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Sourcecode: python-scipy-core version File versions  Download package

shape_base.py

import Numeric
from Numeric import *
from type_check import isscalar, asarray

__all__ = ['atleast_1d','atleast_2d','atleast_3d','vstack','hstack',
           'column_stack','dstack','array_split','split','hsplit',
           'vsplit','dsplit','squeeze','apply_over_axes','expand_dims',
           'apply_along_axis']

def apply_along_axis(func1d,axis,arr,*args):
    """ Execute func1d(arr[i],*args) where func1d takes 1-D arrays
        and arr is an N-d array.  i varies so as to apply the function
        along the given axis for each 1-d subarray in arr.
    """
    nd = Numeric.rank(arr)
    if axis < 0: axis += nd
    if (axis >= nd):
        raise ValueError, "axis must be less than the rank; "+\
              "axis=%d, rank=%d." % (axis,)
    ind = [0]*(nd-1)
    dims = Numeric.shape(arr)
    i = zeros(nd,'O')
    indlist = range(nd)
    indlist.remove(axis)
    i[axis] = slice(None,None)
    outshape = take(shape(arr),indlist)
    put(i,indlist,ind)
    res = func1d(arr[i],*args)
    #  if res is a number, then we have a smaller output array
    if isscalar(res):
        outarr = zeros(outshape,asarray(res).typecode())
        outarr[ind] = res
        Ntot = product(outshape)
        k = 1
        while k < Ntot:
            # increment the index
            ind[-1] += 1
            n = -1
            while (ind[n] >= outshape[n]) and (n > (1-nd)):
                ind[n-1] += 1
                ind[n] = 0
                n -= 1
            put(i,indlist,ind)
            res = func1d(arr[i],*args)
            outarr[ind] = res
            k += 1
        return outarr
    else:
        Ntot = product(outshape)
        holdshape = outshape
        outshape = list(shape(arr))
        outshape[axis] = len(res)
        outarr = zeros(outshape,asarray(res).typecode())
        outarr[i] = res
        k = 1
        while k < Ntot:
            # increment the index
            ind[-1] += 1
            n = -1
            while (ind[n] >= holdshape[n]) and (n > (1-nd)):
                ind[n-1] += 1
                ind[n] = 0
                n -= 1
            put(i,indlist,ind)
            res = func1d(arr[i],*args)
            outarr[i] = res
            k += 1
        return outarr
        
     
def apply_over_axes(func, a, axes):
    """Apply a function over multiple axes, keeping the same shape
    for the resulting array.
    """
    val = asarray(a)
    N = len(val.shape)
    if not type(axes) in SequenceType:
        axes = (axes,)
    for axis in axes:
        if axis < 0: axis = N + axis
        args = (val, axis)
        val = expand_dims(func(*args),axis)
    return val

def expand_dims(a, axis):
    """Expand the shape of a by including NewAxis before given axis.
    """
    a = asarray(a)
    shape = a.shape
    if axis < 0:
        axis = axis + len(shape) + 1
    a.shape = shape[:axis] + (1,) + shape[axis:]
    return a

def squeeze(a):
    "Returns a with any ones from the shape of a removed"
    a = asarray(a)
    b = asarray(a.shape)
    val = reshape (a, tuple (compress (not_equal (b, 1), b)))
    return val

def atleast_1d(*arys):
    """ Force a sequence of arrays to each be at least 1D.

         Description:
            Force an array to be at least 1D.  If an array is 0D, the 
            array is converted to a single row of values.  Otherwise,
            the array is unaltered.
         Arguments:
            *arys -- arrays to be converted to 1 or more dimensional array.
         Returns:
            input array converted to at least 1D array.
    """
    res = []
    for ary in arys:
        ary = asarray(ary)
        if len(ary.shape) == 0: 
            result = Numeric.array([ary[0]])
        else:
            result = ary
        res.append(result)
    if len(res) == 1:
        return res[0]
    else:
        return res

def atleast_2d(*arys):
    """ Force a sequence of arrays to each be at least 2D.

         Description:
            Force an array to each be at least 2D.  If the array
            is 0D or 1D, the array is converted to a single
            row of values.  Otherwise, the array is unaltered.
         Arguments:
            arys -- arrays to be converted to 2 or more dimensional array.
         Returns:
            input array converted to at least 2D array.
    """
    res = []
    for ary in arys:
        ary = asarray(ary)
        if len(ary.shape) == 0: 
            ary = Numeric.array([ary[0]])
        if len(ary.shape) == 1: 
            result = ary[NewAxis,:]
        else: 
            result = ary
        res.append(result)
    if len(res) == 1:
        return res[0]
    else:
        return res
        
def atleast_3d(*arys):
    """ Force a sequence of arrays to each be at least 3D.

