
import unittest
import theano
from theano import tensor as T
from theano import gof
import numpy
from theano.tests import unittest_tools as utt
from theano.tensor.tests import test_basic as TT
from theano import printing

from theano.tensor.nnet import *


class T_sigmoid(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()
    def test_elemwise(self):
        utt.verify_grad(sigmoid, [numpy.random.rand(3,4)])

class T_softplus(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()
    def test_elemwise(self):
        utt.verify_grad(softplus, [numpy.random.rand(3,4)])

class T_Softmax(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()
    def test0(self):
        def f(a):
            return softmax(a)[:,0]
        utt.verify_grad(f, [numpy.random.rand(3,4)])
    def test1(self):
        def f(a):
            return softmax(a)[:,1]
        utt.verify_grad(f, [numpy.random.rand(3,4)])
    def test2(self):
        def f(a):
            return softmax(a)[:,2]
        utt.verify_grad(f, [numpy.random.rand(3,4)])
    def test3(self):
        def f(a):
            return softmax(a)[:,3]
        utt.verify_grad(f, [numpy.random.rand(3,4)])

    def test_infer_shape(self):
        f=theano.function([],softmax(numpy.random.rand(3,4)).shape)
        assert all(f()==[3,4])

    def test_vector(self):
        x = T.vector()
        f = theano.function([x], softmax(x))

        xv = numpy.random.randn(6)
        assert numpy.allclose(f(xv), numpy.exp(xv) / numpy.exp(xv).sum())
    def test_vector_grad(self):
        def f(a):
            return softmax(a)
        utt.verify_grad(f, [numpy.random.rand(4)])


class T_SoftmaxWithBias(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()
    def test0(self):
        def f(a, b):
            return softmax_with_bias(a, b)[:,0]
        utt.verify_grad(f, [numpy.random.rand(3,4),
            numpy.random.rand(4)])
    def test1(self):
        def f(a, b):
            return softmax_with_bias(a, b)[:,1]
        utt.verify_grad(f, [numpy.random.rand(3,4),
            numpy.random.rand(4)])
    def test2(self):
        def f(a, b):
            return softmax_with_bias(a, b)[:,2]
        utt.verify_grad(f, [numpy.random.rand(3,4),
            numpy.random.rand(4)])
    def test3(self):
        def f(a, b):
            return softmax_with_bias(a, b)[:,3]
        utt.verify_grad(f, [numpy.random.rand(3,4),
            numpy.random.rand(4)])
    def test_infer_shape(self):
        fff=theano.function([],outputs=softmax_with_bias(numpy.random.rand(3,4),numpy.random.rand(4)).shape)
        assert all(fff()==[3,4])

class T_SoftmaxGrad(unittest.TestCase):
    def test_infer_shape(self):
        a=T.constant(numpy.random.rand(3,4))
        b=T.constant(numpy.random.rand(3,4))
        f=theano.function([],softmax_grad(a,b).shape)
        assert numpy.all(f()==[3,4])

class T_CrossentropySoftmax1Hot(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()
    def test0(self):
        y_idx = [0,1,3]
        def f(a, b):
            return crossentropy_softmax_1hot_with_bias(a, b, y_idx)[0]
        utt.verify_grad(f, [numpy.random.rand(3,4),
            numpy.random.rand(4)])
    def test1(self):
        y_idx = [0,1,3]
        def f(a):
            return crossentropy_softmax_1hot(a, y_idx)[0]
        utt.verify_grad(f, [numpy.random.rand(3,4)])
    def test_vector(self):
        y_idx = [3]
        def f(a):
            return crossentropy_softmax_1hot(T.shape_padleft(a), y_idx)[0]
        utt.verify_grad(f, [numpy.random.rand(4)])
    def test_vectors(self):
        y_idx = [3]
        def f(a, b):
            return crossentropy_softmax_1hot(T.shape_padleft(a)+b, y_idx)[0]
        utt.verify_grad(f, [numpy.random.rand(4), numpy.random.rand(4)])

