postprocessing.py

#!/usr/bin/env python

# The code in this file was adapted from: https://github.com/C-CINA/focustools

"""
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        Copyright (C) <year>  <name of author>

        This program is free software: you can redistribute it and/or modify
        it under the terms of the GNU General Public License as published by
        the Free Software Foundation, either version 3 of the License, or
        (at your option) any later version.

        This program is distributed in the hope that it will be useful,
        but WITHOUT ANY WARRANTY; without even the implied warranty of
        MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
        GNU General Public License for more details.

        You should have received a copy of the GNU General Public License
        along with this program.  If not, see <https://www.gnu.org/licenses/>.

    Also add information on how to contact you by electronic and paper mail.

    If the program does terminal interaction, make it output a short
    notice like this when it starts in an interactive mode:

        <program>  Copyright (C) <year>  <name of author>
        This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
        This is free software, and you are welcome to redistribute it
        under certain conditions; type `show c' for details.

    The hypothetical commands `show w' and `show c' should show the appropriate
    parts of the General Public License.  Of course, your program's commands
    might be different; for a GUI interface, you would use an "about box".

    You should also get your employer (if you work as a programmer) or school,
    if any, to sign a "copyright disclaimer" for the program, if necessary.
    For more information on this, and how to apply and follow the GNU GPL, see
    <https://www.gnu.org/licenses/>.

    The GNU General Public License does not permit incorporating your program
    into proprietary programs.  If your program is a subroutine library, you
    may consider it more useful to permit linking proprietary applications with
    the library.  If this is what you want to do, use the GNU Lesser General
    Public License instead of this License.  But first, please read
    <https://www.gnu.org/licenses/why-not-lgpl.html>.
"""

import sys
import os
import numpy as np
from pyp.inout.image import mrc
from optparse import OptionParser
import numexpr as ne
import warnings
warnings.filterwarnings("ignore", category=RuntimeWarning)

from pyp.system.logging import initialize_pyp_logger
from pyp.utils import get_relative_path
relative_path = str(get_relative_path(__file__))
logger = initialize_pyp_logger(log_name=relative_path)

pi = np.pi  # global PI

def RadialIndices(imsize=[100, 100], rounding=True, normalize=False, rfft=False, xyz=[0, 0, 0], nozero=True):
    """Returns radius and angles for each pixel (or voxel) in a 2D image or 3D volume of shape = imsize

    Parameters
    ----------
    imsize : list, optional
        _description_, by default [100, 100]
    rounding : bool, optional
        Rounding is to ensure "perfect" radial symmetry, desirable in some applications, by default True
    normalize : bool, optional
        Normalize=True will normalize the radius to values between 0.0 and 1.0, by default False
    rfft : bool, optional
        rfft=True will return only half of the radial indices in a way that is compliant with the FFT of real inputs, by default False
    xyz : list, optional
        _description_, by default [0, 0, 0]
    nozero : bool, optional
        _description_, by default True
    """

    imsize = np.array(imsize)

    if np.isscalar(imsize):

        imsize = [imsize, imsize]

    if len(imsize) > 3:

        raise ValueError(
            "Object should have 2 or 3 dimensions: len(imsize) = %d " % len(imsize))

    xyz = np.flipud(xyz)

    m = np.mod(imsize, 2)  # Check if dimensions are odd or even

    if len(imsize) == 1:

        if not rfft:

            xmesh = np.mgrid[-imsize[0] // 2 + m[0] -
                             xyz[0]:(imsize[0] - 1) // 2 + 1 - xyz[0]]

        else:

            xmesh = np.mgrid[0 - xyz[0]:imsize[0] // 2 + 1 - xyz[0]]

        rmesh = ne.evaluate("sqrt(xmesh * xmesh)")

        amesh = np.zeros(xmesh.shape)

        n = 1  # Normalization factor

    if len(imsize) == 2:

        # The definition below is consistent with numpy np.fft.fftfreq and np.fft.rfftfreq:

        if not rfft:

            [xmesh, ymesh] = np.mgrid[-imsize[0] // 2 + m[0] - xyz[0]
                :(imsize[0] - 1) // 2 + 1 - xyz[0], -imsize[1] // 2 + m[1] - xyz[1]:(imsize[1] - 1) // 2 + 1 - xyz[1]]

        else:

            [xmesh, ymesh] = np.mgrid[-imsize[0] // 2 + m[0] - xyz[0]
                :(imsize[0] - 1) // 2 + 1 - xyz[0], 0 - xyz[1]:imsize[1] // 2 + 1 - xyz[1]]
            xmesh = np.fft.ifftshift(xmesh)

        rmesh = ne.evaluate("sqrt(xmesh * xmesh + ymesh * ymesh)")

        amesh = ne.evaluate("arctan2(ymesh, xmesh)")

        n = 2  # Normalization factor

    if len(imsize) == 3:

        if not rfft:

            [xmesh, ymesh, zmesh] = np.mgrid[-imsize[0] // 2 + m[0] - xyz[0]:(imsize[0] - 1) // 2 + 1 - xyz[0], -imsize[1] // 2 + m[1] - xyz[1]:(
                imsize[1] - 1) // 2 + 1 - xyz[1], -imsize[2] // 2 + m[2] - xyz[2]:(imsize[2] - 1) // 2 + 1 - xyz[2]]

        else:

            [xmesh, ymesh, zmesh] = np.mgrid[-imsize[0] // 2 + m[0] - xyz[0]:(imsize[0] - 1) // 2 + 1 - xyz[0], -imsize[1] // 2 + m[1] - xyz[1]:(
                imsize[1] - 1) // 2 + 1 - xyz[1], 0 - xyz[2]:imsize[2] // 2 + 1 - xyz[2]]
            xmesh = np.fft.ifftshift(xmesh)
            ymesh = np.fft.ifftshift(ymesh)

        rmesh = ne.evaluate(
            "sqrt(xmesh * xmesh + ymesh * ymesh + zmesh * zmesh)")

        amesh = ne.evaluate("arccos(zmesh / rmesh)")

        n = 3  # Normalization factor

    if rounding:

        rmesh = np.round(rmesh)

    if normalize:

        a = np.sum(imsize * imsize)
        ne.evaluate("rmesh / (sqrt(a) / sqrt(n))", out=rmesh)

    if nozero:

        # Replaces the "zero radius" by a small value to prevent division by zero in other programs
        idx = ne.evaluate("rmesh == 0")
        rmesh[idx] = 1e-3

    return rmesh, np.nan_to_num(amesh)


def RotationalAverage(img, nomean=False):
    # Compute the rotational average of a 2D image or 3D volume
    # 'nomean' is a switch to compute the Rotational Sum instead of the Rotational Average

    rmesh = RadialIndices(img.shape, rounding=True)[0]

    rotavg = np.zeros(img.shape)

    idx = np.zeros(rmesh.shape, dtype='bool')

    if nomean:

        for r in np.unique(rmesh):

            ne.evaluate("rmesh == r", out=idx)
            a = img[idx]
            rotavg[idx] = np.sum(a)

        return rotavg

    else:

        nvoxels = np.bincount(rmesh.ravel().astype('int32'))

        for j, r in enumerate(np.unique(rmesh)):

            ne.evaluate("rmesh == r", out=idx)
            a = img[idx]
            b = nvoxels[j]
            rotavg[idx] = np.sum(a) / b

        return rotavg


def RadialProfile(img, amps=False):
    # Compute the 1D radial profile of a 2D image or 3D volume:
    # 'amps' is a flag to tell whether we want a radial profile of the Fourier amplitudes

    orgshape = img.shape

    if amps:

        img = np.abs(np.fft.rfftn(img, norm='ortho'))
        rfft = True

    else:

        rfft = False

    rmesh = RadialIndices(orgshape, rounding=True, rfft=rfft)[
        0].ravel().astype('int32')
    profile = np.bincount(rmesh, img.ravel()) / np.bincount(rmesh)
    return profile


def RadialFilter(img, filt, return_filter=False):
    # Given a list of factors 'filt', radially multiplies the Fourier Transform of 'img' by the corresponding term in 'filt'

