Pythonic way to select elements of an array based on values? - python

I'm looking for a pythonic (1-line) way to extract a range of values from an array
Here's some sample code that will extract the array elements that are >2 and <8 from x,y data, and put them into a new array. Is there a way to accomplish this on a single line? The code below works but seems kludgier than it needs to be. (Note I'm actually working with floats in my application)
import numpy as np
x0 = np.array([0,3,9,8,3,4,5])
y0 = np.array([2,3,5,7,8,1,0])
x1 = x0[x0>2]
y1 = y0[x0>2]
x2 = x1[x1<8]
y2 = y1[x1<8]
print x2, y2
This prints
[3 3 4 5] [3 8 1 0]
Part (b) of the problem would be to extract values say 1 < x < 3 and 7 < x < 9 as well as their corresponding y values.

You can chain together boolean arrays using & for element-wise logical and and | for element-wise logical or, so that the condition 2 < x0 and x0 < 8 becomes
mask = (2 < x0) & (x0 < 8)
For example,
import numpy as np
x0 = np.array([0,3,9,8,3,4,5])
y0 = np.array([2,3,5,7,8,1,0])
mask = (2 < x0) & (x0 < 8)
x2 = x0[mask]
y2 = y0[mask]
print(x2, y2)
# (array([3, 3, 4, 5]), array([3, 8, 1, 0]))
mask2 = ((1 < x0) & (x0 < 3)) | ((7 < x0) & (x0 < 9))
x3 = x0[mask2]
y3 = y0[mask2]
print(x3, y3)
# (array([8]), array([7]))

import numpy as np
x0 = np.array([0,3,9,8,3,4,5])
y0 = np.array([2,3,5,7,8,1,0])
list( zip( *[(x,y) for x, y in zip(x0, y0) if 1<=x<=3 or 7<=x<=9] ) )
# [(3, 9, 8, 3), (3, 5, 7, 8)]

