def compare_fftpack_with_hermft_1d():
mt = flex.mersenne_twister(seed=0)
for n_cmpl in xrange(1, 101):
primes = prime_factors_of(n_cmpl)
if (n_cmpl != 1 and max(primes) > 19): continue
n_real = n_cmpl * 2
m_real = n_real + 2
z = (mt.random_double(size=m_real)*2-1).as_float()
# The imaginary parts of the first and last complex values should
# be zero, but z has random values in these places, to prove that
# they don't change the result.
hermft_xy = z.deep_copy()
hermft_xy[1] = hermft_xy[-2]
# real part of last complex value stored in imaginary part of first
# (see ccp4/doc/libfft.doc)
hermft_xy[-2] = 253
# random value, for consistency check below
d = flex.int((m_real,2,m_real,m_real,m_real))
ccp4io_dev_ext.fftlib_hermft(xy=hermft_xy, n=n_cmpl, d=d)
# consistency check first
assert hermft_xy[-2] == 253
assert hermft_xy[-1] == z[-1]
# reset to zero for comparision with fftpack result further down
hermft_xy[-2] = 0
hermft_xy[-1] = 0
fft = scitbx.fftpack.real_to_complex(n_real)
assert fft.m_real() == m_real
fftpack_xy = z.as_double()
for i in xrange(n_cmpl): fftpack_xy[i*2+1] *= -1 # conjugate
fft.backward(fftpack_xy)
fftpack_xy = fftpack_xy.as_float()
if (flex.max_absolute(hermft_xy-fftpack_xy) > 1e-5):
assert approx_equal(hermft_xy, fftpack_xy, eps=1e-5)
def compare_fftpack_with_hermft_1d():
mt = flex.mersenne_twister(seed=0)
for n_cmpl in xrange(1, 101):
primes = prime_factors_of(n_cmpl)
if (n_cmpl != 1 and max(primes) > 19): continue
n_real = n_cmpl * 2
m_real = n_real + 2
z = (mt.random_double(size=m_real) * 2 - 1).as_float()
# The imaginary parts of the first and last complex values should
# be zero, but z has random values in these places, to prove that
# they don't change the result.
hermft_xy = z.deep_copy()
hermft_xy[1] = hermft_xy[-2]
# real part of last complex value stored in imaginary part of first
# (see ccp4/doc/libfft.doc)
hermft_xy[-2] = 253
# random value, for consistency check below
d = flex.int((m_real, 2, m_real, m_real, m_real))
ccp4io_dev_ext.fftlib_hermft(xy=hermft_xy, n=n_cmpl, d=d)
# consistency check first
assert hermft_xy[-2] == 253
assert hermft_xy[-1] == z[-1]
# reset to zero for comparision with fftpack result further down
hermft_xy[-2] = 0
hermft_xy[-1] = 0
fft = scitbx.fftpack.real_to_complex(n_real)
assert fft.m_real() == m_real
fftpack_xy = z.as_double()
for i in xrange(n_cmpl):
fftpack_xy[i * 2 + 1] *= -1 # conjugate
fft.backward(fftpack_xy)
fftpack_xy = fftpack_xy.as_float()
if (flex.max_absolute(hermft_xy - fftpack_xy) > 1e-5):
assert approx_equal(hermft_xy, fftpack_xy, eps=1e-5)
def exercise_fftlib_real_complex_3d_real_imag_w_given_dims(
mt, nu, nv, nw, verbose):
map_size = nu * nv * (nw + 2)
map = (mt.random_double(size=map_size) * 2 - 1).as_float()
x = map.deep_copy()
ccp4io_dev_ext.fftlib_real_to_complex_3d_real_imag_w(x=x,
nu=nu,
nv=nv,
nw=nw,
complete=True)
f = x.deep_copy()
ccp4io_dev_ext.hermitian_conjugate_3d_real_imag_w(x=x, nu=nu, nv=nv, nw=nw)
ccp4io_dev_ext.fftlib_complex_to_real_3d_real_imag_w(x=x,
nu=nu,
nv=nv,
nw=nw,
complete=True)
x *= 1 / (nu * nv * nw)
xfocus = x[:nu * nv * nw]
mfocus = map[:nu * nv * nw]
if (flex.max_absolute(xfocus - mfocus) > 1e-5):
assert approx_equal(xfocus, mfocus, eps=1e-5)