    rmesh = RadialIndices(img.shape, rounding=True, rfft=True)[0].astype('int')

    ft = np.fft.rfftn(img).astype('complex128')
    # j = 0
    idx = np.zeros(rmesh.shape, dtype='bool')
    filtmat = np.zeros(rmesh.shape)
    for j, r in enumerate(np.unique(rmesh)):
        ne.evaluate("rmesh == r", out=idx)
        filtmat[idx] = filt[j]

    ne.evaluate("ft * filtmat", out=ft)

    if not return_filter:

        return np.fft.irfftn(ft, s=img.shape)

    else:

        return np.fft.irfftn(ft, s=img.shape), filtmat


def SoftMask(imsize=[100, 100], radius=0.5, width=6.0, rounding=False, xyz=[0, 0, 0], rfft=False):
    # Generates a circular or spherical mask with a soft cosine edge
    # If rfft==True, the output shape will not be imsize, be the shape of an rfft of input shape imsize

    if np.isscalar(imsize):

        imsize = [imsize, imsize]

    if len(imsize) > 3:

        raise ValueError(
            "Object should have 2 or 3 dimensions: len(imsize) = %d " % len(imsize))

    rmesh = RadialIndices(imsize, rounding=rounding, xyz=xyz, rfft=rfft)[0]

    if width < 0.0:

        width = 0.0

    if width > 0.0 and width < 1.0:

        width = 0.5 * width * np.min(imsize)

    if radius > 0.0 and radius < 1.0:

        radius = radius * np.min(imsize)

        radius *= 0.5

    if (radius < 0.0) or (np.min(imsize) < radius * 2):

        radius = 0.5 * (np.min(imsize) - float(width) / 2)

    rii = radius + width / 2
    rih = radius - width / 2

    mask = np.zeros(rmesh.shape)

    fill_idx = ne.evaluate("rmesh <= rih")
    mask[fill_idx] = 1.0

    rih_idx = ne.evaluate("rmesh > rih")
    rii_idx = ne.evaluate("rmesh <= rii")
    edge_idx = ne.evaluate("rih_idx & rii_idx")

    a = rmesh[edge_idx]
    ne.evaluate("( 1.0 + cos(pi * (a - rih) / (width))) / 2.0",
                out=mask[edge_idx])
    return mask


def AutoMask(img, apix=1.0, lp=-1, gaussian=False, cosine=True, cosine_edge_width=3.0, absolute_threshold=None, fraction_threshold=None, sigma_threshold=1.0, expand_width=3.0, expand_soft_width=3.0, floodfill_rad=None, floodfill_xyz=[0, 0, 0], floodfill_fraction=None, verbose=False):

    # First we low-pass filter the volume with a Gaussian or Cosine-edge filter:
    if gaussian:

        imglp = FilterGauss(img, apix=apix, lp=lp)
        filter_type = "Gaussian."

    else:

        imglp = FilterCosine(img, apix=apix, lp=lp, width=cosine_edge_width)
        filter_type = "cosine-edge across %.1f Fourier voxels" % cosine_edge_width

    # Then we define a threshold for binarization of the low-pass filtered map:
    if absolute_threshold != None:

        thr = absolute_threshold  # Simply take a user-specified value as threshold
        method = "absolute value"

    elif fraction_threshold != None:

        # Binarize the voxels with the top fraction_threshold densities
        thr = np.percentile(imglp, 100.0 - 100.0 * fraction_threshold)
        method = "highest %.1f percent of densities" % (
            fraction_threshold * 100)

    elif sigma_threshold != None:

        # Or define as threshold a multiple of standard deviations above the mean density value
        thr = imglp.mean() + sigma_threshold * imglp.std()

        method = "%.3f standard deviation(s) above the mean" % sigma_threshold

    else:

        thr = 0.0

    if verbose:

        logger.info("Input volume will be low-pass filtered to %.2f A by a %s" %
              (lp, filter_type))
        logger.info("Stats before filtering: Range = [%.2f, %.3f], Median = %.3f, Mean = %.3f, Std = %.3f" %
              (img.min(), img.max(), np.median(img), img.mean(), img.std()))
        logger.info("Stats after filtering: Range = [%.3f, %.3f], Median = %.3f, Mean = %.3f, Std = %.3f" %
              (imglp.min(), imglp.max(), np.median(imglp), imglp.mean(), imglp.std()))
        logger.info("Thresholding method: %s" % method)
        logger.info("Threshold for initial binarization: %.6f" % thr)
        logger.info("Binary mask will be expanded by %.1f voxel(s) plus a soft cosine-edge of %.1f voxel(s)" %
              (expand_width, expand_soft_width))

    if floodfill_rad == None and floodfill_fraction == None:

        # Binarize the low-pass filtered map with one of the thresholds above
        imglpbin = ne.evaluate("imglp > thr")

    else:

        if floodfill_fraction == None:

            if verbose:

                logger.info("Initializing flood-filling method with a sphere of radius %.1f voxels placed at [%d, %d, %d]" % (
                    floodfill_rad, floodfill_xyz[0], floodfill_xyz[1], floodfill_xyz[2]))

            # This will be the initial mask
            inimask = SoftMask(
                imglp.shape, radius=floodfill_rad, width=0, xyz=floodfill_xyz)

        else:

            if verbose:

                logger.info("Initializing flood-filling method binarizing the highest %.1f percent of densities" %
                      (floodfill_fraction * 100))

            floodfill_fraction_thr = np.sort(np.ravel(imglp))[np.round((1.0 - floodfill_fraction) * np.prod(
                imglp.shape)).astype('int')]  # Binarize the voxels with the top floodfill_fraction densities

            # Binarize the low-pass filtered map with one of the thresholds above
            inimask = ne.evaluate("imglp > floodfill_fraction_thr")

        # Binarize the low-pass filtered map using flood-filling approach, works better on non low-pass filtered volumes.
        imglpbin = FloodFilling(imglp, inimask, thr=thr)

    if expand_width > 0:

        # Creates a kernel for expanding the binary mask
        expand_kernel = SoftMask(imglp.shape, radius=expand_width, width=0)

        a = np.fft.rfftn(imglpbin)
        b = np.fft.rfftn(expand_kernel)
        c = np.fft.irfftn(ne.evaluate("a * b"))
        mask_expanded = np.fft.fftshift(ne.evaluate("real(c) > 1e-6"))

    else:

        mask_expanded = imglpbin

    mask_expanded_prev = mask_expanded
    mask_expanded_soft = mask_expanded

    # Expanding with a soft-edge is the same as above but in a loop, 1-voxel-shell at a time, multiplying by a cosine:
    expand_kernel = SoftMask(mask_expanded_prev.shape, radius=1, width=0)
    if expand_soft_width > 0:

        for i in np.arange(1, np.round(expand_soft_width) + 1):
            a = np.fft.rfftn(mask_expanded_prev)
            b = np.fft.rfftn(expand_kernel)
            c = np.fft.irfftn(ne.evaluate("a * b"))
            mask_expanded_new = np.fft.fftshift(
                ne.evaluate("real(c) > 1e-6")).astype('float32')
            mask_expanded_soft = ne.evaluate(
                "mask_expanded_soft + (mask_expanded_new - mask_expanded_prev) * (1.0 + cos(pi * i / (expand_soft_width + 1))) / 2.0")
            mask_expanded_prev = mask_expanded_new

    return mask_expanded_soft


def FloodFilling(img, inimask, thr=0.0):
    # "Smart" growing of binary volume based on flood-filling algorithm.
    # Similar to mask.auto3d processor in EMAN2

    mask = inimask
    expand_kernel = SoftMask(img.shape, radius=1, width=0)

    mask_expanded_prev = mask
    r = 1
    while True:

        mask_expanded_new = np.fft.fftshift(np.fft.irfftn(np.fft.rfftn(
            mask_expanded_prev) * np.fft.rfftn(expand_kernel)).real) > 1e-6  # To prevent residual non-zeros from FFTSs
        shell = mask_expanded_new - mask_expanded_prev
        imgshell = img * shell
        shellbin = imgshell > thr
        if np.any(shellbin):
            mask = mask + shellbin
            mask_expanded_prev = mask
        else:
            break

        r += 1

    return mask


def GetNumberOfFourierSamples(imsize):

    imsize = np.array(imsize)

    return np.round(np.sqrt(np.sum(np.power(imsize, 2))) / 2.0 / np.sqrt(len(imsize))).astype('int') + 1


def GetFreqArray(NSAM=256, apix=1.0):

    return (np.arange(NSAM) / (2.0 * (NSAM - 1) * apix)).reshape(NSAM, 1)


def MaskAutoExpand(map1, map2, apix=1.0, init_lp=15, fraction_threshold=0.01, init_hard_edge=0, init_soft_edge=3, randomize_below_fsc=0.8, fsc_thr=0.143, random_seed=123456789, interp=False, verbose=False):
    # Starts with a tight mask and expands it until masked FSC (roughly) matches the masked-corrected FSC by High-Resolution Noise Substitution

    fsc = {}
    NSAM = GetNumberOfFourierSamples(map1.shape)

    fsc['freq'] = GetFreqArray(NSAM, apix)

    fsc['unmasked'] = FCC(map1, map2)[:NSAM]
    fsc['randomize_below_thr'] = randomize_below_fsc
    fsc['thr'] = fsc_thr

    fsc['rand_res'] = ResolutionAtThreshold(
        fsc['freq'][1:], fsc['unmasked'][1:], randomize_below_fsc, interp=interp)
    rand_freq = 1/fsc['rand_res']
    fsc['unmasked_res'] = ResolutionAtThreshold(
        fsc['freq'][1:], fsc['unmasked'][1:], fsc_thr, interp=interp)

    map1randphase = HighResolutionNoiseSubstitution(
        map1, apix=apix, lp=fsc['rand_res'], random_seed=random_seed)
    map2randphase = HighResolutionNoiseSubstitution(
        map2, apix=apix, lp=fsc['rand_res'], random_seed=random_seed+1)

    mapsum = map1 + map2

    edge = init_hard_edge
    soft_edge = init_soft_edge
    i = 0

    while True:

        automask = AutoMask(mapsum, apix=apix, lp=init_lp, fraction_threshold=fraction_threshold,
                            expand_width=edge, expand_soft_width=soft_edge, verbose=False)

        fsc['masked'] = FCC(map1 * automask, map2 * automask)[:NSAM]
        fsc['masked_res'] = ResolutionAtThreshold(
            fsc['freq'][1:], fsc['masked'][1:], fsc['thr'], interp=interp)

        fsc['masked_randomized'] = FCC(
            map1randphase * automask, map2randphase * automask)[:NSAM]
        fsc['masked_true'] = (
            (fsc['masked'] - fsc['masked_randomized']) / (1.0 - fsc['masked_randomized']))
        fsc['masked_true'][fsc['freq'] <
                           rand_freq] = fsc['masked'][fsc['freq'] < rand_freq]
        fsc['masked_true'] = np.nan_to_num(fsc['masked_true'])
        fsc['masked_true_res'] = ResolutionAtThreshold(
            fsc['freq'][1:], fsc['masked_true'][1:], fsc['thr'], interp=interp)

        if verbose:

            logger.info('Iteration %d, Masked res: %.3f A, True masked res: %.3f A, Current hard edge = %d pix, Current soft edge = %d pix' % (
                i+1, fsc['masked_res'], fsc['masked_true_res'], edge, soft_edge))

        if fsc['masked_true_res'] <= fsc['masked_res']:

            return automask, fsc

        else:

            if i % 2 == 0:

                soft_edge += 1

            else:

                edge += 1

            i += 1


def FilterGauss(img, apix=1.0, lp=-1, hp=-1, return_filter=False):
    # Gaussian band-pass filtering of images.

    rmesh = RadialIndices(img.shape, rounding=False,
                          normalize=True, rfft=True)[0]
    ne.evaluate("rmesh / apix ", out=rmesh)
    rmesh2 = ne.evaluate("rmesh * rmesh")

    if lp <= 0.0:

        lowpass = 1.0

    else:

        lowpass = ne.evaluate("exp(- lp * lp * rmesh2)")

    if hp <= 0.0:

        highpass = 1.0

    else:

        highpass = ne.evaluate("1.0 - exp(- hp * hp * rmesh2)")

    bandpass = ne.evaluate("lowpass * highpass")

    ft = np.fft.rfftn(img)

    filtered = np.fft.irfftn(ne.evaluate("ft * bandpass"), s=img.shape)

    if return_filter:

        return filtered, bandpass

    else:

        return filtered


def FilterWhiten(img, return_filter=False, ps=False):
    # Whitens the spectrum of an image or map, i.e. the radial amplitude spectrum becomes 1.0 at all frequencies.
    # 'ps' is a switch to whiten the Power Spectrum (radial squared amplitudes profile) instead of the amplitude spectrum.
    # Which one to use depends on the application, but the difference in practice is barely noticeable.

    ft = np.fft.fftshift(np.fft.fftn(img))

    if ps:

        a = RotationalAverage(ne.evaluate("real(ft * conj(ft))"))
        radprof = ne.evaluate("sqrt(a)")

    else:

        radprof = RotationalAverage(ne.evaluate("real(abs(ft))"))

    filtered = np.fft.ifftn(np.fft.ifftshift(ne.evaluate("ft / radprof"))).real

    if return_filter:

        return filtered, radprof

    else:

        return filtered


def FilterBfactor(img, apix=1.0, B=0.0, return_filter=False):
    # Applies a B-factor to images. B can be positive or negative.

    rmesh = RadialIndices(img.shape, rounding=False,
                          normalize=True, rfft=True)[0]
    ne.evaluate("rmesh / apix", out=rmesh)
    rmesh2 = ne.evaluate("rmesh * rmesh")

    bfac = ne.evaluate("exp(- (B * rmesh2) / 4)")

    ft = np.fft.rfftn(img)

    filtered = np.fft.irfftn(ne.evaluate("ft * bfac"), s=img.shape)

    if return_filter:

        return filtered, bfac

    else:

        return filtered


def FilterCosine(img, apix=1.0, lp=-1, hp=-1, width=6.0, return_filter=False):
    # Band-pass filtering of images with a cosine edge. Good to approximate a top-hat filter while still reducing edge artifacts.

    if width < 0.0:

        width = 0.0

    if width > 0.0 and width <= 1.0:

        width = 0.5 * width * np.min(img.shape)

    if lp <= 0.0:

        lowpass = 1.0

    else:

        lowpass = SoftMask(img.shape, radius=np.min(
            img.shape) * apix / lp, width=width, rfft=True)

    if hp <= 0.0:

        highpass = 1.0

    else:

        highpass = 1.0 - \
            SoftMask(img.shape, radius=np.min(img.shape)
                     * apix / hp, width=width, rfft=True)

    bandpass = ne.evaluate("lowpass * highpass")

    ft = np.fft.rfftn(img)

    filtered = np.fft.irfftn(ne.evaluate("ft * bandpass"))

    if return_filter:

        return filtered.real, bandpass

    else:

        return filtered.real

def HighResolutionNoiseSubstitution(img, apix=1.0, lp=-1, random_seed=123456789, parallel=False):
    # Randomizes the phases of a map beyond resolution 'lp'
    # If calling many times in parallel, make sure to set the 'parallel' flag to True

    # Get resolution shells:
    rmesh = RadialIndices(img.shape, rounding=False,
                          normalize=True, rfft=True)[0]
    rmesh = ne.evaluate("rmesh / apix", out=rmesh)

    lp = 1.0 / lp

    ft = np.fft.rfftn(img)

    # Decompose Fourier transform into amplitudes and phases:
    amps = ne.evaluate("real(abs(ft))")
    phases = ne.evaluate("arctan2(imag(ft),real(ft))")

