def exercise_a_tr_diag_a():
a = sparse.matrix(9, 7)
for i in xrange(a.n_rows):
for j in xrange(a.n_cols):
if (2*i + j) % 3 == 1: a[i,j] = 1
w = flex.double([ (-1)**i*i for i in xrange(a.n_rows) ])
b = a.self_transpose_times_diagonal_times_self(w)
b0 = sparse.matrix(7, 7)
b0[0, 0] = 5.
b0[0, 3] = 5.
b0[0, 6] = 5.
b0[1, 1] = 3.
b0[1, 4] = 3.
b0[2, 2] = -4.
b0[2, 5] = -4.
b0[3, 0] = 5.
b0[3, 3] = 5.
b0[3, 6] = 5.
b0[4, 1] = 3.
b0[4, 4] = 3.
b0[5, 2] = -4.
b0[5, 5] = -4.
b0[6, 0] = 5.
b0[6, 3] = 5.
b0[6, 6] = 5.
assert sparse.approx_equal(tolerance=1e-12)(b, b0)
def run(self):
self.reparam.linearise()
self.reparam.store()
uc = self.cs.unit_cell()
_ = mat.col
xh, xo, x1, x2 = [
uc.orthogonalize(sc.site)
for sc in (self.h, self.o, self.c1, self.c2)
]
u_12 = _(x2) - _(x1)
u_o1 = _(x1) - _(xo)
u_oh = _(xh) - _(xo)
assert approx_equal(u_12.cross(u_o1).dot(u_oh), 0, self.eps)
assert approx_equal(
u_12.cross(u_o1).angle(u_oh, deg=True), 90, self.eps)
assert approx_equal(abs(u_oh), self.bond_length, self.eps)
assert approx_equal(u_o1.angle(u_oh, deg=True), 109.47, 0.01)
jt0 = sparse.matrix(3, 14)
for i in xrange(3):
jt0[self.xo + i, self.xo + i] = 1.
jt0[self.xo + i, self.xh + i] = 1.
jt = self.reparam.jacobian_transpose
assert sparse.approx_equal(self.eps)(jt, jt0)
if self.verbose:
# finite difference derivatives to compare with
# the crude riding approximation used for analytical ones
def differentiate(sc):
eta = 1.e-4
jac = []
for i in xrange(3):
x0 = tuple(sc.site)
x = list(x0)
x[i] += eta
sc.site = tuple(x)
self.reparam.linearise()
self.reparam.store()
xp = _(self.h.site)
x[i] -= 2 * eta
sc.site = tuple(x)
self.reparam.linearise()
self.reparam.store()
xm = _(self.h.site)
sc.site = tuple(x0)
jac.extend((xp - xm) / (2 * eta))
return mat.sqr(jac)
jac_o = differentiate(self.o)
jac_1 = differentiate(self.c1)
jac_2 = differentiate(self.c2)
print("staggered: %s" % self.staggered)
print("J_o:")
print(jac_o.mathematica_form())
print("J_1:")
print(jac_1.mathematica_form())
print("J_2:")
print(jac_2.mathematica_form())
def run(self):
self.reparam.linearise()
self.reparam.store()
uc = self.cs.unit_cell()
_ = mat.col
xh, xo, x1, x2 = [ uc.orthogonalize(sc.site)
for sc in (self.h, self.o, self.c1, self.c2) ]
u_12 = _(x2) - _(x1)
u_o1 = _(x1) - _(xo)
u_oh = _(xh) - _(xo)
assert approx_equal(u_12.cross(u_o1).dot(u_oh), 0, self.eps)
assert approx_equal(u_12.cross(u_o1).angle(u_oh, deg=True), 90, self.eps)
assert approx_equal(abs(u_oh), self.bond_length, self.eps)
assert approx_equal(u_o1.angle(u_oh, deg=True), 109.47, 0.01)
jt0 = sparse.matrix(3, 14)
for i in xrange(3):
jt0[self.xo + i, self.xo + i] = 1.
jt0[self.xo + i, self.xh + i] = 1.
