import math from mipylib.numeric import core as _nx from ..core.numerictypes import ScalarType, find_common_type __all__ = ['r_','c_','mgrid'] 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. Parameters ---------- sparse : bool, optional Whether the grid is sparse or not. Default is False. Notes ----- The instances of `nd_grid`, `mgrid`, approximately defined as:: mgrid = nd_grid(sparse=False) Users should use these pre-defined instances instead of using `nd_grid` directly. """ def __init__(self, sparse=False): self.sparse = sparse def __getitem__(self, key): try: num_list = [] for k in range(len(key)): 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): step = abs(step) length = int(step) num_list.insert(0, _nx.linspace(start, stop, length)) else: num_list.insert(0, _nx.arange(start, stop, step)) nn = _nx.meshgrid(*num_list) return nn[::-1] except (IndexError, TypeError): step = key.step stop = key.stop start = key.start if start is None: start = 0 if isinstance(step, complex): # Prevent the (potential) creation of integer arrays step_float = abs(step) length = int(step_float) return _nx.linspace(start, stop, length) else: return _nx.arange(start, stop, step) class MGridClass(nd_grid): """ An instance which returns a dense multi-dimensional "meshgrid". An instance which returns a dense (or fleshed out) mesh-grid when indexed, so that each returned argument has the same shape. The dimensions 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**. Returns ------- mesh-grid `ndarrays` all of the same dimensions See Also -------- ogrid : like `mgrid` but returns open (not fleshed out) mesh grids meshgrid: return coordinate matrices from coordinate vectors r_ : array concatenator :ref:`how-to-partition` Examples -------- >>> np.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]]]) >>> np.mgrid[-1:1:5j] array([-1. , -0.5, 0. , 0.5, 1. ]) """ def __init__(self): super(MGridClass, self).__init__(sparse=False) mgrid = MGridClass() class AxisConcatenator: """ Translates slice objects to concatenation along an axis. For detailed documentation on usage, see `r_`. """ # allow ma.mr_ to override this concatenate = staticmethod(_nx.concatenate) def __init__(self, axis=0, ndmin=1, trans1d=-1): self.axis = axis self.trans1d = trans1d self.ndmin = ndmin def __getitem__(self, key): if not isinstance(key, tuple): key = (key,) # copy attributes, since they can be overridden in the first argument trans1d = self.trans1d ndmin = self.ndmin axis = self.axis objs = [] scalars = [] arraytypes = [] scalartypes = [] for k, item in enumerate(key): scalar = False if isinstance(item, slice): step = item.step start = item.start stop = item.stop if start is None: start = 0 if step is None: step = 1 if isinstance(step, complex): size = int(abs(step)) newobj = _nx.linspace(start, stop, num=size) else: newobj = _nx.arange(start, stop, step) if ndmin > 1: newobj = _nx.array(newobj, copy=False, ndmin=ndmin) if trans1d != -1: newobj = newobj.swapaxes(-1, trans1d) elif isinstance(item, str): if k != 0: raise ValueError("special directives must be the " "first entry.") if item in ('r', 'c'): matrix = True col = (item == 'c') continue if ',' in item: vec = item.split(',') try: axis, ndmin = [int(x) for x in vec[:2]] if len(vec) == 3: trans1d = int(vec[2]) continue except Exception as e: raise ValueError( "unknown special directive {!r}".format(item) ) try: axis = int(item) continue except (ValueError, TypeError): raise ValueError("unknown special directive") elif type(item) in ScalarType: newobj = _nx.array(item, ndmin=ndmin) scalars.append(len(objs)) scalar = True scalartypes.append(newobj.dtype) else: item_ndim = _nx.ndim(item) newobj = _nx.array(item, copy=False, subok=True, ndmin=ndmin) if trans1d != -1 and item_ndim < ndmin: k2 = ndmin - item_ndim k1 = trans1d if k1 < 0: k1 += k2 + 1 defaxes = list(range(ndmin)) axes = defaxes[:k1] + defaxes[k2:] + defaxes[k1:k2] newobj = newobj.transpose(axes) objs.append(newobj) if not scalar and isinstance(newobj, _nx.NDArray): arraytypes.append(newobj.dtype) # Ensure 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 = self.concatenate(tuple(objs), axis=axis) return 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. This is a simple way to build up arrays quickly. There are two use cases. 