class T_CrossentropySoftmax1HotWithBiasDx(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()
    def test0(self):
        def f(sm):
            return (theano.tensor.nnet.crossentropy_softmax_1hot_with_bias_dx(
                numpy.random.rand(10),  # Gradient w.r.t. NLL.
                sm,                     # Softmax output.
                numpy.random.randint(low=0, high=5, size=10))) # Class indices.
        # Build a random softmax output whose rows sum to 1.
        softmax_output = numpy.random.rand(10, 5)
        softmax_output /= softmax_output.sum(axis=1).reshape(10, 1)
        utt.verify_grad(f, [softmax_output])
    def test1(self):
        rng = numpy.random.RandomState(utt.fetch_seed())
        softmax_output = rng.rand(10, 5)
        softmax_output /= softmax_output.sum(axis=1).reshape(10, 1)
        def f(dy):
            return (theano.tensor.nnet.crossentropy_softmax_1hot_with_bias_dx(
                dy,
                softmax_output,
                rng.randint(low=0, high=5, size=10)))
        utt.verify_grad(f, [rng.rand(10)])

class T_CrossentropySoftmaxArgmax1HotWithBias(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()
        self.op = theano.tensor.nnet.crossentropy_softmax_argmax_1hot_with_bias
    def test0(self):
        n_classes = 5
        n_samples = 3
        # First test gradient when getting a gradient on the NLL output.
        def grad_on_nll(x, b):
            return self.op(x, b, y_idx=numpy.random.randint(
                low=0, high=n_classes, size=n_samples))[0]
        utt.verify_grad(grad_on_nll, [numpy.random.rand(n_samples, n_classes),
            numpy.random.rand(n_classes)])
        # Then test gradient when getting a gradient on the softmax output.
        def grad_on_softmax(x, b):
            return self.op(x, b, y_idx=numpy.random.randint(
                low=0, high=n_classes, size=n_samples))[1]
        utt.verify_grad(grad_on_softmax,
                [numpy.random.rand(n_samples, n_classes),
                    numpy.random.rand(n_classes)])

    def test_infer_shape(self):
        var = self.op(numpy.random.rand(3,5),numpy.random.rand(5), y_idx=numpy.random.randint(
                low=0, high=5, size=3))
        assert theano.function([],var[0].shape)() == [3]
        assert all(theano.function([],var[1].shape)() == [3,5])
        assert theano.function([],var[2].shape)() == [3]

class T_prepend(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()
    def test0(self):
        """basic functionality"""
        x=tensor.matrix('x')
        y=Prepend_scalar_constant_to_each_row(4.)(x)
        f=theano.function([x],[y])
        m=numpy.random.rand(3,5)
        my = f(m)
        self.failUnless(my.shape == (3, 6), my.shape)
        self.failUnless(numpy.all( my[:,0] == 4.0))


class T_prepend(unittest.TestCase):
    def test0(self):
        """basic functionality"""
        x=tensor.matrix('x')
        y=Prepend_scalar_to_each_row()(5.,x)
        f=theano.function([x],y)
        m=numpy.ones((3,5),dtype="float32")
        my = f(m)
        self.failUnless(my.shape == (3, 6))
        self.failUnless(numpy.all(my[:,0] == 5.0))

class T_CrossentropyCategorical1Hot(unittest.TestCase):
    def setUp(self):
        utt.seed_rng()

    def test_grad(self):
        x = tensor.matrix('x')
        one_of_n = tensor.lvector('one_of_n')

        op = crossentropy_categorical_1hot

        xe = op(x, one_of_n)

        f = theano.function([x, one_of_n], xe)

        xe_val = f(numpy.asarray([[.4, .6, .0], [.1, .8, .1]]), [0,1])

        assert numpy.allclose(xe_val, -numpy.log([.4, .8]))

        def oplike(x):
            return op(x, [0,1])

        tensor.verify_grad(oplike, [numpy.asarray([[.4, .6, .0], [.1, .8, .1]])],
                rng=numpy.random)


    def test_softmax_optimizations(self):
        x = tensor.matrix('x')
        one_of_n = tensor.lvector('one_of_n')
        op = crossentropy_categorical_1hot

        xe = op(x, one_of_n)

        env = gof.Env(
                [x, one_of_n],
                [op(softmax(x), one_of_n)])
        assert env.outputs[0].owner.op == op

        theano.compile.mode.optdb.query(
                theano.compile.mode.OPT_FAST_RUN).optimize(env)

        assert str(env.outputs[0].owner.op) == 'OutputGuard'
        assert env.outputs[0].owner.inputs[0].owner.op == crossentropy_softmax_argmax_1hot_with_bias

