from __future__ import division, absolute_import, print_function __all__ = ['atleast_1d', 'atleast_2d', 'atleast_3d', 'block', 'hstack', 'stack', 'vstack'] from . import numeric as _nx from .numeric import array, asanyarray, newaxis from .multiarray import normalize_axis_index def atleast_1d(*arys): """ Convert inputs to arrays with at least one dimension. Scalar inputs are converted to 1-dimensional arrays, whilst higher-dimensional inputs are preserved. Parameters ---------- arys1, arys2, ... : array_like One or more input arrays. Returns ------- ret : ndarray An array, or list of arrays, each with ``a.ndim >= 1``. Copies are made only if necessary. See Also -------- atleast_2d, atleast_3d Examples -------- >>> np.atleast_1d(1.0) array([ 1.]) >>> x = np.arange(9.0).reshape(3,3) >>> np.atleast_1d(x) array([[ 0., 1., 2.], [ 3., 4., 5.], [ 6., 7., 8.]]) >>> np.atleast_1d(x) is x True >>> np.atleast_1d(1, [3, 4]) [array([1]), array([3, 4])] """ res = [] for ary in arys: ary = asanyarray(ary) if ary.ndim == 0: result = ary.reshape(1) else: result = ary res.append(result) if len(res) == 1: return res[0] else: return res def atleast_2d(*arys): """ View inputs as arrays with at least two dimensions. Parameters ---------- arys1, arys2, ... : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have two or more dimensions are preserved. Returns ------- res, res2, ... : ndarray An array, or list of arrays, each with ``a.ndim >= 2``. Copies are avoided where possible, and views with two or more dimensions are returned. See Also -------- atleast_1d, atleast_3d Examples -------- >>> np.atleast_2d(3.0) array([[ 3.]]) >>> x = np.arange(3.0) >>> np.atleast_2d(x) array([[ 0., 1., 2.]]) >>> np.atleast_2d(x).base is x True >>> np.atleast_2d(1, [1, 2], [[1, 2]]) [array([[1]]), array([[1, 2]]), array([[1, 2]])] """ res = [] for ary in arys: ary = asanyarray(ary) if ary.ndim == 0: result = ary.reshape(1, 1) elif ary.ndim == 1: result = ary[newaxis,:] else: result = ary res.append(result) if len(res) == 1: return res[0] else: return res def atleast_3d(*arys): """ View inputs as arrays with at least three dimensions. Parameters ---------- arys1, arys2, ... : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have three or more dimensions are preserved. Returns ------- res1, res2, ... : ndarray An array, or list of arrays, each with ``a.ndim >= 3``. Copies are avoided where possible, and views with three or more dimensions are returned. For example, a 1-D array of shape ``(N,)`` becomes a view of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a view of shape ``(M, N, 1)``. See Also -------- atleast_1d, atleast_2d Examples -------- >>> np.atleast_3d(3.0) array([[[ 3.]]]) >>> x = np.arange(3.0) >>> np.atleast_3d(x).shape (1, 3, 1) >>> x = np.arange(12.0).reshape(4,3) >>> np.atleast_3d(x).shape (4, 3, 1) >>> np.atleast_3d(x).base is x.base # x is a reshape, so not base itself True >>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]): ... print(arr, arr.shape) ... [[[1] [2]]] (1, 2, 1) [[[1] [2]]] (1, 2, 1) [[[1 2]]] (1, 1, 2) """ res = [] for ary in arys: ary = asanyarray(ary) if ary.ndim == 0: result = ary.reshape(1, 1, 1) elif ary.ndim == 1: result = ary[newaxis,:, newaxis] elif ary.ndim == 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). Take a sequence of arrays and stack them vertically to make a single array. Rebuild arrays divided by `vsplit`. This function continues to be supported for backward compatibility, but you should prefer ``np.concatenate`` or ``np.stack``. The ``np.stack`` function was added in NumPy 1.10. Parameters ---------- tup : sequence of ndarrays Tuple containing arrays to be stacked. The arrays must have the same shape