I have a numpy array which has only a few non-zero entries which can be either positive or negative. E.g. something like this:
myArray = np.array([[ 0. , 0. , 0. ],
[ 0.32, -6.79, 0. ],
[ 0. , 0. , 0. ],
[ 0. , 1.5 , 0. ],
[ 0. , 0. , -1.71]])
In the end, I would like to receive a list where each entry of this list corresponds to a row of myArray and is a cumulative product of function outputs which depend on the entries of the respective row of myArray and another list (in the example below it is called l).
The individual terms depend on the sign of the myArray entry: When it is positive, I apply "funPos", when it is negative, I apply "funNeg" and if the entry is 0, the term will be 1. So in the example array from above it would be:
output = [1*1*1 ,
funPos(0.32, l[0])*funNeg(-6.79,l[1])*1,
1*1*1,
1*funPos(1.5, l[1])*1,
1*1*funNeg(-1.71, l[2])]
I implemented this as shown below and it gives me the desired output (note: that is just a highly simplified toy example; the actual matrices are far bigger and the functions more complicated). I go through each row of the array, if the sum of the row is 0, I don't have to do any calculations and the output is just 1. If it is not equal 0, I go through this row, check the sign of each value and apply the appropriate function.
import numpy as np
def doCalcOnArray(Array1, myList):
output = np.ones(Array1.shape[0]) #initialize output
for indRow,row in enumerate(Array1):
if sum(row) != 0: #only then calculations are needed
tempProd = 1. #initialize the product that corresponds to the row
for indCol, valCol in enumerate(row):
if valCol > 0:
tempVal = funPos(valCol, myList[indCol])
elif valCol < 0:
tempVal = funNeg(valCol, myList[indCol])
elif valCol == 0:
tempVal = 1
tempProd = tempProd*tempVal
output[indRow] = tempProd
return output
def funPos(val1,val2):
return val1*val2
def funNeg(val1,val2):
return val1*(val2+1)
myArray = np.array([[ 0. , 0. , 0. ],
[ 0.32, -6.79, 0. ],
[ 0. , 0. , 0. ],
[ 0. , 1.5 , 0. ],
[ 0. , 0. , -1.71]])
l = [1.1, 2., 3.4]
op = doCalcOnArray(myArray,l)
print op
The output is
[ 1. -7.17024 1. 3. -7.524 ]
which is the desired one.
My question is whether there is a more efficient way for doing that since that is quite "expensive" for large arrays.
EDIT:
I accepted gabhijit's answer because the pure numpy solution he came up with seems to be the fastest one for the arrays I am dealing with. Please note, that there is also a nice working solution from RaJa that requires panda and also the solution from dave works fine which can serve as a nice example on how to use generators and numpy's "apply_along_axis".
Here's what I have tried - using reduce, map. I am not sure how fast this is - but is this what you are trying to do?
Edit 4: Simplest and most readable - Make l a numpy array and then greatly simplifies where.
import numpy as np
import time
l = np.array([1.0, 2.0, 3.0])
def posFunc(x,y):
return x*y
def negFunc(x,y):
return x*(y+1)
def myFunc(x, y):
if x > 0:
return posFunc(x, y)
if x < 0:
return negFunc(x, y)
else:
return 1.0
myArray = np.array([
[ 0.,0.,0.],
[ 0.32, -6.79, 0.],
[ 0.,0.,0.],
[ 0.,1.5,0.],
[ 0.,0., -1.71]])
t1 = time.time()
a = np.array([reduce(lambda x, (y,z): x*myFunc(z,l[y]), enumerate(x), 1) for x in myArray])
t2 = time.time()
print (t2-t1)*1000000
print a
Basically let's just look at last line it says cumulatively multiply things in enumerate(xx), starting with 1 (last parameter to reduce). myFunc simply takes the element in myArray(row) and element # index row in l and multiplies them as needed.
My output is not same as yours - so I am not sure whether this is exactly what you want, but may be you can follow the logic.
