# -*- Mode: python; tab-width: 4; indent-tabs-mode:nil; coding:utf-8 -*-
# vim: tabstop=4 expandtab shiftwidth=4 softtabstop=4 fileencoding=utf-8
#
# MDAnalysis --- https://www.mdanalysis.org
# Copyright (c) 2006-2017 The MDAnalysis Development Team and contributors
# (see the file AUTHORS for the full list of names)
#
# Released under the Lesser GNU Public Licence, v2.1 or any higher version
#
# Please cite your use of MDAnalysis in published work:
#
# R. J. Gowers, M. Linke, J. Barnoud, T. J. E. Reddy, M. N. Melo, S. L. Seyler,
# D. L. Dotson, J. Domanski, S. Buchoux, I. M. Kenney, and O. Beckstein.
# MDAnalysis: A Python package for the rapid analysis of molecular dynamics
# simulations. In S. Benthall and S. Rostrup editors, Proceedings of the 15th
# Python in Science Conference, pages 102-109, Austin, TX, 2016. SciPy.
# doi: 10.25080/majora-629e541a-00e
#
# N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein.
# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
# J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
#
import re

import numpy as np
import pytest
from numpy.testing import assert_equal, assert_almost_equal, assert_allclose

import MDAnalysis as mda
from MDAnalysis.analysis import helix_analysis as hel
from MDAnalysisTests.datafiles import (
    GRO,
    XTC,
    PSF,
    DCD,
    PDB_small,
    HELANAL_BENDING_MATRIX,
    HELANAL_BENDING_MATRIX_SUBSET,
    XYZ,
)

# reference data from old helix analysis of a single PDB file:
#   data = MDAnalysis.analysis.helanal.helanal_main(PDB_small,
#                    select="name CA and resnum 161-187")
# keys are renamed and local screw angles now use a different
# algorithm
HELANAL_SINGLE_DATA = {
    "global_tilts": np.rad2deg(1.3309656332019535),
    "local_heights summary": np.array(
        [1.5286051, 0.19648294, 0.11384312], dtype=np.float32
    ),
    "local_bends": np.array(
        [
            3.44526005,
            4.85425806,
            4.69548464,
            2.39473653,
            3.56172442,
            3.97128344,
            3.41563916,
            1.86140978,
            5.22997046,
            5.41381264,
            27.49601364,
            39.69839478,
            35.05921936,
            21.78928566,
            9.8632431,
            8.80066967,
            5.5344553,
            6.14356709,
            10.15450764,
            11.07686138,
            9.23541832,
        ],
        dtype=np.float32,
    ),
    "local_nres_per_turn summary": np.array([3.64864163, 0.152694, 0.1131402]),
    "local_twists summary": np.array(
        [98.83011627, 4.08171701, 3.07253003], dtype=np.float32
    ),
    "local_twists": np.array(
        [
            97.23709869,
            99.09676361,
            97.25350952,
            101.76019287,
            100.42689514,
            97.08784485,
            97.07430267,
            98.33553314,
            97.86578369,
            95.45792389,
            97.10089111,
            95.26415253,
            87.93136597,
            108.38458252,
            95.27167511,
            104.01931763,
            100.7199707,
            101.48034668,
            99.64170074,
            94.78946686,
            102.50147247,
            97.25154877,
            104.54204559,
            101.42829895,
        ],
        dtype=np.float32,
    ),
}


def read_bending_matrix(fn):
    """Read helanal_bending_matrix.dat into dict of numpy arrays.

    This is a quick and dirty parser with no error checking.

    Format::

      Mean
         0.0    5.7   10.9 ....
         .

      SD
        ....
        .

      ABDEV
       ....
       .

    Returns
    -------
       data : dict
           dictionary with keys 'Mean', 'SD', 'ABDEV' and NxN matrices.
    """
    data = {}
    current = None
    with open(fn) as bendingmatrix:
        for line in bendingmatrix:
            line = line.strip()
            if not line:
                continue
            if re.match(r"\D+", line):
                label = line.split()[0]
                current = data[label] = []
            else:
                current.append([float(x) for x in line.split()])
    for k, v in data.items():
        data[k] = np.array(v)
    return data


