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# numpy.round

numpy.round(a, decimals=0, out=None)

  Evenly round to the given number of decimals.

  Parameters:
    a array_like

      Input data.

    decimals int, optional

      Number of decimal places to round to (default: 0). If decimals is negative, it specifies the number of positions to the left of the decimal point.

    out ndarray, optional

      Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. See Output type determination for more details.

  Returns:
    rounded_array ndarray

      An array of the same type as a, containing the rounded values. Unless out was specified, a new array is created. A reference to the result is returned.

      The real and imaginary parts of complex numbers are rounded separately. The result of rounding a float is a float.

  See also

  `ndarray.round`

    equivalent method

  `around`

    an alias for this function

  `ceil`, `fix`, `floor`, `rint`, `trunc`

  Notes

  For values exactly halfway between rounded decimal values, NumPy rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, -0.5 and 0.5 round to 0.0, etc.

  `np.round` uses a fast but sometimes inexact algorithm to round floating-point datatypes. For positive decimals it is equivalent to `np.true_divide(np.rint(a * 10**decimals), 10**decimals)`, which has error due to the inexact representation of decimal fractions in the IEEE floating point standard [1] and errors introduced when scaling by powers of ten. For instance, note the extra “1” in the following:

      >>> np.round(56294995342131.5, 3)
      56294995342131.51

  If your goal is to print such values with a fixed number of decimals, it is preferable to use numpy’s float printing routines to limit the number of printed decimals:

      >>> np.format_float_positional(56294995342131.5, precision=3)
      '56294995342131.5'

  The float printing routines use an accurate but much more computationally demanding algorithm to compute the number of digits after the decimal point.

  Alternatively, Python’s builtin `round` function uses a more accurate but slower algorithm for 64-bit floating point values:

      >>> round(56294995342131.5, 3)
      56294995342131.5
      >>> np.round(16.055, 2), round(16.055, 2)  # equals 16.0549999999999997
      (16.06, 16.05)

  References

  [1]

  “Lecture Notes on the Status of IEEE 754”, William Kahan, https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF

  Examples

      >>> import numpy as np
      >>> np.round([0.37, 1.64])
      array([0., 2.])
      >>> np.round([0.37, 1.64], decimals=1)
      array([0.4, 1.6])
      >>> np.round([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
      array([0., 2., 2., 4., 4.])
      >>> np.round([1,2,3,11], decimals=1) # ndarray of ints is returned
      array([ 1,  2,  3, 11])
      >>> np.round([1,2,3,11], decimals=-1)
      array([ 0,  0,  0, 10])