sheetcoords.py

"""
File originally part of the Topographica project. Provides
SheetCoordinateSystem, allowing conversion between continuous 'sheet
coordinates' and integer matrix coordinates.

'Sheet coordinates' allow simulation parameters to be specified in
units that are density-independent, whereas 'matrix coordinates'
provide a means of realizing the continuous sheets.

Hence we can have a pair of 'sheet coordinates' (x,y); floating-point
Cartesian coordinates indicating an arbitrary point on the sheet's plane.
We can also have a pair of 'matrix coordinates' (r,c), which are used
to address an underlying matrix. These matrix coordinates are also
floating-point numbers to allow precise conversion between the two
schemes. Where it is necessary to address a specific element of the
matrix (as is often the case in calculations), we also have the usual
matrix index coordinates (r_idx, c_idx). We refer to these as
matrixidx coordinates. SheetCoordinateSystem proxies methods for converting
between sheet and matrix coordinates, as well as sheet and matrixidx
coordinates.

Everyone should use these facilities for conversions between the two
coordinate systems to guarantee consistency.




Example of how the matrix stores the representation of the Sheet
================================================================

For the purposes of this example, assume the goal is a Sheet with
density=3 that has a 1 at (-1/2,-1/2), a 5 at (0.0,0.0), and a 9 at
(1/2,1/2).  More precisely, for this Sheet,

the continuous area from -1/2,-1/2 to -1/6,-1/6 has value 1,
the continuous area from -1/6,-1/6 to  1/6,1/6  has value 5, and
the continuous area from  1/6,1/6  to  1/2,1/2  has value 9.

With the rest of the elements filled in, the Sheet would look like::

    (-1/2,1/2) -+-----+-----+-----+- (1/2,1/2)
                |     |     |     |
                |  7  |  8  |  9  |
                |     |     |     |
    (-1/2,1/6) -+-----+-----+-----+- (1/2,1/6)
                |     |     |     |
                |  4  |  5  |  6  |
                |     |     |     |
   (-1/2,-1/6) -+-----+-----+-----+- (1/2,-1/6)
                |     |     |     |
                |  1  |  2  |  3  |
                |     |     |     |
   (-1/2,-1/2) -+-----+-----+-----+- (1/2,-1/2)

where element 5 is centered on 0.0,0.0.  A matrix that would match
these Sheet coordinates is::

  [[7 8 9]
   [4 5 6]
   [1 2 3]]

If we have such a matrix, we can access it in one of two ways: Sheet
or matrix/matrixidx coordinates.  In matrixidx coordinates, the matrix is indexed
by rows and columns, and it is possible to ask for the element at
location [0,2] (which returns 9 as in any normal row-major matrix).
But the values can additionally be accessed in Sheet coordinates,
where the matrix is indexed by a point in the Cartesian plane.  In
Sheet coordinates, it is possible to ask for the element at location
(0.3,0.02), which returns floating-point matrix coordinates that can
be cropped to give the nearest matrix element, namely the one with
value 6.

Of course, it would be an error to try to pass matrix coordinates like
[0,2] to the sheet2matrix calls; the result would be a value far
outside of the actual matrix.
"""

