def branch_2_mn(small):
m = []
n = []
while (len(n) == 0 or len(m) == 0):
r1 = random.random()
r2 = random.random()
r3 = random.random()
if (r1 >= r2 and r2 >= r3 and r3 > 0.0):
r = random.random()
if (r > 0.5):
m = [r1, r2, r3, 0, 0, 0]
else:
m = [r1, r1, r1, 0, 0, 0]
assert adptbx.is_positive_definite(m, small)
if (r1 >= r2 and r2 >= r3 and r3 > 0.0):
r = random.random()
if (r > 0.5):
n = [r1, r3, r2, 0, 0, 0]
else:
n = [r1, r1, r1, 0, 0, 0]
assert adptbx.is_positive_definite(n, small)
r = random.random()
if (r > 0.5):
m = adptbx.random_rotate_ellipsoid(u_cart=m)
n = adptbx.random_rotate_ellipsoid(u_cart=n)
return m, n
def branch_3_mn():
m = None
n = None
small = 1.e-15
for i in range(10000):
m2 = []
n2 = []
for i in range(4):
r1 = random.random()
r2 = random.random()
r3 = random.random()
if (r3 > 0.1):
r1 = r2
m2.append(r1)
n2.append(r2)
p1 = 0.5 * (m2[0] + m2[3] + math.sqrt(4 * m2[1] * m2[2] +
(m2[0] - m2[3])**2))
p2 = 0.5 * (m2[0] + m2[3] - math.sqrt(4 * m2[1] * m2[2] +
(m2[0] - m2[3])**2))
q1 = 0.5 * (n2[0] + m2[3] + math.sqrt(4 * n2[1] * n2[2] +
(n2[0] - n2[3])**2))
q2 = 0.5 * (n2[0] + m2[3] - math.sqrt(4 * n2[1] * n2[2] +
(n2[0] - n2[3])**2))
if (min(p1, p2) > 0.0 and min(q1, q2) > 0.0):
r = random.random()
if (r > 0.5):
r1 = r3
r2 = r2
m = [m2[0], m2[3], r1, m2[1], 0, 0]
n = [n2[0], n2[3], r2, n2[1], 0, 0]
if ([
adptbx.is_positive_definite(m),
adptbx.is_positive_definite(n)
].count(True) == 2):
esm = adptbx.eigensystem(m)
esn = adptbx.eigensystem(n)
vn = esn.values()
vm = esm.values()
mmin = flex.min(flex.double(vm))
nmin = flex.min(flex.double(vn))
if (abs(abs(mmin) - abs(nmin)) < small and mmin > 0.
and nmin > 0.):
for i, v in enumerate(vn):
if (abs(abs(nmin) - v) < small): break
for j, v in enumerate(vm):
if (abs(abs(mmin) - v) < small): break
vecn = flex.double(esn.vectors(i))
vecm = flex.double(esm.vectors(j))
if (flex.mean(vecm - vecn) < small): break
else:
m = None
n = None
assert [m, n] != [None, None]
assert [adptbx.is_positive_definite(m),
adptbx.is_positive_definite(n)].count(True) == 2
r = random.random()
if (r > 0.5):
m = adptbx.random_rotate_ellipsoid(u_cart=m)
n = adptbx.random_rotate_ellipsoid(u_cart=n)
return m, n
def branch_2_mn(small):
m=[]
n=[]
while (len(n)==0 or len(m)==0):
r1 = random.random()
r2 = random.random()
r3 = random.random()
if(r1 >= r2 and r2 >= r3 and r3> 0.0):
r = random.random()
if(r > 0.5):
m = [r1,r2,r3,0,0,0]
else:
m = [r1,r1,r1,0,0,0]
assert adptbx.is_positive_definite(m,small)
if(r1 >= r2 and r2 >= r3 and r3 > 0.0):
r = random.random()
if(r > 0.5):
n = [r1,r3,r2,0,0,0]
else:
n = [r1,r1,r1,0,0,0]
assert adptbx.is_positive_definite(n,small)
r = random.random()
if(r > 0.5):
m = adptbx.random_rotate_ellipsoid(u_cart = m)
n = adptbx.random_rotate_ellipsoid(u_cart = n)
return m,n
def branch_3_mn():
m = None
n = None
small = 1.e-15
for i in xrange(10000):
m2=[]
n2=[]
for i in xrange(4):
r1 = random.random()
r2 = random.random()
r3 = random.random()
if(r3 > 0.1):
r1 = r2
m2.append(r1)
n2.append(r2)
p1 = 0.5 * (m2[0]+m2[3] + math.sqrt(4*m2[1]*m2[2]+(m2[0]-m2[3])**2))
p2 = 0.5 * (m2[0]+m2[3] - math.sqrt(4*m2[1]*m2[2]+(m2[0]-m2[3])**2))
q1 = 0.5 * (n2[0]+m2[3] + math.sqrt(4*n2[1]*n2[2]+(n2[0]-n2[3])**2))
q2 = 0.5 * (n2[0]+m2[3] - math.sqrt(4*n2[1]*n2[2]+(n2[0]-n2[3])**2))
if(min(p1,p2) > 0.0 and min(q1,q2) > 0.0):
r = random.random()
if(r > 0.5):
r1 = r3
r2 = r2
m = [m2[0],m2[3],r1,m2[1],0,0]
n = [n2[0],n2[3],r2,n2[1],0,0]
if([adptbx.is_positive_definite(m),
adptbx.is_positive_definite(n)].count(True)==2):
esm = adptbx.eigensystem(m)
esn = adptbx.eigensystem(n)
vn = esn.values()
vm = esm.values()
mmin = flex.min(flex.double(vm))
nmin = flex.min(flex.double(vn))
if(abs(abs(mmin) - abs(nmin)) < small and mmin> 0. and nmin> 0.):
for i, v in enumerate(vn):
if(abs(abs(nmin) - v) < small): break
for j, v in enumerate(vm):
if(abs(abs(mmin) - v) < small): break
vecn = flex.double(esn.vectors(i))
vecm = flex.double(esm.vectors(j))
if(flex.mean(vecm-vecn) < small): break
else:
m = None
n = None
assert [m,n] != [None,None]
assert [adptbx.is_positive_definite(m),
adptbx.is_positive_definite(n)].count(True)==2
r = random.random()
if(r > 0.5):
m = adptbx.random_rotate_ellipsoid(u_cart = m)
n = adptbx.random_rotate_ellipsoid(u_cart = n)
return m,n
def exercise_eigen_core(diag):
u = adptbx.random_rotate_ellipsoid(diag + [0., 0., 0.])
