def recons3d_trl_struct_MPI( myid, main_node, prjlist, paramstructure, refang, rshifts_shrank, delta, upweighted=True, mpi_comm=None, CTF=True, target_size=-1, avgnorm=1.0, norm_per_particle=None, ): """ recons3d_4nn_ctf - calculate CTF-corrected 3-D reconstruction from a set of projections using three Eulerian angles, two shifts, and CTF settings for each projeciton image Input list_of_prjlist: list of lists of projections to be included in the reconstruction """ if mpi_comm == None: mpi_comm = mpi.MPI_COMM_WORLD refvol = sp_utilities.model_blank(target_size) refvol.set_attr("fudge", 1.0) if CTF: do_ctf = 1 else: do_ctf = 0 fftvol = EMAN2_cppwrap.EMData() weight = EMAN2_cppwrap.EMData() params = { "size": target_size, "npad": 2, "snr": 1.0, "sign": 1, "symmetry": "c1", "refvol": refvol, "fftvol": fftvol, "weight": weight, "do_ctf": do_ctf, } r = EMAN2_cppwrap.Reconstructors.get("nn4_ctfw", params) r.setup() if prjlist: if norm_per_particle == None: norm_per_particle = len(prjlist) * [1.0] nnx = prjlist[0].get_xsize() nny = prjlist[0].get_ysize() nshifts = len(rshifts_shrank) for im in range(len(prjlist)): # parse projection structure, generate three lists: # [ipsi+iang], [ishift], [probability] # Number of orientations for a given image numbor = len(paramstructure[im][2]) ipsiandiang = [ old_div(paramstructure[im][2][i][0], 1000) for i in range(numbor) ] allshifts = [ paramstructure[im][2][i][0] % 1000 for i in range(numbor) ] probs = [paramstructure[im][2][i][1] for i in range(numbor)] # Find unique projection directions tdir = list(set(ipsiandiang)) bckgn = prjlist[im].get_attr("bckgnoise") ct = prjlist[im].get_attr("ctf") # For each unique projection direction: data = [None] * nshifts for ii in range(len(tdir)): # Find the number of times given projection direction appears on the list, it is the number of different shifts associated with it. lshifts = sp_utilities.findall(tdir[ii], ipsiandiang) toprab = 0.0 for ki in range(len(lshifts)): toprab += probs[lshifts[ki]] recdata = EMAN2_cppwrap.EMData(nny, nny, 1, False) recdata.set_attr("is_complex", 0) for ki in range(len(lshifts)): lpt = allshifts[lshifts[ki]] if data[lpt] == None: data[lpt] = sp_fundamentals.fshift( prjlist[im], rshifts_shrank[lpt][0], rshifts_shrank[lpt][1]) data[lpt].set_attr("is_complex", 0) EMAN2_cppwrap.Util.add_img( recdata, EMAN2_cppwrap.Util.mult_scalar( data[lpt], old_div(probs[lshifts[ki]], toprab)), ) recdata.set_attr_dict({ "padffted": 1, "is_fftpad": 1, "is_fftodd": 0, "is_complex_ri": 1, "is_complex": 1, }) if not upweighted: recdata = sp_filter.filt_table(recdata, bckgn) recdata.set_attr_dict({"bckgnoise": bckgn, "ctf": ct}) ipsi = tdir[ii] % 100000 iang = old_div(tdir[ii], 100000) r.insert_slice( recdata, EMAN2_cppwrap.Transform({ "type": "spider", "phi": refang[iang][0], "theta": refang[iang][1], "psi": refang[iang][2] + ipsi * delta, }), old_div(toprab * avgnorm, norm_per_particle[im]), ) # clean stuff del bckgn, recdata, tdir, ipsiandiang, allshifts, probs sp_utilities.reduce_EMData_to_root(fftvol, myid, main_node, comm=mpi_comm) sp_utilities.reduce_EMData_to_root(weight, myid, main_node, comm=mpi_comm) if myid == main_node: dummy = r.finish(True) mpi.mpi_barrier(mpi_comm) if myid == main_node: return fftvol, weight, refvol else: return None, None, None
