# Description: General-purpose functions for personal use.
# Author:      André Palóczy
# E-mail:      paloczy@gmail.com

__all__ = ['seasonal_avg',
           'seasonal_std',
           'deseason',
           'blkavg',
           'blkavgdir',
           'blkavgt',
           'blkapply',
           'stripmsk',
           'pydatetime2m_arr',
           'm2pydatetime_arr',
           'npdt2dt',
           'dt2sfloat',
           'doy2date',
           'flowfun',
           'cumsimp',
           'rot_vec',
           'avgdir',
           'lon180to360',
           'lon360to180',
           'bbox2ij',
           'xy2dist',
           'get_xtrackline',
           'get_arrdepth',
           'fpointsbox',
           'near',
           'near2',
           'mnear',
           'refine',
           'denan',
           'standardize',
           'linear_trend',
           'thomas',
           'point_in_poly',
           'get_mask_from_poly',
           'sphericalpolygon_area',
           'greatCircleBearing',
           'weim',
           'smoo2',
           'topo_slope',
           'curvature_geometric',
           'get_isobath',
           'angle_isobath',
           'isopyc_depth',
		   'whiten_zero',
           'wind2stress',
           'gen_dates',
           'fmt_isobath',
           'float2latex',
           'mat2npz',
           'bb_map',
           'dots_dualcolor']

from os import system
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
from matplotlib import path
from mpl_toolkits.basemap import Basemap
from datetime import datetime, timedelta
from dateutil import rrule, parser
from scipy.io import loadmat, savemat
from scipy import signal
from scipy.signal import savgol_filter
from glob import glob
from netCDF4 import Dataset, num2date, date2num
# from pandas import rolling_window # FIXME, new pandas way of doing this is, e.g., arr = Series(...).rolling(...).mean()
from pandas import Timestamp
from gsw import distance
from pygeodesy import Datums, VincentyError
from pygeodesy.ellipsoidalVincenty import LatLon as LatLon
from pygeodesy.sphericalNvector import LatLon as LatLon_sphere

def seasonal_avg(t, F):
    """
    USAGE
    -----
    F_seasonal = seasonal_avg(t, F)

    Calculates the seasonal average of variable F(t).
    Assumes 't' is a 'datetime.datetime' object.
    """
    tmo = np.array([ti.month for ti in t])
    ftmo = [tmo==mo for mo in range(1, 13)]

    return np.array([F[ft].mean() for ft in ftmo])

def seasonal_std(t, F):
    """
    USAGE
    -----
    F_seasonal = seasonal_std(t, F)

    Calculates the seasonal standard deviation of variable F(t).
    Assumes 't' is a 'datetime.datetime' object.
    """
    tmo = np.array([ti.month for ti in t])
    ftmo = [tmo==mo for mo in range(1, 13)]

    return np.array([F[ft].std() for ft in ftmo])

def deseason(t, F):
    """
    USAGE
    -----
    F_nonssn = deseason(t, F)

    Removes the seasonal signal of variable F(t).
    Assumes 't' is a 'datetime.datetime' object.
    Also assumes that F is sampled monthly and only for
    complete years (i.e., t.size is a multiple of 12).
    """
    Fssn = seasonal_avg(t, F)
    nyears = int(t.size/12)
    aux = np.array([])
    for n in range(nyears):
        aux = np.concatenate((aux, Fssn))

    return F - aux

def blkavg(x, y, every=2):
    """
    Block-averages a variable y(x). Returns its block average
    and standard deviation and new x axis.
    """
    nx = x.size
    xblk, yblk, yblkstd = np.array([]), np.array([]), np.array([])
    for i in range(every, nx+every, every):
        yi = y[i-every:i]
        xblk = np.append(xblk, np.nanmean(x[i-every:i]))
        yblk = np.append(yblk, np.nanmean(yi))
        yblkstd = np.append(yblkstd, np.nanstd(yi))

    return xblk, yblk, yblkstd

def blkavgdir(x, ydir, every=2, degrees=False, axis=None):
    """
    Block-averages a PERIODIC variable ydir(x). Returns its
    block average and new x axis.
    """
    nx = x.size
    xblk, yblk, yblkstd = np.array([]), np.array([]), np.array([])
    for i in range(every, nx+every, every):
        xblk = np.append(xblk, np.nanmean(x[i-every:i]))
        yblk = np.append(yblk, avgdir(ydir[i-every:i], degrees=degrees, axis=axis))

    return xblk, yblk

def blkavgt(t, x, every=2):
    """
    Block-averages a variable x(t). Returns its block average
    and the new t axis.
    """
    nt = t.size
    units = 'days since 01-01-01'
    calendar = 'proleptic_gregorian'
    t = date2num(t, units=units, calendar=calendar)
    tblk, xblk = np.array([]), np.array([])
    for i in range(every, nt+every, every):
        xi = x[i-every:i]
        tblk = np.append(tblk, np.nanmean(t[i-every:i]))
        xblk = np.append(xblk, np.nanmean(xi))

    tblk = num2date(tblk, units=units, calendar=calendar)
    return tblk, xblk

def blkapply(x, f, nblks, overlap=0, demean=False, detrend=False, verbose=True):
    """
    Divides array 'x' in 'nblks' blocks and applies function 'f' = f(x) on
    each block.
    """
    x = np.array(x)
    assert callable(f), "f must be a function"

    nx = x.size
    ni = int(nx/nblks)               # Number of data points in each chunk.
    y = np.zeros(ni)                 # Array that will receive each block.
    dn = int(round(ni - overlap*ni)) # How many indices to move forward with
                                     # each chunk (depends on the % overlap).
    # Demean/detrend the full record first (removes the lowest frequencies).
    # Then, also demean/detrend each block beffore applying f().
    if demean: x = x - x.mean()
    if detrend: x = signal.detrend(x, type='linear')

    n=0
    il, ir = 0, ni
    while ir<=nx:
        xn = x[il:ir]
        if demean: xn = xn - xn.mean()
        if detrend: xn = signal.detrend(xn, type='linear')
        y = y + f(xn) # Apply function and accumulate the current bock.
        il+=dn; ir+=dn
        n+=1

    y /= n         # Divide by number of blocks actually used.
    ncap = nx - il # Number of points left out at the end of array.

    if verbose:
        print("")
        print("Left last %d data points out (%.1f %% of all points)."%(ncap,100*ncap/nx))
        if overlap>0:
            print("")
            print("Intended %d blocks, but could fit %d blocks, with"%(nblks,n))
            print('overlap of %.1f %%, %d points per block.'%(100*overlap,dn))
        print("")

    return y

def stripmsk(arr, mask_invalid=False):
    if mask_invalid:
        arr = np.ma.masked_invalid(arr)
    if np.ma.isMA(arr):
        msk = arr.mask
        arr = arr.data
        arr[msk] = np.nan

    return arr

def pydatetime2m_arr(pydt_arr):
    pydt_arr = np.array(pydt_arr)
    secperyr = 86400.0
    timedt = timedelta(days=366)
    matdt = []
    for pydt in pydt_arr.tolist():
        m = pydt.toordinal() + timedt
        dfrac = pydt - datetime(pydt.year,pydt.month,pydt.day,0,0,0).seconds/secperyr
        matdt.append(m.toordinal() + dfrac)

    return np.array(matdt)

def m2pydatetime_arr(mdatenum_arr):
    mdatenum_arr = np.array(mdatenum_arr)
    timedt = timedelta(days=366)
    pydt = []
    for mdt in mdatenum_arr.tolist():
        d = datetime.fromordinal(int(mdt))
        dfrac = timedelta(days=mdt%1) - timedt
        pydt.append(d + dfrac)

    return np.array(pydt)

def npdt2dt(tnp):
    """
    USAGE
    -----
    t_datetime = npdt2dt(t_numpydatetime64)

    Convert an array of numpy.datetime64 timestamps to datetime.datetime.
    """
    return np.array([Timestamp(ti).to_pydatetime() for ti in tnp])

def dt2sfloat(t):
    """
    USAGE
    -----
    t_float = dt2sfloat(t_datetime)

    Convert an array of datetime.datetime timestamps to an array of floats
    representing elapsed seconds since the first timestamp.
    """
    t = np.array(t)
    t0 = t[0]

    return np.array([(tn - t0).total_seconds() for tn in t])

def doy2date(doy, year=2017):
    """
    USAGE
    -----
    t = doy2date(doy, year=2017)

    Convert an array `doy` of decimal yeardays to
    an array of datetime.datetime timestamps.
    """
    doy = np.array(doy)*86400 # [seconds/day].
    tunit = 'seconds since %d-01-01 00:00:00'%year

    return np.array([num2date(dn, tunit) for dn in doy])

def flowfun(x, y, u, v, variable='psi', geographic=True):
	"""
	FLOWFUN  Computes the potential PHI and the streamfunction PSI
	 of a 2-dimensional flow defined by the matrices of velocity
	 components U and V, so that

	       d(PHI)    d(PSI)          d(PHI)    d(PSI)
	  u =  -----  -  ----- ,    v =  -----  +  -----
	        dx        dy              dx        dy

	P = FLOWFUN(x,y,u,v) returns an array P of the same size as u and v,
	which can be the velocity potential (PHI) or the streamfunction (PSI)
	Because these scalar fields are defined up to the integration constant,
	their absolute values are such that PHI[0,0] = PSI[0,0] = 0.

	For a potential (irrotational) flow  PSI = 0, and the Laplacian
	of PSI is equal to the divergence of the velocity field.

	A solenoidal (non-divergent) flow can be described by the
	streamfunction alone, and the Laplacian of the streamfunction
	is equal to the vorticity (curl) of the velocity field.

	The units of the grid coordinates are assumed to be consistent
	with the units of the velocity components, e.g., [m] and [m/s].

	If variable=='psi', the streamfunction (PSI) is returned.

	If variable=='phi', the velocity potential (PHI) is returned.

	If geographic==True (default), (x,y) are assumed to be
	(longitude,latitude) and are converted to meters before
	computing (dx,dy).

	If geographic==False, (x,y) are assumed to be in meters.

	Uses function 'cumsimp()' (Simpson rule summation).

	Author: Kirill K. Pankratov, March 7, 1994.
	Source: http://www-pord.ucsd.edu/~matlab/stream.htm
	Translated to Python by André Palóczy, January 15, 2015.
	Modified by André Palóczy on January 15, 2015.
	"""
	x,y,u,v = map(np.asanyarray, (x,y,u,v))

	if not x.shape==y.shape==u.shape==v.shape:
		print("Error: Arrays (x, y, u, v) must be of equal shape.")
		return

	## Calculating grid spacings.
	if geographic:
		dlat, _ = np.gradient(y)
		_, dlon = np.gradient(x)
		deg2m = 111120.0                     # [m/deg]
		dx = dlon*deg2m*np.cos(y*np.pi/180.) # [m]
		dy = dlat*deg2m                      # [m]
	else:
		dy, _ = np.gradient(y)
		_, dx = np.gradient(x)

	ly, lx = x.shape                         # Shape of the (x,y,u,v) arrays.