         Description:
            Force an array each be at least 3D.  If the array is 0D or 1D, 
            the array is converted to a single 1xNx1 array of values where 
            N is the orginal length of the array. If the array is 2D, the 
            array is converted to a single MxNx1 array of values where MxN
            is the orginal shape of the array. Otherwise, the array is 
            unaltered.
         Arguments:
            arys -- arrays to be converted to 3 or more dimensional array.
         Returns:
            input array converted to at least 3D array.
    """
    res = []
    for ary in arys:
        ary = asarray(ary)
        if len(ary.shape) == 0:
            ary = Numeric.array([ary[0]])
        if len(ary.shape) == 1:
            result = ary[NewAxis,:,NewAxis]
        elif len(ary.shape) == 2:
            result = ary[:,:,NewAxis]
        else: 
            result = ary
        res.append(result)
    if len(res) == 1:
        return res[0]
    else:
        return res


def vstack(tup):
    """ Stack arrays in sequence vertically (row wise)

        Description:
            Take a sequence of arrays and stack them veritcally
            to make a single array.  All arrays in the sequence
            must have the same shape along all but the first axis. 
            vstack will rebuild arrays divided by vsplit.
        Arguments:
            tup -- sequence of arrays.  All arrays must have the same 
                   shape.
        Examples:
            >>> import scipy
            >>> a = array((1,2,3))
            >>> b = array((2,3,4))
            >>> scipy.vstack((a,b))
            array([[1, 2, 3],
                   [2, 3, 4]])
            >>> a = array([[1],[2],[3]])
            >>> b = array([[2],[3],[4]])
            >>> scipy.vstack((a,b))
            array([[1],
                   [2],
                   [3],
                   [2],
                   [3],
                   [4]])

    """
    return Numeric.concatenate(map(atleast_2d,tup),0)

def hstack(tup):
    """ Stack arrays in sequence horizontally (column wise)

        Description:
            Take a sequence of arrays and stack them horizontally
            to make a single array.  All arrays in the sequence
            must have the same shape along all but the second axis.
            hstack will rebuild arrays divided by hsplit.
        Arguments:
            tup -- sequence of arrays.  All arrays must have the same 
                   shape.
        Examples:
            >>> import scipy
            >>> a = array((1,2,3))
            >>> b = array((2,3,4))
            >>> scipy.hstack((a,b))
            array([1, 2, 3, 2, 3, 4])
            >>> a = array([[1],[2],[3]])
            >>> b = array([[2],[3],[4]])
            >>> scipy.hstack((a,b))
            array([[1, 2],
                   [2, 3],
                   [3, 4]])

    """
    return Numeric.concatenate(map(atleast_1d,tup),1)

def column_stack(tup):
    """ Stack 1D arrays as columns into a 2D array

        Description:
            Take a sequence of 1D arrays and stack them as columns
            to make a single 2D array.  All arrays in the sequence
            must have the same length.
        Arguments:
            tup -- sequence of 1D arrays.  All arrays must have the same 
                   length.
        Examples:
            >>> import scipy
            >>> a = array((1,2,3))
            >>> b = array((2,3,4))
            >>> scipy.vstack((a,b))
            array([[1, 2],
                   [2, 3],
                   [3, 4]])

    """
    arrays = map(Numeric.transpose,map(atleast_2d,tup))
    return Numeric.concatenate(arrays,1)
    
def dstack(tup):
    """ Stack arrays in sequence depth wise (along third dimension)

        Description:
            Take a sequence of arrays and stack them along the third axis.
            All arrays in the sequence must have the same shape along all 
            but the third axis.  This is a simple way to stack 2D arrays 
            (images) into a single 3D array for processing.
            dstack will rebuild arrays divided by dsplit.
        Arguments:
            tup -- sequence of arrays.  All arrays must have the same 
                   shape.
        Examples:
            >>> import scipy
            >>> a = array((1,2,3))
            >>> b = array((2,3,4))
            >>> scipy.dstack((a,b))
            array([       [[1, 2],
                    [2, 3],
                    [3, 4]]])
            >>> a = array([[1],[2],[3]])
            >>> b = array([[2],[3],[4]])
            >>> scipy.dstack((a,b))
            array([[        [1, 2]],
                   [        [2, 3]],
                   [        [3, 4]]])
    """
    return Numeric.concatenate(map(atleast_3d,tup),2)

def _replace_zero_by_x_arrays(sub_arys):
    for i in range(len(sub_arys)):
        if len(Numeric.shape(sub_arys[i])) == 0:
            sub_arys[i] = Numeric.array([])
        elif Numeric.sometrue(Numeric.equal(Numeric.shape(sub_arys[i]),0)):
            sub_arys[i] = Numeric.array([])   
    return sub_arys
    
def array_split(ary,indices_or_sections,axis = 0):
    """ Divide an array into a list of sub-arrays.