    def test_softmax_optimizations_vector(self):
        x = tensor.vector('x')
        one_of_n = tensor.lvector('one_of_n')
        op = crossentropy_categorical_1hot
        env = gof.Env(
                [x, one_of_n],
                [op(softmax(x), one_of_n)])
        assert env.outputs[0].owner.op == op

        theano.compile.mode.optdb.query(
                theano.compile.mode.OPT_FAST_RUN).optimize(env)
        assert str(env.outputs[0].owner.op) == 'OutputGuard'
        assert env.outputs[0].owner.inputs[0].owner.op == crossentropy_softmax_argmax_1hot_with_bias

    def test_softmax_optimizations_w_bias(self):
        x = tensor.matrix('x')
        b = tensor.vector('b')
        one_of_n = tensor.lvector('one_of_n')
        op = crossentropy_categorical_1hot

        xe = op(x, one_of_n)

        env = gof.Env(
                [x, b, one_of_n],
                [op(softmax(x+b), one_of_n)])
        assert env.outputs[0].owner.op == op

        print 'BEFORE'
        for node in env.toposort():
            print node.op
        print printing.pprint(node.outputs[0])
        print '----'

        theano.compile.mode.optdb.query(
                theano.compile.mode.OPT_FAST_RUN).optimize(env)

        print 'AFTER'
        for node in env.toposort():
            print node.op
        print printing.pprint(node.outputs[0])
        print '===='
        assert len(env.toposort()) == 2

        assert str(env.outputs[0].owner.op) == 'OutputGuard'
        assert env.outputs[0].owner.inputs[0].owner.op == crossentropy_softmax_argmax_1hot_with_bias

    def test_softmax_optimizations_w_bias2(self):
        x = tensor.matrix('x')
        b = tensor.vector('b')
        c = tensor.vector('c')
        one_of_n = tensor.lvector('one_of_n')
        op = crossentropy_categorical_1hot

        env = gof.Env(
                [x, b, c, one_of_n],
                [op(softmax(T.add(x,b,c)), one_of_n)])
        assert env.outputs[0].owner.op == op

        print 'BEFORE'
        for node in env.toposort():
            print node.op
        print '----'

        theano.compile.mode.optdb.query(
                theano.compile.mode.OPT_FAST_RUN).optimize(env)

        print 'AFTER'
        for node in env.toposort():
            print node.op
        print '===='
        assert len(env.toposort()) == 3

        assert str(env.outputs[0].owner.op) == 'OutputGuard'
        assert env.outputs[0].owner.inputs[0].owner.op == crossentropy_softmax_argmax_1hot_with_bias

    def test_softmax_optimizations_w_bias_vector(self):
        x = tensor.vector('x')
        b = tensor.vector('b')
        one_of_n = tensor.lvector('one_of_n')
        op = crossentropy_categorical_1hot
        env = gof.Env(
                [x, b, one_of_n],
                [op(softmax(x+b), one_of_n)])
        assert env.outputs[0].owner.op == op
        print 'BEFORE'
        for node in env.toposort():
            print node.op
        print printing.pprint(node.outputs[0])
        print '----'

        theano.compile.mode.optdb.query(
                theano.compile.mode.OPT_FAST_RUN).optimize(env)
        print 'AFTER'
        for node in env.toposort():
            print node.op
        print '===='
        assert len(env.toposort()) == 3
        assert str(env.outputs[0].owner.op) == 'OutputGuard'
        assert env.outputs[0].owner.inputs[0].owner.op == crossentropy_softmax_argmax_1hot_with_bias

    def test_softmax_grad_optimizations(self):
        x = tensor.matrix('x')
        one_of_n = tensor.lvector('one_of_n')
        op = crossentropy_categorical_1hot

        xe = op(softmax(x), one_of_n)

        sum_xe = tensor.sum(xe)
        g_x = tensor.grad(sum_xe, x)
        env = gof.Env(
                [x, one_of_n],
                [g_x])

        print 'BEFORE'
        for node in env.toposort():
            print node.op, node.inputs
        print '----'
        theano.compile.mode.optdb.query(
                theano.compile.mode.OPT_FAST_RUN).optimize(env)

        print 'AFTER'
        for node in env.toposort():
            print node.op, node.inputs

