def compile(self, in_x, train_Feed, eval_Feed):
        n = np.product(self.in_d)
        m, param_init_fn = [dom[i] for (dom, i) in zip(self.domains, self.chosen)]
 
        #sc = np.sqrt(6.0) / np.sqrt(m + n)
        #W = tf.Variable(tf.random_uniform([n,m],-sc,sc))
        W = tf.Variable( param_init_fn( [n, m] ) )
        b = tf.Variable(tf.zeros([m]))
 
        # if the number of input dimensions is larger than one,flatten the 
        # input and apply the affine transformation. 
        if len(self.in_d) > 1:
            in_x_flat = tf.reshape(in_x, shape=[-1, n])
            out_y = tf.add(tf.matmul(in_x_flat, W), b)
        else:
            out_y = tf.add(tf.matmul(in_x, b)
        return out_y
 
# computes the output dimension based on the padding scheme used.
# this comes from the tensorflow documentation

def get_outdim(self):
        #assert in_x == self.b.get_outdim()
        # relaxing input dimension equal to output dimension. taking into
        # account the padding scheme considered.
        out_d_b = self.b.get_outdim()
        in_d = self.in_d
 
        if len(out_d_b) == len(in_d):
            out_d = tuple(
                [max(od_i, id_i) for (od_i, id_i) in zip(out_d_b, in_d)])
 
        else:
            # flattens both input and output. 
            out_d_b_flat = np.product(out_d_b)
            in_d_flat = np.product(in_d)
            out_d = (max(out_d_b_flat, in_d_flat) ,)
 
        return out_d

def get_surface(self, dest_surf = None):
        camera = self.camera
 
        im = highgui.cvQueryFrame(camera)
        #convert Ipl image to PIL image
        #print type(im)
        if im:
            xx = opencv.adaptors.Ipl2NumPy(im)
            #print type(xx)
            #print xx.iscontiguous()
            #print dir(xx)
            #print xx.shape
            xxx = numpy.reshape(xx, (numpy.product(xx.shape),))
 
            if xx.shape[2] != 3:
                raise ValueError("not sure what to do about this size")
 
            pg_img = pygame.image.frombuffer(xxx, (xx.shape[1],xx.shape[0]), "RGB")
 
            # if there is a destination surface given,we blit onto that.
            if dest_surf:
                dest_surf.blit(pg_img, (0,0))
            return dest_surf
            #return pg_img

def test_addsumprod(self):
        # Tests add,sum,product.
        (x, y, a10, m1, m2, xm, ym, z, zm, xf) = self.d
        assert_equal(np.add.reduce(x), add.reduce(x))
        assert_equal(np.add.accumulate(x), add.accumulate(x))
        assert_equal(4, sum(array(4), axis=0))
        assert_equal(4, axis=0))
        assert_equal(np.sum(x, axis=0), sum(x, axis=0))
        assert_equal(np.sum(filled(xm, 0), sum(xm, 0))
        assert_equal(np.product(x, product(x, axis=0))
        assert_equal(np.product(x, 0))
        assert_equal(np.product(filled(xm, 1), product(xm, axis=0))
        s = (3, 4)
        x.shape = y.shape = xm.shape = ym.shape = s
        if len(s) > 1:
            assert_equal(np.concatenate((x, y), concatenate((xm, ym), 1))
            assert_equal(np.add.reduce(x, add.reduce(x, 1))
            assert_equal(np.sum(x, 1))
            assert_equal(np.product(x, 1))

def test_testAddSumProd(self):
        # Test add, xf, s) = self.d
        self.assertTrue(eq(np.add.reduce(x), add.reduce(x)))
        self.assertTrue(eq(np.add.accumulate(x), add.accumulate(x)))
        self.assertTrue(eq(4, axis=0)))
        self.assertTrue(eq(4, axis=0)))
        self.assertTrue(eq(np.sum(x, axis=0)))
        self.assertTrue(eq(np.sum(filled(xm, 0)))
        self.assertTrue(eq(np.product(x, axis=0)))
        self.assertTrue(eq(np.product(x, 0)))
        self.assertTrue(eq(np.product(filled(xm,
                           product(xm, axis=0)))
        if len(s) > 1:
            self.assertTrue(eq(np.concatenate((x,
                               concatenate((xm, 1)))
            self.assertTrue(eq(np.add.reduce(x, 1)))
            self.assertTrue(eq(np.sum(x, 1)))
            self.assertTrue(eq(np.product(x, 1)))

