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So this is my line of code so far,
def Adder (i,j,k):
if i<=j:
for x in range (i, j+1):
print(x**k)
else:
print (0)
What it's supposed to do is get inputs (i,j,k) so that each number between [i,j] is multiplied the power of k. For example, Adder(3,6,2) would be 3^2 + 4^2 + 5^2 + 6^2 and eventually output 86. I know how to get the function to output the list of numbers between i and j to the power of K but I don't know how to make it so that the function sums that output. So in the case of my given example, my output would be 9, 16, 25, 36.
Is it possible to make it so that under my if conditional I can generate an output that adds up the numbers in the range after they've been taken to the power of K?
If anyone can give me some advice I would really appreciate it! First week of any coding ever and I don't quite know how to ask this question so sorry for vagueness!
Question now Answered, thanks to everyone who responded so quickly!
You could use built-in function sum()
def adder(i,j,k):
if i <= j:
print(sum(x**k for x in range(i,j+1)))
else:
print(0)
The documentation is here
I'm not sure if this is what you want but
if i<=j:
sum = 0
for x in range (i, j+1):
sum = sum + x**k #sum += x**k for simplicity
this will give you the sum of the powers
Looking at a few of the answers posted, they do a good job of giving you pythonic code for your solution, I thought I could answer your specific questions:
How can I get my function to add together its output?
A perhaps reasonable way is to iteratively and incrementally perform your calculations and store your interim solutions in a variable. See if you can visualize this:
Let's say (i,j,k) = (3,7,2)
We want the output to be: 135 (i.e., the result of the calculation 3^2 + 4^2 + 5^2 + 6^2 + 7^2)
Use a variable, call it result and initialize it to be zero.
As your for loop kicks off with x = 3, perform x^2 and add it to result. So result now stores the interim result 9. Now the loop moves on to x = 4. Same as the first iteration, perform x^2 and add it to result. Now result is 25. You can now imagine that result, by the time x = 7, contains the answer to the calculation 3^2+4^2+5^2+6^2. Let the loop finish, and you will find that 7^2 is also added to result.
Once loop is finished, print result to get the summed up answer.
A thing to note:
Consider where in your code you need to set and initialize the _result_ variable.
If anyone can give me some advice I would really appreciate it! First week of any coding ever and I don't quite know how to ask this question so sorry for vagueness!
Perhaps a bit advanced for you, but helpful to be made aware I think:
Alright, let's get some nuance added to this discussion. Since this is your first week, I wanted to jot down some things I had to learn which have helped greatly.
Iterative and Recursive Algorithms
First off, identify that the solution is an iterative type of algorithm. Where the actual calculation is the same, but is executed over different cumulative data.
In this example, if we were to represent the calculation as an operation called ADDER(i,j,k), then:
ADDER(3,7,2) = ADDER(3,6,2)+ 7^2
ADDER(3,6,2) = ADDER(3,5,2) + 6^2
ADDER(3,5,2) = ADDER(3,4,2) + 5^2
ADDER(3,4,2) = ADDER(3,3,2) + 4^2
ADDER(3,3,2) = 0 + 3^2
Problems like these can be solved iteratively (like using a loop, be it while or for) or recursively (where a function calls itself using a subset of the data). In your example, you can envision a function calling itself and each time it is called it does the following:
calculates the square of j and
adds it to the value returned from calling itself with j decremented
by 1 until
j < i, at which point it returns 0
Once the limiting condition (Point 3) is reached, a bunch of additions that were queued up along the way are triggered.
Learn to Speak The Language before using Idioms
I may get down-voted for this, but you will encounter a lot of advice displaying pythonic idioms for standard solutions. The idiomatic solution for your example would be as follows:
def adder(i,j,k):
return sum(x**k for x in range(i,j+1)) if i<=j else 0
But for a beginner this obscures a lot of the "science". It is far more rewarding to tread the simpler path as a beginner. Once you develop your own basic understanding of devising and implementing algorithms in python, then the idioms will make sense.
Just so you can lean into the above idiom, here's an explanation of what it does:
It calls the standard library function called sum which can operate over a list as well as an iterator. We feed it as argument a generator expression which does the job of the iterator by "drip feeding" the sum function with x^k values as it iterates over the range (1, j+1). In cases when N (which is j-i) is arbitrarily large, using a standard list can result in huge memory overhead and performance disadvantages. Using a generator expression allows us to avoid these issues, as iterators (which is what generator expressions create) will overwrite the same piece of memory with the new value and only generate the next value when needed.
