def upsample(a, m=2):
L = a.shape[0]
dt = a.dtype.char
b = np.zeros((L * m, ), dtype=dt.upper())
b[::m] = m * a
fft1(b, shift=True, inplace=True)
b[:(L * m - L) / 2] = 0.
b[(L * m + L) / 2:] = 0.
P.plot(np.abs(b))
P.show()
ifft1(b, shift=True, inplace=True)
return b.astype(dt)
def upsample(a, m=2):
L = a.shape[0]
dt = a.dtype.char
b = np.zeros((L*m,), dtype=dt.upper())
b[::m] = m*a
fft1(b, shift=True, inplace=True)
b[:(L*m-L)/2] = 0.
b[(L*m+L)/2:] = 0.
P.plot(np.abs(b))
P.show()
ifft1(b, shift=True, inplace=True)
return b.astype(dt)
def run(self, image):
if not verify_scanner_image(self, image):
return
fmap_file = clean_name(self.fmap_file)[0]
## if hasattr(image, 'n_chan'):
## fmap_file += '.c%02d'%image.chan
try:
fmapIm = readImage(fmap_file)
except:
self.log("fieldmap not found: " + fmap_file)
return -1
(nslice, npe, nfe) = image.shape[-3:]
# make sure that the length of the q1 columns of the fmap
# are AT LEAST equal to that of the image
regrid_fac = max(npe, fmapIm.shape[-2])
# fmap and chi-mask are swapped to be of shape (Q1,Q2)
fmap = np.swapaxes(
regrid_bilinear(fmapIm[0], regrid_fac, axis=-2).astype(np.float64),
-1, -2)
chi = np.swapaxes(regrid_bilinear(fmapIm[1], regrid_fac, axis=-2), -1,
-2)
Q1, Q2 = fmap.shape[-2:]
# compute T_n2 vector
Tl = image.T_pe
delT = image.delT
a, b, n2, _ = image.epi_trajectory()
K = get_kernel(Q2, Tl, b, n2, fmap, chi)
for s in range(nslice):
# dchunk is shaped (nvol, npe, nfe)
# inverse transform along nfe (can't do in-place)
dchunk = ifft1(image[:, s, :, :])
# now shape is (nfe, npe, nvol)
dchunk = np.swapaxes(dchunk, 0, 2)
for fe in range(nfe):
# want to solve Kx = y for x
# K is (npe,npe), and y is (npe,nvol)
#
# There seems to be a trade-off here as nvol changes...
# Doing this in two steps is faster for large nvol; I think
# it takes advantage of the faster BLAS matrix-product in dot
# as opposed to LAPACK's linear solver. For smaller values
# of nvol, the overhead seems to outweigh the benefit.
iK = regularized_inverse(K[s, fe], self.lmbda)
dchunk[fe] = np.dot(iK, dchunk[fe])
dchunk = np.swapaxes(dchunk, 0, 2)
# fft x back to kx, can do inplace here
fft1(dchunk, inplace=True)
image[:, s, :, :] = dchunk
def run(self, image):
if not verify_scanner_image(self, image):
return
fmap_file = clean_name(self.fmap_file)[0]
## if hasattr(image, 'n_chan'):
## fmap_file += '.c%02d'%image.chan
try:
fmapIm = readImage(fmap_file)
except:
self.log("fieldmap not found: " + fmap_file)
return -1
(nslice, npe, nfe) = image.shape[-3:]
# make sure that the length of the q1 columns of the fmap
# are AT LEAST equal to that of the image
regrid_fac = max(npe, fmapIm.shape[-2])
# fmap and chi-mask are swapped to be of shape (Q1,Q2)
fmap = np.swapaxes(regrid_bilinear(fmapIm[0], regrid_fac, axis=-2).astype(np.float64), -1, -2)
chi = np.swapaxes(regrid_bilinear(fmapIm[1], regrid_fac, axis=-2), -1, -2)
Q1, Q2 = fmap.shape[-2:]
# compute T_n2 vector
Tl = image.T_pe
delT = image.delT
a, b, n2, _ = image.epi_trajectory()
K = get_kernel(Q2, Tl, b, n2, fmap, chi)
for s in range(nslice):
# dchunk is shaped (nvol, npe, nfe)
# inverse transform along nfe (can't do in-place)
dchunk = ifft1(image[:, s, :, :])
# now shape is (nfe, npe, nvol)
dchunk = np.swapaxes(dchunk, 0, 2)
for fe in range(nfe):