def test_local_screw_angles_plane_circle():
    """
    Test the trivial case of a circle in the xy-plane.
    The global axis is the x-axis and ref axis is the y-axis,
    so angles should be calculated to the xy-plane.
    """
    angdeg = np.arange(0, 360, 12, dtype=np.int32)
    angrad = np.deg2rad(angdeg, dtype=np.float64)
    xyz = np.array(
        [[np.cos(a), np.sin(a), 0] for a in angrad], dtype=np.float64
    )
    xyz[15, 1] = 0  # because np.sin(np.deg2rad(180)) = 1e-16 ?!
    screw = hel.local_screw_angles([1, 0, 0], [0, 1, 0], xyz)
    correct = np.zeros_like(angdeg)
    correct[(angdeg > 180)] = 180
    assert_almost_equal(screw, correct)


def test_local_screw_angles_ortho_circle():
    """
    Test the trivial case of a circle in the xy-plane.
    The global axis is the x-axis and ref axis is the z-axis,
    so angles should be calculated to the xz-plane.
    """
    angdeg = np.arange(0, 360, 12, dtype=np.int32)
    angrad = np.deg2rad(angdeg, dtype=np.float64)
    xyz = np.array(
        [[np.cos(a), np.sin(a), 0] for a in angrad], dtype=np.float64
    )
    xyz[15, 1] = 0  # because np.sin(np.deg2rad(180)) = 1e-16 ?!
    screw = hel.local_screw_angles([1, 0, 0], [0, 0, 1], xyz)
    correct = np.zeros_like(angdeg)
    correct[(angdeg < 180)] = 90
    correct[(angdeg > 180)] = -90
    correct[0] = correct[15] = 0
    assert_almost_equal(screw, correct)


def test_local_screw_angles_around_circle():
    """
    Test an orthogonal circle in the xz-plane.
    The global axis is the y-axis and ref axis is the x-axis,
    so angles should be calculated to the xy-plane.
    """
    # circle in xz-plane
    angdeg = np.arange(0, 360, 12, dtype=int)
    angrad = np.deg2rad(angdeg)
    xyz = np.array([[np.cos(a), 0, np.sin(a)] for a in angrad])
    screw = hel.local_screw_angles([0, 1, 0], [1, 0, 0], xyz)
    angdeg[-14:] = -angdeg[1:15][::-1]
    angdeg[-15] = 180
    assert_almost_equal(screw, angdeg)


def test_local_screw_angles_around_circle_rising():
    """
    Test a circle in the xz-plane, rising on the y-axis.
    The global axis is the y-axis and ref axis is the x-axis,
    so angles should be calculated to the xy-plane.
    The y-axis contribution should be removed so angles should
    be to the circle.
    """
    # circle in xz-plane
    angdeg = np.arange(0, 360, 12, dtype=int)
    angrad = np.deg2rad(angdeg)
    xyz = np.array([[np.cos(a), i, np.sin(a)] for i, a in enumerate(angrad)])
    screw = hel.local_screw_angles([0, 1, 0], [1, 0, 0], xyz)
    angdeg[-14:] = -angdeg[1:15][::-1]
    angdeg[-15] = 180
    assert_almost_equal(screw, angdeg)


def test_local_screw_angles_parallel_axes():
    """
    Test that if global_axis and ref_axis are parallel, it
    picks another one instead. global_axis is the x-axis,
    so the eventual replacement ref_axis should be the z-axis,
    so angles should be calculated to the xz-plane.
    """
    xyz = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
    angles = hel.local_screw_angles([1, 0, 0], [-1, 0, 0], xyz)
    assert_almost_equal(angles, [0, 90, 0])


@pytest.fixture()
def zigzag():
    r"""
    x-axis is from bottom to up in plane of screen
    z-axis is left to right ->
         x    x    x    x    x
        / \  / \  / \  / \  /
      x    x    x    x    x
    """
    n_atoms = 100
    u = mda.Universe.empty(
        100, atom_resindex=np.arange(n_atoms), trajectory=True
    )
    xyz = np.array(
        list(
            zip(
                [1, -1] * (n_atoms // 2),  # x \in {0, 1}
                [0] * n_atoms,  # y == 0
                range(n_atoms),
            )
        )
    )  # z rises continuously
    u.load_new(xyz)
    return u