import numpy as np

from .boundingregion import BoundingBox
from .util import datetime_types

# Note about the 'bounds-master' approach we have adopted
# =======================================================
#
# Our current approach is a "bounds-master" approach, where we trust
# the user's specified x width, and choose the nearest density and y
# height to make that possible.  The advantage of this is that when we
# change the density (which is often), each such simulation is the
# best possible approximation to the given area.  Generally, the area
# is much more meaningful than the density, so this approach makes
# sense.  Plus, the y height is usually the same as the x width, so
# it's not usually a problem that the y height is not respected.  The
# disadvantage is that the user's area can only be trusted in one
# dimension, because of wanting to avoid the complication of separate
# xdensity and ydensity, which makes this approach very difficult to
# explain to the user.
#
# The other approach is density-master: trust the user's specified
# density as-is, and simply choose the nearest area that fits that
# density.  The advantages are that (a) it's very simple to describe
# and reason about, and (b) if a user asks for a different area, they
# get a true subsection of the same simulation they would have gotten
# at the larger area.  The disadvantage is that the simulation isn't
# the best approximation of the given area that it could be -- e.g. at
# low densities, the sheet area could be quite significantly different
# than the one the user requested.  Plus, if we took this approach
# seriously, then we'd let the density specify the matrix coordinate
# system entirely, including the origin, which would mean that the
# actual area would often be offset from the intended one, which is
# even worse.  Differences between the area and the offset could cause
# severe problems in the alignment of projections between sheets with
# different densities, which would make low-density versions of
# hierarchical models behave very strangely.



class SheetCoordinateSystem:
    """
    Provides methods to allow conversion between sheet and matrix
    coordinates.
    """
    def __get_xdensity(self):
        return self.__xdensity
    def __get_ydensity(self):
        return self.__ydensity
    def __get_shape(self):
        return self.__shape

    xdensity = property(__get_xdensity, doc="""
        The spacing between elements in an underlying matrix
        representation, in the x direction.""")

    ydensity = property(__get_ydensity, doc="""
        The spacing between elements in an underlying matrix
        representation, in the y direction.""")

    shape = property(__get_shape)

    # Determines the unit of time densities are defined relative to
    # when one or both axes are datetime types
    _time_unit = 'us'

    def __init__(self,bounds,xdensity,ydensity=None):
        """
        Store the bounds (as l,b,r,t in an array), xdensity, and
        ydensity.

        If ydensity is not specified, it is assumed that the specified
        xdensity is nominal and that the true xdensity should be
        calculated. The top and bottom bounds are adjusted so that the
        ydensity is equal to the xdensity.

        If both xdensity and ydensity are specified, these and the
        bounds are taken to be exact and are not adjusted.
        """
        if not ydensity:
            bounds,xdensity = self.__equalize_densities(bounds,xdensity)

        self.bounds = bounds
        self.__set_xdensity(xdensity)
        self.__set_ydensity(ydensity or xdensity)

        self.lbrt = np.array(bounds.lbrt())

        r1,r2,c1,c2 = Slice._boundsspec2slicespec(self.lbrt,self)
        self.__shape = (r2-r1,c2-c1)

    # xstep and ystep allow division to be avoid for speed reasons
    def __set_xdensity(self,density):
        self.__xdensity=density
        self.__xstep = 1.0/density


    def __set_ydensity(self,density):
        self.__ydensity=density
        self.__ystep = 1.0/density


    def __equalize_densities(self,nominal_bounds,nominal_density):
        """
        Calculate the true density along x, and adjust the top and
        bottom bounds so that the density along y will be equal.

        Returns (adjusted_bounds, true_density)
        """
        left,bottom,right,top = nominal_bounds.lbrt()
        width, height = right-left, top-bottom
        center_y = bottom + height/2.0
        # True density is not equal to the nominal_density when
        # nominal_density*(right-left) is not an integer.
        true_density = int(nominal_density*(width))/float(width)

        n_cells = round(height*true_density,0)
        adjusted_half_height = n_cells/true_density/2.0

        return (BoundingBox(points=((left, center_y-adjusted_half_height),
                                    (right, center_y+adjusted_half_height))),
                true_density)


    def sheet2matrix(self,x,y):
        """
        Convert a point (x,y) in Sheet coordinates to continuous
        matrix coordinates.

        Returns (float_row,float_col), where float_row corresponds to
        y, and float_col to x.

        Valid for scalar or array x and y.