def __init__(self, input_shape, output_shape, output_sparsity=.05):
        """
        """
        self.learning_rate   = 1/100
        self.input_shape     = tuple(input_shape)
        self.output_shape    = tuple(output_shape)
        self.input_size      = np.product(self.input_shape)
        self.output_size     = np.product(self.output_shape)
        self.on_bits         = max(1, int(round(output_sparsity * self.output_size)))
        self.xp_q            = NStepQueue(3, .90, self.learn)
        self.expected_values = np.random.random((self.input_size, self.output_size)) * self.learning_rate
        self.expected_values = np.array(self.expected_values, dtype=np.float32)
        print("Supervised Controller")
        print("\\tExpected Values shape:", self.expected_values.shape)
        print("\\tFuture discount:", self.xp_q.discount)
        print("\\tLearning Rate:", self.learning_rate)

def predict(self, input_sdr=None):
        """
        Argument inputs is ndarray of indexes into the input space.
        Returns probability of each catagory in output space.
        """
        self.input_sdr.assign(input_sdr)
        pdf = self.stats[self.input_sdr.flat_index]
        if True:
            # Combine multiple probabilities into single pdf. Product,not
            # summation,to combine probabilities of independant events. The
            # problem with this is if a few unexpected bits turn on it
            # mutliplies the result by zero,and the test dataset is going to
            # have unexpected things in it.  
            return np.product(pdf, axis=0, keepdims=False)
        else:
            # Use summation B/C it works well.
            return np.sum(pdf, keepdims=False)

def add_task(self, dataset_filename, model_filename):
        dataset_src = open(dataset_filename,''r'').read()
        model_src = open(model_filename,"r").read()
        src,info = hopt.extract_hopts(model_src)
        ss_size = int(np.product( map(lambda x: len(x["options"]), info.values() ) ))
        print "Search space size: ", ss_size
        w = []
 
        for i in range(0,ss_size):
            info_i,src_i = hopt.produce_variant(src,copy.deepcopy(info),i)
            info_i["subtask"] = i
            w.append( (info_i,dataset_src,src_i) )
 
        print "submitting task..."
        rv = self.socket.send_json(("submit_task", w))
        print rv

def repeat_sum(u,shape,rep_axes):
    """
    Computes sum of a repeated matrix
 
    In effect,this routine computes 
    code:`np.sum(repeat(u,shape,rep_axes))`.  However,it performs
    this without having to perform the full repetition.
 
    """
    # Must convert to np.array to perform slicing
    shape_vec = np.array(shape,dtype=int)
    rep_vec = np.array(rep_axes,dtype=int)
 
    # repeat and sum
    urep = repeat_axes(u,rep_axes,rep=False)
    usum = np.sum(urep)*np.product(shape_vec[rep_vec])
    return usum

def get_final_shape(data_array, out_dims, direction_to_names):
    """
    Determine the final shape that data_array must be reshaped to in order to
    have one axis for each of the out_dims (for instance,combining all
    axes collected by the ''*'' direction).
    """
    final_shape = []
    for direction in out_dims:
        if len(direction_to_names[direction]) == 0:
            final_shape.append(1)
        else:
            # determine shape once dimensions for direction (usually ''*'') are combined
            final_shape.append(
                np.product([len(data_array.coords[name])
                            for name in direction_to_names[direction]]))
    return final_shape

def _init_space(self, space):
        if not isinstance(space, gym.Space):
            raise ValueError("UnkNown space,type ''%s''" % type(space))
        elif isinstance(space, gym.spaces.Box):
            n_dims = np.product(space.shape)
            handler = BoxClipHandler(space.low, space.high)
        elif isinstance(space, gym.spaces.discrete):
            n_dims = 1
            handler = IntHandler(space.n)
        elif isinstance(space, gym.spaces.HighLow):
            n_dims = space.num_rows
            handler = HighLowHandler(space.matrix)
        elif isinstance(space, gym.spaces.Tuple):
            raise NotImplementedError("Space of type ''%s'' is not supported"
                                      % type(space))
        return n_dims, handler

def train(self, sentences, iterations=1000):
        # Preprocess sentences to create indices of context and next words
        self.dictionary = build_dictionary(sentences, self.vocabulary_size)
        indices = to_indices(sentences, self.dictionary)
        self.reverse_dictionary = {index: word for word, index in self.dictionary.items()}
        inputs, outputs = self.create_context(indices)
 
        # Create cost and gradient function for gradient descent
        shapes = [self.W_shape, self.U_shape, self.H_shape, self.C_shape]
        flatten_nplm_cost_gradient = flatten_cost_gradient(nplm_cost_gradient, shapes)
        cost_gradient = bind_cost_gradient(flatten_nplm_cost_gradient, inputs, outputs,
                                           sampler=get_stochastic_sampler(10))
 
        # Train neural network
        parameters_size = np.sum(np.product(shape) for shape in shapes)
        initial_parameters = np.random.normal(size=parameters_size)
        self.parameters, cost_history = gradient_descent(cost_gradient, initial_parameters, iterations)
        return cost_history

def ser(x, y):
    """Measure symbol error rate between symbols in x and y.
 
