all i, j, k, l
+    """
+
+    return a.dimshuffle(2, 'x', 1, 0) + b
+
+
+def partial_max(a):
+    """
+    a: a 4D theano tensor
+
+    Returns b, a theano matrix, where
+
+    b[i, j] = max_{k,l} a[i, k, l, j]
+
+    for all i, j
+    """
+
+    return a.max(axis=(1, 2))
+
+a = make_tensor(3)
+b = make_tensor(4)
+c = broadcasted_add(a, b)
+d = partial_max(c)
+
+f = function([a, b], d)
+
+rng = np.random.RandomState([1, 2, 3])
+a_value = rng.randn(2, 2, 2).astype(a.dtype)
+b_value = rng.rand(2, 2, 2, 2).astype(b.dtype)
+c_value = np.transpose(a_value, (2, 1, 0))[:, None, :, :] + b_value
+expected = c_value.max(axis=1).max(axis=1)
+
+actual = f(a_value, b_value)
+
+assert np.allclose(actual, expected), (actual, expected)
+print "SUCCESS!"

ipnb/11_function_soln.py

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+from theano import tensor as T
+from theano import function
+
+
+def evaluate(x, y, expr, x_value, y_value):
+    """
+    x: A theano variable
+    y: A theano variable
+    expr: A theano expression involving x and y
+    x_value: A numpy value
+    y_value: A numpy value
+
+    Returns the value of expr when x_value is substituted for x
+    and y_value is substituted for y
+    """
+
+    return function([x, y], expr)(x_value, y_value)
+
+
+x = T.iscalar()
+y = T.iscalar()
+z = x + y
+assert evaluate(x, y, z, 1, 2) == 3
+print "SUCCESS!"

ipnb/12_shared_soln.py

@@ -0,0 +1,60 @@
+import numpy as np
+from theano.compat.python2x import OrderedDict
+from theano import function
+from theano import shared
+
+
+def make_shared(shape):
+    """
+    Returns a theano shared variable containing a tensor of the specified
+    shape.
+    You can use any value you want.
+    """
+    return shared(np.zeros(shape))
+
+
+def exchange_shared(a, b):
+    """
+    a: a theano shared variable
+    b: a theano shared variable
+    Uses get_value and set_value to swap the values stored in a and b
+    """
+    temp = a.get_value()
+    a.set_value(b.get_value())
+    b.set_value(temp)
+
+
+def make_exchange_func(a, b):
+    """
+    a: a theano shared variable
+    b: a theano shared variable
+    Returns f
+    where f is a theano function, that, when called, swaps the
+    values in a and b
+    f should not return anything
+    """
+
+    updates = OrderedDict()
+    updates[a] = b
+    updates[b] = a
+    f = function([], updates=updates)
+    return f
+
+
+a = make_shared((5, 4, 3))
+assert a.get_value().shape == (5, 4, 3)
+b = make_shared((5, 4, 3))
+assert a.get_value().shape == (5, 4, 3)
+a.set_value(np.zeros((5, 4, 3), dtype=a.dtype))
+b.set_value(np.ones((5, 4, 3), dtype=b.dtype))
+exchange_shared(a, b)
+assert np.all(a.get_value() == 1.)
+assert np.all(b.get_value() == 0.)
+f = make_exchange_func(a, b)
+rval = f()
+assert isinstance(rval, list)
+assert len(rval) == 0
+assert np.all(a.get_value() == 0.)
+assert np.all(b.get_value() == 1.)
+
+print "SUCCESS!"

ipnb/13_bug_soln.py

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+# The weird thing is that the function succeeds.
+#
+# This is weird because the two values passed in for x and y do not
+# have the same shape, yet x is added with something that has the same
+# shape as y (z).
+#
+# This happens because optimizations realize that z is always zero and
+# therefore remove the addition, which removes the error.
+#
+# The problem is more evident if FAST_COMPILE or DEBUG_MODE is used.

ipnb/21_grad_soln.py

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+# Fill in the TODOs in this exercise, then run
+# python 01_grad.py to see if your solution works!
+#
+from theano import tensor as T
+
+
+def grad_sum(x, y, z):
+    """
+    x: A theano variable
+    y: A theano variable
+    z: A theano expression involving x and y
+
+    Returns dz / dx + dz / dy
+    """
+
+    return sum(T.grad(z, [x, y]))
+
+x = T.scalar()
+y = T.scalar()
+z = x + y
+s = grad_sum(x, y, z)
+assert s.eval({x: 0, y: 0}) == 2
+print "SUCCESS!"

ipnb/22_traverse_soln.py

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+import numpy as np
+from theano.gof import Variable
+from theano import tensor as T
+
+
+def arg_to_softmax(prob):
+    """
+    Oh no! Someone has passed you the probability output,
+    "prob", of a softmax function, and you want the unnormalized
+    log probability--the argument to the softmax.
+
+    Verify that prob really is the output of a softmax. Raise a
+    TypeError if it is not.
+
+    If it is, return the argument to the softmax.
+    """
+
+    if not isinstance(prob, Variable):
+        raise TypeError()
+
+    if prob.owner is None:
+        raise TypeError()
+
+    owner = prob.owner
+
+    if not isinstance(owner.op, T.nnet.Softmax):
+        raise TypeError()
+
+    rval, = owner.inputs
+
+    return rval
+
+if __name__ == "__main__":
+    x = np.ones((5, 4))
+    try:
+        arg_to_softmax(x)
+        raise Exception("You should have raised an error.")
+    except TypeError:
+        pass
+
+    x = T.matrix()
+    try:
+        arg_to_softmax(x)
+        raise Exception("You should have raised an error.")
+    except TypeError:
+        pass
+
+    y = T.nnet.sigmoid(x)
+    try:
+        arg_to_softmax(y)
+        raise Exception("You should have raised an error.")
+    except TypeError:
+        pass
+
+    y = T.nnet.softmax(x)
+    rval = arg_to_softmax(y)
+    assert rval is x
+
+    print "SUCCESS!"

ipnb/31_debug_soln.py

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+import numpy as np
+from theano import function
+from theano import tensor as T
+from theano import config
+config.compute_test_value = 'raise'
+a = T.vector()
+a.tag.test_value = np.ones((3,)).astype(a.dtype)
+b = T.log(a)
+c = T.nnet.sigmoid(b)
+d = T.sqrt(c)
+e = T.concatenate((d, c), axis=0)
+f = b * c * d
+# This is the first bad line
+g = e + f
+h = g / c
+fn = function([a], h)
+fn(np.ones((3,)).astype(a.dtype))