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_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 value_weight(self, x, param):
pass
# use sparse storage as only self._naverage (default 3) values are non-zero
weight = sparse.vector(self._nvalues)
# normalised coordinate
z = (x - self._x0) / self._spacing
sumwv = 0.0
sumweight = 0.0
# get values
values = param.value
if self._nvalues <= 3:
i1 = 0
i2 = self._nvalues
else: # in this case, 1st point in array (index 0) is at position -0.5
# find the nearest naverage points that bracket z
i1 = int(round(z - self._half_naverage)) + 1
i2 = i1 + self._naverage
if i1 < 0: # beginning of range
i1 = 0
i2 = max(2, i2) # ensure a separation of at least 2
if i2 > self._nvalues:
i2 = self._nvalues
i1 = min(i1, self._nvalues - 2) # ensure separation of >= 2
# now do stuff
for i in range(i1, i2):
ds = (z - self._positions[i]) / self._sigma
w = exp(-ds*ds)
sumwv += w * values[i]
sumweight += w
weight[i] = w
if sumweight > 0.0:
value = sumwv / sumweight;
else:
value = 0
return value, weight, sumweight
def exercise_dot_product():
u = sparse.vector(8, {0: 1, 3: 2, 6: 3})
v = sparse.vector(8, {1: 1, 3: 2, 5: 6})
assert u * v == 4
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'
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'
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})
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_dot_product():
u = sparse.vector(8, {0:1, 3:2, 6:3})
v = sparse.vector(8, {1:1, 3:2, 5:6})
assert u*v == 4
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'
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})