    # Select only terms beyond desired resolution (not inclusive)
    idx = ne.evaluate("rmesh > lp")

    if lp > 0.0:

        if parallel:

            # Just to make sure that parallel jobs launched nearly at the same time won't get the same seed (truly random here)
            np.random.seed()

        else:

            np.random.seed(seed=random_seed)

        # Generate random phases in radians
        rndvec = np.random.random(phases.shape)
        phasesrnd = ne.evaluate("rndvec * 2.0 * pi")

        phases[idx] = phasesrnd[idx]

    ftnew = ne.evaluate("amps * (cos(phases) + 1j * sin(phases))")

    return np.fft.irfftn(ftnew, s=img.shape)

def FCC(volume1, volume2, phiArray=[0.0], invertCone=False):
    """
    Fourier conic correlation

    Created on Fri Dec  4 16:35:42 2015
    @author: Robert A. McLeod

    Modified by: Ricardo Righetto
    Date of modification: 23.02.2017
    Change: now also supports (conical) FRC

    Returns FCC_normed, which has len(phiArray) Fourier conic correlations
    """

    if volume1.ndim == 3:

        [M, N, P] = volume1.shape
        [zmesh, ymesh, xmesh] = np.mgrid[-M /
                                         2:M / 2, -N / 2:N / 2, -P / 2:P / 2]
        rhomax = np.int32(
            np.ceil(np.sqrt(M * M / 4.0 + N * N / 4.0 + P * P / 4.0)) + 1)
        rhomesh = ne.evaluate(
            "sqrt(xmesh * xmesh + ymesh * ymesh + zmesh * zmesh)")
        phimesh = ne.evaluate("arccos(zmesh / rhomesh)")
        phimesh[M // 2, N // 2, P // 2] = 0.0
        phimesh = np.ravel(phimesh)

    elif volume1.ndim == 2:

        [M, N] = volume1.shape
        [ymesh, xmesh] = np.mgrid[-M / 2:M / 2, -N / 2:N / 2]
        rhomax = np.int32(np.ceil(np.sqrt(M * M / 4.0 + N * N / 4.0)) + 1)
        rhomesh = ne.evaluate("sqrt(xmesh * xmesh + ymesh * ymesh)")
        phimesh = ne.evaluate("arctan2(ymesh, xmesh)")
        phimesh[M // 2, N // 2] = 0.0
        phimesh = np.ravel(phimesh)

    else:

        raise RuntimeError("Error: FCC only supports 2D and 3D objects.")

    phiArray = ne.evaluate("phiArray * pi / 180.0")

    rhoround = np.round(rhomesh.ravel()).astype('int')  # Indices for bincount

    fft1 = np.ravel(np.fft.fftshift(np.fft.fftn(volume1))).astype('complex128')
    conj_fft2 = np.ravel(np.fft.fftshift(
        np.fft.fftn(volume2)).conj()).astype('complex128')

    FCC_normed = np.zeros([rhomax, len(phiArray)])
    for J, phiAngle in enumerate(phiArray):

        if phiAngle == 0.0:
            fft1_conic = fft1
            conj_fft2_conic = conj_fft2
            rhoround_conic = rhoround
        else:
            conic = np.ravel(ne.evaluate(
                "phimesh <= phiAngle + ((abs(phimesh - pi)) <= phiAngle)"))
            if invertCone:
                conic = np.invert(conic)
            rhoround_conic = rhoround[conic]
            fft1_conic = fft1[conic]
            conj_fft2_conic = conj_fft2[conic]
        FCC = np.bincount(rhoround_conic, ne.evaluate(
            "real(fft1_conic * conj_fft2_conic)"))
        Norm1 = np.bincount(rhoround_conic, ne.evaluate(
            "real(abs(fft1_conic)) * real(abs(fft1_conic))"))
        Norm2 = np.bincount(rhoround_conic, ne.evaluate(
            "real(abs(conj_fft2_conic)) * real(abs(conj_fft2_conic))"))

        goodIndices = np.argwhere(ne.evaluate("(Norm1 * Norm2) > 0.0"))[:-1]
        a = FCC[goodIndices]
        b = Norm1[goodIndices]
        c = Norm2[goodIndices]
        FCC_normed[goodIndices, J] = ne.evaluate("a / sqrt( b * c ) ")

    return FCC_normed

def ResolutionAtThreshold(freq, fsc, thr, interp=True, nyquist_is_fine=False, ):
    # Do a simple linear interpolation (optional) to get resolution value at the specified FSC threshold

    if np.isscalar(thr):

        thr *= np.ones(fsc.shape)

    for i, f in enumerate(fsc):

        if f < thr[i]:

            break

    if i < len(fsc) - 1 and i > 1:

        if interp:

            y1 = fsc[i]
            y0 = fsc[i - 1]
            x1 = freq[i]
            x0 = freq[i - 1]

            delta = (y1 - y0) / (x1 - x0)

            res_freq = x0 + (thr[i - 1] - y0) / delta

        else:

            # Just return the highest resolution bin at which FSC is still higher than threshold:
            res_freq = freq[i - 1]

    elif i == 0:

        res_freq = freq[i]

    else:

        res_freq = freq[-1]

    return 1 / res_freq


def Fsc2Xml(filename, x, y):

    with open(filename, 'w+') as f:
        f.write('<fsc title="" xaxis="Resolution (A-1)" yaxis="Correlation Coefficient">\n')

        for i in np.arange(len(x)):

            f.write('  <coordinate>\n')
            f.write('    <x>%.6f</x>\n' % x[i][0])
            f.write('    <y>%.6f</y>\n' % y[i][0])
            f.write('  </coordinate>\n')

        f.write('</fsc>')


def main():

    progname = os.path.basename(sys.argv[0])
    usage = progname + """ <half-map1> [<half-map2>] [options]
	"""

    parser = OptionParser(usage)

    parser.add_option("--out", metavar="postprocess", type="string",
                      default='postprocess', help="Output rootname.")

    parser.add_option("--angpix", metavar=1.0, type="float",
                      help="Pixel size in Angstroems")

    parser.add_option("--fsc_threshold", metavar=0.143, default=0.143, type="float",
                      help="Display the resolution at which the FSC curve crosses this value.")

    parser.add_option("--lowpass", metavar='"auto"', default='auto',
                      help="Resolution (in Angstroems) at which to low-pass filter the final map. A negative value will skip low-pass filtering. Default ('auto') is to low-pass at resolution determined from FSC threshold.")

    parser.add_option("--highpass", metavar='"auto"', default='auto',
                      help="Resolution (in Angstroems) at which to high-pass filter the final map. Useful to to attenuate artefacts such as background ramps (e.g. high-pass at 2/3 of the box size). A negative value will skip high-pass filtering (default).")

    parser.add_option("--mask", metavar="MyMask.mrc", type="string",
                      help="A file containing the mask to be applied to the half-maps before calculating the FSC. Can be combined with other masking options.")

    parser.add_option("--mask_radius", metavar=0.5, default=None, type="float",
                      help="Creates a soft spherical mask. This is the radius of such mask, in pixels or fraction of the box size. Can be combined with other masking options.")

    parser.add_option("--mask_edge_width", metavar=6.0, default=None, type="float",
                      help="This is the width of the cosine edge to soften the outer shells of the spherical mask, in pixels or fraction of the box size.")

    parser.add_option("--automask", action="store_true",
                      help="Do automatic masking of input volumes. Can be combined with other masking options.", default=False)

    parser.add_option("--automask_input", metavar=0, default=0, type="int",
                      help="Which input to provide for auto-masking? 0 = Average of map1 and map2 (default); 1 = Use map1; 2 = Use map2.")

    parser.add_option("--automask_floodfill_radius", metavar=10, default=None, type="float",
                      help="Radius of sphere to initialize flood-filling algorithm in auto-masking, in pixels or fraction of the box size. Typically follows the correct map density for globular-like particles. Use a negative number to disable flood-filling (default).")