jt = self.reparam.jacobian_transpose
assert sparse.approx_equal(self.eps)(jt, jt0)
if self.verbose:
# finite difference derivatives to compare with
# the crude riding approximation used for analytical ones
def differentiate(sc):
eta = 1.e-4
jac = []
for i in xrange(3):
x0 = tuple(sc.site)
x = list(x0)
x[i] += eta
sc.site = tuple(x)
self.reparam.linearise()
self.reparam.store()
xp = _(self.h.site)
x[i] -= 2*eta
sc.site = tuple(x)
self.reparam.linearise()
self.reparam.store()
xm = _(self.h.site)
sc.site = tuple(x0)
jac.extend( (xp - xm)/(2*eta) )
return mat.sqr(jac)
jac_o = differentiate(self.o)
jac_1 = differentiate(self.c1)
jac_2 = differentiate(self.c2)
print "staggered: %s" % self.staggered
print "J_o:"
print jac_o.mathematica_form()
print "J_1:"
print jac_1.mathematica_form()
print "J_2:"
print jac_2.mathematica_form()
def exercise_matrix():
a = sparse.matrix(10, 7)
assert a.n_rows == 10 and a.n_cols == 7
for c in a.cols():
assert c.is_structurally_zero()
a[0, 1] = 1.
a[9, 5] = 2.
assert a.non_zeroes == 2
for i in xrange(10):
for j in xrange(7):
if (i, j) == (0, 1): assert a[i, j] == 1.
elif (i, j) == (9, 5): assert a[i, j] == 2.
else: assert a[i, j] == 0, (i, j, a[i, j])
a = sparse.matrix(6, 3)
assert a.n_rows == 6
a[1, 1] = 1.
a[3, 2] = 2.
a[5, 1] = 2.
a[4, 0] = 1.
assert a.non_zeroes == 4
assert a.n_rows == 6
a[7, 0] = 1.
assert a[7, 0] == 0
assert a.n_rows == 6
a = sparse.matrix(4, 3)
a[0, 1] = 1.01
b = sparse.matrix(4, 3)
b[0, 1] = 1.02
b[3, 2] = 0.001
approx_equal = sparse.approx_equal(tolerance=0.1)
assert approx_equal(a, b)
m = 10
a = sparse.matrix(m, 2)
columns = (sparse.matrix_column(m, {
1: 0.1,
2: 0.2
}), sparse.matrix_column(m, {
4: 0.4,
8: 0.8
}))
a[:, 0] = columns[0]
a[:, 1] = columns[1]
assert a[:, 0], a[:, 1] == columns
try:
a[1, :] = sparse.vector(2, {1: 1})
raise Exception_expected
except RuntimeError, e:
assert str(e)
def exercise_matrix():
a = sparse.matrix(10,7)
assert a.n_rows == 10 and a.n_cols == 7
for c in a.cols():
assert c.is_structurally_zero()
a[0,1] = 1.
a[9,5] = 2.
assert a.non_zeroes == 2
for i in xrange(10):
for j in xrange(7):
if (i,j) == (0,1): assert a[i,j] == 1.
elif (i,j) == (9,5): assert a[i,j] == 2.
else: assert a[i,j] == 0, (i, j, a[i,j])
a = sparse.matrix(6, 3)
assert a.n_rows == 6
a[1,1] = 1.
a[3,2] = 2.
a[5,1] = 2.
a[4,0] = 1.
assert a.non_zeroes == 4
assert a.n_rows == 6
a[7,0] = 1.