Related

Calculate the angle between two lines (2 options) and efficiency

The task: calculate the angle between two lines
input:
float x1, y1 (starting point)
float x2, y2 (end point)
output:
float phi (angle in deg, between the lines)
additionally:
one line is parallel to the x-axis, and phi is 0° ≤ phi < 359°
Task Picture
option 1:
import math
rad_to deg = lambda x: 180.0/math.pi * x
# start-point
x1 = float(input("x1: "))
y1 = float(input("y1: "))
# end-point
x2 = float(input("x2: "))
y2 = float(input("y2: "))
# slope of one line (parallel to the x-axis)
m1 = 0
# slope between the start-point and end-point
# special-case: division with zero
if x1 == x2:
m2 = "Not defined!"
if y2 > y1: # end-point over start-point
phi = 90
elif y2 < y1: # end-point under start-point
phi = 270
else:
m2 = (y2 - y2) / (x2 - x1)
# angle between two lines (smaller angle: 0° < phi < 90°)
angle = rad_to_deg(math.atan(abs((m1 - m2) / (1 + m1 * m2))))
if x1 < x2 and y1 < y2: # 1. quadrant
phi = sw
elif x1 > x2 and y1 < y2: # 2. quadrant
phi = 180 - sw
elif x1 > x2 and y1 > y2: # 3. quadrant
phi = 180 + sw
elif x1 < x2 and y1 > y2: # 4. quadrant
phi = 360 - sw
elif y1 == y2 and x1 > x2: # end-point left from start-point
phi = 180
elif y1 == y2 and x1 < x2 : # end-point right from start-point
phi = 0
elif x1 == x2 and y1 == y2:
phi = "Error, start-point is end-point"
print("angle phi: " + str(phi))
or should be the special-case with try/except?
try:
m2 = (y2 - y2) / (x2 - x1)
except ZeroDivisionError: # x1 == x2
m2 = "Not defined!"
if y2 > y1: # end-point over start-point
phi = 90
elif y2 < y1: # end-point under start-point
phi = 270
option 2: with vectors
for math import sqrt, acos, pi
rad_to_deg = lambda x: 180.0/pi * x
x1 = float(input("x1: "))
y1 = float(input("y1: "))
x2 = float(input("x1: "))
y2 = float(input("x2: "))
# vectors
u = [1, 0] # start-point and (a point right from the start-point)
v = [x2 - x1, y2 - y1]
# calculation
u_scalar_v = u[0] * v[0] + u[1] * v[1]
u_amount = sqrt(u[0] * u[0] + u[1] * u[1])
v_amount = sqrt(v[0] * v[0] + v[1] * v[1])
# scalar product
phi = round(rad_to_deg(acos(u_scalar_v / (u_amount * v_amount))), 5)
if y2 >= y1:
pass
else:
phi = 360 - phi
print(phi)
option 3:
is to see the start-point, the end-point and a point right from s, as a triangle and to calculate over the cosine theorem
What is the most efficient way to calculate this and how can I decide it?
Find the Angle between three points from 2D using python provides a simple solution.
import math
def getAngle(a, b, c):
ang = math.degrees(math.atan2(c[1]-b[1], c[0]-b[0]) - math.atan2(a[1]-b[1], a[0]-b[0]))
return ang + 360 if ang < 0 else ang
# starting-point
x1 = float(input("x1: "))
y1 = float(input("y1: "))
# middle-point (intersection point)
x2 = float(input("x2: "))
y2 = float(input("y2: "))
# ending point of horizontal line
x3 = x2 + 1 # i.e. horizontal offset from mid-point (x2, y2)
y3 = y2
a = (x1, y1)
b = (x2, y2)
c = (x3, y3)
angle = getAngle(a, b, c)
Example
a = (5, 0)
b = (0, 0)
c = (0, 5)
print(getAngle(a, b, c)) # result 90.0
Example 2--test with random points
from random import randrange, sample
radius = 10
points = []
for i1 in range(10):
for i2 in range(10):
points.append((randrange(-radius, radius+1), randrange(-radius, radius+1)))
x1y1 = sample(points[:50], 10)
x2y2 = sample(points[50:], 10)
x3y3 = [(x+1, y) for x, y in x2y2]
for i in range(len(x1y1)):
a, b, c = x1y1[i], x2y2[i], x3y3[i]
angle = getAngle(a, b, c)
print(i, ": ", a, b, c, '=> ', angle)
Result
0 : (10, -6) (8, -10) (9, -10) => 296.565051177078
1 : (0, -9) (-4, -3) (-3, -3) => 56.309932474020215
2 : (-6, 10) (5, 9) (6, 9) => 185.1944289077348
3 : (0, 1) (-2, 1) (-1, 1) => 0.0
4 : (2, -1) (-3, 7) (-2, 7) => 57.9946167919165
5 : (2, -3) (-10, -8) (-9, -8) => 337.3801350519596
6 : (2, -6) (-10, 5) (-9, 5) => 42.510447078000844
7 : (7, 8) (7, 3) (8, 3) => 270.0
8 : (2, -2) (-4, 4) (-3, 4) => 45.0
9 : (1, -2) (-2, 7) (-1, 7) => 71.56505117707799

Is there any operation on two numpy array to discard zero values?

Suppose we have two numpy array x1 and x2 like below:
x1 = np.array([[0,2,9,1,0]])
x2 = np.array([[7,3,0,6,8]])
Is there any operation like:
x2(operation)x1 = array([[ 0, 3, 0, 6, 0]])
i.e. if x1 or x2 is 0 at any index then make the result array's index value as zero. Otherwise, keep x2 as it is.
Use numpy.where:
x3 = np.where(x1 == 0, x1, x2)
print(x3)
Output:
[[0 3 0 6 0]]
Given that you want to keep x2 but make it zero in the case x1 is zero, just multiply x2 by the boolean of x1.
>>> x2 * x1.astype(bool)
array([[0, 3, 0, 6, 0]])
Note that if x2 is zero, the result is zero as expected.

