def gen_rings_ctf(prjref, nx, ctf, numr):
"""
Convert set of ffts of projections to Fourier rings with additional multiplication by a ctf
The command returns list of rings
"""
from math import sin, cos, pi
from sp_fundamentals import fft
from sp_alignment import ringwe
from sp_filter import filt_ctf
mode = "F"
wr_four = ringwe(numr, "F")
cnx = nx // 2 + 1
cny = nx // 2 + 1
qv = pi / 180.0
refrings = [
] # list of (image objects) reference projections in Fourier representation
for i in range(len(prjref)):
cimage = Util.Polar2Dm(filt_ctf(prjref[i], ctf, True), cnx, cny, numr,
mode) # currently set to quadratic....
Util.Normalize_ring(cimage, numr, 0)
Util.Frngs(cimage, numr)
Util.Applyws(cimage, numr, wr_four)
refrings.append(cimage)
phi = prjref[i].get_attr('phi')
theta = prjref[i].get_attr('theta')
psi = prjref[i].get_attr('psi')
n1 = sin(theta * qv) * cos(phi * qv)
n2 = sin(theta * qv) * sin(phi * qv)
n3 = cos(theta * qv)
refrings[i].set_attr_dict({
"n1": n1,
"n2": n2,
"n3": n3,
"phi": phi,
"theta": theta,
"psi": psi
})
return refrings
def mref2polar(refimgs,
firstring=1,
outerradius=-1,
ringstep=1,
mode="F",
normbysquare=0,
log=None,
verbose=False):
"""
Generates polar representations of a series of images to be used as alignment references.
Arguments:
refimgs : Input reference image stack (filename or EMData object)
firstring : Inner alignment radius
outerradius : Outer alignment radius
ringstep : Alignment radius step size
mode : Mode, full circle ("F") vs. half circle ("H)
normbysquare : If other than 0, normalization by setting the norm to 1
log : Logger object
verbose : (boolean) Whether to write additional information to screen
Returns:
alignringlist : List of alignment-ring data
polarreflist : List of polar representation of refernences
"""
# Read reference stack
if isinstance(refimgs, str):
referencelist = EMData.read_images(refimgs)
else:
referencelist = [refimgs] # For single image
numrefs = len(referencelist)
polarreflist = []
# Get image dimensions (assuming square, and that images and references have the same dimension)
#print('referencelist', type(refimgs), type(referencelist), type(referencelist[0]))
#exit()
idim = referencelist[0]['nx']
# Calculate image center
halfdim = idim / 2 + 1
if outerradius <= 0:
outerradius = halfdim - 3
#print('outerradius1', outerradius)
# Prepare alignment rings
alignringlist = Numrinit(firstring, outerradius, ringstep, mode)
# Calculate ring weights
ringweightlist = ringwe(alignringlist, mode)
print_log_msg(
'Converting %s references to polar coordinates from radius %s to %s with step %s and mode "%s"'
% (numrefs, firstring, outerradius, ringstep, mode), log, verbose)
# Loop through reference images (adapted from sxisac2)
for refindex in range(numrefs):
# Convert to polar
cimage = Util.Polar2Dm(referencelist[refindex], halfdim, halfdim,
alignringlist, mode)
# Fourier transform of rings
Util.Frngs(cimage, alignringlist)
# Apply weights to rings
Util.Applyws(cimage, alignringlist, ringweightlist)
# Normalize
Util.Normalize_ring(cimage, alignringlist, normbysquare)
#normbysquare: if other than 0, normalizes by setting the norm to 1
# Copy to reference stack
polarreflist.append(cimage.copy())
