Content with notebooks#
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import numpy as np
import matplotlib.pyplot as plt
plt.style.use('./deeplearning.mplstyle')
np.set_printoptions(precision=2) # reduced display precision on numpy arrays
---------------------------------------------------------------------------
FileNotFoundError Traceback (most recent call last)
File /opt/homebrew/anaconda3/lib/python3.11/site-packages/matplotlib/style/core.py:137, in use(style)
136 try:
--> 137 style = _rc_params_in_file(style)
138 except OSError as err:
File /opt/homebrew/anaconda3/lib/python3.11/site-packages/matplotlib/__init__.py:866, in _rc_params_in_file(fname, transform, fail_on_error)
865 rc_temp = {}
--> 866 with _open_file_or_url(fname) as fd:
867 try:
File /opt/homebrew/anaconda3/lib/python3.11/contextlib.py:137, in _GeneratorContextManager.__enter__(self)
136 try:
--> 137 return next(self.gen)
138 except StopIteration:
File /opt/homebrew/anaconda3/lib/python3.11/site-packages/matplotlib/__init__.py:843, in _open_file_or_url(fname)
842 fname = os.path.expanduser(fname)
--> 843 with open(fname, encoding='utf-8') as f:
844 yield f
FileNotFoundError: [Errno 2] No such file or directory: './deeplearning.mplstyle'
The above exception was the direct cause of the following exception:
OSError Traceback (most recent call last)
Cell In[1], line 3
1 import numpy as np
2 import matplotlib.pyplot as plt
----> 3 plt.style.use('./deeplearning.mplstyle')
4 np.set_printoptions(precision=2)
File /opt/homebrew/anaconda3/lib/python3.11/site-packages/matplotlib/style/core.py:139, in use(style)
137 style = _rc_params_in_file(style)
138 except OSError as err:
--> 139 raise OSError(
140 f"{style!r} is not a valid package style, path of style "
141 f"file, URL of style file, or library style name (library "
142 f"styles are listed in `style.available`)") from err
143 filtered = {}
144 for k in style: # don't trigger RcParams.__getitem__('backend')
OSError: './deeplearning.mplstyle' is not a valid package style, path of style file, URL of style file, or library style name (library styles are listed in `style.available`)
X_train = np.array([[2104, 5, 1, 45], [1416, 3, 2, 40], [852, 2, 1, 35]])
y_train = np.array([460, 232, 178])
# data is stored in numpy array/matrix
print(f"X Shape: {X_train.shape}, X Type:{type(X_train)})")
print(X_train)
print(f"y Shape: {y_train.shape}, y Type:{type(y_train)})")
print(y_train)
X Shape: (3, 4), X Type:<class 'numpy.ndarray'>)
[[2104 5 1 45]
[1416 3 2 40]
[ 852 2 1 35]]
y Shape: (3,), y Type:<class 'numpy.ndarray'>)
[460 232 178]
def gradient_descent(X, y, w_in, b_in, cost_function, gradient_function, alpha, num_iters):
"""
Performs batch gradient descent to learn w and b. Updates w and b by taking
num_iters gradient steps with learning rate alpha
Args:
X (ndarray (m,n)) : Data, m examples with n features
y (ndarray (m,)) : target values
w_in (ndarray (n,)) : initial model parameters
b_in (scalar) : initial model parameter
cost_function : function to compute cost
gradient_function : function to compute the gradient
alpha (float) : Learning rate
num_iters (int) : number of iterations to run gradient descent
Returns:
w (ndarray (n,)) : Updated values of parameters
b (scalar) : Updated value of parameter
"""
# An array to store cost J and w's at each iteration primarily for graphing later
J_history = []
w = copy.deepcopy(w_in) #avoid modifying global w within function
b = b_in
for i in range(num_iters):
# Calculate the gradient and update the parameters
dj_db,dj_dw = gradient_function(X, y, w, b) ##None
# Update Parameters using w, b, alpha and gradient
w = w - alpha * dj_dw ##None
b = b - alpha * dj_db ##None
# Save cost J at each iteration
if i<100000: # prevent resource exhaustion
J_history.append( cost_function(X, y, w, b))
# Print cost every at intervals 10 times or as many iterations if < 10
if i% math.ceil(num_iters / 10) == 0:
print(f"Iteration {i:4d}: Cost {J_history[-1]:8.2f} ")
return w, b, J_history #return final w,b and J history for graphing
# initialize parameters
initial_w = np.zeros_like(w_init)
initial_b = 0.
# some gradient descent settings
iterations = 1000
alpha = 5.0e-7
# run gradient descent
w_final, b_final, J_hist = gradient_descent(X_train, y_train, initial_w, initial_b,
compute_cost, compute_gradient,
alpha, iterations)
print(f"b,w found by gradient descent: {b_final:0.2f},{w_final} ")
m,_ = X_train.shape
for i in range(m):
print(f"prediction: {np.dot(X_train[i], w_final) + b_final:0.2f}, target value: {y_train[i]}")
# plot cost versus iteration
fig, (ax1, ax2) = plt.subplots(1, 2, constrained_layout=True, figsize=(12, 4))
ax1.plot(J_hist)
ax2.plot(100 + np.arange(len(J_hist[100:])), J_hist[100:])
ax1.set_title("Cost vs. iteration"); ax2.set_title("Cost vs. iteration (tail)")
ax1.set_ylabel('Cost') ; ax2.set_ylabel('Cost')
ax1.set_xlabel('iteration step') ; ax2.set_xlabel('iteration step')
plt.show()