def cb_op_as_rational(cb_op):
num = cb_op.c().r().num()
den = cb_op.c().r().den()
rational_list = []
for ii in num:
rational_list.append(rational.int(ii) / rational.int(den))
return matrix.sqr(rational_list).inverse()
def cb_op_as_rational(cb_op):
num = cb_op.c().r().num()
den = cb_op.c().r().den()
rational_list = []
for ii in num:
rational_list.append( rational.int(ii)/rational.int(den) )
return matrix.sqr( rational_list ).inverse()
def as_4x4_rational(self):
r = self.r().as_rational().elems
t = self.t().as_rational().elems
zero = rational.int(0)
one = rational.int(1)
return matrix.rec((r[0], r[1], r[2], t[0], r[3], r[4], r[5], t[1],
r[6], r[7], r[8], t[2], zero, zero, zero, one),
(4, 4))
def as_4x4_rational(self):
r = self.r().as_rational().elems
t = self.t().as_rational().elems
zero = rational.int(0)
one = rational.int(1)
return matrix.rec((
r[0], r[1], r[2], t[0],
r[3], r[4], r[5], t[1],
r[6], r[7], r[8], t[2],
zero, zero, zero, one), (4, 4))
def generate_matrix(order):
""" make all sub lattices generators of order order """
# first get all triples
triples = find_triples(order)
matrices = []
for triple in triples:
# make a list of d and e values
a = triple[0]
b = triple[1]
c = triple[2]
d_and_e = []
f_list = []
if a % 2 == 0:
# a is even
tmp = -a // 2 + 1
while tmp <= a // 2:
d_and_e.append(tmp)
tmp += 1
if a % 2 != 0:
# a is odd
tmp = -(a - 1) // 2
while tmp <= (a - 1) // 2:
d_and_e.append(tmp)
tmp += 1
if b % 2 == 0:
# b is even
tmp = -b // 2 + 1
while tmp <= b // 2:
f_list.append(tmp)
tmp += 1
if b % 2 != 0:
# b is odd
tmp = -(b - 1) // 2
while tmp <= (b - 1) // 2:
f_list.append(tmp)
tmp += 1
for d in d_and_e:
for e in d_and_e:
for f in f_list:
mat = [
rational.int(a),
rational.int(d),
rational.int(e),
rational.int(0),
rational.int(b),
rational.int(f),
rational.int(0),
rational.int(0),
rational.int(c),
]
matrices.append(matrix.sqr(mat))
return matrices
def generate_matrix(order):
""" make all sub lattices generators of order order """
# first get all triples
triples = find_triples(order)
matrices = []
for triple in triples:
# make a list of d and e values
a = triple[0]
b = triple[1]
c = triple[2]
d_and_e = []
f_list = []
if a % 2 == 0:
# a is even
tmp = -a // 2 + 1
while tmp <= a // 2:
d_and_e.append(tmp)
tmp += 1
if a % 2 != 0:
# a is odd
tmp = -(a - 1) // 2
while tmp <= (a - 1) // 2:
d_and_e.append(tmp)
tmp += 1
if b % 2 == 0:
# b is even
tmp = -b // 2 + 1
while tmp <= b // 2:
f_list.append(tmp)
tmp += 1
if b % 2 != 0:
# b is odd
tmp = -(b - 1) // 2
while tmp <= (b - 1) // 2:
f_list.append(tmp)
tmp += 1
for d in d_and_e:
for e in d_and_e:
for f in f_list:
mat = [
rational.int(a),
rational.int(d),
rational.int(e),
rational.int(0),
rational.int(b),
rational.int(f),
rational.int(0),
rational.int(0),
rational.int(c)
]
matrices.append(matrix.sqr(mat))
return matrices
def get_point_in_plane(self):
result = [0, 0, 0]
for i in range(3):
if (self.n[i] != 0):
result[i] = -rational.int(self.c) / self.n[i]
return result
raise RuntimeError("cut_plane normal vector is the null vector.")
def rt_mx_as_rational(rot_mat):
# make sure one provides an integer matrix!
tmp_mat = rot_mat.r().as_double()
rational_list = []
for ij in tmp_mat:
rational_list.append(rational.int(ifloor(ij)))
return matrix.sqr(rational_list)
def rt_mx_as_rational(rot_mat):
# make sure one provides an integer matrix!
tmp_mat = rot_mat.num()
rational_list = []
for ij in tmp_mat:
rational_list.append(rational.int(ifloor(ij)))
return matrix.sqr(rational_list)
def get_point_in_plane(self):
result = [0,0,0]
for i in xrange(3):
if (self.n[i] != 0):
result[i] = -rational.int(self.c) / self.n[i]
return result
raise RuntimeError("cut_plane normal vector is the null vector.")
