def show_trace(res):
n = max(abs(min(res)), abs(max(res)), 10)
f_line = np.arange(-n, n, 0.1)
util.set_figsize()
util.plt.plot(f_line, [x * x for x in f_line]) # 显示f(x)=x*x的图像
util.plt.plot(res, [x * x for x in res], '-o') # 显示梯度下降图像
util.plt.xlabel('x')
util.plt.ylabel('f(x)')
util.plt.show()
def train_gluon_ch7(trainer_name,
trainer_hyperparams,
features,
labels,
batch_size=10,
num_epochs=2):
# 初始化模型
net = gluon.nn.Sequential()
net.add(gluon.nn.Dense(1))
net.initialize(init.Normal(sigma=0.01))
loss = gluon.loss.L2Loss()
def eval_loss():
return loss(net(features), labels).mean().asscalar()
ls = [eval_loss()]
data_iter = gluon.data.DataLoader(gluon.data.ArrayDataset(
features, labels),
batch_size,
shuffle=True)
# 创建Trainer实例来迭代模型参数
trainer = gluon.Trainer(net.collect_params(), trainer_name,
trainer_hyperparams)
start = time.time()
for _ in range(num_epochs):
for batch_i, (X, y) in enumerate(data_iter):
with autograd.record():
l = loss(net(X), y)
l.backward()
trainer.step(batch_size) # 在Trainer实例中做梯度平均
if (batch_i + 1) * batch_size % 100 == 0:
ls.append(eval_loss())
end = time.time()
# 打印结果和作图
print('loss: %f, %f sec per epoch' % (ls[-1], end - start))
util.set_figsize()
util.plt.plot(np.linspace(0, num_epochs, len(ls)), ls)
util.plt.xlabel('epoch')
util.plt.ylabel('loss')
util.plt.show()
def train_ch7(trainer_fn,
states,
hyperparams,
features,
labels,
batch_size=10,
num_epochs=2):
# 初始化模型
net, loss = util.linreg, util.squared_loss
w = nd.random.normal(scale=0.01, shape=(features.shape[1], 1))
b = nd.zeros(1)
w.attach_grad()
b.attach_grad()
def eval_loss():
return loss(net(features, w, b), labels).mean().asscalar()
ls = [eval_loss()]
data_iter = gluon.data.DataLoader(gluon.data.ArrayDataset(
features, labels),
batch_size,
shuffle=True)
start = time.time()
for _ in range(num_epochs):
for batch_i, (X, y) in enumerate(data_iter):
with autograd.record():
l = loss(net(X, w, b), y).mean() # 使用平均损失
l.backward()
trainer_fn([w, b], states, hyperparams) # 迭代模型参数
if (batch_i + 1) * batch_size % 100 == 0:
ls.append(eval_loss()) # 每100个样本记录下当前训练误差
end = time.time()
# 打印结果和作图
print('loss: %f, %f sec per epoch' % (ls[-1], end - start))
util.set_figsize()
util.plt.plot(np.linspace(0, num_epochs, len(ls)), ls)
util.plt.xlabel('epoch')
util.plt.ylabel('loss')
util.plt.show()
X = batch.data[0].as_in_context(ctx)
Y = batch.label[0].as_in_context(ctx)
with autograd.record():
# ⽣成多尺度的锚框，为每个锚框预测类别和偏移量
anchors, cls_preds, bbox_preds = net(X)
# 为每个锚框标注类别和偏移量
bbox_labels, bbox_masks, cls_labels = contrib.nd.MultiBoxTarget(
anchors, Y, cls_preds.transpose((0, 2, 1)))
# 根据类别和偏移量的预测和标注值计算损失函数
l = calc_loss(cls_preds, cls_labels, bbox_preds, bbox_labels,
bbox_masks)
l.backward()
trainer.step(batch_size)
acc_sum += cls_eval(cls_preds, cls_labels)
n += cls_labels.size
mae_sum += bbox_eval(bbox_preds, bbox_labels, bbox_masks)
m += bbox_labels.size
if (epoch + 1) % 5 == 0:
print(
'epoch %2d, class err %.2e, bbox mae %.2e, time %.1f sec' %
(epoch + 1, 1 - acc_sum / n, mae_sum / m, time.time() - start))
# 预测
img = image.imread('../img/pikachu.jpg')
feature = image.imresize(img, 256, 256).astype('float32')
X = feature.transpose((2, 0, 1)).expand_dims(axis=0)
output = predict(X)
util.set_figsize((5, 5))
display(img, output, threshold=0.3)
np.set_printoptions(2)
img = image.imread('../img/catdog.jpg').asnumpy()
h, w = img.shape[0:2]
print(h, w)
# 生成锚框变量Y的形状（批量大小，锚框个数，4）
X = nd.random.uniform(shape=(1, 3, h, w))
Y = contrib.nd.MultiBoxPrior(X,
sizes=[0.75, 0.5, 0.25],
ratios=[1, 2, 0.5])
print(Y.shape)
boxes = Y.reshape((h, w, 5, 4))
print(boxes[250, 250, 0, :])
util.set_figsize()
bbox_scale = nd.array((w, h, w, h))
fig = util.plt.imshow(img)
show_bboxes(fig.axes, boxes[250, 250, :, :] * bbox_scale, [
's=0.75,r=1', 's=0.5,r=1', 's=0.25,r=1', 's=0.75,r=2', 's=0.75,r=0.5'
])
util.plt.show()
ground_truth = nd.array([[0, 0.1, 0.08, 0.52, 0.92],
[1, 0.55, 0.2, 0.9, 0.88]])
anchors = nd.array([[0, 0.1, 0.2, 0.3], [0.15, 0.2, 0.4, 0.4],
[0.63, 0.05, 0.88, 0.98], [0.66, 0.45, 0.8, 0.8],
[0.57, 0.3, 0.92, 0.9]])
fig = util.plt.imshow(img)
show_bboxes(fig.axes, ground_truth[:, 1:] * bbox_scale, ['dog', 'cat'],
from utils import util
from mpl_toolkits import mplot3d
import numpy as np
def f(x):
return x * np.cos(np.pi * x)
def f2(x):
return x**3
if __name__ == '__main__':
# 局部最小值，全局最小值
util.set_figsize((4.5, 2.5))
x = np.arange(-1.0, 2.0, 0.1)
fig, = util.plt.plot(x, f(x))
fig.axes.annotate('local minimum',
xy=(-0.3, -0.25),
xytext=(-0.77, -1.0),
arrowprops=dict(arrowstyle='->'))
fig.axes.annotate('global minimum',
xy=(1.1, -0.95),
xytext=(0.6, 0.8),
arrowprops=dict(arrowstyle='->'))
util.plt.xlabel('x')
util.plt.ylabel('f(x)')
util.plt.show()
# 鞍点，曲线的鞍点