@pytest.mark.parametrize(
    "ref_axis,screw_angles",
    [
        # input vectors zigzag between [-1, 0, 0] and [1, 0, 0]
        # global axis is z-axis
        ([0, 0, 1], [180, 0]),  # calculated to x-z plane
        ([1, 0, 0], [180, 0]),  # calculated to x-z plane
        ([-1, 0, 0], [0, 180]),  # calculated to x-z plane upside down
        ([0, 1, 0], [90, -90]),  # calculated to y-z plane
        ([0, -1, 0], [-90, 90]),  # calculated to x-z plane upside down
        # calculated to diagonal xy-z plane rotating around
        ([1, 1, 0], [135, -45]),
        ([-1, 1, 0], [45, -135]),
        ([1, -1, 0], [-135, 45]),
        ([-1, -1, 0], [-45, 135]),
        # calculated to diagonal xyz-z plane w/o z contribution
        ([1, 1, 1], [135, -45]),
        ([1, 1, -1], [135, -45]),
        ([1, -1, 1], [-135, 45]),
        ([-1, 1, 1], [45, -135]),
        ([-1, -1, 1], [-45, 135]),
        ([-1, -1, -1], [-45, 135]),
    ],
)
def test_helix_analysis_zigzag(zigzag, ref_axis, screw_angles):
    properties = hel.helix_analysis(zigzag.atoms.positions, ref_axis=ref_axis)
    assert_almost_equal(properties["local_twists"], 180, decimal=4)
    assert_almost_equal(properties["local_nres_per_turn"], 2, decimal=4)
    assert_almost_equal(properties["global_axis"], [0, 0, -1], decimal=4)
    # all 0 vectors
    assert_almost_equal(properties["local_axes"], 0, decimal=4)
    assert_almost_equal(properties["local_bends"], 0, decimal=4)
    assert_almost_equal(properties["all_bends"], 0, decimal=4)
    assert_almost_equal(properties["local_heights"], 0, decimal=4)
    assert_almost_equal(
        properties["local_helix_directions"][0::2],
        [[-1, 0, 0]] * 49,
        decimal=4,
    )
    assert_almost_equal(
        properties["local_helix_directions"][1::2], [[1, 0, 0]] * 49, decimal=4
    )
    origins = zigzag.atoms.positions[1:-1].copy()
    origins[:, 0] = 0
    assert_almost_equal(properties["local_origins"], origins, decimal=4)
    assert_almost_equal(
        properties["local_screw_angles"], screw_angles * 49, decimal=4
    )


def square_oct(n_rep=10):
    """
    square-octagon-square-octagon

    y- and z- coordinates create the square and octogon.
    x-coordinates increase continuously.
    """
    # square-octagon-square-octagon
    sq2 = 0.5**0.5
    square = [(1, 0), (0, 1), (-1, 0), (0, -1)]
    octagon = [
        (1, 0),
        (sq2, sq2),
        (0, 1),
        (-sq2, sq2),
        (-1, 0),
        (-sq2, -sq2),
        (0, -1),
        (sq2, -sq2),
    ]
    shapes = (square + octagon) * n_rep
    xyz = np.array(list(zip(np.arange(len(shapes)), *zip(*shapes))))
    n_atoms = len(xyz)
    u = mda.Universe.empty(n_atoms, trajectory=True)
    u.load_new(xyz)
    return u


def test_helix_analysis_square_oct():
    n_rep = 10
    u = square_oct(n_rep=n_rep)
    n_atoms = len(u.atoms)

    properties = hel.helix_analysis(u.atoms.positions, ref_axis=[0, 0, 1])
    twist_trans = [102.76438, 32.235607]
    twists = ([90] * 2 + twist_trans + [45] * 6 + twist_trans[::-1]) * n_rep
    assert_almost_equal(
        properties["local_twists"], twists[: n_atoms - 3], decimal=4
    )
    res_trans = [3.503159, 11.167775]
    res = ([4] * 2 + res_trans + [8] * 6 + res_trans[::-1]) * n_rep
    assert_almost_equal(
        properties["local_nres_per_turn"], res[: n_atoms - 3], decimal=4
    )
    assert_almost_equal(properties["global_axis"], [-1, 0, 0], decimal=3)
    assert_almost_equal(properties["local_axes"] - [1, 0, 0], 0, decimal=4)
    assert_almost_equal(properties["local_bends"], 0, decimal=4)
    assert_almost_equal(properties["all_bends"], 0, decimal=4)
    assert_almost_equal(properties["local_heights"], 1, decimal=4)

    loc_rot = [
        [0.0, 0.0, 1.0],
        [0.0, -1.0, 0.0],
        [0.0, 0.0, -1.0],
        [0.0, 0.97528684, 0.2209424],  # the transition square->oct
        [0.0, 0.70710677, 0.70710677],  # 0.5 ** 0.5
        [0.0, 0.0, 1.0],
        [0.0, -0.70710677, 0.70710677],
        [0.0, -1.0, 0.0],
        [0.0, -0.70710677, -0.70710677],
        [0.0, 0.0, -1.0],
        [0.0, 0.70710677, -0.70710677],
        [0.0, 0.97528684, -0.2209424],
    ] * n_rep
    assert_almost_equal(
        properties["local_helix_directions"], loc_rot[: n_atoms - 2], decimal=4
    )

