numpy.lib.nanfunctions

module documentation

Functions that ignore NaN.

Functions

  • nanmin -- minimum non-NaN value
  • nanmax -- maximum non-NaN value
  • nanargmin -- index of minimum non-NaN value
  • nanargmax -- index of maximum non-NaN value
  • nansum -- sum of non-NaN values
  • nanprod -- product of non-NaN values
  • nancumsum -- cumulative sum of non-NaN values
  • nancumprod -- cumulative product of non-NaN values
  • nanmean -- mean of non-NaN values
  • nanvar -- variance of non-NaN values
  • nanstd -- standard deviation of non-NaN values
  • nanmedian -- median of non-NaN values
  • nanquantile -- qth quantile of non-NaN values
  • nanpercentile -- qth percentile of non-NaN values
Variable array​_function​_dispatch Undocumented
Function ​_copyto Replace values in a with NaN where mask is True. This differs from copyto in that it will deal with the case where a is a numpy scalar.
Function ​_divide​_by​_count No summary
Function ​_nan​_mask No summary
Function ​_nanargmax​_dispatcher Undocumented
Function ​_nanargmin​_dispatcher Undocumented
Function ​_nancumprod​_dispatcher Undocumented
Function ​_nancumsum​_dispatcher Undocumented
Function ​_nanmax​_dispatcher Undocumented
Function ​_nanmean​_dispatcher Undocumented
Function ​_nanmedian Private function that doesn't support extended axis or keepdims. These methods are extended to this function using _ureduce See nanmedian for parameter usage
Function ​_nanmedian1d Private function for rank 1 arrays. Compute the median ignoring NaNs. See nanmedian for parameter usage
Function ​_nanmedian​_dispatcher Undocumented
Function ​_nanmedian​_small sort + indexing median, faster for small medians along multiple dimensions due to the high overhead of apply_along_axis
Function ​_nanmin​_dispatcher Undocumented
Function ​_nanpercentile​_dispatcher Undocumented
Function ​_nanprod​_dispatcher Undocumented
Function ​_nanquantile​_1d Private function for rank 1 arrays. Compute quantile ignoring NaNs. See nanpercentile for parameter usage
Function ​_nanquantile​_dispatcher Undocumented
Function ​_nanquantile​_unchecked Assumes that q is in [0, 1], and is an ndarray
Function ​_nanquantile​_ureduce​_func Private function that doesn't support extended axis or keepdims. These methods are extended to this function using _ureduce See nanpercentile for parameter usage
Function ​_nanstd​_dispatcher Undocumented
Function ​_nansum​_dispatcher Undocumented
Function ​_nanvar​_dispatcher Undocumented
Function ​_remove​_nan​_1d Equivalent to arr1d[~arr1d.isnan()], but in a different order
Function ​_replace​_nan No summary
Function nanargmax Return the indices of the maximum values in the specified axis ignoring NaNs. For all-NaN slices ValueError is raised. Warning: the results cannot be trusted if a slice contains only NaNs and -Infs.
Function nanargmin Return the indices of the minimum values in the specified axis ignoring NaNs. For all-NaN slices ValueError is raised. Warning: the results cannot be trusted if a slice contains only NaNs and Infs.
Function nancumprod Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones.
Function nancumsum Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. The cumulative sum does not change when NaNs are encountered and leading NaNs are replaced by zeros.
Function nanmax Return the maximum of an array or maximum along an axis, ignoring any NaNs. When all-NaN slices are encountered a RuntimeWarning is raised and NaN is returned for that slice.
Function nanmean Compute the arithmetic mean along the specified axis, ignoring NaNs.
Function nanmedian Compute the median along the specified axis, while ignoring NaNs.
Function nanmin Return minimum of an array or minimum along an axis, ignoring any NaNs. When all-NaN slices are encountered a RuntimeWarning is raised and Nan is returned for that slice.
Function nanpercentile Compute the qth percentile of the data along the specified axis, while ignoring nan values.
Function nanprod Return the product of array elements over a given axis treating Not a Numbers (NaNs) as ones.
Function nanquantile Compute the qth quantile of the data along the specified axis, while ignoring nan values. Returns the qth quantile(s) of the array elements.
Function nanstd Compute the standard deviation along the specified axis, while ignoring NaNs.
Function nansum Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.
Function nanvar Compute the variance along the specified axis, while ignoring NaNs.
array_function_dispatch =

Undocumented

def _copyto(a, val, mask):

Replace values in a with NaN where mask is True. This differs from copyto in that it will deal with the case where a is a numpy scalar.

