# Copyright (c) 2014-2018 Michael Hirsch, Ph.D.
#
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"""
 Ported by Michael Hirsch to Python.
"""
import logging
from numpy import (atleast_1d,arctan,sqrt,tan,sign,sin,cos,arctan2,arcsin,
                   ones,empty,zeros,radians,degrees,tile,nan,pi)

def vdist(lat1,lon1,lat2,lon2):
    """
    Using the WGS-84 Earth ellipsoid, compute the distance between two points within a few millimeters of accuracy, compute forward azimuth, and compute backward azimuth, all using a vectorized version of Vincenty's algorithm::

        s = vdist(lat1,lon1,lat2,lon2)
        s,a12 = vdist(lat1,lon1,lat2,lon2)
        s,a12,a21 = vdist(lat1,lon1,lat2,lon2)


    s
         distance in meters (inputs may be scalars, vectors, or matrices)

    a12
         azimuth in degrees from first point to second point (forward)

    a21
         azimuth in degrees from second point to first point (backward)

    (Azimuths are in degrees clockwise from north.)

    lat1
        GEODETIC latitude of first point (degrees)

    lon1
        longitude of first point (degrees)

    lat2, lon2
        second point (degrees)

    Original algorithm source:
    T. Vincenty, "Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations", Survey Review, vol. 23, no. 176,
    April 1975, pp 88-93. Available at: http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf

    Notes:
     1. lat1,lon1,lat2,lon2 can be any (identical) size/shape. Outputs  will have the same size and shape.
     2. Error correcting code, convergence failure traps, antipodal corrections, polar error corrections, WGS84 ellipsoid parameters, testing, and comments: Michael Kleder, 2004.
     3. Azimuth implementation (including quadrant abiguity resolution) and code vectorization, Michael Kleder, Sep 2005.
     4. Vectorization is convergence sensitive; that is, quantities which have already converged to within tolerance are not recomputed during subsequent iterations (while other quantities are still converging).
     5. Vincenty describes his distance algorithm as precise to within 0.01 millimeters, subject to the ellipsoidal model.
     6. For distance calculations, essentially antipodal points are treated as exactly antipodal, potentially reducing accuracy slightly.
     7. Distance failures for points exactly at the poles are eliminated by moving the points by 0.6 millimeters.
     8. The Vincenty distance algorithm was transcribed verbatim by Peter Cederholm, August 12, 2003. It was modified and translated to English by Michael Kleder. Mr. Cederholm's website is http://www.plan.aau.dk/~pce/
     9. Distances agree with the Mapping Toolbox, version 2.2 (R14SP3) with a max relative difference of about 5e-9, except when the two points are nearly antipodal, and except when one point is near the equator and the two longitudes are nearly 180 degrees apart. This function (vdist) is more accurate in such cases.
        For example, note this difference (as of this writing)::

           vdist(0.2,305,15,125)

        > 18322827.0131551

        ::

            distance(0.2,305,15,125,[6378137 0.08181919])

        > 0
     10. Azimuths FROM the north pole (either forward starting at the north pole or backward when ending at the north pole) are set to 180 degrees by convention.
         Azimuths FROM the south pole are set to 0 degrees by convention.
     11. Azimuths agree with the Mapping Toolbox, version 2.2 (R14SP3) to within about a hundred-thousandth of a degree, except when traversing to or from a pole, where the convention for this function is described in (10), and except in the cases noted above in (9).
     12. No warranties; use at your own risk.

    """
#%% reshape inputs
    lat1 = atleast_1d(lat1)
    lat2 = atleast_1d(lat2)
    lon1 = atleast_1d(lon1)
    lon2 = atleast_1d(lon2)
    keepsize = lat1.shape
#%% Input check:
    if ((abs(lat1) > 90) | (abs(lat2) > 90)).any():
        raise ValueError('Input latitudes must be between -90 and 90 degrees, inclusive.')
#%%% Supply WGS84 earth ellipsoid axis lengths in meters:
    a = 6378137 # definitionally
    b = 6356752.31424518 # computed from WGS84 earth flattening coefficient
#%% preserve true input latitudes:
    lat1tr = lat1.copy()
    lat2tr = lat2.copy()
#%% convert inputs in degrees to radians:
    lat1 = radians(lat1)
    lon1 = radians(lon1)
    lat2 = radians(lat2)
    lon2 = radians(lon2)
#%% correct for errors at exact poles by adjusting 0.6 millimeters:
    kidx = abs(pi/2-abs(lat1)) < 1e-10;
    if kidx.any():
        lat1[kidx] = sign(lat1[kidx])*(pi/2-(1e-10))