#
fft = scitbx.fftpack.real_to_complex_3d((nu, nv, nw))
g = flex.double(flex.grid(fft.m_real()).set_focus(fft.n_real()))
assert g.size() == f.size()
for u in xrange(nu):
for v in xrange(nv):
for w in xrange(nw + 2):
g[(u * nv + v) * (nw + 2) + w] = map[(w * nv + v) * nu + u]
fft.forward(g)
for u in xrange(nu):
for v in xrange(nv):
for w in xrange(nw // 2 + 1):
wr = w * 2
wi = wr + 1
for wj in [wr, wi]:
ge = g[(u * nv + v) * (nw + 2) + wj]
fe = f[(wj * nv + v) * nu + u]
assert approx_equal(fe, ge, eps=1e-4)
#
y = map.deep_copy()
ccp4io_dev_ext.fftlib_real_to_complex_3d_real_imag_w(x=y,
nu=nu,
nv=nv,
nw=nw,
complete=False)
ccp4io_dev_ext.hermitian_conjugate_3d_real_imag_w(x=y, nu=nu, nv=nv, nw=nw)
ccp4io_dev_ext.fftlib_complex_to_real_3d_real_imag_w(x=y,
nu=nu,
nv=nv,
nw=nw,
complete=False)
y *= 1 / (nu * nv * nw)
show_complete_true_false_cc(nu, nv, nw, (x, y), verbose)
def exercise_savitzky_golay_smoothing():
plot = False
def rms(flex_double):
return math.sqrt(flex.mean(flex.pow2(flex_double)))
for sigma_frac in (0.005, 0.01, 0.05, 0.1):
mean = random.randint(-5, 5)
scale = flex.random_double() * 10
sigma = flex.random_double() * 5 + 1
gaussian = scitbx.math.curve_fitting.gaussian(scale, mean, sigma)
x = flex.double(frange(-20, 20, 0.1))
y = gaussian(x)
rand_norm = scitbx.random.normal_distribution(mean=0,
sigma=sigma_frac *
flex.max_absolute(y))
g = scitbx.random.variate(rand_norm)
noise = g(y.size())
y_noisy = y + noise
# according to numerical recipes the best results are obtained where the
# full window width is between 1 and 2 times the number of points at fwhm
# for polynomials of degree 4
half_window = int(round(0.5 * 2.355 * sigma * 10))
y_filtered = savitzky_golay_filter(x,
y_noisy,
half_window=half_window,
degree=4)[1]
extracted_noise = y_noisy - y_filtered
rms_noise = rms(noise)
rms_extracted_noise = rms(extracted_noise)
assert is_below_limit(value=abs(rand_norm.sigma - rms_noise) /
rand_norm.sigma,
limit=0.15)
assert is_below_limit(
value=abs(rand_norm.sigma - rms_extracted_noise) / rand_norm.sigma,
limit=0.15)
diff = y_filtered - y
assert is_below_limit(value=(rms(diff) / rand_norm.sigma), limit=0.4)
if plot:
from matplotlib import pyplot
pyplot.plot(x, y)
pyplot.plot(x, noise)
pyplot.scatter(x, y_noisy, marker="x")
pyplot.plot(x, y_filtered)
pyplot.show()
pyplot.plot(x, extracted_noise)
pyplot.plot(x, noise)
pyplot.show()
return
def exercise_savitzky_golay_smoothing():
plot = False
def rms(flex_double):
return math.sqrt(flex.mean(flex.pow2(flex_double)))
for sigma_frac in (0.005, 0.01, 0.05, 0.1):
mean = random.randint(-5,5)
scale = flex.random_double() * 10
sigma = flex.random_double() * 5 + 1
gaussian = curve_fitting.gaussian(scale, mean, sigma)
x = flex.double(frange(-20,20,0.1))
y = gaussian(x)
rand_norm = scitbx.random.normal_distribution(
mean=0, sigma=sigma_frac*flex.max_absolute(y))
g = scitbx.random.variate(rand_norm)
noise = g(y.size())
y_noisy = y + noise
# according to numerical recipes the best results are obtained where the
# full window width is between 1 and 2 times the number of points at fwhm
# for polynomials of degree 4
half_window = int(round(0.5 * 2.355 * sigma * 10))
