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# numpy.trapz

`numpy.``trapz`(y, x=None, dx=1.0, axis=-1)

  Integrate along the given axis using the composite trapezoidal rule.

  Integrate y (x) along given axis.

  Parameters : | y : array_like Input array to integrate. x : array_like, optional If x is None, then spacing between all y elements is dx. dx : scalar, optional If x is None, spacing given by dx is assumed. Default is 1. axis : int, optional Specify the axis.
  Returns : | trapz : float Definite integral as approximated by trapezoidal rule.

  See also

  `sum`, `cumsum`

  Notes

  Image [R249] illustrates trapezoidal rule – y-axis locations of points will be taken from y array, by default x-axis distances between points will be 1.0, alternatively they can be provided with x array or with dx scalar. Return value will be equal to combined area under the red lines.

  References

  [R248] | Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule

  [R249] | (1, 2) Illustration image: http://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png

  Examples

      >>> np.trapz([1,2,3])
      4.0
      >>> np.trapz([1,2,3], x=[4,6,8])
      8.0
      >>> np.trapz([1,2,3], dx=2)
      8.0
      >>> a = np.arange(6).reshape(2, 3)
      >>> a
      array([[0, 1, 2],
             [3, 4, 5]])
      >>> np.trapz(a, axis=0)
      array([ 1.5,  2.5,  3.5])
      >>> np.trapz(a, axis=1)
      array([ 2.,  8.])