1. If the index expression contains comma separated arrays, then stack them along their first axis. 2. If the index expression contains slice notation or scalars then create a 1-D array with a range indicated by the slice notation. If slice notation is used, the syntax ``start:stop:step`` is equivalent to ``np.arange(start, stop, step)`` inside of the brackets. However, if ``step`` is an imaginary number (i.e. 100j) then its integer portion is interpreted as a number-of-points desired and the start and stop are inclusive. In other words ``start:stop:stepj`` is interpreted as ``np.linspace(start, stop, step, endpoint=1)`` inside of the brackets. After expansion of slice notation, all comma separated sequences are concatenated together. Optional character strings placed as the first element of the index expression can be used to change the output. The strings 'r' or 'c' result in matrix output. If the result is 1-D and 'r' is specified a 1 x N (row) matrix is produced. If the result is 1-D and 'c' is specified, then a N x 1 (column) matrix is produced. If the result is 2-D then both provide the same matrix result. A string integer specifies which axis to stack multiple comma separated arrays along. A string of two comma-separated integers allows indication of the minimum number of dimensions to force each entry into as the second integer (the axis to concatenate along is still the first integer). A string with three comma-separated integers allows specification of the axis to concatenate along, the minimum number of dimensions to force the entries to, and which axis should contain the start of the arrays which are less than the specified number of dimensions. In other words the third integer allows you to specify where the 1's should be placed in the shape of the arrays that have their shapes upgraded. By default, they are placed in the front of the shape tuple. The third argument allows you to specify where the start of the array should be instead. Thus, a third argument of '0' would place the 1's at the end of the array shape. Negative integers specify where in the new shape tuple the last dimension of upgraded arrays should be placed, so the default is '-1'. Parameters ---------- Not a function, so takes no parameters Returns ------- A concatenated ndarray or matrix. See Also -------- concatenate : Join a sequence of arrays along an existing axis. c_ : Translates slice objects to concatenation along the second axis. Examples -------- >>> np.r_[np.array([1,2,3]), 0, 0, np.array([4,5,6])] array([1, 2, 3, ..., 4, 5, 6]) >>> np.r_[-1:1:6j, [0]*3, 5, 6] array([-1. , -0.6, -0.2, 0.2, 0.6, 1. , 0. , 0. , 0. , 5. , 6. ]) String integers specify the axis to concatenate along or the minimum number of dimensions to force entries into. >>> a = np.array([[0, 1, 2], [3, 4, 5]]) >>> np.r_['-1', a, a] # concatenate along last axis array([[0, 1, 2, 0, 1, 2], [3, 4, 5, 3, 4, 5]]) >>> np.r_['0,2', [1,2,3], [4,5,6]] # concatenate along first axis, dim>=2 array([[1, 2, 3], [4, 5, 6]]) >>> np.r_['0,2,0', [1,2,3], [4,5,6]] array([[1], [2], [3], [4], [5], [6]]) >>> np.r_['1,2,0', [1,2,3], [4,5,6]] array([[1, 4], [2, 5], [3, 6]]) Using 'r' or 'c' as a first string argument creates a matrix. >>> np.r_['r',[1,2,3], [4,5,6]] matrix([[1, 2, 3, 4, 5, 6]]) """ def __init__(self): AxisConcatenator.__init__(self, 0) r_ = RClass() class CClass(AxisConcatenator): """ Translates slice objects to concatenation along the second axis. This is short-hand for ``np.r_['-1,2,0', index expression]``, which is useful because of its common occurrence. In particular, arrays will be stacked along their last axis after being upgraded to at least 2-D with 1's post-pended to the shape (column vectors made out of 1-D arrays). See Also -------- column_stack : Stack 1-D arrays as columns into a 2-D array. r_ : For more detailed documentation. Examples -------- >>> np.c_[np.array([1,2,3]), np.array([4,5,6])] array([[1, 4], [2, 5], [3, 6]]) >>> np.c_[np.array([[1,2,3]]), 0, 0, np.array([[4,5,6]])] array([[1, 2, 3, ..., 4, 5, 6]]) """ def __init__(self): AxisConcatenator.__init__(self, -1, ndmin=2, trans1d=0) c_ = CClass()