Parameters

a : ndarray or numpy scalar
Array or numpy scalar some of whose values are to be replaced by val.
val : numpy scalar
Value used a replacement.
mask : ndarray, scalar
Boolean array. Where True the corresponding element of a is replaced by val. Broadcasts.

Returns

res : ndarray, scalar
Array with elements replaced or scalar val.
def _divide_by_count(a, b, out=None):

Compute a/b ignoring invalid results. If a is an array the division is done in place. If a is a scalar, then its type is preserved in the output. If out is None, then then a is used instead so that the division is in place. Note that this is only called with a an inexact type.

Parameters

a : {ndarray, numpy scalar}
Numerator. Expected to be of inexact type but not checked.
b : {ndarray, numpy scalar}
Denominator.
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.

Returns

ret : {ndarray, numpy scalar}
The return value is a/b. If a was an ndarray the division is done in place. If a is a numpy scalar, the division preserves its type.
def _nan_mask(a, out=None):

Parameters

a : array-like
Input array with at least 1 dimension.
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 and will prevent the allocation of a new array.

Returns

y : bool ndarray or True
A bool array where np.nan positions are marked with False and other positions are marked with True. If the type of a is such that it can't possibly contain np.nan, returns True.
def _nanargmax_dispatcher(a, axis=None, out=None, *, keepdims=None):

Undocumented

def _nanargmin_dispatcher(a, axis=None, out=None, *, keepdims=None):

Undocumented

def _nancumprod_dispatcher(a, axis=None, dtype=None, out=None):

Undocumented

def _nancumsum_dispatcher(a, axis=None, dtype=None, out=None):

Undocumented

def _nanmax_dispatcher(a, axis=None, out=None, keepdims=None, initial=None, where=None):

Undocumented

def _nanmean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, *, where=None):

Undocumented

def _nanmedian(a, axis=None, out=None, overwrite_input=False):
Private function that doesn't support extended axis or keepdims. These methods are extended to this function using _ureduce See nanmedian for parameter usage
def _nanmedian1d(arr1d, overwrite_input=False):
Private function for rank 1 arrays. Compute the median ignoring NaNs. See nanmedian for parameter usage
def _nanmedian_dispatcher(a, axis=None, out=None, overwrite_input=None, keepdims=None):

Undocumented

def _nanmedian_small(a, axis=None, out=None, overwrite_input=False):

sort + indexing median, faster for small medians along multiple dimensions due to the high overhead of apply_along_axis

see nanmedian for parameter usage

def _nanmin_dispatcher(a, axis=None, out=None, keepdims=None, initial=None, where=None):

Undocumented

def _nanpercentile_dispatcher(a, q, axis=None, out=None, overwrite_input=None, method=None, keepdims=None, *, interpolation=None):

Undocumented

def _nanprod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, initial=None, where=None):

Undocumented

def _nanquantile_1d(arr1d, q, overwrite_input=False, method='linear'):
Private function for rank 1 arrays. Compute quantile ignoring NaNs. See nanpercentile for parameter usage
def _nanquantile_dispatcher(a, q, axis=None, out=None, overwrite_input=None, method=None, keepdims=None, *, interpolation=None):

Undocumented

def _nanquantile_unchecked(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=np._NoValue):
Assumes that q is in [0, 1], and is an ndarray
def _nanquantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False, method='linear'):
Private function that doesn't support extended axis or keepdims. These methods are extended to this function using _ureduce See nanpercentile for parameter usage
def _nanstd_dispatcher(a, axis=None, dtype=None, out=None, ddof=None, keepdims=None, *, where=None):

Undocumented

def _nansum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, initial=None, where=None):

Undocumented

def _nanvar_dispatcher(a, axis=None, dtype=None, out=None, ddof=None, keepdims=None, *, where=None):

Undocumented

def _remove_nan_1d(arr1d, overwrite_input=False):

Equivalent to arr1d[~arr1d.isnan()], but in a different order

Presumably faster as it incurs fewer copies

Parameters

arr1d : ndarray
Array to remove nans from
overwrite_input : bool
True if arr1d can be modified in place

Returns

res : ndarray
Array with nan elements removed
overwrite_input : bool
True if res can be modified in place, given the constraint on the input
def _replace_nan(a, val):

If a is of inexact type, make a copy of a, replace NaNs with the val value, and return the copy together with a boolean mask marking the locations where NaNs were present. If a is not of inexact type, do nothing and return a together with a mask of None.