    origins = u.atoms.positions.copy()[1:-1]
    origins[:, 1:] = (
        [
            [0.0, 0.0],  # square
            [0.0, 0.0],
            [0.0, -0.33318555],  # square -> octagon
            [-1.7878988, -0.6315732],  # square -> octagon
            [0.0, 0.0],  # octagon
            [0.0, 0.0],
            [0.0, 0.0],
            [0.0, 0.0],
            [0.0, 0.0],
            [0.0, 0.0],
            [-1.3141878, 1.3141878],  # octagon -> square
            [0.34966463, 0.14732757],
        ]
        * n_rep
    )[: len(origins)]
    assert_almost_equal(properties["local_origins"], origins, decimal=4)

    # calculated to the x-y plane
    # all input vectors (loc_rot) are in y-z plane
    screw = [
        0,
        90,
        180,  # square
        -77.236,  # transition
        -45,
        0,
        45,
        90,
        135,
        180,
        -135,  # octagon
        -102.764,
    ] * n_rep

    # not quite 0, comes out as 1.32e-06
    assert_almost_equal(
        properties["local_screw_angles"], screw[:-2], decimal=3
    )


class TestHELANAL(object):

    @pytest.fixture()
    def psf_ca(self):
        u = mda.Universe(PSF, DCD)
        ag = u.select_atoms("name CA")
        return ag

    @pytest.fixture()
    def helanal(self, psf_ca):
        ha = hel.HELANAL(
            psf_ca, select="resnum 161-187", flatten_single_helix=True
        )
        return ha.run(start=10, stop=80)

    def test_regression_summary(self, helanal):
        bends = helanal.results.summary["all_bends"]
        old_helanal = read_bending_matrix(HELANAL_BENDING_MATRIX_SUBSET)
        assert_almost_equal(
            np.triu(bends["mean"], 1), old_helanal["Mean"], decimal=1
        )
        assert_almost_equal(
            np.triu(bends["sample_sd"], 1), old_helanal["SD"], decimal=1
        )
        assert_almost_equal(
            np.triu(bends["abs_dev"], 1), old_helanal["ABDEV"], decimal=1
        )

    def test_regression_values(self):
        u = mda.Universe(PDB_small)
        ha = hel.HELANAL(
            u, select="name CA and resnum 161-187", flatten_single_helix=True
        )
        ha.run()

        for key, value in HELANAL_SINGLE_DATA.items():
            if "summary" in key:
                data = ha.results[key.split()[0]]
                calculated = [
                    data.mean(),
                    data.std(ddof=1),
                    np.fabs(data - data.mean()).mean(),
                ]
            else:
                calculated = ha.results[key][0]

            msg = "Mismatch between calculated and reference {}"
            assert_almost_equal(
                calculated, value, decimal=4, err_msg=msg.format(key)
            )

    def test_multiple_selections(self, psf_ca):
        ha = hel.HELANAL(
            psf_ca,
            flatten_single_helix=True,
            select=("resnum 30-40", "resnum 60-80"),
        )
        ha.run()
        n_frames = len(psf_ca.universe.trajectory)
        assert len(ha.atomgroups) == 2
        assert len(ha.results.summary) == 2
        assert len(ha.results.all_bends) == 2
        assert ha.results.all_bends[0].shape == (n_frames, 8, 8)
        assert ha.results.all_bends[1].shape == (n_frames, 18, 18)

    def test_universe_from_origins(self, helanal):
        u = helanal.universe_from_origins()
        assert isinstance(u, mda.Universe)
        assert len(u.atoms) == len(helanal.atomgroups[0]) - 2
        assert len(u.trajectory) == 70

    def test_universe_from_origins_except(self, psf_ca):
        ha = hel.HELANAL(psf_ca, select="resnum 161-187")
        with pytest.raises(ValueError, match=r"before universe_from_origins"):
            u = ha.universe_from_origins()

    def test_multiple_atoms_per_residues(self):
        u = mda.Universe(XYZ)
        with pytest.warns(UserWarning) as rec:
            ha = hel.HELANAL(u, select="name H")
        assert len(rec) == 1
        assert "multiple atoms" in rec[0].message.args[0]