Also I am not so sure how fast this will be for huge arrays.
edit: Following is a 'pure numpy way' to do this.
my = myArray # just for brevity
t1 = time.time()
# First set the positive and negative values
# complicated - [my.itemset((x,y), posFunc(my.item(x,y), l[y])) for (x,y) in zip(*np.where(my > 0))]
# changed to
my = np.where(my > 0, my*l, my)
# complicated - [my.itemset((x,y), negFunc(my.item(x,y), l[y])) for (x,y) in zip(*np.where(my < 0))]
# changed to
my = np.where(my < 0, my*(l+1), my)
# print my - commented out to time it.
# Now set the zeroes to 1.0s
my = np.where(my == 0.0, 1.0, my)
# print my - commented out to time it
a = np.prod(my, axis=1)
t2 = time.time()
print (t2-t1)*1000000
print a
Let me try to explain the zip(*np.where(my != 0)) part as best as I can. np.where simply returns two numpy arrays first array is an index of row, second array is an index of column that matches the condition (my != 0) in this case. We take a tuple of those indices and then use array.itemset and array.item, thankfully, column index is available for free to us, so we can just take the element # that index in the list l. This should be faster than previous (and by orders of magnitude readable!!). Need to timeit to find out whether it indeed is.
Edit 2: Don't have to call separately for positive and negative can be done with one call np.where(my != 0).
So, let's see if I understand your question.
You want to map elements of your matrix to a new matrix such that:
0 maps to 1
x>0 maps to funPos(x)
x<0 maps to funNeg(x)
You want to calculate the product of all elements in the rows this new matrix.
So, here's how I would go about doing it:
1:
def myFun(a):
if a==0:
return 1
if a>0:
return funPos(a)
if a<0:
return funNeg(a)
newFun = np.vectorize(myFun)
newArray = newFun(myArray)
And for 2:
np.prod(newArray, axis = 1)
Edit: To pass the index to funPos, funNeg, you can probably do something like this:
# Python 2.7
r,c = myArray.shape
ctr = -1 # I don't understand why this should be -1 instead of 0
def myFun(a):
global ctr
global c
ind = ctr % c
ctr += 1
if a==0:
return 1
if a>0:
return funPos(a,l[ind])
if a<0:
return funNeg(a,l[ind])
I think this numpy function would be helpful to you
numpy.apply_along_axis
Here is one implementation. Also I would warn against checking if the sum of the array is 0. Comparing floats to 0 can give unexpected behavior due to machine accuracy constraints. Also if you have -5 and 5 the sum is zero and I'm not sure thats what you want. I used numpy's any() function to see if anything was nonzero. For simplicity I also pulled your list (my_list) into global scope.
import numpy as np
my_list = 1.1, 2., 3.4
def func_pos(val1, val2):
return val1 * val2
def func_neg(val1, val2):
return val1 *(val2 + 1)
def my_generator(row):
for i, a in enumerate(row):
if a > 0:
yield func_pos(a, my_list[i])
elif a < 0:
yield func_neg(a, my_list[i])
else:
yield 1
def reduce_row(row):
if not row.any():
return 1.0
else:
return np.prod(np.fromiter(my_generator(row), dtype=float))
def main():
myArray = np.array([
[ 0. , 0. , 0. ],
[ 0.32, -6.79, 0. ],
[ 0. , 0. , 0. ],
[ 0. , 1.5 , 0. ],
[ 0. , 0. , -1.71]])
return np.apply_along_axis(reduce_row, axis=1, arr=myArray)
There are probably faster implmentations, I think apply_along_axis is really just a loop under the covers.
I didn't test, but I bet this is faster than what you started with, and should be more memory efficient.
I've tried your example with the masking function of numpy arrays. However, I couldn't find a solution to replace the values in your array by funPos or funNeg.
So my suggestion would be to try this using pandas instead as it conserves indices while masking.