	## Now the main computations.
	## Integrate velocity fields to get potential and streamfunction.
	## Use Simpson rule summation (function CUMSIMP).

	## Compute velocity potential PHI (non-rotating part).
	if variable=='phi':
		cx = cumsimp(u[0,:]*dx[0,:])         # Compute x-integration constant
		cy = cumsimp(v[:,0]*dy[:,0])         # Compute y-integration constant
		cx = np.expand_dims(cx, 0)
		cy = np.expand_dims(cy, 1)
		phiy = cumsimp(v*dy) + np.tile(cx, (ly,1))
		phix = cumsimp(u.T*dx.T).T + np.tile(cy, (1,lx))
		phi = (phix + phiy)/2.
		return phi

	## Compute streamfunction PSI (non-divergent part).
	if variable=='psi':
		cx = cumsimp(v[0,:]*dx[0,:])         # Compute x-integration constant
		cy = cumsimp(u[:,0]*dy[:,0])         # Compute y-integration constant
		cx = np.expand_dims(cx, 0)
		cy = np.expand_dims(cy, 1)
		psix = -cumsimp(u*dy) + np.tile(cx, (ly,1))
		psiy = cumsimp(v.T*dx.T).T - np.tile(cy, (1,lx))
		psi = (psix + psiy)/2.
		return psi

def cumsimp(y):
	"""
	F = CUMSIMP(Y)    Simpson-rule column-wise cumulative summation.
	Numerical approximation of a function F(x) such that
	Y(X) = dF/dX.  Each column of the input matrix Y represents
	the value of the integrand  Y(X)  at equally spaced points
	X = 0,1,...size(Y,1).
	The output is a matrix  F of the same size as Y.
	The first row of F is equal to zero and each following row
	is the approximation of the integral of each column of matrix
	Y up to the givem row.
	CUMSIMP assumes continuity of each column of the function Y(X)
	and uses Simpson rule summation.
	Similar to the command F = CUMSUM(Y), exept for zero first
	row and more accurate summation (under the assumption of
	continuous integrand Y(X)).

	Author: Kirill K. Pankratov, March 7, 1994.
	Source: http://www-pord.ucsd.edu/~matlab/stream.htm
	Translated to Python by André Palóczy, January 15, 2015.
	"""
	y = np.asanyarray(y)

	## 3-point interpolation coefficients to midpoints.
	## Second-order polynomial (parabolic) interpolation coefficients
	## from  Xbasis = [0 1 2]  to  Xint = [.5 1.5]
	c1 = 3/8.
	c2 = 6/8.
	c3 = -1/8.

	if y.ndim==1:
		y = np.expand_dims(y,1)
		f = np.zeros((y.size,1))    # Initialize summation array.
		squeeze_after = True
	elif y.ndim==2:
		f = np.zeros(y.shape)       # Initialize summation array.
		squeeze_after = False
	else:
		print("Error: Input array has more than 2 dimensions.")
		return

	if y.size==2:                   # If only 2 elements in columns - simple average.
		f[1,:] = (y[0,:] + y[1,:])/2.
		return f
	else:                           # If more than two elements in columns - Simpson summation.
		## Interpolate values of y to all midpoints.
		f[1:-1,:] = c1*y[:-2,:] + c2*y[1:-1,:] + c3*y[2:,:]
		f[2:,:] = f[2:,:] + c3*y[:-2,:] + c2*y[1:-1,:] + c1*y[2:,:]
		f[1,:] = f[1,:]*2
		f[-1,:] = f[-1,:]*2

		## Simpson (1,4,1) rule.
		f[1:,:] = 2*f[1:,:] + y[:-1,:] + y[1:,:]
		f = np.cumsum(f, axis=0)/6. # Cumulative sum, 6 - denominator from the Simpson rule.

	if squeeze_after:
		f = f.squeeze()

	return f

def rot_vec(u, v, angle=-45, degrees=True):
	"""
	USAGE
	-----
	u_rot,v_rot = rot_vec(u,v,angle=-45.,degrees=True)

	Returns the rotated vector components (`u_rot`,`v_rot`)
	from the zonal-meridional input vector components (`u`,`v`).
	The rotation is done using the angle `angle` positive counterclockwise
	(trigonometric convention). If `degrees` is set to `True``(default),
	then `angle` is converted to radians.
	is

	Example
	-------
	>>> from matplotlib.pyplot import quiver
	>>> from ap_tools.utils import rot_vec
	>>> u = -1.
	>>> v = -1.
	>>> u2,v2 = rot_vec(u,v, angle=-30.)
	"""
	u,v = map(np.asanyarray, (u,v))
	if degrees:
		angle = angle*np.pi/180. # Degrees to radians.

	u_rot = +u*np.cos(angle) + v*np.sin(angle) # Usually the across-shore component.
	v_rot = -u*np.sin(angle) + v*np.cos(angle) # Usually the along-shore component.

	return u_rot,v_rot

def avgdir(dirs, degrees=False, axis=None):
    """
    USAGE
    -----
    dirm = avgdir(dirs, degrees=False, axis=None)

    Calculate the mean direction of an array of directions 'dirs'.
    If 'degrees' is 'False' (default), the input directions must be
    in radians. If 'degrees' is 'True', the input directions must be
    in degrees.

    The direction angle is measured from the ZONAL axis, i.e.,
    (0, 90, -90) deg are (Eastward, Northward, Southward).
    180 and -180 deg are both Westward.

    If 'axis' is 'None' (default) the mean is calculated on the
    flattened array. Otherwise, 'axis' is the index of the axis
    to calculate the mean over.
    """
    dirs = np.array(dirs)

    if degrees:
        dirs = dirs*np.pi/180 # Degrees to radians.

    uxs = np.cos(dirs)
    vys = np.sin(dirs)
    dirm = np.arctan2(vys.sum(axis=axis), uxs.sum(axis=axis))

    if degrees:
        dirm = dirm*180/np.pi # From radians to degrees.

    return dirm

def lon180to360(lon):
	"""
	Converts longitude values in the range [-180,+180]
	to longitude values in the range [0,360].
	"""
	lon = np.asanyarray(lon)
	return (lon + 360.0) % 360.0

def lon360to180(lon):
	"""
	Converts longitude values in the range [0,360]
	to longitude values in the range [-180,+180].
	"""
	lon = np.asanyarray(lon)
	return ((lon + 180.) % 360.) - 180.

def bbox2ij(lon, lat, bbox=[-135., -85., -76., -64.], FIX_IDL=True):
    """
	USAGE
	-----
	ilon_start, ilon_end, jlat_start, jlat_end = bbox2ij(lon, lat, bbox=[-135., -85., -76., -64.], FIX_IDL=True)

    OR

    (ilon_start_left, ilon_end_left, jlat_start, jlat_end), (ilon_start_right, ilon_end_right, jlat_start, jlat_end) = ...
    ... bbox2ij(lon, lat, bbox=[-135., -85., -76., -64.], FIX_IDL=True)

    Return indices for i,j that will completely cover the specified bounding box. 'lon' and 'lat' are 2D coordinate arrays
    (generated by meshgrid), and 'bbox' is a list like [lon_start, lon_end, lat_start, lat_end] describing the desired
    longitude-latitude box.

    If the specified bbox is such that it crosses the edges of the longitude array, two tuples of indices are returned.
    The first (second) tuple traces out the left (right) part of the bbox.

    If FIX_IDL is set to 'True' (default), the indices returned correspond to the "short route" around the globe, which
    amounts to assuming that the specified bbox crosses the International Date. If FIX_IDL is set to 'False', the
    "long route" is used instead.

    Example
    -------
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> lon = np.arange(-180., 180.25, 0.25)
    >>> lat = np.arange(-90., 90.25, 0.25)
    >>> lon, lat = np.meshgrid(lon, lat)
    >>> h = np.sin(lon) + np.cos(lat)
    >>> i0, i1, j0, j1 = bbox2ij(lon, lat, bbox=[-71, -63., 39., 46])
    >>> h_subset = h[j0:j1,i0:i1]
    >>> lon_subset = lon[j0:j1,i0:i1]
    >>> lat_subset = lat[j0:j1,i0:i1]
    >>> fig, ax = plt.subplots()
    >>> ax.pcolor(lon_subset,lat_subset,h_subset)
    >>> plt.axis('tight')

    Original function downloaded from http://gis.stackexchange.com/questions/71630/subsetting-a-curvilinear-netcdf-file-roms-model-output-using-a-lon-lat-boundin
    Modified by André Palóczy on August 20, 2016 to handle bboxes that
    cross the International Date Line or the edges of the longitude array.
    """
    lon, lat, bbox = map(np.asanyarray, (lon, lat, bbox))

    # Test whether the wanted bbox crosses the International Date Line (brach cut of the longitude array).
    dlon = bbox[:2].ptp()
    IDL_BBOX=dlon>180.
    IDL_BBOX=np.logical_and(IDL_BBOX, FIX_IDL)

    mypath = np.array([bbox[[0,1,1,0]], bbox[[2,2,3,3]]]).T
    p = path.Path(mypath)
    points = np.vstack((lon.flatten(), lat.flatten())).T
    n, m = lon.shape
    inside = p.contains_points(points).reshape((n, m))

    # Fix mask if bbox goes throught the International Date Line.
    if IDL_BBOX:
        fcol=np.all(~inside, axis=0)
        flin=np.any(inside, axis=1)
        fcol, flin = map(np.expand_dims, (fcol, flin), (0, 1))
        fcol = np.tile(fcol, (n, 1))
        flin = np.tile(flin, (1, m))
        inside=np.logical_and(flin, fcol)
        print("Bbox crosses the International Date Line.")

    ii, jj = np.meshgrid(range(m), range(n))
    iiin, jjin = ii[inside], jj[inside]
    i0, i1, j0, j1 = min(iiin), max(iiin), min(jjin), max(jjin)

    SPLIT_BBOX=(i1-i0)==(m-1) # Test whether the wanted bbox crosses edges of the longitude array.

    # If wanted bbox crosses edges of the longitude array, return indices for the two boxes separately.
    if SPLIT_BBOX:
        Iiin = np.unique(iiin)
        ib0 = np.diff(Iiin).argmax()  # Find edge of the inner side of the left bbox.
        ib1 = ib0 + 1                 # Find edge of the inner side of the right bbox.
        Il, Ir = Iiin[ib0], Iiin[ib1] # Indices of the columns that bound the inner side of the two bboxes.
        print("Bbox crosses edges of the longitude array. Returning two sets of indices.")
        return (i0, Il, j0, j1), (Ir, i1, j0, j1)
    else:
        return i0, i1, j0, j1

def xy2dist(x, y, cyclic=False, datum='WGS84'):
    """
    USAGE
    -----
    d = xy2dist(x, y, cyclic=False, datum='WGS84')

    Calculates a distance axis from a line defined by longitudes and latitudes
    'x' and 'y', using either the Vicenty formulae on an ellipsoidal earth
    (ellipsoid defaults to WGS84) or on a sphere (if datum=='Sphere').

