Statistical#

ivy.bincount(x, /, *, weights=None, minlength=0, out=None)[source]#

Counts the number of occurrences of each value in an integer array.

Parameters:

  • self – Input array.

  • weights (Optional[Array]) – An optional input array. (default: None)

  • minlength (int) – A minimum number of bins for the output array. (default: 0)

Return type:

Array

Returns:

ret – The bincount of the array elements.

Examples

>>> a = ivy.Container([[10.0, ivy.nan, 4], [3, 2, 1]])
>>> a.bincount(a)
    3.0
>>> a.bincount(a, axis=0)
    array([6.5, 2. , 2.5])
ivy.corrcoef(x, /, *, y=None, rowvar=True, out=None)[source]#
Return type:

Array

ivy.histogram(a, /, *, bins=None, axis=None, extend_lower_interval=False, extend_upper_interval=False, dtype=None, range=None, weights=None, density=False, out=None)[source]#

Compute the histogram of the array a.

Note

Given bins = [c0, …, cK], defining intervals I0 = [c0, c1), I1 = [c1, c2), …, I_{K-1} = [c_{K-1}, cK].

Parameters:

  • a (Union[Array, NativeArray]) – input array.

  • bins (Optional[Union[int, Array, NativeArray]]) – if bins is an int, it defines the number of equal-width bins in the given (default: None) range. if bins is an array, it defines a monotonically increasing array of bin edges, including the rightmost edge, allowing for non-uniform bin widths.

  • axis (Optional[int]) – dimension along which maximum values must be computed. By default, the maximum (default: None) value must be computed over the entire array. Default: None.

  • extend_lower_interval (Optional[bool]) – if True, extend the lowest interval I0 to (-inf, c1]. (default: False)

  • extend_upper_interval (Optional[bool]) – ff True, extend the upper interval I_{K-1} to [c_{K-1}, +inf). (default: False)

  • dtype (Optional[Union[Dtype, NativeDtype]]) – the output type. (default: None)

  • range (Optional[Tuple[float]]) – the lower and upper range of the bins. The first element of the range must be (default: None) less than or equal to the second.

  • weights (Optional[Union[Array, NativeArray]]) – each value in a only contributes its associated weight towards the bin count (default: None) (instead of 1). Must be of the same shape as a.

  • density (Optional[bool]) – if True, the result is the value of the probability density function at the (default: False) bin, normalized such that the integral over the range of bins is 1.

  • out (Optional[Array]) – optional output array, for writing the result to. It must have a shape that the (default: None) inputs broadcast to.

Return type:

Array

Returns:

  • ret – a tuple containing the values of the histogram and the bin edges.

  • Both the description and the type hints above assumes an array input for simplicity,

  • but this function is nestable, and therefore also accepts ivy.Container

  • instances in place of any of the arguments.

Examples

With ivy.Array input:

>>> x = ivy.array([0, 1, 2])
>>> y = ivy.array([0., 0.5, 1., 1.5, 2.])
>>> z = ivy.histogram(x, bins=y)
>>> print(z)
(ivy.array([1, 0, 1, 1]), ivy.array([0. , 0.5, 1. , 1.5, 2. ]))

>>> x = ivy.array([[1.1, 2.2, 3.3],
...                [4.4, 5.5, .6]])
>>> bins = 4
>>> range = (0., 5.)
>>> dtype = ivy.int32
>>> y = ivy.histogram(x, bins=bins, range=range, dtype=dtype)
>>> print(y)
(ivy.array([0, 0, 0, 0]), ivy.array([0.   , 0.125, 0.25 , 0.375, 0.5  ]))

>>> x = ivy.array([[1.1, 2.2, 3.3],
...                [-4.4, -5.5, -6.6]])
>>> y = ivy.array([0., 1., 2., 3., 4., 5.])
>>> axis = 1
>>> extend_lower_interval = True
>>> extend_upper_interval = True
>>> dtype = ivy.float32
>>> weights = ivy.array([[1., 1., 1.], [1., 1., 1.]])
>>> z = ivy.histogram(
>>>                     x,
>>>                     bins=y,
>>>                     axis=axis,
>>>                     extend_lower_interval=extend_lower_interval,
>>>                     extend_upper_interval=extend_upper_interval,
>>>                     dtype=dtype,
>>>                     weights=weights)
>>> print(z)
(ivy.array([[0., 3.],
[1., 0.],
[1., 0.],
[1., 0.],
[0., 0.]]), ivy.array([0., 1., 2., 3., 4., 5.]))

>>> x = ivy.Container(a=ivy.array([0., 1., 2.]), b=ivy.array([3., 4., 5.]))
>>> y = ivy.array([0., 1., 2., 3., 4., 5.])
>>> dtype = ivy.int32
>>> z = ivy.histogram(x, bins=y, dtype=dtype)
>>> print(z.a)
>>> print(z.b)
(ivy.array([1, 1, 1, 0, 0]), ivy.array([0., 1., 2., 3., 4., 5.]))
(ivy.array([0, 0, 0, 1, 2]), ivy.array([0., 1., 2., 3., 4., 5.]))
ivy.igamma(a, /, *, x, out=None)[source]#

Compute the regularized lower gamma function of a and x.

Parameters:

  • self – Input array.

  • x (Union[Array, NativeArray]) – An additional input array. x has the same type as a.

  • out (Optional[Union[Array, NativeArray]]) – optional output array, for writing the result to. (default: None)

Return type:

Array

Returns:

ret – The lower incomplete gamma function of the array elements.

