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# numpy.sinh

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

      >>> import numpy as np
      >>> 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=np.float64)
      >>> 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)