return alignringlist, polarreflist
def mref_ali2d_MPI(stack,
refim,
outdir,
maskfile=None,
ir=1,
ou=-1,
rs=1,
xrng=0,
yrng=0,
step=1,
center=1,
maxit=10,
CTF=False,
snr=1.0,
user_func_name="ref_ali2d",
rand_seed=1000):
# 2D multi-reference alignment using rotational ccf in polar coordinates and quadratic interpolation
from sp_utilities import model_circle, combine_params2, inverse_transform2, drop_image, get_image, get_im
from sp_utilities import reduce_EMData_to_root, bcast_EMData_to_all, bcast_number_to_all
from sp_utilities import send_attr_dict
from sp_utilities import center_2D
from sp_statistics import fsc_mask
from sp_alignment import Numrinit, ringwe, search_range
from sp_fundamentals import rot_shift2D, fshift
from sp_utilities import get_params2D, set_params2D
from random import seed, randint
from sp_morphology import ctf_2
from sp_filter import filt_btwl, filt_params
from numpy import reshape, shape
from sp_utilities import print_msg, print_begin_msg, print_end_msg
import os
import sys
import shutil
from sp_applications import MPI_start_end
from mpi import mpi_comm_size, mpi_comm_rank, MPI_COMM_WORLD
from mpi import mpi_reduce, mpi_bcast, mpi_barrier, mpi_recv, mpi_send
from mpi import MPI_SUM, MPI_FLOAT, MPI_INT
number_of_proc = mpi_comm_size(MPI_COMM_WORLD)
myid = mpi_comm_rank(MPI_COMM_WORLD)
main_node = 0
# create the output directory, if it does not exist
if os.path.exists(outdir):
ERROR(
'Output directory exists, please change the name and restart the program',
"mref_ali2d_MPI ", 1, myid)
mpi_barrier(MPI_COMM_WORLD)
import sp_global_def
if myid == main_node:
os.mkdir(outdir)
sp_global_def.LOGFILE = os.path.join(outdir, sp_global_def.LOGFILE)
print_begin_msg("mref_ali2d_MPI")
nima = EMUtil.get_image_count(stack)
image_start, image_end = MPI_start_end(nima, number_of_proc, myid)
nima = EMUtil.get_image_count(stack)
ima = EMData()
ima.read_image(stack, image_start)
first_ring = int(ir)
last_ring = int(ou)
rstep = int(rs)
max_iter = int(maxit)
if max_iter == 0:
max_iter = 10
auto_stop = True
else:
auto_stop = False
if myid == main_node:
print_msg("Input stack : %s\n" % (stack))
print_msg("Reference stack : %s\n" % (refim))
print_msg("Output directory : %s\n" % (outdir))
print_msg("Maskfile : %s\n" % (maskfile))
print_msg("Inner radius : %i\n" % (first_ring))
nx = ima.get_xsize()
# default value for the last ring
if last_ring == -1: last_ring = nx / 2 - 2
if myid == main_node:
print_msg("Outer radius : %i\n" % (last_ring))
print_msg("Ring step : %i\n" % (rstep))
print_msg("X search range : %f\n" % (xrng))
print_msg("Y search range : %f\n" % (yrng))
print_msg("Translational step : %f\n" % (step))
print_msg("Center type : %i\n" % (center))
print_msg("Maximum iteration : %i\n" % (max_iter))
print_msg("CTF correction : %s\n" % (CTF))
print_msg("Signal-to-Noise Ratio : %f\n" % (snr))
print_msg("Random seed : %i\n\n" % (rand_seed))
print_msg("User function : %s\n" % (user_func_name))
import sp_user_functions
user_func = sp_user_functions.factory[user_func_name]
if maskfile:
import types
if type(maskfile) is bytes: mask = get_image(maskfile)
else: mask = maskfile
else: mask = model_circle(last_ring, nx, nx)