def __truediv__(self, other):
assert isinstance(other, int)
assert other != 0
assert self.c != 0
return cut(n=self.n,
c=rational.int(1) * self.c / other,
inclusive=self.inclusive,
cut_expr=self.cut_expr)
def row_as_hkl( row, txt=['h','k','l']):
result = ""
part = 0
for n,j in zip(row,txt):
nn=""
if n != rational.int(0):
part += 1
if n >rational.int(0):
if part==1:
if n==rational.int(1):
nn = j
else:
nn = str(n)+j
if part > 1:
if n==rational.int(1):
nn = "+"+j
else:
nn = "+"+str(n)+j
if n < rational.int(0) :
if part==1:
if n==rational.int(-1):
nn = "-"+j
else:
nn = str(n)+j
else:
if n == rational.int(-1):
nn+="-"+j
else:
nn = str(n)+j
result += nn
return result
def __init__(self):
self.unit = matrix.sqr( [rational.int(1),
rational.int(0),
rational.int(0),
rational.int(0),
rational.int(1),
rational.int(0),
rational.int(0),
rational.int(0),
rational.int(1)
] )
self.ops = [ self.unit ]
self.max_ops = 100
def row_as_hkl(row, txt=['h', 'k', 'l']):
result = ""
part = 0
for n, j in zip(row, txt):
nn = ""
if n != rational.int(0):
part += 1
if n > rational.int(0):
if part == 1:
if n == rational.int(1):
nn = j
else:
nn = str(n) + j
if part > 1:
if n == rational.int(1):
nn = "+" + j
else:
nn = "+" + str(n) + j
if n < rational.int(0):
if part == 1:
if n == rational.int(-1):
nn = "-" + j
else:
nn = str(n) + j
else:
if n == rational.int(-1):
nn += "-" + j
else:
nn = str(n) + j
result += nn
return result
def special_op_simplifier(special_op):
rt = special_op.as_rational()
r = rt.r
t = rt.t
rows = [r[:3], r[3:6], r[6:]]
terms = [None, None, None]
r0 = rational.int(0)
r1 = rational.int(1)
n_done = 0
for i_row, row in enumerate(rows):
if (row == (0, 0, 0)):
terms[i_row] = special_op_simplified_term([], [], t[i_row])
n_done += 1
if (n_done == 3):
return special_op_simplified(terms=terms)
if (n_done == 0):
m, v = [], []
for i in range(3):
m.append([r[i + 0], r[i + 3]])
v.append(r[i + 6])
from scitbx.matrix import row_echelon
free_vars = row_echelon.form_rational(m, v)
if (len(free_vars) == 0):
sol = row_echelon.back_substitution_rational(
m, v, free_vars, [None] * 2)
if (sol is not None and sol.count(0) == 0):
for i_row in [0, 1]:
terms[i_row] = special_op_simplified_term([i_row], [r1],
r0)
terms[2] = special_op_simplified_term(
[0, 1], sol, t[2] - sol[0] * t[0] - sol[1] * t[1])
return special_op_simplified(terms=terms)
for i_row in range(3):
if (terms[i_row] is not None): continue
terms[i_row] = special_op_simplified_term([i_row], [r1], r0)
for j_row in range(i_row + 1, 3):
if (terms[j_row] is not None): continue
m = matrix.linearly_dependent_pair_scaling_factor(
vector_1=rows[i_row], vector_2=rows[j_row])
if (m is None): continue
assert m != 0
terms[j_row] = special_op_simplified_term([i_row], [m],
t[j_row] - m * t[i_row])
return special_op_simplified(terms=terms)
def __init__(self):
self.unit = matrix.sqr([
rational.int(1),
rational.int(0),
rational.int(0),
rational.int(0),
rational.int(1),
rational.int(0),
rational.int(0),
rational.int(0),
rational.int(1)
])
self.ops = [self.unit]
self.max_ops = 100
def special_op_simplifier(special_op):
rt = special_op.as_rational()
r = rt.r
t = rt.t
rows = [r[:3], r[3:6], r[6:]]
terms = [None, None, None]
r0 = rational.int(0)
r1 = rational.int(1)
n_done = 0
for i_row,row in enumerate(rows):
if (row == (0,0,0)):
terms[i_row] = special_op_simplified_term([], [], t[i_row])
n_done += 1
if (n_done == 3):
return special_op_simplified(terms=terms)
if (n_done == 0):
m, v = [], []
for i in xrange(3):
m.append([r[i+0], r[i+3]])
v.append(r[i+6])
from scitbx.matrix import row_echelon
free_vars = row_echelon.form_rational(m, v)
if (len(free_vars) == 0):
sol = row_echelon.back_substitution_rational(m, v, free_vars, [None]*2)
if (sol is not None and sol.count(0) == 0):
for i_row in [0,1]:
terms[i_row] = special_op_simplified_term([i_row], [r1], r0)
terms[2] = special_op_simplified_term(
[0,1], sol, t[2] - sol[0]*t[0] - sol[1]*t[1])
return special_op_simplified(terms=terms)
for i_row in xrange(3):
if (terms[i_row] is not None): continue
terms[i_row] = special_op_simplified_term([i_row], [r1], r0)
for j_row in xrange(i_row+1,3):
if (terms[j_row] is not None): continue
m = matrix.linearly_dependent_pair_scaling_factor(
vector_1=rows[i_row], vector_2=rows[j_row])
if (m is None): continue
assert m != 0
