What does the following code do?
I am confused on how the for loops function here, and would appreciate any help to understand.
average_mae_history = [np.mean([x[i] for x in all_mae_histories]) for i in range(num_epochs)]
Suppose avg_mae_history has say 4 lists each with 500 elements, where the 4 lists correspond to the 4 folds and 500 elements correspond to the 500 epochs performed for each fold.
Asking questions without trying out and telling what you have done in order to clarify your doubt is wrong.
Anyway I will explain the code snippet:
Its a simple list comprehension with two for loops.
What it basically does is:
for i in range(num_epochs):
for j in all_mae_history:
temp = []
temp.append(j[i])
z.append(max(temp))
Next time tell us what you have done before posting code snippets.
The correct answer would be
mean = [np.mean([x[i] for x in all_mae_histories]) for i in range(num_epochs)]
print('mean - ', mean)
z = []
for i in range(num_epochs):
temp = []
for j in all_mae_histories:
temp.append(j[i])
z.append(np.mean(temp))
print('mean z ', z)
Related
I have a problem where I need to do a linear interpolation on some data as it is acquired from a sensor (it's technically position data, but the nature of the data doesn't really matter). I'm doing this now in matlab, but since I will eventually migrate this code to other languages, I want to keep the code as simple as possible and not use any complicated matlab-specific/built-in functions.
My implementation initially seems OK, but when checking my work against matlab's built-in interp1 function, it seems my implementation isn't perfect, and I have no idea why. Below is the code I'm using on a dataset already fully collected, but as I loop through the data, I act as if I only have the current sample and the previous sample, which mirrors the problem I will eventually face.
%make some dummy data
np = 109; %number of data points for x and y
x_data = linspace(3,98,np) + (normrnd(0.4,0.2,[1,np]));
y_data = normrnd(2.5, 1.5, [1,np]);
%define the query points the data will be interpolated over
qp = [1:100];
kk=2; %indexes through the data
cc = 1; %indexes through the query points
qpi = qp(cc); %qpi is the current query point in the loop
y_interp = qp*nan; %this will hold our solution
while kk<=length(x_data)
kk = kk+1; %update the data counter
%perform online interpolation
if cc<length(qp)-1
if qpi>=y_data(kk-1) %the query point, of course, has to be in-between the current value and the next value of x_data
y_interp(cc) = myInterp(x_data(kk-1), x_data(kk), y_data(kk-1), y_data(kk), qpi);
end
if qpi>x_data(kk), %if the current query point is already larger than the current sample, update the sample
kk = kk+1;
else %otherwise, update the query point to ensure its in between the samples for the next iteration
cc = cc + 1;
qpi = qp(cc);
%It is possible that if the change in x_data is greater than the resolution of the query
%points, an update like the above wont work. In this case, we must lag the data
if qpi<x_data(kk),
kk=kk-1;
end
end
end
end
%get the correct interpolation
y_interp_correct = interp1(x_data, y_data, qp);
%plot both solutions to show the difference
figure;
plot(y_interp,'displayname','manual-solution'); hold on;
plot(y_interp_correct,'k--','displayname','matlab solution');
leg1 = legend('show');
set(leg1,'Location','Best');
ylabel('interpolated points');
xlabel('query points');
Note that the "myInterp" function is as follows:
function yi = myInterp(x1, x2, y1, y2, qp)
%linearly interpolate the function value y(x) over the query point qp
yi = y1 + (qp-x1) * ( (y2-y1)/(x2-x1) );
end
And here is the plot showing that my implementation isn't correct :-(
Can anyone help me find where the mistake is? And why? I suspect it has something to do with ensuring that the query point is in-between the previous and current x-samples, but I'm not sure.
The problem in your code is that you at times call myInterp with a value of qpi that is outside of the bounds x_data(kk-1) and x_data(kk). This leads to invalid extrapolation results.
Your logic of looping over kk rather than cc is very confusing to me. I would write a simple for loop over cc, which are the points at which you want to interpolate. For each of these points, advance kk, if necessary, such that qp(cc) is in between x_data(kk) and x_data(kk+1) (you can use kk-1 and kk instead if you prefer, just initialize kk=2 to ensure that kk-1 exists, I just find starting at kk=1 more intuitive).
To simplify the logic here, I'm limiting the values in qp to be inside the limits of x_data, so that we don't need to test to ensure that x_data(kk+1) exists, nor that x_data(1)<pq(cc). You can add those tests in if you wish.
