def compute_gradients(x, values=None):
"""Compute gradients using automatic differentiation.
x: The expression to compute gradients of.
values: As returned by compute_values(x); contains all values to compute
gradients with respect to.
"""
if values is None:
values = compute_values(x)
if not isinstance(values, collections.OrderedDict): raise TypeError()
if x not in values: raise ValueError()
gradients = {x: 1.}
for subx in values:
if isinstance(subx, expr.parameter) or any(arg in gradients for arg in subx.args):
if subx not in gradients:
gradients[subx] = 0.
for subx in reversed(values): # assume values is in topological order
if subx not in gradients:
continue
if logging.trace:
sys.stdout.write("d<%s>/d<%s> = %s" % (x.serial, subx.serial, format_value(gradients[subx])))
try:
subx.backward(values, gradients)
if logging.trace:
for arg in subx.args:
sys.stdout.write(" d<%s>/d<%s> := %s" % (x.serial, arg.serial, format_value(gradients[arg], indent=8)))
except:
if logging.debug:
sys.stderr.write("Expression traceback (most recent call last):\n" + "".join(logging.format_list(subx.stack)))
raise
return gradients
def compute_values(x, initvalues={}):
"""Evaluate an expression and all its subexpressions.
x: The expression to evaluate.
initvalues: Optional dictionary from subexpressions to
precomputed values; can be used to continue a
computation when the expression grows.
"""
values = collections.OrderedDict()
for subx in expr.topological(x):
if subx in initvalues:
values[subx] = initvalues[subx]
else:
try:
subx.forward(values)
except:
if logging.debug:
sys.stderr.write("Expression traceback (most recent call last):\n" + "".join(logging.format_list(subx.stack)))
raise
if logging.trace:
sys.stdout.write("<%s> = %s = %s" % (subx.serial, subx, format_value(values[subx])))
return values