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cov#

ivy.cov(x1, x2=None, /, *, rowVar=True, bias=False, ddof=None, fweights=None, aweights=None, dtype=None)[source]#

Compute the covariance of matrix x1, or variables x1 and x2.

Parameters:

  • x1 (Union[Array, NativeArray]) – a 1D or 2D input array, with a numeric data type.

  • x2 (Optional[Union[Array, NativeArray]], default: None) – optional second 1D or 2D input array, with a numeric data type. Must have the same shape as self.

  • rowVar (bool, default: True) – optional variable where each row of input is interpreted as a variable (default = True). If set to False, each column is instead interpreted as a variable.

  • bias (bool, default: False) – optional variable for normalizing input (default = False) by (N - 1) where N is the number of given observations. If set to True, then normalization is instead by N. Can be overridden by keyword ddof.

  • ddof (Optional[int], default: None) – optional variable to override bias (default = None). ddof=1 will return the unbiased estimate, even with fweights and aweights given. ddof=0 will return the simple average.

  • fweights (Optional[Array], default: None) – optional 1D array of integer frequency weights; the number of times each observation vector should be repeated.

  • aweights (Optional[Array], default: None) – optional 1D array of observation vector weights. These relative weights are typically large for observations considered “important” and smaller for observations considered less “important”. If ddof=0 is specified, the array of weights can be used to assign probabilities to observation vectors.

  • dtype (Optional[Union[Dtype, NativeDtype]], default: None) – optional variable to set data-type of the result. By default, data-type will have at least numpy.float64 precision.

  • out – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

  • ret – an array containing the covariance matrix of an input matrix, or the covariance matrix of two variables. The returned array must have a floating-point data type determined by Type Promotion Rules and must be a square matrix of shape (N, N), where N is the number of variables in the input(s).

  • This function conforms to the `Array API Standard

  • <https (//data-apis.org/array-api/latest/>`_. This docstring is an extension of the)

  • `docstring <https (//data-apis.org/array-api/latest/)

  • extensions/generated/signatures.linalg.cov.html>`_

  • in the standard.

  • 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([[1, 2, 3], … [4, 5, 6]]) >>> y = x[0].cov(x[1]) >>> print(y) ivy.array([[1., 1.],

[1., 1.]])

With ivy.Container inputs: >>> x = ivy.Container(a=ivy.array([1., 2., 3.]), b=ivy.array([1., 2., 3.])) >>> y = ivy.Container(a=ivy.array([3., 2., 1.]), b=ivy.array([3., 2., 1.])) >>> z = ivy.Container.static_cov(x, y) >>> print(z) {

a: ivy.array([[1., -1.],

[-1., 1.]]),

b: ivy.array([[1., -1.],

[-1., 1.]])

}

With a combination of ivy.Array and ivy.Container inputs: >>> x = ivy.array([1., 2., 3.]) >>> y = ivy.Container(a=ivy.array([3. ,2. ,1.]), b=ivy.array([-1., -2., -3.])) >>> z = ivy.cov(x, y) >>> print(z) {

a: ivy.array([[1., -1.],

[-1., 1.]]),

b: ivy.array([[1., -1.],

[-1., 1.]])

}

With ivy.Array input and rowVar flag set to False (True by default): >>> x = ivy.array([[1,2,3], … [4,5,6]]) >>> y = x[0].cov(x[1], rowVar=False) >>> print(y) ivy.array([[1., 1.],

[1., 1.]])

With ivy.Array input and bias flag set to True (False by default): >>> x = ivy.array([[1,2,3], … [4,5,6]]) >>> y = x[0].cov(x[1], bias=True) >>> print(y) ivy.array([[0.66666667, 0.66666667],

[0.66666667, 0.66666667]])

With ivy.Array input with both fweights and aweights given: >>> x = ivy.array([[1,2,3], … [4,5,6]]) >>> fw = ivy.array([1,2,3]) >>> aw = ivy.array([ 1.2, 2.3, 3.4 ]) >>> y = x[0].cov(x[1], fweights=fw, aweights=aw) >>> print(y) ivy.array([[0.48447205, 0.48447205],

[0.48447205, 0.48447205]])

Array.cov(self, x2=None, /, *, rowVar=True, bias=False, ddof=None, fweights=None, aweights=None, dtype=None)[source]#

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

Parameters:

  • self (Array) – a 1D or 2D input array, with a numeric data type.

  • x2 (Optional[Union[Array, NativeArray]], default: None) – optional second 1D or 2D input array, with a numeric data type. Must have the same shape as self.