terms[j_row] = special_op_simplified_term(
[i_row], [m], t[j_row] - m*t[i_row])
return special_op_simplified(terms=terms)
def check_compatibility_with_sampling_grid(asu):
print "Shape vertices:"
n_outside_sampling_grid = 0
for vertex in asu.shape_vertices():
s = ""
for v in vertex:
if (v < -rational.int(1, 2) or v > 1):
s = " outside sampling grid"
n_outside_sampling_grid += 1
break
print " %s%s" % (str(vertex), s)
assert n_outside_sampling_grid == 0
def exercise_float_asu(space_group_info, n_grid=6):
unit_cell = space_group_info.any_compatible_unit_cell(volume=1000)
ref_asu = reference_table.get_asu(space_group_info.type().number())
exercise_cut_planes(ref_asu.cuts)
inp_asu = space_group_info.direct_space_asu()
assert sgtbx.space_group(inp_asu.hall_symbol) == space_group_info.group()
exercise_cut_planes(inp_asu.cuts)
exercise_shape_vertices(inp_asu, unit_cell)
float_asu = inp_asu.add_buffer(unit_cell=unit_cell, thickness=0.001)
cb_mx_ref_inp = space_group_info.type().cb_op().c_inv().as_rational()
n = n_grid
for ref_n in flex.nested_loop((-n // 2, -n // 2, -n // 2), (n, n, n),
False):
# check correctness of space_group_info.direct_space_asu()
ref_r = matrix.col([rational.int(g, n) for g in ref_n])
inp_r = cb_mx_ref_inp * ref_r
assert ref_asu.is_inside(ref_r.elems) == inp_asu.is_inside(inp_r.elems)
# check correctness of cut_plane.add_buffer()
inp_r = inp_r.elems
inp_f = [float(r) for r in inp_r]
for cut in inp_asu.cuts:
r_cut = cut.strip()
r_inside = r_cut.is_inside(inp_r)
for buffer_thickness in [0.001, 1, -1][:1]:
f_cut = cut.as_float_cut_plane().add_buffer(
unit_cell=unit_cell, thickness=buffer_thickness)
f_inside = f_cut.is_inside(inp_f)
if (buffer_thickness < 0):
if (r_inside != f_inside):
assert r_inside
elif (buffer_thickness < 0.01):
assert r_inside == f_inside
elif (r_inside != f_inside):
assert f_inside
# check correctness of float_asu.add_buffer()
assert float_asu.is_inside(inp_f) == inp_asu.shape_only().is_inside(
inp_r)
asu_with_metric = inp_asu.define_metric(unit_cell)
assert asu_with_metric.hall_symbol is inp_asu.hall_symbol
assert len(asu_with_metric.cuts) == len(inp_asu.cuts)
assert asu_with_metric.unit_cell is unit_cell
asu_tight = asu_with_metric.as_float_asu()
asu_buffer = asu_with_metric.add_buffer(thickness=2)
asu_shrunk = asu_with_metric.add_buffer(relative_thickness=-1.e-5)
vertices = facet_analysis.shape_vertices(inp_asu)
for vertex in vertices:
assert inp_asu.shape_only().is_inside(vertex)
for vertex in vertices:
assert asu_tight.is_inside(matrix.col(vertex).as_float().elems)
for vertex in vertices:
assert asu_buffer.is_inside(matrix.col(vertex).as_float().elems)
for vertex in vertices:
assert not asu_shrunk.is_inside(matrix.col(vertex).as_float().elems)
def exercise_float_asu(space_group_info, n_grid=6):
unit_cell = space_group_info.any_compatible_unit_cell(volume=1000)
ref_asu = reference_table.get_asu(space_group_info.type().number())
exercise_cut_planes(ref_asu.cuts)
inp_asu = space_group_info.direct_space_asu()
assert sgtbx.space_group(inp_asu.hall_symbol) == space_group_info.group()
exercise_cut_planes(inp_asu.cuts)
exercise_shape_vertices(inp_asu, unit_cell)
float_asu = inp_asu.add_buffer(unit_cell=unit_cell, thickness=0.001)
cb_mx_ref_inp = space_group_info.type().cb_op().c_inv().as_rational()
n = n_grid
for ref_n in flex.nested_loop((-n//2,-n//2,-n//2),(n,n,n),False):
# check correctness of space_group_info.direct_space_asu()
ref_r = matrix.col([rational.int(g,n) for g in ref_n])
inp_r = cb_mx_ref_inp * ref_r
assert ref_asu.is_inside(ref_r.elems) == inp_asu.is_inside(inp_r.elems)
# check correctness of cut_plane.add_buffer()
inp_r = inp_r.elems
inp_f = [float(r) for r in inp_r]
for cut in inp_asu.cuts:
r_cut = cut.strip()
r_inside = r_cut.is_inside(inp_r)
for buffer_thickness in [0.001, 1, -1][:1]:
f_cut = cut.as_float_cut_plane().add_buffer(
unit_cell=unit_cell,
thickness=buffer_thickness)
f_inside = f_cut.is_inside(inp_f)
if (buffer_thickness < 0):
if (r_inside != f_inside):
assert r_inside
elif (buffer_thickness < 0.01):
assert r_inside == f_inside
elif (r_inside != f_inside):
assert f_inside
# check correctness of float_asu.add_buffer()
assert float_asu.is_inside(inp_f) == inp_asu.shape_only().is_inside(inp_r)
asu_with_metric = inp_asu.define_metric(unit_cell)
assert asu_with_metric.hall_symbol is inp_asu.hall_symbol
