"""Masked arrays add-ons. A collection of utilities for maskedarray :author: Pierre Gerard-Marchant :contact: pierregm_at_uga_dot_edu :version: $Id: extras.py 3473 2007-10-29 15:18:13Z jarrod.millman $ """ __author__ = "Pierre GF Gerard-Marchant ($Author: jarrod.millman $)" __version__ = '1.0' __revision__ = "$Revision: 3473 $" __date__ = '$Date: 2007-10-29 17:18:13 +0200 (Mon, 29 Oct 2007) $' __all__ = ['apply_along_axis', 'atleast_1d', 'atleast_2d', 'atleast_3d', 'average', 'column_stack','compress_cols','compress_rowcols', 'compress_rows', 'count_masked', 'dot','dstack', 'ediff1d','expand_dims', 'flatnotmasked_contiguous','flatnotmasked_edges', 'hsplit','hstack', 'mask_cols','mask_rowcols','mask_rows','masked_all','masked_all_like', 'median','mr_', 'notmasked_contiguous','notmasked_edges', 'polyfit', 'row_stack', 'vander','vstack', ] from itertools import groupby import core from core import MaskedArray, MAError, add, array, asarray, concatenate, count,\ filled, getmask, getmaskarray, masked, masked_array, mask_or, nomask, ones,\ sort, zeros #from core import * import numpy as np from numpy import ndarray, array as nxarray import numpy.core.umath as umath from numpy.lib.index_tricks import AxisConcatenator from numpy.lib.polynomial import _lstsq, _single_eps, _double_eps #............................................................................... def issequence(seq): """Is seq a sequence (ndarray, list or tuple)?""" if isinstance(seq, ndarray): return True elif isinstance(seq, tuple): return True elif isinstance(seq, list): return True return False def count_masked(arr, axis=None): """Count the number of masked elements along the given axis. Parameters ---------- axis : int, optional Axis along which to count. If None (default), a flattened version of the array is used. """ m = getmaskarray(arr) return m.sum(axis) def masked_all(shape, dtype=float): """Return an empty masked array of the given shape and dtype, where all the data are masked. Parameters ---------- dtype : dtype, optional Data type of the output. """ a = masked_array(np.empty(shape, dtype), mask=np.ones(shape, bool)) return a def masked_all_like(arr): """Return an empty masked array of the same shape and dtype as the array `a`, where all the data are masked. """ a = masked_array(np.empty_like(arr), mask=np.ones(arr.shape, bool)) return a #####-------------------------------------------------------------------------- #---- --- Standard functions --- #####-------------------------------------------------------------------------- class _fromnxfunction: """Defines a wrapper to adapt numpy functions to masked arrays.""" def __init__(self, funcname): self._function = funcname self.__doc__ = self.getdoc() def getdoc(self): "Retrieves the __doc__ string from the function." return getattr(np, self._function).__doc__ +\ "*Notes*:\n (The function is applied to both the _data and the _mask, if any.)" def __call__(self, *args, **params): func = getattr(np, self._function) if len(args)==1: x = args[0] if isinstance(x, ndarray): _d = func(nxasarray(x), **params) _m = func(getmaskarray(x), **params) return masked_array(_d, mask=_m) elif isinstance(x, tuple) or isinstance(x, list): _d = func(tuple([np.asarray(a) for a in x]), **params) _m = func(tuple([getmaskarray(a) for a in x]), **params) return masked_array(_d, mask=_m) else: arrays = [] args = list(args) while len(args)>0 and issequence(args[0]): arrays.append(args.pop(0)) res = [] for x in arrays: _d = func(np.asarray(x), *args, **params) _m = func(getmaskarray(x), *args, **params) res.append(masked_array(_d, mask=_m)) return res atleast_1d = _fromnxfunction('atleast_1d') atleast_2d = _fromnxfunction('atleast_2d') atleast_3d = _fromnxfunction('atleast_3d') vstack = row_stack = _fromnxfunction('vstack') hstack = _fromnxfunction('hstack') column_stack = _fromnxfunction('column_stack') dstack = _fromnxfunction('dstack') hsplit = _fromnxfunction('hsplit') def expand_dims(a, axis): """Expands the shape of a by including newaxis before axis. """ if not isinstance(a, MaskedArray): return np.expand_dims(a, axis) elif getmask(a) is nomask: return np.expand_dims(a, axis).view(MaskedArray) m = getmaskarray(a) return masked_array(np.expand_dims(a, axis), mask=np.expand_dims(m, axis)) #####-------------------------------------------------------------------------- #---- #####-------------------------------------------------------------------------- def flatten_inplace(seq): """Flatten a sequence in place.""" k = 0 while (k != len(seq)): while hasattr(seq[k],'__iter__'): seq[k:(k+1)] = seq[k] k += 1 return seq def apply_along_axis(func1d, axis, arr, *args, **kwargs): """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. """ arr = core.array(arr, copy=False, subok=True) nd = arr.ndim if axis < 0: axis += nd if (axis >= nd): raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d." % (axis,nd)) ind = [0]*(nd-1) i = np.zeros(nd,'O') indlist = range(nd) indlist.remove(axis) i[axis] = slice(None,None) outshape = np.asarray(arr.shape).take(indlist) i.put(indlist, ind) j = i.copy() res = func1d(arr[tuple(i.tolist())], *args, **kwargs) # if res is a number, then we have a smaller output array asscalar = np.isscalar(res) if not asscalar: try: len(res) except TypeError: asscalar = True # Note: we shouldn't set the dtype of the output from the first result... #...so we force the type to object, and build a list of dtypes #...we'll just take the largest, to avoid some downcasting dtypes = [] if asscalar: dtypes.append(np.asarray(res).dtype) outarr = zeros(outshape, object) outarr[tuple(ind)] = res Ntot = np.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 i.put(indlist, ind) res = func1d(arr[tuple(i.tolist())], *args, **kwargs) outarr[tuple(ind)] = res dtypes.append(asarray(res).dtype) k += 1 else: res = core.array(res, copy=False, subok=True) j = i.copy() j[axis] = ([slice(None, None)] * res.ndim) j.put(indlist, ind) Ntot = np.product(outshape) holdshape = outshape outshape = list(arr.shape) outshape[axis] = res.shape dtypes.append(asarray(res).dtype) outshape = flatten_inplace(outshape) outarr = zeros(outshape, object_) outarr[tuple(flatten_inplace(j.tolist()))] = 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 i.put(indlist, ind) j.put(indlist, ind) res = func1d(arr[tuple(i.tolist())], *args, **kwargs) outarr[tuple(flatten_inplace(j.tolist()))] = res dtypes.append(asarray(res).dtype) k += 1 max_dtypes = np.dtype(np.asarray(dtypes).max()) if not hasattr(arr, '_mask'): result = np.asarray(outarr, dtype=max_dtypes) else: result = core.asarray(outarr, dtype=max_dtypes) result.fill_value = core.default_fill_value(result) return result def average(a, axis=None, weights=None, returned=False): """Average the array over the given axis. Parameters ---------- axis : int, optional Axis along which to perform the operation. If None, applies to a flattened version of the array. weights : sequence, optional Sequence of weights. The weights must have the shape of a, or be 1D with length the size of a along the given axis. If no weights are given, weights are assumed to be 1. returned : bool Flag indicating whether a tuple (result, sum of weights/counts) should be returned as output (True), or just the result (False). """ a = asarray(a) mask = a.mask ash = a.shape if ash == (): ash = (1,) if axis is None: if mask is nomask: if weights is None: n = a.sum(axis=None) d = float(a.size) else: w = filled(weights, 0.0).ravel() n = umath.add.reduce(a._data.ravel() * w) d = umath.add.reduce(w) del w else: if weights is None: n = a.filled(0).sum(axis=None) d = umath.add.reduce((-mask).ravel().astype(int)) else: w = array(filled(weights, 0.0), float, mask=mask).ravel() n = add.reduce(a.ravel() * w) d = add.reduce(w) del w else: if mask is nomask: if weights is None: d = ash[axis] * 1.0 n = add.reduce(a._data, axis, dtype=float) else: w = filled(weights, 0.0) wsh = w.shape if wsh == (): wsh = (1,) if wsh == ash: w = np.array(w, float, copy=0) n = add.reduce(a*w, axis) d = add.reduce(w, axis) del w elif wsh == (ash[axis],): ni = ash[axis] r = [None]*len(ash) r[axis] = slice(None, None, 1) w = eval ("w["+ repr(tuple(r)) + "] * ones(ash, float)") n = add.reduce(a*w, axis, dtype=float) d = add.reduce(w, axis, dtype=float) del w, r else: raise ValueError, 'average: weights wrong shape.' else: if weights is None: n = add.reduce(a, axis, dtype=float) d = umath.add.reduce((-mask), axis=axis, dtype=float) else: w = filled(weights, 0.0) wsh = w.shape if wsh == (): wsh = (1,) if wsh == ash: w = array(w, dtype=float, mask=mask, copy=0) n = add.reduce(a*w, axis, dtype=float) d = add.reduce(w, axis, dtype=float) elif wsh == (ash[axis],): ni = ash[axis] r = [None]*len(ash) r[axis] = slice(None, None, 1) w = eval ("w["+ repr(tuple(r)) + \ "] * masked_array(ones(ash, float), mask)") n = add.reduce(a*w, axis, dtype=float) d = add.reduce(w, axis, dtype=float) else: raise ValueError, 'average: weights wrong shape.' del w if n is masked or d is masked: