mirror of https://github.com/da0c/DL_Course_SamU
You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
134 lines
3.9 KiB
Python
134 lines
3.9 KiB
Python
from __future__ import print_function
|
|
from builtins import range
|
|
from past.builtins import xrange
|
|
|
|
import numpy as np
|
|
from random import randrange
|
|
|
|
|
|
def eval_numerical_gradient(f, x, verbose=True, h=0.00001):
|
|
"""
|
|
a naive implementation of numerical gradient of f at x
|
|
- f should be a function that takes a single argument
|
|
- x is the point (numpy array) to evaluate the gradient at
|
|
"""
|
|
|
|
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
|
|
|
|
|
|
def eval_numerical_gradient_array(f, x, df, h=1e-5):
|
|
"""
|
|
Evaluate a numeric gradient for a function that accepts a numpy
|
|
array and returns a numpy array.
|
|
"""
|
|
grad = np.zeros_like(x)
|
|
it = np.nditer(x, flags=["multi_index"], op_flags=["readwrite"])
|
|
while not it.finished:
|
|
ix = it.multi_index
|
|
|
|
oldval = x[ix]
|
|
x[ix] = oldval + h
|
|
pos = f(x).copy()
|
|
x[ix] = oldval - h
|
|
neg = f(x).copy()
|
|
x[ix] = oldval
|
|
|
|
grad[ix] = np.sum((pos - neg) * df) / (2 * h)
|
|
it.iternext()
|
|
return grad
|
|
|
|
|
|
def eval_numerical_gradient_blobs(f, inputs, output, h=1e-5):
|
|
"""
|
|
Compute numeric gradients for a function that operates on input
|
|
and output blobs.
|
|
|
|
We assume that f accepts several input blobs as arguments, followed by a
|
|
blob where outputs will be written. For example, f might be called like:
|
|
|
|
f(x, w, out)
|
|
|
|
where x and w are input Blobs, and the result of f will be written to out.
|
|
|
|
Inputs:
|
|
- f: function
|
|
- inputs: tuple of input blobs
|
|
- output: output blob
|
|
- h: step size
|
|
"""
|
|
numeric_diffs = []
|
|
for input_blob in inputs:
|
|
diff = np.zeros_like(input_blob.diffs)
|
|
it = np.nditer(input_blob.vals, flags=["multi_index"], op_flags=["readwrite"])
|
|
while not it.finished:
|
|
idx = it.multi_index
|
|
orig = input_blob.vals[idx]
|
|
|
|
input_blob.vals[idx] = orig + h
|
|
f(*(inputs + (output,)))
|
|
pos = np.copy(output.vals)
|
|
input_blob.vals[idx] = orig - h
|
|
f(*(inputs + (output,)))
|
|
neg = np.copy(output.vals)
|
|
input_blob.vals[idx] = orig
|
|
|
|
diff[idx] = np.sum((pos - neg) * output.diffs) / (2.0 * h)
|
|
|
|
it.iternext()
|
|
numeric_diffs.append(diff)
|
|
return numeric_diffs
|
|
|
|
|
|
def eval_numerical_gradient_net(net, inputs, output, h=1e-5):
|
|
return eval_numerical_gradient_blobs(
|
|
lambda *args: net.forward(), inputs, output, h=h
|
|
)
|
|
|
|
|
|
def grad_check_sparse(f, x, analytic_grad, num_checks=10, h=1e-5):
|
|
"""
|
|
sample a few random elements and only return numerical
|
|
in this dimensions.
|
|
"""
|
|
|
|
for i in range(num_checks):
|
|
ix = tuple([randrange(m) for m in x.shape])
|
|
|
|
oldval = x[ix]
|
|
x[ix] = oldval + h # increment by h
|
|
fxph = f(x) # evaluate f(x + h)
|
|
x[ix] = oldval - h # increment by h
|
|
fxmh = f(x) # evaluate f(x - h)
|
|
x[ix] = oldval # reset
|
|
|
|
grad_numerical = (fxph - fxmh) / (2 * h)
|
|
grad_analytic = analytic_grad[ix]
|
|
rel_error = abs(grad_numerical - grad_analytic) / (
|
|
abs(grad_numerical) + abs(grad_analytic)
|
|
)
|
|
print(
|
|
"numerical: %f analytic: %f, relative error: %e"
|
|
% (grad_numerical, grad_analytic, rel_error)
|
|
)
|