__all__ = ['unravel_index',
           'mgrid',
           'ogrid',
           'r_', 'c_', 's_',
           'index_exp', 'ix_',
           'ndenumerate','ndindex']

import sys
import numpy.core.numeric as _nx
from numpy.core.numeric import asarray, ScalarType, array
from numpy.core.numerictypes import find_common_type
import math

import function_base
import numpy.core.defmatrix as matrix
makemat = matrix.matrix

# contributed by Stefan van der Walt
def unravel_index(x,dims):
    """
    Convert a flat index into an index tuple for an array of given shape.

    Parameters
    ----------
    x : int
        Flattened index.
    dims : shape tuple
        Input shape.

    Notes
    -----
    In the Examples section, since ``arr.flat[x] == arr.max()`` it may be
    easier to use flattened indexing than to re-map the index to a tuple.

    Examples
    --------
    >>> arr = np.arange(20).reshape(5,4)
    >>> arr
    array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11],
           [12, 13, 14, 15],
           [16, 17, 18, 19]])
    >>> x = arr.argmax()
    >>> x
    19
    >>> dims = arr.shape
    >>> idx = np.unravel_index(x, dims)
    >>> idx
    (4, 3)
    >>> arr[idx] == arr.max()
    True

    """
    if x > _nx.prod(dims)-1 or x < 0:
        raise ValueError("Invalid index, must be 0 <= x <= number of elements.")

    idx = _nx.empty_like(dims)

    # Take dimensions
    # [a,b,c,d]
    # Reverse and drop first element
    # [d,c,b]
    # Prepend [1]
    # [1,d,c,b]
    # Calculate cumulative product
    # [1,d,dc,dcb]
    # Reverse
    # [dcb,dc,d,1]
    dim_prod = _nx.cumprod([1] + list(dims)[:0:-1])[::-1]
    # Indices become [x/dcb % a, x/dc % b, x/d % c, x/1 % d]
    return tuple(x/dim_prod % dims)

def ix_(*args):
    """ Construct an open mesh from multiple sequences.

    This function takes n 1-d sequences and returns n outputs with n
    dimensions each such that the shape is 1 in all but one dimension and
    the dimension with the non-unit shape value cycles through all n
    dimensions.

    Using ix_() one can quickly construct index arrays that will index
    the cross product.

    a[ix_([1,3,7],[2,5,8])]  returns the array

    a[1,2]  a[1,5]  a[1,8]
    a[3,2]  a[3,5]  a[3,8]
    a[7,2]  a[7,5]  a[7,8]
    """
    out = []
    nd = len(args)
    baseshape = [1]*nd
    for k in range(nd):
        new = _nx.asarray(args[k])
        if (new.ndim != 1):
            raise ValueError, "Cross index must be 1 dimensional"
        if issubclass(new.dtype.type, _nx.bool_):
            new = new.nonzero()[0]
        baseshape[k] = len(new)
        new = new.reshape(tuple(baseshape))
        out.append(new)
        baseshape[k] = 1
    return tuple(out)

class nd_grid(object):
    """
    Construct a multi-dimensional "meshgrid".

    grid = nd_grid() creates an instance which will return a mesh-grid
    when indexed.  The dimension and number of the output arrays are equal
    to the number of indexing dimensions.  If the step length is not a
    complex number, then the stop is not inclusive.

    However, if the step length is a **complex number** (e.g. 5j), then the
    integer part of its magnitude is interpreted as specifying the
    number of points to create between the start and stop values, where
    the stop value **is inclusive**.

    If instantiated with an argument of sparse=True, the mesh-grid is
    open (or not fleshed out) so that only one-dimension of each returned
    argument is greater than 1

    Examples
    --------
    >>> mgrid = np.lib.index_tricks.nd_grid()
    >>> mgrid[0:5,0:5]
    array([[[0, 0, 0, 0, 0],
            [1, 1, 1, 1, 1],
            [2, 2, 2, 2, 2],
            [3, 3, 3, 3, 3],
            [4, 4, 4, 4, 4]],
           [[0, 1, 2, 3, 4],
            [0, 1, 2, 3, 4],
            [0, 1, 2, 3, 4],
            [0, 1, 2, 3, 4],
            [0, 1, 2, 3, 4]]])
    >>> mgrid[-1:1:5j]
    array([-1. , -0.5,  0. ,  0.5,  1. ])
    >>> ogrid = np.lib.index_tricks.nd_grid(sparse=True)
    >>> ogrid[0:5,0:5]
    [array([[0],
            [1],
            [2],
            [3],
            [4]]), array([[0, 1, 2, 3, 4]])]