    def test_residue_gaps_split(self, psf_ca):
        sel = "resid 6:50 or resid 100:130 or resid 132:148"
        with pytest.warns(UserWarning) as rec:
            ha = hel.HELANAL(psf_ca, select=sel).run()
            assert len(ha.atomgroups) == 3
            assert len(ha.atomgroups[0]) == 45
            assert len(ha.atomgroups[1]) == 31
            assert len(ha.atomgroups[2]) == 17
        assert len(rec) == 1
        warnmsg = rec[0].message.args[0]
        assert "has gaps in the residues" in warnmsg
        assert "Splitting into 3 helices" in warnmsg

    def test_residue_gaps_no_split(self, psf_ca):
        sel = "resid 6:50 or resid 100:130 or resid 132:148"
        with pytest.warns(UserWarning) as rec:
            ha = hel.HELANAL(psf_ca, select=sel, split_residue_sequences=False)
            ha.run()
            assert len(ha.atomgroups) == 1
            assert len(ha.atomgroups[0]) == 45 + 31 + 17
        assert len(rec) == 1
        warnmsg = rec[0].message.args[0]
        assert "has gaps in the residues" in warnmsg
        assert "Splitting into" not in warnmsg

    def test_len_groups_short(self, psf_ca):
        sel = "resnum 161-168"
        with pytest.warns(UserWarning, match="Fewer than 9 atoms found"):
            ha = hel.HELANAL(psf_ca, select=sel)
            assert len(ha.atomgroups) < 9

    @pytest.mark.parametrize(
        "ref_axis,screw_angles",
        [
            # input vectors zigzag between [-1, 0, 0] and [1, 0, 0]
            # global axis is z-axis
            ([0, 0, 1], [180, 0]),  # calculated to x-z plane
            ([1, 0, 0], [180, 0]),  # calculated to x-z plane
            ([-1, 0, 0], [0, 180]),  # calculated to x-z plane upside down
            ([0, 1, 0], [90, -90]),  # calculated to y-z plane
            ([0, -1, 0], [-90, 90]),  # calculated to x-z plane upside down
            # calculated to diagonal xy-z plane rotating around
            ([1, 1, 0], [135, -45]),
            ([-1, 1, 0], [45, -135]),
            ([1, -1, 0], [-135, 45]),
            ([-1, -1, 0], [-45, 135]),
            # calculated to diagonal xyz-z plane w/o z contribution
            ([1, 1, 1], [135, -45]),
            ([1, 1, -1], [135, -45]),
            ([1, -1, 1], [-135, 45]),
            ([-1, 1, 1], [45, -135]),
            ([-1, -1, 1], [-45, 135]),
            ([-1, -1, -1], [-45, 135]),
        ],
    )
    def test_helanal_zigzag(self, zigzag, ref_axis, screw_angles):
        ha = hel.HELANAL(
            zigzag, select="all", ref_axis=ref_axis, flatten_single_helix=True
        ).run()
        assert_almost_equal(ha.results.local_twists, 180, decimal=4)
        assert_almost_equal(ha.results.local_nres_per_turn, 2, decimal=4)
        assert_almost_equal(ha.results.global_axis, [[0, 0, -1]], decimal=4)
        # all 0 vectors
        assert_almost_equal(ha.results.local_axes, 0, decimal=4)
        assert_almost_equal(ha.results.local_bends, 0, decimal=4)
        assert_almost_equal(ha.results.all_bends, 0, decimal=4)
        assert_almost_equal(ha.results.local_heights, 0, decimal=4)
        assert_almost_equal(
            ha.results.local_helix_directions[0][0::2],
            [[-1, 0, 0]] * 49,
            decimal=4,
        )
        assert_almost_equal(
            ha.results.local_helix_directions[0][1::2],
            [[1, 0, 0]] * 49,
            decimal=4,
        )
        origins = zigzag.atoms.positions[1:-1].copy()
        origins[:, 0] = 0
        assert_almost_equal(ha.results.local_origins[0], origins, decimal=4)
        assert_almost_equal(
            ha.results.local_screw_angles[0], screw_angles * 49, decimal=4
        )


def test_vector_of_best_fit():
    line = np.random.rand(3)
    unit = line / np.linalg.norm(line)
    points = line * np.arange(1000)[:, np.newaxis]
    noise = np.random.normal(size=(1000, 3))
    data = points + noise

    vector = hel.vector_of_best_fit(data)
    cos = np.dot(vector, unit)
    assert_almost_equal(abs(cos), 1.0, decimal=5)