        # the function has 9 ops because the dimshuffle and elemwise{second} aren't getting
        # cleaned up as well as we'd like.
        has_cx1hot = False
        has_cx1hotdx = False
        has_softmax = False
        has_softmaxdx = False
        for node in env.toposort():
            if node.op == crossentropy_softmax_argmax_1hot_with_bias:
                has_cx1hot = True
            if node.op == crossentropy_softmax_1hot_with_bias_dx :
                has_cx1hotdx = True
            if node.op == softmax:
                has_softmax = True
            if node.op == softmax_grad:
                has_softmaxdx = True

        assert has_cx1hot
        assert has_cx1hotdx
        assert not has_softmax
        assert not has_softmaxdx

    def test_softmax_grad_optimizations_vector(self):
        x = tensor.vector('x')
        one_of_n = tensor.lvector('one_of_n')
        op = crossentropy_categorical_1hot
        xe = op(softmax(x), one_of_n)
        sum_xe = tensor.sum(xe)
        g_x = tensor.grad(sum_xe, x)
        env = gof.Env(
                [x, one_of_n],
                [g_x])

        print 'BEFORE'
        for node in env.toposort():
            print node.op, node.inputs
        print '----'
        theano.compile.mode.optdb.query(
                theano.compile.mode.OPT_FAST_RUN).optimize(env)

        print 'AFTER'
        for node in env.toposort():
            print node.op, node.inputs

        # the function has 9 ops because the dimshuffle and elemwise{second} aren't getting
        # cleaned up as well as we'd like.
        has_cx1hot = False
        has_cx1hotdx = False
        has_softmax = False
        has_softmaxdx = False
        for node in env.toposort():
            if node.op == crossentropy_softmax_argmax_1hot_with_bias:
                has_cx1hot = True
            if node.op == crossentropy_softmax_1hot_with_bias_dx :
                has_cx1hotdx = True
            if node.op == softmax:
                has_softmax = True
            if node.op == softmax_grad:
                has_softmaxdx = True

        assert has_cx1hot
        assert has_cx1hotdx
        assert not has_softmax
        assert not has_softmaxdx

    def test_get_rid_of_advanced_indexing_version_of_xent(self):
        verbose = 0
        if verbose:
            from theano.printing import pprint
        # TODO: add the optimization in FAST_COMPILE?
        # In the mean time, run it as 'FAST_RUN' instead
        mode = theano.compile.mode.get_default_mode()
        if mode == theano.compile.mode.get_mode('FAST_COMPILE'):
            mode = 'FAST_RUN'

        rng = numpy.random.RandomState(utt.fetch_seed())

        x_val = rng.randn(3,5)
        b_val = rng.randn(5)
        y_val = numpy.asarray([2,4,1])

        x = T.dmatrix('x')
        b = T.dvector('b')
        y = T.lvector('y')

        def print_graph(func):
            for i, node in enumerate(func.maker.env.toposort()):
                print i, node
            # Last node should be the output
            print i, pprint(node.outputs[0])
            print

        ## Basic case
        expressions = [
                T.sum(-T.log(softmax(x)[T.arange(y.shape[0]), y])),
                -T.sum(T.log(softmax(x)[T.arange(y.shape[0]), y])),
                -T.sum(T.log(softmax(x))[T.arange(y.shape[0]), y]),
                T.sum(-T.log(softmax(x))[T.arange(y.shape[0]), y])
                ]

        for expr in expressions:
            # Verify the optimizer worked on the expressions
            f = theano.function([x,y], expr, mode=mode)
            if verbose: print_graph(f)
            try:
                assert len(f.maker.env.toposort()) == 4
                f(x_val, y_val)
            except:
                theano.printing.debugprint(f)
                raise

            # Also verify the gradient wrt x
            g = theano.function([x,y], T.grad(expr, x), mode=mode)
            if verbose: print_graph(g)
            try:
                assert len(g.maker.env.toposort()) == 4
                g(x_val, y_val)
            except:
                theano.printing.debugprint(g)
                raise