Of course it only does all this if i <= j else it will return 0.
Lastly, make mistakes and ask questions. The community is great and very helpful
Well, do not use print. It is easy to modify your function like this,
if i<=j:
s = 0
for x in range (i, j+1):
s += x**k
return s # print(s) if you really want to
else:
return 0
Usually functions do not print anything. Instead they return values for their caller to either print or further process. For example, someone may want to find the value of Adder(3, 6, 2)+1, but if you return nothing, they have no way to do this, since the result is not passed to the program. A side note, do not capitalize functions. Those are for classes.
I know you can probably do a limit of a mathematical operation, say the limit of n + 1 as n approaches infinity, but can I do the limit of a function? For instances the limit of dividing to Fibonacci numbers as their index (and value) gets greater, approaching infinity? For example
lim(func, start, approach)
I have looked at sympy, and it is either not possible or I don't know how to pass a symbol argument as an integer. Eg:
iters = Symbol("iters")
print limit(main(iters),iters,0)
I didn't need to make my integer a symbol.
The code above works.
I've got a pandas series of data which is a curve.
I want to round it in such a way as to make it 'stepped'. Furthermore, I want the steps to be roughly within 10% of the present value. (Another way of putting this is I want the steps to increase in increments of 10%, i.e. geometrically).
I've written something that's iterative and slow:
def chunk_trades(A):
try:
last = A[0]
except:
print(A)
raise
new = []
for x in A.iteritems():
if not last or np.abs((x[1]-last)/last) > 0.1:
new.append(x[1])
last = x[1]
else:
new.append(last)
s = pd.Series(new, index=A.index)
return s
I don't want to use this code.
I'm trying to find a faster, pythonic way of doing this. I've tried using numpy.digitize() but I don't think that's what I'm looking for. Any ideas for how best to approach this?
OK, I think the solution should be something like:
np.exp(np.around(np.log(np.abs(j)), decimals=1)) * np.sign(j)
Map to logarithmic space, do the rounding, transform back.
I'm trying to use Python and Numpy/Scipy to implement an image processing algorithm. The profiler tells me a lot of time is being spent in the following function (called often), which tells me the sum of square differences between two images
def ssd(A,B):
s = 0
for i in range(3):
s += sum(pow(A[:,:,i] - B[:,:,i],2))
return s
How can I speed this up? Thanks.
Just
s = numpy.sum((A[:,:,0:3]-B[:,:,0:3])**2)
(which I expect is likely just sum((A-B)**2) if the shape is always (,,3))
You can also use the sum method: ((A-B)**2).sum()
Right?
Just to mention that one can also use np.dot:
def ssd(A,B):
dif = A.ravel() - B.ravel()
return np.dot( dif, dif )
This might be a bit faster and possibly more accurate than alternatives using np.sum and **2, but doesn't work if you want to compute ssd along a specified axis. In that case, there might be a magical subscript formula using np.einsum.
I am confused why you are taking i in range(3). Is that supposed to be the whole array, or just part?
Overall, you can replace most of this with operations defined in numpy:
def ssd(A,B):
squares = (A[:,:,:3] - B[:,:,:3]) ** 2
return numpy.sum(squares)
This way you can do one operation instead of three and using numpy.sum may be able to optimize the addition better than the builtin sum.
Further to Ritsaert Hornstra's answer that got 2 negative marks (admittedly I didn't see it in it's original form...)
This is actually true.
For a large number of iterations it can often take twice as long to use the '**' operator or the pow(x,y) method as to just manually multiply the pairs together. If necessary use the math.fabs() method if it's throwing out NaN's (which it sometimes does especially when using int16s etc.), and it still only takes approximately half the time of the two functions given.
Not that important to the original question I know, but definitely worth knowing.
I do not know if the pow() function with power 2 will be fast. Try:
def ssd(A,B):
s = 0
for i in range(3):
s += sum((A[:,:,i] - B[:,:,i])*(A[:,:,i] - B[:,:,I]))
return s
You can try this one:
dist_sq = np.sum((A[:, np.newaxis, :] - B[np.newaxis, :, :]) ** 2, axis=-1)
More details can be found here (the 'k-Nearest Neighbors' example):
https://jakevdp.github.io/PythonDataScienceHandbook/02.08-sorting.html
In Ruby language you can achieve this in this way
def diff_btw_sum_of_squars_and_squar_of_sum(from=1,to=100) # use default values from 1..100.