Note that scalars will end up as array scalars, which is important for using the result as the value of the out argument in some operations.

Parameters

a : array-like
Input array.
val : float
NaN values are set to val before doing the operation.

Returns

y : ndarray
If a is of inexact type, return a copy of a with the NaNs replaced by the fill value, otherwise return a.
mask: {bool, None}
If a is of inexact type, return a boolean mask marking locations of NaNs, otherwise return None.
@array_function_dispatch(_nanargmax_dispatcher)
def nanargmax(a, axis=None, out=None, *, keepdims=np._NoValue):

Return the indices of the maximum values in the specified axis ignoring NaNs. For all-NaN slices ValueError is raised. Warning: the results cannot be trusted if a slice contains only NaNs and -Infs.

Parameters

a : array_like
Input data.
axis : int, optional
Axis along which to operate. By default flattened input is used.
out : array, optional

If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.

New in version 1.22.0.
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 array.

New in version 1.22.0.

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])
@array_function_dispatch(_nanargmin_dispatcher)
def nanargmin(a, axis=None, out=None, *, keepdims=np._NoValue):

Return the indices of the minimum values in the specified axis ignoring NaNs. For all-NaN slices ValueError is raised. Warning: the results cannot be trusted if a slice contains only NaNs and Infs.

Parameters

a : array_like
Input data.
axis : int, optional
Axis along which to operate. By default flattened input is used.
out : array, optional

If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.

New in version 1.22.0.
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 array.

New in version 1.22.0.

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])
@array_function_dispatch(_nancumprod_dispatcher)
def nancumprod(a, axis=None, dtype=None, out=None):

Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones.

Ones are returned for slices that are all-NaN or empty.

New in version 1.12.0.

Parameters

a : array_like
Input array.
axis : int, optional
Axis along which the cumulative product is computed. By default the input is flattened.
dtype : dtype, optional
Type of the returned array, as well as of the accumulator in which the elements are multiplied. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead.
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 of the resulting values will be cast if necessary.

Returns

nancumprod : ndarray
A new array holding the result is returned unless out is specified, in which case it is returned.

See Also

numpy.cumprod : Cumulative product across array propagating NaNs. isnan : Show which elements are NaN.

Examples

>>> np.nancumprod(1)
array([1])
>>> np.nancumprod([1])
array([1])
>>> np.nancumprod([1, np.nan])
array([1.,  1.])
>>> a = np.array([[1, 2], [3, np.nan]])
>>> np.nancumprod(a)
array([1.,  2.,  6.,  6.])
>>> np.nancumprod(a, axis=0)
array([[1.,  2.],
       [3.,  2.]])
>>> np.nancumprod(a, axis=1)
array([[1.,  2.],
       [3.,  3.]])
@array_function_dispatch(_nancumsum_dispatcher)
def nancumsum(a, axis=None, dtype=None, out=None):

Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. The cumulative sum does not change when NaNs are encountered and leading NaNs are replaced by zeros.

Zeros are returned for slices that are all-NaN or empty.

New in version 1.12.0.

Parameters

a : array_like
Input array.
axis : int, optional
Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array.
dtype : dtype, optional
Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used.
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. See :ref:`ufuncs-output-type` for more details.

Returns

nancumsum : ndarray.
A new array holding the result is returned unless out is specified, in which it is returned. The result has the same size as a, and the same shape as a if axis is not None or a is a 1-d array.

See Also

numpy.cumsum : Cumulative sum across array propagating NaNs. isnan : Show which elements are NaN.