How to loop through lists from pandas dataframe in a function

Here is my dataframe,
df = pd.DataFrame({'Id': [102,103,104,303,305],'ExpG_Home':[1.8,1.5,1.6,1.8,2.9],
'ExpG_Away':[2.2,1.3,1.2,2.8,0.8],
'HomeG_Time':[[93, 109, 187],[169], [31, 159],[176],[16, 48, 66, 128]],
'AwayG_Time':[[90, 177],[],[],[123,136],[40]]})
First, I need to create an array y, for a given Id number, it takes values from same row (ExpG_Home & ExpG_Away).
y = [1 - (ExpG_Home + ExpG_Away), ExpG_Home, ExpG_Away]
Second, I found this much harder, for the Id used in creating y, the function below takes the corresponding lists from HomeG_Time & AwayG_Time and creates an array. Unfortunately, my function takes one row at a time. I need to do this for a large dataset.
x1 = [1,0,0]
x2 = [0,1,0]
x3 = [0,0,1]
total_timeslot = 200 # number of timeslot per game.
k = 1 # constant
#For Id=102 with ExpG_Home=2.2 and ExpG_Away=1.8
HomeG_Time = [93, 109, 187]
AwayG_Time = [90, 177]
y = np.array([1-(2.2 + 1.8)/k, 2.2/k, 1.8/k])
# output of y = [0.98 , 0.011, 0.009]
def squared_diff(x1, x2, x3, y):
ssd = []
for k in range(total_timeslot):
if k in HomeG_Time:
ssd.append(sum((x2 - y) ** 2))
elif k in AwayG_Time:
ssd.append(sum((x3 - y) ** 2))
else:
ssd.append(sum((x1 - y) ** 2))
return ssd
sum(squared_diff(x1, x2, x3, y))
Out[37]: 7.880400000000012
This output is for the first row only.
Here is the complete snippet given,
>>> import numpy as np
>>> x1 = np.array( [1,0,0] )
>>> x2 = np.array( [0,1,0] )
>>> x3 = np.array( [0,0,1] )
>>> total_timeslot = 200
>>> HomeG_Time = [93, 109, 187]
>>> AwayG_Time = [90, 177]
>>> ExpG_Home=2.2
>>> ExpG_Away=1.8
>>> y = np.array( [1 - (ExpG_Home + ExpG_Away), ExpG_Home, ExpG_Away] )
>>> def squared_diff(x1, x2, x3, y):
... ssd = []
... for k in range(total_timeslot):
... if k in HomeG_Time:
... ssd.append(sum((x2 - y) ** 2))
... elif k in AwayG_Time:
... ssd.append(sum((x3 - y) ** 2))
... else:
... ssd.append(sum((x1 - y) ** 2))
... return ssd
...
>>> sum(squared_diff(x1, x2, x3, y))
4765.599999999989
Assuming this. Calculate y as (N,3) using pandas.DataFrame.apply
>>> y = np.array( df.apply(lambda row: [1 - (row.ExpG_Home + row.ExpG_Away),
... row.ExpG_Home, row.ExpG_Away ],