    Example
    -------
    >>> yi, yf = -23.550520, 32.71573800
    >>> xi, xf = -46.633309, -117.161084
    >>> x, y = np.linspace(xi, xf), np.linspace(yi, yf)
    >>> d_ellipse = xy2dist(x, y, datum='WGS84')[-1]*1e-3            # [km].
    >>> d_sphere = xy2dist(x, y, datum='Sphere')[-1]*1e-3            # [km].
    >>> dd = np.abs(d_ellipse - d_sphere)
    >>> dperc = 100*dd/d_ellipse
    >>> msg = 'Difference of %.1f km over a %.0f km-long line (%.3f %% difference)'%(dd, d_ellipse, dperc)
    >>> print(msg)
    """
    if datum!="Sphere":
        xy = [LatLon(y0, x0, datum=Datums[datum]) for x0, y0 in zip(x, y)]
    else:
        xy = [LatLon_sphere(y0, x0) for x0, y0 in zip(x, y)]
    d = np.array([xy[n].distanceTo(xy[n+1]) for n in range(len(xy)-1)])

    return np.append(0, np.cumsum(d))

def get_xtrackline(lon1, lon2, lat1, lat2, L=200, dL=10):
    """
    USAGE
    -----
    lonp, latp = get_xtrackline(lon1, lon2, lat1, lat2, L=200, dL=13)

    Generates a great-circle line with length 2L (with L in km) that is perpendicular to the great-circle line
    defined by the input points (lon1, lat1) and (lon2, lat2). The spacing between the points along the output
    line is dL km. Assumes a spherical Earth.
    """
    km2m = 1e3
    L, dL = L*km2m, dL*km2m
    nh = int(L/dL)

    p1, p2 = LatLon_sphere(lat1, lon1), LatLon_sphere(lat2, lon2)
    angperp = p1.initialBearingTo(p2) + 90
    angperpb = angperp + 180
    pm = p1.midpointTo(p2)

    # Create perpendicular line starting from the midpoint.
    N = range(1, nh + 1)
    pperp = []
    _ = [pperp.append(pm.destination(dL*n, angperpb)) for n in N]
    pperp.reverse()
    pperp.append(pm)
    _ = [pperp.append(pm.destination(dL*n, angperp)) for n in N]

    lonperp = np.array([p.lon for p in pperp])
    latperp = np.array([p.lat for p in pperp])

    return lonperp, latperp

def get_arrdepth(arr):
    """
    USAGE
    -----
    arr_depths = get_arrdepth(arr)

    Determine number of nested levels in each
    element of an array of arrays of arrays...
    (or other array-like objects).
    """
    arr = np.array(arr) # Make sure first level is an array.

    all_nlevs = []
    for i in range(arr.size):
        nlev=0
        wrk_arr = arr[i]
        while np.size(wrk_arr)>0:
            try:
                wrk_arr = np.array(wrk_arr[i])
            except Exception:
                all_nlevs.append(nlev)
                nlev=0
                break
            nlev+=1

    return np.array(all_nlevs)

def fpointsbox(x, y, fig, ax, nboxes=1, plot=True, pause_secs=5, return_index=True):
    """
    USAGE
    -----
    fpts = fpointsbox(x, y, fig, ax, nboxes=1, plot=True, pause_secs=5, return_index=True)

    Find points in a rectangle made with 2 ginput points.
    """
    fpts = np.array([])
    for n in range(nboxes):
        box = np.array(fig.ginput(n=2, timeout=0))
        try:
            xb, yb = box[:,0], box[:,1]
        except IndexError:
            print("No points selected. Skipping box \# %d."%(n+1))
            continue
        xl, xr, yd, yu = xb.min(), xb.max(), yb.min(), yb.max()
        xbox = np.array([xl, xr, xr, xl, xl])
        ybox = np.array([yd, yd, yu, yu, yd])
        fxbox, fybox = np.logical_and(x>xl, x<xr), np.logical_and(y>yd, y<yu)
        fptsi = np.logical_and(fxbox, fybox)
        if return_index:
            fptsi = np.where(fptsi)[0]
        fpts = np.append(fpts, fptsi)
        if plot:
            ax.plot(xbox, ybox, 'r', linestyle='solid', marker='o', ms=4)
            ax.plot(x[fptsi], y[fptsi], 'r', linestyle='none', marker='+', ms=5)
            plt.draw()
            fig.show()
        else:
            fig.close()

    if plot:
        plt.draw()
        fig.show()
        system("sleep %d"%pause_secs)

    return fpts

def near(x, x0, npts=1, return_index=False):
    """
    USAGE
    -----
    xnear = near(x, x0, npts=1, return_index=False)

    Finds 'npts' points (defaults to 1) in array 'x'
    that are closest to a specified 'x0' point.
    If 'return_index' is True (defauts to False),
    then the indices of the closest points are
    returned. The indices are ordered in order of
    closeness.
    """
    x = list(x)
    xnear = []
    xidxs = []
    for n in range(npts):
        idx = np.nanargmin(np.abs(np.array(x)-x0))
        xnear.append(x.pop(idx))
        if return_index:
            xidxs.append(idx)
    if return_index: # Sort indices according to the proximity of wanted points.
        xidxs = [xidxs[i] for i in np.argsort(xnear).tolist()]
    xnear.sort()

    if npts==1:
        xnear = xnear[0]
        if return_index:
            xidxs = xidxs[0]
    else:
        xnear = np.array(xnear)

    if return_index:
        return xidxs
    else:
        return xnear

def near2(x, y, x0, y0, npts=1, return_index=False):
    """
    USAGE
    -----
    xnear, ynear = near2(x, y, x0, y0, npts=1, return_index=False)

    Finds 'npts' points (defaults to 1) in arrays 'x' and 'y'
    that are closest to a specified '(x0, y0)' point. If
    'return_index' is True (defauts to False), then the
    indices of the closest point(s) are returned.

    Example
    -------
    >>> x = np.arange(0., 100., 0.25)
    >>> y = np.arange(0., 100., 0.25)
    >>> x, y = np.meshgrid(x, y)
    >>> x0, y0 = 44.1, 30.9
    >>> xn, yn = near2(x, y, x0, y0, npts=1)
    >>> print("(x0, y0) = (%f, %f)"%(x0, y0))
    >>> print("(xn, yn) = (%f, %f)"%(xn, yn))
    """
    x, y = map(np.array, (x, y))
    shp = x.shape

    xynear = []
    xyidxs = []
    dx = x - x0
    dy = y - y0
    dr = dx**2 + dy**2
    for n in range(npts):
        xyidx = np.unravel_index(np.nanargmin(dr), dims=shp)
        if return_index:
            xyidxs.append(xyidx)
        xyn = (x[xyidx], y[xyidx])
        xynear.append(xyn)
        dr[xyidx] = np.nan

    if npts==1:
        xynear = xynear[0]
        if return_index:
            xyidxs = xyidxs[0]

    if return_index:
        return xyidxs
    else:
        return xynear

def mnear(x, y, x0, y0):
	"""
	USAGE
	-----
	xmin,ymin = mnear(x, y, x0, y0)

	Finds the the point in a (lons,lats) line
	that is closest to a specified (lon0,lat0) point.
	"""
	x,y,x0,y0 = map(np.asanyarray, (x,y,x0,y0))
	point = (x0,y0)

	d = np.array([])
	for n in range(x.size):
		xn,yn = x[n],y[n]
		dn = distance((xn,x0),(yn,y0)) # Calculate distance point-wise.
		d = np.append(d,dn)

	idx = d.argmin()

	return x[idx],y[idx]

def refine(line, nref=100, close=True):
	"""
	USAGE
	-----
	ref_line = refine(line, nref=100, close=True)

	Given a 1-D sequence of points 'line', returns a
	new sequence 'ref_line', which is built by linearly
	interpolating 'nref' points between each pair of
	subsequent points in the original line.

	If 'close' is True (default), the first value of
	the original line is repeated at the end of the
	refined line, as in a closed polygon.
	"""
	line = np.squeeze(np.asanyarray(line))

	if close:
		line = np.append(line,line[0])

	ref_line = np.array([])
	for n in range(line.shape[0]-1):
		xi, xf = line[n], line[n+1]
		xref = np.linspace(xi,xf,nref)
		ref_line = np.append(ref_line, xref)

	return ref_line

def point_in_poly(x,y,poly):
	"""
	USAGE
	-----
	isinside = point_in_poly(x,y,poly)

	Determine if a point is inside a given polygon or not
	Polygon is a list of (x,y) pairs. This fuction
	returns True or False.  The algorithm is called
	'Ray Casting Method'.

	Source: http://pseentertainmentcorp.com/smf/index.php?topic=545.0
	"""
	n = len(poly)
	inside = False

	p1x,p1y = poly[0]
	for i in range(n+1):
		p2x,p2y = poly[i % n]
		if y > min(p1y,p2y):
			if y <= max(p1y,p2y):
				if x <= max(p1x,p2x):
					if p1y != p2y:
						xinters = (y-p1y)*(p2x-p1x)/(p2y-p1y)+p1x
					if p1x == p2x or x <= xinters:
						inside = not inside
		p1x,p1y = p2x,p2y

	return inside

def get_mask_from_poly(xp, yp, poly, verbose=False):
	"""
	USAGE
	-----

	mask = get_mask_from_poly(xp, yp, poly, verbose=False)

	Given two arrays 'xp' and 'yp' of (x,y) coordinates (generated by meshgrid)
	and a polygon defined by an array of (x,y) coordinates 'poly', with
	shape = (n,2), return a boolean array 'mask', where points that lie inside
	'poly' are set to 'True'.
	"""
	print('Building the polygon mask...')
	jmax, imax = xp.shape
	mask = np.zeros((jmax,imax))
	for j in range(jmax):
		if verbose:
			print("Row %s of %s"%(j+1,jmax))
		for i in range(imax):
			px, py = xp[j,i], yp[j,i]
			# Test if this point is within the polygon.
			mask[j,i] = point_in_poly(px, py, poly)

	return mask

def sphericalpolygon_area(lons, lats, R=6371000.):
	"""
	USAGE
	-----
	area = sphericalpolygon_area(lons, lats, R=6371000.)

	Calculates the area of a polygon on the surface of a sphere of
	radius R using Girard's Theorem, which states that the area of
	a polygon of great circles is R**2 times the sum of the angles
	between the polygons minus (N-2)*pi, where N is number of corners.
	R = 6371000 m (6371 km, default) is a typical value for the mean
	radius of the Earth.

	Source: http://stackoverflow.com/questions/4681737/how-to-calculate-the-area-of-a-polygon-on-the-earths-surface-using-python
	"""
	lons, lats = map(np.asanyarray, (lons, lats))
	N = lons.size

	angles = np.empty(N)
	for i in range(N):

	    phiB1, phiA, phiB2 = np.roll(lats, i)[:3]
	    LB1, LA, LB2 = np.roll(lons, i)[:3]

	    # calculate angle with north (eastward)
	    beta1 = greatCircleBearing(LA, phiA, LB1, phiB1)
	    beta2 = greatCircleBearing(LA, phiA, LB2, phiB2)

	    # calculate angle between the polygons and add to angle array
	    angles[i] = np.arccos(np.cos(-beta1)*np.cos(-beta2) + np.sin(-beta1)*np.sin(-beta2))

	return (np.sum(angles) - (N-2)*np.pi)*R**2

def greatCircleBearing(lon1, lat1, lon2, lat2):
	"""
	USAGE
	-----
	angle = greatCircleBearing(lon1, lat1, lon2, lat2)

	Calculates the angle (positive eastward) a
	great circle passing through points (lon1,lat1)
	and (lon2,lat2) makes with true nirth.

