numpy.atan#

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

Trigonometric inverse tangent, element-wise.

The inverse of tan, so that ify=tan(x) thenx=arctan(y).

Parameters:

xarray_like

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:

outndarray or scalar

Out has the same shape asx. Its real part is in[-pi/2,pi/2] (arctan(+/-inf) returns+/-pi/2).This is a scalar ifx is a scalar.

See also

arctan2

The “four quadrant” arctan of the angle formed by (x,y) and the positivex-axis.

angle

Argument of complex values.

Notes

arctan is a multi-valued function: for eachx there are infinitelymany numbersz such that tan(z) =x. The convention is to returnthe anglez whose real part lies in [-pi/2, pi/2].

For real-valued input data types,arctan always returns real output.For each value that cannot be expressed as a real number or infinity,it yieldsnan and sets theinvalid floating point error flag.

For complex-valued input,arctan is a complex analytic function thathas [1j,infj] and [-1j,-infj] as branch cuts, and is continuousfrom the left on the former and from the right on the latter.

The inverse tangent is also known asatan or tan^{-1}.

References

Abramowitz, M. and Stegun, I. A.,Handbook of Mathematical Functions,10th printing, New York: Dover, 1964, pp. 79.https://personal.math.ubc.ca/~cbm/aands/page_79.htm

Examples

Try it in your browser!

We expect the arctan of 0 to be 0, and of 1 to be pi/4:

>>>importnumpyasnp>>>np.arctan([0,1])array([ 0.        ,  0.78539816])

>>>np.pi/40.78539816339744828

Plot arctan:

>>>importmatplotlib.pyplotasplt>>>x=np.linspace(-10,10)>>>plt.plot(x,np.arctan(x))>>>plt.axis('tight')>>>plt.show()

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