assert len(asu_with_metric.cuts) == len(inp_asu.cuts)
assert asu_with_metric.unit_cell is unit_cell
asu_tight = asu_with_metric.as_float_asu()
asu_buffer = asu_with_metric.add_buffer(thickness=2)
asu_shrunk = asu_with_metric.add_buffer(relative_thickness=-1.e-5)
vertices = facet_analysis.shape_vertices(inp_asu)
for vertex in vertices:
assert inp_asu.shape_only().is_inside(vertex)
for vertex in vertices:
assert asu_tight.is_inside(matrix.col(vertex).as_float().elems)
for vertex in vertices:
assert asu_buffer.is_inside(matrix.col(vertex).as_float().elems)
for vertex in vertices:
assert not asu_shrunk.is_inside(matrix.col(vertex).as_float().elems)
def vec3_rat_from_str(s):
flds = s.split(",")
assert len(flds) == 3
result = []
for fld in flds:
slash_count = fld.count("/")
assert slash_count < 2
if (slash_count == 0):
n, d = int(fld), 1
else:
n, d = [int(t) for t in fld.split("/")]
result.append(rational.int(n, d))
return result
def vec3_rat_from_str(s):
flds = s.split(",")
assert len(flds) == 3
result = []
for fld in flds:
slash_count = fld.count("/")
assert slash_count < 2
if (slash_count == 0):
n, d = int(fld), 1
else:
n, d = [int(t) for t in fld.split("/")]
result.append(rational.int(n, d))
return result
def __init__(self, space_group):
self.space_group = space_group
nc_dict = {}
self.list = []
for i_smx in xrange(space_group.order_p()):
s = space_group(i_smx)
r_info = s.r().info()
if (r_info.type() < 2): continue
if (r_info.sense() < 0): continue
n = r_info.ev()
p = s.t().mod_positive()
assert p.den() == space_group.t_den()
c = -dot3(n, p.num())
if (not nc_dict.has_key((n,c))):
nc_dict[(n,c)] = 0
self.list.append(
plane_fractional(s=s, n=n, p=p, c=rational.int(c,p.den())))
def __init__(self, space_group):
self.space_group = space_group
nc_dict = {}
self.list = []
for i_smx in xrange(space_group.order_p()):
s = space_group(i_smx)
r_info = s.r().info()
if (r_info.type() < 2): continue
if (r_info.sense() < 0): continue
n = r_info.ev()
p = s.t().mod_positive()
assert p.den() == space_group.t_den()
c = -dot3(n, p.num())
if (not nc_dict.has_key((n, c))):
nc_dict[(n, c)] = 0
self.list.append(
plane_fractional(s=s, n=n, p=p, c=rational.int(c,
p.den())))
def intersection(cuts):
assert len(cuts) == 3
m = flex.int()
t = flex.int()
denominator = 1
for cut in cuts:
denominator = cut.lcm_of_denominators(start_lcm=denominator)
for cut in cuts:
for e in cut.n: m.append(int(e * denominator))
t.append(-int(cut.c * denominator))
m.reshape(flex.grid(3,3))
t.reshape(flex.grid(3,1))
r = scitbx.math.row_echelon_form_t(m, t)
assert r in (2,3)
if (r != 3): return None
t.reshape(flex.grid(3))
sol = flex.int(3)
d = scitbx.math.row_echelon_back_substitution_int(m, t, sol)
assert d > 0
return tuple([rational.int(s,d) for s in sol])
def intersection(cuts):
assert len(cuts) == 3
m = flex.int()
t = flex.int()
denominator = 1
for cut in cuts:
denominator = cut.lcm_of_denominators(start_lcm=denominator)
for cut in cuts:
for e in cut.n:
m.append(int(e * denominator))
t.append(-int(cut.c * denominator))
m.reshape(flex.grid(3, 3))
t.reshape(flex.grid(3, 1))
r = scitbx.math.row_echelon_form_t(m, t)
assert r in (2, 3)
if (r != 3): return None
t.reshape(flex.grid(3))
sol = flex.int(3)
d = scitbx.math.row_echelon_back_substitution_int(m, t, sol)
assert d > 0
return tuple([rational.int(s, d) for s in sol])
def line_sample_point(a, b, f, gridding): return [a[i]+rational.int(f,gridding)*(b[i]-a[i]) for i in xrange(3)]
def __truediv__(self, other):
assert isinstance(other, int)
assert other != 0
assert self.c != 0
return cut(n=self.n, c=rational.int(1)*self.c/other,
inclusive=self.inclusive, cut_expr=self.cut_expr)
def rr(): return rational.int(rng.randrange(-5,6), rng.randrange(1,10))
def rr():
return rational.int(rng.randrange(-5, 6), rng.randrange(1, 10))
def lcm_of_denominators(self, start_lcm=1):
result = start_lcm
for e in self.n:
result = rational.lcm(result, rational.int(e).denominator())
result = rational.lcm(result, rational.int(self.c).denominator())
return result
def line_sample_point(a, b, f, gridding):
return [
a[i] + rational.int(f, gridding) * (b[i] - a[i]) for i in xrange(3)
]
def exercise_int():
ri = rational.int
r = ri()
assert r.numerator() == 0
assert r.denominator() == 1
assert r.as_tuple() == (0, 1)
assert int(r) == 0