ev = list(adptbx.eigenvalues(u))
diag.sort()
ev.sort()
for i in xrange(3):
check_eigenvalue(u, ev[i])
for i in xrange(3):
assert abs(diag[i] - ev[i]) < 1.e-4
if (adptbx.is_positive_definite(ev)):
es = adptbx.eigensystem(u)
ev = list(es.values())
ev.sort()
for i in xrange(3):
check_eigenvalue(u, ev[i])
for i in xrange(3):
assert abs(diag[i] - ev[i]) < 1.e-4
evec = []
for i in xrange(3):
check_eigenvector(u, es.values()[i], es.vectors(i))
evec.extend(es.vectors(i))
return # XXX following tests disabled for the moment
# sometimes fail if eigenvalues are very similar but not identical
sqrt_eval = matrix.diag(flex.sqrt(flex.double(es.values())))
evec = matrix.sqr(evec).transpose()
sqrt_u = evec * sqrt_eval * evec.transpose()
u_full = matrix.sym(sym_mat3=u).elems
assert approx_equal(u_full, (sqrt_u.transpose() * sqrt_u).elems,
eps=1.e-3)
assert approx_equal(u_full, (sqrt_u * sqrt_u.transpose()).elems,
eps=1.e-3)
assert approx_equal(u_full, (sqrt_u * sqrt_u).elems, eps=1.e-3)
sqrt_u_plus_shifts = matrix.sym(sym_mat3=[
x + 10 * (random.random() - .5) for x in sqrt_u.as_sym_mat3()
])
sts = (sqrt_u_plus_shifts.transpose() *
sqrt_u_plus_shifts).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
sts = (sqrt_u_plus_shifts *
sqrt_u_plus_shifts.transpose()).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
sts = (sqrt_u_plus_shifts * sqrt_u_plus_shifts).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
def exercise_eigen_core(diag):
u = adptbx.random_rotate_ellipsoid(diag + [0.0, 0.0, 0.0])
ev = list(adptbx.eigenvalues(u))
diag.sort()
ev.sort()
for i in xrange(3):
check_eigenvalue(u, ev[i])
for i in xrange(3):
assert abs(diag[i] - ev[i]) < 1.0e-4
if adptbx.is_positive_definite(ev):
es = adptbx.eigensystem(u)
ev = list(es.values())
ev.sort()
for i in xrange(3):
check_eigenvalue(u, ev[i])
for i in xrange(3):
assert abs(diag[i] - ev[i]) < 1.0e-4
evec = []
for i in xrange(3):
check_eigenvector(u, es.values()[i], es.vectors(i))
evec.extend(es.vectors(i))
return # XXX following tests disabled for the moment
# sometimes fail if eigenvalues are very similar but not identical
sqrt_eval = matrix.diag(flex.sqrt(flex.double(es.values())))
evec = matrix.sqr(evec).transpose()
sqrt_u = evec * sqrt_eval * evec.transpose()
u_full = matrix.sym(sym_mat3=u).elems
assert approx_equal(u_full, (sqrt_u.transpose() * sqrt_u).elems, eps=1.0e-3)
assert approx_equal(u_full, (sqrt_u * sqrt_u.transpose()).elems, eps=1.0e-3)
assert approx_equal(u_full, (sqrt_u * sqrt_u).elems, eps=1.0e-3)
sqrt_u_plus_shifts = matrix.sym(sym_mat3=[x + 10 * (random.random() - 0.5) for x in sqrt_u.as_sym_mat3()])
sts = (sqrt_u_plus_shifts.transpose() * sqrt_u_plus_shifts).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
sts = (sqrt_u_plus_shifts * sqrt_u_plus_shifts.transpose()).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
sts = (sqrt_u_plus_shifts * sqrt_u_plus_shifts).as_sym_mat3()
ev = adptbx.eigenvalues(sts)
assert min(ev) >= 0
