def gradient_descent(D,X0,feedback=False,plot=False,**kwargs):
"""\
Solution to MDS problem using gradient descent
--- arguments ---
D : target distance matrix (n x n)
X0 : initial positions, organized by row (n x p)
feedback = prints feedback if set to True
--- kwargs ---
rate, max_iters, min_step, max_step, trajectory, costs
"""
if feedback is True:
print("\nmds.gradient_descent():")
if plot is True:
kwargs['step_history'] = True
kwargs['cost_history'] = True
df = lambda x: gradient(x,D)
f = lambda x: stress(x,D)
results = gd.gradient_descent(X0,df,f=f,feedback=feedback,plot_history=plot,
**kwargs)
return results
def Xdescent(X0, Qs, Ds, feedback=False, **kwargs):
"""\
X solution to multiview-MDSq problem using gradient descent.
--- arguments ---
X0 : initial positions, organized by row (n x p)
Qs = list of orthogonal matrices
Ds : list of target distance matrices (n x n)
"""
if feedback is True:
print("\nmmdsq.Xdescent():")
df = lambda x: Xgradient(x, Qs, Ds)
f = lambda x: stress(x, Qs, Ds)
results = gd.gradient_descent(X0, df, f=f, feedback=feedback, **kwargs)
return results
def Qdescent(X, Q0, D, feedback=False, plot=False, **kwargs):
"""\
MDSq Q optimization
--- arguments ---
X = node positions
Q0 = initial orthogonal matrix
D = target distances
feedback = set to True to print feedback
plot = set to True to return stress plot
"""
if feedback is True:
print("\nmdsq.Qdescent():")
print(f" initial stress = {stress(X,Q0,D):.2e}")
if plot is True:
kwargs['cost_history'] = True
kwargs['step_history'] = True
df = lambda Q: Qgradient(X, Q, D)
f = lambda Q: stress(X, Q, D)
p = lambda Q: nearest_orthogonal(Q)
results = gd.gradient_descent(Q0,
df,
projection=p,
f=f,
plot_history=True,
**kwargs)
if feedback is True:
Q = results['output']
print(f" final stress = {stress(X,Q,D):.2e}")
if plot is True:
plt.show()
return results
from matplotlib import pyplot as plt
from gd import gradient_descent
if __name__ == '__main__':
lr = [0.001, 0.005, 0.01, 0.05, 0.1, 0.5]
for a in lr:
path = gradient_descent(50, a, 0.01)
plt.plot(path[:, 0], path[:, 1], label=str(a))
plt.legend()
plt.xlabel("x1")
plt.ylabel("x2")
plt.savefig("gd_random_lr_fun.png")
plt.show()
import sys
from matplotlib import pyplot as plt
from gd import gradient_descent
if __name__ == '__main__':
iter = int(sys.argv[1])
alpha = float(sys.argv[2])
epsilon = float(sys.argv[3])
fig, ax = plt.subplots()
for i in range(10):
path = gradient_descent(iter, alpha, epsilon)
ax.plot(path[:, 0], path[:, 1])
ax.set_xlabel("x1")
ax.set_ylabel("x2")
plt.savefig("gd_random_init_fun.png")
plt.show()
import gd
from functools import *
import numpy as np
def residuals(betas, x, y):
X = np.full((x.size, 2), 1.0)
X[:,1] = x
return y - np.matmul(X, betas)
def ssr_grad(betas, x, y):
r = residuals(betas, x, y)
return [-2 * r.sum(), -2 * np.dot(r, x)]
def ssr_loss(betas, x, y):
r = residuals(betas, x, y)
return np.dot(r, r)
if __name__ == "__main__":
x = np.linspace(0.0, 16.0, 8)
y = 1 + 2 * x
search = gd.gradient_descent(
gradient = lambda b : ssr_grad(b, x, y),
start = [0.1, 3.4],
learn_rate = 0.0001,
n_iter = 100000)
for it in search:
print(f'{it.i} {it.step} {it.result}')
import gd
from functools import *
if __name__ == "__main__":
f = lambda x: x * x
g = lambda x: 2 * x
print('descending')
r = reduce(lambda v, e: f'{v}\n{e.i} {e.step} {e.result}',
gd.gradient_descent(g, 4, 0.8, 1000), '')
print(f'{r}')
y = np.linspace(-1.5, 1.5, 50)
X, Y = np.meshgrid(x, y)
zs = np.array([func(x,y) for x,y in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)
ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
cmap='viridis', edgecolor='none')
x0 = max(x)
y0 = max(y)
learning_rate = 2
epoch = 500
x_gd, y_gd, z_gd = gradient_descent(x0, y0, learning_rate, epoch)
min_point = np.array([max(x), max(y)])
min_point_ = min_point[:, np.newaxis]
ax.plot(*min_point_, func(*min_point_), 'r*', markersize=10)
ax.set_title('surface')
ax.plot(x_gd, y_gd, 'go')
'''for i in range(1, epoch+1):
ax.annotate('', xy=(x_gd[i], y_gd[i]), xytext=(x_gd[i-1], y_gd[i-1]),
arrowprops={'arrowstyle': '->', 'color': 'r', 'lw': 1},
va='center', ha='center')
some = list(zs)
#print(some.index(min(some)))
#print(some[2210])'''
plt.show()