assert float(r) == 0
assert rational.int(rational.int(3)).as_tuple() == (3, 1)
assert rational.int(2).as_tuple() == (2, 1)
assert rational.int(2, 3).as_tuple() == (2, 3)
assert str(rational.int()) == "0"
assert str(rational.int(2)) == "2"
assert str(rational.int(-2, 3)) == "-2/3"
assert (-rational.int(2, 3)).as_tuple() == (-2, 3)
assert (rational.int(2, 3) + rational.int(3, 4)).as_tuple() == (17, 12)
assert (rational.int(2, 3) - rational.int(3, 4)).as_tuple() == (-1, 12)
assert (rational.int(2, 3) * rational.int(3, 4)).as_tuple() == (1, 2)
assert (rational.int(2, 3) / rational.int(3, 4)).as_tuple() == (8, 9)
assert (rational.int(2, 3) // rational.int(3, 4)) == 0
assert (rational.int(2, 3) % rational.int(1, 2)).as_tuple() == (1, 6)
assert (rational.int(2, 3) + 4).as_tuple() == (14, 3)
assert (rational.int(2, 3) - 4).as_tuple() == (-10, 3)
assert (rational.int(2, 3) * 4).as_tuple() == (8, 3)
assert (rational.int(2, 3) / 4).as_tuple() == (1, 6)
assert (rational.int(2, 3) // 4) == 0
assert (rational.int(7, 3) % 2).as_tuple() == (1, 3)
assert (5 + rational.int(2, 3)).as_tuple() == (17, 3)
assert (5 - rational.int(2, 3)).as_tuple() == (13, 3)
assert (5 * rational.int(2, 3)).as_tuple() == (10, 3)
assert (5 / rational.int(2, 3)).as_tuple() == (15, 2)
assert (5 // rational.int(2, 3)) == 7
assert (5 % rational.int(2, 3)).as_tuple() == (1, 3)
assert rational.int(2, 3) == rational.int(2, 3)
assert not rational.int(2, 3) == rational.int(2, 5)
assert rational.int(2, 3) != rational.int(2, 5)
assert not rational.int(2, 3) != rational.int(2, 3)
assert rational.int(2, 3) < rational.int(3, 4)
assert not rational.int(2, 3) < rational.int(2, 3)
assert rational.int(2, 3) > rational.int(1, 2)
assert not rational.int(2, 3) > rational.int(2, 3)
assert rational.int(2, 3) <= rational.int(3, 4)
assert not rational.int(2, 3) <= rational.int(1, 2)
assert rational.int(2, 3) >= rational.int(1, 2)
assert not rational.int(2, 3) >= rational.int(3, 4)
assert rational.int(4, 2) == 2
assert not rational.int(4, 2) == 3
assert rational.int(4, 2) != 3
assert not rational.int(4, 2) != 2
assert rational.int(4, 2) < 3
assert not rational.int(4, 2) < 2
assert rational.int(4, 2) > 1
assert not rational.int(4, 2) > 2
assert rational.int(4, 2) <= 3
assert not rational.int(4, 2) <= 1
assert rational.int(4, 2) >= 1
assert not rational.int(4, 2) >= 3
assert 2 == rational.int(4, 2)
assert not 3 == rational.int(4, 2)
assert 3 != rational.int(4, 2)
assert not 2 != rational.int(4, 2)
assert 3 > rational.int(4, 2)
assert not 2 > rational.int(4, 2)
assert 1 < rational.int(4, 2)
assert not 2 < rational.int(4, 2)
assert 3 >= rational.int(4, 2)
assert not 1 >= rational.int(4, 2)
assert 1 <= rational.int(4, 2)
assert not 3 <= rational.int(4, 2)
r = rational.int(4, 3)
r += 1
assert r.as_tuple() == (7, 3)
assert approx_equal(float(r), 7. / 3)
s = rational.int(4, 3)
assert hash(s) == hash(rational.int(4, 3))
assert hash(s) != hash(r)
for n in xrange(-100, 100):
assert hash(n) == hash(rational.int(n))
for d in xrange(1, 8):
assert hash(rational.int(n, d)) == hash(rational.int(n, d))
assert hash(rational.int(n, d)) == hash(rational.int(3 * n, 3 * d))
assert hash(rational.int(n,
d)) == hash(rational.int(-3 * n, -3 * d))
try:
int(r)
except RuntimeError, e:
assert str(e) == "boost.rational: as_int() conversion error:" \
" denominator is different from one."
from __future__ import absolute_import, division, print_function from cctbx.sgtbx.direct_space_asu.cut_plane import cut from boost import rational r1 = rational.int(1) x1 = cut((-1,0,0), 1) x0 = -x1*0 x2 = x1/2 x3 = x1/3 x4 = x1/4 x8 = x1/8 x34 = x1*3/4 y1 = cut((0,-1,0), 1) y0 = -y1*0 y2 = y1/2 y3 = y1/3 y4 = y1/4 y8 = y1/8 z1 = cut((0,0,-1), 1) z0 = -z1*0 z2 = z1/2 z3 = z1/3 z4 = z1/4 z6 = z1/6 z8 = z1/8 z12 = z1/12 p1 = cut((-1,1,0), 1) p0 = -p1*0 p2 = p1/2 p3 = p1/3
assert hash(s) == hash(rational.int(4,3))
assert hash(s) != hash(r)
for n in xrange(-100,100):
assert hash(n) == hash(rational.int(n))
for d in xrange(1,8):
assert hash(rational.int(n,d)) == hash(rational.int(n,d))
assert hash(rational.int(n,d)) == hash(rational.int(3*n,3*d))
assert hash(rational.int(n,d)) == hash(rational.int(-3*n,-3*d))
try: int(r)
except RuntimeError, e:
assert str(e) == "boost.rational: as_int() conversion error:" \
" denominator is different from one."
