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tensors.py
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tensors.py
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from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from .utils.array_ops_utils import *
from .utils.math_ops_utils import *
import numpy as np
class Tensor(object):
def __init__(self, data, parents=None, op=None, auto_grad=False, id=None):
"""Initialize tensor
Args:
data: ndarray, input tensor data
parents: list, source tensor node to generate new tensor
op: str, tensor operation key work, i.g. add, subtract, multiply, dot etc..
auto_grad: str, automatic gradient keyword and check actual node whether could backpropagate
id: tensor node id that could be generate by function unique_id from tensor_utils.py
"""
# all data MUST BE numpy ndarray type data
self.data = np.array(data)
self.parents = parents
# define operations on tensor
self.op = op
self.op_params = None
# define automatic gradient and check actual node whether could backpropagate
self.auto_grad = auto_grad
self.trainable = False
# create node unique id
if id is None:
id = unique_id('Tensor')
self.id = id
# init gradient of node
self.grad = None
self.momentum = None
# define a hashmap as childrens node of parents node
# it contains child_id and child_cnt: the number of count about child node appeared
self.children = {}
# create parents and children of tensor dependency relation
# first, parents node must be not None, make sure that children node should be existed
# increments children node, one parent could have plural children
if parents is None:
return
for parent in parents:
if self.id not in parent.children:
parent.children[self.id] = 0
parent.children[self.id] += 1
def set_trainable(self, trainable):
self.trainable = trainable
def has_received_all_children_grads(self):
"""check actual node whether has received gradients from all children node
"""
# children: child_id + child_cnt
for child_id, child_cnt in self.children.items():
if child_cnt > 0:
# if child_cnt sup 0, which means receive children grads
return False
return True
def backward(self, child_grad=None, child_node=None):
"""back propagatation function
Args:
child_gard: gradient of child node
child_node: child node
"""
# 1. make sure if actual node could be backprobagate, before, have defined auto_grad
# if not, class object will be deleted
if not self.auto_grad:
del self
return
# actual node received gradients from childs nodes
# make sure that child node grad and actual node grad are same type data
assert isinstance(child_grad, Tensor)
# if gradient is none, create a new tensor as gradient
if self.grad is None:
self.grad = Tensor(child_grad.data)
else:
self.grad.data += child_grad.data
# decrements child node id, if child_id is not None
if child_node is not None:
self.children[child_node.id] -= 1
# make sure the number of children nodes is not None
assert self.children[child_node.id] >= 0
# if parents nodes doensn exists, need not to backpropagate to child node
if self.parents is None:
return
# if child_node is existed, and actual node has not received gradients from children node
if child_node is not None and not self.has_received_all_children_grads():
return
# 2. actual node backpropagate to parents nodes
# define gradient operator for each math ops
if self.op == 'add':
grad = Tensor(self.grad.data)
self.parents[0].backward(grad, self)
self.parents[1].backward(grad, self)
elif self.op == 'sub':
grad1 = Tensor(self.grad.data)
grad2 = Tensor(-self.grad.data)
self.parents[0].backward(grad1, self)
self.parents[1].backward(grad2, self)
elif self.op == 'neg':
grad = Tensor(-self.grad.data)
self.parents[0].backward(grad, self)
# multiplication of scalar
elif self.op == 'mul':
grad1 = Tensor(self.grad.data * self.parents[1].data)
grad2 = Tensor(self.grad.data * self.parents[0].data)
self.parents[0].backward(grad1, self)
self.parents[1].backward(grad2, self)
# multiplication of tensor
elif self.op == 'matmul':
grad1 = Tensor(self.grad.data.dot(self.parents[1].data.transpose()))
if len(self.grad.data.shape) == 2:
grad2 = Tensor(self.parents[0].data.transpose().dot(self.grad.data))
elif len(self.grad.data.shape) == 3:
batch_size, _, input_dims = self.parents[0].data.shape
_, _, output_dims = self.grad.data.shape
# here, new_orders = [-1, 0, 1], which presents [channel, height, width]
input_data = self.parents[0].data.transpose(-1, 0, 1).reshape(input_dims, -1)
grad_data = self.grad.data.reshape((-1, output_dims))
grad2 = Tensor(input_data.dot(grad_data))
else:
raise TypeError('Input tensor dimension should be 2 or 3!')
