#!/usr/bin/env python
# -*- coding: utf-8 -*-
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# pylint: disable=no-member
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# @Author: oesteban
# @Date:   2016-02-23 19:25:39
# @Email:  code@oscaresteban.es
# @Last Modified by:   oesteban
# @Last Modified time: 2018-03-12 11:44:09
"""

Measures for the spatial information
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Definitions are given in the
:ref:`summary of structural IQMs <iqms_t1w>`.

.. _iqms_efc:

- **Entropy-focus criterion** (:py:func:`~mriqc.qc.anatomical.efc`).

.. _iqms_fber:

- **Foreground-Background energy ratio** (:py:func:`~mriqc.qc.anatomical.fber`,  [Shehzad2015]_).

.. _iqms_fwhm:

- **Full-width half maximum smoothness** (``fwhm_*``).

.. _iqms_snr:

- **Signal-to-noise ratio** (:py:func:`~mriqc.qc.anatomical.snr`).

.. _iqms_summary:

- **Summary statistics** (:py:func:`~mriqc.qc.anatomical.summary_stats`).


Measures for the temporal information
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. _iqms_dvars:

- **DVARS** - D referring to temporal derivative of timecourses, VARS referring to
  RMS variance over voxels ([Power2012]_ ``dvars_nstd``) indexes the rate of change of
  BOLD signal across the entire brain at each frame of data. DVARS is calculated
  `with nipype <http://nipype.readthedocs.io/en/latest/interfaces/generated/\
nipype.algorithms.confounds.html#computedvars>`_ after motion correction:

  .. math ::

      \\text{DVARS}_t = \\sqrt{\\frac{1}{N}\\sum_i \\left[x_{i,t} - x_{i,t-1}\\right]^2}


  .. note ::

    Intensities are scaled to 1000 leading to the units being expressed in x10
    :math:`\\%\\Delta\\text{BOLD}` change.

  .. note ::

    MRIQC calculates two additional standardized values of the DVARS.
    The ``dvars_std`` metric is normalized with the standard deviation of the
    temporal difference time series. The ``dvars_vstd`` is a voxel-wise
    standardization of DVARS, where the temporal difference time series is
    normalized across time by that voxel standard deviation across time, before
    computing the RMS of the temporal difference [Nichols2013]_.

.. _iqms_gcor:

- **Global Correlation** (``gcor``) calculates an optimized summary of time-series
    correlation as in [Saad2013]_ using AFNI's ``@compute_gcor``:

  .. math ::

      \\text{GCOR} = \\frac{1}{N}\\mathbf{g}_u^T\\mathbf{g}_u

  where :math:`\\mathbf{g}_u` is the average of all unit-variance time series in a
  :math:`T` (\# timepoints) :math:`\\times` :math:`N` (\# voxels) matrix.

.. _iqms_tsnr:

- **Temporal SNR** (:abbr:`tSNR (temporal SNR)`, ``tsnr``) is a simplified
  interpretation of the tSNR definition [Kruger2001]_. We report the median value
  of the `tSNR map <http://nipype.readthedocs.io/en/latest/interfaces/generated/\
nipype.algorithms.confounds.html#tsnr>`_ calculated like:

  .. math ::

      \\text{tSNR} = \\frac{\\langle S \\rangle_t}{\\sigma_t},

  where :math:`\\langle S \\rangle_t` is the average BOLD signal (across time),
  and :math:`\\sigma_t` is the corresponding temporal standard-deviation map.


Measures for artifacts and other
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. _iqms_fd:

- **Framewise Displacement**: expresses instantaneous head-motion.
  MRIQC reports the average FD, labeled as ``fd_mean``.
  Rotational displacements are calculated as the displacement on the surface of a
  sphere of radius 50 mm [Power2012]_:

  .. math ::

      \\text{FD}_t = |\\Delta d_{x,t}| + |\\Delta d_{y,t}| + \
|\\Delta d_{z,t}| + |\\Delta \\alpha_t| + |\\Delta \\beta_t| + |\\Delta \\gamma_t|

  Along with the base framewise displacement, MRIQC reports the
  **number of timepoints above FD threshold** (``fd_num``), and the
  **percent of FDs above the FD threshold** w.r.t. the full timeseries (``fd_perc``).
  In both cases, the threshold is set at 0.20mm.

.. _iqms_gsr:

- **Ghost to Signal Ratio** (:py:func:`~mriqc.qc.functional.gsr`, labeled
  in the reports as ``gsr_x`` and ``gsr_y``):
  along the two possible phase-encoding axes **x**, **y**:

  .. math ::

      \\text{GSR} = \\frac{\\mu_G - \\mu_{NG}}{\\mu_S}

  .. image :: ../_static/epi-gsrmask.png
    :width: 200px
    :align: center

.. _iqms_aor:

- **AFNI's outlier ratio** (``aor``) - Mean fraction of outliers per fMRI volume
  as given by AFNI's ``3dToutcount``.

.. _iqms_aqi:

- **AFNI's quality index** (``aqi``) - Mean quality index as computed by AFNI's ``3dTqual``.

