pywafo/wafo/kdetools/gridding.py

'''
Created on 15. des. 2016

@author: pab
'''
from __future__ import division
from scipy import sparse
import numpy as np
from wafo.testing import test_docstrings
from itertools import product

__all__ = ['accum',  'gridcount']


def bitget(int_type, offset):
    """Returns the value of the bit at the offset position in int_type.

    Example
    -------
    >>> bitget(5, np.r_[0:4])
    array([1, 0, 1, 0])

    """
    return np.bitwise_and(int_type, 1 << offset) >> offset


def accumsum(accmap, a, shape, dtype=None):
    """
    Example
    -------
    >>> from numpy import array
    >>> a = array([[1,2,3],[4,-1,6],[-1,8,9]])
    >>> a
    array([[ 1,  2,  3],
           [ 4, -1,  6],
           [-1,  8,  9]])
    >>> # Sum the diagonals.
    >>> accmap = array([[0,1,2],[2,0,1],[1,2,0]])
    >>> s = accumsum(accmap, a, (3,))
    >>> np.allclose(s.toarray().T, [ 9,  7, 15])
    True

    """
    if dtype is None:
        dtype = a.dtype
    shape = np.atleast_1d(shape)
    if len(shape) > 1:
        binx = accmap[:, 0]
        biny = accmap[:, 1]
        out = sparse.coo_matrix(
            (a.ravel(), (binx, biny)), shape=shape, dtype=dtype).tocsr()
    else:
        binx = accmap.ravel()
        zero = np.zeros(len(binx))
        out = sparse.coo_matrix(
            (a.ravel(), (binx, zero)), shape=(shape, 1), dtype=dtype).tocsr()
    return out


def accumsum2(accmap, a, shape):
    """
    Example
    -------
    >>> from numpy import array
    >>> a = array([[1,2,3],[4,-1,6],[-1,8,9]])
    >>> a
    array([[ 1,  2,  3],
           [ 4, -1,  6],
           [-1,  8,  9]])

    >>> accmap = array([[0,1,2],[2,0,1],[1,2,0]])  # Sum the diagonals.
    >>> s = accumsum2(accmap, a, (3,))
    >>> np.allclose(s, [ 9,  7, 15])
    True

    """
    return np.bincount(accmap.ravel(), a.ravel(), np.array(shape).max())


def accum(accmap, a, func=None, shape=None, fill_value=0, dtype=None):
    """An accumulation function similar to Matlab's `accumarray` function.

    Parameters
    ----------
    accmap : ndarray
        This is the "accumulation map".  It maps input (i.e. indices into
        `a`) to their destination in the output array.  The first `a.ndim`
        dimensions of `accmap` must be the same as `a.shape`.  That is,
        `accmap.shape[:a.ndim]` must equal `a.shape`.  For example, if `a`
        has shape (15,4), then `accmap.shape[:2]` must equal (15,4).  In this
        case `accmap[i,j]` gives the index into the output array where
        element (i,j) of `a` is to be accumulated.  If the output is, say,
        a 2D, then `accmap` must have shape (15,4,2).  The value in the
        last dimension give indices into the output array. If the output is
        1D, then the shape of `accmap` can be either (15,4) or (15,4,1)
    a : ndarray
        The input data to be accumulated.
    func : callable or None
        The accumulation function.  The function will be passed a list
        of values from `a` to be accumulated.
        If None, numpy.sum is assumed.
    shape : ndarray or None
        The shape of the output array.  If None, the shape will be determined
        from `accmap`.
    fill_value : scalar
        The default value for elements of the output array.
    dtype : numpy data type, or None
        The data type of the output array.  If None, the data type of
        `a` is used.

    Returns
    -------
    out : ndarray
        The accumulated results.

        The shape of `out` is `shape` if `shape` is given.  Otherwise the
        shape is determined by the (lexicographically) largest indices of
        the output found in `accmap`.


    Examples
    --------
    >>> from numpy import array, prod
    >>> a = array([[1,2,3],[4,-1,6],[-1,8,9]])
    >>> a
    array([[ 1,  2,  3],
           [ 4, -1,  6],
           [-1,  8,  9]])
    >>> accmap = array([[0,1,2],[2,0,1],[1,2,0]])  # Sum the diagonals.
    >>> s = accum(accmap, a)
    >>> s
    array([ 9,  7, 15])

    # A 2D output, from sub-arrays with shapes and positions like this:
    # [ (2,2) (2,1)]
    # [ (1,2) (1,1)]
    >>> accmap = array([
    ...        [[0,0],[0,0],[0,1]],
    ...        [[0,0],[0,0],[0,1]],
    ...        [[1,0],[1,0],[1,1]]])

    # Accumulate using a product.
    >>> accum(accmap, a, func=prod, dtype=float)
    array([[ -8.,  18.],
           [ -8.,   9.]])

    # Same accmap, but create an array of lists of values.
    >>> accum(accmap, a, func=lambda x: x, dtype='O')
    array([[[1, 2, 4, -1], [3, 6]],
           [[-1, 8], [9]]], dtype=object)

    """

    def create_array_of_python_lists(accmap, a, shape):
        vals = np.empty(shape, dtype='O')
        for s in product(*[range(k) for k in shape]):
            vals[s] = []

        for s in product(*[range(k) for k in a.shape]):
            indx = tuple(accmap[s])
            val = a[s]
            vals[indx].append(val)

        return vals

    # Check for bad arguments and handle the defaults.
    if accmap.shape[:a.ndim] != a.shape:
        raise ValueError(
            "The initial dimensions of accmap must be the same as a.shape")
    if func is None:
        func = np.sum
    if dtype is None:
        dtype = a.dtype
    if accmap.shape == a.shape:
        accmap = np.expand_dims(accmap, -1)
    adims = tuple(range(a.ndim))
    if shape is None:
        shape = 1 + np.squeeze(np.apply_over_axes(np.max, accmap, axes=adims))
    shape = np.atleast_1d(shape)

    # Create an array of python lists of values.
    vals = create_array_of_python_lists(accmap, a, shape)

    # Create the output array.
    out = np.empty(shape, dtype=dtype)
    for s in product(*[range(k) for k in shape]):
        if vals[s] == []:
            out[s] = fill_value
        else:
            out[s] = func(vals[s])
    return out


def gridcount(data, X, y=1):
    '''
    Returns D-dimensional histogram using linear binning.

