def exercise_prime_factors_of():
from libtbx.math_utils import prime_factors_of
assert prime_factors_of(n=1) == []
prime_set = set()
for n in xrange(2, 100):
primes = prime_factors_of(n)
pp = 1
for p in primes:
pp *= p
assert pp == n
prime_set.update(primes)
if (n == 30):
assert prime_set == set([2,3,5,7,11,13,17,19,23,29])
for n in prime_set:
assert prime_factors_of(n) == [n]
assert len(prime_set) == 25
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_prime_factors_of():
from libtbx.math_utils import prime_factors_of
assert prime_factors_of(n=1) == []
prime_set = set()
for n in xrange(2, 100):
primes = prime_factors_of(n)
pp = 1
for p in primes:
pp *= p
assert pp == n
prime_set.update(primes)
if (n == 30):
assert prime_set == set([2, 3, 5, 7, 11, 13, 17, 19, 23, 29])
for n in prime_set:
assert prime_factors_of(n) == [n]
assert len(prime_set) == 25
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_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_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 run(args):
for arg in args:
n = int(arg)
assert n > 0
print "prime factors of %d:" % n, prime_factors_of(n)
def run(args):
for arg in args:
n = int(arg)
assert n > 0
print "prime factors of %d:" % n, prime_factors_of(n)