# references, do them on all processors...
refi = []
numref = EMUtil.get_image_count(refim)
# IMAGES ARE SQUARES! center is in SPIDER convention
cnx = nx / 2 + 1
cny = cnx
mode = "F"
#precalculate rings
numr = Numrinit(first_ring, last_ring, rstep, mode)
wr = ringwe(numr, mode)
# prepare reference images on all nodes
ima.to_zero()
for j in range(numref):
# even, odd, numer of even, number of images. After frc, totav
refi.append([get_im(refim, j), ima.copy(), 0])
# for each node read its share of data
data = EMData.read_images(stack, list(range(image_start, image_end)))
for im in range(image_start, image_end):
data[im - image_start].set_attr('ID', im)
if myid == main_node: seed(rand_seed)
a0 = -1.0
again = True
Iter = 0
ref_data = [mask, center, None, None]
while Iter < max_iter and again:
ringref = []
mashi = cnx - last_ring - 2
for j in range(numref):
refi[j][0].process_inplace("normalize.mask", {
"mask": mask,
"no_sigma": 1
}) # normalize reference images to N(0,1)
cimage = Util.Polar2Dm(refi[j][0], cnx, cny, numr, mode)
Util.Frngs(cimage, numr)
Util.Applyws(cimage, numr, wr)
ringref.append(cimage)
# zero refi
refi[j][0].to_zero()
refi[j][1].to_zero()
refi[j][2] = 0
assign = [[] for i in range(numref)]
# begin MPI section
for im in range(image_start, image_end):
alpha, sx, sy, mirror, scale = get_params2D(data[im - image_start])
# Why inverse? 07/11/2015 PAP
alphai, sxi, syi, scalei = inverse_transform2(alpha, sx, sy)
# normalize
data[im - image_start].process_inplace("normalize.mask", {
"mask": mask,
"no_sigma": 0
}) # subtract average under the mask
# If shifts are outside of the permissible range, reset them
if (abs(sxi) > mashi or abs(syi) > mashi):
sxi = 0.0
syi = 0.0
set_params2D(data[im - image_start], [0.0, 0.0, 0.0, 0, 1.0])
ny = nx
txrng = search_range(nx, last_ring, sxi, xrng, "mref_ali2d_MPI")
txrng = [txrng[1], txrng[0]]
tyrng = search_range(ny, last_ring, syi, yrng, "mref_ali2d_MPI")
tyrng = [tyrng[1], tyrng[0]]
# align current image to the reference
[angt, sxst, syst, mirrort, xiref,
peakt] = Util.multiref_polar_ali_2d(data[im - image_start],
ringref, txrng, tyrng, step,
mode, numr, cnx + sxi,
cny + syi)
iref = int(xiref)
# combine parameters and set them to the header, ignore previous angle and mirror
[alphan, sxn, syn,
mn] = combine_params2(0.0, -sxi, -syi, 0, angt, sxst, syst,
(int)(mirrort))
set_params2D(data[im - image_start],
[alphan, sxn, syn, int(mn), scale])
data[im - image_start].set_attr('assign', iref)
# apply current parameters and add to the average
temp = rot_shift2D(data[im - image_start], alphan, sxn, syn, mn)
it = im % 2
Util.add_img(refi[iref][it], temp)
assign[iref].append(im)
#assign[im] = iref
refi[iref][2] += 1.0
del ringref
# end MPI section, bring partial things together, calculate new reference images, broadcast them back
for j in range(numref):
reduce_EMData_to_root(refi[j][0], myid, main_node)
reduce_EMData_to_root(refi[j][1], myid, main_node)
refi[j][2] = mpi_reduce(refi[j][2], 1, MPI_FLOAT, MPI_SUM,
main_node, MPI_COMM_WORLD)
if (myid == main_node): refi[j][2] = int(refi[j][2][0])
# gather assignements
for j in range(numref):
if myid == main_node:
for n in range(number_of_proc):
if n != main_node:
import sp_global_def
ln = mpi_recv(1, MPI_INT, n,
sp_global_def.SPARX_MPI_TAG_UNIVERSAL,
MPI_COMM_WORLD)
lis = mpi_recv(ln[0], MPI_INT, n,
sp_global_def.SPARX_MPI_TAG_UNIVERSAL,
MPI_COMM_WORLD)
for l in range(ln[0]):
assign[j].append(int(lis[l]))
else:
import sp_global_def
mpi_send(len(assign[j]), 1, MPI_INT, main_node,
sp_global_def.SPARX_MPI_TAG_UNIVERSAL, MPI_COMM_WORLD)
mpi_send(assign[j], len(assign[j]), MPI_INT, main_node,
sp_global_def.SPARX_MPI_TAG_UNIVERSAL, MPI_COMM_WORLD)
if myid == main_node:
# replace the name of the stack with reference with the current one
refim = os.path.join(outdir, "aqm%03d.hdf" % Iter)
