def kernapply(x, k, circular=False):
"""Convolve a sequence x with a Kernel k"""
x = flex.double(x).deep_copy()
lenx = len(x)
w = flex.double(lenx, 0.0)
w.set_selected(flex.size_t_range(k.m + 1), k.coef)
sel = lenx -1 - flex.size_t_range(k.m)
w.set_selected(sel, k.coef[1:])
# do convolution in the Fourier domain
fft = fftpack.real_to_complex(lenx)
n = fft.n_real()
m = fft.m_real()
x.extend(flex.double(m-n, 0.))
w.extend(flex.double(m-n, 0.))
conv = fft.forward(x) * fft.forward(w)
# extend result by the reverse conjugate, omitting the DC offset and Nyquist
# frequencies. If fft.n_real() is odd there is no Nyquist term.
end = fft.n_complex() - (fft.n_real() + 1) % 2
conv.extend(flex.conj(conv[1:end]).reversed())
# transform back, take real part and scale
fft = fftpack.complex_to_complex(len(conv))
result = fft.backward(conv).parts()[0] / n
if circular:
return result
else:
return result[(k.m):(lenx-k.m)]
def good2n(nmax, coefs_list, ref_coefs, threshold=0.90, outfile=''):
## cc=0.90 is equivalent to 5% mutation in real space at nmax<=10
max_indx = math.nlm_array(nmax).nlm().size()
for nn in range(nmax, 1, -1):
min_indx = math.nlm_array(nn - 1).nlm().size()
#coef_0 = ref_coefs[min_indx:max_indx]
coef_0 = ref_coefs[0:max_indx]
mean_0 = abs(ref_coefs[0])
sigma_0 = flex.sum(flex.norm(coef_0)) - mean_0**2
sigma_0 = smath.sqrt(sigma_0)
cc_array = flex.double()
#out = open(outfile,"w")
for coef in coefs_list:
#coef_1 = coef[min_indx:max_indx]
coef_1 = coef[0:max_indx]
mean_1 = abs(coef[0])
sigma_1 = flex.sum(flex.norm(coef_1)) - mean_1**2
sigma_1 = smath.sqrt(sigma_1)
cov_01 = abs(flex.sum(coef_0 * flex.conj(coef_1)))
cov_01 = cov_01 - mean_0 * mean_1
this_cc = cov_01 / sigma_1 / sigma_0
cc_array.append(this_cc)
out = open(outfile, "a")
print >> out, this_cc
out.close()
print this_cc
mean_cc = flex.mean(cc_array)
out = open(outfile, "a")
print >> out, "level n: ", nn, mean_cc
out.close()
print "level n: ", nn, mean_cc
if (mean_cc >= threshold): return nn
max_indx = min_indx
return nn
def tst_zernike_grid(skip_iteration_probability=0.95):
#THIS TEST TAKES A BIT OF TIME
M=20
N=4
ddd = (M*2+1)
zga = math.zernike_grid(M,N,False)
zgb = math.zernike_grid(M,N,False)
xyz = zga.xyz()
coefs = zga.coefs()
nlm = zga.nlm()
import random
rng = random.Random(x=None)
for ii in range(nlm.size()):
for jj in range(ii+1,nlm.size()):
if (rng.random() < skip_iteration_probability):
continue
coefsa = coefs*0.0
coefsb = coefs*0.0
coefsa[ii]=1.0+1.0j
coefsb[jj]=1.0+1.0j
zga.load_coefs( nlm, coefsa )
zgb.load_coefs( nlm, coefsb )
fa = zga.f()
fb = zgb.f()
prodsum = flex.sum(fa*flex.conj(fb) )/xyz.size()
prodsuma= flex.sum(fa*flex.conj(fa) )/xyz.size()
prodsumb= flex.sum(fb*flex.conj(fb) )/xyz.size()
t1 = abs(prodsum)
t2 = abs(prodsuma)
t3 = abs(prodsumb)
t1 = 100.0*(t1/t2)
t2 = 100.0*(abs(t2-t3)/t3)
# unfortunately, this numerical integration scheme is not optimal. For certain
# combinations of nlm, we see significant non-orthogonality that reduces when
# we increase the number of points. A similar behavior is seen in the radial
# part of the Zernike polynome. If we compile withiout the radial function, similar
# behavior is seen using only the spherical harmonics functions.
# For this reason, the liberal limts set below are ok
assert t1<2.0
assert t2<5.0
def tst_zernike_grid(skip_iteration_probability=0.95):
#THIS TEST TAKES A BIT OF TIME
M=20
N=4
ddd = (M*2+1)
zga = math.zernike_grid(M,N,False)
zgb = math.zernike_grid(M,N,False)
xyz = zga.xyz()
coefs = zga.coefs()
nlm = zga.nlm()
import random
rng = random.Random(x=None)
for ii in range(nlm.size()):
for jj in range(ii+1,nlm.size()):
if (rng.random() < skip_iteration_probability):
continue
coefsa = coefs*0.0
coefsb = coefs*0.0
coefsa[ii]=1.0+1.0j
coefsb[jj]=1.0+1.0j
zga.load_coefs( nlm, coefsa )
zgb.load_coefs( nlm, coefsb )
fa = zga.f()
fb = zgb.f()
prodsum = flex.sum(fa*flex.conj(fb) )/xyz.size()
prodsuma= flex.sum(fa*flex.conj(fa) )/xyz.size()
prodsumb= flex.sum(fb*flex.conj(fb) )/xyz.size()
t1 = abs(prodsum)
t2 = abs(prodsuma)
t3 = abs(prodsumb)
t1 = 100.0*(t1/t2)
t2 = 100.0*(abs(t2-t3)/t3)
# unfortunately, this numerical integration scheme is not optimal. For certain
# combinations of nlm, we see significant non-orthogonality that reduces when
# we increase the number of points. A similar behavior is seen in the radial
# part of the Zernike polynome. If we compile withiout the radial function, similar
# behavior is seen using only the spherical harmonics functions.
# For this reason, the liberal limts set below are ok
assert t1<2.0
assert t2<5.0