((1..100).inject(:+)**2) -(1..100).map {|num| num ** 2}.inject(:+)
end
diff_btw_sum_of_squars_and_squar_of_sum #call for above method
So in Ruby there is a trick to specify infinity:
1.0/0
=> Infinity
I believe in Python you can do something like this
float('inf')
These are just examples though, I'm sure most languages have infinity in some capacity. When would you actually use this construct in the real world? Why would using it in a range be better than just using a boolean expression? For instance
(0..1.0/0).include?(number) == (number >= 0) # True for all values of number
=> true
To summarize, what I'm looking for is a real world reason to use Infinity.
EDIT: I'm looking for real world code. It's all well and good to say this is when you "could" use it, when have people actually used it.
Dijkstra's Algorithm typically assigns infinity as the initial edge weights in a graph. This doesn't have to be "infinity", just some arbitrarily constant but in java I typically use Double.Infinity. I assume ruby could be used similarly.
Off the top of the head, it can be useful as an initial value when searching for a minimum value.
For example:
min = float('inf')
for x in somelist:
if x<min:
min=x
Which I prefer to setting min initially to the first value of somelist
Of course, in Python, you should just use the min() built-in function in most cases.
There seems to be an implied "Why does this functionality even exist?" in your question. And the reason is that Ruby and Python are just giving access to the full range of values that one can specify in floating point form as specified by IEEE.
This page seems to describe it well:
http://steve.hollasch.net/cgindex/coding/ieeefloat.html
As a result, you can also have NaN (Not-a-number) values and -0.0, while you may not immediately have real-world uses for those either.
In some physics calculations you can normalize irregularities (ie, infinite numbers) of the same order with each other, canceling them both and allowing a approximate result to come through.
When you deal with limits, calculations like (infinity / infinity) -> approaching a finite a number could be achieved. It's useful for the language to have the ability to overwrite the regular divide-by-zero error.
Use Infinity and -Infinity when implementing a mathematical algorithm calls for it.
In Ruby, Infinity and -Infinity have nice comparative properties so that -Infinity < x < Infinity for any real number x. For example, Math.log(0) returns -Infinity, extending to 0 the property that x > y implies that Math.log(x) > Math.log(y). Also, Infinity * x is Infinity if x > 0, -Infinity if x < 0, and 'NaN' (not a number; that is, undefined) if x is 0.
For example, I use the following bit of code in part of the calculation of some log likelihood ratios. I explicitly reference -Infinity to define a value even if k is 0 or n AND x is 0 or 1.
Infinity = 1.0/0.0
def Similarity.log_l(k, n, x)
unless x == 0 or x == 1
k * Math.log(x.to_f) + (n-k) * Math.log(1.0-x)
end
-Infinity
end
end
Alpha-beta pruning
I use it to specify the mass and inertia of a static object in physics simulations. Static objects are essentially unaffected by gravity and other simulation forces.
In Ruby infinity can be used to implement lazy lists. Say i want N numbers starting at 200 which get successively larger by 100 units each time:
Inf = 1.0 / 0.0
(200..Inf).step(100).take(N)
More info here: http://banisterfiend.wordpress.com/2009/10/02/wtf-infinite-ranges-in-ruby/
I've used it for cases where you want to define ranges of preferences / allowed.
For example in 37signals apps you have like a limit to project number
Infinity = 1 / 0.0
FREE = 0..1
BASIC = 0..5
PREMIUM = 0..Infinity
then you can do checks like
if PREMIUM.include? current_user.projects.count
# do something
end
I used it for representing camera focus distance and to my surprise in Python:
>>> float("inf") is float("inf")
False
>>> float("inf") == float("inf")
True
I wonder why is that.
I've used it in the minimax algorithm. When I'm generating new moves, if the min player wins on that node then the value of the node is -∞. Conversely, if the max player wins then the value of that node is +∞.
Also, if you're generating nodes/game states and then trying out several heuristics you can set all the node values to -∞/+∞ which ever makes sense and then when you're running a heuristic its easy to set the node value:
node_val = -∞
node_val = max(heuristic1(node), node_val)
node_val = max(heuristic2(node), node_val)
node_val = max(heuristic2(node), node_val)
I've used it in a DSL similar to Rails' has_one and has_many:
has 0..1 :author
has 0..INFINITY :tags
This makes it easy to express concepts like Kleene star and plus in your DSL.
I use it when I have a Range object where one or both ends need to be open
I've used symbolic values for positive and negative infinity in dealing with range comparisons to eliminate corner cases that would otherwise require special handling:
Given two ranges A=[a,b) and C=[c,d) do they intersect, is one greater than the other, or does one contain the other?
