numpy.sinh

numpy.sinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'sinh'>

Hyperbolic sine, element-wise.

Equivalent to 1/2 * (np.exp(x) - np.exp(-x)) or -1j * np.sin(1j*x).

Parameters:

x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the ufunc docs.

Returns:

y : ndarray The corresponding hyperbolic sine values. This is a scalar if x is a scalar.

Notes

If out is provided, the function writes the result into it, and returns a reference to out. (See Examples)

References

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972, pg. 83.

Examples

>>> np.sinh(0)
0.0
>>> np.sinh(np.pi*1j/2)
1j
>>> np.sinh(np.pi*1j) # (exact value is 0)
1.2246063538223773e-016j
>>> # Discrepancy due to vagaries of floating point arithmetic.

>>> # Example of providing the optional output parameter
>>> out1 = np.array([0], dtype='d')
>>> out2 = np.sinh([0.1], out1)
>>> out2 is out1
True

>>> # Example of ValueError due to provision of shape mis-matched `out`
>>> np.sinh(np.zeros((3,3)),np.zeros((2,2)))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: operands could not be broadcast together with shapes (3,3) (2,2)