y_filtered = savitzky_golay_filter(x, y_noisy, half_window=half_window, degree=4)[1]
extracted_noise = y_noisy - y_filtered
rms_noise = rms(noise)
rms_extracted_noise = rms(extracted_noise)
assert is_below_limit(
value=abs(rand_norm.sigma - rms_noise)/rand_norm.sigma,
limit=0.15)
assert is_below_limit(
value=abs(rand_norm.sigma - rms_extracted_noise)/rand_norm.sigma,
limit=0.15)
diff = y_filtered - y
assert is_below_limit(
value=(rms(diff)/ rand_norm.sigma),
limit=0.4)
if plot:
from matplotlib import pyplot
pyplot.plot(x, y)
pyplot.plot(x, noise)
pyplot.scatter(x, y_noisy, marker="x")
pyplot.plot(x, y_filtered)
pyplot.show()
pyplot.plot(x, extracted_noise)
pyplot.plot(x, noise)
pyplot.show()
return
def compare_fftpack_with_cmplft_1d():
mt = flex.mersenne_twister(seed=0)
for n in xrange(1, 101):
primes = prime_factors_of(n)
if (n != 1 and max(primes) > 19): continue
z = (mt.random_double(size=n*2)*2-1).as_float()
cmplft_xy = z.deep_copy()
d = flex.int((2*n,2,2*n,2*n,2*n))
ccp4io_dev_ext.fftlib_cmplft(xy=cmplft_xy, n=n, d=d)
fft = scitbx.fftpack.complex_to_complex(n)
fftpack_xy = z.as_double()
fft.forward(fftpack_xy)
fftpack_xy = fftpack_xy.as_float()
if (flex.max_absolute(cmplft_xy-fftpack_xy) > 1e-5):
assert approx_equal(cmplft_xy, fftpack_xy, eps=1e-5)
def compare_fftpack_with_cmplft_1d():
mt = flex.mersenne_twister(seed=0)
for n in xrange(1, 101):
primes = prime_factors_of(n)
if (n != 1 and max(primes) > 19): continue
z = (mt.random_double(size=n * 2) * 2 - 1).as_float()
cmplft_xy = z.deep_copy()
d = flex.int((2 * n, 2, 2 * n, 2 * n, 2 * n))
ccp4io_dev_ext.fftlib_cmplft(xy=cmplft_xy, n=n, d=d)
fft = scitbx.fftpack.complex_to_complex(n)
fftpack_xy = z.as_double()
fft.forward(fftpack_xy)
fftpack_xy = fftpack_xy.as_float()
if (flex.max_absolute(cmplft_xy - fftpack_xy) > 1e-5):
assert approx_equal(cmplft_xy, fftpack_xy, eps=1e-5)
def compare_fftpack_with_realft_1d():
mt = flex.mersenne_twister(seed=0)
for n_cmpl in xrange(1, 101):
primes = prime_factors_of(n_cmpl)
if (n_cmpl != 1 and max(primes) > 19): continue
n_real = n_cmpl * 2
m_real = n_real + 2
z = (mt.random_double(size=m_real)*2-1).as_float()
realft_xy = z.deep_copy()
d = flex.int((m_real,2,m_real,m_real,m_real))
ccp4io_dev_ext.fftlib_realft(xy=realft_xy, n=n_cmpl, d=d)
fft = scitbx.fftpack.real_to_complex(n_real)
assert fft.m_real() == m_real
fftpack_xy = z.as_double()
fft.forward(fftpack_xy)
fftpack_xy = fftpack_xy.as_float()
if (flex.max_absolute(realft_xy-fftpack_xy) > 1e-5):
assert approx_equal(realft_xy, fftpack_xy, eps=1e-5)
def compare_fftpack_with_cmplft_3d():
mt = flex.mersenne_twister(seed=0)
for nx,ny,nz in [(30,20,40), (7,19,13), (5,11,4)]:
z = (mt.random_double(size=2*nx*ny*nz)*2-1).as_float()
cmplft_xy = z.deep_copy()
d = flex.int([2*nx*ny*nz, 2*nx*ny, 2*nx*ny*nz, 2*nx*ny, 2])
ccp4io_dev_ext.fftlib_cmplft(xy=cmplft_xy, n=nz, d=d)
d = flex.int([2*nx*ny*nz, 2*nx, 2*nx*ny, 2*nx, 2])
ccp4io_dev_ext.fftlib_cmplft(xy=cmplft_xy, n=ny, d=d)
d = flex.int([2*nx*ny*nz, 2, 2*nx*ny*nz, 2*nx*ny*nz, 2*nx])
ccp4io_dev_ext.fftlib_cmplft(xy=cmplft_xy, n=nx, d=d)
fft = scitbx.fftpack.complex_to_complex_3d((nz,ny,nx))
fftpack_xy = z.as_double()
fftpack_xy.reshape(flex.grid(nz,ny,2*nx))
fft.forward(fftpack_xy)
