numpy.arctan2#

numpy.arctan2(x1,x2,/,out=None,*,where=True,casting='same_kind',order='K',dtype=None,subok=True[,signature])=<ufunc'arctan2'>#

Element-wise arc tangent ofx1/x2 choosing the quadrant correctly.

The quadrant (i.e., branch) is chosen so thatarctan2(x1,x2) isthe signed angle in radians between the ray ending at the origin andpassing through the point (1,0), and the ray ending at the origin andpassing through the point (x2,x1). (Note the role reversal: the“y-coordinate” is the first function parameter, the “x-coordinate”is the second.) By IEEE convention, this function is defined forx2 = +/-0 and for either or both ofx1 andx2 = +/-inf (seeNotes for specific values).

This function is not defined for complex-valued arguments; for theso-called argument of complex values, useangle.

Parameters:

x1array_like, real-valued

y-coordinates.

x2array_like, real-valued

x-coordinates.Ifx1.shape!=x2.shape, they must be broadcastable to a commonshape (which becomes the shape of the output).

outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must havea shape that the inputs broadcast to. If not provided or None,a freshly-allocated array is returned. A tuple (possible only as akeyword argument) must have length equal to the number of outputs.

wherearray_like, optional

This condition is broadcast over the input. At locations where thecondition is True, theout array will be set to the ufunc result.Elsewhere, theout array will retain its original value.Note that if an uninitializedout array is created via the defaultout=None, locations within it where the condition is False willremain uninitialized.

**kwargs

For other keyword-only arguments, see theufunc docs.

Returns:

anglendarray

Array of angles in radians, in the range[-pi,pi].This is a scalar if bothx1 andx2 are scalars.

See also

arctan,tan,angle

Notes

arctan2 is identical to theatan2 function of the underlyingC library. The following special values are defined in the Cstandard:[1]

x1	x2	arctan2(x1,x2)
+/- 0	+0	+/- 0
+/- 0	-0	+/- pi
> 0	+/-inf	+0 / +pi
< 0	+/-inf	-0 / -pi
+/-inf	+inf	+/- (pi/4)
+/-inf	-inf	+/- (3*pi/4)

Note that +0 and -0 are distinct floating point numbers, as are +infand -inf.

References

[1]

ISO/IEC standard 9899:1999, “Programming language C.”

Examples

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Consider four points in different quadrants:

>>>importnumpyasnp>>>x=np.array([-1,+1,+1,-1])>>>y=np.array([-1,-1,+1,+1])>>>np.arctan2(y,x)*180/np.piarray([-135.,  -45.,   45.,  135.])

Note the order of the parameters.arctan2 is defined also whenx2 = 0and at several other special points, obtaining values inthe range[-pi,pi]:

>>>np.arctan2([1.,-1.],[0.,0.])array([ 1.57079633, -1.57079633])>>>np.arctan2([0.,0.,np.inf],[+0.,-0.,np.inf])array([0.        , 3.14159265, 0.78539816])

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