        ## Test that a biased softmax is optimized correctly
        bias_expressions = [
                T.sum(-T.log(softmax(x+b)[T.arange(y.shape[0]), y])),
                -T.sum(T.log(softmax(b+x)[T.arange(y.shape[0]), y])),
                -T.sum(T.log(softmax(x+b))[T.arange(y.shape[0]), y]),
                T.sum(-T.log(softmax(b+x))[T.arange(y.shape[0]), y])]

        for expr in bias_expressions:
            f = theano.function([x,b,y], expr, mode=mode)
            if verbose: print_graph(f)
            try:
                assert len(f.maker.env.toposort()) == 2 # [big_op, sum]
                f(x_val, b_val, y_val)
            except:
                theano.printing.debugprint(f)
                raise

            g = theano.function([x,b,y], T.grad(expr, x), mode=mode)
            if verbose: print_graph(g)
            try:
                assert len(g.maker.env.toposort()) == 4
                g(x_val, b_val, y_val)
            except:
                theano.printing.debugprint(g)
                raise

        ## Test that using "mean" instead of sum works, too
        mean_expressions = [
                T.mean(-T.log(softmax(x)[T.arange(y.shape[0]), y])),
                -T.mean(T.log(softmax(x)[T.arange(y.shape[0]), y])),
                -T.mean(T.log(softmax(x))[T.arange(y.shape[0]), y]),
                T.mean(-T.log(softmax(x))[T.arange(y.shape[0]), y])]

        for expr in mean_expressions:
            f = theano.function([x,y], expr, mode=mode)
            if verbose: print_graph(f)
            try:
                assert len(f.maker.env.toposort()) == 6
                f(x_val, y_val)
            except:
                theano.printing.debugprint(f)
                raise

            g = theano.function([x,y], T.grad(expr, x), mode=mode)
            if verbose: print_graph(g)
            try:
                assert len(g.maker.env.toposort()) in (6,7) #there's an extra dimshuffle in there
                # but I can't think of a good rule to get rid of it
                g(x_val, y_val)
            except:
                theano.printing.debugprint(g)
                raise

        mean_bias_expressions = [
                T.mean(-T.log(softmax(x+b)[T.arange(y.shape[0]), y])),
                -T.mean(T.log(softmax(b+x)[T.arange(y.shape[0]), y])),
                -T.mean(T.log(softmax(x+b))[T.arange(y.shape[0]), y]),
                T.mean(-T.log(softmax(b+x))[T.arange(y.shape[0]), y])]

        for expr in mean_bias_expressions:
            f = theano.function([x,b,y], expr, mode=mode)
            if verbose: print_graph(f)
            try:
                assert len(f.maker.env.toposort()) == 4
            except:
                theano.printing.debugprint(f)
                raise

            g = theano.function([x,b,y], T.grad(expr, x), mode=mode)
            if verbose: print_graph(g)
            try:
                assert len(g.maker.env.toposort()) in (6,7)
                g(x_val, b_val, y_val)
            except:
                theano.printing.debugprint(g)
                raise

    def test_optimize_xent_vector(self):
        verbose = 0
        mode = theano.compile.mode.get_default_mode()
        if mode == theano.compile.mode.get_mode('FAST_COMPILE'):
            mode = 'FAST_RUN'
        rng = numpy.random.RandomState(utt.fetch_seed())
        x_val = rng.randn(5)
        y_val = numpy.asarray([2])

        x = T.dvector('x')
        y = T.lvector('y')

        def print_graph(func):
            for i, node in enumerate(func.maker.env.toposort()):
                print i, node
            # Last node should be the output
            print i, printing.pprint(node.outputs[0])
            print

        ## Test that a biased softmax is optimized correctly
        bias_expressions = [
                T.sum(-T.log(softmax(x)[T.arange(y.shape[0]), y])),
                -T.sum(T.log(softmax(x)[T.arange(y.shape[0]), y]))]

        for expr in bias_expressions:
            f = theano.function([x,y], expr, mode=mode)
            if verbose: print_graph(f)
            try:
                prev, last = f.maker.env.toposort()[-2:]
                assert len(f.maker.env.toposort()) == 5
                f(x_val, y_val)
            except:
                theano.printing.debugprint(f)
                raise

            g = theano.function([x,y], T.grad(expr, x), mode=mode)
            print_graph(g)
            try:
                ops = [node.op for node in g.maker.env.toposort()]
                assert len(ops) == 4
                assert crossentropy_softmax_1hot_with_bias_dx in ops
                assert softmax in ops
                assert softmax_grad not in ops
                g(x_val, y_val)
            except:
                theano.printing.debugprint(g)
                raise

    def test_optimize_xent_vector2(self):
        verbose = 0
        mode = theano.compile.mode.get_default_mode()
        if mode == theano.compile.mode.get_mode('FAST_COMPILE'):
            mode = 'FAST_RUN'
        rng = numpy.random.RandomState(utt.fetch_seed())
        x_val = rng.randn(5)
        b_val = rng.randn(5)
        y_val = numpy.asarray([2])

        x = T.dvector('x')
        b = T.dvector('b')
        y = T.lvector('y')

        def print_graph(func):
            for i, node in enumerate(func.maker.env.toposort()):
                print i, node
            # Last node should be the output
            print i, printing.pprint(node.outputs[0])
            print