a1 = 0.0
ave_fsc = []
for j in range(numref):
if refi[j][2] < 4:
#ERROR("One of the references vanished","mref_ali2d_MPI",1)
# if vanished, put a random image (only from main node!) there
assign[j] = []
assign[j].append(
randint(image_start, image_end - 1) - image_start)
refi[j][0] = data[assign[j][0]].copy()
#print 'ERROR', j
else:
#frsc = fsc_mask(refi[j][0], refi[j][1], mask, 1.0, os.path.join(outdir,"drm%03d%04d"%(Iter, j)))
from sp_statistics import fsc
frsc = fsc(
refi[j][0], refi[j][1], 1.0,
os.path.join(outdir, "drm%03d%04d.txt" % (Iter, j)))
Util.add_img(refi[j][0], refi[j][1])
Util.mul_scalar(refi[j][0], 1.0 / float(refi[j][2]))
if ave_fsc == []:
for i in range(len(frsc[1])):
ave_fsc.append(frsc[1][i])
c_fsc = 1
else:
for i in range(len(frsc[1])):
ave_fsc[i] += frsc[1][i]
c_fsc += 1
#print 'OK', j, len(frsc[1]), frsc[1][0:5], ave_fsc[0:5]
#print 'sum', sum(ave_fsc)
if sum(ave_fsc) != 0:
for i in range(len(ave_fsc)):
ave_fsc[i] /= float(c_fsc)
frsc[1][i] = ave_fsc[i]
for j in range(numref):
ref_data[2] = refi[j][0]
ref_data[3] = frsc
refi[j][0], cs = user_func(ref_data)
# write the current average
TMP = []
for i_tmp in range(len(assign[j])):
TMP.append(float(assign[j][i_tmp]))
TMP.sort()
refi[j][0].set_attr_dict({'ave_n': refi[j][2], 'members': TMP})
del TMP
refi[j][0].process_inplace("normalize.mask", {
"mask": mask,
"no_sigma": 1
})
refi[j][0].write_image(refim, j)
Iter += 1
msg = "ITERATION #%3d %d\n\n" % (Iter, again)
print_msg(msg)
for j in range(numref):
msg = " group #%3d number of particles = %7d\n" % (
j, refi[j][2])
print_msg(msg)
Iter = bcast_number_to_all(Iter, main_node) # need to tell all
if again:
for j in range(numref):
bcast_EMData_to_all(refi[j][0], myid, main_node)
# clean up
del assign
# write out headers and STOP, under MPI writing has to be done sequentially (time-consumming)
mpi_barrier(MPI_COMM_WORLD)
if CTF and data_had_ctf == 0:
for im in range(len(data)):
data[im].set_attr('ctf_applied', 0)
par_str = ['xform.align2d', 'assign', 'ID']
if myid == main_node:
from sp_utilities import file_type
if (file_type(stack) == "bdb"):
from sp_utilities import recv_attr_dict_bdb
recv_attr_dict_bdb(main_node, stack, data, par_str, image_start,
image_end, number_of_proc)
else:
from sp_utilities import recv_attr_dict
recv_attr_dict(main_node, stack, data, par_str, image_start,
image_end, number_of_proc)
else:
send_attr_dict(main_node, data, par_str, image_start, image_end)
if myid == main_node:
print_end_msg("mref_ali2d_MPI")
def mref_ali2d(stack,
refim,
outdir,
maskfile=None,
ir=1,
ou=-1,
rs=1,
xrng=0,
yrng=0,
step=1,
center=1,
maxit=0,
CTF=False,
snr=1.0,
user_func_name="ref_ali2d",
rand_seed=1000,
MPI=False):
"""
Name
mref_ali2d - Perform 2-D multi-reference alignment of an image series
Input
stack: set of 2-D images in a stack file, images have to be squares
refim: set of initial reference 2-D images in a stack file
maskfile: optional maskfile to be used in the alignment
inner_radius: inner radius for rotational correlation > 0
outer_radius: outer radius for rotational correlation < nx/2-1
ring_step: step between rings in rotational correlation >0
x_range: range for translation search in x direction, search is +/xr
y_range: range for translation search in y direction, search is +/yr
translation_step: step of translation search in both directions
center: center the average
max_iter: maximum number of iterations the program will perform
CTF: if this flag is set, the program will use CTF information provided in file headers
snr: signal-to-noise ratio of the data
rand_seed: the seed used for generating random numbers
MPI: whether to use MPI version
Output
output_directory: directory name into which the output files will be written.
header: the alignment parameters are stored in the headers of input files as 'xform.align2d'.