Examples

>>> np.nancumsum(1)
array([1])
>>> np.nancumsum([1])
array([1])
>>> np.nancumsum([1, np.nan])
array([1.,  1.])
>>> a = np.array([[1, 2], [3, np.nan]])
>>> np.nancumsum(a)
array([1.,  3.,  6.,  6.])
>>> np.nancumsum(a, axis=0)
array([[1.,  2.],
       [4.,  2.]])
>>> np.nancumsum(a, axis=1)
array([[1.,  3.],
       [3.,  3.]])
@array_function_dispatch(_nanmax_dispatcher)
def nanmax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue, where=np._NoValue):

Return the maximum of an array or maximum along an axis, ignoring any NaNs. When all-NaN slices are encountered a RuntimeWarning is raised and NaN is returned for that slice.

Parameters

a : array_like
Array containing numbers whose maximum is desired. If a is not an array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the maximum is computed. The default is to compute the maximum of the flattened array.
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 :ref:`ufuncs-output-type` for more details.

New in version 1.8.0.
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 a.

If the value is anything but the default, then keepdims will be passed through to the max method of sub-classes of ndarray. If the sub-classes methods does not implement keepdims any exceptions will be raised.

New in version 1.8.0.
initial : scalar, optional

The minimum value of an output element. Must be present to allow computation on empty slice. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.
where : array_like of bool, optional

Elements to compare for the maximum. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.

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
@array_function_dispatch(_nanmean_dispatcher)
def nanmean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, *, where=np._NoValue):

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.

For all-NaN slices, NaN is returned and a RuntimeWarning is raised.

New in version 1.8.0.

Parameters

a : array_like
Array containing numbers whose mean is desired. If a is not an array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes 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 inexact 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 :ref:`ufuncs-output-type` for more 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 a.

If the value is anything but the default, then keepdims will be passed through to the mean or sum methods of sub-classes of ndarray. If the sub-classes methods does not implement keepdims any exceptions will be raised.

where : array_like of bool, optional

Elements to include in the mean. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.

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. Nan is returned for slices that contain only NaNs.

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]) # may vary
@array_function_dispatch(_nanmedian_dispatcher)
def nanmedian(a, axis=None, out=None, overwrite_input=False, keepdims=np._NoValue):

Compute the median along the specified axis, while ignoring NaNs.

Returns the median of the array elements.

New in version 1.9.0.

Parameters

a : array_like
Input array or object that can be converted to an array.
axis : {int, sequence of int, None}, optional
Axis or axes along which the medians are computed. The default is to compute the median along a flattened version of the array. A sequence of axes is supported since version 1.9.0.
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 (of the output) will be cast if necessary.
overwrite_input : bool, 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. If overwrite_input is True and a is not already an ndarray, an error will be raised.
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 a.

If this is anything but the default value it will be passed through (in the special case of an empty array) to the mean function of the underlying array. If the array is a sub-class and mean does not have the kwarg keepdims this will raise a RuntimeError.

Returns

median : ndarray
A new array holding the result. If the input contains integers or floats smaller than float64, then the output data-type is np.float64. Otherwise, the data-type of the output is the same as that of the input. If out is specified, that array is returned instead.

See Also

mean, median, percentile

Notes

Given a vector V of length N, the median of V is the middle value of a sorted copy of V, V_sorted - i.e., V_sorted[(N-1)/2], when N is odd and the average of the two middle values of V_sorted when N is even.

Examples

>>> a = np.array([[10.0, 7, 4], [3, 2, 1]])
>>> a[0, 1] = np.nan
>>> a
array([[10., nan,  4.],
       [ 3.,  2.,  1.]])
>>> np.median(a)
nan
>>> np.nanmedian(a)
3.0
>>> np.nanmedian(a, axis=0)
array([6.5, 2. , 2.5])
>>> np.median(a, axis=1)
array([nan,  2.])
>>> b = a.copy()
>>> np.nanmedian(b, axis=1, overwrite_input=True)
array([7.,  2.])
>>> assert not np.all(a==b)
>>> b = a.copy()
>>> np.nanmedian(b, axis=None, overwrite_input=True)
3.0
>>> assert not np.all(a==b)
@array_function_dispatch(_nanmin_dispatcher)
def nanmin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue, where=np._NoValue):

Return minimum of an array or minimum along an axis, ignoring any NaNs. When all-NaN slices are encountered a RuntimeWarning is raised and Nan is returned for that slice.