assert a[7,0] == 0
assert a.n_rows == 6
a = sparse.matrix(4,3)
a[0,1] = 1.01
b = sparse.matrix(4,3)
b[0,1] = 1.02
b[3,2] = 0.001
approx_equal = sparse.approx_equal(tolerance=0.1)
assert approx_equal(a,b)
m = 10
a = sparse.matrix(m, 2)
columns = ( sparse.matrix_column(m, {1:0.1, 2:0.2}),
sparse.matrix_column(m, {4:0.4, 8:0.8}) )
a[:,0] = columns[0]
a[:,1] = columns[1]
assert a[:,0], a[:,1] == columns
try:
a[1,:] = sparse.vector(2, {1:1})
raise Exception_expected
except RuntimeError, e:
assert str(e)
def run(self):
self.reparam.linearise()
self.reparam.store()
assert approx_equal(self.sc.u_star, (19/6, 19/6, 17/2,
11/6, 9/2, 9/2), self.eps)
jt0 = sparse.matrix(2, 8)
jt0[0, 0] = 1
jt0[1, 1] = 1
jac_u_star_trans = self.site_symm.adp_constraints().gradient_sum_matrix()
jac_u_star_trans.reshape(flex.grid(
self.site_symm.adp_constraints().n_independent_params(), 6))
(m,n) = jac_u_star_trans.focus()
for i in xrange(m):
for j in xrange(n):
jt0[i, j + 2] = jac_u_star_trans[i, j]
jt = self.reparam.jacobian_transpose
assert sparse.approx_equal(self.eps)(jt, jt0)
def run(self):
self.reparam.linearise()
self.reparam.store()
x_c0, x_c1, x_h = [
mat.col(sc.site) for sc in (self.c0, self.c1, self.h)
]
if self.with_special_position_pivot:
assert approx_equal(x_c0, self.site_symm.exact_site(), self.eps)
assert approx_equal(self.uc.angle(x_c1, x_c0, x_h), 180, self.eps)
assert approx_equal(self.uc.distance(x_c0, x_h), self.bond_length,
self.eps)
if self.with_special_position_pivot:
jt0 = sparse.matrix(
1 + 3, # y0, x1
1 + 3 + 3 + 1 + 3) # y0, x0, x1, l, x_h
else:
jt0 = sparse.matrix(
3 + 3, # x0, x1
3 + 3 + +1 + 3) # x0, x1, l, x_h
# Identity for independent parameters
if self.with_special_position_pivot:
jt0[self.y0, self.y0] = 1.
for i in xrange(3):
jt0[self.x0 + i, self.x0 + i] = 1.
for i in xrange(3):
jt0[self.x1 + i, self.x1 + i] = 1.
# special position x0
if self.with_special_position_pivot:
jt0[self.y0, self.x0] = 0
jt0[self.y0, self.x0 + 1] = 0
jt0[self.y0, self.x0 + 2] = 1.
# riding
if self.with_special_position_pivot:
jt0[self.y0, self.x_h + 2] = 1.
else:
for i in xrange(3):
jt0[self.x0 + i, self.x_h + i] = 1.
jt = self.reparam.jacobian_transpose
assert sparse.approx_equal(self.eps)(jt, jt0)
def exercise_u_iso_proportional_to_pivot_u_eq():
xs = xray.structure(crystal_symmetry=crystal.symmetry(
unit_cell=(), space_group_symbol='hall: P 2x 2y'),
scatterers=flex.xray_scatterer((
xray.scatterer('C0', u=(1, 1, 1, 0, 0, 0)),
xray.scatterer('C1'),
xray.scatterer('C2',
site=(0.1, 0.2, 0.3),
u=(1, 2, 3, 0, 0, 0)),
xray.scatterer('C3'),
)))
r = constraints.ext.reparametrisation(xs.unit_cell())
sc = xs.scatterers()
sc[0].flags.set_grad_u_aniso(True)
sc[2].flags.set_grad_u_aniso(True)
u_0 = r.add(constraints.special_position_u_star_parameter,
site_symmetry=xs.site_symmetry_table().get(0),
scatterer=sc[0])
u_iso_1 = r.add(constraints.u_iso_proportional_to_pivot_u_eq,
pivot_u=u_0,
multiplier=3,
scatterer=sc[1])
u_2 = r.add(constraints.independent_u_star_parameter, sc[2])
u_iso_3 = r.add(constraints.u_iso_proportional_to_pivot_u_eq,
pivot_u=u_2,
multiplier=2,
scatterer=sc[3])
r.finalise()
m = 3 + 6
n = m + 6 + 1 + 1
r.linearise()
assert approx_equal(u_iso_1.value, 3, eps=1e-15)
