numpy.arctan2 () in Python

arctan | arctan2 | NumPy | Python Methods and Functions


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

x1 array_like, real-valued


x2 array_like, real-valued

x-coordinates. If x1.shape != x2.shape , they must be broadcastable to a common shape (which becomes the shape of the output).

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

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


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

angle ndarray

Array of angles in radians, in the range [-pi, pi]. This is a scalar if both x1 and x2 are scalars.

We will cover NumPy arctan2. Along with that, for a better general understanding, we will also look at its syntax and parameter. Then, we will see the application of the whole theoretical part through some examples. But first, let's try to analyze the function through its definition. First, arctan means the inverse of a tan function. Now the NumPy arctan2 function helps us to calculate the arc tan value between X1 and X2 in radians. Here, X1 and 2 are parameters that we will discuss later. As we progress through this article, things will become clearer for you. Next, let's look at the syntax associated with it.
The method numpy.arctan2() calculates the element-wise arctangent of arr1 / arr2 and selects the quadrant correctly. The quadrant is chosen so that arctan2(x1, x2) is the signed angle in radians between the ray ending at the origin and passing through point (1, 0) and the ray ending at the origin and passing through point (x2, x1).
Arctan2 is a 4-quadrant inverse function. Taking this into account, it gives a value between 0 and 2pi. The range of this function is -180 to 180 degrees. These are the 2 key points that distinguish Arctan2 from arctan features.

Difference Between Arctan and Arctan2

In this section we will discuss the difference between 2 Numpy functions.

NumPy arctanNumPy arctan2
arctan is a 2 quadrant inverse function.arctan2 is a 4 quadrant inverse function.
The range of the arctan function is from -90 to 90 degree.The range for arctan2 is -180 to 180 degree.
This function accepts a single array.This function as discussed take 2 input arrays.

Now we are finished with the theoretical part for NumPy arctan2. This section explores how this feature works and how it helps us get the output we want. We'll start with an elementary example and gradually move on to a more complicated example.

NumPy Arctan2 Example

import numpy as ppool

[0.78539816 0.52361148]
Above we see a simple example of our arctan2 function. Now let's walk line by line and understand how we got the result. First, we imported the NumPy function. Then we defined our 2 sets of the array. By using the syntax of our function and the print statement, we get the result we want. Here both values ​​are given in radians. Now if you want to check the result to some extent. To do this, we need to use this particular method:
Angle in degree = angle in radian * 180/pi

If we make calculations on our results, we get a 45 and 30-degree answer. Here we considered pi to 3.14. The responses match and therefore the result is verified.

Numpy Arctan() Example #2

Now suppose that we also want to obtain the values ​​in degrees. It is a simple process and can be done with the help of the for loop and the formula discussed above. Let's see how:
import numpy as ppool
for vals in b:


[-0.46364761  1.04718485]
See how we get the values ​​in radians and degrees. All steps are similar to the first example. The only difference we used a "for loop". If you want something simpler we can also use another method
import numpy as ppool
Here all you need to do is multiply the value (180 / 3.14) or (180 / ppool.pi) by the array. You can definitely use this method on the for loop method. But either way, you will get the desired output which is a degree value.


[-26.57852536  60.02970472]

NumPy Arctan2 Example #3

def doa(self, receiver, source):
        ''' Computes the direction of arrival wrt a source and receiver '''

        s_ind = self.key2ind(source)
        r_ind = self.key2ind(receiver)

        # vector from receiver to source
        v = self.X[:,s_ind] - self.X[:,r_ind]

        azimuth = np.arctan2(v[1], v[0])
        elevation = np.arctan2(v[2], la.norm(v[:2]))

        azimuth = azimuth + 2*np.pi if azimuth < 0. else azimuth
        elevation = elevation + 2*np.pi if elevation < 0. else elevation

        return np.array([azimuth, elevation]) 