        Note about Bounds For a Sheet with
        BoundingBox(points=((-0.5,-0.5),(0.5,0.5))) and density=3,
        x=-0.5 corresponds to float_col=0.0 and x=0.5 corresponds to
        float_col=3.0.  float_col=3.0 is not inside the matrix
        representing this Sheet, which has the three columns
        (0,1,2). That is, x=-0.5 is inside the BoundingBox but x=0.5
        is outside. Similarly, y=0.5 is inside (at row 0) but y=-0.5
        is outside (at row 3) (it's the other way round for y because
        the matrix row index increases as y decreases).
        """
        # First translate to (left,top), which is [0,0] in the matrix,
        # then scale to the size of the matrix. The y coordinate needs
        # to be flipped, because the points are moving down in the
        # sheet as the y index increases in the matrix.
        xdensity = self.__xdensity
        if ((isinstance(x, np.ndarray) and x.dtype.kind == 'M') or
            isinstance(x, datetime_types)):
            xdensity = np.timedelta64(int(round(1./xdensity)), self._time_unit)
            float_col = (x-self.lbrt[0]) / xdensity
        else:
            float_col = (x-self.lbrt[0]) * xdensity

        ydensity = self.__ydensity
        if ((isinstance(y, np.ndarray) and y.dtype.kind == 'M') or
            isinstance(y, datetime_types)):
            ydensity = np.timedelta64(int(round(1./ydensity)), self._time_unit)
            float_row = (self.lbrt[3]-y) / ydensity
        else:
            float_row = (self.lbrt[3]-y) * ydensity

        return float_row, float_col


    def sheet2matrixidx(self,x,y):
        """
        Convert a point (x,y) in sheet coordinates to the integer row
        and column index of the matrix cell in which that point falls,
        given a bounds and density.  Returns (row,column).

        Note that if coordinates along the right or bottom boundary
        are passed into this function, the returned matrix coordinate
        of the boundary will be just outside the matrix, because the
        right and bottom boundaries are exclusive.

        Valid for scalar or array x and y.
        """
        r,c = self.sheet2matrix(x,y)
        r = np.floor(r)
        c = np.floor(c)

        if hasattr(r,'astype'):
            return r.astype(int), c.astype(int)
        else:
            return int(r),int(c)


    def matrix2sheet(self,float_row,float_col):
        """
        Convert a floating-point location (float_row,float_col) in
        matrix coordinates to its corresponding location (x,y) in
        sheet coordinates.

        Valid for scalar or array float_row and float_col.

        Inverse of sheet2matrix().
        """
        xoffset = float_col*self.__xstep
        if isinstance(self.lbrt[0], datetime_types):
            xoffset = np.timedelta64(int(round(xoffset)), self._time_unit)
        x = self.lbrt[0] + xoffset
        yoffset = float_row*self.__ystep
        if isinstance(self.lbrt[3], datetime_types):
            yoffset = np.timedelta64(int(round(yoffset)), self._time_unit)
        y = self.lbrt[3] - yoffset
        return x, y


    def matrixidx2sheet(self,row,col):
        """
        Return (x,y) where x and y are the floating point coordinates
        of the *center* of the given matrix cell (row,col). If the
        matrix cell represents a 0.2 by 0.2 region, then the center
        location returned would be 0.1,0.1.

        NOTE: This is NOT the strict mathematical inverse of
        sheet2matrixidx(), because sheet2matrixidx() discards all but
        the integer portion of the continuous matrix coordinate.

        Valid only for scalar or array row and col.
        """
        x,y = self.matrix2sheet((row+0.5), (col+0.5))

        # Rounding allows easier comparison with user specified values
        if not isinstance(x, datetime_types):
            x = np.around(x,10)
        if not isinstance(y, datetime_types):
            y = np.around(y,10)
        return x, y


    def closest_cell_center(self,x,y):
        """
        Given arbitrary sheet coordinates, return the sheet coordinates
        of the center of the closest unit.
        """
        return self.matrixidx2sheet(*self.sheet2matrixidx(x,y))


    def sheetcoordinates_of_matrixidx(self):
        """
        Return x,y where x is a vector of sheet coordinates
        representing the x-center of each matrix cell, and y
        represents the corresponding y-center of the cell.
        """
        rows,cols = self.shape
        return self.matrixidx2sheet(np.arange(rows), np.arange(cols))



class Slice(np.ndarray):
    """
    Represents a slice of a SheetCoordinateSystem; i.e., an array
    specifying the row and column start and end points for a submatrix
    of the SheetCoordinateSystem.

