def test_auto_corr_scat_factor():
num_levels, num_bufs = 3, 4
tot_channels, lags = utils.multi_tau_lags(num_levels, num_bufs)
beta = 0.5
relaxation_rate = 10.0
baseline = 1.0
g2 = corr.auto_corr_scat_factor(lags, beta, relaxation_rate, baseline)
assert_array_almost_equal(g2, np.array([1.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]), decimal=8)
def test_multi_tau_lags():
multi_tau_levels = 3
multi_tau_channels = 8
delay_steps = [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 20, 24, 28]
tot_channels, lag_steps = core.multi_tau_lags(multi_tau_levels,
multi_tau_channels)
assert_array_equal(16, tot_channels)
assert_array_equal(delay_steps, lag_steps)
def multi_tau_auto_corr(num_levels, num_bufs, labels, images):
##comments, please add start_image, end_image, the default as None
from skxray.core import roi
from skxray.core import utils as core
"""
This function computes one-time correlations.
It uses a scheme to achieve long-time correlations inexpensively
by downsampling the data, iteratively combining successive frames.
The longest lag time computed is num_levels * num_bufs.
Parameters
----------
num_levels : int
how many generations of downsampling to perform, i.e.,
the depth of the binomial tree of averaged frames
num_bufs : int, must be even
maximum lag step to compute in each generation of
downsampling
labels : array
labeled array of the same shape as the image stack;
each ROI is represented by a distinct label (i.e., integer)
images : iterable of 2D arrays
dimensions are: (rr, cc)
Returns
-------
g2 : array
matrix of normalized intensity-intensity autocorrelation
shape (num_levels, number of labels(ROI))
lag_steps : array
delay or lag steps for the multiple tau analysis
shape num_levels
Notes
-----
The normalized intensity-intensity time-autocorrelation function
is defined as
:math ::
g_2(q, t') = \frac{<I(q, t)I(q, t + t')> }{<I(q, t)>^2}
; t' > 0
Here, I(q, t) refers to the scattering strength at the momentum
transfer vector q in reciprocal space at time t, and the brackets
<...> refer to averages over time t. The quantity t' denotes the
delay time
This implementation is based on code in the language Yorick
by Mark Sutton, based on published work. [1]_
References
----------
.. [1] D. Lumma, L. B. Lurio, S. G. J. Mochrie and M. Sutton,
"Area detector based photon correlation in the regime of
short data batches: Data reduction for dynamic x-ray
scattering," Rev. Sci. Instrum., vol 70, p 3274-3289, 2000.
"""
# In order to calculate correlations for `num_bufs`, images must be
# kept for up to the maximum lag step. These are stored in the array
# buffer. This algorithm only keeps number of buffers and delays but
# several levels of delays number of levels are kept in buf. Each
# level has twice the delay times of the next lower one. To save
# needless copying, of cyclic storage of images in buf is used.
if num_bufs % 2 != 0:
raise ValueError("number of channels(number of buffers) in "
"multiple-taus (must be even)")
if hasattr(images, 'frame_shape'):
# Give a user-friendly error if we can detect the shape from pims.
if labels.shape != images.frame_shape:
raise ValueError("Shape of the image stack should be equal to"
" shape of the labels array")
# get the pixels in each label
label_mask, pixel_list = roi.extract_label_indices(labels)
num_rois = np.max(label_mask)
# number of pixels per ROI
num_pixels = np.bincount(label_mask, minlength=(num_rois + 1))
num_pixels = num_pixels[1:]
if np.any(num_pixels == 0):
raise ValueError("Number of pixels of the required roi's"
" cannot be zero, "
"num_pixels = {0}".format(num_pixels))
# G holds the un normalized auto-correlation result. We
# accumulate computations into G as the algorithm proceeds.
G = np.zeros(((num_levels + 1) * num_bufs / 2, num_rois), dtype=np.float64)
# matrix of past intensity normalizations
past_intensity_norm = np.zeros(((num_levels + 1) * num_bufs / 2, num_rois),
dtype=np.float64)
# matrix of future intensity normalizations
future_intensity_norm = np.zeros(
((num_levels + 1) * num_bufs / 2, num_rois), dtype=np.float64)