Here's my code:
qp = [ceil(x_data(1)+0.1):floor(x_data(end)-0.1)];
y_interp = qp*nan; % this will hold our solution
kk=1; % indexes through the data
for cc=1:numel(qp)
% advance kk to where we can interpolate
% (this loop is guaranteed to not index out of bounds because x_data(end)>qp(end),
% but needs to be adjusted if this is not ensured prior to the loop)
while x_data(kk+1) < qp(cc)
kk = kk + 1;
end
% perform online interpolation
y_interp(cc) = myInterp(x_data(kk), x_data(kk+1), y_data(kk), y_data(kk+1), qp(cc));
end
As you can see, the logic is a lot simpler this way. The result is identical to y_interp_correct. The inner while x_data... loop serves the same purpose as your outer while loop, and would be the place where you read your data from wherever it's coming from.
When I run this code (in a programming assignment for Coursera):
J = 1/m * [-y.*log(sigmoid((theta)'*X))-(1-y).*log(1-sigmoid((theta)'*X))]
where m = length(y), y is an m-dimensional vector, X is an m*2 matrix, and theta = 0.1, Octave outputs:
g =
[long (#rows)*2 matrix, each entry <1 but extremely close to 1]
g =
[another long (#rows)*2 matrix as before]
J =
[(#rows)*2 matrix with entries such as 3.4932e-002 and 7.8914e-005]
What is g? I never defined it, and it does not appear in my code, yet is outputted with some seemingly unrelated numbers? (I know that the function itself may have problems, but that is a separate issue from what I'm interested in here. I figured that if I know what g is, I might be able to troubleshoot better. If you have any comments on the function, please don't hesitate to point out what's wrong.)
Whenever you have a statement (inside a function or otherwise) which is not terminated with a semicolon, the output of that statement will display on the terminal.
Assuming that this is the only code you're running, then my guess is that inside your sigmoid function there is a statement of this kind:
g = dosomething() % note: not semicolon terminated!
resulting in terminal output during its execution.
The fact that g is reported twice in the terminal also makes sense, since you are calling the sigmoid function twice in that expression you just wrote.
Also, for the sake of clarity, please do not refer to your one-liner as a function, since that means something entirely different in the context of programming.
I am currently having issues with figuring our some recurrence stuff and since I have midterms about it coming up soon I could really use some help and maybe an explanation on how it works.
So I basically have pseudocode for solving the Tower of Hanoi
TOWER_OF_HANOI ( n, FirstRod, SecondRod, ThirdRod)
if n == 1
move disk from FirstRod to ThirdRod
else
TOWER_OF_HANOI(n-1, FirstRod, ThirdRod, SecondRod)
move disk from FirstRod to ThirdRod
TOWER_OF_HANOI(n-1, SecondRod, FirstRod, ThirdRod)
And provided I understand how to write the relation (which, honestly I'm not sure I do...) it should be T(n) = 2T(n-1)+Ɵ(n), right? I sort of understand how to make a tree with fractional subproblems, but even then I don't fully understand the process that would give you the end solution of Ɵ(n) or Ɵ(n log n) or whatnot.
Thanks for any help, it would be greatly appreciated.
Assume the time complexity is T(n), it is supposed to be: T(n) = T(n-1) + T(n-1) + 1 = 2T(n-1) + 1. Why "+1" but not "+n"? Since "move disk from FirstRod to ThirdRod" costs you only one move.
For T(n) = 2T(n-1) + 1, its recursion tree will exactly look like this:
https://www.quora.com/What-is-the-complexity-of-T-n-2T-n-1-+-C (You might find it helpful, the image is neat.) C is a constant; it means the cost per operation. In the case of Tower of Hanoi, C = 1.
Calculate the sum of the cost each level, you will easily find out in this case, the total cost will be 2^n-1, which is exponential(expensive). Therefore, the answer of this recursion equation is Ɵ(2^n).
Ok, here it goes another Euler problem question.
I've started to learn Lua by solving Euler project problems and got stuck on Euler problem 12.
It looks to me very straightforward and I don't understand why is my result incorrect?