# want to solve Kx = y for x
# K is (npe,npe), and y is (npe,nvol)
#
# There seems to be a trade-off here as nvol changes...
# Doing this in two steps is faster for large nvol; I think
# it takes advantage of the faster BLAS matrix-product in dot
# as opposed to LAPACK's linear solver. For smaller values
# of nvol, the overhead seems to outweigh the benefit.
iK = regularized_inverse(K[s, fe], self.lmbda)
dchunk[fe] = np.dot(iK, dchunk[fe])
dchunk = np.swapaxes(dchunk, 0, 2)
# fft x back to kx, can do inplace here
fft1(dchunk, inplace=True)
image[:, s, :, :] = dchunk
def bench_fft1_time(self):
from numpy.fft import fft as numpy_fft
from scipy.fftpack import fft as scipy_fft
print
print ' 1D Double Precision Fast Fourier Transform'
print '================================================='
print ' | complex input '
print '-------------------------------------------------'
print ' size | recon | numpy | scipy |'
print '-------------------------------------------------'
for size,repeat in [(100,7000),(1000,2000),
(256,10000),
(512,10000),
(1024,1000),
(2048,1000),
(2048*2,500),
(2048*4,500),
]:
print '%5s' % size,
sys.stdout.flush()
x = random(repeat, size).astype(cdouble) + \
random(repeat, size).astype(cdouble)*1j
tr0 = time.time()
y = fft1(x, shift=False)
trf = time.time()
print '|%8.2f' % (trf-tr0),
sys.stdout.flush()
tn0 = time.time()
ny = numpy_fft(x)
tnf = time.time()
assert_array_almost_equal(ny,y)
print '|%8.2f' % (tnf-tn0),
sys.stdout.flush()
ts0 = time.time()
sy = scipy_fft(x)
tsf = time.time()
assert_array_almost_equal(sy,y)
print '|%8.2f' % (tsf-ts0),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
sys.stdout.flush()
print
print ' 1D Double Precision Fast Fourier Transform'
print '================================================='
print ' | complex input shifted '
print '-------------------------------------------------'
print ' size | recon | numpy | scipy |'
print '-------------------------------------------------'
for size,repeat in [(100,7000),(1000,2000),
(256,10000),
(512,10000),
(1024,1000),
(2048,1000),
(2048*2,500),
(2048*4,500),
]:
chk = checkerline(size).astype(double)
print '%5s' % size,
sys.stdout.flush()
x = random(repeat, size).astype(cdouble) + \
random(repeat, size).astype(cdouble)*1j
tr0 = time.time()
y = fft1(x, shift=True)
trf = time.time()
print '|%8.2f' % (trf-tr0),
sys.stdout.flush()
tn0 = time.time()
ny = chk*numpy_fft(chk*x)
tnf = time.time()
assert_array_almost_equal(ny,y)
print '|%8.2f' % (tnf-tn0),
sys.stdout.flush()
ts0 = time.time()
sy = chk*scipy_fft(chk*x)
tsf = time.time()
assert_array_almost_equal(sy,y)
print '|%8.2f' % (tsf-ts0),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
sys.stdout.flush()
print
print ' 1D Single Precision Fast Fourier Transform'
print '================================================='
print ' | complex input '
print '-------------------------------------------------'
print ' size | recon | numpy | scipy* |'
print '-------------------------------------------------'
for size,repeat in [(100,7000),(1000,2000),
(256,10000),
(512,10000),
(1024,1000),
(2048,1000),
(2048*2,500),
(2048*4,500),
]:
print '%5s' % size,
sys.stdout.flush()
x = random(repeat, size).astype(csingle) + \
random(repeat, size).astype(csingle)*1j
tr0 = time.time()
y = fft1(x, shift=False)
trf = time.time()
print '|%8.2f' % (trf-tr0),
sys.stdout.flush()
tn0 = time.time()
ny = numpy_fft(x)
tnf = time.time()
assert_array_almost_equal(ny,y, decimal=2)
print '|%8.2f' % (tnf-tn0),
sys.stdout.flush()
ts0 = time.time()
sy = scipy_fft(x.astype(cdouble)).astype(csingle)
tsf = time.time()
assert_array_almost_equal(sy,y, decimal=2)
print '|%8.2f' % (tsf-ts0),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
print "(* casted float->FT{double}->float)"
sys.stdout.flush()
print
print ' 1D Single Precision Fast Fourier Transform'
print '================================================='
print ' | complex input shifted '
print '-------------------------------------------------'
print ' size | recon | numpy | scipy* |'
print '-------------------------------------------------'
for size,repeat in [(100,7000),(1000,2000),
(256,10000),
(512,10000),
(1024,1000),
(2048,1000),
(2048*2,500),
(2048*4,500),
]:
chk = checkerline(size).astype(single)
print '%5s' % size,
sys.stdout.flush()
x = random(repeat, size).astype(csingle) + \
random(repeat, size).astype(csingle)*1j
tr0 = time.time()
y = fft1(x, shift=True)
trf = time.time()
print '|%8.2f' % (trf-tr0),
sys.stdout.flush()
tn0 = time.time()
ny = chk*numpy_fft(chk*x)
tnf = time.time()
assert_array_almost_equal(ny,y, decimal=2)
print '|%8.2f' % (tnf-tn0),
sys.stdout.flush()
ts0 = time.time()
sy = chk*(scipy_fft((chk*x).astype(cdouble))).astype(csingle)