# Ring buffer, a buffer with periodic boundary conditions.
# Images must be keep for up to maximum delay in buf.
buf = np.zeros((num_levels, num_bufs, np.sum(num_pixels)),
dtype=np.float64)
# to track processing each level
track_level = np.zeros(num_levels)
# to increment buffer
cur = np.ones(num_levels, dtype=np.int64)
# to track how many images processed in each level
img_per_level = np.zeros(num_levels, dtype=np.int64)
start_time = time.time() # used to log the computation time (optionally)
for n, img in enumerate(images):
cur[0] = (1 + cur[0]) % num_bufs # increment buffer
# Put the image into the ring buffer.
buf[0, cur[0] - 1] = (np.ravel(img))[pixel_list]
# Compute the correlations between the first level
# (undownsampled) frames. This modifies G,
# past_intensity_norm, future_intensity_norm,
# and img_per_level in place!
_process(buf,
G,
past_intensity_norm,
future_intensity_norm,
label_mask,
num_bufs,
num_pixels,
img_per_level,
level=0,
buf_no=cur[0] - 1)
# check whether the number of levels is one, otherwise
# continue processing the next level
processing = num_levels > 1
# Compute the correlations for all higher levels.
level = 1
while processing:
if not track_level[level]:
track_level[level] = 1
processing = False
else:
prev = 1 + (cur[level - 1] - 2) % num_bufs
cur[level] = 1 + cur[level] % num_bufs
buf[level,
cur[level] - 1] = (buf[level - 1, prev - 1] +
buf[level - 1, cur[level - 1] - 1]) / 2
# make the track_level zero once that level is processed
track_level[level] = 0
# call the _process function for each multi-tau level
# for multi-tau levels greater than one
# Again, this is modifying things in place. See comment
# on previous call above.
_process(
buf,
G,
past_intensity_norm,
future_intensity_norm,
label_mask,
num_bufs,
num_pixels,
img_per_level,
level=level,
buf_no=cur[level] - 1,
)
level += 1
# Checking whether there is next level for processing
processing = level < num_levels
# ending time for the process
end_time = time.time()
logger.info("Processing time for {0} images took {1} seconds."
"".format(n, (end_time - start_time)))
# the normalization factor
if len(np.where(past_intensity_norm == 0)[0]) != 0:
g_max = np.where(past_intensity_norm == 0)[0][0]
else:
g_max = past_intensity_norm.shape[0]
# g2 is normalized G
g2 = (G[:g_max] /
(past_intensity_norm[:g_max] * future_intensity_norm[:g_max]))
# Convert from num_levels, num_bufs to lag frames.
tot_channels, lag_steps = core.multi_tau_lags(num_levels, num_bufs)
lag_steps = lag_steps[:g_max]
return g2, lag_steps
def multi_tau_auto_corr(num_levels, num_bufs, labels, images):
##comments, please add start_image, end_image, the default as None
from skxray.core import roi
from skxray.core import utils as core
"""
This function computes one-time correlations.
It uses a scheme to achieve long-time correlations inexpensively
by downsampling the data, iteratively combining successive frames.
The longest lag time computed is num_levels * num_bufs.
Parameters
----------
num_levels : int
how many generations of downsampling to perform, i.e.,
the depth of the binomial tree of averaged frames
num_bufs : int, must be even
maximum lag step to compute in each generation of
downsampling
labels : array
labeled array of the same shape as the image stack;
each ROI is represented by a distinct label (i.e., integer)
images : iterable of 2D arrays
dimensions are: (rr, cc)
Returns
-------
g2 : array
matrix of normalized intensity-intensity autocorrelation
shape (num_levels, number of labels(ROI))
lag_steps : array
delay or lag steps for the multiple tau analysis
shape num_levels
Notes
-----
The normalized intensity-intensity time-autocorrelation function
is defined as
:math ::
g_2(q, t') = \frac{<I(q, t)I(q, t + t')> }{<I(q, t)>^2}
; t' > 0
Here, I(q, t) refers to the scattering strength at the momentum
transfer vector q in reciprocal space at time t, and the brackets
<...> refer to averages over time t. The quantity t' denotes the
delay time
This implementation is based on code in the language Yorick
by Mark Sutton, based on published work. [1]_
References
----------
.. [1] D. Lumma, L. B. Lurio, S. G. J. Mochrie and M. Sutton,
"Area detector based photon correlation in the regime of
short data batches: Data reduction for dynamic x-ray
scattering," Rev. Sci. Instrum., vol 70, p 3274-3289, 2000.