.. _iqms_dummy:

- **Number of *dummy* scans** (``dummy``) - A number of volumes in the begining of the
  fMRI timeseries identified as non-steady state.

.. topic:: References

  .. [Atkinson1997] Atkinson et al., *Automatic correction of motion artifacts
    in magnetic resonance images using an entropy
    focus criterion*, IEEE Trans Med Imag 16(6):903-910, 1997.
    doi:`10.1109/42.650886 <http://dx.doi.org/10.1109/42.650886>`_.

  .. [Friedman2008] Friedman, L et al., *Test--retest and between‐site reliability in a multicenter
    fMRI study*. Hum Brain Mapp, 29(8):958--972, 2008. doi:`10.1002/hbm.20440
    <http://dx.doi.org/10.1002/hbm.20440>`_.

  .. [Giannelli2010] Giannelli et al., *Characterization of Nyquist ghost in
    EPI-fMRI acquisition sequences implemented on two clinical 1.5 T MR scanner
    systems: effect of readout bandwidth and echo spacing*. J App Clin Med Phy,
    11(4). 2010.
    doi:`10.1120/jacmp.v11i4.3237 <http://dx.doi.org/10.1120/jacmp.v11i4.3237>`_.

  .. [Jenkinson2002] Jenkinson et al., *Improved Optimisation for the Robust and
    Accurate Linear Registration and Motion Correction of Brain Images*.
    NeuroImage, 17(2), 825-841, 2002.
    doi:`10.1006/nimg.2002.1132 <http://dx.doi.org/10.1006/nimg.2002.1132>`_.

  .. [Kruger2001] Krüger et al., *Physiological noise in oxygenation-sensitive
    magnetic resonance imaging*, Magn. Reson. Med. 46(4):631-637, 2001.
    doi:`10.1002/mrm.1240 <http://dx.doi.org/10.1002/mrm.1240>`_.

  .. [Nichols2013] Nichols, `Notes on Creating a Standardized Version of DVARS
      <http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research\
/nichols/scripts/fsl/standardizeddvars.pdf>`_, 2013.

  .. [Power2012] Power et al., *Spurious but systematic correlations in
    functional connectivity MRI networks arise from subject motion*,
    NeuroImage 59(3):2142-2154,
    2012, doi:`10.1016/j.neuroimage.2011.10.018
    <http://dx.doi.org/10.1016/j.neuroimage.2011.10.018>`_.

  .. [Saad2013] Saad et al. *Correcting Brain-Wide Correlation Differences
     in Resting-State FMRI*, Brain Conn 3(4):339-352,
     2013, doi:`10.1089/brain.2013.0156
     <http://dx.doi.org/10.1089/brain.2013.0156>`_.


mriqc.qc.functional module
^^^^^^^^^^^^^^^^^^^^^^^^^^

"""
import os.path as op
import numpy as np

RAS_AXIS_ORDER = {'x': 0, 'y': 1, 'z': 2}


def gsr(epi_data, mask, direction="y", ref_file=None, out_file=None):
    """
    Computes the :abbr:`GSR (ghost to signal ratio)` [Giannelli2010]_. The
    procedure is as follows:

      #. Create a Nyquist ghost mask by circle-shifting the original mask by :math:`N/2`.

      #. Rotate by :math:`N/2`

      #. Remove the intersection with the original mask

      #. Generate a non-ghost background

      #. Calculate the :abbr:`GSR (ghost to signal ratio)`


    .. warning ::

      This should be used with EPI images for which the phase
      encoding direction is known.

    :param str epi_file: path to epi file
    :param str mask_file: path to brain mask
    :param str direction: the direction of phase encoding (x, y, all)
    :return: the computed gsr

    """

    direction = direction.lower()
    if direction[-1] not in ['x', 'y', 'all']:
        raise Exception("Unknown direction {}, should be one of x, -x, y, -y, all".format(
            direction))

    if direction == 'all':
        result = []
        for newdir in ['x', 'y']:
            ofile = None
            if out_file is not None:
                fname, ext = op.splitext(ofile)
                if ext == '.gz':
                    fname, ext2 = op.splitext(fname)
                    ext = ext2 + ext
                ofile = '{0}_{1}{2}'.format(fname, newdir, ext)
            result += [gsr(epi_data, mask, newdir,
                           ref_file=ref_file, out_file=ofile)]
        return result

    # Roll data of mask through the appropriate axis
    axis = RAS_AXIS_ORDER[direction]
    n2_mask = np.roll(mask, mask.shape[axis] // 2, axis=axis)

    # Step 3: remove from n2_mask pixels inside the brain
    n2_mask = n2_mask * (1 - mask)

    # Step 4: non-ghost background region is labeled as 2
    n2_mask = n2_mask + 2 * (1 - n2_mask - mask)

    # Step 5: signal is the entire foreground image
    ghost = np.mean(epi_data[n2_mask == 1]) - np.mean(epi_data[n2_mask == 2])
    signal = np.median(epi_data[n2_mask == 0])
    return float(ghost / signal)