Here is my solution so far:
-- return triangular number of the specified number
function get_tri_num(num)
local n = 0
for i=1, num do
n = n + i
end
return n
end
-- return all factors of the specifeid number
function factors(num)
local factors = {}
for i=1, num/2 do
if num%i == 0 then
factors[#factors+1] = i
end
end
factors[#factors+1] = num
return factors
end
-- get the first triangle number with >500 divisors
function euler12()
local n = 0
local trinum = 1
while true do
n = n + 7
trinum = get_tri_num(n)
if #factors(trinum) > 500 then break end
end
print(trinum, n)
end
euler12()
This problem is computation intensive, well, at least the way I am solving it, so I use luajit.
time luajit euler12.lua
103672800 14399
real 3m14.971s
user 3m15.033s
sys 0m0.000s
First, I try this solution on the toy example provided in the problem description. Changing the line of euler12() to if #factors(trinum) > 5 then break end, I get:
28 7
Which corresponds to the results shown in the problem example.
Second, after I see that the toy example is working I run euler12() with >500 condition. According to my solution the answer is 103672800 and yes, if I separately check the number of divisors for this result is >500:
print(#factors(103672800))
648
But...
The problem is here:
while true do
n = n + 7
Why does n increaments 7 each time? That doesn't make sense, change it to 1, and you could get the correct answer.
However, the performance is still poor. Several places that could be improved:
Every time the function get_tri_num is called, it's calculating
from scratch, that's not necessary.
You don't need the factors of a number, you only need the number of
factors of a number, so why return a table in factors?
for i=1, num/2 do is not necessary. Iterating to the square root of
num is enough to get the number of factors.
Refer to my code for the same problem.
I am trying to solve a problem, for example I have a 4 point and each two point has a cost between them. Now I want to find a sequence of nodes which total cost would be less than a bound. I have written a code but it seems not working. The main problem is I have define a python function and trying to call it with in a constraint.
Here is my code: I have a function def getVal(n1,n2): where n1, n2 are Int Sort. The line Nodes = [ Int("n_%s" % (i)) for i in range(totalNodeNumber) ] defines 4 points as Int sort and when I am adding a constraint s.add(getVal(Nodes[0], Nodes[1]) + getVal(Nodes[1], Nodes[2]) < 100) then it calls getVal function immediately. But I want that, when Z3 will decide a value for Nodes[0], Nodes[1], Nodes[2], Nodes[3] then the function should be called for getting the cost between to points.
from z3 import *
import random
totalNodeNumber = 4
Nodes = [ Int("n_%s" % (i)) for i in range(totalNodeNumber) ]
def getVal(n1,n2):
# I need n1 and n2 values those assigned by Z3
cost = random.randint(1,20)
print cost
return IntVal(cost)
s = Solver()
#constraint: Each Nodes value should be distinct
nodes_index_distinct_constraint = Distinct(Nodes)
s.add(nodes_index_distinct_constraint)
#constraint: Each Nodes value should be between 0 and totalNodeNumber
def get_node_index_value_constraint(i):
return And(Nodes[i] >= 0, Nodes[i] < totalNodeNumber)
nodes_index_constraint = [ get_node_index_value_constraint(i) for i in range(totalNodeNumber)]
s.add(nodes_index_constraint)
#constraint: Problem with this constraint
# Here is the problem it's just called python getVal function twice without assiging Nodes[0],Nodes[1],Nodes[2] values
# But I want to implement that - Z3 will call python function during his decission making of variables
s.add(getVal(Nodes[0], Nodes[1]) + getVal(Nodes[1], Nodes[2]) + getVal(Nodes[2], Nodes[3]) < 100)
if s.check() == sat:
print "SAT"
print "Model: "
m = s.model()
nodeIndex = [ m.evaluate(Nodes[i]) for i in range(totalNodeNumber) ]
print nodeIndex
else:
print "UNSAT"
print "No solution found !!"
If this is not a right way to solve the problem then could you please tell me what would be other alternative way to solve it. Can I encode this kind of problem to find optimal sequence of way points using Z3 solver?
I don't understand what problem you need to solve. Definitely, the way getVal is formulated does not make sense. It does not use the arguments n1, n2. If you want to examine values produced by a model, then you do this after Z3 returns from a call to check().
I don't think you can use a python function in your SMT logic. What you could alternatively is define getVal as a Function like this
getVal = Function('getVal',IntSort(),IntSort(),IntSort())
And constraint the edge weights as
s.add(And(getVal(0,1)==1,getVal(1,2)==2,getVal(0,2)==3))
The first two input parameters of getVal represent the node ids and the last integer represents the weight.