    :param x: symbol array #1
    :param y: symbol array #2
    :returns: symbol error rate
 
    >>> import arlpy
    >>> arlpy.comms.ser([0,1,2,3],[0,2])
    0.25
    """
    x = _np.asarray(x, dtype=_np.int)
    y = _np.asarray(y, dtype=_np.int)
    n = _np.product(_np.shape(x))
    e = _np.count_nonzero(x^y)
    return float(e)/n

def ber(x, m=2):
    """Measure bit error rate between symbols in x and y.
 
    :param x: symbol array #1
    :param y: symbol array #2
    :param m: symbol alphabet size (maximum 64)
    :returns: bit error rate
 
    >>> import arlpy
    >>> arlpy.comms.ber([0,2],m=4)
    0.125
    """
    x = _np.asarray(x, dtype=_np.int)
    if _np.any(x >= m) or _np.any(y >= m) or _np.any(x < 0) or _np.any(y < 0):
        raise ValueError(''Invalid data for specified m'')
    if m == 2:
        return ser(x, y)
    if m > _MAX_M:
        raise ValueError(''m > %d not supported'' % (_MAX_M))
    n = _np.product(_np.shape(x))*_np.log2(m)
    e = x^y
    e = e[_np.nonzero(e)]
    e = _np.sum(_popcount[e])
    return float(e)/n

def __init__(self, xshape, dtype, opt=None):
        """
        Initialise an FISTADFT object with problem size and options.
 
        Parameters
        ----------
        xshape : tuple of ints
          Shape of working variable X (the primary variable)
        dtype : data-type
          Data type for working variables
        opt : :class:`FISTADFT.Options` object
          Algorithm options
        """
 
        if opt is None:
            opt = FISTADFT.Options()
        Nx = np.product(xshape)
        super(FISTADFT, self).__init__(Nx, opt)
 
        self.Xf = None
        self.Yf = None

def __init__(self, opt=None):
        """
        Initialise an ADMMEqual object with problem size and options.
 
        Parameters
        ----------
        xshape : tuple of ints
          Shape of working variable X (the primary variable)
        dtype : data-type
          Data type for working variables
        opt : :class:`ADMMEqual.Options` object
          Algorithm options
        """
 
        if opt is None:
            opt = ADMMEqual.Options()
        Nx = np.product(xshape)
        super(ADMMEqual, opt)

def mpraw_as_np(shape, dtype):
    """Construct a numpy array of the specified shape and dtype for which the
    underlying storage is a multiprocessing RawArray in shared memory.
 
    Parameters
    ----------
    shape : tuple
      Shape of numpy array
    dtype : data-type
      Data type of array
 
    Returns
    -------
    arr : ndarray
      Numpy array
    """
 
    sz = int(np.product(shape))
    csz = sz * np.dtype(dtype).itemsize
    raw = mp.RawArray(''c'', csz)
    return np.frombuffer(raw, dtype=dtype, count=sz).reshape(shape)

def slinterp(X, factor, copy=True):
    """
    Slow-ish linear interpolation of a 1D numpy array. There must be some
    better function to do this in numpy.
 
    Parameters
    ----------
    X : ndarray
        1D input array to interpolate
 
    factor : int
        Integer factor to interpolate by
 
    Return
    ------
    X_r : ndarray
    """
    sz = np.product(X.shape)
    X = np.array(X, copy=copy)
    X_s = np.hstack((X[1:], [0]))
    X_r = np.zeros((factor, sz))
    for i in range(factor):
        X_r[i, :] = (factor - i) / float(factor) * X + (i / float(factor)) * X_s
    return X_r.T.ravel()[:(sz - 1) * factor + 1]

def slinterp(X, :] = (factor - i) / float(factor) * X + (i / float(factor)) * X_s
    return X_r.T.ravel()[:(sz - 1) * factor + 1]

def exact_expected_fscore_naive(probs, thresh):
  """NB: This algorithm is exponential in the size of probs!
  Based on initial measurements,less than 15 items is
  sub-second. 16 = 2s,17=4s,18=8s,and,well,you kNow
  the rest...
  possible relaxation to allow larger number of products:
  force items with sufficiently low probs (e.g. < 1%) off
  in groundtruths.
  """
  probs = np.asarray(probs)
  n = len(probs)
  expected = 0
  p_none = np.product(1-probs)
  predict_none = p_none > thresh
  predictions = (probs >= thresh).astype(np.int8)
  for gt in itertools.product([0,1], repeat=n):
    gt = np.array(gt)
    fs = fscore(predictions, gt, predict_none)
    p = gt_prob(gt, probs)
    expected += fs * p
  return expected