"""
# 2D multi-reference alignment using rotational ccf in polar coordinates and quadratic interpolation
if MPI:
mref_ali2d_MPI(stack, refim, outdir, maskfile, ir, ou, rs, xrng, yrng,
step, center, maxit, CTF, snr, user_func_name,
rand_seed)
return
from sp_utilities import model_circle, combine_params2, inverse_transform2, drop_image, get_image
from sp_utilities import center_2D, get_im, get_params2D, set_params2D
from sp_statistics import fsc
from sp_alignment import Numrinit, ringwe, fine_2D_refinement, search_range
from sp_fundamentals import rot_shift2D, fshift
from random import seed, randint
import os
import sys
from sp_utilities import print_begin_msg, print_end_msg, print_msg
import shutil
# create the output directory, if it does not exist
if os.path.exists(outdir):
shutil.rmtree(
outdir
) #ERROR('Output directory exists, please change the name and restart the program', "mref_ali2d", 1)
os.mkdir(outdir)
import sp_global_def
sp_global_def.LOGFILE = os.path.join(outdir, sp_global_def.LOGFILE)
first_ring = int(ir)
last_ring = int(ou)
rstep = int(rs)
max_iter = int(maxit)
print_begin_msg("mref_ali2d")
print_msg("Input stack : %s\n" % (stack))
print_msg("Reference stack : %s\n" % (refim))
print_msg("Output directory : %s\n" % (outdir))
print_msg("Maskfile : %s\n" % (maskfile))
print_msg("Inner radius : %i\n" % (first_ring))
ima = EMData()
ima.read_image(stack, 0)
nx = ima.get_xsize()
# default value for the last ring
if last_ring == -1: last_ring = nx / 2 - 2
print_msg("Outer radius : %i\n" % (last_ring))
print_msg("Ring step : %i\n" % (rstep))
print_msg("X search range : %i\n" % (xrng))
print_msg("Y search range : %i\n" % (yrng))
print_msg("Translational step : %i\n" % (step))
print_msg("Center type : %i\n" % (center))
print_msg("Maximum iteration : %i\n" % (max_iter))
print_msg("CTF correction : %s\n" % (CTF))
print_msg("Signal-to-Noise Ratio : %f\n" % (snr))
print_msg("Random seed : %i\n\n" % (rand_seed))
print_msg("User function : %s\n" % (user_func_name))
output = sys.stdout
import sp_user_functions
user_func = sp_user_functions.factory[user_func_name]
if maskfile:
import types
if type(maskfile) is bytes: mask = get_image(maskfile)
else: mask = maskfile
else: mask = model_circle(last_ring, nx, nx)
# references
refi = []
numref = EMUtil.get_image_count(refim)
# IMAGES ARE SQUARES! center is in SPIDER convention
cnx = nx / 2 + 1
cny = cnx
mode = "F"
#precalculate rings
numr = Numrinit(first_ring, last_ring, rstep, mode)
wr = ringwe(numr, mode)
# reference images
params = []
#read all data
data = EMData.read_images(stack)
nima = len(data)
# prepare the reference
ima.to_zero()
for j in range(numref):
temp = EMData()
temp.read_image(refim, j)
# eve, odd, numer of even, number of images. After frc, totav
refi.append([temp, ima.copy(), 0])
seed(rand_seed)
again = True
ref_data = [mask, center, None, None]
Iter = 0
while Iter < max_iter and again:
ringref = []
#print "numref",numref
### Reference ###
mashi = cnx - last_ring - 2
for j in range(numref):
refi[j][0].process_inplace("normalize.mask", {
"mask": mask,
"no_sigma": 1
})
cimage = Util.Polar2Dm(refi[j][0], cnx, cny, numr, mode)
Util.Frngs(cimage, numr)
Util.Applyws(cimage, numr, wr)
ringref.append(cimage)
assign = [[] for i in range(numref)]
sx_sum = [0.0] * numref
sy_sum = [0.0] * numref
for im in range(nima):
alpha, sx, sy, mirror, scale = get_params2D(data[im])
# Why inverse? 07/11/2015 PAP
alphai, sxi, syi, scalei = inverse_transform2(alpha, sx, sy)
# normalize
data[im].process_inplace("normalize.mask", {
"mask": mask,
"no_sigma": 0
})