NumPy Arctan2 Example #4

def mtx_freq2visi(M, p_mic_x, p_mic_y):
    build the matrix that maps the Fourier series to the visibility
    :param M: the Fourier series expansion is limited from -M to M
    :param p_mic_x: a vector that constains microphones x coordinates
    :param p_mic_y: a vector that constains microphones y coordinates
    num_mic = p_mic_x.size
    ms = np.reshape(np.arange(-M, M + 1, step=1), (1, -1), order='F')
    G = np.zeros((num_mic * (num_mic - 1), 2 * M + 1), dtype=complex, order='C')
    count_G = 0
    for q in range(num_mic):
        p_x_outer = p_mic_x[q]
        p_y_outer = p_mic_y[q]
        for qp in range(num_mic):
            if not q == qp:
                p_x_qqp = p_x_outer - p_mic_x[qp]
                p_y_qqp = p_y_outer - p_mic_y[qp]
                norm_p_qqp = np.sqrt(p_x_qqp ** 2 + p_y_qqp ** 2)
                phi_qqp = np.arctan2(p_y_qqp, p_x_qqp)
                G[count_G, :] = (-1j) ** ms * sp.special.jv(ms, norm_p_qqp) * \
                                np.exp(1j * ms * phi_qqp)
                count_G += 1
    return G 

NumPy Arctan2 Example #5

def vector_angle(u, v, direction=None):
    vector_angle(u, v) yields the angle between the two vectors u and v. The optional argument 
    direction is by default None, which specifies that the smallest possible angle between the
    vectors be reported; if the vectors u and v are 2D vectors and direction parameters True and
    False specify the clockwise or counter-clockwise directions, respectively; if the vectors are
    3D vectors, then direction may be a 3D point that is not in the plane containing u, v, and the
    origin, and it specifies around which direction (u x v or v x u) the the counter-clockwise angle
    from u to v should be reported (the cross product vector that has a positive dot product with
    the direction argument is used as the rotation axis).
    if direction is None:
        return np.arccos(vector_angle_cos(u, v))
    elif direction is True:
        return np.arctan2(v[1], v[0]) - np.arctan2(u[1], u[0])
    elif direction is False:
        return np.arctan2(u[1], u[0]) - np.arctan2(v[1], v[0])
        axis1 = normalize(u)
        axis2 = normalize(np.cross(u, v))
        if, direction) < 0:
            axis2 = -axis2
        return np.arctan2(, v),, v)) 

NumPy Arctan2 Example #6

def __init__(self, line):
        data = line.split(' ')
        data[1:] = [float(x) for x in data[1:]]
        self.classname = data[0]
        self.xmin = data[1] 
        self.ymin = data[2]
        self.xmax = data[1]+data[3]
        self.ymax = data[2]+data[4]
        self.box2d = np.array([self.xmin,self.ymin,self.xmax,self.ymax])
        self.centroid = np.array([data[5],data[6],data[7]])
        self.unused_dimension = np.array([data[8],data[9],data[10]])
        self.w = data[8]
        self.l = data[9]
        self.h = data[10]
        self.orientation = np.zeros((3,))
        self.orientation[0] = data[11]
        self.orientation[1] = data[12]
        self.heading_angle = -1 * np.arctan2(self.orientation[1], self.orientation[0]) 

np.arctan2 Example #7

def stanleyControl(state, cx, cy, cyaw, last_target_idx):
    :param state: (State object)
    :param cx: ([float])
    :param cy: ([float])
    :param cyaw: ([float])
    :param last_target_idx: (int)
    :return: (float, int, float)
    # Cross track error
    current_target_idx, error_front_axle = calcTargetIndex(state, cx, cy)

    if last_target_idx >= current_target_idx:
        current_target_idx = last_target_idx

    # theta_e corrects the heading error
    theta_e = normalizeAngle(cyaw[current_target_idx] - state.yaw)
    # theta_d corrects the cross track error
    theta_d = np.arctan2(K_STANLEY_CONTROL * error_front_axle, state.v)
    # Steering control
    delta = theta_e + theta_d

    return delta, current_target_idx, error_front_axle 

np arctan2 Example #8

def calcTargetIndex(state, cx, cy):
    :param state: (State object)
    :param cx: [float]
    :param cy: [float]
    :return: (int, float)
    # Calc front axle position
    fx = state.x + CAR_LENGTH * np.cos(state.yaw)
    fy = state.y + CAR_LENGTH * np.sin(state.yaw)

    # Search nearest point index
    dx = [fx - icx for icx in cx]
    dy = [fy - icy for icy in cy]
    d = [np.sqrt(idx ** 2 + idy ** 2) for (idx, idy) in zip(dx, dy)]
    error_front_axle = min(d)
    target_idx = d.index(error_front_axle)

    target_yaw = normalizeAngle(np.arctan2(fy - cy[target_idx], fx - cx[target_idx]) - state.yaw)
    if target_yaw > 0.0:
        error_front_axle = - error_front_axle

    return target_idx, error_front_axle 

NumPy Arctan2 Example #9

def vehicle_flat_reverse(zflag, params={}):
    # Get the parameter values
    b = params.get('wheelbase', 3.)