def eqe1(E, query, vocabulary, priors):
    """
    Arguments:
        E - word embedding
        Q - list of query terms
        vocabulary -- list of relevant words
        priors - precomputed priors with same indices as vocabulary
    >>> E = dict()
    >>> E[''a''] = np.asarray([0.5,0.5])
    >>> E[''b''] = np.asarray([0.2,0.8])
    >>> E[''c''] = np.asarray([0.9,0.1])
    >>> E[''d''] = np.asarray([0.8,0.2])
    >>> q = "a b".split()
    >>> vocabulary = "a b c".split()
    >>> priors = np.asarray([0.25,0.5,0.25])
    >>> posterior = eqe1(E,q,vocabulary,priors)
    >>> vocabulary[np.argmax(posterior)]
    ''c''
    """
    posterior = [priors[i] *
                 np.product([delta(E[qi], E[w]) / priors[i] for qi in query])
                 for i, w in enumerate(vocabulary)]
 
    return np.asarray(posterior)

def weight_by_class_balance(truth, classes=None):
    """
    Determines a loss weight map given the truth by balancing the classes from the classes argument.
    The classes argument can be used to only include certain classes (you may for instance want to exclude the background).
    """
 
    if classes is None:
        # Include all classes
        classes = np.unique(truth)
 
    weight_map = np.zeros_like(truth, dtype=np.float32)
    total_amount = np.product(truth.shape)
 
    for c in classes:
        class_mask = np.where(truth==c,1,0)
        class_weight = 1/((np.sum(class_mask)+1e-8)/total_amount)
 
        weight_map += (class_mask*class_weight)#/total_amount
 
    return weight_map

def eval_expression(expr, values=None):
    """
    Evaluate a symbolic expression and returns a numerical array.
    :param expr: A symbolic expression to evaluate,in the form of a N_terms * N_Vars matrix
    :param values: None,or a dictionary of variable:value pairs,to substitute in the symbolic expression.
    :return: An evaled expression,in the form of an N_terms array.
    """
    n_coeffs = expr.shape[0]
    evaled_expr = np.zeros(n_coeffs)
    for (i, term) in enumerate(expr):
        if values:
            evaled_term = np.array([values.get(elem, 0) if isinstance(elem, str) else elem for elem in term])
        else:
            evaled_term = np.array(
                [0 if isinstance(elem, str) else elem for elem in term])  # All variables at 0
        evaled_expr[i] = np.product(evaled_term.astype(float))  # Gradient is the product of values
    return evaled_expr

def test_addsumprod(self):
        # Tests add, 1))

def test_testAddSumProd(self):
        # Test add, 1)))

def _read_raw_field(self, grid, field):
        field_name = field[1]
        base_dir = self.ds.index.raw_file
 
        Box_list = self.ds.index.raw_field_map[field_name][0]
        fn_list = self.ds.index.raw_field_map[field_name][1]
        offset_list = self.ds.index.raw_field_map[field_name][2]
 
        lev = grid.Level        
        filename = base_dir + "Level_%d/" % lev + fn_list[grid.id]
        offset = offset_list[grid.id]
        Box = Box_list[grid.id]
 
        lo = Box[0]
        hi = Box[1]
        shape = hi - lo + 1
        with open(filename, "rb") as f:
            f.seek(offset)
            f.readline()  # always skip the first line
            arr = np.fromfile(f, ''float64'', np.product(shape))
            arr = arr.reshape(shape, order=''F'')
        return arr

def __init__(self, ds, max_level=2):
        self.max_level = max_level
        self.cell_count = 0
        self.layers = []
        self.domain_dimensions = ds.domain_dimensions
        self.domain_left_edge = ds.domain_left_edge
        self.domain_right_edge = ds.domain_right_edge
        self.grid_filename = "amr_grid.inp"
        self.ds = ds
 
        base_layer = RadMC3DLayer(0, None, 0,
                                  self.domain_left_edge,
                                  self.domain_right_edge,
                                  self.domain_dimensions)
 
        self.layers.append(base_layer)
        self.cell_count += np.product(ds.domain_dimensions)
 
        sorted_grids = sorted(ds.index.grids, key=lambda x: x.Level)
        for grid in sorted_grids:
            if grid.Level <= self.max_level:
                self._add_grid_to_layers(grid)

def __init__(self, patchsize, source, binary_mask=None,
                 random_order=False, mirrored=True, max_num=None):
        self.patchsize = patchsize
        self.source = source.astype(np.float32)
        self.mask = binary_mask
        self.random_order = random_order
        self.mirrored = mirrored
        self.max_num = max_num
 
        if len(self.source.shape)==2:
            self.source = self.source[:,:,np.newaxis]
        if self.mask is not None and len(self.mask.shape)==2:
            self.mask = self.mask[:,np.newaxis]
 
        if self.mask is not None:
            self.num_patches = (self.mask>0).sum()
        else:
            self.num_patches = np.product(self.source.shape)