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pow#

ivy.pow(x1, x2, /, *, out=None)[source]#

Calculate an implementation-dependent approximation of exponentiation by raising each element x1_i (the base) of the input array x1 to the power of x2_i (the exponent), where x2_i is the corresponding element of the input array x2.

Special cases

For floating-point operands,

  • If x1_i is not equal to 1 and x2_i is NaN, the result is NaN.

  • If x2_i is +0, the result is 1, even if x1_i is NaN.

  • If x2_i is -0, the result is 1, even if x1_i is NaN.

  • If x1_i is NaN and x2_i is not equal to 0, the result is NaN.

  • If abs(x1_i) is greater than 1 and x2_i is +infinity, the result is +infinity.

  • If abs(x1_i) is greater than 1 and x2_i is -infinity, the result is +0.

  • If abs(x1_i) is 1 and x2_i is +infinity, the result is 1.

  • If abs(x1_i) is 1 and x2_i is -infinity, the result is 1.

  • If x1_i is 1 and x2_i is not NaN, the result is 1.

  • If abs(x1_i) is less than 1 and x2_i is +infinity, the result is +0.

  • If abs(x1_i) is less than 1 and x2_i is -infinity, the result is +infinity.

  • If x1_i is +infinity and x2_i is greater than 0, the result is +infinity.

  • If x1_i is +infinity and x2_i is less than 0, the result is +0.

  • If x1_i is -infinity, x2_i is greater than 0, and x2_i is an odd integer value, the result is -infinity.

  • If x1_i is -infinity, x2_i is greater than 0, and x2_i is not an odd integer value, the result is +infinity.

  • If x1_i is -infinity, x2_i is less than 0, and x2_i is an odd integer value, the result is -0.

  • If x1_i is -infinity, x2_i is less than 0, and x2_i is not an odd integer value, the result is +0.

  • If x1_i is +0 and x2_i is greater than 0, the result is +0.

  • If x1_i is +0 and x2_i is less than 0, the result is +infinity.

  • If x1_i is -0, x2_i is greater than 0, and x2_i is an odd integer value, the result is -0.

  • If x1_i is -0, x2_i is greater than 0, and x2_i is not an odd integer value, the result is +0.

  • If x1_i is -0, x2_i is less than 0, and x2_i is an odd integer value, the result is -infinity.

  • If x1_i is -0, x2_i is less than 0, and x2_i is not an odd integer value, the result is +infinity.

  • If x1_i is less than 0, x1_i is a finite number, x2_i is a finite number, and x2_i is not an integer value, the result is NaN.

For complex floating-point operands, special cases should be handled as if the operation is implemented as exp(x2*log(x1)).

Note

Conforming implementations are allowed to treat special cases involving complex floating-point operands more carefully than as described in this specification.

Parameters:

  • x1 (Union[Array, NativeArray]) – first input array whose elements correspond to the exponentiation base. Should have a numeric data type.

  • x2 (Union[int, float, Array, NativeArray]) – second input array whose elements correspond to the exponentiation exponent. Must be compatible with x1 (see broadcasting). Should have a numeric data type.

  • out (Optional[Array], default: None) – 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 element-wise results. The returned array must have a data type determined by type-promotion.

This function conforms to the Array API Standard. This docstring is an extension of the docstring 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])
>>> y = ivy.pow(x, 3)
>>> print(y)
ivy.array([1, 8, 27])

>>> x = ivy.array([1.5, -0.8, 0.3])
>>> y = ivy.zeros(3)
>>> ivy.pow(x, 2, out=y)
>>> print(y)
ivy.array([2.25, 0.64, 0.09])

>>> x = ivy.array([[1.2, 2, 3.1], [1, 2.5, 9]])
>>> ivy.pow(x, 2.3, out=x)
>>> print(x)
ivy.array([[  1.52095687,   4.92457771,  13.49372482],
       [  1.        ,   8.22738838, 156.5877228 ]])

With ivy.Container input:

>>> x = ivy.Container(a=ivy.array([0, 1]), b=ivy.array([2, 3]))
>>> y = ivy.pow(x, 3)
>>> print(y)
{
    a:ivy.array([0,1]),
    b:ivy.array([8,27])
}
Array.pow(self, x2, /, *, out=None)[source]#

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

Parameters:

  • self (Array) – first input array whose elements correspond to the exponentiation base. Should have a real-valued data type.

  • x2 (Union[int, float, Array, NativeArray]) – second input array whose elements correspond to the exponentiation exponent. Must be compatible with self (see broadcasting). Should have a real-valued data type.

  • out (Optional[Array], default: None) – 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 element-wise results. The returned array must have a data type determined by type-promotion.

Examples

With ivy.Array input:

>>> x = ivy.array([1, 2, 3])
>>> y = x.pow(3)
>>> print(y)
ivy.array([1, 8, 27])

>>> x = ivy.array([1.5, -0.8, 0.3])
>>> y = ivy.zeros(3)
>>> x.pow(2, out=y)
>>> print(y)
ivy.array([2.25, 0.64, 0.09])
Container.pow(self, x2, /, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)[source]#

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

Parameters:

  • self (Container) – input array or container. Should have a real-valued data type.

  • x2 (Union[int, float, Container, Array, NativeArray]) – input array or container. Must be compatible with self (see broadcasting). Should have a real-valued data type.

  • 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[Container], default: None) – 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 element-wise results. The returned container must have a data type determined by type-promotion.

Examples

With ivy.Container input:

>>> x = ivy.Container(a=ivy.array([0, 1]), b=ivy.array([2, 3]))
>>> y = x.pow(3)
>>> print(y)
{
    a:ivy.array([0,1]),
    b:ivy.array([8,27])
}
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