    parser.add_option("--automask_floodfill_center", metavar="0,0,0", default=None, type="string",
                      help="Three numbers describing where the center of the sphere should be placed to initialize flood-filling approach in auto-masking (in pixels). Useful to mask parts of the 3D map that are not close to the center. Default is the middle of the box: 0,0,0. Can be positive or negative.")

    parser.add_option("--automask_floodfill_fraction", metavar=0.10, default=None, type="float",
                      help="Use this fraction of the voxels with the highest densities (0.10 = top 10 percent highest densities) to initialize the flood-filling algorithm. Typically follows the correct map density for capsid-like or hollow-center particles. Note that this is only used to initialize the smart masking algorithm and has no influence on the threshold, that is defined independently (see options below).")

    parser.add_option("--automask_lp", metavar=14.0, default=14.0, type="float",
                      help="Resolution (in Angstroems) at which to low-pass filter the input map for auto-masking purposes. Should typically be in the range of 10-20 A. However if using the flood-filling approach a value in the range 5-10 A might work better. Use a negative number to disable this filter.")

    parser.add_option("--automask_lp_edge_width", metavar=5.0, default=5.0, type="float",
                      help="Width of the cosine-edge low-pass filter to be used for auto-masking (in Fourier pixels).")

    parser.add_option("--automask_lp_gauss", action="store_true", default=False,
                      help="Use a Gaussian instead of cosine-edge low-pass filter for auto-masking.")

    parser.add_option("--automask_threshold", metavar=0.02, default=None, type="float",
                      help="Absolute threshold to generate the initial binary volume in auto-masking. This has precedence over --automask_fraction and --automask_sigma.")

    parser.add_option("--automask_fraction", metavar=0.10, default=None, type="float",
                      help="Use this fraction of the voxels with the highest densities (0.10 = top 10 percent highest densities) to generate the initial binary volume in auto-masking. This has precedence over --automask_sigma.")

    parser.add_option("--automask_sigma", metavar=1.0, default=1.0, type="float",
                      help="Use this many standard deviation(s) above the mean density value as threshold for initial binary volume generation in auto-masking. This is the default option.")

    parser.add_option("--automask_expand_width", metavar=3.0, default=3.0, type="float",
                      help="Width in pixels to expand the binary mask in auto-masking. Useful to make the mask more generous and correct for imperfections of the initial binarization.")

    parser.add_option("--automask_soft_width", metavar=6.0, default=6.0, type="float",
                      help="Width in pixels to expand the binary mask in auto-masking with a soft cosine edge. Very important to prevent artificial correlations induced by the mask.")

    parser.add_option("--automask_optimize", action="store_true",
                      help="Will generate a mask automatically based on the automask procedure, and then tune it to optimize the masked FSC corrected by High-Resolution Noise Substitution (Chen et al, Ultramicroscopy 2013)", default=False)

    parser.add_option("--skip_fsc", action="store_true",
                      help="Skip all FSC calculations, only do masking and filtering stuff.", default=False)

    parser.add_option("--mw", metavar=1000.0, type="float", help="Molecular mass in kDa of particle or helical segment comprised within the mask. Needed to calculate volume-normalized Single-Particle Wiener filter (Sindelar & Grigorieff, JSB 2012). If not specified, will do conventional FSC weighting on the final map (Rosenthal & Henderson, JMB 2003).")

    parser.add_option("--mw_ignore", metavar=0.0, type="float", default=0.0, help="CAUTION! EXPERIMENTAL OPTION: Molecular mass in kDa present within the mask that needs to be ignored. Needed to calculate an adaptation of the volume-normalized Single-Particle Wiener filter (Sindelar & Grigorieff, JSB 2012). Only used if --mw is also specified. May be useful if your particles are extracted from 2D crystals.")

    parser.add_option("--skip_fsc_weighting", action="store_true",
                      help="Do NOT apply FSC weighting (Rosenthal & Henderson, JMB 2003) to the final map, nor the Single-Particle Wiener filter (Sindelar & Grigorieff, JSB 2012).", default=False)

    parser.add_option("--gaussian", action="store_true",
                      help="Apply a Gaussian (instead of cosine-edge) low-pass filter to the map, with cutoffs defined by --highpass and --lowpass.", default=False)

    parser.add_option("--cosine", action="store_true", help="Apply a cosine-edge low-pass filter to the final map, with cutoffs defined by --highpass and --lowpass. This is the default. The width of the cosine edge can be specified with the option --edge_width.", default=True)

    parser.add_option("--cosine_edge_width", metavar=3.0, type="float",
                      help="Width of the cosine-edge filter (in Fourier pixels). The cutoff frequency will have a weight of 0.5, with corresponding weighting above and below following the cosine falloff. If set to zero, becomes a top-hat filter with weighting of 1.0 at the cutoff frequency.", default=3.0)

    parser.add_option("--tophat", action="store_true",
                      help="Apply a top-hat low-pass filter to the final map. Equivalent to specifying --cosine with --cosine_edge_width=0.", default=False)

    parser.add_option("--mtf", type="string",
                      help="File containing the detector MTF for sharpening of the final map.")

    parser.add_option("--auto_bfac", metavar="10.0,0.0", default=None, type="string", help="Estimate B-factor automatically using information in this resolution range, in Angstroems (lowres,highres). This works based on the Guinier plot, which should ideally be a straight line from ~10.0 A and beyond (Rosenthal & Henderson, JMB 2003).'If you set lowres and/or maxres to -1, these values will be calculated automatically. MTF and FSC weighting information are employed, if not ommitted.")

    parser.add_option("--adhoc_bfac", metavar=0.0, type="float",
                      help="Apply an ad-hoc B-factor to the map (in Angstroems^2). Can be positive (smoothing) or negative (sharpening).", default=0.0)

    parser.add_option("--whiten", action="store_true", help="Whiten the final map (that is, makes the radial Amplitude Spectrum equal to 1.0 across all frequencies). Should normally be used in combination with the option --gaussian and --skip_fsc_weighting, and also --highpass in some cases. If using this option, B-factor and MTF sharpening become meaningless.", default=False)

    parser.add_option("--whiten_amps", action="store_true", help="Whiten the radial Amplitude Spectrum instead of the radial Power Spectrum (Amplitudes^2). Whitening amplitudes seems to give a slightly more peaky (sharp) map as measured by kurtosis, but the results are visually almost identical. Only valid if using option --whiten above.", default=False)

    parser.add_option("--randomize_below_fsc", metavar=0.8, type="float", default=None,
                      help="If provided, will randomize phases for all Fourier shells beyond the point where the FSC drops below this value, to assess correlations introduced by the mask by High-Resolution Noise Substitution (Chen et al, Ultramicroscopy 2013). Be aware that this procedure may introduce a 'dip' in the FSC curves at the corresponding resolution value, but that is normal.")

    parser.add_option("--randomize_beyond", metavar=10, type="float", default=None,
                      help="If provided, will randomize phases for all Fourier shells beyond this resolution shell, to assess correlations introduced by the mask by High-Resolution Noise Substitution (Chen et al, Ultramicroscopy 2013). Be aware that this procedure may introduce a 'dip' in the FSC curves at the corresponding resolution value, but that is normal.")

    parser.add_option("--random_seed", metavar=123456789, type="int", default=123456789,
                      help="Choose the random seed for High-Resolution Noise Substitution (see option --randomize_below_fsc above)")

    parser.add_option("--flip_x", action="store_true", default=False,
                      help="Invert handedness of input volumes along the X axis.")

    parser.add_option("--flip_y", action="store_true", default=False,
                      help="Invert handedness of input volumes along the Y axis.")

    parser.add_option("--flip_z", action="store_true", default=False,
                      help="Invert handedness of input volumes along the Z axis.")

    parser.add_option("--xml", action="store_true", default=False,
                      help="Save FSC curves also in XML format for EMDB deposition.")

