# sinh#

ivy.sinh(x, /, *, out=None)[source]#

Calculate an implementation-dependent approximation to the hyperbolic sine, having domain [-infinity, +infinity] and codomain [-infinity, +infinity], for each element x_i of the input array x.

$\operatorname{sinh}(x) = \frac{e^x - e^{-x}}{2}$

Note

The hyperbolic sine is an entire function in the complex plane and has no branch cuts. The function is periodic, with period $$2\pi j$$, with respect to the imaginary component.

Special cases

For floating-point operands,

• If x_i is NaN, the result is NaN.

• If x_i is +0, the result is +0.

• If x_i is -0, the result is -0.

• If x_i is +infinity, the result is +infinity.

• If x_i is -infinity, the result is -infinity.

For complex floating-point operands, let a = real(x_i), b = imag(x_i), and

Note

For complex floating-point operands, sinh(conj(x)) must equal conj(sinh(x)).

• If a is +0 and b is +0, the result is +0 + 0j.

• If a is +0 and b is +infinity, the result is 0 + NaN j (sign of the real component is unspecified).

• If a is +0 and b is NaN, the result is 0 + NaN j (sign of the real component is unspecified).

• If a is a positive (i.e., greater than 0) finite number and b is +infinity, the result is NaN + NaN j.

• If a is a positive (i.e., greater than 0) finite number and b is NaN, the result is NaN + NaN j.

• If a is +infinity and b is +0, the result is +infinity + 0j.

• If a is +infinity and b is a positive finite number, the result is +infinity * cis(b).

• If a is +infinity and b is +infinity, the result is infinity + NaN j (sign of the real component is unspecified).

• If a is +infinity and b is NaN, the result is infinity + NaN j (sign of the real component is unspecified).

• If a is NaN and b is +0, the result is NaN + 0j.

• If a is NaN and b is a nonzero finite number, the result is NaN + NaN j.

• If a is NaN and b is NaN, the result is NaN + NaN j.

where cis(v) is cos(v) + sin(v)*1j.

Parameters:
• x (Union[Array, NativeArray]) – input array whose elements each represent a hyperbolic angle. Should have a floating-point 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 hyperbolic sine of each element in x. The returned array must have a floating-point 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.sinh(x)
>>> print(y)
ivy.array([1.18, 3.63, 10.])

>>> x = ivy.array([0.23, 3., -1.2])
>>> ivy.sinh(x, out=x)
>>> print(x)
ivy.array([0.232, 10., -1.51])


With ivy.Container input:

>>> x = ivy.Container(a=ivy.array([0.23, -0.25, 1]), b=ivy.array([3, -4, 1.26]))
>>> y = ivy.sinh(x)
>>> print(y)
{
a: ivy.array([0.232, -0.253, 1.18]),
b: ivy.array([10., -27.3, 1.62])
}

Array.sinh(self, *, out=None)[source]#

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

Parameters:
• self (Array) – input array whose elements each represent a hyperbolic angle. Should have a floating-point 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 hyperbolic sine of each element in self. The returned array must have a floating-point data type determined by type-promotion.

Examples

>>> x = ivy.array([1., 2., 3.])
>>> print(x.sinh())
ivy.array([1.18, 3.63, 10.])

>>> x = ivy.array([0.23, 3., -1.2])
>>> y = ivy.zeros(3)
>>> print(x.sinh(out=y))
ivy.array([0.232, 10., -1.51])

Container.sinh(self, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)[source]#

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

Parameters:
• self (Container) – input container whose elements each represent a hyperbolic angle. Should have a floating-point 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 – an container containing the hyperbolic sine of each element in self. The returned container must have a floating-point data type determined by type-promotion.

Examples

>>> x = ivy.Container(a=ivy.array([-1, 0.23, 1.12]), b=ivy.array([1, -2, 0.76]))
>>> y = x.sinh()
>>> print(y)
{
a: ivy.array([-1.18, 0.232, 1.37]),
b: ivy.array([1.18, -3.63, 0.835])
}

>>> x = ivy.Container(a=ivy.array([-3, 0.34, 2.]),
...                   b=ivy.array([0.67, -0.98, -3]))
>>> y = ivy.Container(a=ivy.zeros(3), b=ivy.zeros(3))
>>> x.sinh(out=y)
>>> print(y)
{
a: ivy.array([-10., 0.347, 3.63]),
b: ivy.array([0.721, -1.14, -10.])
}