    # Create a vector to store the state and inputs
    x = np.zeros(3)
    u = np.zeros(2)

    # Given the flat variables, solve for the state
    x[0] = zflag[0][0]  # x position
    x[1] = zflag[1][0]  # y position
    x[2] = np.arctan2(zflag[1][1], zflag[0][1])  # tan(theta) = ydot/xdot

    # And next solve for the inputs
    u[0] = zflag[0][1] * np.cos(x[2]) + zflag[1][1] * np.sin(x[2])
    thdot_v = zflag[1][2] * np.cos(x[2]) - zflag[0][2] * np.sin(x[2])
    u[1] = np.arctan2(thdot_v, u[0]**2 / b)

    return x, u

# Function to compute the RHS of the system dynamics

np.arctan2 Example #10

def GetNeighborCells(self, p, nr, dp = None):
        Returns all cells no more than a given distance in any direction
        from a specified cell
        p:      The cell of which to get the neighbors
        nr:     Neighbor radius
        dp:     Direction preference
        pi, pj, pk = p
        tqm = self.qm * self.qp
        nc = [(pi - i * tqm, pj - j * tqm, pk) for i in range(-nr, nr + 1) for j in range(-nr, nr + 1)]
        if dp is not None:                      #Sort points based on direction preference
            dpa = np.arctan2(dp[1], dp[0])      #Get angle of direction prefered
            #Prefer directions in the direction of dp; sort based on magnitude of angle from last direction
            nc = sorted(nc,  key = lambda t : np.abs(np.arctan2(t[1], t[0]) - dpa)) 
        return nc
    #Gets the current 3d position of the player 
In this article, we cover NumPy's arctan2. In addition, we also saw its syntax and parameters. For better understanding, we saw some examples. In the end, we can conclude that NumPy arctan2 is a function that this function helps us to find the inverse tan value between 2 points. By default it returns the value in radians, but we can convert it to degrees using the methods discussed above. We hope this article has clarified all your doubts. But in case you have any unresolved questions, feel free to write them down in the comments section. Having read that, why not read about the following identity matrix.

Python atan or atan2, what should I use?

StackOverflow question

My formula f=arctan(ImZ/ReZ)

There are two options:

Option 1 (atan):


>>> z=y/x
>>> f1=math.atan(z)
>>> f1

Option 2 (atan2)

>>> f=math.atan2(y,x)
>>> f

Why are these two results different?


Atan takes single argument and Atan2 takes two arguments.The purpose of using two arguments instead of one is to gather information on the signs of the inputs in order to return the appropriate quadrant of the computed angle, which is not possible for the single-argument Atan

atan2 results for each x,y

Atan2 result is always between -pi and pi.


Archived version

numpy.arctan2 (arr1, arr2, casting = & # 39; same_kind & # 39 ;, order = & # 39; K & # 39 ;, dtype = None, ufunc & # 39; arctan & # 39;) :
Calculates the element-wise arctangent of arr1 / arr2 by choosing the correct quadrant. The quadrant is chosen so that arctan2 (x1, x2) is the angle sign in radians between a ray ending at the origin and passing through point (1, 0) and a ray ending at the origin and passing through through point (x2) x1).


arr1: [array_like] real valued; y-coordinates
arr2: [array_like] real valued; x-coordinates. It must match shape of y-cordinates.
out: [ndarray, array_like [ OPTIONAL ]] array of same shape as x .
where: [array_like, optional] True value means to calculate the universal functions (ufunc) at that position, False value means to leave the value in the output alone.

2pi Radians = 360 degrees
The convention is to return the angle z whose real part lies in [-pi / 2 , pi / 2].

Return: Element-wise arc tangent of arr1 / arr2. The values ​​are in the closed interval [-pi / 2, pi / 2].

