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

Return the positive square-root of an array, element-wise.


x : array_like

The values whose square-roots are required.

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

Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.


For other keyword-only arguments, see the ufunc docs.


y : ndarray

An array of the same shape as x, containing the positive square-root of each element in x. If any element in x is complex, a complex array is returned (and the square-roots of negative reals are calculated). If all of the elements in x are real, so is y, with negative elements returning nan. If out was provided, y is a reference to it.

See also

A version which returns complex numbers when given negative reals.


sqrt has–consistent with common convention–as its branch cut the real “interval” [-inf, 0), and is continuous from above on it. A branch cut is a curve in the complex plane across which a given complex function fails to be continuous.


>>> np.sqrt([1,4,9])
array([ 1.,  2.,  3.])
>>> np.sqrt([4, -1, -3+4J])
array([ 2.+0.j,  0.+1.j,  1.+2.j])
>>> np.sqrt([4, -1, numpy.inf])
array([  2.,  NaN,  Inf])

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