def exercise_matrix_x_vector():
from scitbx.random import variate, uniform_distribution
for m,n in [(5,5), (3,5), (5,3)]:
random_vectors = variate(
sparse.vector_distribution(
n, density=0.4,
elements=uniform_distribution(min=-2, max=2)))
random_matrices = variate(
sparse.matrix_distribution(
m, n, density=0.3,
elements=uniform_distribution(min=-2, max=2)))
for n_test in xrange(50):
a = random_matrices.next()
x = random_vectors.next()
y = a*x
aa = a.as_dense_matrix()
xx = x.as_dense_vector()
yy1 = y.as_dense_vector()
yy2 = aa.matrix_multiply(xx)
assert approx_equal(yy1,yy2)
for m,n in [(5,5), (3,5), (5,3)]:
random_matrices = variate(
sparse.matrix_distribution(
m, n, density=0.4,
elements=uniform_distribution(min=-2, max=2)))
for n_test in xrange(50):
a = random_matrices.next()
x = flex.random_double(n)
y = a*x
aa = a.as_dense_matrix()
yy = aa.matrix_multiply(x)
assert approx_equal(y, yy)
def exercise_random():
from scitbx.random import variate, uniform_distribution
g = random_matrices = variate(
sparse.matrix_distribution(5,
3,
density=0.4,
elements=uniform_distribution(min=-1,
max=0.5)))
for a in itertools.islice(g, 10):
assert a.n_rows == 5 and a.n_cols == 3
assert approx_equal(a.non_zeroes, a.n_rows * a.n_cols * 0.4, eps=1)
for j in range(a.n_cols):
for i, x in a.col(j):
assert -1 <= x < 0.5, (i, j, x)
g = random_vectors = variate(
sparse.vector_distribution(6,
density=0.3,
elements=uniform_distribution(min=-2,
max=2)))
for v in itertools.islice(g, 10):
assert v.size == 6
assert approx_equal(v.non_zeroes, v.size * 0.3, eps=1)
for i, x in v:
assert -2 <= x < 2, (i, j, x)
def exercise_matrix_x_matrix():
from scitbx.random import variate, uniform_distribution
mat = lambda m, n: variate(
sparse.matrix_distribution(
m, n, density=0.4, elements=uniform_distribution(min=-10, max=10))
)()
a, b = mat(3, 4), mat(4, 2)
c = a * b
aa, bb, cc = [m.as_dense_matrix() for m in (a, b, c)]
cc1 = aa.matrix_multiply(bb)
assert approx_equal(cc, cc1)
def exercise_matrix_x_matrix():
from scitbx.random import variate, uniform_distribution
mat = lambda m,n: variate(
sparse.matrix_distribution(
m, n, density=0.4,
elements=uniform_distribution(min=-10, max=10)))()
a,b = mat(3,4), mat(4,2)
c = a*b
aa, bb, cc = [ m.as_dense_matrix() for m in (a,b,c) ]
cc1 = aa.matrix_multiply(bb)
assert approx_equal(cc, cc1)
def exercise_a_b_a_tr():
from scitbx.random import variate, uniform_distribution
for m,n in [(5,5), (3,5), (5,3)]:
random_matrices = variate(
sparse.matrix_distribution(
m, n, density=0.6,
elements=uniform_distribution(min=-3, max=10)))
for n_test in xrange(50):
b = flex.random_double(n*(n+1)//2)
a = random_matrices.next()
c = a.self_times_symmetric_times_self_transpose(b)
aa = a.as_dense_matrix()
bb = b.matrix_packed_u_as_symmetric()
cc = c.matrix_packed_u_as_symmetric()
assert approx_equal(
cc,
aa.matrix_multiply(bb.matrix_multiply(aa.matrix_transpose())))
def exercise_random():
from scitbx.random import variate, uniform_distribution
g = random_matrices = variate(
sparse.matrix_distribution(
5, 3, density=0.4,
elements=uniform_distribution(min=-1, max=0.5)))
for a in itertools.islice(g, 10):
assert a.n_rows== 5 and a.n_cols == 3
assert approx_equal(a.non_zeroes, a.n_rows*a.n_cols*0.4, eps=1)
for j in xrange(a.n_cols):
for i,x in a.col(j):
assert -1 <= x < 0.5, (i,j, x)
g = random_vectors = variate(
sparse.vector_distribution(
6, density=0.3,
elements=uniform_distribution(min=-2, max=2)))
for v in itertools.islice(g, 10):
assert v.size == 6
assert approx_equal(v.non_zeroes, v.size*0.3, eps=1)
for i,x in v:
assert -2 <= x < 2, (i,j, x)
def exercise_a_tr_diag_a_and_a_diag_a_tr():
from scitbx.random import variate, uniform_distribution
for m, n in [(5, 5), (3, 5), (5, 3)]:
random_matrices = variate(
sparse.matrix_distribution(m,
n,
density=0.6,
elements=uniform_distribution(min=-3,
max=10)))
w = flex.double_range(0, m)
ww = flex.double(m * m)
ww.resize(flex.grid(m, m))
ww.matrix_diagonal_set_in_place(diagonal=w)
for n_test in range(50):
a = next(random_matrices)
b = a.self_transpose_times_diagonal_times_self(w)
aa = a.as_dense_matrix()
bb = b.as_dense_matrix()
assert approx_equal(
bb,
aa.matrix_transpose().matrix_multiply(ww).matrix_multiply(aa))
c = a.transpose().self_times_diagonal_times_self_transpose(w)
cc = c.as_dense_matrix()
assert approx_equal(cc, bb)