        ## Test that a biased softmax is optimized correctly
        bias_expressions = [
                T.sum(-T.log(softmax(x+b)[T.arange(y.shape[0]), y])),
                -T.sum(T.log(softmax(b+x)[T.arange(y.shape[0]), y])),
                -T.sum(T.log(softmax(x+b))[T.arange(y.shape[0]), y]),
                T.sum(-T.log(softmax(b+x))[T.arange(y.shape[0]), y])]

        for expr in bias_expressions:
            f = theano.function([x,b,y], expr, mode=mode)
            if verbose: print_graph(f)
            try:
                prev, last = f.maker.env.toposort()[-2:]
                assert len(f.maker.env.toposort()) == 3 # [big_op, sum, dim_shuffle]
                f(x_val, b_val, y_val)
            except:
                theano.printing.debugprint(f)
                raise

            g = theano.function([x,b,y], T.grad(expr, x), mode=mode)
            print_graph(g)
            try:
                ops = [node.op for node in g.maker.env.toposort()]
                assert len(ops) <= 6
                assert crossentropy_softmax_1hot_with_bias_dx in ops
                assert softmax_with_bias in ops
                assert softmax_grad not in ops
                g(x_val, b_val, y_val)
            except:
                theano.printing.debugprint(g)
                raise

    def test_scale_cost(self):
        # TODO: add the optimization in FAST_COMPILE?
        # In the mean time, run it as 'FAST_RUN' instead
        mode = theano.compile.mode.get_default_mode()
        if mode == theano.compile.mode.get_mode('FAST_COMPILE'):
            mode = 'FAST_RUN'

        rng = numpy.random.RandomState(utt.fetch_seed())

        x_val = rng.randn(3,5)
        b_val = rng.randn(5)
        y_val = numpy.asarray([2,4,1])

        x = T.dmatrix('x')
        b = T.dvector('b')
        y = T.lvector('y')
        a = T.dscalar('a')

        def print_graph(func):
            for i, node in enumerate(func.maker.env.toposort()):
                print i, node
            # Last node should be the output
            print i, pprint(node.outputs[0])

        def validate_fn_graph(func):
            # The graph of the function should not have softmax anymore
            has_cx1hot = False
            has_softmax = False
            for node in func.maker.env.toposort():
                if node.op == crossentropy_softmax_argmax_1hot_with_bias:
                    has_cx1hot = True
                if node.op == softmax:
                    has_softmax = True

            assert has_cx1hot
            assert not has_softmax

        def validate_grad_graph(func):
            # The graph of the gradient should not have softmaxgrad anymore
            has_cx1hotdx = False
            has_softmax = False
            has_softmaxdx = False
            for node in func.maker.env.toposort():
                if node.op == crossentropy_softmax_1hot_with_bias_dx:
                    has_cx1hotdx = True
                if node.op == softmax:
                    has_softmax = True
                if node.op == softmax_grad:
                    has_softmaxdx = True

            assert has_cx1hotdx
            assert has_softmax
            assert not has_softmaxdx


        ## Cases to test
        expressions = [
                a * T.sum(-T.log(softmax(x)[T.arange(y.shape[0]), y])),
                -a * T.sum(T.log(softmax(x)[T.arange(y.shape[0]), y])),
                a * (-T.sum(T.log(softmax(x)[T.arange(y.shape[0]), y]))),
                a * T.sum(T.log(softmax(x)[T.arange(y.shape[0]), y])),

                a * T.sum(-T.log(softmax(x))[T.arange(y.shape[0]), y]),
                -a * T.sum(T.log(softmax(x))[T.arange(y.shape[0]), y]),
                a * (-T.sum(T.log(softmax(x))[T.arange(y.shape[0]), y])),
                a * T.sum(T.log(softmax(x))[T.arange(y.shape[0]), y]),

