"""
 This tutorial introduces stacked denoising auto-encoders (SdA) using Theano.

 Denoising autoencoders are the building blocks for SdA. 
 They are based on auto-encoders as the ones used in Bengio et al. 2007.
 An autoencoder takes an input x and first maps it to a hidden representation
 y = f_{\theta}(x) = s(Wx+b), parameterized by \theta={W,b}. The resulting 
 latent representation y is then mapped back to a "reconstructed" vector 
 z \in [0,1]^d in input space z = g_{\theta'}(y) = s(W'y + b').  The weight 
 matrix W' can optionally be constrained such that W' = W^T, in which case 
 the autoencoder is said to have tied weights. The network is trained such 
 that to minimize the reconstruction error (the error between x and z).

 For the denosing autoencoder, during training, first x is corrupted into 
 \tilde{x}, where \tilde{x} is a partially destroyed version of x by means 
 of a stochastic mapping. Afterwards y is computed as before (using 
 \tilde{x}), y = s(W\tilde{x} + b) and z as s(W'y + b'). The reconstruction 
 error is now measured between z and the uncorrupted input x, which is 
 computed as the cross-entropy : 
      - \sum_{k=1}^d[ x_k \log z_k + (1-x_k) \log( 1-z_k)]


 References :
   - P. Vincent, H. Larochelle, Y. Bengio, P.A. Manzagol: Extracting and 
   Composing Robust Features with Denoising Autoencoders, ICML'08, 1096-1103,
   2008
   - Y. Bengio, P. Lamblin, D. Popovici, H. Larochelle: Greedy Layer-Wise
   Training of Deep Networks, Advances in Neural Information Processing 
   Systems 19, 2007

"""

import numpy, time, cPickle, gzip, sys, os

import theano
import theano.tensor as T
from theano.tensor.shared_randomstreams import RandomStreams

from logistic_sgd import load_data
from mlp import HiddenLayer
from dA import dA



class BinaryLogisticRegressions(object):
    """Multiple 2-class Logistic Regressions Class

    The logistic regressions are fully described by a weight matrix :math:`W` 
    and bias vector :math:`b`. Classification is done by projecting data 
    points onto a set of hyperplanes, the distance to which is used to 
    determine a class membership probability. 
    """




    def __init__(self, input, n_in, n_out):
        """ Initialize the parameters of the logistic regression

        :type input: theano.tensor.TensorType
        :param input: symbolic variable that describes the input of the 
                      architecture (one minibatch)
        
        :type n_in: int
        :param n_in: number of input units, the dimension of the space in 
                     which the datapoints lie

        :type n_out: int
        :param n_out: number of output units, the dimension of the space in 
                      which the labels lie

        """ 

        # initialize with 0 the weights W as a matrix of shape (n_in, n_out) 
        self.W = theano.shared(value=numpy.zeros((n_in,n_out), dtype = theano.config.floatX),
                                name='W')
        # initialize the baises b as a vector of n_out 0s
        self.b = theano.shared(value=numpy.zeros((n_out,), dtype = theano.config.floatX),
                               name='b')


        # compute vector of class-membership probabilities in symbolic form
        self.p_y_given_x = T.nnet.sigmoid(T.dot(input, self.W)+self.b)

        # compute prediction as class whose probability is maximal in 
        # symbolic form
        self.y_pred=T.argmax(self.p_y_given_x, axis=1)

        # parameters of the model
        self.params = [self.W, self.b]





    def negative_log_likelihood(self, y):
        """Return the mean of the negative log-likelihood of the prediction
        of this model under a given target distribution.

        .. math::

            \frac{1}{|\mathcal{D}|} \mathcal{L} (\theta=\{W,b\}, \mathcal{D}) =
            \frac{1}{|\mathcal{D}|} \sum_{i=0}^{|\mathcal{D}|} \log(P(Y^{(i)}=y^{(i)}|x^{(i)}, W,b)) \\
                \ell (\theta=\{W,b\}, \mathcal{D})

        :type y: theano.tensor.TensorType
        :param y: corresponds to a vector that gives for each example the
                  correct label

        Note: we use the mean instead of the sum so that
              the learning rate is less dependent on the batch size
        """
        return -T.mean(T.sum( y*T.log(self.p_y_given_x) + (1-y)*T.log(1-self.p_y_given_x), axis=1 ) )


    def errors(self, y):
        """Return a float representing the number of errors in the minibatch 
        over the total number of examples of the minibatch ; zero one
        loss over the size of the minibatch

        :type y: theano.tensor.TensorType
        :param y: corresponds to a vector that gives for each example the 
                  correct label
        """