else: raise Exception_expected
for n in xrange(-5,6):
for d in xrange(1,10):
r = rational.int(n, d)
p = pickle.dumps(r)
l = pickle.loads(p)
assert l == r
assert str(l) == str(r)
#
ee = "bad rational: zero denominator"
lhs = ri(1)
for rhs in [ri(0), 0]:
try: lhs / rhs
except RuntimeError, e: assert not show_diff(str(e), ee)
else: raise Exception_expected
try: lhs % rhs
except RuntimeError, e: assert not show_diff(str(e), ee)
else: raise Exception_expected
#
assert hash(n) == hash(rational.int(n))
for d in xrange(1, 8):
assert hash(rational.int(n, d)) == hash(rational.int(n, d))
assert hash(rational.int(n, d)) == hash(rational.int(3 * n, 3 * d))
assert hash(rational.int(n,
d)) == hash(rational.int(-3 * n, -3 * d))
try:
int(r)
except RuntimeError, e:
assert str(e) == "boost.rational: as_int() conversion error:" \
" denominator is different from one."
else:
raise Exception_expected
for n in xrange(-5, 6):
for d in xrange(1, 10):
r = rational.int(n, d)
p = pickle.dumps(r)
l = pickle.loads(p)
assert l == r
assert str(l) == str(r)
#
ee = "bad rational: zero denominator"
lhs = ri(1)
for rhs in [ri(0), 0]:
try:
lhs / rhs
except RuntimeError, e:
assert not show_diff(str(e), ee)
else:
raise Exception_expected
try:
def exercise_int():
ri = rational.int
r = ri()
assert r.numerator() == 0
assert r.denominator() == 1
assert r.as_tuple() == (0, 1)
assert int(r) == 0
assert float(r) == 0
assert rational.int(rational.int(3)).as_tuple() == (3, 1)
assert rational.int(2).as_tuple() == (2, 1)
assert rational.int(2, 3).as_tuple() == (2, 3)
assert str(rational.int()) == "0"
assert str(rational.int(2)) == "2"
assert str(rational.int(-2, 3)) == "-2/3"
assert (-rational.int(2, 3)).as_tuple() == (-2, 3)
assert (rational.int(2, 3) + rational.int(3, 4)).as_tuple() == (17, 12)
assert (rational.int(2, 3) - rational.int(3, 4)).as_tuple() == (-1, 12)
assert (rational.int(2, 3) * rational.int(3, 4)).as_tuple() == (1, 2)
assert (rational.int(2, 3) / rational.int(3, 4)).as_tuple() == (8, 9)
assert (rational.int(2, 3) // rational.int(3, 4)) == 0
assert (rational.int(2, 3) % rational.int(1, 2)).as_tuple() == (1, 6)
assert (rational.int(2, 3) + 4).as_tuple() == (14, 3)
assert (rational.int(2, 3) - 4).as_tuple() == (-10, 3)
assert (rational.int(2, 3) * 4).as_tuple() == (8, 3)
assert (rational.int(2, 3) / 4).as_tuple() == (1, 6)
assert (rational.int(2, 3) // 4) == 0
assert (rational.int(7, 3) % 2).as_tuple() == (1, 3)
assert (5 + rational.int(2, 3)).as_tuple() == (17, 3)
assert (5 - rational.int(2, 3)).as_tuple() == (13, 3)
assert (5 * rational.int(2, 3)).as_tuple() == (10, 3)
assert (5 / rational.int(2, 3)).as_tuple() == (15, 2)
assert (5 // rational.int(2, 3)) == 7
assert (5 % rational.int(2, 3)).as_tuple() == (1, 3)
assert rational.int(2, 3) == rational.int(2, 3)
assert not rational.int(2, 3) == rational.int(2, 5)
assert rational.int(2, 3) != rational.int(2, 5)
assert not rational.int(2, 3) != rational.int(2, 3)
assert rational.int(2, 3) < rational.int(3, 4)
assert not rational.int(2, 3) < rational.int(2, 3)
assert rational.int(2, 3) > rational.int(1, 2)
assert not rational.int(2, 3) > rational.int(2, 3)
assert rational.int(2, 3) <= rational.int(3, 4)
assert not rational.int(2, 3) <= rational.int(1, 2)
assert rational.int(2, 3) >= rational.int(1, 2)
assert not rational.int(2, 3) >= rational.int(3, 4)
assert rational.int(4, 2) == 2
assert not rational.int(4, 2) == 3
assert rational.int(4, 2) != 3
assert not rational.int(4, 2) != 2
assert rational.int(4, 2) < 3
assert not rational.int(4, 2) < 2
assert rational.int(4, 2) > 1
assert not rational.int(4, 2) > 2
assert rational.int(4, 2) <= 3
assert not rational.int(4, 2) <= 1
assert rational.int(4, 2) >= 1
assert not rational.int(4, 2) >= 3
assert 2 == rational.int(4, 2)
assert not 3 == rational.int(4, 2)
assert 3 != rational.int(4, 2)
assert not 2 != rational.int(4, 2)
assert 3 > rational.int(4, 2)
assert not 2 > rational.int(4, 2)
assert 1 < rational.int(4, 2)
assert not 2 < rational.int(4, 2)
assert 3 >= rational.int(4, 2)
assert not 1 >= rational.int(4, 2)
assert 1 <= rational.int(4, 2)
assert not 3 <= rational.int(4, 2)
r = rational.int(4, 3)
r += 1
assert r.as_tuple() == (7, 3)
assert approx_equal(float(r), 7. / 3)
s = rational.int(4, 3)
assert hash(s) == hash(rational.int(4, 3))
assert hash(s) != hash(r)
for n in range(-100, 100):
assert hash(n) == hash(rational.int(n))
for d in range(1, 8):
assert hash(rational.int(n, d)) == hash(rational.int(n, d))
assert hash(rational.int(n, d)) == hash(rational.int(3 * n, 3 * d))
assert hash(rational.int(n,
d)) == hash(rational.int(-3 * n, -3 * d))
try:
int(r)
except RuntimeError as e:
assert str(e) == "boost.rational: as_int() conversion error:" \
" denominator is different from one."