    (options, args) = parser.parse_args()

    command = ' '.join(sys.argv)

    if options.lowpass != 'auto':

        options.lowpass = float(options.lowpass)

    if options.highpass != 'auto':

        options.highpass = float(options.highpass)

    if options.mw != None and options.mw < 0.0:

        logger.error('Molecular mass cannot be negative!')
        sys.exit(1)

    if options.mw_ignore != None and options.mw_ignore < 0.0:

        logger.error('Molecular mass to be ignored cannot be negative!')
        sys.exit(1)

    if options.angpix == None:

        logger.warning('Pixel size was not specified. Assuming 1.0 A/pixel.')
        options.angpix = 1.0

    elif options.angpix <= 0.0:

        logger.error('Pixel size must be greater than zero!')
        sys.exit(1)

    if options.cosine_edge_width != None and options.cosine_edge_width < 0.0:

        logger.error('Cosine edge width cannot be negative!')
        sys.exit(1)

    if options.randomize_below_fsc != None and (options.randomize_below_fsc < -1.0 or options.randomize_below_fsc > 1.0):

        logger.error(
            'FSC values for phase-randomization must be in the range [-1,1]!')
        sys.exit(1)

    if options.tophat:

        options.gaussian = False
        options.cosine = True
        options.cosine_edge_width = 0.0

    mask_center = [0, 0, 0]

    if options.automask_floodfill_center == None:

        options.automask_floodfill_center = [0, 0, 0]

    else:

        options.automask_floodfill_center = np.array(
            map(int, options.automask_floodfill_center.split(',')))

    if options.skip_fsc and options.lowpass == "auto":

        options.lowpass = -1
        options.skip_fsc_weighting = True

    fsc_interp = False

    # Read in the two maps:
    map1 = mrc.read(args[0])
    common_header = mrc.readHeaderFromFile(args[0])

    if len(args) > 1:
        map2 = mrc.read(args[1])
    else:
        map2 = map1
    sys.stdout = sys.__stdout__

    if options.flip_x:

        logger.info('Flipping input maps along X')

        map1 = map1[:, :, ::-1]
        map2 = map2[:, :, ::-1]

    if options.flip_y:

        logger.info('Flipping input maps along Y')

        map1 = map1[:, ::-1, :]
        map2 = map2[:, ::-1, :]

    if options.flip_z:

        logger.info('Flipping input maps along Z')

        map1 = map1[::-1, :, :]
        map2 = map2[::-1, :, :]

    if np.any(map1.shape != map2.shape):

        logger.error('Input maps must be the same size!')
        sys.exit(1)

    # We check if there is a mask file and if not, should we create one?
    if options.mask != None:

        sys.stdout = open(os.devnull, "w")  # Suppress output
        maskfile = mrc.read(options.mask)
        sys.stdout = sys.__stdout__

    else:

        maskfile = np.ones( map1.shape )

    mask = maskfile

    if options.mask_radius != None or options.mask_edge_width != None:

        if options.mask_radius == None:

            options.mask_radius = 0.5

        if options.mask_edge_width == None:

            options.mask_edge_width = 6.0

        masksphere = SoftMask(
            map1.shape, radius=options.mask_radius, width=options.mask_edge_width, xyz=mask_center)

        ne.evaluate( "mask * masksphere", out=mask)

    if options.automask:

        if options.automask_input == 0:

            maskautoin = ne.evaluate( "0.5 * (map1 + map2)" )

        elif options.automask_input == 1:

            maskautoin = map1

        elif options.automask_input == 2:

            maskautoin = map2

        maskauto = AutoMask(maskautoin, apix=options.angpix, lp=options.automask_lp, gaussian=options.automask_lp_gauss, cosine_edge_width=options.automask_lp_edge_width, absolute_threshold=options.automask_threshold, fraction_threshold=options.automask_fraction, sigma_threshold=options.automask_sigma,
                                 expand_width=options.automask_expand_width, expand_soft_width=options.automask_soft_width, floodfill_rad=options.automask_floodfill_radius, floodfill_xyz=options.automask_floodfill_center, floodfill_fraction=options.automask_floodfill_fraction, verbose=True)

        ne.evaluate( "mask * maskauto ", out=mask)

    if options.automask_optimize:

        logger.info('Starting mask optimization')
        mask,fsc_optimized = MaskAutoExpand(map1, map2, apix=options.angpix, init_lp=options.automask_lp, fraction_threshold=0.01, init_hard_edge=0, init_soft_edge=3, randomize_below_fsc=0.8, fsc_thr=options.fsc_threshold, random_seed=options.random_seed, interp=False, verbose=True)
        logger.info('Done optimizing mask.')

    # If a spherical mask or an auto-mask were created, we need to save it (this will be the combination of all masks provided or created!):
    if options.mask_radius or options.automask or options.automask_optimize:

        mrc.write(mask, options.out + '-mask.mrc', header=common_header)

        options.mask = options.out + '-mask.mrc'

    # Resolution range to estimate B-factor:
    if options.auto_bfac != None:

        resrange = options.auto_bfac.split(',')
        minres = float(resrange[0])
        maxres = float(resrange[1])

    # For cubic volumes this is just half the box size + 1.
    NSAM = GetNumberOfFourierSamples( map1.shape )

    freq = GetFreqArray( NSAM, options.angpix )

    freq[0] = 1.0 / 999  # Just to avoid dividing by zero later
    freq2 = ne.evaluate( "freq * freq" )

    # Start creating the matrix that will be written to an output file
    dat = np.append(1.0 / freq, freq, axis=1)
    # Header of the output file describing the data columns
    head = 'Res       \t1/Res     \t'

    if not options.skip_fsc:

        # logger.info('Calculating unmasked FSC')

        fsc = FCC(map1, map2)

        res = ResolutionAtThreshold(
            freq[1:], fsc[1:NSAM], options.fsc_threshold, fsc_interp)
        # logger.info('FSC >= %.3f until %.3f A (unmasked)' %
        #        (options.fsc_threshold, res))

        # logger.info('Area under FSC (unmasked): %.3f' % fsc[1:NSAM].sum())

        dat = np.append(dat, fsc[:NSAM], axis=1)  # Append the unmasked FSC
        head += 'FSC-unmasked\t'
        if options.xml:
          Fsc2Xml( options.out+'_fsc-unmasked.xml', freq, fsc[:NSAM] )


        # Now we go to the mask-related operations which are activated if a mask or MW are specified. If only
        if options.mask != None or options.mw != None:

            if options.mask == None:  # If MW is specified but no mask, we issue a warning:

                logger.warning('You specified MW without a mask. This may produce inaccurate results!')

                mask = np.ones(map1.shape, dtype='float')
                mrc.write(mask, options.out + '-mask.mrc', header=common_header)
                options.mask = options.out + '-mask.mrc'

            map1masked = ne.evaluate( "map1 * mask" )
            map2masked = ne.evaluate( "map2 * mask" )

            # logger.info('Calculating masked FSC')

            fsc_mask = FCC(map1masked, map2masked)

            res_mask = ResolutionAtThreshold(
                freq[1:], fsc_mask[1:NSAM], options.fsc_threshold, fsc_interp)
            # logger.info('FSC >= %.3f until %.3f A (masked)' %
            #        (options.fsc_threshold, res_mask))

            # logger.info('Area under FSC (masked): %.3f' % fsc_mask[1:NSAM].sum())

            # Append the masked FSC
            dat = np.append(dat, fsc_mask[:NSAM], axis=1)
            head += 'FSC-masked\t'
            if options.xml:
              Fsc2Xml( options.out+'_fsc-masked.xml', freq, fsc_mask[:NSAM] )

            if options.randomize_below_fsc == None and options.randomize_beyond == None:
                pass
            else:

                if options.randomize_beyond == None:

                  rand_res = ResolutionAtThreshold(
                      freq[1:], fsc[1:NSAM], options.randomize_below_fsc, fsc_interp)

                else:

                  rand_res = options.randomize_beyond

                logger.info('Randomizing phases beyond %.3f A' % rand_res)
                rand_freq = 1.0 / rand_res

                # We have to enforce the random seed otherwise different runs would not be comparable
                map1randphase = HighResolutionNoiseSubstitution(
                    map1, apix=options.angpix, lp=rand_res, random_seed=options.random_seed )