Code # 1: Work

# Python3 program explaining
# arctan2 () function


import numpy as np


arr1 = [ - 1 , + 1 , + 1 , - 1 ]

arr2 = [ - 1 , - 1 , + 1 , + 1 ]


ans = np.arctan2 (arr2, arr1) * 180 / np.pi


print ( "x-coordinates:" , arr1)

print ( "y-coordin ates: " , arr2)


print ( "arctan2 values:" , ans)


 x-coordinates: [-1, 1, 1, -1] y-coordinates: [-1, -1, 1, 1] arctan2 values: [-135. -45. 45. 135.] 

Code # 2: Work

# Python3 program showing
# arctan2 () functions


import numpy as np


a = np.arctan2 ([ 0. , 0. , np.inf ], [ + 0. , - 0. , np.inf])


b = np.arctan2 ([ 1. , - 1. ], [ 0. , 0. ])


print ( " a : " , a)


print ( "b:" , b )


 a: [0. 3.14159265 0.78539816] b: [1.57079633 -1.57079633] 

arctan2.html#numpy.arctan2> enerated / numpy.arctan2.html # numpy.arctan2

numpy.arctan2 () in Python: StackOverflow Questions

Answer #1

Update: User cphyc has kindly created a Github repository for the code in this answer (see here), and bundled the code into a package which may be installed using pip install matplotlib-label-lines.

Pretty Picture:

semi-automatic plot-labeling

In matplotlib it"s pretty easy to label contour plots (either automatically or by manually placing labels with mouse clicks). There does not (yet) appear to be any equivalent capability to label data series in this fashion! There may be some semantic reason for not including this feature which I am missing.

Regardless, I have written the following module which takes any allows for semi-automatic plot labelling. It requires only numpy and a couple of functions from the standard math library.


The default behaviour of the labelLines function is to space the labels evenly along the x axis (automatically placing at the correct y-value of course). If you want you can just pass an array of the x co-ordinates of each of the labels. You can even tweak the location of one label (as shown in the bottom right plot) and space the rest evenly if you like.

In addition, the label_lines function does not account for the lines which have not had a label assigned in the plot command (or more accurately if the label contains "_line").

Keyword arguments passed to labelLines or labelLine are passed on to the text function call (some keyword arguments are set if the calling code chooses not to specify).


  • Annotation bounding boxes sometimes interfere undesirably with other curves. As shown by the 1 and 10 annotations in the top left plot. I"m not even sure this can be avoided.
  • It would be nice to specify a y position instead sometimes.
  • It"s still an iterative process to get annotations in the right location
  • It only works when the x-axis values are floats


  • By default, the labelLines function assumes that all data series span the range specified by the axis limits. Take a look at the blue curve in the top left plot of the pretty picture. If there were only data available for the x range 0.5-1 then then we couldn"t possibly place a label at the desired location (which is a little less than 0.2). See this question for a particularly nasty example. Right now, the code does not intelligently identify this scenario and re-arrange the labels, however there is a reasonable workaround. The labelLines function takes the xvals argument; a list of x-values specified by the user instead of the default linear distribution across the width. So the user can decide which x-values to use for the label placement of each data series.

Also, I believe this is the first answer to complete the bonus objective of aligning the labels with the curve they"re on. :)

from math import atan2,degrees
import numpy as np

#Label line with line2D label data
def labelLine(line,x,label=None,align=True,**kwargs):

    ax = line.axes
    xdata = line.get_xdata()
    ydata = line.get_ydata()

    if (x < xdata[0]) or (x > xdata[-1]):
        print("x label location is outside data range!")

    #Find corresponding y co-ordinate and angle of the line
    ip = 1
    for i in range(len(xdata)):
        if x < xdata[i]:
            ip = i

    y = ydata[ip-1] + (ydata[ip]-ydata[ip-1])*(x-xdata[ip-1])/(xdata[ip]-xdata[ip-1])

    if not label:
        label = line.get_label()

    if align:
        #Compute the slope
        dx = xdata[ip] - xdata[ip-1]
        dy = ydata[ip] - ydata[ip-1]
        ang = degrees(atan2(dy,dx))