    """
    def __init__(self, sparse=False):
        self.sparse = sparse
    def __getitem__(self,key):
        try:
            size = []
            typ = int
            for k in range(len(key)):
                step = key[k].step
                start = key[k].start
                if start is None: start=0
                if step is None: step=1
                if isinstance(step, complex):
                    size.append(int(abs(step)))
                    typ = float
                else:
                    size.append(math.ceil((key[k].stop - start)/(step*1.0)))
                if isinstance(step, float) or \
                    isinstance(start, float) or \
                    isinstance(key[k].stop, float):
                    typ = float
            if self.sparse:
                nn = map(lambda x,t: _nx.arange(x, dtype=t), size, \
                                     (typ,)*len(size))
            else:
                nn = _nx.indices(size, typ)
            for k in range(len(size)):
                step = key[k].step
                start = key[k].start
                if start is None: start=0
                if step is None: step=1
                if isinstance(step, complex):
                    step = int(abs(step))
                    if step != 1:
                        step = (key[k].stop - start)/float(step-1)
                nn[k] = (nn[k]*step+start)
            if self.sparse:
                slobj = [_nx.newaxis]*len(size)
                for k in range(len(size)):
                    slobj[k] = slice(None,None)
                    nn[k] = nn[k][slobj]
                    slobj[k] = _nx.newaxis
            return nn
        except (IndexError, TypeError):
            step = key.step
            stop = key.stop
            start = key.start
            if start is None: start = 0
            if isinstance(step, complex):
                step = abs(step)
                length = int(step)
                if step != 1:
                    step = (key.stop-start)/float(step-1)
                stop = key.stop+step
                return _nx.arange(0, length,1, float)*step + start
            else:
                return _nx.arange(start, stop, step)

    def __getslice__(self,i,j):
        return _nx.arange(i,j)

    def __len__(self):
        return 0

mgrid = nd_grid(sparse=False)
ogrid = nd_grid(sparse=True)
mgrid.__doc__ = None # set in numpy.add_newdocs
ogrid.__doc__ = None # set in numpy.add_newdocs

class AxisConcatenator(object):
    """Translates slice objects to concatenation along an axis.
    """
    def _retval(self, res):
        if self.matrix:
            oldndim = res.ndim
            res = makemat(res)
            if oldndim == 1 and self.col:
                res = res.T
        self.axis = self._axis
        self.matrix = self._matrix
        self.col = 0
        return res

    def __init__(self, axis=0, matrix=False, ndmin=1, trans1d=-1):
        self._axis = axis
        self._matrix = matrix
        self.axis = axis
        self.matrix = matrix
        self.col = 0
        self.trans1d = trans1d
        self.ndmin = ndmin

    def __getitem__(self,key):
        trans1d = self.trans1d
        ndmin = self.ndmin
        if isinstance(key, str):
            frame = sys._getframe().f_back
            mymat = matrix.bmat(key,frame.f_globals,frame.f_locals)
            return mymat
        if type(key) is not tuple:
            key = (key,)
        objs = []
        scalars = []
        arraytypes = []
        scalartypes = []
        for k in range(len(key)):
            scalar = False
            if type(key[k]) is slice:
                step = key[k].step
                start = key[k].start
                stop = key[k].stop
                if start is None: start = 0
                if step is None:
                    step = 1
                if isinstance(step, complex):
                    size = int(abs(step))
                    newobj = function_base.linspace(start, stop, num=size)
                else:
                    newobj = _nx.arange(start, stop, step)
                if ndmin > 1:
                    newobj = array(newobj,copy=False,ndmin=ndmin)
                    if trans1d != -1:
                        newobj = newobj.swapaxes(-1,trans1d)
            elif isinstance(key[k],str):
                if k != 0:
                    raise ValueError, "special directives must be the"\
                          "first entry."
                key0 = key[0]
                if key0 in 'rc':
                    self.matrix = True
                    self.col = (key0 == 'c')
                    continue
                if ',' in key0:
                    vec = key0.split(',')
                    try:
                        self.axis, ndmin = \
                                   [int(x) for x in vec[:2]]
                        if len(vec) == 3:
                            trans1d = int(vec[2])
                        continue
                    except:
                        raise ValueError, "unknown special directive"
                try:
                    self.axis = int(key[k])
                    continue
                except (ValueError, TypeError):
                    raise ValueError, "unknown special directive"
            elif type(key[k]) in ScalarType:
                newobj = array(key[k],ndmin=ndmin)
                scalars.append(k)
                scalar = True
                scalartypes.append(newobj.dtype)
            else:
                newobj = key[k]
                if ndmin > 1:
                    tempobj = array(newobj, copy=False, subok=True)
                    newobj = array(newobj, copy=False, subok=True,
                                   ndmin=ndmin)
                    if trans1d != -1 and tempobj.ndim < ndmin:
                        k2 = ndmin-tempobj.ndim
                        if (trans1d < 0):
                            trans1d += k2 + 1
                        defaxes = range(ndmin)
                        k1 = trans1d
                        axes = defaxes[:k1] + defaxes[k2:] + \
                               defaxes[k1:k2]
                        newobj = newobj.transpose(axes)
                    del tempobj
            objs.append(newobj)
            if not scalar and isinstance(newobj, _nx.ndarray):
                arraytypes.append(newobj.dtype)