    The slice is created from the supplied bounds by calculating the
    slice that corresponds most closely to the specified bounds.
    Therefore, the slice does not necessarily correspond exactly to
    the specified bounds. The bounds that do exactly correspond to the
    slice are available via the 'bounds' attribute.

    Note that the slice does not respect the bounds of the
    SheetCoordinateSystem, and that actions such as translate() also
    do not respect the bounds. To ensure that the slice is within the
    SheetCoordinateSystem's bounds, use crop_to_sheet().
    """

    __slots__ = []

    def compute_bounds(self,scs):
        spec = self._slicespec2boundsspec(self,scs)
        return BoundingBox(points=spec)


    def __new__(cls, bounds, sheet_coordinate_system, force_odd=False,
                min_matrix_radius=1):
        """
        Create a slice of the given sheet_coordinate_system from the
        specified bounds.
        """
        if force_odd:
            slicespec=Slice._createoddslicespec(bounds,sheet_coordinate_system,
                                                min_matrix_radius)
        else:
            slicespec=Slice._boundsspec2slicespec(bounds.lbrt(),sheet_coordinate_system)
        # Using numpy.int32 for legacy reasons
        a = np.array(slicespec, dtype=np.int32, copy=False).view(cls)
        return a


    def submatrix(self,matrix):
        """
        Return the submatrix of the given matrix specified by this
        slice.

        Equivalent to computing the intersection between the
        SheetCoordinateSystem's bounds and the bounds, and returning
        the corresponding submatrix of the given matrix.

        The submatrix is just a view into the sheet_matrix; it is not
        an independent copy.
        """
        return matrix[self[0]:self[1],self[2]:self[3]]

    @staticmethod
    def findinputslice(coord, sliceshape, sheetshape):
        """
        Gets the matrix indices of a slice within an array of size
        sheetshape from a sliceshape, positioned at coord.
        """
        center_row, center_col = coord
        n_rows, n_cols = sliceshape
        sheet_rows, sheet_cols = sheetshape

        c1 = -min(0, center_col-n_cols/2)  # assuming odd shape (n_cols/2)
        r1 = -min(0, center_row-n_rows/2)  # top and bottom
        c2 = -max(-n_cols, center_col-sheet_cols-n_cols/2)
        r2 = -max(-n_rows, center_row-sheet_rows-n_rows/2)

        return (r1, r2, c1, c2)


    def positionlesscrop(self,x,y,sheet_coord_system):
        """
        Return the correct slice for a weights/mask matrix at this
        ConnectionField's location on the sheet (i.e. for getting the
        correct submatrix of the weights or mask in case the unit is
        near the edge of the sheet).
        """
        slice_inds = self.findinputslice(
            sheet_coord_system.sheet2matrixidx(x,y),
            self.shape_on_sheet(), sheet_coord_system.shape)

        self.set(slice_inds)


    def positionedcrop(self,x,y,sheet_coord_system):
        """
        Offset the bounds_template to this cf's location and store the
        result in the 'bounds' attribute.