    kidx = abs(pi/2-abs(lat2)) < 1e-10
    if kidx.any():
        lat2[kidx] = sign(lat2[kidx])*(pi/2-(1e-10))

    f = (a-b)/a
    U1 = arctan((1-f)*tan(lat1))
    U2 = arctan((1-f)*tan(lat2))
    lon1 = lon1 % (2*pi)
    lon2 = lon2 % (2*pi)
    L = abs(lon2-lon1)
    kidx = L > pi
    if kidx.any():
        L[kidx] = 2*pi - L[kidx]

    lamb = L.copy()  # NOTE: program will fail without copy!
    lambdaold = zeros(lat1.shape)
    itercount = 0
    notdone = ones(lat1.shape,dtype=bool)
    alpha = zeros(lat1.shape)
    sigma = zeros(lat1.shape)
    cos2sigmam = zeros(lat1.shape)
    C = zeros(lat1.shape)
    warninggiven = False
    sinsigma = empty(notdone.shape)
    cossigma = empty(notdone.shape)
    while notdone.any():  # force at least one execution
        #print('iter:',itercount)
        #print(f'lambda[21752] = {lamb[21752],20}')
        itercount += 1
        if itercount > 50:
            if not warninggiven:
                logging.warning('Essentially antipodal points encountered. Precision may be reduced slightly.')

            lamb[notdone] = pi
            break

        lambdaold[notdone] = lamb[notdone]

        sinsigma[notdone] = sqrt(
                (cos(U2[notdone])*sin(lamb[notdone]))**2+(cos(U1[notdone])*sin(U2[notdone])-sin(U1[notdone])*
            cos(U2[notdone])*cos(lamb[notdone]))**2)

        cossigma[notdone] = (sin(U1[notdone])*sin(U2[notdone])+
            cos(U1[notdone])*cos(U2[notdone])*cos(lamb[notdone]))
        # eliminate rare imaginary portions at limit of numerical precision:
        sinsigma[notdone]= sinsigma[notdone].real
        cossigma[notdone]= cossigma[notdone].real

        sigma[notdone] = arctan2(sinsigma[notdone],cossigma[notdone])

        alpha[notdone] = (arcsin(cos(U1[notdone])*cos(U2[notdone])*
            sin(lamb[notdone])/sin(sigma[notdone])))

        cos2sigmam[notdone] = (cos(sigma[notdone])-2*sin(U1[notdone])*
            sin(U2[notdone])/cos(alpha[notdone])**2)

        C[notdone] = f/16*cos(alpha[notdone])**2*(4+f*(4-3*cos(alpha[notdone])**2))

        lamb[notdone] = (L[notdone]+(1-C[notdone])*f*sin(alpha[notdone])
            *(sigma[notdone]+C[notdone]*sin(sigma[notdone])*
            (cos2sigmam[notdone]+C[notdone]*cos(sigma[notdone])*
            (-1+2.*cos2sigmam[notdone]**2))))
        #print(f'then, lambda(21752) = {lamb[21752],20})
        # correct for convergence failure in the case of essentially antipodal points
        if (lamb[notdone] > pi).any():
            logging.warning('Essentially antipodal points encountered. Precision may be reduced slightly.')
            warninggiven = True
            lambdaold[lamb>pi] = pi
            lamb[lamb>pi] = pi

        notdone = abs(lamb-lambdaold) > 1e-12

    u2 = cos(alpha)**2*(a**2-b**2)/b**2
    A = 1+u2/16384*(4096+u2*(-768+u2*(320-175*u2)))
    B = u2/1024*(256+u2*(-128+u2*(74-47*u2)))
    deltasigma = B*sin(sigma)*(cos2sigmam+B/4*(cos(sigma)*(-1+2*
        cos2sigmam**2)-B/6*cos2sigmam*(-3+4*sin(sigma)**2)*(-3+4*cos2sigmam**2)))

    dist_m = (b*A*(sigma-deltasigma)).reshape(keepsize)

#%% From point #1 to point #2
    # correct sign of lambda for azimuth calcs:
    lamb = abs(lamb)
    kidx=sign(sin(lon2-lon1)) * sign(sin(lamb)) < 0
    lamb[kidx] = -lamb[kidx]
    numer = cos(U2)*sin(lamb)
    denom = cos(U1)*sin(U2)-sin(U1)*cos(U2)*cos(lamb)
    a12 = arctan2(numer,denom)
    kidx = a12 < 0
    a12[kidx]=a12[kidx] + 2*pi
    #%% from poles
    a12[lat1tr <= -90] = 0
    a12[lat1tr >=  90] = pi
    az = degrees(a12).reshape(keepsize)