... axis=1).tolist() )
>>> y.shape
(5, 3)
Now calcualte squared error for a given x
>>> def squared_diff(x, y):
... return np.sum( np.square(x - y), axis=1)
In your case, if error2 is squared_diff(x2,y) you are adding this the number of occuerences of HomeG_Time
>>> n3 = df.AwayG_Time.apply(len)
>>> n2 = df.HomeG_Time.apply(len)
>>> n1 = 200 - (n2 + n3)
The final sum of squared error is (as per your calculation)
>>> squared_diff(x1, y) * n1 + squared_diff(x2, y) * n2 + squared_diff(x3, y) * n3
0 4766.4
1 2349.4
2 2354.4
3 6411.6
4 4496.2
dtype: float64
>>>
try this,
import pandas as pd
import numpy as np
df = pd.DataFrame({'Id': [102,103,104,303,305],'ExpG_Home':[1.8,1.5,1.6,1.8,2.9],
'ExpG_Away':[2.2,1.3,1.2,2.8,0.8],
'HomeG_Time':[[93, 109, 187],[169], [31, 159],[176],[16, 48, 66, 128]],
'AwayG_Time':[[90, 177],[],[],[123,136],[40]]})
x1 = [1,0,0]
x2 = [0,1,0]
x3 = [0,0,1]
k=1
total_timeslot = 200 # number of timeslot per game.
def squared_diff(x1, x2, x3,AwayG_Time,HomeG_Time, y):
ssd = []
for k in range(total_timeslot):
if k in HomeG_Time:
ssd.append(sum((x2 - y) ** 2))
elif k in AwayG_Time:
ssd.append(sum((x3 - y) ** 2))
else:
ssd.append(sum((x1 - y) ** 2))
return ssd
s=pd.DataFrame( pd.concat([df,1-(df['ExpG_Home']+df['ExpG_Away'])/k,df['ExpG_Home']/k,df['ExpG_Away']/k],axis=1).values)
df['res']=s.apply(lambda x: sum(squared_diff(x1,x2,x3,x[0],x[3],np.array([x[5],x[6],x[7]]))),axis=1)
del s
print df
Output:
AwayG_Time ExpG_Away ExpG_Home HomeG_Time Id res
0 [90, 177] 2.2 1.8 [93, 109, 187] 102 4766.4
1 [] 1.3 1.5 [169] 103 2349.4
2 [] 1.2 1.6 [31, 159] 104 2354.4
3 [123, 136] 2.8 1.8 [176] 303 6411.6
4 [40] 0.8 2.9 [16, 48, 66, 128] 305 4496.2
def squared_diff(row):
y = np.array([1 - (row.ExpG_Home + row.ExpG_Away), row.ExpG_Home, row.ExpG_Away])
HomeG_Time = row.HomeG_Time
AwayG_Time = row.AwayG_Time
x1 = np.array([1, 0, 0])
x2 = np.array([0, 1, 0])
x3 = np.array([0, 0, 1])
total_timeslot = 200
ssd = []
for k in range(total_timeslot):
if k in HomeG_Time:
ssd.append(sum((x2 - y) ** 2))
elif k in AwayG_Time:
ssd.append(sum((x3 - y) ** 2))
else:
ssd.append(sum((x1 - y) ** 2))
return sum(ssd)
df.apply(squared_diff, axis=1)
Out[]:
0 4766.4
1 2349.4
2 2354.4
3 6411.6
4 4496.2