"""
# In order to calculate correlations for `num_bufs`, images must be
# kept for up to the maximum lag step. These are stored in the array
# buffer. This algorithm only keeps number of buffers and delays but
# several levels of delays number of levels are kept in buf. Each
# level has twice the delay times of the next lower one. To save
# needless copying, of cyclic storage of images in buf is used.
if num_bufs % 2 != 0:
raise ValueError("number of channels(number of buffers) in " "multiple-taus (must be even)")
if hasattr(images, "frame_shape"):
# Give a user-friendly error if we can detect the shape from pims.
if labels.shape != images.frame_shape:
raise ValueError("Shape of the image stack should be equal to" " shape of the labels array")
# get the pixels in each label
label_mask, pixel_list = roi.extract_label_indices(labels)
num_rois = np.max(label_mask)
# number of pixels per ROI
num_pixels = np.bincount(label_mask, minlength=(num_rois + 1))
num_pixels = num_pixels[1:]
if np.any(num_pixels == 0):
raise ValueError(
"Number of pixels of the required roi's" " cannot be zero, " "num_pixels = {0}".format(num_pixels)
)
# G holds the un normalized auto-correlation result. We
# accumulate computations into G as the algorithm proceeds.
G = np.zeros(((num_levels + 1) * num_bufs / 2, num_rois), dtype=np.float64)
# matrix of past intensity normalizations
past_intensity_norm = np.zeros(((num_levels + 1) * num_bufs / 2, num_rois), dtype=np.float64)
# matrix of future intensity normalizations
future_intensity_norm = np.zeros(((num_levels + 1) * num_bufs / 2, num_rois), dtype=np.float64)
# Ring buffer, a buffer with periodic boundary conditions.
# Images must be keep for up to maximum delay in buf.
buf = np.zeros((num_levels, num_bufs, np.sum(num_pixels)), dtype=np.float64)
# to track processing each level
track_level = np.zeros(num_levels)
# to increment buffer
cur = np.ones(num_levels, dtype=np.int64)
# to track how many images processed in each level
img_per_level = np.zeros(num_levels, dtype=np.int64)
start_time = time.time() # used to log the computation time (optionally)
for n, img in enumerate(images):
cur[0] = (1 + cur[0]) % num_bufs # increment buffer
# Put the image into the ring buffer.
buf[0, cur[0] - 1] = (np.ravel(img))[pixel_list]
# Compute the correlations between the first level
# (undownsampled) frames. This modifies G,
# past_intensity_norm, future_intensity_norm,
# and img_per_level in place!
_process(
buf,
G,
past_intensity_norm,
future_intensity_norm,
label_mask,
num_bufs,
num_pixels,
img_per_level,
level=0,
buf_no=cur[0] - 1,
)
# check whether the number of levels is one, otherwise
# continue processing the next level
processing = num_levels > 1
# Compute the correlations for all higher levels.
level = 1
while processing:
if not track_level[level]:
track_level[level] = 1
processing = False
else:
prev = 1 + (cur[level - 1] - 2) % num_bufs
cur[level] = 1 + cur[level] % num_bufs
buf[level, cur[level] - 1] = (buf[level - 1, prev - 1] + buf[level - 1, cur[level - 1] - 1]) / 2
# make the track_level zero once that level is processed
track_level[level] = 0
# call the _process function for each multi-tau level
# for multi-tau levels greater than one
# Again, this is modifying things in place. See comment
# on previous call above.
_process(
buf,
G,
past_intensity_norm,
future_intensity_norm,
label_mask,
num_bufs,
num_pixels,
img_per_level,
level=level,
buf_no=cur[level] - 1,
)
level += 1
# Checking whether there is next level for processing
processing = level < num_levels
# ending time for the process
end_time = time.time()
logger.info("Processing time for {0} images took {1} seconds." "".format(n, (end_time - start_time)))
# the normalization factor
if len(np.where(past_intensity_norm == 0)[0]) != 0:
g_max = np.where(past_intensity_norm == 0)[0][0]
else:
g_max = past_intensity_norm.shape[0]
# g2 is normalized G
g2 = G[:g_max] / (past_intensity_norm[:g_max] * future_intensity_norm[:g_max])
# Convert from num_levels, num_bufs to lag frames.
tot_channels, lag_steps = core.multi_tau_lags(num_levels, num_bufs)
lag_steps = lag_steps[:g_max]
return g2, lag_steps