        Description:
           Divide ary into a list of sub-arrays along the
           specified axis.  If indices_or_sections is an integer,
           ary is divided into that many equally sized arrays.
           If it is impossible to make an equal split, each of the
           leading arrays in the list have one additional member.  If
           indices_or_sections is a list of sorted integers, its
           entries define the indexes where ary is split.

        Arguments:
           ary -- N-D array.
              Array to be divided into sub-arrays.
           indices_or_sections -- integer or 1D array.
              If integer, defines the number of (close to) equal sized
              sub-arrays.  If it is a 1D array of sorted indices, it
              defines the indexes at which ary is divided.  Any empty
              list results in a single sub-array equal to the original
              array.
           axis -- integer. default=0.
              Specifies the axis along which to split ary.
        Caveats:
           Currently, the default for axis is 0.  This
           means a 2D array is divided into multiple groups
           of rows.  This seems like the appropriate default, but
           we've agreed most other functions should default to
           axis=-1.  Perhaps we should use axis=-1 for consistency.
           However, we could also make the argument that SciPy
           works on "rows" by default.  sum() sums up rows of
           values.  split() will split data into rows.  Opinions?
    """
    try:
        Ntotal = ary.shape[axis]
    except AttributeError:
        Ntotal = len(ary)
    try: # handle scalar case.
        Nsections = len(indices_or_sections) + 1
        div_points = [0] + list(indices_or_sections) + [Ntotal]
    except TypeError: #indices_or_sections is a scalar, not an array.
        Nsections = int(indices_or_sections)
        if Nsections <= 0:
            raise ValueError, 'number sections must be larger than 0.'
        Neach_section,extras = divmod(Ntotal,Nsections)
        section_sizes = [0] + \
                        extras * [Neach_section+1] + \
                        (Nsections-extras) * [Neach_section]
        div_points = Numeric.add.accumulate(Numeric.array(section_sizes))

    sub_arys = []
    sary = Numeric.swapaxes(ary,axis,0)
    for i in range(Nsections):
        st = div_points[i]; end = div_points[i+1]
        sub_arys.append(Numeric.swapaxes(sary[st:end],axis,0))

    # there is a wierd issue with array slicing that allows
    # 0x10 arrays and other such things.  The following cluge is needed
    # to get around this issue.
    sub_arys = _replace_zero_by_x_arrays(sub_arys)
    # end cluge.

    return sub_arys

def split(ary,indices_or_sections,axis=0):
    """ Divide an array into a list of sub-arrays.

        Description:
           Divide ary into a list of sub-arrays along the
           specified axis.  If indices_or_sections is an integer,
           ary is divided into that many equally sized arrays.
           If it is impossible to make an equal split, an error is 
           raised.  This is the only way this function differs from
           the array_split() function. If indices_or_sections is a 
           list of sorted integers, its entries define the indexes
           where ary is split.

        Arguments:
           ary -- N-D array.
              Array to be divided into sub-arrays.
           indices_or_sections -- integer or 1D array.
              If integer, defines the number of (close to) equal sized
              sub-arrays.  If it is a 1D array of sorted indices, it
              defines the indexes at which ary is divided.  Any empty
              list results in a single sub-array equal to the original
              array.
           axis -- integer. default=0.
              Specifies the axis along which to split ary.
        Caveats:
           Currently, the default for axis is 0.  This
           means a 2D array is divided into multiple groups
           of rows.  This seems like the appropriate default, but
           we've agreed most other functions should default to
           axis=-1.  Perhaps we should use axis=-1 for consistency.
           However, we could also make the argument that SciPy
           works on "rows" by default.  sum() sums up rows of
           values.  split() will split data into rows.  Opinions?
    """
    try: len(indices_or_sections)
    except TypeError:
        sections = indices_or_sections
        N = ary.shape[axis]
        if N % sections:
            raise ValueError, 'array split does not result in an equal division'
    res = array_split(ary,indices_or_sections,axis)
    return res

def hsplit(ary,indices_or_sections):
    """ Split ary into multiple columns of sub-arrays