Examples

>>> a = ivy.array([2.5])
>>> x = ivy.array([1.7, 1.2])
>>> a.igamma(x)
    ivy.array([0.3614, 0.2085])
ivy.median(input, /, *, axis=None, keepdims=False, out=None)[source]#

Compute the median along the specified axis.

Parameters:

  • input (Array) – Input array.

  • axis (Optional[Union[int, Tuple[int]]]) – Axis or axes along which the medians are computed. The default is to compute (default: None) the median along a flattened version of the array.

  • keepdims (bool) – If this is set to True, the axes which are reduced are left in the result (default: False) as dimensions with size one.

  • out (Optional[Array]) – optional output array, for writing the result to. (default: None)

Return type:

Array

Returns:

ret – The median of the array elements.

Functional Examples

>>> a = ivy.array([[10, 7, 4], [3, 2, 1]])
>>> ivy.median(a)
3.5
>>> ivy.median(a, axis=0)
ivy.array([6.5, 4.5, 2.5])
ivy.nanmean(a, /, *, axis=None, keepdims=False, dtype=None, out=None)[source]#

Compute the mean of all non-NaN elements along the specified dimensions.

Parameters:

  • a (Array) – Input array.

  • axis (Optional[Union[int, Tuple[int]]]) – Axis or axes along which the means are computed. (default: None) The default is to compute the mean of the flattened array.

  • keepdims (bool) – If this is set to True, the axes which are reduced are left in the result (default: False) 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.

  • dtype (Optional[Union[Dtype, NativeDtype]]) – The desired data type of returned tensor. Default is None. (default: None)

  • out (Optional[Array]) – optional output array, for writing the result to. (default: None)

Return type:

Array

Returns:

ret – The nanmean of the array elements.

Functional Examples

>>> a = ivy.array([[1, ivy.nan], [3, 4]])
>>> ivy.nanmean(a)
2.6666666666666665
>>> ivy.nanmean(a, axis=0)
ivy.array([2.,  4.])
ivy.nanmedian(input, /, *, axis=None, keepdims=False, overwrite_input=False, out=None)[source]#

ivy.Array instance method variant of ivy.nanmedian. This method simply wraps the function, and so the docstring for ivy.nanmedian also applies to this method with minimal changes.

Parameters:

  • self – Input array.

  • axis (Optional[Union[int, Tuple[int]]]) – Axis or axes along which the means are computed. (default: None) The default is to compute the mean of the flattened array.

  • keepdims (bool) – If this is set to True, the axes which are reduced are left in the result (default: False) 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.

  • overwrite_input (bool) – If True, then allow use of memory of input array a for calculations. (default: False) 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.

  • out (Optional[Array]) – optional output array, for writing the result to. (default: None)

Return type:

Array

Returns:

  • ret – A new array holding the result. If the input contains integers

  • This function is *nestable*, and therefore also accepts (code:’ivy.Container’)

  • instance in place of the argument.

Examples

With ivy.Array input:

>>> x = ivy.array([[12.0, 10.0, 34.0], [45.0, 23.0, ivy.nan]])
>>> ivy.nanmedian(x)
    ivy.array(23.)
With a mix of :class:`ivy.Container` and :class:`ivy.Array` input:
>>> x = ivy.Container(a=ivy.array([[10.0, ivy.nan, 4], [3, 2, 1]]),
        b=ivy.array([[12, 10, 34], [45, 23, ivy.nan]]))
>>> ivy.nanmedian(x)
{
    a: ivy.array(3.),
    b: ivy.array(23.)
}
ivy.quantile(a, q, /, *, axis=None, keepdims=False, interpolation='linear', out=None)[source]#

Compute the q-th quantile of the data along the specified axis.

Parameters:

  • a (Array) – Input array.

  • q (Union[Array, float]) – Quantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive.

  • axis (Optional[Union[int, Sequence[int]]]) – Axis or axes along which the quantiles are computed. The default (default: None) is to compute the quantile(s) along a flattened version of the array.

  • keepdims (bool) – If this is set to True, the axes which are reduced are left in the result (default: False) as dimensions with size one. With this option, the result will broadcast correctly against the original array a.

  • interpolation (str) – {‘nearest’, ‘linear’, ‘lower’, ‘higher’, ‘midpoint’}. Default value: ‘linear’. (default: 'linear') This specifies the interpolation method to use when the desired quantile lies between two data points i < j: - linear: i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j. - lower: i. - higher: j. - nearest: i or j, whichever is nearest. - midpoint: (i + j) / 2. linear and midpoint interpolation do not work with integer dtypes.

  • out (Optional[Array]) – optional output array, for writing the result to. (default: None)

Return type:

Array

Returns:

ret – A (rank(q) + N - len(axis)) dimensional array of same dtype as a, or, if axis is None, a rank(q) array. The first rank(q) dimensions index quantiles for different values of q.

Examples

>>> a = ivy.array([[10., 7., 4.], [3., 2., 1.]])
>>> q = ivy.array(0.5)
>>> ivy.quantile(a, q)
ivy.array(3.5)

>>> a = ivy.array([[10., 7., 4.], [3., 2., 1.]])
>>> q = 0.5
>>> ivy.quantile(a, q)
ivy.array(3.5)

>>> ivy.quantile(a, q, axis=0)
ivy.array([6.5, 4.5, 2.5])

>>> ivy.quantile(a, q, axis=1)
ivy.array([7.,  2.])

>>> ivy.quantile(a, q, axis=1, keepdims=True)
ivy.array([[7.],[2.]])

>>> a = ivy.array([1., 2., 3., 4.])
>>> q = ivy.array([0.3, 0.7])
>>> ivy.quantile(a, q, interpolation='lower')
ivy.array([1., 3.])