        #  Esure that scalars won't up-cast unless warranted
        final_dtype = find_common_type(arraytypes, scalartypes)
        if final_dtype is not None:
            for k in scalars:
                objs[k] = objs[k].astype(final_dtype)

        res = _nx.concatenate(tuple(objs),axis=self.axis)
        return self._retval(res)

    def __getslice__(self,i,j):
        res = _nx.arange(i,j)
        return self._retval(res)

    def __len__(self):
        return 0

# separate classes are used here instead of just making r_ = concatentor(0),
# etc. because otherwise we couldn't get the doc string to come out right
# in help(r_)

class RClass(AxisConcatenator):
    """Translates slice objects to concatenation along the first axis.

    For example:
    >>> np.r_[np.array([1,2,3]), 0, 0, np.array([4,5,6])]
    array([1, 2, 3, 0, 0, 4, 5, 6])

    """
    def __init__(self):
        AxisConcatenator.__init__(self, 0)

r_ = RClass()

class CClass(AxisConcatenator):
    """Translates slice objects to concatenation along the second axis.

    For example:
    >>> np.c_[np.array([[1,2,3]]), 0, 0, np.array([[4,5,6]])]
    array([1, 2, 3, 0, 0, 4, 5, 6])
    """
    def __init__(self):
        AxisConcatenator.__init__(self, -1, ndmin=2, trans1d=0)

c_ = CClass()

class ndenumerate(object):
    """
    Multidimensional index iterator.

    Return an iterator yielding pairs of array coordinates and values.

    Parameters
    ----------
    a : ndarray
      Input array.

    Examples
    --------
    >>> a = np.array([[1,2],[3,4]])
    >>> for index, x in np.ndenumerate(a):
    ...     print index, x
    (0, 0) 1
    (0, 1) 2
    (1, 0) 3
    (1, 1) 4

    """
    def __init__(self, arr):
        self.iter = asarray(arr).flat

    def next(self):
        return self.iter.coords, self.iter.next()

    def __iter__(self):
        return self


class ndindex(object):
    """
    An N-dimensional iterator object to index arrays.

    Given the shape of an array, an `ndindex` instance iterates over
    the N-dimensional index of the array. At each iteration, the index of the
    last dimension is incremented by one.

    Parameters
    ----------
    `*args` : integers
      The size of each dimension in the counter.

    Examples
    --------
    >>> for index in np.ndindex(3,2,1):
    ...     print index
    (0, 0, 0)
    (0, 1, 0)
    (1, 0, 0)
    (1, 1, 0)
    (2, 0, 0)
    (2, 1, 0)

    """

    def __init__(self, *args):
        if len(args) == 1 and isinstance(args[0], tuple):
            args = args[0]
        self.nd = len(args)
        self.ind = [0]*self.nd
        self.index = 0
        self.maxvals = args
        tot = 1
        for k in range(self.nd):
            tot *= args[k]
        self.total = tot

    def _incrementone(self, axis):
        if (axis < 0):  # base case
            return
        if (self.ind[axis] < self.maxvals[axis]-1):
            self.ind[axis] += 1
        else:
            self.ind[axis] = 0
            self._incrementone(axis-1)

    def ndincr(self):
        self._incrementone(self.nd-1)

    def next(self):
        if (self.index >= self.total):
            raise StopIteration
        val = tuple(self.ind)
        self.index += 1
        self.ndincr()
        return val

    def __iter__(self):
        return self




# You can do all this with slice() plus a few special objects,
# but there's a lot to remember. This version is simpler because
# it uses the standard array indexing syntax.
#
# Written by Konrad Hinsen <hinsen@cnrs-orleans.fr>
# last revision: 1999-7-23
#
# Cosmetic changes by T. Oliphant 2001
#
#

class IndexExpression(object):
    """
    A nicer way to build up index tuples for arrays.

    For any index combination, including slicing and axis insertion,
    'a[indices]' is the same as 'a[index_exp[indices]]' for any
    array 'a'. However, 'index_exp[indices]' can be used anywhere
    in Python code and returns a tuple of slice objects that can be
    used in the construction of complex index expressions.
    """
    maxint = sys.maxint
    def __init__(self, maketuple):
        self.maketuple = maketuple

    def __getitem__(self, item):
        if self.maketuple and type(item) != type(()):
            return (item,)
        else:
            return item

    def __len__(self):
        return self.maxint

    def __getslice__(self, start, stop):
        if stop == self.maxint:
            stop = None
        return self[start:stop:None]

index_exp = IndexExpression(maketuple=True)
s_ = IndexExpression(maketuple=False)

# End contribution from Konrad.