#%% From point #2 to point #1
    # correct sign of lambda for azimuth calcs:
    lamb = abs(lamb);
    kidx=sign(sin(lon1-lon2)) * sign(sin(lamb)) < 0
    lamb[kidx]=-lamb[kidx]
    numer = cos(U1)*sin(lamb)
    denom = sin(U1)*cos(U2)-cos(U1)*sin(U2)*cos(lamb)
    a21 = arctan2(numer,denom)
    kidx=a21<0;
    a21[kidx] = a21[kidx] + 2*pi
    #%% backwards from poles:
    a21[lat2tr >= 90] = pi
    a21[lat2tr <= -90] = 0.
    backaz = degrees(a21).reshape(keepsize)

    return dist_m.squeeze()[()], az.squeeze()[()], backaz.squeeze()[()]


def vreckon(lat1, lon1, rng, azim, ellipsoid=None):
    """
    Computes points at a specified azimuth and range in an ellipsoidal earth.
    Using the WGS-84 Earth ellipsoid, travel a given distance along a given azimuth starting at a given initial point,
    and return the endpoint within a few millimeters of accuracy, using Vincenty's algorithm.

    USAGE::

        lat2,lon2 = vreckon(lat1, lon1, rng, azim)

    Transmits ellipsoid definition (either as [a,b] or [a,f]) as fifth argument ELLIPSOID


    VARIABLES

    lat1
        inital latitude (degrees)

    lon1
        initial longitude (degrees)

    rng
        distance (meters). Scalar or a vector. Latter case computes a series of circles (or arc circles, see azim) centered on X,Y (which are scalars)

    azim
        intial azimuth (degrees). "azim" is a scalar or vector

    ellipsoid
        two-element ellipsoid vector. Either [a b] or [a f] If omitted, defaults to WGS-84

    lat2, lon2
        second point (degrees)

    a21
        reverse azimuth (degrees), at final point facing back toward the intial point

    :Original algorithm: T. Vincenty, "Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations", Survey Review, vol. 23, no. 176, April 1975, pp 88-93. http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf

    Notes:

      1. The Vincenty reckoning algorithm was transcribed verbatim into JavaScript by Chris Veness.
         It was modified and translated to Matlab by Michael Kleder.
         Mr. Veness's website is: http://www.movable-type.co.uk/scripts/latlong-vincenty-direct.html
      2. Error correcting code, polar error corrections, WGS84 ellipsoid parameters, testing, and comments by Michael Kleder.
      3. By convention, when starting at a pole, the longitude of the initial point (otherwise meaningless) determines the longitude line along which to traverse, and hence the longitude of the final point.
      4. The convention noted in (3) above creates a discrepancy with VDIST when the the intial or final point is at a pole. In the VDIST
         function, when traversing from a pole, the azimuth is  0 when
         heading away from the south pole and 180 when heading away from the north pole. In contrast, this VRECKON function uses the azimuth as noted in (3) above when traversing away form a pole.
      5. In testing, where the traversal subtends no more than 178 degrees, this function correctly inverts the VDIST function to within 0.2 millimeters of distance, 5e-10 degrees of forward azimuth,
         and 5e-10 degrees of reverse azimuth. Precision reduces as test
         points approach antipodal because the precision of VDIST is reduced
         for nearly antipodal points. (A warning is given by VDIST.)
      6. Tested but no warranty. Use at your own risk.
      7. Ver 1.0, Michael Kleder, November 2007. Ver 2.0, Joaquim Luis, September 2008

    Added ellipsoid and vectorized whenever possible. Also, lon2 is always converted to the [-180 180] interval.
    Joaquim Luis

    """

    lat1 = atleast_1d(lat1)
    lon1 = atleast_1d(lon1)
    rng = atleast_1d(rng)
    azim = atleast_1d(azim)

    assert abs(lat1) <= 90, (
        'VRECKON: Input lat. must be between -90 and 90 deg., inclusive.')
    if lat1.size != 1 and rng.size > 1:
        raise ValueError(
            'VRECKON: Variable ranges are only allowed for a single point.')
    if ellipsoid is not None:  # An ellipsoid vector (with a & b OR a & f)
        a = ellipsoid[0]           # b = ellipsoid(2);
        # Second ellipsoid argument contains flattening instead of minor axis
        if ellipsoid[1] < 1:
            f = ellipsoid[1]
            b = a * (1 - f)
        else:               # Second ellipsoid argument contains minor axis
            f = (a - ellipsoid[1]) / a
    else:   # Supply WGS84 earth ellipsoid axis lengths in meters:
        a = 6378137                 # semimajor axis
        b = 6356752.31424518   # WGS84 earth flattening coefficient definition
        f = (a - b) / a

    lat1 = radians(lat1)            # intial latitude in radians
    lon1 = radians(lon1)            # intial longitude in radians