# If shifts are outside of the permissible range, reset them
if (abs(sxi) > mashi or abs(syi) > mashi):
sxi = 0.0
syi = 0.0
set_params2D(data[im], [0.0, 0.0, 0.0, 0, 1.0])
ny = nx
txrng = search_range(nx, last_ring, sxi, xrng, "mref_ali2d")
txrng = [txrng[1], txrng[0]]
tyrng = search_range(ny, last_ring, syi, yrng, "mref_ali2d")
tyrng = [tyrng[1], tyrng[0]]
# align current image to the reference
#[angt, sxst, syst, mirrort, xiref, peakt] = Util.multiref_polar_ali_2d_p(data[im],
# ringref, txrng, tyrng, step, mode, numr, cnx+sxi, cny+syi)
#print(angt, sxst, syst, mirrort, xiref, peakt)
[angt, sxst, syst, mirrort, xiref,
peakt] = Util.multiref_polar_ali_2d(data[im], ringref, txrng,
tyrng, step, mode, numr,
cnx + sxi, cny + syi)
iref = int(xiref)
# combine parameters and set them to the header, ignore previous angle and mirror
[alphan, sxn, syn, mn] = combine_params2(0.0, -sxi, -syi, 0, angt,
sxst, syst, int(mirrort))
set_params2D(data[im], [alphan, sxn, syn, int(mn), scale])
if mn == 0: sx_sum[iref] += sxn
else: sx_sum[iref] -= sxn
sy_sum[iref] += syn
data[im].set_attr('assign', iref)
# apply current parameters and add to the average
temp = rot_shift2D(data[im], alphan, sxn, syn, mn)
it = im % 2
Util.add_img(refi[iref][it], temp)
assign[iref].append(im)
refi[iref][2] += 1
del ringref
if again:
a1 = 0.0
for j in range(numref):
msg = " group #%3d number of particles = %7d\n" % (
j, refi[j][2])
print_msg(msg)
if refi[j][2] < 4:
#ERROR("One of the references vanished","mref_ali2d",1)
# if vanished, put a random image there
assign[j] = []
assign[j].append(randint(0, nima - 1))
refi[j][0] = data[assign[j][0]].copy()
else:
max_inter = 0 # switch off fine refi.
br = 1.75
# the loop has to
for INter in range(max_inter + 1):
# Calculate averages at least ones, meaning even if no within group refinement was requested
frsc = fsc(
refi[j][0], refi[j][1], 1.0,
os.path.join(outdir,
"drm_%03d_%04d.txt" % (Iter, j)))
Util.add_img(refi[j][0], refi[j][1])
Util.mul_scalar(refi[j][0], 1.0 / float(refi[j][2]))
ref_data[2] = refi[j][0]
ref_data[3] = frsc
refi[j][0], cs = user_func(ref_data)
if center == -1:
cs[0] = sx_sum[j] / len(assign[j])
cs[1] = sy_sum[j] / len(assign[j])
refi[j][0] = fshift(refi[j][0], -cs[0], -cs[1])
for i in range(len(assign[j])):
im = assign[j][i]
alpha, sx, sy, mirror, scale = get_params2D(
data[im])
alphan, sxn, syn, mirrorn = combine_params2(
alpha, sx, sy, mirror, 0.0, -cs[0], -cs[1], 0)
set_params2D(
data[im],
[alphan, sxn, syn,
int(mirrorn), scale])
# refine images within the group
# Do the refinement only if max_inter>0, but skip it for the last iteration.
if INter < max_inter:
fine_2D_refinement(data, br, mask, refi[j][0], j)
# Calculate updated average
refi[j][0].to_zero()
refi[j][1].to_zero()
for i in range(len(assign[j])):
im = assign[j][i]
alpha, sx, sy, mirror, scale = get_params2D(
data[im])
# apply current parameters and add to the average
temp = rot_shift2D(data[im], alpha, sx, sy, mn)
it = im % 2
Util.add_img(refi[j][it], temp)
# write the current average
TMP = []
for i_tmp in range(len(assign[j])):
TMP.append(float(assign[j][i_tmp]))
TMP.sort()
refi[j][0].set_attr_dict({'ave_n': refi[j][2], 'members': TMP})
del TMP
# replace the name of the stack with reference with the current one
newrefim = os.path.join(outdir, "aqm%03d.hdf" % Iter)
refi[j][0].write_image(newrefim, j)
Iter += 1
msg = "ITERATION #%3d \n" % (Iter)
print_msg(msg)
newrefim = os.path.join(outdir, "multi_ref.hdf")
for j in range(numref):
refi[j][0].write_image(newrefim, j)
from sp_utilities import write_headers
write_headers(stack, data, list(range(nima)))
print_end_msg("mref_ali2d")