A > C iff a >= d
A < C iff b <= c
etc...
If you have values for positive and negative infinity that respectively compare greater than and less than all other values, you don't need to do any special handling for open-ended ranges. Since floats and doubles already implement these values, you might as well use them instead of trying to find the largest/smallest values on your platform. With integers, it's more difficult to use "infinity" since it's not supported by hardware.
I ran across this because I'm looking for an "infinite" value to set for a maximum, if a given value doesn't exist, in an attempt to create a binary tree. (Because I'm selecting based on a range of values, and not just a single value, I quickly realized that even a hash won't work in my situation.)
Since I expect all numbers involved to be positive, the minimum is easy: 0. Since I don't know what to expect for a maximum, though, I would like the upper bound to be Infinity of some sort. This way, I won't have to figure out what "maximum" I should compare things to.
Since this is a project I'm working on at work, it's technically a "Real world problem". It may be kindof rare, but like a lot of abstractions, it's convenient when you need it!
Also, to those who say that this (and other examples) are contrived, I would point out that all abstractions are somewhat contrived; that doesn't mean they are useful when you contrive them.
When working in a problem domain where trig is used (especially tangent) infinity is an answer that can come up. Trig ends up being used heavily in graphics applications, games, and geospatial applications, plus the obvious math applications.
I'm sure there are other ways to do this, but you could use Infinity to check for reasonable inputs in a String-to-Float conversion. In Java, at least, the Float.isNaN() static method will return false for numbers with infinite magnitude, indicating they are valid numbers, even though your program might want to classify them as invalid. Checking against the Float.POSITIVE_INFINITY and Float.NEGATIVE_INFINITY constants solves that problem. For example:
// Some sample values to test our code with
String stringValues[] = {
"-999999999999999999999999999999999999999999999",
"12345",
"999999999999999999999999999999999999999999999"
};
// Loop through each string representation
for (String stringValue : stringValues) {
// Convert the string representation to a Float representation
Float floatValue = Float.parseFloat(stringValue);
System.out.println("String representation: " + stringValue);
System.out.println("Result of isNaN: " + floatValue.isNaN());
// Check the result for positive infinity, negative infinity, and
// "normal" float numbers (within the defined range for Float values).
if (floatValue == Float.POSITIVE_INFINITY) {
System.out.println("That number is too big.");
} else if (floatValue == Float.NEGATIVE_INFINITY) {
System.out.println("That number is too small.");
} else {
System.out.println("That number is jussssst right.");
}
}
Sample Output:
String representation: -999999999999999999999999999999999999999999999
Result of isNaN: false
That number is too small.
String representation: 12345
Result of isNaN: false
That number is jussssst right.
String representation: 999999999999999999999999999999999999999999999
Result of isNaN: false
That number is too big.
It is used quite extensively in graphics. For example, any pixel in a 3D image that is not part of an actual object is marked as infinitely far away. So that it can later be replaced with a background image.
I'm using a network library where you can specify the maximum number of reconnection attempts. Since I want mine to reconnect forever:
my_connection = ConnectionLibrary(max_connection_attempts = float('inf'))
In my opinion, it's more clear than the typical "set to -1 to retry forever" style, since it's literally saying "retry until the number of connection attempts is greater than infinity".
Some programmers use Infinity or NaNs to show a variable has never been initialized or assigned in the program.
If you want the largest number from an input but they might use very large negatives. If I enter -13543124321.431 it still works out as the largest number since it's bigger than -inf.
enter code here
initial_value = float('-inf')
while True:
try:
x = input('gimmee a number or type the word, stop ')
except KeyboardInterrupt:
print("we done - by yo command")
break
if x == "stop":
print("we done")
break
try:
x = float(x)
except ValueError:
print('not a number')
continue
if x > initial_value: initial_value = x
print("The largest number is: " + str(initial_value))
You can to use:
import decimal
decimal.Decimal("Infinity")
or:
from decimal import *
Decimal("Infinity")
For sorting
I've seen it used as a sort value, to say "always sort these items to the bottom".
To specify a non-existent maximum
If you're dealing with numbers, nil represents an unknown quantity, and should be preferred to 0 for that case. Similarly, Infinity represents an unbounded quantity, and should be preferred to (arbitrarily_large_number) in that case.
I think it can make the code cleaner. For example, I'm using Float::INFINITY in a Ruby gem for exactly that: the user can specify a maximum string length for a message, or they can specify :all. In that case, I represent the maximum length as Float::INFINITY, so that later when I check "is this message longer than the maximum length?" the answer will always be false, without needing a special case.