Parameters

a : array_like
Array containing numbers whose minimum is desired. If a is not an array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the minimum is computed. The default is to compute the minimum of the flattened array.
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 :ref:`ufuncs-output-type` for more details.

New in version 1.8.0.
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 a.

If the value is anything but the default, then keepdims will be passed through to the min method of sub-classes of ndarray. If the sub-classes methods does not implement keepdims any exceptions will be raised.

New in version 1.8.0.
initial : scalar, optional

The maximum value of an output element. Must be present to allow computation on empty slice. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.
where : array_like of bool, optional

Elements to compare for the minimum. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.

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
@array_function_dispatch(_nanpercentile_dispatcher)
def nanpercentile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=np._NoValue, *, interpolation=None):

Compute the qth percentile of the data along the specified axis, while ignoring nan values.

Returns the qth percentile(s) of the array elements.

New in version 1.9.0.

Parameters

a : array_like
Input array or object that can be converted to an array, containing nan values to be ignored.
q : array_like of float
Percentile or sequence of percentiles to compute, which must be between 0 and 100 inclusive.
axis : {int, tuple of int, None}, optional
Axis or axes along which the percentiles are computed. The default is to compute the percentile(s) along a flattened version of the 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 (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow the input array a to be modified by intermediate calculations, to save memory. In this case, the contents of the input a after this function completes is undefined.
method : str, optional

This parameter specifies the method to use for estimating the percentile. There are many different methods, some unique to NumPy. See the notes for explanation. The options sorted by their R type as summarized in the H&F paper [1] are:

  1. 'inverted_cdf'
  2. 'averaged_inverted_cdf'
  3. 'closest_observation'
  4. 'interpolated_inverted_cdf'
  5. 'hazen'
  6. 'weibull'
  7. 'linear' (default)
  8. 'median_unbiased'
  9. 'normal_unbiased'

The first three methods are discontiuous. NumPy further defines the following discontinuous variations of the default 'linear' (7.) option:

  • 'lower'
  • 'higher',
  • 'midpoint'
  • 'nearest'
Changed in version 1.22.0: This argument was previously called "interpolation" and only offered the "linear" default and last four options.
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 array a.

If this is anything but the default value it will be passed through (in the special case of an empty array) to the mean function of the underlying array. If the array is a sub-class and mean does not have the kwarg keepdims this will raise a RuntimeError.

interpolation : str, optional

Deprecated name for the method keyword argument.

Deprecated since version 1.22.0.

Returns

percentile : scalar or ndarray
If q is a single percentile and axis=None, then the result is a scalar. If multiple percentiles are given, first axis of the result corresponds to the percentiles. The other axes are the axes that remain after the reduction of a. If the input contains integers or floats smaller than float64, the output data-type is float64. Otherwise, the output data-type is the same as that of the input. If out is specified, that array is returned instead.

See Also

nanmean nanmedian : equivalent to nanpercentile(..., 50) percentile, median, mean nanquantile : equivalent to nanpercentile, except q in range [0, 1].

Notes

For more information please see numpy.percentile

Examples

>>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
>>> a[0][1] = np.nan
>>> a
array([[10.,  nan,   4.],
      [ 3.,   2.,   1.]])
>>> np.percentile(a, 50)
nan
>>> np.nanpercentile(a, 50)
3.0
>>> np.nanpercentile(a, 50, axis=0)
array([6.5, 2. , 2.5])
>>> np.nanpercentile(a, 50, axis=1, keepdims=True)
array([[7.],
       [2.]])
>>> m = np.nanpercentile(a, 50, axis=0)
>>> out = np.zeros_like(m)
>>> np.nanpercentile(a, 50, axis=0, out=out)
array([6.5, 2. , 2.5])
>>> m
array([6.5,  2. ,  2.5])

>>> b = a.copy()
>>> np.nanpercentile(b, 50, axis=1, overwrite_input=True)
array([7., 2.])
>>> assert not np.all(a==b)

References

[1]R. J. Hyndman and Y. Fan, "Sample quantiles in statistical packages," The American Statistician, 50(4), pp. 361-365, 1996
@array_function_dispatch(_nanprod_dispatcher)
def nanprod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, initial=np._NoValue, where=np._NoValue):

Return the product of array elements over a given axis treating Not a Numbers (NaNs) as ones.