along all but the first axis. Returns ------- stacked : ndarray The array formed by stacking the given arrays. See Also -------- stack : Join a sequence of arrays along a new axis. hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third dimension). concatenate : Join a sequence of arrays along an existing axis. vsplit : Split array into a list of multiple sub-arrays vertically. block : Assemble arrays from blocks. Notes ----- Equivalent to ``np.concatenate(tup, axis=0)`` if `tup` contains arrays that are at least 2-dimensional. Examples -------- >>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.vstack((a,b)) array([[1, 2, 3], [2, 3, 4]]) >>> a = np.array([[1], [2], [3]]) >>> b = np.array([[2], [3], [4]]) >>> np.vstack((a,b)) array([[1], [2], [3], [2], [3], [4]]) """ return _nx.concatenate([atleast_2d(_m) for _m in tup], 0) def hstack(tup): """ Stack arrays in sequence horizontally (column wise). Take a sequence of arrays and stack them horizontally to make a single array. Rebuild arrays divided by `hsplit`. This function continues to be supported for backward compatibility, but you should prefer ``np.concatenate`` or ``np.stack``. The ``np.stack`` function was added in NumPy 1.10. Parameters ---------- tup : sequence of ndarrays All arrays must have the same shape along all but the second axis. Returns ------- stacked : ndarray The array formed by stacking the given arrays. See Also -------- stack : Join a sequence of arrays along a new axis. vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third axis). concatenate : Join a sequence of arrays along an existing axis. hsplit : Split array along second axis. block : Assemble arrays from blocks. Notes ----- Equivalent to ``np.concatenate(tup, axis=1)`` if `tup` contains arrays that are at least 2-dimensional. Examples -------- >>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.hstack((a,b)) array([1, 2, 3, 2, 3, 4]) >>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.hstack((a,b)) array([[1, 2], [2, 3], [3, 4]]) """ arrs = [atleast_1d(_m) for _m in tup] # As a special case, dimension 0 of 1-dimensional arrays is "horizontal" if arrs and arrs[0].ndim == 1: return _nx.concatenate(arrs, 0) else: return _nx.concatenate(arrs, 1) def stack(arrays, axis=0): """ Join a sequence of arrays along a new axis. The `axis` parameter specifies the index of the new axis in the dimensions of the result. For example, if ``axis=0`` it will be the first dimension and if ``axis=-1`` it will be the last dimension. .. versionadded:: 1.10.0 Parameters ---------- arrays : sequence of array_like Each array must have the same shape. axis : int, optional The axis in the result array along which the input arrays are stacked. Returns ------- stacked : ndarray The stacked array has one more dimension than the input arrays. See Also -------- concatenate : Join a sequence of arrays along an existing axis. split : Split array into a list of multiple sub-arrays of equal size. block : Assemble arrays from blocks. Examples -------- >>> arrays = [np.random.randn(3, 4) for _ in range(10)] >>> np.stack(arrays, axis=0).shape (10, 3, 4) >>> np.stack(arrays, axis=1).shape (3, 10, 4) >>> np.stack(arrays, axis=2).shape (3, 4, 10) >>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.stack((a, b)) array([[1, 2, 3], [2, 3, 4]]) >>> np.stack((a, b), axis=-1) array([[1, 2], [2, 3], [3, 4]]) """ arrays = [asanyarray(arr) for arr in arrays] if not arrays: raise ValueError('need at least one array to stack') shapes = set(arr.shape for arr in arrays) if len(shapes) != 1: raise ValueError('all input arrays must have the same shape') result_ndim = arrays[0].ndim + 1 axis = normalize_axis_index(axis, result_ndim) sl = (slice(None),) * axis + (_nx.newaxis,) expanded_arrays = [arr[sl] for arr in arrays] return _nx.concatenate(expanded_arrays, axis=axis) class _Recurser(object): """ Utility class for recursing over nested iterables """ def __init__(self, recurse_if): self.recurse_if = recurse_if def map_reduce(self, x, f_map=lambda x, **kwargs: x, f_reduce=lambda x, **kwargs: x, f_kwargs=lambda **kwargs: kwargs, **kwargs): """ Iterate over the nested list, applying: * ``f_map`` (T -> U) to items * ``f_reduce`` (Iterable[U] -> U) to mapped items For instance, ``map_reduce([[1, 2], 3, 4])`` is:: f_reduce([ f_reduce([ f_map(1), f_map(2) ]), f_map(3), f_map(4) ]]) State can be passed down through the calls with `f_kwargs`, to iterables of mapped items. When kwargs are passed, as in ``map_reduce([[1, 2], 3, 4], **kw)``, this becomes:: kw1 = f_kwargs(**kw) kw2 = f_kwargs(**kw1) f_reduce([ f_reduce([ f_map(1), **kw2) f_map(2, **kw2) ], **kw1), f_map(3, **kw1), f_map(4, **kw1) ]], **kw) """ def f(x, **kwargs): if not self.recurse_if(x): return f_map(x, **kwargs) else: next_kwargs = f_kwargs(**kwargs) return f_reduce(( f(xi, **next_kwargs) for xi in x ), **kwargs) return f(x, **kwargs) def walk(self, x, index=()): """ Iterate over x, yielding (index, value, entering), where * ``index``: a tuple of indices up to this point * ``value``: equal to ``x[index[0]][...][index[-1]]``. On the first iteration, is ``x`` itself * ``entering``: bool. The result of ``recurse_if(value)`` """ do_recurse = self.recurse_if(x) yield index, x, do_recurse if not do_recurse: return for i, xi in enumerate(x): # yield from ... for v in self.walk(xi, index + (i,)): yield v def block(arrays): """ Assemble an nd-array from nested lists of blocks. Blocks in the innermost lists are concatenated (see `concatenate`) along the last dimension (-1), then these are concatenated along the second-last dimension (-2), and so on until the outermost list is reached. Blocks can be of any dimension, but will not be broadcasted using the normal rules. Instead, leading axes of size 1 are inserted, to make ``block.ndim`` the same for all blocks. This is primarily useful for working with scalars, and means that code like ``np.block([v, 1])`` is valid, where ``v.ndim == 1``. When the nested list is two levels deep, this allows block matrices to be constructed from their components. .. versionadded:: 1.13.0 Parameters ---------- arrays : nested list of array_like or scalars (but not tuples) If passed a single ndarray or scalar (a nested list of depth 0), this is returned unmodified (and not copied). Elements shapes must match along the appropriate axes (without broadcasting), but leading 1s will be prepended to the shape as necessary to make the dimensions match. Returns ------- block_array : ndarray The array assembled from the given blocks. The dimensionality of the output is equal to the greatest of: * the dimensionality of all the inputs * the depth to which the input list is nested Raises ------ ValueError * If list depths are mismatched - for instance, ``[[a, b], c]`` is illegal, and should be spelt ``[[a, b], [c]]`` * If lists are empty - for instance, ``[[a, b], []]`` See Also -------- concatenate : Join a sequence of arrays together. stack : Stack arrays in sequence along a new dimension. hstack : Stack arrays in sequence horizontally (column wise). vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third dimension). vsplit : Split array into a list of multiple sub-arrays vertically. Notes ----- When called with only scalars, ``np.block`` is equivalent to an ndarray call. So ``np.block([[1, 2], [3, 4]])`` is equivalent to ``np.array([[1, 2], [3, 4]])``. This function does not enforce that the blocks lie on a fixed grid. ``np.block([[a, b], [c, d]])`` is not restricted to arrays of the form:: AAAbb AAAbb cccDD But is also allowed to produce, for some ``a, b, c, d``:: AAAbb AAAbb cDDDD Since concatenation happens along the last axis first, `block` is _not_ capable of producing the following directly:: AAAbb cccbb cccDD Matlab's "square bracket stacking", ``[A, B, ...; p, q, ...]