See my example:
import numpy as np
import pandas as pd
def funPos(a, b):
return a * b
def funNeg(a, b):
return a * (b + 1)
myPosFunc = np.vectorize(funPos) #vectorized form of funPos
myNegFunc = np.vectorize(funNeg) #vectorized form of funNeg
#Input
I = [1.0, 2.0, 3.0]
x = pd.DataFrame([
[ 0.,0.,0.],
[ 0.32, -6.79, 0.],
[ 0.,0.,0.],
[ 0.,1.5,0.],
[ 0.,0., -1.71]])
b = pd.DataFrame(myPosFunc(x[x>0], I)) #calculate all positive values
c = pd.DataFrame(myNegFunc(x[x<0], I)) #calculate all negative values
b = b.combineMult(c) #put values of c in b
b = b.fillna(1) #replace all missing values that were '0' in the raw array
y = b.product() #multiply all elements in one row
#Output
print ('final result')
print (y)
print (y.tolist())
Related
there is such question, it seems elementary, but for some reason at me it does not turn out. I have the 2 d list, I need to add a line to a line so that the sum on the first number was not less than 5 (it is possible to sum up only the next lines). For example
array([[ 0. , 3.817549],
[ 3. , 21.275711],
[ 11. , 59.286198],
[ 47. , 110.136649],
[132. , 153.451585],
[263. , 171.041259],
[301. , 158.872652],
[198. , 126.488376],
[ 50. , 200.63002 ]])
and I need outpuut like this:
array([[ 14. , 84.3794...],
[ 47. , 110.136649],
[132. , 153.451585],
[263. , 171.041259],
[301. , 158.872652],
[198. , 126.488376],
[ 50. , 200.63002 ]])
Try:
arr = np.array([[ 0. , 3.817549],
[ 3. , 21.275711],
[ 11. , 59.286198],
[ 47. , 110.136649],
[132. , 153.451585],
[263. , 171.041259],
[301. , 158.872652],
[198. , 126.488376],
[ 50. , 200.63002 ]])
for i in range(len(arr)):
if arr[i, 0] >= 5.0:
arr = arr[i:, :]
break
else:
arr[i + 1, :] += arr[i, :]
I'm not entirely sure if I understand the question, but I will try to help.
I would approach this problem with the following steps:
Create a separate 2D list to store your final output and a two-value accumulator list to temporary store values. Initialize the accumulator to the values at index [0][] of your input array
Iterate over the values in the original 2D list
For each item:
a. if accumulator[0] >= 5, add the accumulated values to your output and then set the accumulator to the values at current_index + 1
b. otherwise, add the values at current_index + 1 to your accumulator
The following code was able to take your input and reproduce the exact ouput you wanted:
# Assuming current_vals is the input list...
final_vals = []
accumulator = [current_vals[0][0], current_vals[0][1]]
for sublist_index in range(1, len(current_vals) - 1):
if accumulator[0] >= 5:
final_vals.append([accumulator[0], accumulator[1]])
accumulator[0] = current_vals[sublist_index][0]
accumulator[1] = current_vals[sublist_index][1]
else:
accumulator[0] += current_vals[sublist_index][0]
accumulator[1] += current_vals[sublist_index][1]
return final_vals
I have a numpy array:
array([[ 0.68597575, 0.05544651, -1. ],
[ 0.33494648, 0.46368367, 1. ],
[ 0.42486765, 0.89427025, 1. ],
[ 0.62408611, 0.64633939, 1. ],
[ 0.37087957, 0.53077302, -1. ],
[ 0.21664159, 0.10786084, -1. ],
[ 0.13003626, 0.18425347, -1. ]])
I want the rows having last values -1 to be multiplied by -1 and also replaced in the actual matrix.
I tried this:
def transform(data):
for row in data:
if row[-1] == -1:
row = row * -1
but I know there would be something simpler than this.
You can avoid the for loop by doing:
data[data[:, -1] == -1] *= -1
i prefer to do this in two steps for two reasons: (i) easier to understand the code; and (ii) often the boolean index created in the first step can be reused elsewhere in the data pipeline
create the Boolean index that selects the rows:
idx = M[:,-1] == -1
do the transform on the indexed data:
M[idx,] *= -1
So here is the thing.