self.parents[0].backward(grad1, self)
self.parents[1].backward(grad2, self)
elif self.op == 'power':
num = self.op_params['num']
grad_data = self.grad.data * num * np.power(self.parents[0].data, num-1)
grad = Tensor(grad_data)
self.parents[0].backward(grad, self)
elif self.op == 'sum':
axis = self.op_params['axis']
grad = Tensor(self.parents[0].data.sum(axis))
self.parents[0].backward(grad, self)
elif self.op == 'max':
arg_max = self.op_params['arg_max']
shape = self.parents[0].data.shape
grad_data = np.zeros(shape)
# grad_data[np.arange(shape[0]), arg_max] = self.grad.data
grad_data[:, arg_max] = self.grad.data
grad = Tensor(grad_data)
self.parents[0].backward(grad, self)
elif self.op == 'reshape':
shape = self.parents[0].data.shape
grad = Tensor(self.grad.data.reshape(shape))
self.parents[0].backward(grad, self)
elif self.op == 'expand':
axis = self.op_params['axis']
repeats = self.parents[0].data.shape[axis]
expanded_vals = expand_data(self.grad.data, axis, repeats)
grad = Tensor(expanded_vals)
self.parents[0].backward(grad, self)
elif self.op == 'transpose':
if self.op_params['axes'] is not None:
axes = self.op_params['axes']
revert_axes = tuple([axes.index(i) for i in range(len(axes))])
grad = Tensor(self.grad.data.transpose(revert_axes))
else:
grad = Tensor(self.grad.data.transpose())
self.parents[0].backward(grad, self)
elif self.op == 'flatten':
grad = Tensor(self.grad.data.reshape(self.parents[0].data.shape))
self.parents[0].backward(grad, self)
elif self.op == 'concatenate':
axis = self.op_params['axis']
lens = [parent.data.shape[axis] for parent in self.parents]
idxs = np.cumsum(lens)
for i in range(len(self.parents)):
select_range = range(0, idxs[i]) if i == 0 else range(idxs[i-1], idxs[i])
grad_data = array_index_select(self.grad.data, axis, select_range)
self.parents[i].backward(Tensor(grad_data), self)
# tensor_to_matrix equal to im2col
elif self.op == 'tensor_to_matrix':
inputs = self.grad.data
shape = self.parents[0].data.shape
ksize = self.op_params['ksize']
stride = self.op_params['stride']
pad = self.op_params['pad']
grad_data = matrix_to_tensor(inputs, shape, ksize, stride, pad)
grad = Tensor(grad_data)
self.parents[0].backward(grad, self)
elif self.op == 'select_array_indice':
grad_data = np.zeros_like(self.parents[0].data).astype('float64')
plus_array_indice(self.grad.data, grad_data, self.op_params['axis'], self.op_params['i'])
self.parents[0].backward(Tensor(grad_data), self)
# define gradient operation for activiation function:
# relu: f'(x) = {0, x<0; 1, x>0}
elif self.op == 'relu':
if self.parents[0].data > 0:
# grad_data = self.grad.data * (self.parents[0].data * np.ones_like(self.parents[0].data))
grad_data = self.grad.data * (self.data * np.ones_like(self.data))
else:
# grad_data = self.grad.data * (self.parents[0].data * np.zeros_like(self.parents[0].data))
grad_data = self.grad.data * (self.data * np.zeros_like(self.data))
grad = Tensor(grad_data)
self.parents[0].backward(grad, self)
# sigmoid: f'(x) = f(x)*(1-f(x))
elif self.op == 'sigmoid':
grad_data = self.grad.data * self.data * (1 - self.data)
grad = Tensor(grad_data)
self.parents[0].backward(grad, self)
# tanh: f'(x) = 1 - (f(x))²
elif self.op == 'tanh':
grad_data = self.grad.data * (1 - np.power(self.data, 2))
grad = Tensor(grad_data)
self.parents[0].backward(grad, self)
# softmax: f'(x) = (1(i==j)-f(x))
elif self.op == 'softmax':
grad_data = self.data * (1 - self.data)
grad = Tensor(grad_data)
self.parents[0].backward(grad, self)
elif self.op == 'cross_entropy':
logits = self.op_params['logits']
# limit logit values range
logits = np.clip(logits, 1e-15, 1 - 1e-15)
labels = self.parents[1].data
grad_data = (logits - labels) / logits.shape[0]
self.parents[0].backward(Tensor(grad_data), self)
elif self.op == 'dropout':
grad_data = self.grad.data * self.op_params['mask']
self.parents[0].backward(Tensor(grad_data), self)
if not self.trainable:
del self
def __repr__(self):
return str(self.data.__repr__())
def __str__(self):
return str(self.data.__str__())
def __add__(self, other):
add_vals = add(self.data, other.data)
output = Tensor(add_vals, parents=[self, other], op='add', auto_grad=True)
return output
def __sub__(self, other):
sub_vals = sub(self.data, other.data)
output = Tensor(sub_vals, parents=[self, other], op='sub', auto_grad=True)
return output