                a * T.mean(-T.log(softmax(x)[T.arange(y.shape[0]), y])),
                -a * T.mean(T.log(softmax(x)[T.arange(y.shape[0]), y])),
                a * (-T.mean(T.log(softmax(x)[T.arange(y.shape[0]), y]))),
                a * T.mean(T.log(softmax(x)[T.arange(y.shape[0]), y])),

                a * T.mean(-T.log(softmax(x))[T.arange(y.shape[0]), y]),
                -a * T.mean(T.log(softmax(x))[T.arange(y.shape[0]), y]),
                a * (-T.mean(T.log(softmax(x))[T.arange(y.shape[0]), y])),
                a * T.mean(T.log(softmax(x))[T.arange(y.shape[0]), y]),
                ]

        for expr in expressions:
            # Verify the optimizer worked on the expressions
            f = theano.function([x,y,a], expr, mode=mode)
            try:
                assert 5 <= len(f.maker.env.toposort()) <= 10
                validate_fn_graph(f)
                f(x_val, y_val, 0.1)
            except:
                theano.printing.debugprint(f)
                raise

            # Verify the gradient wrt x
            g = theano.function([x,y,a], T.grad(expr, x), mode=mode)
            try:
                assert 5 <= len(g.maker.env.toposort()) <= 12
                validate_grad_graph(g)
                g(x_val, y_val, 0.1)
            except:
                theano.printing.debugprint(g)
                raise

            # Verify the gradient when providing output gradient
            h = theano.function([x,y,a], T.grad(expr, x, g_cost=a*x.sum()), mode=mode)
            try:
                assert 8 <= len(h.maker.env.toposort()) <= 17
                validate_grad_graph(h)
                h(x_val, y_val, 0.1)
            except:
                theano.printing.debugprint(h)
                raise


def test_argmax_pushdown():
    x = tensor.dmatrix()

    #test that the max_and_argmax is pushed down if the max is not used
    out = tensor.max_and_argmax(softmax(tensor.exp(tensor.tanh(sigmoid(x)))))[1]
    env = gof.Env(
            [x],
            [out])

    theano.compile.mode.optdb.query(
            theano.compile.mode.OPT_FAST_RUN).optimize(env)

    #print 'AFTER'
    #for node in env.toposort():
        #print node.op
    assert len(env.toposort()) == 2 # an output_guard is second
    assert env.toposort()[0].op == tensor._max_and_argmax
    assert str(env.toposort()[1].op) == 'OutputGuard'
    x = tensor.dmatrix()
    #test that the max_and_argmax is not pushed down if the max is used
    out = tensor.max_and_argmax(softmax(tensor.exp(tensor.tanh(sigmoid(x)))))[0]
    env = gof.Env(
            [x],
            [out])

    theano.compile.mode.optdb.query(
            theano.compile.mode.OPT_FAST_RUN).optimize(env)

    #print 'AFTER'
    #for node in env.toposort():
        #print node.op
    assert len(env.toposort()) == 4 # an output_guard is second
    assert isinstance(env.toposort()[0].op, tensor.Elemwise)
    assert isinstance(env.toposort()[1].op, Softmax)
    assert isinstance(env.toposort()[2].op, tensor.MaxAndArgmax)
    assert str(env.toposort()[3].op) == 'OutputGuard'


def test_argmax_pushdown_bias():
    x = tensor.dmatrix()
    b = tensor.dvector()

    out = tensor.argmax(softmax_with_bias(x, b))
    env = gof.Env(
            [x,b],
            [out])

    theano.compile.mode.optdb.query(
            theano.compile.mode.OPT_FAST_RUN).optimize(env)

    #print 'AFTER'
    #for node in env.toposort():
    #    print node.op
    assert len(env.toposort()) == 4
    assert isinstance(env.toposort()[0].op, tensor.DimShuffle)
    assert isinstance(env.toposort()[1].op, tensor.Elemwise)
    assert isinstance(env.toposort()[2].op, tensor.MaxAndArgmax)
    assert str(env.toposort()[3].op) == 'OutputGuard'

    x = tensor.dmatrix()
    b = tensor.dvector()

    out = tensor.max_and_argmax(softmax_with_bias(x, b))[0]
    env = gof.Env(
            [x,b],
            [out])

    theano.compile.mode.optdb.query(
            theano.compile.mode.OPT_FAST_RUN).optimize(env)