        # check if y has same dimension of y_pred 
        if y.ndim != self.y_pred.ndim:
            raise TypeError('y should have the same shape as self.y_pred', 
                ('y', target.type, 'y_pred', self.y_pred.type))
        # check if y is of the correct datatype        
        if y.dtype.startswith('int'):
            # the T.neq operator returns a vector of 0s and 1s, where 1
            # represents a mistake in prediction
            return T.mean(T.neq(self.y_pred, y))
        else:
            raise NotImplementedError()



class SdA(object):
    """Stacked denoising auto-encoder class (SdA)

    A stacked denoising autoencoder model is obtained by stacking several
    dAs. The hidden layer of the dA at layer `i` becomes the input of 
    the dA at layer `i+1`. The first layer dA gets as input the input of 
    the SdA, and the hidden layer of the last dA represents the output. 
    Note that after pretraining, the SdA is dealt with as a normal MLP, 
    the dAs are only used to initialize the weights.
    """

    def __init__(self, numpy_rng, theano_rng = None, n_ins = 784, 
                 hidden_layers_sizes = [500,500], n_outs = 10, 
                 corruption_levels = [0.1, 0.1]):
        """ This class is made to support a variable number of layers. 

        :type numpy_rng: numpy.random.RandomState
        :param numpy_rng: numpy random number generator used to draw initial 
                    weights

        :type theano_rng: theano.tensor.shared_randomstreams.RandomStreams
        :param theano_rng: Theano random generator; if None is given one is 
                           generated based on a seed drawn from `rng`

        :type n_ins: int
        :param n_ins: dimension of the input to the sdA

        :type n_layers_sizes: list of ints
        :param n_layers_sizes: intermidiate layers size, must contain 
                               at least one value

        :type n_outs: int
        :param n_outs: dimension of the output of the network
        
        :type corruption_levels: list of float
        :param corruption_levels: amount of corruption to use for each 
                                  layer
        """
        
        self.sigmoid_layers = []
        self.dA_layers      = []
        self.params         = []
        self.n_layers       = len(hidden_layers_sizes)

        assert self.n_layers > 0

        if not theano_rng:
            theano_rng = RandomStreams(numpy_rng.randint(2**30))
        # allocate symbolic variables for the data
        self.x  = T.matrix('x')  # the data is presented as rasterized images
        self.y  = T.ivector('y') # the labels are presented as 1D vector of 
                                 # [int] labels

        # The SdA is an MLP, for which all weights of intermidiate layers
        # are shared with a different denoising autoencoders 
        # We will first construct the SdA as a deep multilayer perceptron,
        # and when constructing each sigmoidal layer we also construct a 
        # denoising autoencoder that shares weights with that layer 
        # During pretraining we will train these autoencoders (which will
        # lead to chainging the weights of the MLP as well)
        # During finetunining we will finish training the SdA by doing 
        # stochastich gradient descent on the MLP

        for i in xrange( self.n_layers ):
            # construct the sigmoidal layer

            # the size of the input is either the number of hidden units of 
            # the layer below or the input size if we are on the first layer
            if i == 0 :
                input_size = n_ins
            else:
                input_size = hidden_layers_sizes[i-1]

            # the input to this layer is either the activation of the hidden
            # layer below or the input of the SdA if you are on the first
            # layer
            if i == 0 : 
                layer_input = self.x
            else:
                layer_input = self.sigmoid_layers[-1].output

            sigmoid_layer = HiddenLayer(rng   = numpy_rng, 
                                           input = layer_input, 
                                           n_in  = input_size, 
                                           n_out = hidden_layers_sizes[i],
                                           activation = T.nnet.sigmoid)
            # add the layer to our list of layers 
            self.sigmoid_layers.append(sigmoid_layer)
            # its arguably a philosophical question...
            # but we are going to only declare that the parameters of the 
            # sigmoid_layers are parameters of the StackedDAA
            # the visible biases in the dA are parameters of those
            # dA, but not the SdA
            self.params.extend(sigmoid_layer.params)
        
            # Construct a denoising autoencoder that shared weights with this
            # layer
            dA_layer = dA(numpy_rng = numpy_rng, theano_rng = theano_rng, input = layer_input, 
                          n_visible = input_size, 
                          n_hidden  = hidden_layers_sizes[i],  
                          W = sigmoid_layer.W, bhid = sigmoid_layer.b)
            self.dA_layers.append(dA_layer)        

        
        # We now need to add a logistic layer on top of the MLP
        #self.logLayer = LogisticRegression(\
        #                 input = self.sigmoid_layers[-1].output,\
        #                 n_in = hidden_layers_sizes[-1], n_out = n_outs)

        self.logLayer = BinaryLogisticRegressions(\
                         input = self.sigmoid_layers[-1].output,\
                         n_in = hidden_layers_sizes[-1], n_out = n_outs)
        
        self.params.extend(self.logLayer.params)
        # construct a function that implements one step of finetunining

        # compute the cost for second phase of training, 
        # defined as the negative log likelihood 
        #self.finetune_cost = self.logLayer.negative_log_likelihood(self.y)
        self.finetune_cost = self.logLayer.negative_log_likelihood(self.y)
        
        # compute the gradients with respect to the model parameters
        # symbolic variable that points to the number of errors made on the
        # minibatch given by self.x and self.y
        self.errors = self.logLayer.errors(self.y)

    def pretraining_functions(self, train_set_x, batch_size):
        ''' Generates a list of functions, each of them implementing one 
        step in trainnig the dA corresponding to the layer with same index.
        The function will require as input the minibatch index, and to train
        a dA you just need to iterate, calling the corresponding function on 
        all minibatch indexes.