	Source: http://stackoverflow.com/questions/4681737/how-to-calculate-the-area-of-a-polygon-on-the-earths-surface-using-python
	"""
	lon1, lat1, lon2, lat2 = map(np.asanyarray, (lon1, lat1, lon2, lat2))
	dLong = lon1 - lon2
	d2r = np.pi/180.

	s = np.cos(d2r*lat2)*np.sin(d2r*dLong)
	c = np.cos(d2r*lat1)*np.sin(d2r*lat2) - np.sin(lat1*d2r)*np.cos(d2r*lat2)*np.cos(d2r*dLong)

	return np.arctan2(s, c)

def weim(x, N, kind='hann', badflag=-9999, beta=14):
	"""
	Usage
	-----
	xs = weim(x, N, kind='hann', badflag=-9999, beta=14)

	Description
	-----------
	Calculates the smoothed array 'xs' from the original array 'x' using the specified
	window of type 'kind' and size 'N'. 'N' must be an odd number.

	Parameters
	----------
	x       : 1D array
	        Array to be smoothed.

	N       : integer
	        Window size. Must be odd.

	kind    : string, optional
	        One of the window types available in the numpy module:

	        hann (default) : Gaussian-like. The weight decreases toward the ends. Its end-points are zeroed.
	        hamming        : Similar to the hann window. Its end-points are not zeroed, therefore it is
	                         discontinuous at the edges, and may produce undesired artifacts.
	        blackman       : Similar to the hann and hamming windows, with sharper ends.
	        bartlett       : Triangular-like. Its end-points are zeroed.
	        kaiser         : Flexible shape. Takes the optional parameter "beta" as a shape parameter.
	                         For beta=0, the window is rectangular. As beta increases, the window gets narrower.

	        Refer to the numpy functions for details about each window type.

	badflag : float, optional
	        The bad data flag. Elements of the input array 'A' holding this value are ignored.

	beta    : float, optional
	        Shape parameter for the kaiser window. For windows other than the kaiser window,
	        this parameter does nothing.

	Returns
	-------
	xs      : 1D array
	        The smoothed array.

	---------------------------------------
	André Palóczy Filho (paloczy@gmail.com)
	June 2012
	==============================================================================================================
	"""
	###########################################
	### Checking window type and dimensions ###
	###########################################
	kinds = ['hann', 'hamming', 'blackman', 'bartlett', 'kaiser']
	if ( kind not in kinds ):
		raise ValueError('Invalid window type requested: %s'%kind)

	if np.mod(N,2) == 0:
		raise ValueError('Window size must be odd')

	###########################
	### Creating the window ###
	###########################
	if ( kind == 'kaiser' ): # If the window kind is kaiser (beta is required).
		wstr = 'np.kaiser(N, beta)'
	else: # If the window kind is hann, hamming, blackman or bartlett (beta is not required).
		if kind == 'hann':
			kind = 'hanning'

	wstr = 'np.' + kind + '(N)'
	w = eval(wstr)

	x = np.asarray(x).flatten()
	Fnan = np.isnan(x).flatten()

	ln = (N-1)/2
	lx = x.size
	lf = lx - ln
	xs = np.nan*np.ones(lx)

	# Eliminating bad data from mean computation.
	fbad=x==badflag
	x[fbad] = np.nan

	for i in range(lx):
		if i <= ln:
			xx = x[:ln+i+1]
			ww = w[ln-i:]
		elif i >= lf:
			xx = x[i-ln:]
			ww = w[:lf-i-1]
		else:
			xx = x[i-ln:i+ln+1]
			ww = w.copy()

		f = ~np.isnan(xx) # Counting only NON-NaNs, both in the input array and in the window points.
		xx = xx[f]
		ww = ww[f]

		if f.sum() == 0: # Thou shalt not divide by zero.
			xs[i] = x[i]
		else:
			xs[i] = np.sum(xx*ww)/np.sum(ww)

		xs[Fnan] = np.nan # Assigning NaN to the positions holding NaNs in the input array.

	return xs

def smoo2(A, hei, wid, kind='hann', badflag=-9999, beta=14):
	"""
	Usage
	-----
	As = smoo2(A, hei, wid, kind='hann', badflag=-9999, beta=14)

	Description
	-----------
	Calculates the smoothed array 'As' from the original array 'A' using the specified
	window of type 'kind' and shape ('hei','wid').

	Parameters
	----------
	A       : 2D array
	        Array to be smoothed.

	hei     : integer
	        Window height. Must be odd and greater than or equal to 3.

	wid     : integer
	        Window width. Must be odd and greater than or equal to 3.

	kind    : string, optional
	        One of the window types available in the numpy module:

	        hann (default) : Gaussian-like. The weight decreases toward the ends. Its end-points are zeroed.
	        hamming        : Similar to the hann window. Its end-points are not zeroed, therefore it is
	                         discontinuous at the edges, and may produce undesired artifacts.
	        blackman       : Similar to the hann and hamming windows, with sharper ends.
	        bartlett       : Triangular-like. Its end-points are zeroed.
	        kaiser         : Flexible shape. Takes the optional parameter "beta" as a shape parameter.
	                         For beta=0, the window is rectangular. As beta increases, the window gets narrower.

	        Refer to the numpy functions for details about each window type.

	badflag : float, optional
	        The bad data flag. Elements of the input array 'A' holding this value are ignored.

	beta    : float, optional
	        Shape parameter for the kaiser window. For windows other than the kaiser window,
	        this parameter does nothing.

	Returns
	-------
	As      : 2D array
	        The smoothed array.

	---------------------------------------
	André Palóczy Filho (paloczy@gmail.com)
	April 2012
	==============================================================================================================
	"""
	###########################################
	### Checking window type and dimensions ###
	###########################################
	kinds = ['hann', 'hamming', 'blackman', 'bartlett', 'kaiser']
	if ( kind not in kinds ):
		raise ValueError('Invalid window type requested: %s'%kind)

	if ( np.mod(hei,2) == 0 ) or ( np.mod(wid,2)  == 0 ):
		raise ValueError('Window dimensions must be odd')

	if (hei <= 1) or (wid <= 1):
		raise ValueError('Window shape must be (3,3) or greater')

	##############################
	### Creating the 2D window ###
	##############################
	if ( kind == 'kaiser' ): # If the window kind is kaiser (beta is required).
		wstr = 'np.outer(np.kaiser(hei, beta), np.kaiser(wid, beta))'
	else: # If the window kind is hann, hamming, blackman or bartlett (beta is not required).
		if kind == 'hann':
			kind = 'hanning'

		# computing outer product to make a 2D window out of the original 1d windows.
		wstr = 'np.outer(np.' + kind + '(hei), np.' + kind + '(wid))'
		wdw = eval(wstr)

	A = np.asanyarray(A)
	Fnan = np.isnan(A)
	imax, jmax = A.shape
	As = np.nan*np.ones( (imax, jmax) )

	for i in range(imax):
		for j in range(jmax):
			### Default window parameters.
			wupp = 0
			wlow = hei
			wlef = 0
			wrig = wid
			lh = np.floor(hei/2)
			lw = np.floor(wid/2)

			### Default array ranges (functions of the i,j indices).
			upp = i-lh
			low = i+lh+1
			lef = j-lw
			rig = j+lw+1

			##################################################
			### Tiling window and input array at the edges ###
			##################################################
			# Upper edge.
			if upp < 0:
				wupp = wupp-upp
				upp = 0

			# Left edge.
			if lef < 0:
				wlef = wlef-lef
				lef = 0

			# Bottom edge.
			if low > imax:
				ex = low-imax
				wlow = wlow-ex
				low = imax

			# Right edge.
			if rig > jmax:
				ex = rig-jmax
				wrig = wrig-ex
				rig = jmax

			###############################################
			### Computing smoothed value at point (i,j) ###
			###############################################
			Ac = A[upp:low, lef:rig]
			wdwc = wdw[wupp:wlow, wlef:wrig]
			fnan = np.isnan(Ac)
			Ac[fnan] = 0; wdwc[fnan] = 0 # Eliminating NaNs from mean computation.
			fbad = Ac==badflag
			wdwc[fbad] = 0               # Eliminating bad data from mean computation.
			a = Ac * wdwc
			As[i,j] = a.sum() / wdwc.sum()

	As[Fnan] = np.nan # Assigning NaN to the positions holding NaNs in the input array.

	return As

def denan(arr):
	"""
	USAGE
	-----
	denaned_arr = denan(arr)

	Remove the NaNs from an array.
	"""
	f = np.isnan(arr)
	return arr[~f]

def standardize(series):
	"""
	USAGE
	-----
	series2 = standardize(series)

	Standardizes a series by subtracting its mean value
	and dividing by its standard deviation. The result is
	a dimensionless series. Inputs can be of type
	"np.array", or "Pandas.Series"/"Pandas.TimeSeries".
	"""
	Mean, Std = series.mean(), series.std()
	return (series - Mean)/Std

def linear_trend(series, return_line=True):
	"""
	USAGE
	-----
	line = linear_trend(series, return_line=True)

	OR

	b, a, x = linear_trend(series, return_line=False)

	Returns the linear fit (line = b*x + a) associated
	with the 'series' array.

	Adapted from pylab.detrend_linear.
	"""
	series = np.asanyarray(series)
	x = np.arange(series.size, dtype=np.float_)

	C = np.cov(x, series, bias=1) # Covariance matrix.
	b = C[0, 1]/C[0, 0] # Angular coefficient.

	a = series.mean() - b*x.mean() # Linear coefficient.
	line = b*x + a

	if return_line:
		return line
	else:
		return b, a, x

def thomas(A, b):
    """
    USAGE
    -----
    x = thomas(A,b)

    Solve Ax = b (where A is a tridiagonal matrix)
    using the Thomas Algorithm.