tsf = time.time()
assert_array_almost_equal(sy,y, decimal=2)
print '|%8.2f' % (tsf-ts0),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
print "(* casted float->FT{double}->float)"
sys.stdout.flush()
def bench_fft1_time(self):
from numpy.fft import fft as numpy_fft
from scipy.fftpack import fft as scipy_fft
print
print ' 1D Double Precision Fast Fourier Transform'
print '================================================='
print ' | complex input '
print '-------------------------------------------------'
print ' size | recon | numpy | scipy |'
print '-------------------------------------------------'
for size, repeat in [
(100, 7000),
(1000, 2000),
(256, 10000),
(512, 10000),
(1024, 1000),
(2048, 1000),
(2048 * 2, 500),
(2048 * 4, 500),
]:
print '%5s' % size,
sys.stdout.flush()
x = random(repeat, size).astype(cdouble) + \
random(repeat, size).astype(cdouble)*1j
tr0 = time.time()
y = fft1(x, shift=False)
trf = time.time()
print '|%8.2f' % (trf - tr0),
sys.stdout.flush()
tn0 = time.time()
ny = numpy_fft(x)
tnf = time.time()
assert_array_almost_equal(ny, y)
print '|%8.2f' % (tnf - tn0),
sys.stdout.flush()
ts0 = time.time()
sy = scipy_fft(x)
tsf = time.time()
assert_array_almost_equal(sy, y)
print '|%8.2f' % (tsf - ts0),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
sys.stdout.flush()
print
print ' 1D Double Precision Fast Fourier Transform'
print '================================================='
print ' | complex input shifted '
print '-------------------------------------------------'
print ' size | recon | numpy | scipy |'
print '-------------------------------------------------'
for size, repeat in [
(100, 7000),
(1000, 2000),
(256, 10000),
(512, 10000),
(1024, 1000),
(2048, 1000),
(2048 * 2, 500),
(2048 * 4, 500),
]:
chk = checkerline(size).astype(double)
print '%5s' % size,
sys.stdout.flush()
x = random(repeat, size).astype(cdouble) + \
random(repeat, size).astype(cdouble)*1j
tr0 = time.time()
y = fft1(x, shift=True)
trf = time.time()
print '|%8.2f' % (trf - tr0),
sys.stdout.flush()
tn0 = time.time()
ny = chk * numpy_fft(chk * x)
tnf = time.time()
assert_array_almost_equal(ny, y)
print '|%8.2f' % (tnf - tn0),
sys.stdout.flush()
ts0 = time.time()
sy = chk * scipy_fft(chk * x)
tsf = time.time()
assert_array_almost_equal(sy, y)
print '|%8.2f' % (tsf - ts0),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
sys.stdout.flush()
print
print ' 1D Single Precision Fast Fourier Transform'
print '================================================='
print ' | complex input '
print '-------------------------------------------------'
print ' size | recon | numpy | scipy* |'
print '-------------------------------------------------'
for size, repeat in [
(100, 7000),
(1000, 2000),
(256, 10000),
(512, 10000),
(1024, 1000),
(2048, 1000),
(2048 * 2, 500),
(2048 * 4, 500),
]:
print '%5s' % size,
sys.stdout.flush()
x = random(repeat, size).astype(csingle) + \
random(repeat, size).astype(csingle)*1j
tr0 = time.time()
y = fft1(x, shift=False)
trf = time.time()
print '|%8.2f' % (trf - tr0),
sys.stdout.flush()
tn0 = time.time()
ny = numpy_fft(x)
tnf = time.time()
assert_array_almost_equal(ny, y, decimal=2)
print '|%8.2f' % (tnf - tn0),
sys.stdout.flush()
ts0 = time.time()
sy = scipy_fft(x.astype(cdouble)).astype(csingle)
tsf = time.time()
assert_array_almost_equal(sy, y, decimal=2)
print '|%8.2f' % (tsf - ts0),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
print "(* casted float->FT{double}->float)"
sys.stdout.flush()
print
print ' 1D Single Precision Fast Fourier Transform'
print '================================================='
print ' | complex input shifted '
print '-------------------------------------------------'
print ' size | recon | numpy | scipy* |'
print '-------------------------------------------------'
for size, repeat in [
(100, 7000),
(1000, 2000),
(256, 10000),
(512, 10000),
(1024, 1000),
(2048, 1000),
(2048 * 2, 500),
(2048 * 4, 500),
]:
chk = checkerline(size).astype(single)
print '%5s' % size,
sys.stdout.flush()
x = random(repeat, size).astype(csingle) + \
random(repeat, size).astype(csingle)*1j
tr0 = time.time()
y = fft1(x, shift=True)
trf = time.time()
print '|%8.2f' % (trf - tr0),
sys.stdout.flush()
tn0 = time.time()
ny = chk * numpy_fft(chk * x)
tnf = time.time()
assert_array_almost_equal(ny, y, decimal=2)
print '|%8.2f' % (tnf - tn0),
sys.stdout.flush()
ts0 = time.time()
sy = chk * (scipy_fft((chk * x).astype(cdouble))).astype(csingle)
tsf = time.time()
assert_array_almost_equal(sy, y, decimal=2)
print '|%8.2f' % (tsf - ts0),
sys.stdout.flush()
print ' (secs for %s calls)' % (repeat)
print "(* casted float->FT{double}->float)"
sys.stdout.flush()