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# scipy.special.erfcinv

scipy.special.erfcinv(y, out=None) = <ufunc 'erfcinv'>

  Inverse of the complementary error function.

  Computes the inverse of the complementary error function.

  In the complex domain, there is no unique complex number \(w\) satisfying \(\operatorname{erfc}(w) = z\). This indicates a true inverse function would be multivalued. When the domain restricts to the real interval \(0 < x < 2\), there is a unique real number satisfying

  \[\operatorname{erfc}(\operatorname{erfcinv}(x)) = x\]

  It is related to the inverse of the error function by

  \[\operatorname{erfcinv}(1 - x) = \operatorname{erfinv}(x)\]
  Parameters:
    y ndarray

      Argument at which to evaluate. Domain: \([0, 2]\)

    out ndarray, optional

      Optional output array for the function values

  Returns:
    erfcinv scalar or ndarray

      The inverse of \(\operatorname{erfc}\) of \(y\), element-wise

  See also

  `erf`

    Error function

  `erfc`

    Complementary error function

  `erfinv`

    Inverse of the error function

  Examples

      >>> import numpy as np
      >>> import matplotlib.pyplot as plt
      >>> from scipy.special import erfcinv

      >>> erfcinv(0.5)
      0.4769362762044699

      >>> y = np.linspace(0.0, 2.0, num=11)
      >>> erfcinv(y)
      array([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,
             -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,
                    -inf])

  Plot the function:

      >>> y = np.linspace(0, 2, 200)
      >>> fig, ax = plt.subplots()
      >>> ax.plot(y, erfcinv(y))
      >>> ax.grid(True)
      >>> ax.set_xlabel('y')
      >>> ax.set_title('erfcinv(y)')
      >>> plt.show()