        Also stores the input_sheet_slice for access by C.
        """
        cf_row,cf_col = sheet_coord_system.sheet2matrixidx(x,y)
        bounds_x,bounds_y=self.compute_bounds(sheet_coord_system).centroid()

        b_row,b_col=sheet_coord_system.sheet2matrixidx(bounds_x,bounds_y)

        row_offset = cf_row-b_row
        col_offset = cf_col-b_col
        self.translate(row_offset,col_offset)


    def translate(self, r, c):
        "Translate the slice by the given number of rows and columns."
        self+=[r,r,c,c]


    def set(self,slice_specification):
        "Set this slice from some iterable that specifies (r1,r2,c1,c2)."
        self.put([0,1,2,3],slice_specification) # pylint: disable-msg=E1101


    def shape_on_sheet(self):
        "Return the shape of the array of the Slice on its sheet."
        return self[1]-self[0],self[3]-self[2]


    def crop_to_sheet(self,sheet_coord_system):
        "Crop the slice to the SheetCoordinateSystem's bounds."
        maxrow,maxcol = sheet_coord_system.shape

        self[0] = max(0,self[0])
        self[1] = min(maxrow,self[1])
        self[2] = max(0,self[2])
        self[3] = min(maxcol,self[3])


    @staticmethod
    def _createoddslicespec(bounds,scs,min_matrix_radius):
        """
        Create the 'odd' Slice that best approximates the specified
        sheet-coordinate bounds.

        The supplied bounds are translated to have a center at the
        center of one of the sheet's units (we arbitrarily use the
        center unit), and then these bounds are converted to a slice
        in such a way that the slice exactly includes all units whose
        centers are within the bounds (see boundsspec2slicespec()).
        However, to ensure that the bounds are treated symmetrically,
        we take the right and bottom bounds and reflect these about
        the center of the slice (i.e. we take the 'xradius' to be
        right_col-center_col and the 'yradius' to be
        bottom_col-center_row). Hence, if the bounds happen to go
        through units, if the units are included on the right and
        bottom bounds, they will be included on the left and top
        bounds. This ensures that the slice has odd dimensions.
        """
        bounds_xcenter,bounds_ycenter=bounds.centroid()
        sheet_rows,sheet_cols = scs.shape

        center_row,center_col = sheet_rows/2,sheet_cols/2
        unit_xcenter,unit_ycenter=scs.matrixidx2sheet(center_row,
                                                      center_col)

        bounds.translate(unit_xcenter-bounds_xcenter,
                         unit_ycenter-bounds_ycenter)

        r1,r2,c1,c2 = Slice._boundsspec2slicespec(bounds.lbrt(),scs)

        xrad=max(c2-center_col-1,min_matrix_radius)
        yrad=max(r2-center_row-1,min_matrix_radius)

        r2=center_row+yrad+1
        c2=center_col+xrad+1
        r1=center_row-yrad
        c1=center_col-xrad
        return (r1,r2,c1,c2)


    @staticmethod
    def _boundsspec2slicespec(boundsspec,scs):
        """
        Convert an iterable boundsspec (supplying l,b,r,t of a
        BoundingRegion) into a Slice specification.

        Includes all units whose centers are within the specified
        sheet-coordinate bounds specified by boundsspec.

        Exact inverse of _slicespec2boundsspec().
        """
        l,b,r,t = boundsspec

        t_m,l_m = scs.sheet2matrix(l,t)
        b_m,r_m = scs.sheet2matrix(r,b)

        l_idx = int(np.ceil(l_m-0.5))
        t_idx = int(np.ceil(t_m-0.5))
        r_idx = int(np.floor(r_m+0.5))
        b_idx = int(np.floor(b_m+0.5))

        return t_idx,b_idx,l_idx,r_idx


    @staticmethod
    def _slicespec2boundsspec(slicespec,scs):
        """
        Convert an iterable slicespec (supplying r1,r2,c1,c2 of a
        Slice) into a BoundingRegion specification.

        Exact inverse of _boundsspec2slicespec().
        """
        r1,r2,c1,c2 = slicespec

        left,bottom = scs.matrix2sheet(r2,c1)
        right, top  = scs.matrix2sheet(r1,c2)

        return ((left,bottom),(right,top))