assert approx_equal(u_iso_3.value, 4, eps=1e-15)
jt0 = sparse.matrix(m, n)
for i in xrange(m):
jt0[i, i] = 1
p, q = u_0.argument(0).index, u_0.index
jt0[p, q] = jt0[p + 1, q + 1] = jt0[p + 2, q + 2] = 1
q = u_iso_1.index
jt0[p, q] = jt0[p + 1, q] = jt0[p + 2, q] = 1
p, q = u_2.index, u_iso_3.index
jt0[p, q] = jt0[p + 1, q] = jt0[p + 2, q] = 2 / 3
assert sparse.approx_equal(tolerance=1e-15)(r.jacobian_transpose, jt0)
def exercise_u_iso_proportional_to_pivot_u_eq():
xs = xray.structure(
crystal_symmetry=crystal.symmetry(
unit_cell=(),
space_group_symbol='hall: P 2x 2y'),
scatterers=flex.xray_scatterer((
xray.scatterer('C0', u=(1, 1, 1, 0, 0, 0)),
xray.scatterer('C1'),
xray.scatterer('C2', site=(0.1, 0.2, 0.3), u=(1, 2, 3, 0, 0, 0)),
xray.scatterer('C3'),
)))
r = constraints.ext.reparametrisation(xs.unit_cell())
sc = xs.scatterers()
sc[0].flags.set_grad_u_aniso(True)
sc[2].flags.set_grad_u_aniso(True)
u_0 = r.add(constraints.special_position_u_star_parameter,
site_symmetry=xs.site_symmetry_table().get(0),
scatterer=sc[0])
u_iso_1 = r.add(constraints.u_iso_proportional_to_pivot_u_eq,
pivot_u=u_0,
multiplier=3,
scatterer=sc[1])
u_2 = r.add(constraints.independent_u_star_parameter, sc[2])
u_iso_3 = r.add(constraints.u_iso_proportional_to_pivot_u_eq,
pivot_u=u_2,
multiplier=2,
scatterer=sc[3])
r.finalise()
m = 3 + 6
n = m + 6 + 1 + 1
r.linearise()
assert approx_equal(u_iso_1.value, 3, eps=1e-15)
assert approx_equal(u_iso_3.value, 4, eps=1e-15)
jt0 = sparse.matrix(m, n)
for i in xrange(m): jt0[i, i] = 1
p, q = u_0.argument(0).index, u_0.index
jt0[p, q] = jt0[p+1, q+1] = jt0[p+2, q+2] = 1
q = u_iso_1.index
jt0[p, q] = jt0[p+1, q] = jt0[p+2, q] = 1
p, q = u_2.index, u_iso_3.index
jt0[p, q] = jt0[p+1, q] = jt0[p+2, q] = 2/3
assert sparse.approx_equal(tolerance=1e-15)(r.jacobian_transpose, jt0)
def run(self):
self.reparam.linearise()
self.reparam.store()
assert approx_equal(self.sc.u_star,
(19 / 6, 19 / 6, 17 / 2, 11 / 6, 9 / 2, 9 / 2),
self.eps)
jt0 = sparse.matrix(2, 8)
jt0[0, 0] = 1
jt0[1, 1] = 1
jac_u_star_trans = self.site_symm.adp_constraints(
).gradient_sum_matrix()
jac_u_star_trans.reshape(
flex.grid(self.site_symm.adp_constraints().n_independent_params(),
6))
(m, n) = jac_u_star_trans.focus()
for i in xrange(m):
for j in xrange(n):
jt0[i, j + 2] = jac_u_star_trans[i, j]
jt = self.reparam.jacobian_transpose
assert sparse.approx_equal(self.eps)(jt, jt0)
def run(self):
self.reparam.linearise()
self.reparam.store()
x_c0, x_c1, x_h = [ mat.col(sc.site)
for sc in (self.c0, self.c1, self.h) ]
if self.with_special_position_pivot:
assert approx_equal(x_c0, self.site_symm.exact_site(), self.eps)
assert approx_equal(self.uc.angle(x_c1, x_c0, x_h), 180, self.eps)
assert approx_equal(
self.uc.distance(x_c0, x_h), self.bond_length, self.eps)
if self.with_special_position_pivot:
jt0 = sparse.matrix(1 + 3, # y0, x1
1 + 3 + 3 + 1 + 3) # y0, x0, x1, l, x_h
else:
jt0 = sparse.matrix(3 + 3, # x0, x1
3 + 3 + + 1 + 3) # x0, x1, l, x_h
# Identity for independent parameters
if self.with_special_position_pivot:
jt0[self.y0, self.y0] = 1.
for i in xrange(3): jt0[self.x0 + i, self.x0 + i] = 1.
for i in xrange(3): jt0[self.x1 + i, self.x1 + i] = 1.