def helicalshiftali_MPI(stack, maskfile=None, maxit=100, CTF=False, snr=1.0, Fourvar=False, search_rng=-1): nproc = mpi.mpi_comm_size(mpi.MPI_COMM_WORLD) myid = mpi.mpi_comm_rank(mpi.MPI_COMM_WORLD) main_node = 0 ftp = file_type(stack) if myid == main_node: print_begin_msg("helical-shiftali_MPI") max_iter = int(maxit) if (myid == main_node): infils = EMUtil.get_all_attributes(stack, "filament") ptlcoords = EMUtil.get_all_attributes(stack, 'ptcl_source_coord') filaments = ordersegments(infils, ptlcoords) total_nfils = len(filaments) inidl = [0] * total_nfils for i in range(total_nfils): inidl[i] = len(filaments[i]) linidl = sum(inidl) nima = linidl tfilaments = [] for i in range(total_nfils): tfilaments += filaments[i] del filaments else: total_nfils = 0 linidl = 0 total_nfils = bcast_number_to_all(total_nfils, source_node=main_node) if myid != main_node: inidl = [-1] * total_nfils inidl = bcast_list_to_all(inidl, myid, source_node=main_node) linidl = bcast_number_to_all(linidl, source_node=main_node) if myid != main_node: tfilaments = [-1] * linidl tfilaments = bcast_list_to_all(tfilaments, myid, source_node=main_node) filaments = [] iendi = 0 for i in range(total_nfils): isti = iendi iendi = isti + inidl[i] filaments.append(tfilaments[isti:iendi]) del tfilaments, inidl if myid == main_node: print_msg("total number of filaments: %d" % total_nfils) if total_nfils < nproc: ERROR( 'number of CPUs (%i) is larger than the number of filaments (%i), please reduce the number of CPUs used' % (nproc, total_nfils), myid=myid) # balanced load temp = chunks_distribution([[len(filaments[i]), i] for i in range(len(filaments))], nproc)[myid:myid + 1][0] filaments = [filaments[temp[i][1]] for i in range(len(temp))] nfils = len(filaments) #filaments = [[0,1]] #print "filaments",filaments list_of_particles = [] indcs = [] k = 0 for i in range(nfils): list_of_particles += filaments[i] k1 = k + len(filaments[i]) indcs.append([k, k1]) k = k1 data = EMData.read_images(stack, list_of_particles) ldata = len(data) sxprint("ldata=", ldata) nx = data[0].get_xsize() ny = data[0].get_ysize() if maskfile == None: mrad = min(nx, ny) // 2 - 2 mask = pad(model_blank(2 * mrad + 1, ny, 1, 1.0), nx, ny, 1, 0.0) else: mask = get_im(maskfile) # apply initial xform.align2d parameters stored in header init_params = [] for im in range(ldata): t = data[im].get_attr('xform.align2d') init_params.append(t) p = t.get_params("2d") data[im] = rot_shift2D(data[im], p['alpha'], p['tx'], p['ty'], p['mirror'], p['scale']) if CTF: from sp_filter import filt_ctf from sp_morphology import ctf_img ctf_abs_sum = EMData(nx, ny, 1, False) ctf_2_sum = EMData(nx, ny, 1, False) else: ctf_2_sum = None ctf_abs_sum = None from sp_utilities import info for im in range(ldata): data[im].set_attr('ID', list_of_particles[im]) st = Util.infomask(data[im], mask, False) data[im] -= st[0] if CTF: ctf_params = data[im].get_attr("ctf") qctf = data[im].get_attr("ctf_applied") if qctf == 0: data[im] = filt_ctf(fft(data[im]), ctf_params) data[im].set_attr('ctf_applied', 1) elif qctf != 1: ERROR('Incorrectly set qctf flag', myid=myid) ctfimg = ctf_img(nx, ctf_params, ny=ny) Util.add_img2(ctf_2_sum, ctfimg) Util.add_img_abs(ctf_abs_sum, ctfimg) else: data[im] = fft(data[im]) del list_of_particles if CTF: reduce_EMData_to_root(ctf_2_sum, myid, main_node) reduce_EMData_to_root(ctf_abs_sum, myid, main_node) if CTF: if myid != main_node: del ctf_2_sum del ctf_abs_sum else: temp = EMData(nx, ny, 1, False) tsnr = 1. / snr for i in range(0, nx + 2, 2): for j in range(ny): temp.set_value_at(i, j, tsnr) temp.set_value_at(i + 1, j, 0.0) #info(ctf_2_sum) Util.add_img(ctf_2_sum, temp) #info(ctf_2_sum) del temp total_iter = 0 shift_x = [0.0] * ldata for Iter in range(max_iter): if myid == main_node: start_time = time() print_msg("Iteration #%4d\n" % (total_iter)) total_iter += 1 avg = EMData(nx, ny, 1, False) for im in range(ldata): Util.add_img(avg, fshift(data[im], shift_x[im])) reduce_EMData_to_root(avg, myid, main_node) if myid == main_node: if CTF: tavg = Util.divn_filter(avg, ctf_2_sum) else: tavg = Util.mult_scalar(avg, 1.0 / float(nima)) else: tavg = model_blank(nx, ny) if Fourvar: bcast_EMData_to_all(tavg, myid, main_node) vav, rvar = varf2d_MPI(myid, data, tavg, mask, "a", CTF) if myid == main_node: if Fourvar: tavg = fft(Util.divn_img(fft(tavg), vav)) vav_r = Util.pack_complex_to_real(vav) # normalize and mask tavg in real space tavg = fft(tavg) stat = Util.infomask(tavg, mask, False) tavg -= stat[0] Util.mul_img(tavg, mask) tavg.write_image("tavg.hdf", Iter) # For testing purposes: shift tavg to some random place and see if the centering is still correct #tavg = rot_shift3D(tavg,sx=3,sy=-4) if Fourvar: del vav bcast_EMData_to_all(tavg, myid, main_node) tavg = fft(tavg) sx_sum = 0.0 nxc = nx // 2 for ifil in range(nfils): """ # Calculate filament average avg = EMData(nx, ny, 1, False) filnima = 0 for im in xrange(indcs[ifil][0], indcs[ifil][1]): Util.add_img(avg, data[im]) filnima += 1 tavg = Util.mult_scalar(avg, 1.0/float(filnima)) """ # Calculate 1D ccf between each segment and filament average nsegms = indcs[ifil][1] - indcs[ifil][0] ctx = [None] * nsegms pcoords = [None] * nsegms for im in range(indcs[ifil][0], indcs[ifil][1]): ctx[im - indcs[ifil][0]] = Util.window(ccf(tavg, data[im]), nx, 1) pcoords[im - indcs[ifil][0]] = data[im].get_attr( 'ptcl_source_coord') #ctx[im-indcs[ifil][0]].write_image("ctx.hdf",im-indcs[ifil][0]) #print " CTX ",myid,im,Util.infomask(ctx[im-indcs[ifil][0]], None, True) # search for best x-shift cents = nsegms // 2 dst = sqrt( max((pcoords[cents][0] - pcoords[0][0])**2 + (pcoords[cents][1] - pcoords[0][1])**2, (pcoords[cents][0] - pcoords[-1][0])**2 + (pcoords[cents][1] - pcoords[-1][1])**2)) maxincline = atan2(ny // 2 - 2 - float(search_rng), dst) kang = int(dst * tan(maxincline) + 0.5) #print " settings ",nsegms,cents,dst,search_rng,maxincline,kang # ## C code for alignment. @ming results = [0.0] * 3 results = Util.helixshiftali(ctx, pcoords, nsegms, maxincline, kang, search_rng, nxc) sib = int(results[0]) bang = results[1] qm = results[2] #print qm, sib, bang # qm = -1.e23 # # for six in xrange(-search_rng, search_rng+1,1): # q0 = ctx[cents].get_value_at(six+nxc) # for incline in xrange(kang+1): # qt = q0 # qu = q0 # if(kang>0): tang = tan(maxincline/kang*incline) # else: tang = 0.0 # for kim in xrange(cents+1,nsegms): # dst = sqrt((pcoords[cents][0] - pcoords[kim][0])**2 + (pcoords[cents][1] - pcoords[kim][1])**2) # xl = dst*tang+six+nxc # ixl = int(xl) # dxl = xl - ixl # #print " A ", ifil,six,incline,kim,xl,ixl,dxl # qt += (1.0-dxl)*ctx[kim].get_value_at(ixl) + dxl*ctx[kim].get_value_at(ixl+1) # xl = -dst*tang+six+nxc # ixl = int(xl) # dxl = xl - ixl # qu += (1.0-dxl)*ctx[kim].get_value_at(ixl) + dxl*ctx[kim].get_value_at(ixl+1) # for kim in xrange(cents): # dst = sqrt((pcoords[cents][0] - pcoords[kim][0])**2 + (pcoords[cents][1] - pcoords[kim][1])**2) # xl = -dst*tang+six+nxc # ixl = int(xl) # dxl = xl - ixl # qt += (1.0-dxl)*ctx[kim].get_value_at(ixl) + dxl*ctx[kim].get_value_at(ixl+1) # xl = dst*tang+six+nxc # ixl = int(xl) # dxl = xl - ixl # qu += (1.0-dxl)*ctx[kim].get_value_at(ixl) + dxl*ctx[kim].get_value_at(ixl+1) # if( qt > qm ): # qm = qt # sib = six # bang = tang # if( qu > qm ): # qm = qu # sib = six # bang = -tang #if incline == 0: print "incline = 0 ",six,tang,qt,qu #print qm,six,sib,bang #print " got results ",indcs[ifil][0], indcs[ifil][1], ifil,myid,qm,sib,tang,bang,len(ctx),Util.infomask(ctx[0], None, True) for im in range(indcs[ifil][0], indcs[ifil][1]): kim = im - indcs[ifil][0] dst = sqrt((pcoords[cents][0] - pcoords[kim][0])**2 + (pcoords[cents][1] - pcoords[kim][1])**2) if (kim < cents): xl = -dst * bang + sib else: xl = dst * bang + sib shift_x[im] = xl # Average shift sx_sum += shift_x[indcs[ifil][0] + cents] # #print myid,sx_sum,total_nfils sx_sum = mpi.mpi_reduce(sx_sum, 1, mpi.MPI_FLOAT, mpi.MPI_SUM, main_node, mpi.MPI_COMM_WORLD) if myid == main_node: sx_sum = float(sx_sum[0]) / total_nfils print_msg("Average shift %6.2f\n" % (sx_sum)) else: sx_sum = 0.0 sx_sum = 0.0 sx_sum = bcast_number_to_all(sx_sum, source_node=main_node) for im in range(ldata): shift_x[im] -= sx_sum #print " %3d %6.3f"%(im,shift_x[im]) #exit() # combine shifts found with the original parameters for im in range(ldata): t1 = Transform() ##import random ##shix=random.randint(-10, 10) ##t1.set_params({"type":"2D","tx":shix}) t1.set_params({"type": "2D", "tx": shift_x[im]}) # combine t0 and t1 tt = t1 * init_params[im] data[im].set_attr("xform.align2d", tt) # write out headers and STOP, under MPI writing has to be done sequentially mpi.mpi_barrier(mpi.MPI_COMM_WORLD) par_str = ["xform.align2d", "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, 0, ldata, nproc) else: from sp_utilities import recv_attr_dict recv_attr_dict(main_node, stack, data, par_str, 0, ldata, nproc) else: send_attr_dict(main_node, data, par_str, 0, ldata) if myid == main_node: print_end_msg("helical-shiftali_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")