else:
raise Exception_expected
for n in range(-5, 6):
for d in range(1, 10):
r = rational.int(n, d)
p = pickle.dumps(r)
l = pickle.loads(p)
assert l == r
assert str(l) == str(r)
#
ee = "bad rational: zero denominator"
lhs = ri(1)
for rhs in [ri(0), 0]:
try:
lhs / rhs
except RuntimeError as e:
assert not show_diff(str(e), ee)
else:
raise Exception_expected
try:
lhs % rhs
except RuntimeError as e:
assert not show_diff(str(e), ee)
else:
raise Exception_expected
#
try:
import fractions
except ImportError:
fractions = None
def check(nd1, nd2, expected=None):
r1, r2 = ri(*nd1), ri(*nd2)
rm = r1 % r2
assert (r1 // r2) * r2 + rm == r1
if (fractions is not None):
ff = fractions.Fraction
f1, f2 = ff(*nd1), ff(*nd2)
fm = f1 % f2
assert (fm.numerator, fm.denominator) == rm.as_tuple()
if (expected is not None):
assert rm.as_tuple() == expected
check((2, 3), (1, 2), (1, 6))
check((2, 3), (-1, 2), (-1, 3))
check((-2, 3), (1, 2), (1, 3))
check((-2, 3), (-1, 2), (-1, 6))
for ln in range(-7, 7 + 1):
for rn in range(-9, 9 + 1):
if (rn == 0): continue
check((ln, 3), (rn, 4))
#
ri = rational.int
def check(r, e):
assert isinstance(r, ri)
assert r == e
check(ri(3, 2) + ri(4, 5), ri(23, 10))
check(ri(3, 2) + 4, ri(11, 2))
check(2 + ri(4, 5), ri(14, 5))
check(ri(3, 2) - ri(4, 5), ri(7, 10))
check(ri(3, 2) - 4, ri(-5, 2))
check(2 - ri(4, 5), ri(6, 5))
check(ri(3, 2) * ri(4, 5), ri(6, 5))
check(ri(3, 2) * 4, ri(6, 1))
check(2 * ri(4, 5), ri(8, 5))
check(ri(3, 2) / ri(4, 5), ri(15, 8))
check(ri(3, 2) / 4, ri(3, 8))
check(2 / ri(4, 5), ri(5, 2))
#
def check(r, e):
assert isinstance(r, int)
assert r == e
check(ri(3, 2) // ri(4, 5), 1)
check(ri(3, 2) // 4, 0)
check(2 // ri(4, 5), 2)
#
def check(r, e):
assert isinstance(r, float)
assert approx_equal(r, e)
check(ri(3, 2) + 4., 5.5)
check(2. + ri(4, 5), 2.8)
check(ri(3, 2) - 4., -2.5)
check(2. - ri(4, 5), 1.2)
check(ri(3, 2) * 4., 6.0)
check(2. * ri(4, 5), 1.6)
check(ri(3, 2) / 4., 0.375)
check(2. / ri(4, 5), 2.5)
#
try:
ri(3, 2) // 4.
except TypeError as e:
assert str(e).startswith("unsupported operand type(s)")
else:
raise Exception_expected
try:
2. // ri(4, 5)
except TypeError as e:
assert str(e).startswith("unsupported operand type(s)")
else:
raise Exception_expected
#
try:
ri(3, 2) % 4.
except TypeError as e:
assert str(e).startswith("unsupported operand type(s)")
else:
raise Exception_expected
try:
2. % ri(4, 5)
except TypeError as e:
assert str(e).startswith("unsupported operand type(s)")
else:
raise Exception_expected
#
try:
ri(1) / 0.