# special position x0
if self.with_special_position_pivot:
jt0[self.y0, self.x0 ] = 0
jt0[self.y0, self.x0 + 1] = 0
jt0[self.y0, self.x0 + 2] = 1.
# riding
if self.with_special_position_pivot:
jt0[self.y0, self.x_h + 2] = 1.
else:
for i in xrange(3): jt0[self.x0 + i, self.x_h + i] = 1.
jt = self.reparam.jacobian_transpose
assert sparse.approx_equal(self.eps)(jt, jt0)
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 = random_vectors.next()
v = random_vectors.next()
w = list(-2 * u.as_dense_vector() + 3 * v.as_dense_vector())
yield u, v, w
def exercise_affine_occupancy_parameter():
xs = xray.structure(crystal_symmetry=crystal.symmetry(
unit_cell=(), space_group_symbol='hall: P 1'),
scatterers=flex.xray_scatterer((
xray.scatterer('C0', occupancy=1),
xray.scatterer('C1', occupancy=1),
xray.scatterer('C2', occupancy=1),
xray.scatterer('C3', occupancy=1),
)))
sc = xs.scatterers()
sc.flags_set_grad_occupancy(flex.size_t_range(4))
# Two occupancies adding up to 1 (most common case of disorder)
r = constraints.ext.reparametrisation(xs.unit_cell())
occ_1 = r.add(constraints.independent_occupancy_parameter, sc[1])
occ_3 = r.add(constraints.affine_asu_occupancy_parameter,
dependee=occ_1,
a=-1,
b=1,
scatterer=sc[3])
r.finalise()
r.linearise()
assert approx_equal(occ_1.value, 1)
assert approx_equal(occ_3.value, 0)
jt0 = sparse.matrix(
1,
2,
[
{
0: 1
}, # 1st col = derivatives of occ_1
{
0: -1
}, # 2nd col = derivatives of occ_3
])
assert sparse.approx_equal(tolerance=1e-15)(r.jacobian_transpose, jt0)
# Example illustrating the instruction SUMP in SHELX 97 manual (p. 7-26)
# We disregard the issue of the special position which is orthogonal to the
# point we want to test here.
xs = xray.structure(crystal_symmetry=crystal.symmetry(
unit_cell=(), space_group_symbol='hall: P 1'),
scatterers=flex.xray_scatterer((
xray.scatterer('Na+', occupancy=1),
xray.scatterer('Ca2+', occupancy=1),
xray.scatterer('Al3+', occupancy=0.35),
xray.scatterer('K+', occupancy=0.15),
)))
sc = xs.scatterers()
sc.flags_set_grad_occupancy(flex.size_t_range(4))
# The constraints are:
# fully occupied: occ(Na+) + occ(Ca2+) + occ(Al3+) + occ(K+) = 1
# average charge +2: occ(Na+) + 2 occ(Ca2+) + 3 occ(Al3+) + occ(K+) = +2
# This can be solved as:
# occ(Na+) = occ(Al3+) - occ(K+)
# occ(Ca2+) = 1 - 2 occ(Al3+)
r = constraints.ext.reparametrisation(xs.unit_cell())
occ_Al = r.add(constraints.independent_occupancy_parameter, sc[2])
occ_K = r.add(constraints.independent_occupancy_parameter, sc[3])
occ_Na = r.add(constraints.affine_asu_occupancy_parameter,
occ_Al,
1,
occ_K,
-1,
0,
scatterer=sc[0])
occ_Ca = r.add(constraints.affine_asu_occupancy_parameter,
occ_Al,
-2,
1,
scatterer=sc[1])
r.finalise()
r.linearise()
assert approx_equal(occ_Na.value, 0.2)
assert approx_equal(occ_Ca.value, 0.3)
assert approx_equal(occ_Al.value, 0.35)
assert approx_equal(occ_K.value, 0.15)
jt0 = sparse.matrix(
2,
4,
[
{
0: 1
}, # diff occ(Al3+)
{
1: 1
}, # diff occ(K+)
{