iterating through multiple equations [closed]

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I have a problem simplified into the following:
Xn+1 = Xn + Yn
Yn+1= Yn + Zn
Zn+1= Zn+ Xn
I know the values of X0,Y0,Z0 to be equal to 1.
I want to tell python to find the values of X1,Y1,Z1 and then X2,Y2,Z2,...etc. Can anyone help me with that? I think I have to use a nested loop but I am not sure exactly how to go about it. Thanks!
Are we talking about something as simple as:
x, y, z = 1, 1, 1
for i in range(10):
print("X{i} = {x}, Y{i} = {y}, Z{i} = {z}".format(**locals()))
x, y, z = x + y, y + z, z + x
which doesn't seem right as the output is so uninteresting:
X0 = 1, Y0 = 1, Z0 = 1
X1 = 2, Y1 = 2, Z1 = 2
X2 = 4, Y2 = 4, Z2 = 4
X3 = 8, Y3 = 8, Z3 = 8
X4 = 16, Y4 = 16, Z4 = 16
X5 = 32, Y5 = 32, Z5 = 32
X6 = 64, Y6 = 64, Z6 = 64
X7 = 128, Y7 = 128, Z7 = 128
X8 = 256, Y8 = 256, Z8 = 256
X9 = 512, Y9 = 512, Z9 = 512
Below is the sample function to achieve it:
def solve_equation(n):
X = {0: 1}
Y = {0: 1}
Z = {0: 1}
for i in range(n):
print 'For n: ', i+1
X[i+1] = X[i] + Y[i]
Y[i+1] = Y[i] + Z[i]
Z[i+1] = Z[i] + X[i]
print 'X = ', X[i+1], ' Y = ', Y[i+1], ' Z = ', Z[i+1]
Sample run:
>>> solve_equation(3)
For n: 1
X = 2 Y = 2 Z = 2
For n: 2
X = 4 Y = 4 Z = 4
For n: 3
X = 8 Y = 8 Z = 8
You can use recursive functions. For a faster and better code you can consider using yield
def Cvalue(c,xyz , n):
if n == 0 :
res = c
else :
if xyz == 1: res = Cvalue(c,1, n-1) + Cvalue(c,2, n-1)
elif xyz == 2: res = Cvalue(c,2, n-1) + Cvalue(c,3, n-1)
elif xyz == 3: res = Cvalue(c,3, n-1) + Cvalue(c,1, n-1)
else: print("Error\n")
return res
def XYZvalues(x0, y0, z0, n):
x = Cvalue(x0,1, n)
y = Cvalue(y0,2, n)
z = Cvalue(z0,3, n)
return (x, y , z)
print(XYZvalues(1,1,1, 3))

Linear programming, unexpected solution with equality constraint

I'm trying to figure out what is wrong with my implementation, I expect the result to be [5, 10], I don't understand how it gets [7.5, 7.5], x1 should be half of x2.
from scipy.optimize import linprog
import numpy as np
c = [-1, -1]
A_eq = np.array([
[1, 0.5],
[1, -0.5],
])
b_eq = [15, 0]
x0_bounds = (0, None)
x1_bounds = (0, None)
res = linprog(
c,
A_eq=A_eq.transpose(),
b_eq=b_eq,
bounds=(x0_bounds, x1_bounds),
options={"disp": True})
print res.x
# =>
# Optimization terminated successfully.
# Current function value: -15.000000
# Iterations: 2
# [ 7.5 7.5]
Update from the author:
As it was said matrix transposition is not needed here.
The problem was in the matrix itself, in order to get desired result, which is [5, 10], it has to be:
A_eq = np.array([
[1, 1],
[1, -0.5],
])
Per the scipy linprog docs:
Minimize: c^T * x
Subject to:
A_ub * x <= b_ub
A_eq * x == b_eq
So, you are now solving the following equations:
Minimize -x1 -x2
Subject to,*
x1 + x2 = 15 (i)
0.5 * x1 - 0.5 * x2 = 0 (ii)
Now, (ii) implies x1 = x2 (so your desired solution is infeasable), and then (i) fixes x1 = x2 = 7.5. So, the solution returned by linprog() is indeed correct. Since you are expecting a different result, maybe you should look into the way you translated your problem into code, as I think that's where you will find both the issue and the solution.
*) Since you are taking the transpose.
Your problem is:
x1 + x2 == 15
0.5 * x1 - 0.5 * x2 == 0
minimize -x1 -x2
So obviously you have x1 == x2 (second constraint), and thus x1 = x2 = 7.5 (first constraint).
Looking at your question, you probably don't want to transpose A:
res = linprog(
c,
A_eq=A_eq,
b_eq=b_eq,
bounds=(x0_bounds, x1_bounds),
options={"disp": True}
)
Why gives you the problem:
x1 + 0.5 * x2 == 15
x1 - 0.5 * x2 == 0
minimize -x1 -x2
And you get x1 = 7.5 and x2 = 15 (the only possible values).

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