return masked result = n/d del n if isinstance(result, MaskedArray): if ((axis is None) or (axis==0 and a.ndim == 1)) and \ (result.mask is nomask): result = result._data if returned: if not isinstance(d, MaskedArray): d = masked_array(d) if isinstance(d, ndarray) and (not d.shape == result.shape): d = ones(result.shape, dtype=float) * d if returned: return result, d else: return result def median(a, axis=0, out=None, overwrite_input=False): """Compute the median along the specified axis. Returns the median of the array elements. The median is taken over the first axis of the array by default, otherwise over the specified axis. Parameters ---------- a : array-like Input array or object that can be converted to an array axis : {int, None}, optional Axis along which the medians are computed. The default is to compute the median along the first dimension. axis=None returns the median of the flattened array out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. overwrite_input : {False, True}, optional If True, then allow use of memory of input array (a) for calculations. The input array will be modified by the call to median. This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted. Default is False. Note that, if overwrite_input is true, and the input is not already an ndarray, an error will be raised. Returns ------- median : ndarray. A new array holding the result is returned unless out is specified, in which case a reference to out is returned. Return datatype is float64 for ints and floats smaller than float64, or the input datatype otherwise. See Also ------- mean Notes ----- Given a vector V length N, the median of V is the middle value of a sorted copy of V (Vs) - i.e. Vs[(N-1)/2], when N is odd. It is the mean of the two middle values of Vs, when N is even. """ def _median1D(data): counts = filled(count(data, axis),0) (idx, rmd) = divmod(counts, 2) if rmd: choice = slice(idx, idx+1) else: choice = slice(idx-1, idx+1) return data[choice].mean(0) # if overwrite_input: if axis is None: sorted = a.ravel() sorted.sort() else: a.sort(axis=axis) sorted = a else: sorted = sort(a, axis=axis) if axis is None: result = _median1D(sorted) else: result = apply_along_axis(_median1D, axis, sorted) return result #.............................................................................. def compress_rowcols(x, axis=None): """Suppress the rows and/or columns of a 2D array that contains masked values. The suppression behavior is selected with the `axis`parameter. - If axis is None, rows and columns are suppressed. - If axis is 0, only rows are suppressed. - If axis is 1 or -1, only columns are suppressed. Parameters ---------- axis : int, optional Axis along which to perform the operation. If None, applies to a flattened version of the array. Returns ------- compressed_array : an ndarray. """ x = asarray(x) if x.ndim != 2: raise NotImplementedError, "compress2d works for 2D arrays only." m = getmask(x) # Nothing is masked: return x if m is nomask or not m.any(): return x._data # All is masked: return empty if m.all(): return nxarray([]) # Builds a list of rows/columns indices (idxr, idxc) = (range(len(x)), range(x.shape[1])) masked = m.nonzero() if not axis: for i in np.unique(masked[0]): idxr.remove(i) if axis in [None, 1, -1]: for j in np.unique(masked[1]): idxc.remove(j) return x._data[idxr][:,idxc] def compress_rows(a): """Suppress whole rows of a 2D array that contain masked values. """ return compress_rowcols(a, 0) def compress_cols(a): """Suppress whole columnss of a 2D array that contain masked values. """ return compress_rowcols(a, 1) def mask_rowcols(a, axis=None): """Mask whole rows and/or columns of a 2D array that contain masked values. The masking behavior is selected with the `axis`parameter. - If axis is None, rows and columns are masked. - If axis is 0, only rows are masked. - If axis is 1 or -1, only columns are masked. Parameters ---------- axis : int, optional Axis along which to perform the operation. If None, applies to a flattened version of the array. Returns ------- a *pure* ndarray. """ a = asarray(a) if a.ndim != 2: raise NotImplementedError, "compress2d works for 2D arrays only." m = getmask(a) # Nothing is masked: return a if m is nomask or not m.any(): return a maskedval = m.nonzero() a._mask = a._mask.copy() if not axis: a[np.unique(maskedval[0])] = masked if axis in [None, 1, -1]: a[:,np.unique(maskedval[1])] = masked return a def mask_rows(a, axis=None): """Mask whole rows