        #Transform to screen co-ordinates
        pt = np.array([x,y]).reshape((1,2))
        trans_angle = ax.transData.transform_angles(np.array((ang,)),pt)[0]

        trans_angle = 0

    #Set a bunch of keyword arguments
    if "color" not in kwargs:
        kwargs["color"] = line.get_color()

    if ("horizontalalignment" not in kwargs) and ("ha" not in kwargs):
        kwargs["ha"] = "center"

    if ("verticalalignment" not in kwargs) and ("va" not in kwargs):
        kwargs["va"] = "center"

    if "backgroundcolor" not in kwargs:
        kwargs["backgroundcolor"] = ax.get_facecolor()

    if "clip_on" not in kwargs:
        kwargs["clip_on"] = True

    if "zorder" not in kwargs:
        kwargs["zorder"] = 2.5


def labelLines(lines,align=True,xvals=None,**kwargs):

    ax = lines[0].axes
    labLines = []
    labels = []

    #Take only the lines which have labels other than the default ones
    for line in lines:
        label = line.get_label()
        if "_line" not in label:

    if xvals is None:
        xmin,xmax = ax.get_xlim()
        xvals = np.linspace(xmin,xmax,len(labLines)+2)[1:-1]

    for line,x,label in zip(labLines,xvals,labels):

Test code to generate the pretty picture above:

from matplotlib import pyplot as plt
from scipy.stats import loglaplace,chi2

from labellines import *

X = np.linspace(0,1,500)
A = [1,2,5,10,20]
funcs = [np.arctan,np.sin,loglaplace(4).pdf,chi2(5).pdf]

for a in A:


for a in A:


for a in A:

xvals = [0.8,0.55,0.22,0.104,0.045]

for a in A:

lines = plt.gca().get_lines()
labelLine(l1,0.6,label=r"$Re=${}".format(l1.get_label()),ha="left",va="bottom",align = False)

Answer #2

First find the difference between the start point and the end point (here, this is more of a directed line segment, not a "line", since lines extend infinitely and don"t start at a particular point).

deltaY = P2_y - P1_y
deltaX = P2_x - P1_x

Then calculate the angle (which runs from the positive X axis at P1 to the positive Y axis at P1).

angleInDegrees = arctan(deltaY / deltaX) * 180 / PI

But arctan may not be ideal, because dividing the differences this way will erase the distinction needed to distinguish which quadrant the angle is in (see below). Use the following instead if your language includes an atan2 function:

angleInDegrees = atan2(deltaY, deltaX) * 180 / PI

EDIT (Feb. 22, 2017): In general, however, calling atan2(deltaY,deltaX) just to get the proper angle for cos and sin may be inelegant. In those cases, you can often do the following instead:

  1. Treat (deltaX, deltaY) as a vector.
  2. Normalize that vector to a unit vector. To do so, divide deltaX and deltaY by the vector"s length (sqrt(deltaX*deltaX+deltaY*deltaY)), unless the length is 0.
  3. After that, deltaX will now be the cosine of the angle between the vector and the horizontal axis (in the direction from the positive X to the positive Y axis at P1).
  4. And deltaY will now be the sine of that angle.
  5. If the vector"s length is 0, it won"t have an angle between it and the horizontal axis (so it won"t have a meaningful sine and cosine).

EDIT (Feb. 28, 2017): Even without normalizing (deltaX, deltaY):

  • The sign of deltaX will tell you whether the cosine described in step 3 is positive or negative.
  • The sign of deltaY will tell you whether the sine described in step 4 is positive or negative.
  • The signs of deltaX and deltaY will tell you which quadrant the angle is in, in relation to the positive X axis at P1:
    • +deltaX, +deltaY: 0 to 90 degrees.
    • -deltaX, +deltaY: 90 to 180 degrees.
    • -deltaX, -deltaY: 180 to 270 degrees (-180 to -90 degrees).
    • +deltaX, -deltaY: 270 to 360 degrees (-90 to 0 degrees).