    Parameters
    ----------
    data = column vectors with D-dimensional data, shape D x Nd
    X    = row vectors defining discretization, shape D x N
            Must include the range of the data.

    Returns
    -------
    c    = gridcount,  shape N x N x ... x N

    GRIDCOUNT obtains the grid counts using linear binning.
    There are 2 strategies: simple- or linear- binning.
    Suppose that an observation occurs at x and that the nearest point
    below and above is y and z, respectively. Then simple binning strategy
    assigns a unit weight to either y or z, whichever is closer. Linear
    binning, on the other hand, assigns the grid point at y with the weight
    of (z-x)/(z-y) and the gridpoint at z a weight of (y-x)/(z-y).

    In terms of approximation error of using gridcounts as pdf-estimate,
    linear binning is significantly more accurate than simple binning.

     NOTE: The interval [min(X);max(X)] must include the range of the data.
           The order of C is permuted in the same order as
           meshgrid for D==2 or D==3.

    Example
    -------
    >>> import numpy as np
    >>> import wafo.kdetools as wk
    >>> import pylab as plb
    >>> N = 20
    >>> data  = np.random.rayleigh(1,N)
    >>> data = np.array(
    ...    [ 1.07855907,  1.51199717,  1.54382893,  1.54774808,  1.51913566,
    ...     1.11386486,  1.49146216,  1.51127214,  2.61287913,  0.94793051,
    ...     2.08532731,  1.35510641,  0.56759888,  1.55766981,  0.77883602,
    ...     0.9135759 ,  0.81177855,  1.02111483,  1.76334202,  0.07571454])
    >>> x = np.linspace(0,max(data)+1,50)
    >>> dx = x[1]-x[0]

    >>> c = wk.gridcount(data, x)
    >>> np.allclose(c[:5], [ 0.,  0.9731147,  0.0268853,  0.,  0.])
    True

    >>> pdf = c/dx/N
    >>> np.allclose(np.trapz(pdf, x), 1)
    True

    h = plb.plot(x,c,'.')   # 1D histogram
    h1 = plb.plot(x, pdf) #  1D probability density plot

    See also
    --------
    bincount, accum, kdebin

    Reference
    ----------
    Wand,M.P. and Jones, M.C. (1995)
    'Kernel smoothing'
    Chapman and Hall, pp 182-192
    '''
    dat = np.atleast_2d(data)
    x = np.atleast_2d(X)
    y = np.atleast_1d(y).ravel()
    d = dat.shape[0]
    d1, inc = x.shape

    if d != d1:
        raise ValueError('Dimension 0 of data and X do not match.')

    dx = np.diff(x[:, :2], axis=1)
    xlo = x[:, 0]
    xup = x[:, -1]

    datlo = dat.min(axis=1)
    datup = dat.max(axis=1)
    if ((datlo < xlo) | (xup < datup)).any():
        raise ValueError('X does not include whole range of the data!')

    csiz = np.repeat(inc, d)
    use_sparse = False
    if use_sparse:
        acfun = accumsum  # faster than accum
    else:
        acfun = accumsum2  # accum

    binx = np.asarray(np.floor((dat - xlo[:, np.newaxis]) / dx), dtype=int)
    w = dx.prod()
    if d == 1:
        x.shape = (-1,)
        c = np.asarray((acfun(binx, (x[binx + 1] - dat) * y, shape=(inc, )) +
                        acfun(binx + 1, (dat - x[binx]) * y, shape=(inc, ))) /
                       w).ravel()
    else:  # d>2

        Nc = csiz.prod()
        c = np.zeros((Nc,))

        fact2 = np.asarray(np.reshape(inc * np.arange(d), (d, -1)), dtype=int)
        fact1 = np.asarray(
            np.reshape(csiz.cumprod() / inc, (d, -1)), dtype=int)
        # fact1 = fact1(ones(n,1),:);
        bt0 = [0, 0]
        X1 = X.ravel()
        for ir in range(2 ** (d - 1)):
            bt0[0] = np.reshape(bitget(ir, np.arange(d)), (d, -1))
            bt0[1] = 1 - bt0[0]
            for ix in range(2):
                one = np.mod(ix, 2)
                two = np.mod(ix + 1, 2)
                # Convert to linear index
                # linear index to c
                b1 = np.sum((binx + bt0[one]) * fact1, axis=0)
                bt2 = bt0[two] + fact2
                b2 = binx + bt2                     # linear index to X
                c += acfun(b1, np.abs(np.prod(X1[b2] - dat, axis=0)) * y,
                           shape=(Nc,))

        c = np.reshape(c / w, csiz, order='F')

        T = [i for i in range(d)]
        T[1], T[0] = T[0], T[1]
        # make sure c is stored in the same way as meshgrid
        c = c.transpose(*T)
    return c


if __name__ == '__main__':
    test_docstrings(__file__)