fftpack_xy = fftpack_xy.as_float().as_1d()
if (flex.max_absolute(cmplft_xy-fftpack_xy) > 1e-4):
assert approx_equal(cmplft_xy, fftpack_xy, eps=1e-4)
def compare_fftpack_with_realft_1d():
mt = flex.mersenne_twister(seed=0)
for n_cmpl in xrange(1, 101):
primes = prime_factors_of(n_cmpl)
if (n_cmpl != 1 and max(primes) > 19): continue
n_real = n_cmpl * 2
m_real = n_real + 2
z = (mt.random_double(size=m_real) * 2 - 1).as_float()
realft_xy = z.deep_copy()
d = flex.int((m_real, 2, m_real, m_real, m_real))
ccp4io_dev_ext.fftlib_realft(xy=realft_xy, n=n_cmpl, d=d)
fft = scitbx.fftpack.real_to_complex(n_real)
assert fft.m_real() == m_real
fftpack_xy = z.as_double()
fft.forward(fftpack_xy)
fftpack_xy = fftpack_xy.as_float()
if (flex.max_absolute(realft_xy - fftpack_xy) > 1e-5):
assert approx_equal(realft_xy, fftpack_xy, eps=1e-5)
def exercise_fftlib_real_complex_3d_real_imag_w_given_dims(
mt, nu, nv, nw, verbose):
map_size = nu * nv * (nw+2)
map = (mt.random_double(size=map_size)*2-1).as_float()
x = map.deep_copy()
ccp4io_dev_ext.fftlib_real_to_complex_3d_real_imag_w(
x=x, nu=nu, nv=nv, nw=nw, complete=True)
f = x.deep_copy()
ccp4io_dev_ext.hermitian_conjugate_3d_real_imag_w(x=x, nu=nu, nv=nv, nw=nw)
ccp4io_dev_ext.fftlib_complex_to_real_3d_real_imag_w(
x=x, nu=nu, nv=nv, nw=nw, complete=True)
x *= 1/(nu*nv*nw)
xfocus = x[:nu*nv*nw]
mfocus = map[:nu*nv*nw]
if (flex.max_absolute(xfocus-mfocus) > 1e-5):
assert approx_equal(xfocus, mfocus, eps=1e-5)
#
fft = scitbx.fftpack.real_to_complex_3d((nu, nv, nw))
g = flex.double(flex.grid(fft.m_real()).set_focus(fft.n_real()))
assert g.size() == f.size()
for u in xrange(nu):
for v in xrange(nv):
for w in xrange(nw+2):
g[(u*nv+v)*(nw+2)+w] = map[(w*nv+v)*nu+u]
fft.forward(g)
for u in xrange(nu):
for v in xrange(nv):
for w in xrange(nw//2+1):
wr = w*2
wi = wr+1
for wj in [wr, wi]:
ge = g[(u*nv+v)*(nw+2)+wj]
fe = f[(wj*nv+v)*nu+u]
assert approx_equal(fe, ge, eps=1e-4)
#
y = map.deep_copy()
ccp4io_dev_ext.fftlib_real_to_complex_3d_real_imag_w(
x=y, nu=nu, nv=nv, nw=nw, complete=False)
ccp4io_dev_ext.hermitian_conjugate_3d_real_imag_w(x=y, nu=nu, nv=nv, nw=nw)
ccp4io_dev_ext.fftlib_complex_to_real_3d_real_imag_w(
x=y, nu=nu, nv=nv, nw=nw, complete=False)
y *= 1/(nu*nv*nw)
show_complete_true_false_cc(nu, nv, nw, (x, y), verbose)
def compare_fftpack_with_cmplft_3d():
mt = flex.mersenne_twister(seed=0)
for nx, ny, nz in [(30, 20, 40), (7, 19, 13), (5, 11, 4)]:
z = (mt.random_double(size=2 * nx * ny * nz) * 2 - 1).as_float()
cmplft_xy = z.deep_copy()
d = flex.int(
[2 * nx * ny * nz, 2 * nx * ny, 2 * nx * ny * nz, 2 * nx * ny, 2])
ccp4io_dev_ext.fftlib_cmplft(xy=cmplft_xy, n=nz, d=d)
d = flex.int([2 * nx * ny * nz, 2 * nx, 2 * nx * ny, 2 * nx, 2])
ccp4io_dev_ext.fftlib_cmplft(xy=cmplft_xy, n=ny, d=d)
d = flex.int(
[2 * nx * ny * nz, 2, 2 * nx * ny * nz, 2 * nx * ny * nz, 2 * nx])
ccp4io_dev_ext.fftlib_cmplft(xy=cmplft_xy, n=nx, d=d)
fft = scitbx.fftpack.complex_to_complex_3d((nz, ny, nx))
fftpack_xy = z.as_double()
fftpack_xy.reshape(flex.grid(nz, ny, 2 * nx))
fft.forward(fftpack_xy)
fftpack_xy = fftpack_xy.as_float().as_1d()
if (flex.max_absolute(cmplft_xy - fftpack_xy) > 1e-4):
assert approx_equal(cmplft_xy, fftpack_xy, eps=1e-4)