An implementation in Python using radians (provided on July 19, 2015 by Eric Leschinski, who edited my answer):

from math import *
def angle_trunc(a):
    while a < 0.0:
        a += pi * 2
    return a

def getAngleBetweenPoints(x_orig, y_orig, x_landmark, y_landmark):
    deltaY = y_landmark - y_orig
    deltaX = x_landmark - x_orig
    return angle_trunc(atan2(deltaY, deltaX))

angle = getAngleBetweenPoints(5, 2, 1,4)
assert angle >= 0, "angle must be >= 0"
angle = getAngleBetweenPoints(1, 1, 2, 1)
assert angle == 0, "expecting angle to be 0"
angle = getAngleBetweenPoints(2, 1, 1, 1)
assert abs(pi - angle) <= 0.01, "expecting angle to be pi, it is: " + str(angle)
angle = getAngleBetweenPoints(2, 1, 2, 3)
assert abs(angle - pi/2) <= 0.01, "expecting angle to be pi/2, it is: " + str(angle)
angle = getAngleBetweenPoints(2, 1, 2, 0)
assert abs(angle - (pi+pi/2)) <= 0.01, "expecting angle to be pi+pi/2, it is: " + str(angle)
angle = getAngleBetweenPoints(1, 1, 2, 2)
assert abs(angle - (pi/4)) <= 0.01, "expecting angle to be pi/4, it is: " + str(angle)
angle = getAngleBetweenPoints(-1, -1, -2, -2)
assert abs(angle - (pi+pi/4)) <= 0.01, "expecting angle to be pi+pi/4, it is: " + str(angle)
angle = getAngleBetweenPoints(-1, -1, -1, 2)
assert abs(angle - (pi/2)) <= 0.01, "expecting angle to be pi/2, it is: " + str(angle)

All tests pass. See

Answer #3

Sorry EMS, but I actually just got another response from the matplotlib mailling list (Thanks goes out to Benjamin Root).

The code I am looking for is adjusting the savefig call to:

fig.savefig("samplefigure", bbox_extra_artists=(lgd,), bbox_inches="tight")
#Note that the bbox_extra_artists must be an iterable

This is apparently similar to calling tight_layout, but instead you allow savefig to consider extra artists in the calculation. This did in fact resize the figure box as desired.

import matplotlib.pyplot as plt
import numpy as np

x = np.arange(-2*np.pi, 2*np.pi, 0.1)
fig = plt.figure(1)
ax = fig.add_subplot(111)
ax.plot(x, np.sin(x), label="Sine")
ax.plot(x, np.cos(x), label="Cosine")
ax.plot(x, np.arctan(x), label="Inverse tan")
handles, labels = ax.get_legend_handles_labels()
lgd = ax.legend(handles, labels, loc="upper center", bbox_to_anchor=(0.5,-0.1))
text = ax.text(-0.2,1.05, "Aribitrary text", transform=ax.transAxes)
fig.savefig("samplefigure", bbox_extra_artists=(lgd,text), bbox_inches="tight")

This produces:

[edit] The intent of this question was to completely avoid the use of arbitrary coordinate placements of arbitrary text as was the traditional solution to these problems. Despite this, numerous edits recently have insisted on putting these in, often in ways that led to the code raising an error. I have now fixed the issues and tidied the arbitrary text to show how these are also considered within the bbox_extra_artists algorithm.

Answer #4

Last time I checked it, the scipy __init__ method executes a

from numpy import *

so that the whole numpy namespace is included into scipy when the scipy module is imported.

The log10 behavior you are describing is interesting, because both versions are coming from numpy. One is a ufunc, the other is a numpy.lib function. Why scipy is preferring the library function over the ufunc, I don"t know off the top of my head.

EDIT: In fact, I can answer the log10 question. Looking in the scipy __init__ method I see this:

# Import numpy symbols to scipy name space
import numpy as _num
from numpy import oldnumeric
from numpy import *
from numpy.random import rand, randn
from numpy.fft import fft, ifft
from numpy.lib.scimath import *

The log10 function you get in scipy comes from numpy.lib.scimath. Looking at that code, it says:

Wrapper functions to more user-friendly calling of certain math functions
whose output data-type is different than the input data-type in certain
domains of the input.

For example, for functions like log() with branch cuts, the versions in this
module provide the mathematically valid answers in the complex plane:

>>> import math
>>> from numpy.lib import scimath
>>> scimath.log(-math.exp(1)) == (1+1j*math.pi)

Similarly, sqrt(), other base logarithms, power() and trig functions are
correctly handled.  See their respective docstrings for specific examples.

It seems that module overlays the base numpy ufuncs for sqrt, log, log2, logn, log10, power, arccos, arcsin, and arctanh. That explains the behavior you are seeing. The underlying design reason why it is done like that is probably buried in a mailing list post somewhere.

numpy.arctan2 () in Python: StackOverflow Questions

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