def hessian_analytical(self, x):
x1,x2,x3 = x
result = flex.double(flex.grid(3,3), 0)
for ti in meyer_function.ts:
denominator = ti + x3
assert denominator != 0
denominator_sq = denominator**2
assert denominator_sq != 0
denominator_cu = denominator**3
assert denominator_cu != 0
denominator_qa = denominator**4
assert denominator_qa != 0
term = math.exp(x2/denominator)
result[(0,0)] -= 0
result[(0,1)] -= term/denominator
result[(0,2)] -= -x2*term/denominator_sq
result[(1,1)] -= x1*term/denominator_sq
result[(1,2)] -= -x1*x2*term/denominator_cu - x1*term/denominator_sq
result[(2,2)] -= x1*x2**2*term/denominator_qa \
+ 2*x1*x2*term/denominator_cu
for i in range(0,3):
for j in range(i+1,3):
result[(j,i)] = result[(i,j)]
j = self.jacobian_analytical(x=x)
result += j.matrix_transpose().matrix_multiply(j)
return result
def hessian_analytical(self, x):
x1,x2,x3 = x
result = flex.double(flex.grid(3,3), 0)
for ti in meyer_function.ts:
denominator = ti + x3
assert denominator != 0
denominator_sq = denominator**2
assert denominator_sq != 0
denominator_cu = denominator**3
assert denominator_cu != 0
denominator_qa = denominator**4
assert denominator_qa != 0
term = math.exp(x2/denominator)
result[(0,0)] -= 0
result[(0,1)] -= term/denominator
result[(0,2)] -= -x2*term/denominator_sq
result[(1,1)] -= x1*term/denominator_sq
result[(1,2)] -= -x1*x2*term/denominator_cu - x1*term/denominator_sq
result[(2,2)] -= x1*x2**2*term/denominator_qa \
+ 2*x1*x2*term/denominator_cu
for i in xrange(0,3):
for j in xrange(i+1,3):
result[(j,i)] = result[(i,j)]
j = self.jacobian_analytical(x=x)
result += j.matrix_transpose().matrix_multiply(j)
return result
def exercise_1():
x = flex.double()
y = flex.double()
for x_ in range(0, 10):
x_ = x_ / 10.
x.append(x_)
y.append(2. * math.exp(-3. * x_**2))
r = scitbx.math.gaussian_fit_1d_analytical(x=x, y=y)
assert approx_equal(r.a, 2., 1.e-6)
assert approx_equal(r.b, 3., 1.e-6)
def exercise_1():
x = flex.double()
y = flex.double()
for x_ in xrange(0, 10):
x_ = x_/10.
x.append(x_)
y.append( 2.*math.exp(-3.*x_**2) )
r = scitbx.math.gaussian_fit_1d_analytical(x = x, y = y)
assert approx_equal(r.a, 2., 1.e-6)
assert approx_equal(r.b, 3., 1.e-6)
def f(self, x):
x1,x2,x3 = x
result = flex.double()
for yi,ti in zip(meyer_function.ys,
meyer_function.ts):
denominator = ti + x3
assert denominator != 0
result.append(x1 * math.exp(x2/denominator) - yi)
if (x[0] > 100): # numerical instability on some platforms
raise MeyerFunctionError
return result
def f(self, x):
x1,x2,x3 = x
result = flex.double()
for yi,ti in zip(meyer_function.ys,
meyer_function.ts):
denominator = ti + x3
assert denominator != 0
result.append(x1 * math.exp(x2/denominator) - yi)
if (x[0] > 100): # numerical instability on some platforms
raise MeyerFunctionError
return result
def mod_scores( self, x, k ):
if x> 10: x=10.0
gam = gamma_complete(k/2.0)
part1 = 2**(k/2.0)
part2 = x**((k/2.0)-1)
part3 = math.exp(-x/2.0)
tot1 = part2*part3/(part1*gam)
bart1 = gamma_incomplete_complement(k/2.0, x/2.0)
tot2 = bart1/gam
return math.log(tot1), math.log(tot2)
def jacobian_analytical(self, x):
x1,x2,x3 = x
result = flex.double()
for ti in meyer_function.ts:
denominator = ti + x3
assert denominator != 0
denominator_sq = denominator**2
assert denominator_sq != 0
term = math.exp(x2/denominator)
result.extend(flex.double([
term,
x1*term/denominator,
-x1*term*x2/denominator_sq]))
result.resize(flex.grid(self.m, self.n))
return result
def jacobian_analytical(self, x):
x1,x2,x3 = x
result = flex.double()
for ti in meyer_function.ts:
denominator = ti + x3
assert denominator != 0
denominator_sq = denominator**2
assert denominator_sq != 0
term = math.exp(x2/denominator)
result.extend(flex.double([
term,
x1*term/denominator,
-x1*term*x2/denominator_sq]))
result.resize(flex.grid(self.m, self.n))
return result
def compute_all( self ):
self.rg2s = []
self.lnis = []
self.free_scores = []
self.stop_qs = []
self.start_qs = []
for lim in self.lims:
rg2, lni, score, free_score, stop_q, start_q = self.compute_rg( lim[0], lim[1] )
rg2, lni, score, free_score, start_q, stop_q = self.filter( rg2, lni, score, free_score, stop_q, start_q )
if rg2 is not None:
self.accumulator.add_data( math.sqrt(rg2), math.exp(lni), free_score )
self.rg2s.append( math.sqrt(rg2) )
self.lnis.append( lni )
self.free_scores.append( score )
self.stop_qs.append( stop_q )
self.start_qs.append( stop_q )
def gradient(self, occupancy):
if (occupancy > self.occupancy_max): return 0
if (occupancy < -1): occupancy = -1 - math.log(-occupancy)
s = self.penalty_scale
return -s * self.penalty_factor * math.exp(
-s * occupancy * self.penalty_factor)
def functional(self, occupancy):
if (occupancy > self.occupancy_max): return 0
if (occupancy < -1): occupancy = -1 - math.log(-occupancy)
s = self.penalty_scale
return math.exp(-s * occupancy * self.penalty_factor)
def gradient(self, occupancy): if (occupancy > self.occupancy_max): return 0 if (occupancy < -1): occupancy = -1 - math.log(-occupancy) s = self.penalty_scale return -s*self.penalty_factor*math.exp(-s*occupancy*self.penalty_factor)
def functional(self, occupancy): if (occupancy > self.occupancy_max): return 0 if (occupancy < -1): occupancy = -1 - math.log(-occupancy) s = self.penalty_scale return math.exp(-s*occupancy*self.penalty_factor)