def compute_restraints_functional_gradients_and_curvatures(self):
'''use the restraints_parameterisation object, if present, to
calculate the least squares restraints objective plus gradients and
approximate curvatures'''
if not self._restraints_parameterisation: return None
residuals, jacobian, weights = \
self._restraints_parameterisation.get_residuals_gradients_and_weights()
w_resid = weights * residuals
residuals2 = residuals * residuals
# calculate target function
L = 0.5 * flex.sum(weights * residuals2)
# calculate gradients using the scalar product of sparse vector col with
# dense vector w_resid
dL_dp = [col * w_resid for col in jacobian.cols()]
# calculate lsq approximation to curvatures using weighted dot product
curvs = [
sparse.weighted_dot(col, weights, col) for col in jacobian.cols()
]
return (L, dL_dp, curvs)
def compute_restraints_functional_gradients_and_curvatures(self):
'''use the restraints_parameterisation object, if present, to
calculate the least squares restraints objective plus gradients and
approximate curvatures'''
if not self._restraints_parameterisation: return None
residuals, jacobian, weights = \
self._restraints_parameterisation.get_residuals_gradients_and_weights()
w_resid = weights * residuals
residuals2 = residuals * residuals
# calculate target function
L = 0.5 * flex.sum(weights * residuals2)
# calculate gradients using the scalar product of sparse vector col with
# dense vector w_resid
dL_dp = [col * w_resid for col in jacobian.cols()]
# calculate lsq approximation to curvatures using weighted dot product
curvs = [sparse.weighted_dot(col, weights, col) for col in jacobian.cols()]
return (L, dL_dp, curvs)
def exercise_vector():
v = sparse.vector(5)
assert v.size == 5
assert v.is_structurally_zero()
v[1] = 2
v[2] = 0
v[3] = 6
assert list(v) == [(1, 2.), (2, 0.), (3, 6.)]
assert list(v.compact()) == [(1, 2.), (2, 0.), (3, 6.)]
assert [v[i] for i in xrange(5)] == [0, 2, 0, 6, 0]
p = flex.size_t([1, 2, 3, 4, 0])
assert list(v.permute(p)) == [(2, 2.), (3, 0.), (4, 6.)]
assert v.non_zeroes == 3
v = sparse.vector(10)
v[7] = -5
v[1] = -1
v[4] = 0
v[1] = 2
v[9] = 9.
v[7] = 6
v[4] = 1
v[1] = 3
v[4] = 0
assert list(v.compact()) == [(1, 3.), (4, 0.), (7, 6.), (9, 9.)]
assert ([v.is_structural_zero(i) for i in xrange(10)] == [
True, False, True, True, False, True, True, False, True, False
])
v = sparse.vector(10)
v[4] += 1
v[5] += 2
v[4] += 2
v[5] = 1
v[3] = 2
v[5] += 3
assert list(v.compact()) == [(3, 2.), (4, 3.), (5, 4.)]
assert v.non_zeroes == 3
v = sparse.vector(6)
v[3] = 1
v[2] = 1
v[5] = 1
assert v.size == 6
v[7] = 1
assert v[7] == 0
assert v.size == 6
u = flex.double((1, -1, 2, 0, -2))
v = sparse.vector(5)
v[0] = 10
v[3] = 4
v[4] = 5
assert u * v == 0
u = sparse.vector(10, {1: 1, 3: 3, 7: 7})
v = sparse.vector(10, {0: -1, 1: 2, 7: -1, 8: 2})
assert u * v == -5
assert sparse.weighted_dot(u, flex.double_range(10), v) == -47
a = flex.double()
for i in xrange(10):
for j in xrange(i, 10):
a.append(1 / (i + j + 1))
assert approx_equal(sparse.quadratic_form(u, a, v), 4003 / 1980, eps=1e-15)
assert approx_equal(sparse.quadratic_form(a, u),
sparse.quadratic_form(u, a, u),
eps=1e-15)
sparse_approx_equal = sparse.approx_equal(tolerance=0.1)
u = sparse.vector(4)
u[0] = 1.01
v = sparse.vector(4)
v[0] = 1.02
v[3] = 0.001
assert sparse_approx_equal(u, v)
u = sparse.vector(4)
v = sparse.vector(4)
v[3] = 0.001
assert sparse_approx_equal(u, v)
u = sparse.vector(5, {3: 0.3, 1: 0.1})
assert list(u.as_dense_vector()) == [0, 0.1, 0, 0.3, 0]
try:
sparse.vector(4, [1, 2, 3, 4])
raise Exception_expected
except Exception, e:
assert e.__class__.__module__ == 'Boost.Python'
assert e.__class__.__name__ == 'ArgumentError'
def exercise_vector():
v = sparse.vector(5)
assert v.size == 5
assert v.is_structurally_zero()
v[1] = 2
v[2] = 0
v[3] = 6
assert list(v) == [(1, 2.), (2, 0.), (3, 6.)]