of a 2D array that contain masked values. Parameters ---------- axis : int, optional Axis along which to perform the operation. If None, applies to a flattened version of the array. """ return mask_rowcols(a, 0) def mask_cols(a, axis=None): """Mask whole columns of a 2D array that contain masked values. Parameters ---------- axis : int, optional Axis along which to perform the operation. If None, applies to a flattened version of the array. """ return mask_rowcols(a, 1) def dot(a,b, strict=False): """Return the dot product of two 2D masked arrays a and b. Like the generic numpy equivalent, the product sum is over the last dimension of a and the second-to-last dimension of b. If strict is True, masked values are propagated: if a masked value appears in a row or column, the whole row or column is considered masked. Parameters ---------- strict : {boolean} Whether masked data are propagated (True) or set to 0 for the computation. Notes ----- The first argument is not conjugated. """ #TODO: Works only with 2D arrays. There should be a way to get it to run with higher dimension if strict and (a.ndim == 2) and (b.ndim == 2): a = mask_rows(a) b = mask_cols(b) # d = np.dot(filled(a, 0), filled(b, 0)) # am = (~getmaskarray(a)) bm = (~getmaskarray(b)) m = ~np.dot(am, bm) return masked_array(d, mask=m) #............................................................................... def ediff1d(array, to_end=None, to_begin=None): """Return the differences between consecutive elements of an array, possibly with prefixed and/or appended values. Parameters ---------- array : {array} Input array, will be flattened before the difference is taken. to_end : {number}, optional If provided, this number will be tacked onto the end of the returned differences. to_begin : {number}, optional If provided, this number will be taked onto the beginning of the returned differences. Returns ------- ed : {array} The differences. Loosely, this will be (ary[1:] - ary[:-1]). """ a = masked_array(array, copy=True) if a.ndim > 1: a.reshape((a.size,)) (d, m, n) = (a._data, a._mask, a.size-1) dd = d[1:]-d[:-1] if m is nomask: dm = nomask else: dm = m[1:]-m[:-1] # if to_end is not None: to_end = asarray(to_end) nend = to_end.size if to_begin is not None: to_begin = asarray(to_begin) nbegin = to_begin.size r_data = np.empty((n+nend+nbegin,), dtype=a.dtype) r_mask = np.zeros((n+nend+nbegin,), dtype=bool) r_data[:nbegin] = to_begin._data r_mask[:nbegin] = to_begin._mask r_data[nbegin:-nend] = dd r_mask[nbegin:-nend] = dm else: r_data = np.empty((n+nend,), dtype=a.dtype) r_mask = np.zeros((n+nend,), dtype=bool) r_data[:-nend] = dd r_mask[:-nend] = dm r_data[-nend:] = to_end._data r_mask[-nend:] = to_end._mask # elif to_begin is not None: to_begin = asarray(to_begin) nbegin = to_begin.size r_data = np.empty((n+nbegin,), dtype=a.dtype) r_mask = np.zeros((n+nbegin,), dtype=bool) r_data[:nbegin] = to_begin._data r_mask[:nbegin] = to_begin._mask r_data[nbegin:] = dd r_mask[nbegin:] = dm # else: r_data = dd r_mask = dm return masked_array(r_data, mask=r_mask) #####-------------------------------------------------------------------------- #---- --- Concatenation helpers --- #####-------------------------------------------------------------------------- class MAxisConcatenator(AxisConcatenator): """Translate slice objects to concatenation along an axis. """ def __init__(self, axis=0): AxisConcatenator.__init__(self, axis, matrix=False) def __getitem__(self,key): if isinstance(key, str): raise MAError, "Unavailable for masked array." if type(key) is not tuple: key = (key,) objs = [] scalars = [] final_dtypedescr = None 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 type(step) is type(1j): size = int(abs(step)) newobj = np.linspace(start, stop, num=size) else: newobj = np.arange(start, stop, step) elif type(key[k]) is str: if (key[k] in 'rc'): self.matrix = True self.col = (key[k] == 'c') continue try: self.axis = int(key[k]) continue except (ValueError, TypeError): raise ValueError, "Unknown special directive" elif type(key[k]) in np.ScalarType: newobj = asarray([key[k]]) scalars.append(k) scalar = True else: newobj = key[k] objs.append(newobj) if isinstance(newobj, ndarray) and not scalar: if final_dtypedescr is None: final_dtypedescr = newobj.dtype elif newobj.dtype > final_dtypedescr: final_dtypedescr = newobj.dtype if final_dtypedescr is not None: for k in scalars: objs[k] = objs[k].astype(final_dtypedescr) res = concatenate(tuple(objs),axis=self.axis) return self._retval(res) class mr_class(MAxisConcatenator): """Translate slice objects to concatenation along the first axis. For example: >>> mr_[array([1,2,3]), 0, 0, array([4,5,6])] array([1, 2, 3, 0, 0, 4, 5, 6]) """ def __init__(self): MAxisConcatenator.