    # correct for errors at exact poles by adjusting 0.6 millimeters:
    kidx = abs(pi / 2 - abs(lat1)) < 1e-10
    lat1[kidx] = sign(lat1[kidx]) * (pi / 2 - (1e-10))

    #  Allow for multiple circles starting from the same point
    if lat1.size == 1 and lon1.size == 1 and rng.size > 1:
        lat1 = tile(lat1, rng.shape)
        lon1 = tile(lon1, rng.shape)

    if rng.size == 1:
        rng = tile(rng, azim.shape)

    if azim.size == 1:
        azim = tile(azim, rng.shape)

    assert rng.size == azim.shape[0], (
        'Range must be a scalar or vector with the same shape as azim.')

    alpha1 = radians(azim)  # inital azimuth in radians
    sinAlpha1 = sin(alpha1)
    cosAlpha1 = cos(alpha1)

    tanU1 = (1 - f) * tan(lat1)
    cosU1 = 1 / sqrt(1 + tanU1 ** 2)
    sinU1 = tanU1 * cosU1
    sigma1 = arctan2(tanU1, cosAlpha1)
    sinAlpha = cosU1 * sinAlpha1
    cosSqAlpha = 1 - sinAlpha * sinAlpha
    uSq = cosSqAlpha * (a**2 - b**2) / b**2
    A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)))
    B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)))
    sigma = rng / (b * A)
    sigmaP = 2*pi

    if sigma.size == 1:
        sinSigma = nan
        cosSigma = nan
        cos2SigmaM = nan
        while abs(sigma - sigmaP) > 1e-12:
            cos2SigmaM = cos(2 * sigma1 + sigma)
            sinSigma = sin(sigma)
            cosSigma = cos(sigma)
            deltaSigma = (B * sinSigma *
                          (cos2SigmaM + B / 4 *
                           (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) -
                            B / 6 * cos2SigmaM *
                            (-3 + 4 * sinSigma * sinSigma) *
                            (-3 + 4 * cos2SigmaM * cos2SigmaM))))
            sigmaP = sigma
            sigma = rng / (b * A) + deltaSigma
    else:
        # This part is not vectorized
        cos2SigmaM = empty(sigma.shape)
        sinSigma = empty(sigma.shape)
        cosSigma = empty(sigma.shape)

        for k in range(sigma.size):
            while (abs(sigma[k] - sigmaP) > 1e-12).any():
                cos2SigmaM[k] = cos(2 * sigma1[k] + sigma[k])
                sinSigma[k] = sin(sigma[k])
                cosSigma[k] = cos(sigma[k])
                tmp = 2 * cos2SigmaM[k] * cos2SigmaM[k]
                deltaSigma = (B[k] * sinSigma[k] *
                              (cos2SigmaM[k] + B[k] / 4 *
                               (cosSigma[k] * (-1 + tmp) -
                                B[k] / 6 * cos2SigmaM[k] *
                                (-3 + 4 * sinSigma[k] * sinSigma[k]) *
                                  (-3 + 2 * tmp))))
                sigmaP = sigma[k]
                sigma[k] = rng[k] / (b * A[k]) + deltaSigma

    tmp = sinU1 * sinSigma - cosU1 * cosSigma * cosAlpha1
    lat2 = arctan2(sinU1 * cosSigma + cosU1 * sinSigma * cosAlpha1,
                   (1 - f) * sqrt(sinAlpha * sinAlpha + tmp**2))

    lamb = arctan2(sinSigma * sinAlpha1,
                   cosU1 * cosSigma - sinU1 * sinSigma * cosAlpha1)

    C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha))
    L = lamb - (f * (1 - C) *
                sinAlpha * (sigma + C * sinSigma *
                            (cos2SigmaM + C * cosSigma *
                             (-1 + 2 * cos2SigmaM * cos2SigmaM))))

    lon2 = degrees(lon1 + L)

    # Truncates angles into the [-pi pi] range
    # if (lon2 > pi).any():
    #    lon2 = pi*((absolute(lon2)/pi) -
    #       2*ceil(((absolute(lon2)/pi)-1)/2)) * sign(lon2)

    # lon2 = mod(lon2,360); % follow [0,360] convention
    lon2 = (lon2 + 180) % 360 - 180  # no parenthesis on RHS

    a21 = arctan2(sinAlpha, -tmp)
    a21 = 180. + degrees(a21)  # note direction reversal

    return degrees(lat2).squeeze()[()], lon2.squeeze()[()], a21.squeeze()[()] % 360.