assert list(v.compact()) == [(1, 2.), (2, 0.), (3, 6.)]
assert [v[i] for i in range(5)] == [0, 2, 0, 6, 0]
p = flex.size_t([1, 2, 3, 4, 0])
assert list(v.permute(p)) == [(2, 2.), (3, 0.), (4, 6.)]
assert v.non_zeroes == 3
v = sparse.vector(10)
v[7] = -5
v[1] = -1
v[4] = 0
v[1] = 2
v[9] = 9.
v[7] = 6
v[4] = 1
v[1] = 3
v[4] = 0
assert list(v.compact()) == [(1, 3.), (4, 0.), (7, 6.), (9, 9.)]
assert ([v.is_structural_zero(i) for i in range(10)] == [
True, False, True, True, False, True, True, False, True, False
])
v = sparse.vector(10)
v[4] += 1
v[5] += 2
v[4] += 2
v[5] = 1
v[3] = 2
v[5] += 3
assert list(v.compact()) == [(3, 2.), (4, 3.), (5, 4.)]
assert v.non_zeroes == 3
v = sparse.vector(6)
v[3] = 1
v[2] = 1
v[5] = 1
assert v.size == 6
v[7] = 1
assert v[7] == 0
assert v.size == 6
u = flex.double((1, -1, 2, 0, -2))
v = sparse.vector(5)
v[0] = 10
v[3] = 4
v[4] = 5
assert u * v == 0
u = sparse.vector(10, {1: 1, 3: 3, 7: 7})
v = sparse.vector(10, {0: -1, 1: 2, 7: -1, 8: 2})
assert u * v == -5
assert sparse.weighted_dot(u, flex.double_range(10), v) == -47
a = flex.double()
for i in range(10):
for j in range(i, 10):
a.append(1 / (i + j + 1))
assert approx_equal(sparse.quadratic_form(u, a, v), 4003 / 1980, eps=1e-15)
assert approx_equal(sparse.quadratic_form(a, u),
sparse.quadratic_form(u, a, u),
eps=1e-15)
sparse_approx_equal = sparse.approx_equal(tolerance=0.1)
u = sparse.vector(4)
u[0] = 1.01
v = sparse.vector(4)
v[0] = 1.02
v[3] = 0.001
assert sparse_approx_equal(u, v)
u = sparse.vector(4)
v = sparse.vector(4)
v[3] = 0.001
assert sparse_approx_equal(u, v)
u = sparse.vector(5, {3: 0.3, 1: 0.1})
assert list(u.as_dense_vector()) == [0, 0.1, 0, 0.3, 0]
try:
sparse.vector(4, [1, 2, 3, 4])
raise Exception_expected
except Exception as e:
assert e.__class__.__module__ == 'Boost.Python'
assert e.__class__.__name__ == 'ArgumentError'
u = sparse.vector(4, {1: 1, 3: 3})
v = flex.double([1, 2, 3, 4])
assert u * v == 14
u = sparse.vector(5)
s = flex.bool((True, False, False, True, True))
v = flex.double((1, 2, 3, 4, 5))
u.set_selected(s, v)
assert u == sparse.vector(5, {0: 1, 3: 4, 4: 5})
u = sparse.vector(7)
i = flex.size_t((2, 4, 5))
v = flex.double((-2.0, -4.0, -5.0))
u.set_selected(i, v)
assert u == sparse.vector(7, {2: -2.0, 4: -4.0, 5: -5.0})
sparse_approx_equal = sparse.approx_equal(tolerance=1e-15)
def linear_combination_trial_vectors():
u = sparse.vector(8, {1: 1.1, 3: 1.3})
v = sparse.vector(8, {0: 2.0, 2: 2.2, 3: 2.3, 4: 2.4})
w = list(-2 * u.as_dense_vector() + 3 * v.as_dense_vector())
yield u, v, w
random_vectors = scitbx.random.variate(
sparse.vector_distribution(
