def tst():
M = 10
xy = []
for ii in range(M):
r = 10.0
phi = ii * (math.pi * 2 / M)
x = r * math.cos(phi)
y = r * math.sin(phi)
xy.append(flex.double([x, y]))
# build distance matrix
dmat = []
for ii in range(M):
tmp = []
for jj in range(M):
x1 = xy[ii][0]
x2 = xy[jj][0]
y1 = xy[ii][1]
y2 = xy[jj][1]
dd = math.sqrt((x1 - x2)**2.0 + (y1 - y2)**2.0)
if jj != ii:
tmp.append((jj, dd))
dmat.append(tmp)
spee = classic_spe_engine(dmat, l=1.0, max_cycle=5000)
x, s = spee.embed(2, M)
assert s < 1e-4
print("OK")
def tst_dmatrix():
# expected values are the d_jmn at beta=1.0 and j=2, m=-2, -2<=n<=2
expect = [0.593133, 0.64806, 0.433605, 0.193411, 0.0528305]
eps = 1e-4
d2 = dmatrix(2, 1.0) # dmatrix( max_L, beta )
for n in range(-2, 3):
assert abs(expect[n + 2] - d2.djmn(2, -2, n)) < eps
d4 = dmatrix(4, 1.0)
for n in range(-2, 3):
assert abs(expect[n + 2] - d4.djmn(2, -2, n)) < eps
d7 = dmatrix(2, 1.0)
for n in range(-2, 3):
assert abs(expect[n + 2] - d7.djmn(2, -2, n)) < eps
# check agains d(2,2,1) = -(1+cos(beta))*sin(beta)/2.0
for ii in range(10):
expt = -(1.0 + math.cos(ii)) * math.sin(ii) / 2.0
assert abs(dmatrix(2, ii).djmn(2, 2, 1) - expt) < eps
# check beta= multiple of pi/2
assert abs(dmatrix(20, math.pi).djmn(2, 2, 0)) < eps
assert abs(dmatrix(2, math.pi * 2).djmn(2, 2, 0)) < eps
assert abs(
dmatrix(20, math.pi * 0.5).djmn(2, 2, 0) - math.sqrt(6.0) / 4.0) < eps
def rosca(m=9, hemisphere=True):
"""
Regular grid on the unit sphere, Rosca (2010).
"""
def truncate(x):
if (abs(x) < 1.e-6): return 0
else: return x
def add(result, new):
foud = False
for s in result:
d = math.sqrt((s[0] - new[0])**2 + (s[1] - new[1])**2 +
(s[2] - new[2])**2)
if (d < 1.e-3): return
result.append(new)
return
d_l = math.sqrt(2) / m
result = flex.vec3_double()
for m_ in xrange(m + 1):
if (m_ == 0):
add(result, [0, 0, 1])
else:
l_m = m_ * d_l
d_phi = math.pi / (4 * m_)
assert l_m >= 0 and l_m <= math.sqrt(2)
for k in xrange(m_ + 1):
arg1 = k * d_phi
arg2 = l_m * math.sqrt(1 - l_m**2 / 4)
x_km = truncate(math.cos(arg1) * arg2)
y_km = truncate(math.sin(arg1) * arg2)
z_m = truncate(1. - l_m**2 / 2)
add(result, [x_km, y_km, z_m])
add(result, [y_km, x_km, z_m])
add(result, [-y_km, x_km, z_m])
add(result, [-x_km, y_km, z_m])
add(result, [x_km, -y_km, z_m])
add(result, [y_km, -x_km, z_m])
add(result, [-x_km, -y_km, z_m])
add(result, [-y_km, -x_km, z_m])
if (not hemisphere):
add(result, [x_km, y_km, -z_m])
add(result, [y_km, x_km, -z_m])
add(result, [-y_km, x_km, -z_m])
add(result, [-x_km, y_km, -z_m])
add(result, [x_km, -y_km, -z_m])
add(result, [y_km, -x_km, -z_m])
add(result, [-x_km, -y_km, -z_m])
add(result, [-y_km, -x_km, -z_m])
for r in result:
assert abs(1. - math.sqrt(r[0]**2 + r[1]**2 + r[2]**2)) < 1.e-6
# XXX for debugging
if (0):
f = "HETATM%5d O HOH A%4d %8.3f%8.3f%8.3f 1.00 23.99 O "
o = open("junk.pdb", "w")
for i, r in enumerate(result):
print >> o, f % (i, i, r[0], r[1], r[2])
o.close()
return result