One is returned for slices that are all-NaN or empty.

New in version 1.10.0.

Parameters

a : array_like
Array containing numbers whose product is desired. If a is not an array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the product is computed. The default is to compute the product of the flattened array.
dtype : data-type, optional
The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of a is used. An exception is when a has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact.
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 :ref:`ufuncs-output-type` for more details. The casting of NaN to integer can yield unexpected results.
keepdims : bool, optional
If 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.
initial : scalar, optional

The starting value for this product. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.
where : array_like of bool, optional

Elements to include in the product. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.

Returns

nanprod : ndarray
A new array holding the result is returned unless out is specified, in which case it is returned.

See Also

numpy.prod : Product across array propagating NaNs. isnan : Show which elements are NaN.

Examples

>>> np.nanprod(1)
1
>>> np.nanprod([1])
1
>>> np.nanprod([1, np.nan])
1.0
>>> a = np.array([[1, 2], [3, np.nan]])
>>> np.nanprod(a)
6.0
>>> np.nanprod(a, axis=0)
array([3., 2.])
@array_function_dispatch(_nanquantile_dispatcher)
def nanquantile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=np._NoValue, *, interpolation=None):

Compute the qth quantile of the data along the specified axis, while ignoring nan values. Returns the qth quantile(s) of the array elements.

New in version 1.15.0.

Parameters

a : array_like
Input array or object that can be converted to an array, containing nan values to be ignored
q : array_like of float
Quantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive.
axis : {int, tuple of int, None}, optional
Axis or axes along which the quantiles are computed. The default is to compute the quantile(s) along a flattened version of the 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 (of the output) will be cast if necessary.
overwrite_input : bool, optional
If True, then allow the input array a to be modified by intermediate calculations, to save memory. In this case, the contents of the input a after this function completes is undefined.
method : str, optional

This parameter specifies the method to use for estimating the quantile. There are many different methods, some unique to NumPy. See the notes for explanation. The options sorted by their R type as summarized in the H&F paper [1] are:

  1. 'inverted_cdf'
  2. 'averaged_inverted_cdf'
  3. 'closest_observation'
  4. 'interpolated_inverted_cdf'
  5. 'hazen'
  6. 'weibull'
  7. 'linear' (default)
  8. 'median_unbiased'
  9. 'normal_unbiased'

The first three methods are discontiuous. NumPy further defines the following discontinuous variations of the default 'linear' (7.) option:

  • 'lower'
  • 'higher',
  • 'midpoint'
  • 'nearest'
Changed in version 1.22.0: This argument was previously called "interpolation" and only offered the "linear" default and last four options.
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 array a.

If this is anything but the default value it will be passed through (in the special case of an empty array) to the mean function of the underlying array. If the array is a sub-class and mean does not have the kwarg keepdims this will raise a RuntimeError.

interpolation : str, optional

Deprecated name for the method keyword argument.

Deprecated since version 1.22.0.

Returns

quantile : scalar or ndarray
If q is a single percentile and axis=None, then the result is a scalar. If multiple quantiles are given, first axis of the result corresponds to the quantiles. The other axes are the axes that remain after the reduction of a. If the input contains integers or floats smaller than float64, the output data-type is float64. Otherwise, the output data-type is the same as that of the input. If out is specified, that array is returned instead.

See Also

quantile nanmean, nanmedian nanmedian : equivalent to nanquantile(..., 0.5) nanpercentile : same as nanquantile, but with q in the range [0, 100].