__init__(self, 0) mr_ = mr_class() #####-------------------------------------------------------------------------- #---- Find unmasked data --- #####-------------------------------------------------------------------------- def flatnotmasked_edges(a): """Find the indices of the first and last not masked values in a 1D masked array. If all values are masked, returns None. """ m = getmask(a) if m is nomask or not np.any(m): return [0,-1] unmasked = np.flatnonzero(~m) if len(unmasked) > 0: return unmasked[[0,-1]] else: return None def notmasked_edges(a, axis=None): """Find the indices of the first and last not masked values along the given axis in a masked array. If all values are masked, return None. Otherwise, return a list of 2 tuples, corresponding to the indices of the first and last unmasked values respectively. Parameters ---------- axis : int, optional Axis along which to perform the operation. If None, applies to a flattened version of the array. """ a = asarray(a) if axis is None or a.ndim == 1: return flatnotmasked_edges(a) m = getmask(a) idx = array(np.indices(a.shape), mask=np.asarray([m]*a.ndim)) return [tuple([idx[i].min(axis).compressed() for i in range(a.ndim)]), tuple([idx[i].max(axis).compressed() for i in range(a.ndim)]),] def flatnotmasked_contiguous(a): """Find contiguous unmasked data in a flattened masked array. Return a sorted sequence of slices (start index, end index). """ m = getmask(a) if m is nomask: return (a.size, [0,-1]) unmasked = np.flatnonzero(~m) if len(unmasked) == 0: return None result = [] for k, group in groupby(enumerate(unmasked), lambda (i,x):i-x): tmp = np.array([g[1] for g in group], int) # result.append((tmp.size, tuple(tmp[[0,-1]]))) result.append( slice(tmp[0], tmp[-1]) ) result.sort() return result def notmasked_contiguous(a, axis=None): """Find contiguous unmasked data in a masked array along the given axis. Parameters ---------- axis : int, optional Axis along which to perform the operation. If None, applies to a flattened version of the array. Returns ------- A sorted sequence of slices (start index, end index). Notes ----- Only accepts 2D arrays at most. """ a = asarray(a) nd = a.ndim if nd > 2: raise NotImplementedError,"Currently limited to atmost 2D array." if axis is None or nd == 1: return flatnotmasked_contiguous(a) # result = [] # other = (axis+1)%2 idx = [0,0] idx[axis] = slice(None, None) # for i in range(a.shape[other]): idx[other] = i result.append( flatnotmasked_contiguous(a[idx]) ) return result #####-------------------------------------------------------------------------- #---- Polynomial fit --- #####-------------------------------------------------------------------------- def vander(x, n=None): """%s Notes ----- Masked values in x will result in rows of zeros. """ _vander = np.vander(x, n) m = getmask(x) if m is not nomask: _vander[m] = 0 return _vander def polyfit(x, y, deg, rcond=None, full=False): """%s Notes ----- Any masked values in x is propagated in y, and vice-versa. """ order = int(deg) + 1 x = asarray(x) mx = getmask(x) y = asarray(y) if y.ndim == 1: m = mask_or(mx, getmask(y)) elif y.ndim == 2: y = mask_rows(y) my = getmask(y) if my is not nomask: m = mask_or(mx, my[:,0]) else: m = mx else: raise TypeError,"Expected a 1D or 2D array for y!" if m is not nomask: x[m] = y[m] = masked # Set rcond if rcond is None : if x.dtype in (np.single, np.csingle): rcond = len(x)*_single_eps else : rcond = len(x)*_double_eps # Scale x to improve condition number scale = abs(x).max() if scale != 0 : x = x / scale # solve least squares equation for powers of x v = vander(x, order) c, resids, rank, s = _lstsq(v, y.filled(0), rcond) # warn on rank reduction, which indicates an ill conditioned matrix if rank != order and not full: warnings.warn("Polyfit may be poorly conditioned", np.RankWarning) # scale returned coefficients if scale != 0 : if c.ndim == 1 : c /= np.vander([scale], order)[0] else : c /= np.vander([scale], order).T if full : return c, resids, rank, s, rcond else : return c _g = globals() for nfunc in ('vander', 'polyfit'): _g[nfunc].func_doc = _g[nfunc].func_doc % getattr(np,nfunc).__doc__ ################################################################################