        :type train_set_x: theano.tensor.TensorType
        :param train_set_x: Shared variable that contains all datapoints used
                            for training the dA

        :type batch_size: int
        :param batch_size: size of a [mini]batch

        :type learning_rate: float
        :param learning_rate: learning rate used during training for any of 
                              the dA layers
        '''

        # index to a [mini]batch
        index            = T.lscalar('index')   # index to a minibatch
        corruption_level = T.scalar('corruption')    # amount of corruption to use
        learning_rate    = T.scalar('lr')    # learning rate to use
        # number of batches
        n_batches = train_set_x.value.shape[0] / batch_size
        # begining of a batch, given `index`
        batch_begin = index * batch_size
        # ending of a batch given `index`
        batch_end = batch_begin+batch_size

        pretrain_fns = []
        for dA in self.dA_layers:
            # get the cost and the updates list
            cost,updates = dA.get_cost_updates( corruption_level, learning_rate)
            # compile the theano function    
            fn = theano.function( inputs = [index, 
                              theano.Param(corruption_level, default = 0.2),
                              theano.Param(learning_rate, default = 0.1)], 
                    outputs = cost, 
                    updates = updates,
                    givens  = {self.x :train_set_x[batch_begin:batch_end]})
            # append `fn` to the list of functions
            pretrain_fns.append(fn)

        return pretrain_fns
 

    def build_finetune_functions(self, datasets, batch_size, learning_rate):
        '''Generates a function `train` that implements one step of 
        finetuning, a function `validate` that computes the error on 
        a batch from the validation set, and a function `test` that 
        computes the error on a batch from the testing set

        :type datasets: list of pairs of theano.tensor.TensorType
        :param datasets: It is a list that contain all the datasets;  
                         the has to contain three pairs, `train`, 
                         `valid`, `test` in this order, where each pair
                         is formed of two Theano variables, one for the 
                         datapoints, the other for the labels

        :type batch_size: int
        :param batch_size: size of a minibatch

        :type learning_rate: float
        :param learning_rate: learning rate used during finetune stage
        '''

        (train_set_x, train_set_y) = datasets[0]
        (valid_set_x, valid_set_y) = datasets[1]
        (test_set_x , test_set_y ) = datasets[2]

        # compute number of minibatches for training, validation and testing
        n_valid_batches = valid_set_x.value.shape[0] / batch_size
        n_test_batches  = test_set_x.value.shape[0]  / batch_size

        index   = T.lscalar('index')    # index to a [mini]batch 

        # compute the gradients with respect to the model parameters
        gparams = T.grad(self.finetune_cost, self.params)

        # compute list of fine-tuning updates
        updates = {}
        for param, gparam in zip(self.params, gparams):
            updates[param] = param - gparam*learning_rate

        train_fn = theano.function(inputs = [index], 
              outputs =   self.finetune_cost, 
              updates = updates,
              givens  = {
                self.x : train_set_x[index*batch_size:(index+1)*batch_size],
                self.y : train_set_y[index*batch_size:(index+1)*batch_size]})

        test_score_i = theano.function([index], self.errors,
                 givens = {
                   self.x: test_set_x[index*batch_size:(index+1)*batch_size],
                   self.y: test_set_y[index*batch_size:(index+1)*batch_size]})

        valid_score_i = theano.function([index], self.errors,
              givens = {
                 self.x: valid_set_x[index*batch_size:(index+1)*batch_size],
                 self.y: valid_set_y[index*batch_size:(index+1)*batch_size]})

        # Create a function that scans the entire validation set
        def valid_score():
            return [valid_score_i(i) for i in xrange(n_valid_batches)]

        # Create a function that scans the entire test set
        def test_score():
            return [test_score_i(i) for i in xrange(n_test_batches)]

        return train_fn, valid_score, test_score






def test_SdA( finetune_lr = 0.1, pretraining_epochs = 15, \
              pretrain_lr = 0.05, training_epochs = 1000, \
              dataset='../data/mnist.pkl.gz', batch_size = 1):
    """
    Demonstrates how to train and test a stochastic denoising autoencoder.

    This is demonstrated on MNIST.