8,
density=0.4,
elements=scitbx.random.uniform_distribution(min=-2, max=2)))
u = next(random_vectors)
v = next(random_vectors)
w = list(-2 * u.as_dense_vector() + 3 * v.as_dense_vector())
yield u, v, w
for u, v, w in itertools.islice(linear_combination_trial_vectors(), 50):
w1 = -2 * u + 3 * v
w2 = 3 * v - 2 * u
assert sparse_approx_equal(w1, w2)
assert approx_equal(list(w1.as_dense_vector()), w, eps=1e-15)
w1 += 2 * u
w1 /= 3
assert sparse_approx_equal(w1, v)
w2 -= 3 * v
w2 /= -2
assert sparse_approx_equal(w2, u)
u = sparse.vector(3, {1: 2})
v = u / 2
assert v == sparse.vector(3, {1: 1})
def exercise_vector():
v = sparse.vector(5)
assert v.size == 5
assert v.is_structurally_zero()
v[1] = 2
v[2] = 0
v[3] = 6
assert list(v) == [(1,2.), (2,0.), (3,6.)]
assert list(v.compact()) == [(1,2.), (2,0.), (3,6.)]
assert [ v[i] for i in xrange(5) ] == [0, 2, 0, 6, 0]
p = flex.size_t([1,2,3,4,0])
assert list(v.permute(p)) == [(2,2.), (3,0.), (4,6.)]
assert v.non_zeroes == 3
v = sparse.vector(10)
v[7] = -5
v[1] = -1
v[4] = 0
v[1] = 2
v[9] = 9.
v[7] = 6
v[4] = 1
v[1] = 3
v[4] = 0
assert list(v.compact()) == [(1,3.), (4,0.), (7,6.), (9,9.)]
assert ([ v.is_structural_zero(i) for i in xrange(10) ]
==
[ True, False, True, True, False, True, True, False, True, False ])
v = sparse.vector(10)
v[4] += 1
v[5] += 2
v[4] += 2
v[5] = 1
v[3] = 2
v[5] += 3
assert list(v.compact()) == [ (3,2.), (4,3.), (5,4.) ]
assert v.non_zeroes == 3
v = sparse.vector(6)
v[3] = 1
v[2] = 1
v[5] = 1
assert v.size == 6
v[7] = 1
assert v[7] == 0
assert v.size == 6
u = flex.double((1, -1, 2, 0, -2))
v = sparse.vector(5)
v[0] = 10
v[3] = 4
v[4] = 5
assert u*v == 0
u = sparse.vector(10, {1:1, 3:3, 7:7})
v = sparse.vector(10, {0:-1, 1:2, 7:-1, 8:2})
assert u*v == -5
assert sparse.weighted_dot(u, flex.double_range(10), v) == -47
a = flex.double()
for i in xrange(10):
for j in xrange(i,10):
a.append(1/(i+j+1))
assert approx_equal(sparse.quadratic_form(u, a, v), 4003/1980,
eps=1e-15)
assert approx_equal(sparse.quadratic_form(a, u),
sparse.quadratic_form(u, a, u),
eps=1e-15)
sparse_approx_equal = sparse.approx_equal(tolerance=0.1)
u = sparse.vector(4)
u[0] = 1.01
v = sparse.vector(4)
v[0] = 1.02
v[3] = 0.001
assert sparse_approx_equal(u,v)
u = sparse.vector(4)
v = sparse.vector(4)
v[3] = 0.001
assert sparse_approx_equal(u,v)
u = sparse.vector(5, {3: 0.3, 1: 0.1})
assert list(u.as_dense_vector()) == [ 0, 0.1, 0, 0.3, 0 ]
try:
sparse.vector(4, [1, 2, 3, 4])
raise Exception_expected
except Exception, e:
assert e.__class__.__module__ == 'Boost.Python'
assert e.__class__.__name__ == 'ArgumentError'