I have a list of lists and some of the list are empty... but if it is not empty.. all the list are of fix length.. the length which I dont know..
For example
for feature in features:
print len(feature)
This will print either 0 or length k.
I am trying to write a function
def generate_matrix(features):
# return matrix
Which returns a numpy matrix.. with empty rows replaces with zero vector.
Is there a way to do this efficiently?
I mean... I don't want to loop thru to find the shape of matrix and then again loop thru to generate row (with either np.array(feature) or np.zeros(shape)..
Edit: I didn't realize that all of the non-empty features were the same length. If that is the case then you can just use the length of the first non-zero one. I added a function that does that.
f0 = [0,1,2]
f1 = []
f2 = [4,5,6]
features = [f0, f1, f2]
def get_nonempty_len(features):
"""
returns the length of the first non-empty element
of features.
"""
for f in features:
if len(f) > 0:
return len(f)
return 0
def generate_matrix(features):
rows = len(features)
cols = get_nonempty_len(features)
m = np.zeros((rows, cols))
for i, f in enumerate(features):
m[i,:len(f)]=f
return m
print(generate_matrix(features))
Output looks like:
[[ 0. 1. 2.]
[ 0. 0. 0.]
[ 4. 5. 6.]]
I have the following array:
array([[ 0. , -1.22474487, 1.40182605],
[ 1.22474487, 0. , -0.53916387],
[-1.22474487, 1.22474487, -0.86266219]])
What is the best way to parse each of its elements and assign a string depending on the value? For example: if value < 0 then set "LOW" else set "HIGH"?
If a is your array use
import numpy as np
np.where(a<0,'LOW','HIGH')
Edit:
When you have 3 choices you can do something like
b = np.where(a < 0.,'LOW','HIGH').astype('S7')
c = np.where((-1. < a) & (a < 1.), 'MIDDLE',b)
I'm trying to vectorize a simple function in numpy and getting inconsistent behavior. I expect my code to return 0 for values < 0.5 and the unchanged value otherwise. Strangely, different runs of the script from the command line yield varying results: sometimes it works correctly, and sometimes I get all 0's. It doesn't matter which of the three lines I use for the case when d <= T. It does seem to be correlated with whether the first value to be returned is 0. Any ideas? Thanks.
import numpy as np
def my_func(d, T=0.5):
if d > T: return d
#if d <= T: return 0
else: return 0
#return 0
N = 4
A = np.random.uniform(size=N**2)
A.shape = (N,N)
print A
f = np.vectorize(my_func)
print f(A)
$ python x.py
[[ 0.86913815 0.96833127 0.54539153 0.46184594]
[ 0.46550903 0.24645558 0.26988519 0.0959257 ]
[ 0.73356391 0.69363161 0.57222389 0.98214089]
[ 0.15789303 0.06803493 0.01601389 0.04735725]]
[[ 0.86913815 0.96833127 0.54539153 0. ]
[ 0. 0. 0. 0. ]
[ 0.73356391 0.69363161 0.57222389 0.98214089]
[ 0. 0. 0. 0. ]]
$ python x.py
[[ 0.37127366 0.77935622 0.74392301 0.92626644]
[ 0.61639086 0.32584431 0.12345342 0.17392298]
[ 0.03679475 0.00536863 0.60936931 0.12761859]
[ 0.49091897 0.21261635 0.37063752 0.23578082]]
[[0 0 0 0]
[0 0 0 0]
[0 0 0 0]
[0 0 0 0]]
If this really is the problem you want to solve, then there's a much better solution:
A[A<=0.5] = 0.0
The problem with your code, however, is that if the condition passes, you are returning the integer 0, not the float 0.0. From the documentation:
The data type of the output of vectorized is determined by calling the function with the first element of the input. This can be avoided by specifying the otypes argument.
So when the very first entry is <0.5, it tries to create an integer, not float, array.
You should change return 0 to
return 0.0
Alternately, if you don't want to touch my_func, you can use
f = np.vectorize(my_func, otypes=[np.float])