    :type learning_rate: float
    :param learning_rate: learning rate used in the finetune stage 
    (factor for the stochastic gradient)

    :type pretraining_epochs: int
    :param pretraining_epochs: number of epoch to do pretraining

    :type pretrain_lr: float
    :param pretrain_lr: learning rate to be used during pre-training

    :type n_iter: int
    :param n_iter: maximal number of iterations ot run the optimizer 

    :type dataset: string
    :param dataset: path the the pickled dataset

    """

    datasets = load_data(dataset)

    train_set_x, train_set_y = datasets[0]
    valid_set_x, valid_set_y = datasets[1]
    test_set_x , test_set_y  = datasets[2]


    # compute number of minibatches for training, validation and testing
    n_train_batches = train_set_x.value.shape[0] / batch_size

    # numpy random generator
    numpy_rng = numpy.random.RandomState(123)
    print '... building the model'
    # construct the stacked denoising autoencoder class
    sda = SdA( numpy_rng = numpy_rng, n_ins = 28*28, 
                      hidden_layers_sizes = [1000,1000,1000],
                      n_outs = 10)
    

    #########################
    # PRETRAINING THE MODEL #
    #########################
    print '... getting the pretraining functions'
    pretraining_fns = sda.pretraining_functions( 
                                        train_set_x   = train_set_x, 
                                        batch_size    = batch_size ) 

    print '... pre-training the model'
    start_time = time.clock()  
    ## Pre-train layer-wise 
    corruption_levels = [.1,.1,.0]
    for i in xrange(sda.n_layers):
        # go through pretraining epochs 
        for epoch in xrange(pretraining_epochs):
            # go through the training set
            c = []
            for batch_index in xrange(n_train_batches):
                c.append( pretraining_fns[i](index = batch_index, 
                         corruption = corruption_levels[i], 
                         lr = pretrain_lr ) )
            print 'Pre-training layer %i, epoch %d, cost '%(i,epoch),numpy.mean(c)
 
    end_time = time.clock()

    print >> sys.stderr, ('The pretraining code for file '+os.path.split(__file__)[1]+' ran for %.2fm expected 4.58m in our buildbot' % ((end_time-start_time)/60.))
    
    ########################
    # FINETUNING THE MODEL #
    ########################

    # get the training, validation and testing function for the model
    print '... getting the finetuning functions'
    train_fn, validate_model, test_model = sda.build_finetune_functions ( 
                datasets = datasets, batch_size = batch_size, 
                learning_rate = finetune_lr) 

    print '... finetunning the model'
    # early-stopping parameters
    patience              = 10*n_train_batches # look as this many examples regardless
    patience_increase     = 2.    # wait this much longer when a new best is 
                                  # found
    improvement_threshold = 0.995 # a relative improvement of this much is 
                                  # considered significant
    validation_frequency  = min(n_train_batches, patience/2)
                                  # go through this many 
                                  # minibatche before checking the network 
                                  # on the validation set; in this case we 
                                  # check every epoch 


    best_params          = None
    best_validation_loss = float('inf')
    test_score           = 0.
    start_time = time.clock()

    done_looping = False
    epoch = 0

    while (epoch < training_epochs) and (not done_looping):
        for minibatch_index in xrange(n_train_batches):
            minibatch_avg_cost = train_fn(minibatch_index)
            iter    = epoch * n_train_batches + minibatch_index

            if (iter+1) % validation_frequency == 0:
                validation_losses = validate_model()
                this_validation_loss = numpy.mean(validation_losses)
                print('epoch %i, minibatch %i/%i, validation error %f %%' % \
                   (epoch, minibatch_index+1, n_train_batches, \
                    this_validation_loss*100.))


                # if we got the best validation score until now
                if this_validation_loss < best_validation_loss:

                    #improve patience if loss improvement is good enough
                    if this_validation_loss < best_validation_loss *  \
                                                improvement_threshold :
                        patience = max(patience, iter * patience_increase)

                    # save best validation score and iteration number
                    best_validation_loss = this_validation_loss
                    best_iter = iter

                    # test it on the test set
                    test_losses = test_model()
                    test_score = numpy.mean(test_losses)
                    print(('     epoch %i, minibatch %i/%i, test error of best '
                          'model %f %%') % 
                             (epoch, minibatch_index+1, n_train_batches,
                              test_score*100.))


            if patience <= iter :
                done_looping = True
                break
        epoch = epoch + 1

    end_time = time.clock()
    print(('Optimization complete with best validation score of %f %%,'
           'with test performance %f %%') %  
                 (best_validation_loss * 100., test_score*100.))
    print >> sys.stderr, ('The training code for file '+os.path.split(__file__)[1]+' ran for %.2fm expected 3.91m in our buildbot' % ((end_time-start_time)/60.))






if __name__ == '__main__':
    test_SdA()