Notes

For more information please see numpy.quantile

Examples

>>> a = np.array([[10., 7., 4.], [3., 2., 1.]])
>>> a[0][1] = np.nan
>>> a
array([[10.,  nan,   4.],
      [ 3.,   2.,   1.]])
>>> np.quantile(a, 0.5)
nan
>>> np.nanquantile(a, 0.5)
3.0
>>> np.nanquantile(a, 0.5, axis=0)
array([6.5, 2. , 2.5])
>>> np.nanquantile(a, 0.5, axis=1, keepdims=True)
array([[7.],
       [2.]])
>>> m = np.nanquantile(a, 0.5, axis=0)
>>> out = np.zeros_like(m)
>>> np.nanquantile(a, 0.5, axis=0, out=out)
array([6.5, 2. , 2.5])
>>> m
array([6.5,  2. ,  2.5])
>>> b = a.copy()
>>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True)
array([7., 2.])
>>> assert not np.all(a==b)

References

[1]R. J. Hyndman and Y. Fan, "Sample quantiles in statistical packages," The American Statistician, 50(4), pp. 361-365, 1996
@array_function_dispatch(_nanstd_dispatcher)
def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue, *, where=np._NoValue):

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.

For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a RuntimeWarning is raised.

New in version 1.8.0.

Parameters

a : array_like
Calculate the standard deviation of the non-NaN values.
axis : {int, tuple of int, None}, optional
Axis or axes 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 non-NaN 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 a.

If this value is anything but the default it is passed through as-is to the relevant functions of the sub-classes. If these functions do not have a keepdims kwarg, a RuntimeError will be raised.

where : array_like of bool, optional

Elements to include in the standard deviation. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.

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. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN.

See Also

var, mean, std nanvar, nanmean :ref:`ufuncs-output-type`

Notes

The standard deviation is the square root of the average of the squared deviations from the mean: 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]) # may vary
@array_function_dispatch(_nansum_dispatcher)
def nansum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, initial=np._NoValue, where=np._NoValue):

Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.

In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or empty. In later versions zero is returned.

Parameters

a : array_like
Array containing numbers whose sum is desired. If a is not an array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes along which the sum is computed. The default is to compute the sum of the flattened array.
dtype : data-type, optional

The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of a is used. An exception is when a has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact.

New in version 1.8.0.
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 :ref:`ufuncs-output-type` for more details. The casting of NaN to integer can yield unexpected results.

New in version 1.8.0.
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 a.

If the value is anything but the default, then keepdims will be passed through to the mean or sum methods of sub-classes of ndarray. If the sub-classes methods does not implement keepdims any exceptions will be raised.

New in version 1.8.0.
initial : scalar, optional

Starting value for the sum. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.
where : array_like of bool, optional

Elements to include in the sum. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.

Returns

nansum : ndarray.
A new array holding the result is returned unless out is specified, in which it is returned. The result has the same size as a, and the same shape as a if axis is not None or a is a 1-d array.

See Also

numpy.sum : Sum across array propagating NaNs. isnan : Show which elements are NaN. isfinite : Show which elements are not NaN or +/-inf.

Notes

If both positive and negative infinity are present, the sum will be Not A Number (NaN).

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.])
>>> np.nansum([1, np.nan, np.inf])
inf
>>> np.nansum([1, np.nan, np.NINF])
-inf
>>> from numpy.testing import suppress_warnings
>>> with suppress_warnings() as sup:
...     sup.filter(RuntimeWarning)
...     np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present
nan
@array_function_dispatch(_nanvar_dispatcher)
def nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue, *, where=np._NoValue):

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.

For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a RuntimeWarning is raised.

New in version 1.8.0.

Parameters

a : array_like
Array containing numbers whose variance is desired. If a is not an array, a conversion is attempted.
axis : {int, tuple of int, None}, optional
Axis or axes 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 float64; 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 non-NaN 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 a.
where : array_like of bool, optional

Elements to include in the variance. See ~numpy.ufunc.reduce for details.

New in version 1.22.0.

Returns

variance : ndarray, see dtype parameter above
If out is None, return a new array containing the variance, otherwise return a reference to the output array. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN.

See Also

std : Standard deviation mean : Average var : Variance while not ignoring NaNs nanstd, nanmean :ref:`ufuncs-output-type`

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.

For this function to work on sub-classes of ndarray, they must define sum with the kwarg keepdims

Examples

>>> a = np.array([[1, np.nan], [3, 4]])
>>> np.nanvar(a)
1.5555555555555554
>>> np.nanvar(a, axis=0)
array([1.,  0.])
>>> np.nanvar(a, axis=1)
array([0.,  0.25])  # may vary