    References
    ----------
    For a step-by-step derivation of the algorithm, see
    e.g., http://www3.ul.ie/wlee/ms6021_thomas.pdf
    """
    # Step 1: Sweep rows from top to bottom,
    # calculating gammas and rhos along the way.
    N = b.size
    gam = [float(A[0,1]/A[0,0])]
    rho = [float(b[0]/A[0,0])]
    for i in range(0, N):
        rho.append(float((b[i] - A[i,i-1]*rho[-1])/(A[i,i] - A[i,i-1]*gam[-1])))
        if i<N-1: # No gamma in the last row.
            gam.append(float(A[i,i+1]/(A[i,i] - A[i,i-1]*gam[-1])))

    # Step 2: Substitute solutions for unknowns
    # starting from the bottom row all the way up.
    x = [] # Vector of unknowns.
    x.append(rho.pop()) # Last row is already solved.
    for i in range(N-2, -1, -1):
        x.append(float(rho.pop() - gam.pop()*x[-1]))

    x.reverse()
    return np.array(x)

def topo_slope(lon, lat, h):
	"""
	USAGE
	-----
	lons, lats, slope = topo_slope(lon, lat, h)

	Calculates bottom slope for a topography fields 'h' at
	coordinates ('lon', 'lat') using first-order finite differences.
	The output arrays have shape (M-1,L-1), where M,L = h.shape().
	"""
	lon,lat,h = map(np.asanyarray, (lon,lat,h))
	deg2m = 1852.*60.    # m/deg.
	deg2rad = np.pi/180. # rad/deg.

	x = lon*deg2m*np.cos(lat*deg2rad)
	y = lat*deg2m

	# First-order differences, accurate to O(dx) and O(dy),
	# respectively.
	sx = (h[:,1:] - h[:,:-1]) / (x[:,1:] - x[:,:-1])
	sy = (h[1:,:] - h[:-1,:]) / (y[1:,:] - y[:-1,:])

	# Finding the values of the derivatives sx and sy
	# at the same location in physical space.
	sx = 0.5*(sx[1:,:]+sx[:-1,:])
	sy = 0.5*(sy[:,1:]+sy[:,:-1])

	# Calculating the bottom slope.
	slope = np.sqrt(sx**2 + sy**2)

	# Finding the lon,lat coordinates of the
	# values of the derivatives sx and sy.
	lons = 0.5*(lon[1:,:]+lon[:-1,:])
	lats = 0.5*(lat[1:,:]+lat[:-1,:])
	lons = 0.5*(lons[:,1:]+lons[:,:-1])
	lats = 0.5*(lats[:,1:]+lats[:,:-1])

	return lons, lats, slope

def curvature_geometric(x, y):
	"""
	USAGE
	-----
	k = curvature_geometric(x, y)

	Estimates the curvature k of a 2D curve (x,y) using a geometric method.

	If your curve is given by two arrays, x and y, you can
	approximate its curvature at each point by the reciprocal of the
	radius of a circumscribing triangle with that point, the preceding
	point, and the succeeding point as vertices. The radius of such a
	triangle is one fourth the product of the three sides divided by its
	area.

	The curvature will be positive for curvature to the left and
	negative for curvature to the right as you advance along the curve.

	Note that if your data are too closely spaced together or subject
	to substantial noise errors, this formula will not be very accurate.

	Author: Roger Stafford
	Source: http://www.mathworks.com/matlabcentral/newsreader/view_thread/125637
	Translated to Python by André Palóczy, January 19, 2015.
	"""
	x,y = map(np.asanyarray, (x,y))

	x1 = x[:-2]; x2 = x[1:-1]; x3 = x[2:]
	y1 = y[:-2]; y2 = y[1:-1]; y3 = y[2:]
	## a, b, and c are the three sides of the triangle.
	a = np.sqrt((x3-x2)**2 + (y3-y2)**2)
	b = np.sqrt((x1-x3)**2 + (y1-y3)**2)
	c = np.sqrt((x2-x1)**2 + (y2-y1)**2)
	## A is the area of the triangle.
	A = 0.5*(x1*y2 + x2*y3 + x3*y1 - x1*y3 - x2*y1 - x3*y2)
	## The reciprocal of the circumscribed radius, i.e., the curvature.
	k = 4.0*A/(a*b*c)

	return np.squeeze(k)

def get_isobath(lon, lat, topo, iso, cyclic=False, smooth_isobath=False, window_length=21, win_type='barthann', **kw):
    """
    USAGE
    -----
    lon_isob, lat_isob = get_isobath(lon, lat, topo, iso, cyclic=False, smooth_isobath=False, window_length=21, win_type='barthann', **kw)

    Retrieves the 'lon_isob','lat_isob' coordinates of a wanted 'iso'
    isobath from a topography array 'topo', with 'lon_topo','lat_topo'
    coordinates.
    """
    lon, lat, topo = map(np.array, (lon, lat, topo))

    fig, ax = plt.subplots()
    cs = ax.contour(lon, lat, topo, [iso])
    coll = cs.collections[0]
    ## Test all lines to find thel ongest one.
    ## This is assumed to be the wanted isobath.
    ncoll = len(coll.get_paths())
    siz = np.array([])
    for n in range(ncoll):
        path = coll.get_paths()[n]
        siz = np.append(siz, path.vertices.shape[0])

    f = siz.argmax()
    xiso = coll.get_paths()[f].vertices[:, 0]
    yiso = coll.get_paths()[f].vertices[:, 1]
    plt.close()

    # Smooth the isobath with a moving window.
    # Periodize according to window length to avoid losing edges.
    if smooth_isobath:
        fleft = window_length//2
        fright = -window_length//2 + 1
        if cyclic:
            xl = xiso[:fleft] + 360
            xr = xiso[fright:] - 360
            yl = yiso[:fleft]
            yr = yiso[fright:]
            xiso = np.concatenate((xr, xiso, xl))
            yiso = np.concatenate((yr, yiso, yl))
            # xiso = rolling_window(xiso, window=window_length, win_type=win_type, center=True, **kw)[fleft:fright] # FIXME
            # yiso = rolling_window(yiso, window=window_length, win_type=win_type, center=True, **kw)[fleft:fright] # FIXME
        # else:
            # xiso = rolling_window(xiso, window=window_length, win_type=win_type, center=True, **kw) # FIXME
            # yiso = rolling_window(yiso, window=window_length, win_type=win_type, center=True, **kw) # FIXME

    return xiso, yiso

def angle_isobath(lon, lat, h, isobath=100, cyclic=False, smooth_isobath=True, window_length=21, win_type='barthann', plot_map=False, **kw):
    """
    USAGE
    -----
    lon_isob, lat_isob, angle = angle_isobath(lon, lat, h, isobath=100, cyclic=False, smooth_isobath=True, window_length=21, win_type='barthann', plot_map=False, **kw)

    Returns the coordinates ('lon_isob', 'lat_isob') and the angle an isobath
    makes with the zonal direction for a topography array 'h' at coordinates
    ('lon', 'lat'). Defaults to the 100 m isobath.

    If 'smooth_isobath'==True, smooths the isobath with a rolling window of type
    'win_type' and 'window_length' points wide.
    All keyword arguments are passed to 'pandas.rolling_window()'.

    If 'plot_map'==True, plots a map showing
    the isobath (and its soothed version if smooth_isobath==True).
    """
    lon, lat, h = map(np.array, (lon, lat, h))
    R = 6371000.0 # Mean radius of the earth in meters (6371 km), from gsw.constants.earth_radius.
    deg2rad = np.pi/180. # [rad/deg]

    # Extract isobath coordinates
    xiso, yiso = get_isobath(lon, lat, h, isobath)

    if cyclic: # Add cyclic point.
        xiso = np.append(xiso, xiso[0])
        yiso = np.append(yiso, yiso[0])

    # Smooth the isobath with a moving window.
    if smooth_isobath:
        xiso = rolling_window(xiso, window=window_length, win_type=win_type, **kw)
        yiso = rolling_window(yiso, window=window_length, win_type=win_type, **kw)

    # From the coordinates of the isobath, find the angle it forms with the
    # zonal axis, using points k+1 and k.
    shth = yiso.size-1
    theta = np.zeros(shth)
    for k in range(shth):
        dyk = R*(yiso[k+1]-yiso[k])
        dxk = R*(xiso[k+1]-xiso[k])*np.cos(yiso[k]*deg2rad)
        theta[k] = np.arctan2(dyk,dxk)

    xisom = 0.5*(xiso[1:] + xiso[:-1])
    yisom = 0.5*(yiso[1:] + yiso[:-1])

    # Plots map showing the extracted isobath.
    if plot_map:
        fig, ax = plt.subplots()
        m = bb_map([lon.min(), lon.max()], [lat.min(), lat.max()], projection='cyl', resolution='h', ax=ax)
        m.plot(xisom, yisom, color='b', linestyle='-', zorder=3, latlon=True)
        input("Press any key to continue.")
        plt.close()

    return xisom, yisom, theta

def isopyc_depth(z, dens0, isopyc=1027.75, dzref=1.):
    """
    USAGE
    -----
    hisopyc = isopyc_depth(z, dens0, isopyc=1027.75)

    Calculates the spatial distribution of the depth of a specified isopycnal 'isopyc'
    (defaults to 1027.75 kg/m3) from a 3D density array rho0 (in kg/m3) with shape
    (nz,ny,nx) and a 1D depth array 'z' (in m) with shape (nz).

    'dzref' is the desired resolution for the refined depth array (defaults to 1 m) which
    is generated for calculating the depth of the isopycnal. The smaller 'dzref', the smoother
    the resolution of the returned isopycnal depth array 'hisopyc'.
    """
    z, dens0 = map(np.asanyarray, (z, dens0))
    ny, nx = dens0.shape[1:]
    zref = np.arange(z.min(), z.max(), dzref)

    if np.ma.isMaskedArray(dens0):
        dens0 = np.ma.filled(dens0, np.nan)

    hisopyc = np.nan*np.ones((ny,nx))
    for j in range(ny):
        for i in range(nx):
            dens0ij = dens0[:,j,i]
            if np.logical_or(np.logical_or(isopyc<np.nanmin(dens0ij), np.nanmax(dens0ij)<isopyc), np.isnan(dens0ij).all()):
                continue
            else:
                dens0ref = np.interp(zref, z, dens0ij) # Refined density profile.
                dens0refn = near(dens0ref, isopyc)
                fz=dens0ref==dens0refn
                try:
                    hisopyc[j,i] = zref[fz]
                except ValueError:
                    print("Warning: More than 1 (%d) nearest depths found. Using the median of the depths for point (j=%d,i=%d)."%(fz.sum(), j, i))
                    hisopyc[j,i] = np.nanmedian(zref[fz])

    return hisopyc

def whiten_zero(x, y, z, ax, cs, n=1, cmap=plt.cm.RdBu_r, zorder=9):
	"""
	USAGE
	-----
	whiten_zero(x, y, z, ax, cs, n=1, cmap=plt.cm.RdBu_r, zorder=9)

	Changes to white the color of the 'n' (defaults to 1)
	neighboring patches about the zero contour created
	by a command like 'cs = ax.contourf(x, y, z)'.
	"""
	x, y, z = map(np.asanyarray, (x,y,z))
	white = (1.,1.,1.)
	cslevs = cs.levels
	assert 0. in cslevs
	f0=np.where(cslevs==0.)[0][0]
	f0m, f0p = f0-n, f0+n
	c0m, c0p = cslevs[f0m], cslevs[f0p]
	ax.contourf(x, y, z, levels=[c0m, c0p], linestyles='none', colors=[white, white], cmap=None, zorder=zorder)

def wind2stress(u, v, formula='large_pond1981-modified'):
	"""
	USAGE
	-----
	taux,tauy = wind2stress(u, v, formula='mellor2004')

	Converts u,v wind vector components to taux,tauy
	wind stress vector components.
	"""
	rho_air = 1.226            # kg/m3
	mag = np.sqrt(u**2+v**2)   # m/s
	Cd = np.zeros( mag.shape ) # Drag coefficient.

	if formula=='large_pond1981-modified':
		# Large and Pond (1981) formula
		# modified for light winds, as
		# in Trenberth et al. (1990).
		f=mag<=1.
		Cd[f] = 2.18e-3
		f=np.logical_and(mag>1.,mag<3.)
		Cd[f] = (0.62+1.56/mag[f])*1e-3
		f=np.logical_and(mag>=3.,mag<10.)
		Cd[f] = 1.14e-3
		f=mag>=10.
		Cd[f] = (0.49 + 0.065*mag[f])*1e-3
	elif formula=='mellor2004':
		Cd = 7.5e-4 + 6.7e-5*mag
	else:
		np.disp('Unknown formula for Cd.')
		pass

	# Computing wind stress [N/m2]
	taux = rho_air*Cd*mag*u
	tauy = rho_air*Cd*mag*v

	return taux,tauy

def gen_dates(start, end, dt='day', input_datetime=False):
	"""
	Returns a list of datetimes within the date range
	from `start` to `end`, at a `dt` time interval.

