# numpy.isclose

numpy.isclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)

  Returns a boolean array where two arrays are element-wise equal within a tolerance.

  The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.

  Warning

  The default atol is not appropriate for comparing numbers that are much smaller than one (see Notes).

  Parameters:
    a, b array_like

      Input arrays to compare.

    rtol float

      The relative tolerance parameter (see Notes).

    atol float

      The absolute tolerance parameter (see Notes).

    equal_nan bool

      Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.

  Returns:
    y array_like

      Returns a boolean array of where a and b are equal within the given tolerance. If both a and b are scalars, returns a single boolean value.

  See also

  `allclose`
  `math.isclose`

  Notes

  New in version 1.7.0.

  For finite values, isclose uses the following equation to test whether two floating point values are equivalent.

  > absolute(a - b) <= (atol + rtol * absolute(b))

  Unlike the built-in `math.isclose`, the above equation is not symmetric in a and b – it assumes b is the reference value – so that isclose(a, b) might be different from isclose(b, a). Furthermore, the default value of atol is not zero, and is used to determine what small values should be considered close to zero. The default value is appropriate for expected values of order unity: if the expected values are significantly smaller than one, it can result in false positives. atol should be carefully selected for the use case at hand. A zero value for atol will result in False if either a or b is zero.

  `isclose` is not defined for non-numeric data types. bool is considered a numeric data-type for this purpose.

  Examples

      >>> np.isclose([1e10,1e-7], [1.00001e10,1e-8])
      array([ True, False])
      >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9])
      array([ True, True])
      >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9])
      array([False,  True])
      >>> np.isclose([1.0, np.nan], [1.0, np.nan])
      array([ True, False])
      >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
      array([ True, True])
      >>> np.isclose([1e-8, 1e-7], [0.0, 0.0])
      array([ True, False])
      >>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0)
      array([False, False])
      >>> np.isclose([1e-10, 1e-10], [1e-20, 0.0])
      array([ True,  True])
      >>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0)
      array([False,  True])