                # Cannot use same random seed for both maps!!!
                map2randphase = HighResolutionNoiseSubstitution(
                    map2, apix=options.angpix, lp=rand_res, random_seed=options.random_seed + 1 )

                # We mask the phase-randomized maps:
                map1randphasemasked = ne.evaluate( "map1randphase * mask" )
                map2randphasemasked = ne.evaluate( "map2randphase * mask" )

                # logger.info('Calculating masked FSC for phase-randomized maps')

                fsc_mask_rnd = FCC(
                    map1randphasemasked, map2randphasemasked)

                dat = np.append(dat, fsc_mask_rnd[:NSAM], axis=1)
                head += 'FSC-phase-randomized\t'
                # We compute FSCtrue following (Chen et al, Ultramicroscopy 2013). For masked maps this will correct the FSC for eventual refinement overfitting, including from the mask:

                # fsc_mask_true[freq >= rand_freq] = (fsc_mask[freq >= rand_freq] - fsc_mask_rnd[freq >= rand_freq]) / (1 - fsc_mask_rnd[freq >= rand_freq])
                rand_freq_2step = 1.0 / (rand_res - 2)
                fsc_mask_true = ((fsc_mask - fsc_mask_rnd) / (1.0 - fsc_mask_rnd))
                fsc_mask_true[:NSAM][freq < rand_freq_2step] = fsc_mask[:NSAM][freq < rand_freq_2step]
                fsc_mask_true = np.nan_to_num(fsc_mask_true)

                res_mask_true = ResolutionAtThreshold(
                    freq[1:], fsc_mask_true[1:NSAM], options.fsc_threshold, fsc_interp)
                # logger.info('FSC >= %.3f until %.3f A (masked - true)' %
                #        (options.fsc_threshold, res_mask_true))

                # logger.info('Area under FSC (masked - true): %.3f' % fsc_mask_true[1:NSAM].sum())

                # Append the true masked FSC
                dat = np.append(dat, fsc_mask_true[:NSAM], axis=1)
                head += 'FSC-masked_true\t'
                if options.xml:
                  Fsc2Xml( options.out+'_fsc-masked_true.xml', freq, fsc_mask_true[:NSAM] )

                res_mask = res_mask_true

            if options.mw != None:

                DALT = 0.81  # Da/A^3

                # Estimate fraction of volume occupied by the molecule:
                fpart = 1000.0 * options.mw / DALT / \
                    (options.angpix * 2 * NSAM)**3

                fignore = 1000.0 * options.mw_ignore / \
                    DALT / (options.angpix * 2 * NSAM)**3

                # Fraction of the volume occupied by the mask:
                maskvoxsum = ne.evaluate( "sum(mask * mask)" )
                fmask = maskvoxsum / np.prod(mask.shape)

                logger.info('Calculating Single-Particle Wiener filter')
                logger.info('Fraction of particle within the volume (Fpart): %.6f' % fpart)
                logger.info('Fraction of mask within the volume (Fmask): %.6f' % fmask)
                if options.mw_ignore > 0.0:

                    logger.info(
                        'Fraction of densities to be ignored within the volume (Fignore): %.6f' % fignore)
                    logger.info('Fpart/(Fmask-Fignore) ratio: %.6f' %
                          (fpart / (fmask - fignore)))

                    if (fpart / (fmask - fignore)) >= 1.0:

                        logger.warning('Your particle occupies a volume bigger than the mask. Mask is probably too tight or even too small!')

                else:

                    logger.info('Fpart/Fmask ratio: %.6f' % (fpart / fmask))

                    if (fpart / fmask) >= 1.0:

                        logger.warning('Your particle occupies a volume bigger than the mask. Mask is probably too tight or even too small!')

                # Let's do Single-Particle Wiener filtering following (Sindelar & Grigorieff, 2012):

                if options.randomize_below_fsc == None:

                    fsc_spw = fsc_mask / \
                        (fsc_mask + (fpart / (fmask - fignore)) * (1.0 - fsc_mask))

                else:

                    fsc_spw = fsc_mask_true / \
                        (fsc_mask_true + (fpart / (fmask - fignore))
                         * (1.0 - fsc_mask_true))

                res_spw = ResolutionAtThreshold(
                    freq[1:], fsc_spw[1:NSAM], options.fsc_threshold, fsc_interp)
                # logger.info('FSC >= %.3f until %.3f A (volume-normalized)' %
                #        (options.fsc_threshold, res_spw))

                # logger.info('Area under FSC (volume-normalized): %.3f' % fsc_spw[1:NSAM].sum())

                # Append the FSC-SPW
                dat = np.append(dat, fsc_spw[:NSAM], axis=1)
                head += 'FSC-SPW   \t'
                if options.xml:
                  Fsc2Xml( options.out+'_fsc-spw.xml', freq, fsc_spw[:NSAM] )

    else:

        logger.info('Skipping FSC calculations')

    # 1. Sum the two half-reconstructions:
    fullmap = ne.evaluate( "0.5 * (map1 + map2)" )

    radamp_original = RadialProfile( fullmap, amps=True )[:NSAM]
    lnF_original = np.log(radamp_original)

    # 2. Apply FSC weighting or SPW filter to the final map, accordingly:
    if options.skip_fsc_weighting == False:

        logger.info('Applying FSC weighting')
        if options.mask == None and options.mw == None:

            # Derive weights from unmasked FSC
            fsc_weights = np.zeros(fsc.shape)
            idx = fsc > 0.0
            fsc_weights[idx] = np.sqrt(2 * fsc[idx] / (1 + fsc[idx]))

        elif options.mw == None:

            # Derive weights from masked FSC
            if options.randomize_below_fsc != None:

                fsc_weights = np.zeros(fsc_mask_true.shape)
                idx = fsc_mask_true > 0.0
                fsc_weights[idx] = np.sqrt(
                    2 * fsc_mask_true[idx] / (1 + fsc_mask_true[idx]))

            else:

                fsc_weights = np.zeros(fsc_mask.shape)
                idx = fsc_mask > 0.0
                fsc_weights[idx] = np.sqrt(
                    2 * fsc_mask[idx] / (1 + fsc_mask[idx]))

        else:

            fsc_weights = np.zeros(fsc_spw.shape)
            idx = fsc_spw > 0.0
            fsc_weights[idx] = np.sqrt(2 * fsc_spw[idx] / (1 + fsc_spw[idx]))

        if options.mw != None:

          rmax = res_spw

        elif options.mask != None:

          rmax = res_mask

        else:

          rmax = res

        fullmap = RadialFilter(fullmap, fsc_weights, return_filter=False)

        # Append the FSC weighting
        dat = np.append(dat, fsc_weights[:NSAM], axis=1)
        head += 'Cref_Weights\t'

    # 3. Sharpen map by recovering amplitudes from detector's MTF:
    if options.mtf != None:

        logger.info('Dividing map by the detector MTF')

        try:

            mtf = np.loadtxt(options.mtf)

            ignore_mtf = False

        except ValueError:

            if options.mtf[-5:] == '.star':

                mtf = np.loadtxt(options.mtf, skiprows=4)

                ignore_mtf = False

            else:

                logger.warning('Could not read MTF file! Ignoring MTF')
                ignore_mtf = True

        if ignore_mtf == False:

            # We need to know the MTF values at the Fourier bins of our map. So we interpolate from the MTF description available:

            # For cubic volumes this is just half the box size multiplied by sqrt(2).
            NSAMfull = np.ceil(
                np.sqrt(np.sum(np.power(map1.shape, 2))) / 2.0 + 1).astype('int')
            freqfull = (np.arange(NSAMfull) / (2.0 * NSAM *
                                               options.angpix)).reshape(NSAMfull, 1)
            freqfull[0] = 1.0 / 999  # Just to avoid dividing by zero later

            interp_mtf = np.interp(
                freqfull, mtf[:, 0] / options.angpix, mtf[:, 1])

            # Divide Fourier components by the detector MTF:
            inv_mtf = 1.0 / interp_mtf

            fullmap = RadialFilter(fullmap, inv_mtf, return_filter=False)