	`dt` can be 'second', 'minute', 'hour', 'day', 'week',
	'month' or 'year'.

	If `input_datetime` is False (default), `start` and `end`
	must be a date in string form. If `input_datetime` is True,
	`start` and `end` must be datetime objects.

	Note
	----
	Modified from original function
	by Filipe Fernandes (ocefpaf@gmail.com).

	Example
	-------
	>>> from ap_tools.utils import gen_dates
	>>> from datetime import datetime
	>>> start = '1989-08-19'
	>>> end = datetime.utcnow().strftime("%Y-%m-%d")
	>>> gen_dates(start, end, dt='day')
	"""
	DT = dict(second=rrule.SECONDLY,
		      minute=rrule.MINUTELY,
		      hour=rrule.HOURLY,
		      day=rrule.DAILY,
		      week=rrule.WEEKLY,
		      month=rrule.MONTHLY,
		      year=rrule.YEARLY)

	dt = DT[dt]

	if input_datetime: # Input are datetime objects. No parsing needed.
		dates = rrule.rrule(dt, dtstart=start, until=end)
	else:              # Input in string form, parse into datetime objects.
		dates = rrule.rrule(dt, dtstart=parser.parse(start), until=parser.parse(end))
	return list(dates)

def fmt_isobath(cs, fontsize=8, fmt='%g', inline=True, inline_spacing=7, manual=True, **kw):
	"""
	Formats the labels of isobath contours. `manual` is set to `True` by default,
	but can be `False`, or a tuple/list of tuples with the coordinates of the labels.
	All options are passed to plt.clabel().
	"""
	isobstrH = plt.clabel(cs, fontsize=fontsize, fmt=fmt, inline=inline, \
                          inline_spacing=inline_spacing, manual=manual, **kw)
	for ih in range(0, len(isobstrH)): # Appends 'm' for meters at the end of the label.
		isobstrh = isobstrH[ih]
		isobstr = isobstrh.get_text()
		isobstr = isobstr.replace('-','') + ' m'
		isobstrh.set_text(isobstr)

def float2latex(f, ndigits=1):
	"""
	USAGE
	-----
	texstr = float2latex(f, ndigits=1)

	Converts a float input into a latex-formatted
	string with 'ndigits' (defaults to 1).

	Adapted from:
	http://stackoverflow.com/questions/13490292/format-number-using-latex-notation-in-python
	"""
	float_str = "{0:.%se}"%ndigits
	float_str = float_str.format(f)
	base, exponent = float_str.split("e")
	return "${0} \times 10^{{{1}}}$".format(base, int(exponent))

def mat2npz(matname):
	"""
	USAGE
	-----
	mat2npz(matname)

	Extract variables stored in a .mat file,
	and saves them in a .npz file.
	"""
	d = loadmat(matname)
	_ = d.pop('__header__')
	_ = d.pop('__globals__')
	_ = d.pop('__version__')
	npzname = matname[:-4] + '.npz'
	np.savez(npzname,**d)
	return None

def bb_map(lons, lats, ax, projection='merc', resolution='i', drawparallels=True, drawmeridians=True):
	"""
	USAGE
	-----
	m = bb_map(lons, lats, **kwargs)

	Returns a Basemap instance with lon,lat bounding limits
	inferred from the input arrays `lons`,`lats`.
	Coastlines, countries, states, parallels and meridians
	are drawn, and continents are filled.
	"""
	lons,lats = map(np.asanyarray, (lons,lats))
	lonmin,lonmax = lons.min(),lons.max()
	latmin,latmax = lats.min(),lats.max()

	m = Basemap(llcrnrlon=lonmin,
				urcrnrlon=lonmax,
				llcrnrlat=latmin,
				urcrnrlat=latmax,
				projection=projection,
				resolution=resolution,
				ax=ax)

	plt.ioff() # Avoid showing the figure.
	m.fillcontinents(color='0.9', zorder=9)
	m.drawcoastlines(zorder=10)
	m.drawstates(zorder=10)
	m.drawcountries(linewidth=2.0, zorder=10)
	m.drawmapboundary(zorder=9999)
	if drawmeridians:
		m.drawmeridians(np.arange(np.floor(lonmin), np.ceil(lonmax), 1), linewidth=0.15, labels=[1, 0, 1, 0], zorder=12)
	if drawparallels:
		m.drawparallels(np.arange(np.floor(latmin), np.ceil(latmax), 1), linewidth=0.15, labels=[1, 0, 0, 0], zorder=12)
	plt.ion()
	return m

def dots_dualcolor(x, y, z, thresh=20., color_low='b', color_high='r', marker='o', markersize=5):
	"""
	USAGE
	-----
    dots_dualcolor(x, y, z, thresh=20., color_low='b', color_high='r')

	Plots dots colored with a dual-color criterion,
	separated by a threshold value.
	"""
	ax = plt.gca()
	# Below-threshold dots.
	f=z<=thresh
	ax.plot(x[f], y[f], lw=0, marker=marker, ms=markersize, mfc=color_low, mec=color_low)
	# Above-threshold dots.
	f=z>thresh
	ax.plot(x[f], y[f], lw=0, marker=marker, ms=markersize, mfc=color_high, mec=color_high)

if __name__=='__main__':
  import doctest
  doctest.testmod()


#!/usr/bin/env python2
# -*- coding: utf-8 -*-
"""
Created on Sun Jul 23 16:02:07 2017

@author: zqwu
"""

from __future__ import print_function
from __future__ import division
from __future__ import unicode_literals

import numpy as np
import deepchem as dc
import tempfile
from sklearn.svm import SVC

# Only for debug!
np.random.seed(123)

# Load Tox21 dataset
n_features = 1024
tox21_tasks, tox21_datasets, transformers = dc.molnet.load_tox21()
train_dataset, valid_dataset, test_dataset = tox21_datasets

# Fit models
metric = dc.metrics.Metric(dc.metrics.roc_auc_score, np.mean)

def model_builder(model_dir):
  sklearn_model = SVC(C=1.0, class_weight="balanced", probability=True)
  return dc.models.SklearnModel(sklearn_model, model_dir)

model_dir = tempfile.mkdtemp()
model = dc.models.SingletaskToMultitask(tox21_tasks, model_builder, model_dir)

# Fit trained model
model.fit(train_dataset)
model.save()

print("Evaluating model")
train_scores = model.evaluate(train_dataset, [metric], transformers)
valid_scores = model.evaluate(valid_dataset, [metric], transformers)

print("Train scores")
print(train_scores)

print("Validation scores")
print(valid_scores)


# -*- coding: utf-8 -*-

"""
The :mod:`sklearn.naive_bayes` module implements Naive Bayes algorithms. These
are supervised learning methods based on applying Bayes' theorem with strong
(naive) feature independence assumptions.
"""

# Author: Vincent Michel <vincent.michel@inria.fr>
#         Minor fixes by Fabian Pedregosa
#         Amit Aides <amitibo@tx.technion.ac.il>
#         Yehuda Finkelstein <yehudaf@tx.technion.ac.il>
#         Lars Buitinck <L.J.Buitinck@uva.nl>
#         Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
#         (parts based on earlier work by Mathieu Blondel)
#
# License: BSD 3 clause

from abc import ABCMeta, abstractmethod

import numpy as np
from scipy.sparse import issparse

from .base import BaseEstimator, ClassifierMixin
from .preprocessing import binarize
from .preprocessing import LabelBinarizer
from .preprocessing import label_binarize
from .utils import check_X_y, check_array
from .utils.extmath import safe_sparse_dot, logsumexp
from .utils.multiclass import _check_partial_fit_first_call
from .utils.fixes import in1d
from .utils.validation import check_is_fitted
from .externals import six

__all__ = ['BernoulliNB', 'GaussianNB', 'MultinomialNB']

class BaseNB(six.with_metaclass(ABCMeta, BaseEstimator, ClassifierMixin)):
    """Abstract base class for naive Bayes estimators"""

    @abstractmethod
    def _joint_log_likelihood(self, X):
        """Compute the unnormalized posterior log probability of X

        I.e. ``log P(c) + log P(x|c)`` for all rows x of X, as an array-like of
        shape [n_classes, n_samples].

        Input is passed to _joint_log_likelihood as-is by predict,
        predict_proba and predict_log_proba.
        """

    def predict(self, X):
        """
        Perform classification on an array of test vectors X.

        Parameters
        ----------
        X : array-like, shape = [n_samples, n_features]

        Returns
        -------
        C : array, shape = [n_samples]
            Predicted target values for X
        """
        jll = self._joint_log_likelihood(X)
        return self.classes_[np.argmax(jll, axis=1)]

    def predict_log_proba(self, X):
        """
        Return log-probability estimates for the test vector X.

        Parameters
        ----------
        X : array-like, shape = [n_samples, n_features]

        Returns
        -------
        C : array-like, shape = [n_samples, n_classes]
            Returns the log-probability of the samples for each class in
            the model. The columns correspond to the classes in sorted
            order, as they appear in the attribute `classes_`.
        """
        jll = self._joint_log_likelihood(X)
        # normalize by P(x) = P(f_1, ..., f_n)
        log_prob_x = logsumexp(jll, axis=1)
        return jll - np.atleast_2d(log_prob_x).T

    def predict_proba(self, X):
        """
        Return probability estimates for the test vector X.

        Parameters
        ----------
        X : array-like, shape = [n_samples, n_features]

        Returns
        -------
        C : array-like, shape = [n_samples, n_classes]
            Returns the probability of the samples for each class in
            the model. The columns correspond to the classes in sorted
            order, as they appear in the attribute `classes_`.
        """
        return np.exp(self.predict_log_proba(X))

class GaussianNB(BaseNB):
    """
    Gaussian Naive Bayes (GaussianNB)

    Can perform online updates to model parameters via `partial_fit` method.
    For details on algorithm used to update feature means and variance online,
    see Stanford CS tech report STAN-CS-79-773 by Chan, Golub, and LeVeque:

        http://i.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf

    Read more in the :ref:`User Guide <gaussian_naive_bayes>`.

