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util.py
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util.py
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"""Some auxiliary files used for honor track numpy assignment"""
import numpy as np
from random import randrange
def eval_numerical_gradient(f, x, verbose=False, h=0.00001):
"""Evaluates gradient df/dx via finite differences:
df/dx ~ (f(x+h) - f(x-h)) / 2h
Adopted from https://github.com/ddtm/dl-course/ (our ysda course).
"""
fx = f(x) # evaluate function value at original point
grad = np.zeros_like(x)
# iterate over all indexes in x
it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
while not it.finished:
# evaluate function at x+h
ix = it.multi_index
oldval = x[ix]
x[ix] = oldval + h # increment by h
fxph = f(x) # evalute f(x + h)
x[ix] = oldval - h
fxmh = f(x) # evaluate f(x - h)
x[ix] = oldval # restore
# compute the partial derivative with centered formula
grad[ix] = (fxph - fxmh) / (2 * h) # the slope
if verbose:
print (ix, grad[ix])
it.iternext() # step to next dimension
return grad
import sys
import os
import time
import numpy as np
def load_mnist(flatten=False):
"""taken from https://github.com/Lasagne/Lasagne/blob/master/examples/mnist.py"""
# We first define a download function, supporting both Python 2 and 3.
if sys.version_info[0] == 2:
from urllib import urlretrieve
else:
from urllib.request import urlretrieve
def download(filename, source='http://yann.lecun.com/exdb/mnist/'):
print("Downloading %s" % filename)
urlretrieve(source + filename, filename)
# We then define functions for loading MNIST images and labels.
# For convenience, they also download the requested files if needed.
import gzip
def load_mnist_images(filename):
if not os.path.exists(filename):
download(filename)
# Read the inputs in Yann LeCun's binary format.
with gzip.open(filename, 'rb') as f:
data = np.frombuffer(f.read(), np.uint8, offset=16)
# The inputs are vectors now, we reshape them to monochrome 2D images,
# following the shape convention: (examples, channels, rows, columns)
data = data.reshape(-1, 1, 28, 28)
# The inputs come as bytes, we convert them to float32 in range [0,1].
# (Actually to range [0, 255/256], for compatibility to the version
# provided at http://deeplearning.net/data/mnist/mnist.pkl.gz.)
return data / np.float32(256)
def load_mnist_labels(filename):
if not os.path.exists(filename):
download(filename)
# Read the labels in Yann LeCun's binary format.
with gzip.open(filename, 'rb') as f:
data = np.frombuffer(f.read(), np.uint8, offset=8)
# The labels are vectors of integers now, that's exactly what we want.
return data
# We can now download and read the training and test set images and labels.
X_train = load_mnist_images('train-images-idx3-ubyte.gz')
y_train = load_mnist_labels('train-labels-idx1-ubyte.gz')
X_test = load_mnist_images('t10k-images-idx3-ubyte.gz')
y_test = load_mnist_labels('t10k-labels-idx1-ubyte.gz')
# We reserve the last 10000 training examples for validation.
X_train, X_val = X_train[:-10000], X_train[-10000:]
y_train, y_val = y_train[:-10000], y_train[-10000:]
if flatten:
X_train = X_train.reshape([X_train.shape[0],-1])
X_val = X_val.reshape([X_val.shape[0],-1])
X_test = X_test.reshape([X_test.shape[0],-1])
# We just return all the arrays in order, as expected in main().
# (It doesn't matter how we do this as long as we can read them again.)
return X_train, y_train, X_val, y_val, X_test, y_test
import matplotlib.pyplot as plt
def plot_embedding(X, y):
x_min, x_max = np.min(X, 0), np.max(X, 0)
X = (X - x_min) / (x_max - x_min)
plt.figure()
ax = plt.subplot(111)
for i in range(X.shape[0]):
plt.text(X[i, 0], X[i, 1], str(y[i]),
color=plt.cm.Set1(y[i] / 10.),
fontdict={'weight': 'bold', 'size': 9})
plt.xticks([]), plt.yticks([])