except ZeroDivisionError as e:
assert not show_diff(str(e), "float division by zero")
else:
raise Exception_expected
try:
1. / ri(0)
except ZeroDivisionError as e:
assert not show_diff(str(e), "float division by zero")
else:
raise Exception_expected
def lcm_of_denominators(self, start_lcm=1):
result = start_lcm
for e in self.n:
result = rational.lcm(result, rational.int(e).denominator())
result = rational.lcm(result, rational.int(self.c).denominator())
return result
from __future__ import division from cctbx.sgtbx.direct_space_asu.cut_plane import cut from boost import rational r1 = rational.int(1) x1 = cut((-1,0,0), 1) x0 = -x1*0 x2 = x1/2 x3 = x1/3 x4 = x1/4 x8 = x1/8 x34 = x1*3/4 y1 = cut((0,-1,0), 1) y0 = -y1*0 y2 = y1/2 y3 = y1/3 y4 = y1/4 y8 = y1/8 z1 = cut((0,0,-1), 1) z0 = -z1*0 z2 = z1/2 z3 = z1/3 z4 = z1/4 z6 = z1/6 z8 = z1/8 z12 = z1/12 p1 = cut((-1,1,0), 1) p0 = -p1*0 p2 = p1/2 p3 = p1/3
def exercise_int():
ri = rational.int
r = ri()
assert r.numerator() == 0
assert r.denominator() == 1
assert r.as_tuple() == (0,1)
assert int(r) == 0
assert float(r) == 0
assert rational.int(rational.int(3)).as_tuple() == (3,1)
assert rational.int(2).as_tuple() == (2,1)
assert rational.int(2,3).as_tuple() == (2,3)
assert str(rational.int()) == "0"
assert str(rational.int(2)) == "2"
assert str(rational.int(-2,3)) == "-2/3"
assert (-rational.int(2,3)).as_tuple() == (-2,3)
assert (rational.int(2,3) + rational.int(3,4)).as_tuple() == (17,12)
assert (rational.int(2,3) - rational.int(3,4)).as_tuple() == (-1,12)
assert (rational.int(2,3) * rational.int(3,4)).as_tuple() == (1,2)
assert (rational.int(2,3) / rational.int(3,4)).as_tuple() == (8,9)
assert (rational.int(2,3) // rational.int(3,4)) == 0
assert (rational.int(2,3) % rational.int(1,2)).as_tuple() == (1,6)
assert (rational.int(2,3) + 4).as_tuple() == (14,3)
assert (rational.int(2,3) - 4).as_tuple() == (-10,3)
assert (rational.int(2,3) * 4).as_tuple() == (8,3)
assert (rational.int(2,3) / 4).as_tuple() == (1,6)
assert (rational.int(2,3) // 4) == 0
assert (rational.int(7,3) % 2).as_tuple() == (1,3)
assert (5 + rational.int(2,3)).as_tuple() == (17,3)
assert (5 - rational.int(2,3)).as_tuple() == (13,3)
assert (5 * rational.int(2,3)).as_tuple() == (10,3)
assert (5 / rational.int(2,3)).as_tuple() == (15,2)
assert (5 // rational.int(2,3)) == 7
assert (5 % rational.int(2,3)).as_tuple() == (1,3)
assert rational.int(2,3) == rational.int(2,3)
assert not rational.int(2,3) == rational.int(2,5)
assert rational.int(2,3) != rational.int(2,5)
assert not rational.int(2,3) != rational.int(2,3)
assert rational.int(2,3) < rational.int(3,4)
assert not rational.int(2,3) < rational.int(2,3)
assert rational.int(2,3) > rational.int(1,2)
assert not rational.int(2,3) > rational.int(2,3)
assert rational.int(2,3) <= rational.int(3,4)
assert not rational.int(2,3) <= rational.int(1,2)
assert rational.int(2,3) >= rational.int(1,2)
assert not rational.int(2,3) >= rational.int(3,4)
assert rational.int(4,2) == 2
assert not rational.int(4,2) == 3
assert rational.int(4,2) != 3
assert not rational.int(4,2) != 2
assert rational.int(4,2) < 3
assert not rational.int(4,2) < 2
assert rational.int(4,2) > 1
assert not rational.int(4,2) > 2
assert rational.int(4,2) <= 3
assert not rational.int(4,2) <= 1
assert rational.int(4,2) >= 1
assert not rational.int(4,2) >= 3
assert 2 == rational.int(4,2)
assert not 3 == rational.int(4,2)
assert 3 != rational.int(4,2)
assert not 2 != rational.int(4,2)
assert 3 > rational.int(4,2)
assert not 2 > rational.int(4,2)
assert 1 < rational.int(4,2)
assert not 2 < rational.int(4,2)
assert 3 >= rational.int(4,2)
assert not 1 >= rational.int(4,2)
assert 1 <= rational.int(4,2)
assert not 3 <= rational.int(4,2)
r = rational.int(4,3)
r += 1
assert r.as_tuple() == (7,3)
assert approx_equal(float(r), 7./3)
s = rational.int(4,3)
assert hash(s) == hash(rational.int(4,3))
assert hash(s) != hash(r)
for n in xrange(-100,100):
assert hash(n) == hash(rational.int(n))
for d in xrange(1,8):
assert hash(rational.int(n,d)) == hash(rational.int(n,d))
assert hash(rational.int(n,d)) == hash(rational.int(3*n,3*d))
assert hash(rational.int(n,d)) == hash(rational.int(-3*n,-3*d))
try: int(r)
except RuntimeError, e:
assert str(e) == "boost.rational: as_int() conversion error:" \
" denominator is different from one."