    Attributes
    ----------
    class_prior_ : array, shape (n_classes,)
        probability of each class.

    class_count_ : array, shape (n_classes,)
        number of training samples observed in each class.

    theta_ : array, shape (n_classes, n_features)
        mean of each feature per class

    sigma_ : array, shape (n_classes, n_features)
        variance of each feature per class

    Examples
    --------
    >>> import numpy as np
    >>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
    >>> Y = np.array([1, 1, 1, 2, 2, 2])
    >>> from sklearn.naive_bayes import GaussianNB
    >>> clf = GaussianNB()
    >>> clf.fit(X, Y)
    GaussianNB()
    >>> print(clf.predict([[-0.8, -1]]))
    [1]
    >>> clf_pf = GaussianNB()
    >>> clf_pf.partial_fit(X, Y, np.unique(Y))
    GaussianNB()
    >>> print(clf_pf.predict([[-0.8, -1]]))
    [1]
    """

    def fit(self, X, y, sample_weight=None):
        """Fit Gaussian Naive Bayes according to X, y

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            Training vectors, where n_samples is the number of samples
            and n_features is the number of features.

        y : array-like, shape (n_samples,)
            Target values.

        sample_weight : array-like, shape (n_samples,), optional
            Weights applied to individual samples (1. for unweighted).

            .. versionadded:: 0.17
               Gaussian Naive Bayes supports fitting with *sample_weight*.

        Returns
        -------
        self : object
            Returns self.
        """
        X, y = check_X_y(X, y)
        return self._partial_fit(X, y, np.unique(y), _refit=True,
                                 sample_weight=sample_weight)

    @staticmethod
    def _update_mean_variance(n_past, mu, var, X, sample_weight=None):
        """Compute online update of Gaussian mean and variance.

        Given starting sample count, mean, and variance, a new set of
        points X, and optionally sample weights, return the updated mean and
        variance. (NB - each dimension (column) in X is treated as independent
        -- you get variance, not covariance).

        Can take scalar mean and variance, or vector mean and variance to
        simultaneously update a number of independent Gaussians.

        See Stanford CS tech report STAN-CS-79-773 by Chan, Golub, and LeVeque:

        http://i.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf

        Parameters
        ----------
        n_past : int
            Number of samples represented in old mean and variance. If sample
            weights were given, this should contain the sum of sample
            weights represented in old mean and variance.

        mu : array-like, shape (number of Gaussians,)
            Means for Gaussians in original set.

        var : array-like, shape (number of Gaussians,)
            Variances for Gaussians in original set.

        sample_weight : array-like, shape (n_samples,), optional
            Weights applied to individual samples (1. for unweighted).

        Returns
        -------
        total_mu : array-like, shape (number of Gaussians,)
            Updated mean for each Gaussian over the combined set.

        total_var : array-like, shape (number of Gaussians,)
            Updated variance for each Gaussian over the combined set.
        """
        if X.shape[0] == 0:
            return mu, var

        # Compute (potentially weighted) mean and variance of new datapoints
        if sample_weight is not None:
            n_new = float(sample_weight.sum())
            new_mu = np.average(X, axis=0, weights=sample_weight / n_new)
            new_var = np.average((X - new_mu) ** 2, axis=0,
                                 weights=sample_weight / n_new)
        else:
            n_new = X.shape[0]
            new_var = np.var(X, axis=0)
            new_mu = np.mean(X, axis=0)

        if n_past == 0:
            return new_mu, new_var

        n_total = float(n_past + n_new)

        # Combine mean of old and new data, taking into consideration
        # (weighted) number of observations
        total_mu = (n_new * new_mu + n_past * mu) / n_total

        # Combine variance of old and new data, taking into consideration
        # (weighted) number of observations. This is achieved by combining
        # the sum-of-squared-differences (ssd)
        old_ssd = n_past * var
        new_ssd = n_new * new_var
        total_ssd = (old_ssd + new_ssd +
                     (n_past / float(n_new * n_total)) *
                     (n_new * mu - n_new * new_mu) ** 2)
        total_var = total_ssd / n_total

        return total_mu, total_var

    def partial_fit(self, X, y, classes=None, sample_weight=None):
        """Incremental fit on a batch of samples.

        This method is expected to be called several times consecutively
        on different chunks of a dataset so as to implement out-of-core
        or online learning.

        This is especially useful when the whole dataset is too big to fit in
        memory at once.

        This method has some performance and numerical stability overhead,
        hence it is better to call partial_fit on chunks of data that are
        as large as possible (as long as fitting in the memory budget) to
        hide the overhead.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            Training vectors, where n_samples is the number of samples and
            n_features is the number of features.

        y : array-like, shape (n_samples,)
            Target values.

        classes : array-like, shape (n_classes,)
            List of all the classes that can possibly appear in the y vector.

            Must be provided at the first call to partial_fit, can be omitted
            in subsequent calls.

        sample_weight : array-like, shape (n_samples,), optional
            Weights applied to individual samples (1. for unweighted).

            .. versionadded:: 0.17

        Returns
        -------
        self : object
            Returns self.
        """
        return self._partial_fit(X, y, classes, _refit=False,
                                 sample_weight=sample_weight)

    def _partial_fit(self, X, y, classes=None, _refit=False,
                     sample_weight=None):
        """Actual implementation of Gaussian NB fitting.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            Training vectors, where n_samples is the number of samples and
            n_features is the number of features.

        y : array-like, shape (n_samples,)
            Target values.

        classes : array-like, shape (n_classes,)
            List of all the classes that can possibly appear in the y vector.

            Must be provided at the first call to partial_fit, can be omitted
            in subsequent calls.

        _refit: bool
            If true, act as though this were the first time we called
            _partial_fit (ie, throw away any past fitting and start over).

        sample_weight : array-like, shape (n_samples,), optional
            Weights applied to individual samples (1. for unweighted).

        Returns
        -------
        self : object
            Returns self.
        """
        X, y = check_X_y(X, y)

        # If the ratio of data variance between dimensions is too small, it
        # will cause numerical errors. To address this, we artificially
        # boost the variance by epsilon, a small fraction of the standard
        # deviation of the largest dimension.
        epsilon = 1e-9 * np.var(X, axis=0).max()

        if _refit:
            self.classes_ = None

        if _check_partial_fit_first_call(self, classes):
            # This is the first call to partial_fit:
            # initialize various cumulative counters
            n_features = X.shape[1]
            n_classes = len(self.classes_)
            self.theta_ = np.zeros((n_classes, n_features))
            self.sigma_ = np.zeros((n_classes, n_features))
            self.class_prior_ = np.zeros(n_classes)
            self.class_count_ = np.zeros(n_classes)
        else:
            if X.shape[1] != self.theta_.shape[1]:
                msg = "Number of features %d does not match previous data %d."
                raise ValueError(msg % (X.shape[1], self.theta_.shape[1]))
            # Put epsilon back in each time
            self.sigma_[:, :] -= epsilon

        classes = self.classes_

        unique_y = np.unique(y)
        unique_y_in_classes = in1d(unique_y, classes)

        if not np.all(unique_y_in_classes):
            raise ValueError("The target label(s) %s in y do not exist in the "
                             "initial classes %s" %
                             (y[~unique_y_in_classes], classes))

        for y_i in unique_y:
            i = classes.searchsorted(y_i)
            X_i = X[y == y_i, :]

            if sample_weight is not None:
                sw_i = sample_weight[y == y_i]
                N_i = sw_i.sum()
            else:
                sw_i = None
                N_i = X_i.shape[0]

            new_theta, new_sigma = self._update_mean_variance(
                self.class_count_[i], self.theta_[i, :], self.sigma_[i, :],
                X_i, sw_i)

            self.theta_[i, :] = new_theta
            self.sigma_[i, :] = new_sigma
            self.class_count_[i] += N_i

        self.sigma_[:, :] += epsilon
        self.class_prior_[:] = self.class_count_ / np.sum(self.class_count_)
        return self

    def _joint_log_likelihood(self, X):
        check_is_fitted(self, "classes_")

        X = check_array(X)
        joint_log_likelihood = []
        for i in range(np.size(self.classes_)):
            jointi = np.log(self.class_prior_[i])
            n_ij = - 0.5 * np.sum(np.log(2. * np.pi * self.sigma_[i, :]))
            n_ij -= 0.5 * np.sum(((X - self.theta_[i, :]) ** 2) /
                                 (self.sigma_[i, :]), 1)
            joint_log_likelihood.append(jointi + n_ij)

        joint_log_likelihood = np.array(joint_log_likelihood).T
        return joint_log_likelihood

class BaseDiscreteNB(BaseNB):
    """Abstract base class for naive Bayes on discrete/categorical data

    Any estimator based on this class should provide:

    __init__
    _joint_log_likelihood(X) as per BaseNB
    """

    def _update_class_log_prior(self, class_prior=None):
        n_classes = len(self.classes_)
        if class_prior is not None:
            if len(class_prior) != n_classes:
                raise ValueError("Number of priors must match number of"
                                 " classes.")
            self.class_log_prior_ = np.log(class_prior)
        elif self.fit_prior:
            # empirical prior, with sample_weight taken into account
            self.class_log_prior_ = (np.log(self.class_count_)
                                     - np.log(self.class_count_.sum()))
        else:
            self.class_log_prior_ = np.zeros(n_classes) - np.log(n_classes)

    def partial_fit(self, X, y, classes=None, sample_weight=None):
        """Incremental fit on a batch of samples.

        This method is expected to be called several times consecutively
        on different chunks of a dataset so as to implement out-of-core
        or online learning.

        This is especially useful when the whole dataset is too big to fit in
        memory at once.

        This method has some performance overhead hence it is better to call
        partial_fit on chunks of data that are as large as possible
        (as long as fitting in the memory budget) to hide the overhead.

        Parameters
        ----------
        X : {array-like, sparse matrix}, shape = [n_samples, n_features]
            Training vectors, where n_samples is the number of samples and
            n_features is the number of features.

        y : array-like, shape = [n_samples]
            Target values.

        classes : array-like, shape = [n_classes]
            List of all the classes that can possibly appear in the y vector.

            Must be provided at the first call to partial_fit, can be omitted
            in subsequent calls.

        sample_weight : array-like, shape = [n_samples], optional
            Weights applied to individual samples (1. for unweighted).

