def scales_and_derivatives(self, phi):
"""Calculate the overall scale factor at each position in 'phi' and the
derivatives of that scale factor wrt all parameters of the model"""
# obtain data from all scale factor components
data = [f.get_factors_and_derivatives(phi) for f in self._factors]
# FIXME only using phi at the moment. In future will need other information
# such as s1 directions or central impacts, and will have to pass the right
# bits of information to the right ScaleFactor components contained here
scale_components, grad_components = zip(*data)
# the overall scale is the product of the separate scale components
overall_scale = reduce(lambda fac1, fac2: fac1 * fac2,
scale_components)
# to convert derivatives of each scale component to derivatives of the
# overall scale we multiply by the product of the other scale components,
# omitting the factor that has been differentiated
if len(scale_components) > 1:
omit_one_prods = products_omitting_one_item(scale_components)
grad_components = [row_multiply(g, coeff) for g, coeff in \
zip(grad_components, omit_one_prods)]
# Now combine the gradient components by columns to produce a single
# gradient matrix for the overall scale
each_ncol = [g.n_cols for g in grad_components]
tot_ncol = sum(each_ncol)
grad = sparse.matrix(len(overall_scale), tot_ncol)
col_start = [0] + each_ncol[:-1]
for icol, g in zip(col_start, grad_components):
grad.assign_block(g, 0, icol)
return overall_scale, grad
def scales_and_derivatives(self, phi):
"""Calculate the overall scale factor at each position in 'phi' and the
derivatives of that scale factor wrt all parameters of the model"""
# obtain data from all scale factor components
data = [f.get_factors_and_derivatives(phi) for f in self._factors]
# FIXME only using phi at the moment. In future will need other information
# such as s1 directions or central impacts, and will have to pass the right
# bits of information to the right ScaleFactor components contained here
scale_components, grad_components = zip(*data)
# the overall scale is the product of the separate scale components
overall_scale = reduce(lambda fac1, fac2: fac1 * fac2, scale_components)
# to convert derivatives of each scale component to derivatives of the
# overall scale we multiply by the product of the other scale components,
# omitting the factor that has been differentiated
if len(scale_components) > 1:
omit_one_prods = products_omitting_one_item(scale_components)
grad_components = [row_multiply(g, coeff) for g, coeff in \
zip(grad_components, omit_one_prods)]
# Now combine the gradient components by columns to produce a single
# gradient matrix for the overall scale
each_ncol = [g.n_cols for g in grad_components]
tot_ncol = sum(each_ncol)
grad = sparse.matrix(len(overall_scale), tot_ncol)
col_start = [0] + each_ncol[:-1]
for icol, g in zip(col_start, grad_components):
grad.assign_block(g, 0, icol)
return overall_scale, grad
def test_products_omitting_one_item():
def explicit_method(items, omit_idx=0):
"""Do the explicit (slow) calculation for comparison with the
products_omitting_one_item function"""
items = list(items)
del items[omit_idx]
return reduce(lambda x, y: x * y, items)
# test various random sequences of lengths between 2 and 10
for l in range(2, 10):
vals = [random.randrange(100) for i in range(l)]
prods = products_omitting_one_item(vals)
tst = [explicit_method(vals, i) for i in range(len(vals))]
for a, b in zip(prods, tst):
assert a == b
def test_products_omitting_one_item():
def explicit_method(items, omit_idx=0):
"""Do the explicit (slow) calculation for comparison with the
products_omitting_one_item function"""
items = list(items)
del items[omit_idx]
return reduce(lambda x, y: x*y, items)
# test various random sequences of lengths between 2 and 10
for l in range(2, 10):
vals = [random.randrange(100) for i in range(l)]
prods = products_omitting_one_item(vals)
tst = [explicit_method(vals, i) for i in range(len(vals))]
for a, b in zip(prods, tst):
assert a == b
print "OK"