    #print 'AFTER'
    #for node in env.toposort():
    #    print node.op
    assert len(env.toposort()) == 3
    assert isinstance(env.toposort()[0].op, SoftmaxWithBias)
    assert isinstance(env.toposort()[1].op, tensor.MaxAndArgmax)
    assert str(env.toposort()[2].op) == 'OutputGuard'

def test_asymptotic_32():
    """
    This test makes sure that our functions behave sensibly when huge values are present
    """

    #TODO: consider adding the optimization of crossentropy into the current mode for the
    # purpose of running this test

    for dtype in 'float32', 'float64':
        if dtype == 'float32':
            x = tensor.fmatrix()
            x2 = tensor.fvector()
        else:
            x = tensor.dmatrix()
            x2 = tensor.dvector()
        y = tensor.lvector()

        c = categorical_crossentropy(softmax(x+x2), y)
        f = theano.function([x,y,x2], [c.sum(), tensor.grad(c.sum(), x)], mode='FAST_RUN')
        if 0:
            for i, n in enumerate( f.maker.env.toposort()):
                print i, n

        xval = numpy.zeros((5, 5), dtype=dtype)
        x2val = numpy.zeros(5, dtype=xval.dtype)
        for i in xrange(100):

            cval, gxval =  f(xval, numpy.arange(5), x2val)
            xval -= 100.3 * gxval
            #print cval, gxval
        assert cval == 0 # no problem going to zero error

        #what about when x gets really big?

        xval = numpy.zeros((5, 5), dtype=dtype)
        x2val = numpy.zeros(5, dtype=xval.dtype)
        for i in xrange(100):

            cval, gxval =  f(xval, numpy.arange(5), x2val)
            xval += 100000.3 * gxval
            #print cval, gxval

        assert cval > 61750000
        assert gxval[0,0] == -1.0
        assert gxval[0,1] == 0.25


class Test_softmax_opt():
    # Test that expressions of softmax in terms of exponentiated things divided by row sums
    # are replaced by softmax expressions.

    #
    # Softmax_grad isn't that interesting as an Op, but it's the signature we look for when
    # trying to insert CrossEntropySoftmax... grad.  So for now, we add softmax_grad to graphs.
    # In future, we may modify the CrossEntropySoftmax...grad to look for the more basic
    # pattern.
    #

    def setUp(self):
        utt.seed_rng()
        self.rng = numpy.random.RandomState(utt.fetch_seed())

    def test_basic(self):
        c = T.matrix()
        p_y = T.exp(c) / T.exp(c).sum(axis=1).dimshuffle(0,'x')

        # test that function contains softmax and no div.
        f = theano.function([c],p_y)
        f_ops = [n.op for n in f.maker.env.toposort()]
        print '--- f ='
        printing.debugprint(f)
        print '==='
        assert len(f_ops) == 1
        assert softmax in f_ops
        f(self.rng.rand(3,4))

        # test that function contains softmax and no div.
        w = T.matrix()
        g = theano.function([c,w],T.grad((p_y*w).sum(), c))
        g_ops = [n.op for n in g.maker.env.toposort()]
        print '--- g ='
        printing.debugprint(g)
        print '==='
        assert len(g_ops) == 2
        assert softmax in g_ops
        assert softmax_grad in g_ops
        g(self.rng.rand(3,4), self.rng.uniform(.5, 1, (3,4)))

    def test_transpose_basic(self):
        # this should be a transposed softmax
        c = T.matrix()
        p_y = T.exp(c) / T.exp(c).sum(axis=0)

        # test that function contains softmax and no div.
        f = theano.function([c],p_y)
        printing.debugprint(f)

        # test that function contains softmax and no div.
        g = theano.function([c],T.grad(p_y.sum(), c))
        printing.debugprint(g)

    def test_1d_basic(self):
        # this should be a softmax, but of a one-row matrix
        c = T.vector()
        p_y = T.exp(c) / T.exp(c).sum()

        # test that function contains softmax and no div.
        f = theano.function([c], p_y)
        printing.debugprint(f)

        # test that function contains softmax and no div.
        g = theano.function([c], T.grad(p_y.sum(), c))
        printing.debugprint(g)

    # REPEAT 3 CASES in presence of log(softmax) with the advanced indexing etc.

if __name__ == '__main__':
    unittest.main()