``, is equivalent to ``np.block([[A, B, ...], [p, q, ...]])``. Examples -------- The most common use of this function is to build a block matrix >>> A = np.eye(2) * 2 >>> B = np.eye(3) * 3 >>> np.block([ ... [A, np.zeros((2, 3))], ... [np.ones((3, 2)), B ] ... ]) array([[ 2., 0., 0., 0., 0.], [ 0., 2., 0., 0., 0.], [ 1., 1., 3., 0., 0.], [ 1., 1., 0., 3., 0.], [ 1., 1., 0., 0., 3.]]) With a list of depth 1, `block` can be used as `hstack` >>> np.block([1, 2, 3]) # hstack([1, 2, 3]) array([1, 2, 3]) >>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.block([a, b, 10]) # hstack([a, b, 10]) array([1, 2, 3, 2, 3, 4, 10]) >>> A = np.ones((2, 2), int) >>> B = 2 * A >>> np.block([A, B]) # hstack([A, B]) array([[1, 1, 2, 2], [1, 1, 2, 2]]) With a list of depth 2, `block` can be used in place of `vstack`: >>> a = np.array([1, 2, 3]) >>> b = np.array([2, 3, 4]) >>> np.block([[a], [b]]) # vstack([a, b]) array([[1, 2, 3], [2, 3, 4]]) >>> A = np.ones((2, 2), int) >>> B = 2 * A >>> np.block([[A], [B]]) # vstack([A, B]) array([[1, 1], [1, 1], [2, 2], [2, 2]]) It can also be used in places of `atleast_1d` and `atleast_2d` >>> a = np.array(0) >>> b = np.array([1]) >>> np.block([a]) # atleast_1d(a) array([0]) >>> np.block([b]) # atleast_1d(b) array([1]) >>> np.block([[a]]) # atleast_2d(a) array([[0]]) >>> np.block([[b]]) # atleast_2d(b) array([[1]]) """ def atleast_nd(x, ndim): x = asanyarray(x) diff = max(ndim - x.ndim, 0) return x[(None,)*diff + (Ellipsis,)] def format_index(index): return 'arrays' + ''.join('[{}]'.format(i) for i in index) rec = _Recurser(recurse_if=lambda x: type(x) is list) # ensure that the lists are all matched in depth list_ndim = None any_empty = False for index, value, entering in rec.walk(arrays): if type(value) is tuple: # not strictly necessary, but saves us from: # - more than one way to do things - no point treating tuples like # lists # - horribly confusing behaviour that results when tuples are # treated like ndarray raise TypeError( '{} is a tuple. ' 'Only lists can be used to arrange blocks, and np.block does ' 'not allow implicit conversion from tuple to ndarray.'.format( format_index(index) ) ) if not entering: curr_depth = len(index) elif len(value) == 0: curr_depth = len(index) + 1 any_empty = True else: continue if list_ndim is not None and list_ndim != curr_depth: raise ValueError( "List depths are mismatched. First element was at depth {}, " "but there is an element at depth {} ({})".format( list_ndim, curr_depth, format_index(index) ) ) list_ndim = curr_depth # do this here so we catch depth mismatches first if any_empty: raise ValueError('Lists cannot be empty') # convert all the arrays to ndarrays arrays = rec.map_reduce(arrays, f_map=asanyarray, f_reduce=list ) # determine the maximum dimension of the elements elem_ndim = rec.map_reduce(arrays, f_map=lambda xi: xi.ndim, f_reduce=max ) ndim = max(list_ndim, elem_ndim) # first axis to concatenate along first_axis = ndim - list_ndim # Make all the elements the same dimension arrays = rec.map_reduce(arrays, f_map=lambda xi: atleast_nd(xi, ndim), f_reduce=list ) # concatenate innermost lists on the right, outermost on the left return rec.map_reduce(arrays, f_reduce=lambda xs, axis: _nx.concatenate(list(xs), axis=axis), f_kwargs=lambda axis: dict(axis=axis+1), axis=first_axis )