"""Functions that ignore nan. """ from __future__ import division, absolute_import, print_function import numpy as np __all__ = [ 'nansum', 'nanmax', 'nanmin', 'nanargmax', 'nanargmin', 'nanmean', 'nanvar', 'nanstd' ] def _nanmean(a, axis=None, dtype=None, out=None, keepdims=False): # Using array() instead of asanyarray() because the former always # makes a copy, which is important due to the copyto() action later arr = np.array(a, subok=True) mask = np.isnan(arr) # Cast bool, unsigned int, and int to float64 if np.dtype is None and issubclass(arr.dtype.type, (np.integer, np.bool_)): ret = np.add.reduce(arr, axis=axis, dtype='f8', out=out, keepdims=keepdims) else: np.copyto(arr, 0.0, where=mask) ret = np.add.reduce(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims) rcount = (~mask).sum(axis=axis) if isinstance(ret, np.ndarray): ret = np.true_divide(ret, rcount, out=ret, casting='unsafe', subok=False) else: ret = ret / rcount return ret def _nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False): # Using array() instead of asanyarray() because the former always # makes a copy, which is important due to the copyto() action later arr = np.array(a, subok=True) mask = np.isnan(arr) # First compute the mean, saving 'rcount' for reuse later if dtype is None and issubclass(arr.dtype.type, (np.integer, np.bool_)): arrmean = np.add.reduce(arr, axis=axis, dtype='f8', keepdims=True) else: np.copyto(arr, 0.0, where=mask) arrmean = np.add.reduce(arr, axis=axis, dtype=dtype, keepdims=True) rcount = (~mask).sum(axis=axis, keepdims=True) if isinstance(arrmean, np.ndarray): arrmean = np.true_divide(arrmean, rcount, out=arrmean, casting='unsafe', subok=False) else: arrmean = arrmean / rcount # arr - arrmean x = arr - arrmean np.copyto(x, 0.0, where=mask) # (arr - arrmean) ** 2 if issubclass(arr.dtype.type, np.complex_): x = np.multiply(x, np.conjugate(x), out=x).real else: x = np.multiply(x, x, out=x) # add.reduce((arr - arrmean) ** 2, axis) ret = np.add.reduce(x, axis=axis, dtype=dtype, out=out, keepdims=keepdims) # add.reduce((arr - arrmean) ** 2, axis) / (n - ddof) if not keepdims and isinstance(rcount, np.ndarray): rcount = rcount.squeeze(axis=axis) rcount -= ddof if isinstance(ret, np.ndarray): ret = np.true_divide(ret, rcount, out=ret, casting='unsafe', subok=False) else: ret = ret / rcount return ret def _nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False): ret = _nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof, keepdims=keepdims) if isinstance(ret, np.ndarray): ret = np.sqrt(ret, out=ret) else: ret = np.sqrt(ret) return ret def _nanop(op, fill, a, axis=None): """ General operation on arrays with not-a-number values. Parameters ---------- op : callable Operation to perform. fill : float NaN values are set to fill before doing the operation. a : array-like Input array. axis : {int, None}, optional Axis along which the operation is computed. By default the input is flattened. Returns ------- y : {ndarray, scalar} Processed data. """ y = np.array(a, subok=True) # We only need to take care of NaN's in floating point arrays dt = y.dtype if np.issubdtype(dt, np.integer) or np.issubdtype(dt, np.bool_): return op(y, axis=axis) mask = np.isnan(a) # y[mask] = fill # We can't use fancy indexing here as it'll mess w/ MaskedArrays # Instead, let's fill the array directly... np.copyto(y, fill, where=mask) res = op(y, axis=axis) mask_all_along_axis = mask.all(axis=axis) # Along some axes, only nan's were encountered. As such, any values # calculated along that axis should be set to nan. if mask_all_along_axis.any(): if np.isscalar(res): res = np.nan else: res[mask_all_along_axis] = np.nan return res def nansum(a, axis=None): """ Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. Parameters ---------- a : array_like Array containing numbers whose sum is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the sum is computed. The default is to compute the sum of the flattened array. Returns ------- y : ndarray An array with the same shape as a, with the specified axis removed. If a is a 0-d array, or if axis is None, a scalar is returned with the same dtype as `a`. See Also -------- numpy.sum : Sum across array including Not a Numbers. isnan : Shows which elements are Not a Number (NaN). isfinite: Shows which elements are not: Not a Number, positive and negative infinity Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. If positive or negative infinity are present the result is positive or negative infinity. But if both positive and negative infinity are present, the result is Not A Number (NaN). Arithmetic is modular when using integer types (all elements of `a` must be finite i.e. no elements that are NaNs, positive infinity and negative infinity because NaNs are floating point types), and no error is raised on overflow. Examples -------- >>> np.nansum(1) 1 >>> np.nansum([1]) 1 >>> np.nansum([1, np.nan]) 1.0 >>> a = np.array([[1, 1], [1, np.nan]]) >>> np.nansum(a) 3.0 >>> np.nansum(a, axis=0) array([ 2., 1.]) When positive infinity and negative infinity are present >>> np.nansum([1, np.nan, np.inf]) inf >>> np.nansum([1, np.nan, np.NINF]) -inf >>> np.nansum([1, np.nan, np.inf, np.NINF]) nan """ return _nanop(np.sum, 0, a, axis) def nanmin(a, axis=None): """ Return the minimum of an array or minimum along an axis, ignoring any NaNs. Parameters ---------- a : array_like Array containing numbers whose minimum is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the minimum is computed. The default is to compute the minimum of the flattened array. Returns ------- nanmin : ndarray An array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if axis is None, an ndarray scalar is returned. The same dtype as `a` is returned. See Also -------- nanmax : The maximum value of an array along a given axis, ignoring any NaNs. amin : The minimum value of an array along a given axis, propagating any NaNs. fmin : Element-wise minimum of two arrays, ignoring any NaNs. minimum : Element-wise minimum of two arrays, propagating any NaNs. isnan : Shows which elements are Not a Number (NaN). isfinite: Shows which elements are neither NaN nor infinity. amax, fmax, maximum Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number. If the input has a integer type the function is equivalent to np.min. Examples -------- >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanmin(a) 1.0 >>> np.nanmin(a, axis=0) array([ 1., 2.]) >>> np.nanmin(a, axis=1) array([ 1., 3.]) When positive infinity and negative infinity are present: >>> np.nanmin([1, 2, np.nan, np.inf]) 1.0 >>> np.nanmin([1, 2, np.nan, np.NINF]) -inf """ a = np.asanyarray(a) if axis is not None: return np.fmin.reduce(a, axis) else: return np.fmin.reduce(a.flat) def nanargmin(a, axis=None): """ Return indices of the minimum values over an axis, ignoring NaNs. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default flattened input is used. Returns ------- index_array : ndarray An array of indices or a single index value. See Also -------- argmin, nanargmax Examples -------- >>> a = np.array([[np.nan, 4], [2, 3]]) >>> np.argmin(a) 0 >>> np.nanargmin(a) 2 >>> np.nanargmin(a, axis=0) array([1, 1]) >>> np.nanargmin(a, axis=1) array([1, 0]) """ return _nanop(np.argmin, np.inf, a, axis) def nanmax(a, axis=None): """ Return the maximum of an array or maximum along an axis, ignoring any NaNs. Parameters ---------- a : array_like Array containing numbers whose maximum is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the maximum is computed. The default is to compute the maximum of the flattened array. Returns ------- nanmax : ndarray An array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if axis is None, an ndarray scalar is returned. The same dtype as `a` is returned. See Also -------- nanmin : The minimum value of an array along a given axis, ignoring any NaNs. amax : The maximum value of an array along a given axis, propagating any NaNs. fmax : Element-wise maximum of two arrays, ignoring any NaNs. maximum : Element-wise maximum of two arrays, propagating any NaNs. isnan : Shows which elements are Not a Number (NaN). isfinite: Shows which elements are neither NaN nor infinity. amin, fmin, minimum Notes ----- Numpy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number. If the input has a integer type the function is equivalent to np.max. Examples -------- >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanmax(a) 3.0 >>> np.nanmax(a, axis=0) array([ 3., 2.]) >>> np.nanmax(a, axis=1) array([ 2., 3.]) When positive infinity and negative infinity are present: >>> np.nanmax([1, 2, np.nan, np.NINF]) 2.0 >>> np.nanmax([1, 2, np.nan, np.inf]) inf """ a = np.asanyarray(a) if axis is not None: return np.fmax.reduce(a, axis) else: return np.fmax.reduce(a.flat) def nanargmax(a, axis=None): """ Return indices of the maximum values over an axis, ignoring NaNs. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default flattened input is used. Returns ------- index_array : ndarray An array of indices or a single index value. See Also -------- argmax, nanargmin Examples -------- >>> a = np.array([[np.nan, 4], [2, 3]]) >>> np.argmax(a) 0 >>> np.nanargmax(a) 1 >>> np.nanargmax(a, axis=0) array([1, 0]) >>> np.nanargmax(a, axis=1) array([1, 1]) """ return _nanop(np.argmax, -np.inf, a, axis) def nanmean(a, axis=None, dtype=None, out=None, keepdims=False): """ Compute the arithmetic mean along the specified axis, ignoring NaNs. Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. `float64` intermediate and return values are used for integer inputs. Parameters ---------- a : array_like Array containing numbers whose mean is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the means are computed. The default is to compute the mean of the flattened array. dtype : data-type, optional Type to use in computing the mean. For integer inputs, the default is `float64`; for floating point inputs, it is the same as the input dtype. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See `doc.ufuncs` for details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- m : ndarray, see dtype parameter above If `out=None`, returns a new array containing the mean values, otherwise a reference to the output array is returned. See Also -------- average : Weighted average mean : Arithmetic mean taken while not ignoring NaNs var, nanvar Notes ----- The arithmetic mean is the sum of the non-nan elements along the axis divided by the number of non-nan elements. Note that for floating-point input, the mean is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32`. Specifying a higher-precision accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanmean(a) 2.6666666666666665 >>> np.nanmean(a, axis=0) array([ 2., 4.]) >>> np.nanmean(a, axis=1) array([ 1., 3.5]) """ if not (type(a) is np.ndarray): try: mean = a.nanmean return mean(axis=axis, dtype=dtype, out=out) except AttributeError: pass return _nanmean(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims) def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False): """ Compute the standard deviation along the specified axis, while ignoring NaNs. Returns the standard deviation, a measure of the spread of a distribution, of the non-NaN array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis. Parameters ---------- a : array_like Calculate the standard deviation of the non-NaN values. axis : int, optional Axis along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array. dtype : dtype, optional Type to use in computing the standard deviation. For arrays of integer type the default is float64, for arrays of float types it is the same as the array type. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary. ddof : int, optional Means Delta Degrees of Freedom. The divisor used in calculations is ``N - ddof``, where ``N`` represents the number of elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- standard_deviation : ndarray, see dtype parameter above. If `out` is None, return a new array containing the standard deviation, otherwise return a reference to the output array. See Also -------- var, mean, std nanvar, nanmean numpy.doc.ufuncs : Section "Output arguments" Notes ----- The standard deviation is the square root of the average of the squared deviations from the mean, i.e., ``std = sqrt(mean(abs(x - x.mean())**2))``. The average squared deviation is normally calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of the infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even with ``ddof=1``, it will not be an unbiased estimate of the standard deviation per se. Note that, for complex numbers, `std` takes the absolute value before squaring, so that the result is always real and nonnegative. For floating-point input, the *std* is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higher-accuracy accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanstd(a) 1.247219128924647 >>> np.nanstd(a, axis=0) array([ 1., 0.]) >>> np.nanstd(a, axis=1) array([ 0., 0.5]) """ if not (type(a) is np.ndarray): try: nanstd = a.nanstd return nanstd(axis=axis, dtype=dtype, out=out, ddof=ddof) except AttributeError: pass return _nanstd(a, axis=axis, dtype=dtype, out=out, ddof=ddof, keepdims=keepdims) def nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False): """ Compute the variance along the specified axis, while ignoring NaNs. Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis. Parameters ---------- a : array_like Array containing numbers whose variance is desired. If `a` is not an array, a conversion is attempted. axis : int, optional Axis along which the variance is computed. The default is to compute the variance of the flattened array. dtype : data-type, optional Type to use in computing the variance. For arrays of integer type the default is `float32`; for arrays of float types it is the same as the array type. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary. ddof : int, optional "Delta Degrees of Freedom": the divisor used in the calculation is ``N - ddof``, where ``N`` represents the number of elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- variance : ndarray, see dtype parameter above If ``out=None``, returns a new array containing the variance; otherwise, a reference to the output array is returned. See Also -------- std : Standard deviation mean : Average var : Variance while not ignoring NaNs nanstd, nanmean numpy.doc.ufuncs : Section "Output arguments" Notes ----- The variance is the average of the squared deviations from the mean, i.e., ``var = mean(abs(x - x.mean())**2)``. The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of a hypothetical infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative. For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32` (see example below). Specifying a higher-accuracy accumulator using the ``dtype`` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.var(a) 1.5555555555555554 >>> np.nanvar(a, axis=0) array([ 1., 0.]) >>> np.nanvar(a, axis=1) array([ 0., 0.25]) """ if not (type(a) is np.ndarray): try: nanvar = a.nanvar return nanvar(axis=axis, dtype=dtype, out=out, ddof=ddof) except AttributeError: pass return _nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof, keepdims=keepdims)