0: 1,
1: -1
}, # diff occ(Na+)
{
0: -2
}, # diff occ(Ca2+)
])
assert sparse.approx_equal(tolerance=1e-15)(r.jacobian_transpose, jt0)
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_affine_occupancy_parameter():
xs = xray.structure(
crystal_symmetry=crystal.symmetry(unit_cell=(), space_group_symbol='hall: P 1'),
scatterers=flex.xray_scatterer((
xray.scatterer('C0', occupancy=1),
xray.scatterer('C1', occupancy=1),
xray.scatterer('C2', occupancy=1),
xray.scatterer('C3', occupancy=1),
)))
sc = xs.scatterers()
sc.flags_set_grad_occupancy(flex.size_t_range(4))
# Two occupancies adding up to 1 (most common case of disorder)
r = constraints.ext.reparametrisation(xs.unit_cell())
occ_1 = r.add(constraints.independent_occupancy_parameter, sc[1])
occ_3 = r.add(constraints.affine_asu_occupancy_parameter,
dependee=occ_1, a=-1, b=1, scatterer=sc[3])
r.finalise()
r.linearise()
assert approx_equal(occ_1.value, 1)
assert approx_equal(occ_3.value, 0)
jt0 = sparse.matrix(1, 2,
[ {0:1}, # 1st col = derivatives of occ_1
{0:-1}, # 2nd col = derivatives of occ_3
])
assert sparse.approx_equal(tolerance=1e-15)(r.jacobian_transpose, jt0)
# Example illustrating the instruction SUMP in SHELX 97 manual (p. 7-26)
# We disregard the issue of the special position which is orthogonal to the
# point we want to test here.
xs = xray.structure(
crystal_symmetry=crystal.symmetry(unit_cell=(), space_group_symbol='hall: P 1'),
scatterers=flex.xray_scatterer((
xray.scatterer('Na+', occupancy=1),
xray.scatterer('Ca2+', occupancy=1),
xray.scatterer('Al3+', occupancy=0.35),
xray.scatterer('K+', occupancy=0.15),
)))
sc = xs.scatterers()
sc.flags_set_grad_occupancy(flex.size_t_range(4))
# The constraints are:
# fully occupied: occ(Na+) + occ(Ca2+) + occ(Al3+) + occ(K+) = 1
# average charge +2: occ(Na+) + 2 occ(Ca2+) + 3 occ(Al3+) + occ(K+) = +2
# This can be solved as:
# occ(Na+) = occ(Al3+) - occ(K+)
# occ(Ca2+) = 1 - 2 occ(Al3+)
r = constraints.ext.reparametrisation(xs.unit_cell())
occ_Al = r.add(constraints.independent_occupancy_parameter, sc[2])
occ_K = r.add(constraints.independent_occupancy_parameter, sc[3])
occ_Na = r.add(constraints.affine_asu_occupancy_parameter,
occ_Al, 1, occ_K, -1, 0, scatterer=sc[0])
occ_Ca = r.add(constraints.affine_asu_occupancy_parameter,
occ_Al, -2, 1, scatterer=sc[1])
r.finalise()
r.linearise()
assert approx_equal(occ_Na.value, 0.2)
assert approx_equal(occ_Ca.value, 0.3)
assert approx_equal(occ_Al.value, 0.35)
assert approx_equal(occ_K.value, 0.15)
jt0 = sparse.matrix(2, 4,
[
{0:1}, # diff occ(Al3+)
{1:1} , # diff occ(K+)
{0:1, 1:-1}, # diff occ(Na+)
{0:-2}, # diff occ(Ca2+)
])
assert sparse.approx_equal(tolerance=1e-15)(r.jacobian_transpose, jt0)
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 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'
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 = random_vectors.next()
v = random_vectors.next()
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):