  • rowVar (bool, default: True) – optional variable where each row of input is interpreted as a variable (default = True). If set to False, each column is instead interpreted as a variable.

  • bias (bool, default: False) – optional variable for normalizing input (default = False) by (N - 1) where N is the number of given observations. If set to True, then normalization is instead by N. Can be overridden by keyword ddof.

  • ddof (Optional[int], default: None) – optional variable to override bias (default = None). ddof=1 will return the unbiased estimate, even with fweights and aweights given. ddof=0 will return the simple average.

  • fweights (Optional[Array], default: None) – optional 1D array of integer frequency weights; the number of times each observation vector should be repeated.

  • aweights (Optional[Array], default: None) – optional 1D array of observation vector weights. These relative weights are typically large for observations considered “important” and smaller for observations considered less “important”. If ddof=0 is specified, the array of weights can be used to assign probabilities to observation vectors.

  • dtype (Optional[type], default: None) – optional variable to set data-type of the result. By default, data-type will have at least float64 precision.

  • out – optional output array, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – an array containing the covariance matrix of an input matrix, or the covariance matrix of two variables. The returned array must have a floating-point data type determined by Type Promotion Rules and must be a square matrix of shape (N, N), where N is the number of variables in the input(s).

Examples

>>> x = ivy.array([[1, 2, 3],
...                [4, 5, 6]])
>>> y = x[0].cov(x[1])
>>> print(y)
ivy.array([[1., 1.],
       [1., 1.]])

>>> x = ivy.array([1,2,3])
>>> y = ivy.array([4,5,6])
>>> z = x.cov(y)
>>> print(z)
ivy.array([[1., 1.],
       [1., 1.]])
Container.cov(self, x2=None, /, *, rowVar=True, bias=False, ddof=None, fweights=None, aweights=None, dtype=None, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False)[source]#

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

Parameters:

  • self (Container) – a 1D or 2D input container, with a numeric data type.

  • x2 (Optional[Container], default: None) – optional second 1D or 2D input array, nativearray, or container, with a numeric data type. Must have the same shape as self.

  • rowVar (Union[bool, Container], default: True) – optional variable where each row of input is interpreted as a variable (default = True). If set to False, each column is instead interpreted as a variable.

  • bias (Union[bool, Container], default: False) – optional variable for normalizing input (default = False) by (N - 1) where N is the number of given observations. If set to True, then normalization is instead by N. Can be overridden by keyword ddof.

  • ddof (Optional[Union[int, Container]], default: None) – optional variable to override bias (default = None). ddof=1 will return the unbiased estimate, even with fweights and aweights given. ddof=0 will return the simple average.

  • fweights (Optional[Union[Array, Container]], default: None) – optional 1D array of integer frequency weights; the number of times each observation vector should be repeated.

  • aweights (Optional[Union[Array, Container]], default: None) – optional 1D array of observation vector weights. These relative weights are typically large for observations considered “important” and smaller for observations considered less “important”. If ddof=0 is specified, the array of weights can be used to assign probabilities to observation vectors.

  • dtype (Optional[Union[Dtype, NativeDtype, Container]], default: None) – optional variable to set data-type of the result. By default, data-type will have at least numpy.float64 precision.

  • key_chains (Optional[Union[List[str], Dict[str, str], Container]], default: None) – The key-chains to apply or not apply the method to. Default is None.

  • to_apply (Union[bool, Container], default: True) – If True, the method will be applied to key_chains, otherwise key_chains will be skipped. Default is True.

  • prune_unapplied (Union[bool, Container], default: False) – Whether to prune key_chains for which the function was not applied. Default is False.

  • map_sequences (Union[bool, Container], default: False) – Whether to also map method to sequences (lists, tuples). Default is False.

  • out – optional output container, for writing the result to. It must have a shape that the inputs broadcast to.

Return type:

Container

Returns:

ret – a container containing the covariance matrix of an input matrix, or the covariance matrix of two variables. The returned container must have a floating-point data type determined by Type Promotion Rules and must be a square matrix of shape (N, N), where N is the number of variables in the input(s).

Examples

>>> x = ivy.Container(a=ivy.array([1., 2., 3.]), b=ivy.array([1., 2., 3.]))
>>> y = ivy.Container(a=ivy.array([3., 2., 1.]), b=ivy.array([3., 2., 1.]))
>>> z = x.cov(y)
>>> print(z)
{
a: ivy.array([[1., -1.],

[-1., 1.]]),

b: ivy.array([[1., -1.],

[-1., 1.]])

}

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