        Description:
            Split a single array into multiple sub arrays.  The array is
            divided into groups of columns.  If indices_or_sections is
            an integer, ary is divided into that many equally sized sub arrays.
            If it is impossible to make the sub-arrays equally sized, the
            operation throws a ValueError exception. See array_split and
            split for other options on indices_or_sections.                        
        Arguments:
           ary -- N-D array.
              Array to be divided into sub-arrays.
           indices_or_sections -- integer or 1D array.
              If integer, defines the number of (close to) equal sized
              sub-arrays.  If it is a 1D array of sorted indices, it
              defines the indexes at which ary is divided.  Any empty
              list results in a single sub-array equal to the original
              array.
        Returns:
            sequence of sub-arrays.  The returned arrays have the same 
            number of dimensions as the input array.
        Related:
            hstack, split, array_split, vsplit, dsplit.           
        Examples:
            >>> import scipy
            >>> a= array((1,2,3,4))
            >>> scipy.hsplit(a,2)
            [array([1, 2]), array([3, 4])]
            >>> a = array([[1,2,3,4],[1,2,3,4]])
            [array([[1, 2],
                   [1, 2]]), array([[3, 4],
                   [3, 4]])]
                   
    """
    if len(Numeric.shape(ary)) == 0:
        raise ValueError, 'hsplit only works on arrays of 1 or more dimensions'
    if len(ary.shape) > 1:
        return split(ary,indices_or_sections,1)
    else:
        return split(ary,indices_or_sections,0)
        
def vsplit(ary,indices_or_sections):
    """ Split ary into multiple rows of sub-arrays

        Description:
            Split a single array into multiple sub arrays.  The array is
            divided into groups of rows.  If indices_or_sections is
            an integer, ary is divided into that many equally sized sub arrays.
            If it is impossible to make the sub-arrays equally sized, the
            operation throws a ValueError exception. See array_split and
            split for other options on indices_or_sections.
        Arguments:
           ary -- N-D array.
              Array to be divided into sub-arrays.
           indices_or_sections -- integer or 1D array.
              If integer, defines the number of (close to) equal sized
              sub-arrays.  If it is a 1D array of sorted indices, it
              defines the indexes at which ary is divided.  Any empty
              list results in a single sub-array equal to the original
              array.
        Returns:
            sequence of sub-arrays.  The returned arrays have the same 
            number of dimensions as the input array.      
        Caveats:
           How should we handle 1D arrays here?  I am currently raising
           an error when I encounter them.  Any better approach?      
           
           Should we reduce the returned array to their minium dimensions
           by getting rid of any dimensions that are 1?
        Related:
            vstack, split, array_split, hsplit, dsplit.
        Examples:
            import scipy
            >>> a = array([[1,2,3,4],
            ...            [1,2,3,4]])
            >>> scipy.vsplit(a)
            [array([       [1, 2, 3, 4]]), array([       [1, 2, 3, 4]])]
                   
    """
    if len(Numeric.shape(ary)) < 2:
        raise ValueError, 'vsplit only works on arrays of 2 or more dimensions'
    return split(ary,indices_or_sections,0)

def dsplit(ary,indices_or_sections):
    """ Split ary into multiple sub-arrays along the 3rd axis (depth)

        Description:
            Split a single array into multiple sub arrays.  The array is
            divided into groups along the 3rd axis.  If indices_or_sections is
            an integer, ary is divided into that many equally sized sub arrays.
            If it is impossible to make the sub-arrays equally sized, the
            operation throws a ValueError exception. See array_split and
            split for other options on indices_or_sections.                        
        Arguments:
           ary -- N-D array.
              Array to be divided into sub-arrays.
           indices_or_sections -- integer or 1D array.
              If integer, defines the number of (close to) equal sized
              sub-arrays.  If it is a 1D array of sorted indices, it
              defines the indexes at which ary is divided.  Any empty
              list results in a single sub-array equal to the original
              array.
        Returns:
            sequence of sub-arrays.  The returned arrays have the same 
            number of dimensions as the input array.
        Caveats:
           See vsplit caveats.       
        Related:
            dstack, split, array_split, hsplit, vsplit.
        Examples:
            >>> a = array([[[1,2,3,4],[1,2,3,4]]])
            [array([       [[1, 2],
                    [1, 2]]]), array([       [[3, 4],
                    [3, 4]]])]
                                       
    """
    if len(Numeric.shape(ary)) < 3:
        raise ValueError, 'vsplit only works on arrays of 3 or more dimensions'
    return split(ary,indices_or_sections,2)


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