        Returns
        -------
        self : object
            Returns self.
        """
        X = check_array(X, accept_sparse='csr', dtype=np.float64)
        _, n_features = X.shape

        if _check_partial_fit_first_call(self, classes):
            # This is the first call to partial_fit:
            # initialize various cumulative counters
            n_effective_classes = len(classes) if len(classes) > 1 else 2
            self.class_count_ = np.zeros(n_effective_classes, dtype=np.float64)
            self.feature_count_ = np.zeros((n_effective_classes, n_features),
                                           dtype=np.float64)
        elif n_features != self.coef_.shape[1]:
            msg = "Number of features %d does not match previous data %d."
            raise ValueError(msg % (n_features, self.coef_.shape[-1]))

        Y = label_binarize(y, classes=self.classes_)
        if Y.shape[1] == 1:
            Y = np.concatenate((1 - Y, Y), axis=1)

        n_samples, n_classes = Y.shape

        if X.shape[0] != Y.shape[0]:
            msg = "X.shape[0]=%d and y.shape[0]=%d are incompatible."
            raise ValueError(msg % (X.shape[0], y.shape[0]))

        # label_binarize() returns arrays with dtype=np.int64.
        # We convert it to np.float64 to support sample_weight consistently
        Y = Y.astype(np.float64)
        if sample_weight is not None:
            sample_weight = np.atleast_2d(sample_weight)
            Y *= check_array(sample_weight).T

        class_prior = self.class_prior

        # Count raw events from data before updating the class log prior
        # and feature log probas
        self._count(X, Y)

        # XXX: OPTIM: we could introduce a public finalization method to
        # be called by the user explicitly just once after several consecutive
        # calls to partial_fit and prior any call to predict[_[log_]proba]
        # to avoid computing the smooth log probas at each call to partial fit
        self._update_feature_log_prob()
        self._update_class_log_prior(class_prior=class_prior)
        return self

    def fit(self, X, y, sample_weight=None):
        """Fit Naive Bayes classifier according to X, y

        Parameters
        ----------
        X : {array-like, sparse matrix}, shape = [n_samples, n_features]
            Training vectors, where n_samples is the number of samples and
            n_features is the number of features.

        y : array-like, shape = [n_samples]
            Target values.

        sample_weight : array-like, shape = [n_samples], optional
            Weights applied to individual samples (1. for unweighted).

        Returns
        -------
        self : object
            Returns self.
        """
        X, y = check_X_y(X, y, 'csr')
        _, n_features = X.shape

        labelbin = LabelBinarizer()
        Y = labelbin.fit_transform(y)
        self.classes_ = labelbin.classes_
        if Y.shape[1] == 1:
            Y = np.concatenate((1 - Y, Y), axis=1)

        # LabelBinarizer().fit_transform() returns arrays with dtype=np.int64.
        # We convert it to np.float64 to support sample_weight consistently;
        # this means we also don't have to cast X to floating point
        Y = Y.astype(np.float64)
        if sample_weight is not None:
            sample_weight = np.atleast_2d(sample_weight)
            Y *= check_array(sample_weight).T

        class_prior = self.class_prior

        # Count raw events from data before updating the class log prior
        # and feature log probas
        n_effective_classes = Y.shape[1]
        self.class_count_ = np.zeros(n_effective_classes, dtype=np.float64)
        self.feature_count_ = np.zeros((n_effective_classes, n_features),
                                       dtype=np.float64)
        self._count(X, Y)
        self._update_feature_log_prob()
        self._update_class_log_prior(class_prior=class_prior)
        return self

    # XXX The following is a stopgap measure; we need to set the dimensions
    # of class_log_prior_ and feature_log_prob_ correctly.
    def _get_coef(self):
        return (self.feature_log_prob_[1:]
                if len(self.classes_) == 2 else self.feature_log_prob_)

    def _get_intercept(self):
        return (self.class_log_prior_[1:]
                if len(self.classes_) == 2 else self.class_log_prior_)

    coef_ = property(_get_coef)
    intercept_ = property(_get_intercept)

class MultinomialNB(BaseDiscreteNB):
    """
    Naive Bayes classifier for multinomial models

    The multinomial Naive Bayes classifier is suitable for classification with
    discrete features (e.g., word counts for text classification). The
    multinomial distribution normally requires integer feature counts. However,
    in practice, fractional counts such as tf-idf may also work.

    Read more in the :ref:`User Guide <multinomial_naive_bayes>`.

    Parameters
    ----------
    alpha : float, optional (default=1.0)
        Additive (Laplace/Lidstone) smoothing parameter
        (0 for no smoothing).

    fit_prior : boolean
        Whether to learn class prior probabilities or not.
        If false, a uniform prior will be used.

    class_prior : array-like, size (n_classes,)
        Prior probabilities of the classes. If specified the priors are not
        adjusted according to the data.

    Attributes
    ----------
    class_log_prior_ : array, shape (n_classes, )
        Smoothed empirical log probability for each class.

    intercept_ : property
        Mirrors ``class_log_prior_`` for interpreting MultinomialNB
        as a linear model.

    feature_log_prob_ : array, shape (n_classes, n_features)
        Empirical log probability of features
        given a class, ``P(x_i|y)``.

    coef_ : property
        Mirrors ``feature_log_prob_`` for interpreting MultinomialNB
        as a linear model.

    class_count_ : array, shape (n_classes,)
        Number of samples encountered for each class during fitting. This
        value is weighted by the sample weight when provided.

    feature_count_ : array, shape (n_classes, n_features)
        Number of samples encountered for each (class, feature)
        during fitting. This value is weighted by the sample weight when
        provided.

    Examples
    --------
    >>> import numpy as np
    >>> X = np.random.randint(5, size=(6, 100))
    >>> y = np.array([1, 2, 3, 4, 5, 6])
    >>> from sklearn.naive_bayes import MultinomialNB
    >>> clf = MultinomialNB()
    >>> clf.fit(X, y)
    MultinomialNB(alpha=1.0, class_prior=None, fit_prior=True)
    >>> print(clf.predict(X[2:3]))
    [3]

    Notes
    -----
    For the rationale behind the names `coef_` and `intercept_`, i.e.
    naive Bayes as a linear classifier, see J. Rennie et al. (2003),
    Tackling the poor assumptions of naive Bayes text classifiers, ICML.

    References
    ----------
    C.D. Manning, P. Raghavan and H. Schuetze (2008). Introduction to
    Information Retrieval. Cambridge University Press, pp. 234-265.
    http://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html
    """

    def __init__(self, alpha=1.0, fit_prior=True, class_prior=None):
        self.alpha = alpha
        self.fit_prior = fit_prior
        self.class_prior = class_prior

    def _count(self, X, Y):
        """Count and smooth feature occurrences."""
        if np.any((X.data if issparse(X) else X) < 0):
            raise ValueError("Input X must be non-negative")
        self.feature_count_ += safe_sparse_dot(Y.T, X)
        self.class_count_ += Y.sum(axis=0)

    def _update_feature_log_prob(self):
        """Apply smoothing to raw counts and recompute log probabilities"""
        smoothed_fc = self.feature_count_ + self.alpha
        smoothed_cc = smoothed_fc.sum(axis=1)

        self.feature_log_prob_ = (np.log(smoothed_fc)
                                  - np.log(smoothed_cc.reshape(-1, 1)))

    def _joint_log_likelihood(self, X):
        """Calculate the posterior log probability of the samples X"""
        check_is_fitted(self, "classes_")

        X = check_array(X, accept_sparse='csr')
        return (safe_sparse_dot(X, self.feature_log_prob_.T)
                + self.class_log_prior_)

class BernoulliNB(BaseDiscreteNB):
    """Naive Bayes classifier for multivariate Bernoulli models.

    Like MultinomialNB, this classifier is suitable for discrete data. The
    difference is that while MultinomialNB works with occurrence counts,
    BernoulliNB is designed for binary/boolean features.

    Read more in the :ref:`User Guide <bernoulli_naive_bayes>`.

    Parameters
    ----------
    alpha : float, optional (default=1.0)
        Additive (Laplace/Lidstone) smoothing parameter
        (0 for no smoothing).

    binarize : float or None, optional
        Threshold for binarizing (mapping to booleans) of sample features.
        If None, input is presumed to already consist of binary vectors.

    fit_prior : boolean
        Whether to learn class prior probabilities or not.
        If false, a uniform prior will be used.

    class_prior : array-like, size=[n_classes,]
        Prior probabilities of the classes. If specified the priors are not
        adjusted according to the data.

    Attributes
    ----------
    class_log_prior_ : array, shape = [n_classes]
        Log probability of each class (smoothed).

    feature_log_prob_ : array, shape = [n_classes, n_features]
        Empirical log probability of features given a class, P(x_i|y).

    class_count_ : array, shape = [n_classes]
        Number of samples encountered for each class during fitting. This
        value is weighted by the sample weight when provided.

    feature_count_ : array, shape = [n_classes, n_features]
        Number of samples encountered for each (class, feature)
        during fitting. This value is weighted by the sample weight when
        provided.

    Examples
    --------
    >>> import numpy as np
    >>> X = np.random.randint(2, size=(6, 100))
    >>> Y = np.array([1, 2, 3, 4, 4, 5])
    >>> from sklearn.naive_bayes import BernoulliNB
    >>> clf = BernoulliNB()
    >>> clf.fit(X, Y)
    BernoulliNB(alpha=1.0, binarize=0.0, class_prior=None, fit_prior=True)
    >>> print(clf.predict(X[2:3]))
    [3]

    References
    ----------

    C.D. Manning, P. Raghavan and H. Schuetze (2008). Introduction to
    Information Retrieval. Cambridge University Press, pp. 234-265.
    http://nlp.stanford.edu/IR-book/html/htmledition/the-bernoulli-model-1.html

    A. McCallum and K. Nigam (1998). A comparison of event models for naive
    Bayes text classification. Proc. AAAI/ICML-98 Workshop on Learning for
    Text Categorization, pp. 41-48.

    V. Metsis, I. Androutsopoulos and G. Paliouras (2006). Spam filtering with
    naive Bayes -- Which naive Bayes? 3rd Conf. on Email and Anti-Spam (CEAS).
    """

    def __init__(self, alpha=1.0, binarize=.0, fit_prior=True,
                 class_prior=None):
        self.alpha = alpha
        self.binarize = binarize
        self.fit_prior = fit_prior
        self.class_prior = class_prior

    def _count(self, X, Y):
        """Count and smooth feature occurrences."""
        if self.binarize is not None:
            X = binarize(X, threshold=self.binarize)
        self.feature_count_ += safe_sparse_dot(Y.T, X)
        self.class_count_ += Y.sum(axis=0)

    def _update_feature_log_prob(self):
        """Apply smoothing to raw counts and recompute log probabilities"""
        smoothed_fc = self.feature_count_ + self.alpha
        smoothed_cc = self.class_count_ + self.alpha * 2

        self.feature_log_prob_ = (np.log(smoothed_fc)
                                  - np.log(smoothed_cc.reshape(-1, 1)))

    def _joint_log_likelihood(self, X):
        """Calculate the posterior log probability of the samples X"""
        check_is_fitted(self, "classes_")

        X = check_array(X, accept_sparse='csr')

        if self.binarize is not None:
            X = binarize(X, threshold=self.binarize)

        n_classes, n_features = self.feature_log_prob_.shape
        n_samples, n_features_X = X.shape

        if n_features_X != n_features:
            raise ValueError("Expected input with %d features, got %d instead"
                             % (n_features, n_features_X))

        neg_prob = np.log(1 - np.exp(self.feature_log_prob_))
        # Compute  neg_prob · (1 - X).T  as  ∑neg_prob - X · neg_prob
        jll = safe_sparse_dot(X, (self.feature_log_prob_ - neg_prob).T)
        jll += self.class_log_prior_ + neg_prob.sum(axis=1)

        return jll