def __neg__(self):
neg_vals = neg(self.data)
output = Tensor(neg_vals, parents=[self], op='neg', auto_grad=True)
return output
def __mul__(self, other):
mul_vals = mul(self.data, other.data)
output = Tensor(mul_vals, parents=[self, other], op='mul', auto_grad=True)
return output
def __matmul__(self, other):
matmul_vals = matmul(self.data, other.data)
return Tensor(matmul_vals, parents=[self, other], op='matmul', auto_grad=True)
def __power__(self, num):
power_vals = power(self.data, num)
output = Tensor(power_vals, parents=[self], op='power', auto_grad=True)
output.op_params = {'num': num}
return output
def sum(self, axis=None):
sum_vals = sum(self.data, axis)
output = Tensor(sum_vals, parents=[self], op='sum', auto_grad=True)
output.op_params = {'axis': axis}
return output
def max(self):
"""Find maximal of array elements and corresponding indices along axis = 1
"""
max_vals, max_inds = max(self.data)
output = Tensor(max_vals, parents=[self], op='max', auto_grad=True)
output.op_params = {'argmax': max_inds}
return output
def reshape(self, new_shape):
shaped_vals = reshape(self.data, new_shape)
output = Tensor(shaped_vals, parents=[self], op='reshape', auto_grad=True)
# output.op_params = {'new_shape': new_shape}
return output
def expand(self, axis, repeats):
expanded_vals = expand_data(self.data, axis, repeats)
output = Tensor(expanded_vals, parents=[self], op='expand', auto_grad=True)
output.op_params = {'axis': axis}
return output
def transpose(self, axes=None):
trans_vals = transpose(self.data, axes=axes)
output = Tensor(trans_vals, parents=[self], op='transpose', auto_grad=True)
output.op_params = {'axes': axes}
return output
def flatten(self):
flatted_vals = flatten(self.data)
output = Tensor(flatted_vals, parents=[self], op='flatten', auto_grad=True)
return output
@staticmethod
def concatenate(tensors, axis):
tensors_data = [tensor.data for tensor in tensors]
concate_vals = np.concatenate(tensors_data, axis)
output = Tensor(concate_vals, parents=tensors, op='concatenate', auto_grad=True)
output.op_params = {'axis': axis}
return output
# im2col function
def tensor_to_matrix(self, ksize, stride=1, pad=0):
matrix = tensor_to_matrix(self.data, ksize, stride, pad)
op_params = {'ksize': ksize,
'stride': stride,
'pad': pad}
output = Tensor(matrix, parents=[self], op='tensor_to_matrix', auto_grad=True)
output.op_params = op_params
return output
def select_array_indice(self, axis, i):
selected_array = select_array_indice(self.data, axis, i)
output = Tensor(selected_array, parents=[self], op='select_array_indice', auto_grad=True)
output.op_params = {'axis': axis, 'i': i}
return output
def relu(self):
relu_vals = relu(self.data)
output = Tensor(relu_vals, parents=[self], op='relu', auto_grad=True)
return output
def sigmoid(self):
sigmoid_vals = sigmoid(self.data)
output = Tensor(sigmoid_vals, parents=[self], op='sigmoid', auto_grad=True)
return output
def tanh(self):
tanh_vals = tanh(self.data)
output = Tensor(tanh_vals, parents=[self], op='tanh', auto_grad=True)
return output
def activation(self, type):
if type == 'relu':
return self.relu()
elif type == 'sigmoid':
return self.sigmoid()
elif type == 'tanh':
return self.tanh()
def softmax(self):
softmax_vals = softmax(self.data)
output = Tensor(softmax_vals, parents=[self], op='softmax', auto_grad=True)
return output
def cross_entropy(self, target):
logits = softmax(self.data)
labels = target.data
delta = 1e-7
batch_size = self.data.shape[0]
cross_entropy = -np.sum(labels * np.log(logits + delta))/batch_size
output = Tensor(cross_entropy, parents=[self, target], op='cross_entropy', auto_grad=True)
output.op_params = {'logits': logits}
return output
def dropout(self, rate):
mask = get_dropout_mask(self.data, rate)
if self.auto_grad:
output = Tensor(mask, parents=[self], op='dropout', auto_grad=True)
output.op_params = {'mask': mask}
return output
def clean_dependencies(self):
"""clean node dependencies
"""
self.children = {}
if self.parents is not None:
for parent in self.parents:
parent.clean_dependencies()
def create_dependencies(self):
if self.parents is not None:
for parent in self.parents:
if self.id not in parent.children:
parent.children[self.id] = 0
parent.children[self.id] += 1
parent.create_dependencies()
def refresh_dependencies(self):
self.clean_dependencies()
self.create_dependencies()