            # Append the inverse MTF applied
            dat = np.append(dat, inv_mtf[:NSAM], axis=1)
            head += 'InverseMTF\t'

    # 4. Perform automatic sharpening based on the Guinier plot:

    ##### GUINIER PLOT #####
    if options.auto_bfac != None:

        # Here we use the same method as relion_postprocess. Note there is a difference in the normalization of the FFT, but that doesn't affect the results (only the intercept of fit).
        # NOTE: the bfactor.exe and EM-BFACTOR programs use a different fitting method.
        radamp = RadialProfile( fullmap, amps=True )[:NSAM] # We use the unmasked map to avoid overestimating the sharpening B-factor
        lnF = np.log(radamp)
        if minres <= 0:
            minres = 10.0
        if maxres <= 0:

            if not options.skip_fsc:

                if options.mw != None:

                    maxres = res_spw

                elif options.mask != None:

                    if options.randomize_below_fsc != None:

                        maxres = res_mask_true

                    else:

                        maxres = res_mask

                else:

                    maxres = res

            else:

              maxres = 2 * options.angpix
        logger.info('Estimating contrast decay (B-factor) from Guinier plot between %.2f A and %.2f A' % (float(minres), float(maxres[0])))

        hirange = 1. / freq <= minres
        lorange = 1. / freq >= maxres
        resrange = hirange * lorange
        resrange = resrange[:, 0]
        fit = np.polyfit(freq2[resrange, 0], lnF[resrange], deg=1)
        fitline = fit[0] * freq2 + fit[1]
        logger.info('Slope of fit: %.4f' % (fit[0]))
        logger.info('Intercept of fit: %.4f' % (fit[1]))
        logger.info('Correlation of fit: %.5f' %
              (np.corrcoef(lnF[resrange], fitline[resrange, 0])[0, 1]))
        logger.info('B-factor for contrast restoration: %.4f A^2' % (4.0 * fit[0]))

        fullmap = FilterBfactor(
            fullmap, apix=options.angpix, B=4.0 * fit[0], return_filter=False)
        # Just for appending to the output data file
        guinierfilt = np.exp(- fit[0] * freq2)
        # Append the B-factor filter derived from the Guinier plot
        dat = np.append(dat, guinierfilt[:NSAM], axis=1)
        head += 'Auto_B-factor\t'

        radampnew = RadialProfile(fullmap, amps=True)[:NSAM]
        lnFnew = np.log(radampnew)

        if options.cosine == False:

            logger.warning('You should probably specify --cosine or --tophat option to band-pass filter your map after sharpening!')

    # 5. Apply an ad-hoc B-factor for smoothing or sharpening the map, if provided:
    if options.adhoc_bfac != 0.0:
        logger.info('Applying ad-hoc B-factor to the map')

        fullmap = FilterBfactor(
            fullmap, apix=options.angpix, B=options.adhoc_bfac, return_filter=False)
        freq2 = freq * freq
        # Just for appending to the output data file
        bfacfilt = np.exp(- options.adhoc_bfac * freq2 / 4.0)

        # Append the ad-hoc B-factor filter applied
        dat = np.append(dat, bfacfilt[:NSAM], axis=1)
        head += 'Adhoc_B-factor\t'

        if options.cosine == False:

            logger.warning('You should probably specify --cosine or --tophat option to band-pass filter your map after sharpening!')

    if options.whiten:

        logger.info('Whitening the map')
        # Below, use ps=True to whiten the radial Power Spectrum (cisTEM) instead of the Amplitude Spectrum (IMAGIC). Results are visually almost identical, but whitening amplitudes seems to give a slightly more "peaky" (sharp) map as measured by kurtosis.
        whitened, filt = FilterWhiten(
            ne.evaluate( "fullmap * mask" ), ps=~options.whiten_amps, return_filter=True)
        fullmap = RadialFilter(fullmap, 1. / RadialProfile(filt))

    # 7. Impose a Gaussian or Cosine or Top-hat low-pass filter with cutoff at given resolution, or resolution determined from FSC threshold:
    if options.lowpass == 'auto' or options.lowpass >= 0.0 or options.highpass >= 0.0:

        if options.lowpass == 'auto':

            if options.mw != None:

                options.lowpass = res_spw

            elif options.mask != None:

                options.lowpass = res_mask

            else:

                options.lowpass = res

        # if options.highpass == 'auto':

        # 	options.highpass = 2.0 * ( NSAM - 1 ) * options.angpix / 3

        if options.highpass == 'auto':

            hipass_print = 2.0 * (NSAM - 1) * options.angpix
            options.highpass = -1

        else:

            hipass_print = options.highpass

        if options.lowpass <= 0.0:

            lopass_print = 2 * options.angpix

        else:

            lopass_print = options.lowpass

        logger.info('Band-pass filtering between resolution cutoffs %.3f A and %.3f A' %
              (float(hipass_print), float(lopass_print[0])))

        if options.gaussian:

            fullmap = FilterGauss(
                fullmap, apix=options.angpix, lp=options.lowpass, hp=options.highpass, return_filter=False)
            if options.lowpass <= 0.0:

                lp = np.ones(freq2[:, 0].shape)

            else:

                lp = np.exp(- options.lowpass ** 2 * freq2[:, 0])

            if options.highpass <= 0.0:

                hp = np.ones(freq2[:, 0].shape)

            else:

                hp = 1.0 - np.exp(- options.highpass ** 2 * freq2[:, 0])

            bp = hp * lp

        else:

            fullmap = FilterCosine(fullmap, apix=options.angpix, lp=options.lowpass,
                                        hp=options.highpass, return_filter=False, width=options.cosine_edge_width)

            if options.lowpass <= 0.0:

                lp = np.ones(freq2[:, 0].shape)

            else:

                cosrad = np.argmin(np.abs(1. / freq - options.lowpass))
                rii = cosrad + options.cosine_edge_width / 2
                rih = cosrad - options.cosine_edge_width / 2
                lp = np.zeros(freq[:, 0].shape)
                r = np.arange(len(freq))
                fill_idx = r <= rih
                lp[fill_idx] = 1.0
                rih_idx = r > rih
                rii_idx = r <= rii
                edge_idx = rih_idx * rii_idx
                lp[edge_idx] = (
                    1.0 + np.cos(np.pi * (r[edge_idx] - rih) / options.cosine_edge_width)) / 2.0

            if options.highpass <= 0.0:

                hp = np.ones(freq2[:, 0].shape)

            else:

                # The 1e-8 is just to ensure that the specified frequency is INCLUDED in the filter (not cancelled)
                cosrad = np.argmin(np.abs(1. / freq - options.highpass))
                rii = cosrad + options.cosine_edge_width / 2
                rih = cosrad - options.cosine_edge_width / 2
                hp = np.zeros(freq[:, 0].shape)
                r = np.arange(len(freq))
                fill_idx = r <= rih
                hp[fill_idx] = 1.0
                rih_idx = r > rih
                rii_idx = r <= rii
                edge_idx = rih_idx * rii_idx
                hp[edge_idx] = (
                    1.0 + np.cos(np.pi * (r[edge_idx] - rih) / options.cosine_edge_width)) / 2.0
                hp = 1.0 - hp

            bp = hp * lp

        # Append the band-pass filter applied
        dat = np.append(dat, bp.reshape(NSAM, 1), axis=1)
        head += 'Band-pass  \t'

    # 8. Apply mask, if provided:
    if options.mask != None or options.mw != None:
        # logger.info('Masking the map')
        masked = ne.evaluate( "fullmap * mask" )

        mrc.write(masked, options.out + '-masked.mrc', header=common_header)

    # Write filtered, unmasked map
    mrc.write(fullmap, options.out + '-unmasked.mrc', header=common_header)

    if not options.skip_fsc:

        # Save output file with all relevant FSC data
        np.savetxt(options.out + '_data.fsc', np.matrix(dat),
                   header=command + '\n' + head, delimiter='\t', fmt='%.6f')

if __name__ == "__main__":
    main()