I am usually programming in Python, but for an assignment, I am using Simulink. I am wondering why the above elseif ladder does not generate an incremental increase of the variable [IP3] over time. What I would think it should do is return 0.01 until t = 500, then 0.03 until t = 1000, then 0.1 until 1500, 1 until 2000, and 10 from then on. Apologies for the older image btw, I updated the variables in the mean time.
In the Simulink model that you showed, elseif parts will never execute since:
if u1>0 is satisfied, none of the other conditions will be checked and thus it will always be returning 0.01 for all u1>0.
And when u1<=0, all the conditions will be checked but none of them
will be satisfied. (u1 may never be less than zero in your case as u1 is time).
This behavior is same in every programming language.
Fixing your If-elseif Statements:
You need to add this in the If block:
Under If expression (e.g. u1 ~= 0), write this:
u1>0 & u1<=500
Under Elseif expressions (comma-separated list, e.g. u2 ~= 0, u3(2) < u2):, write this:
u1>500 & u1<=1000, u1>1000 & u1<=1500, u1>1500 & u1<=2000, u1>2000
Since u1 is time in your case which cannot be negative, you may also want to use the else part. So instead of the last step you can also do this:
Under Elseif expressions (comma-separated list, e.g. u2 ~= 0, u3(2) < u2):, write this:
u1>500 & u1<=1000, u1>1000 & u1<=1500, u1>1500 & u1<=2000
and connect the output of the else part which was connected with the output of u1>2000 before.
Related
I am currently taking an online algorithms course in which the teacher doesn't give code to solve the algorithm, but rather rough pseudo code. So before taking to the internet for the answer, I decided to take a stab at it myself.
In this case, the algorithm that we were looking at is merge sort algorithm. After being given the pseudo code we also dove into analyzing the algorithm for run times against n number of items in an array. After a quick analysis, the teacher arrived at 6nlog(base2)(n) + 6n as an approximate run time for the algorithm.
The pseudo code given was for the merge portion of the algorithm only and was given as follows:
C = output [length = n]
A = 1st sorted array [n/2]
B = 2nd sorted array [n/2]
i = 1
j = 1
for k = 1 to n
if A(i) < B(j)
C(k) = A(i)
i++
else [B(j) < A(i)]
C(k) = B(j)
j++
end
end
He basically did a breakdown of the above taking 4n+2 (2 for the declarations i and j, and 4 for the number of operations performed -- the for, if, array position assignment, and iteration). He simplified this, I believe for the sake of the class, to 6n.
This all makes sense to me, my question arises from the implementation that I am performing and how it effects the algorithms and some of the tradeoffs/inefficiencies it may add.
Below is my code in swift using a playground:
func mergeSort<T:Comparable>(_ array:[T]) -> [T] {
guard array.count > 1 else { return array }
let lowerHalfArray = array[0..<array.count / 2]
let upperHalfArray = array[array.count / 2..<array.count]
let lowerSortedArray = mergeSort(array: Array(lowerHalfArray))
let upperSortedArray = mergeSort(array: Array(upperHalfArray))
return merge(lhs:lowerSortedArray, rhs:upperSortedArray)
}
func merge<T:Comparable>(lhs:[T], rhs:[T]) -> [T] {
guard lhs.count > 0 else { return rhs }
guard rhs.count > 0 else { return lhs }
var i = 0
var j = 0
var mergedArray = [T]()
let loopCount = (lhs.count + rhs.count)
for _ in 0..<loopCount {
if j == rhs.count || (i < lhs.count && lhs[i] < rhs[j]) {
mergedArray.append(lhs[i])
i += 1
} else {
mergedArray.append(rhs[j])
j += 1
}
}
return mergedArray
}
let values = [5,4,8,7,6,3,1,2,9]
let sortedValues = mergeSort(values)
My questions for this are as follows:
Do the guard statements at the start of the merge<T:Comparable> function actually make it more inefficient? Considering we are always halving the array, the only time that it will hold true is for the base case and when there is an odd number of items in the array.
This to me seems like it would actually add more processing and give minimal return since the time that it happens is when we have halved the array to the point where one has no items.
Concerning my if statement in the merge. Since it is checking more than one condition, does this effect the overall efficiency of the algorithm that I have written? If so, the effects to me seems like they vary based on when it would break out of the if statement (e.g at the first condition or the second).
Is this something that is considered heavily when analyzing algorithms, and if so how do you account for the variance when it breaks out from the algorithm?
Any other analysis/tips you can give me on what I have written would be greatly appreciated.
You will very soon learn about Big-O and Big-Theta where you don't care about exact runtimes (believe me when I say very soon, like in a lecture or two). Until then, this is what you need to know:
Yes, the guards take some time, but it is the same amount of time in every iteration. So if each iteration takes X amount of time without the guard and you do n function calls, then it takes X*n amount of time in total. Now add in the guards who take Y amount of time in each call. You now need (X+Y)*n time in total. This is a constant factor, and when n becomes very large the (X+Y) factor becomes negligible compared to the n factor. That is, if you can reduce a function X*n to (X+Y)*(log n) then it is worthwhile to add the Y amount of work because you do fewer iterations in total.
The same reasoning applies to your second question. Yes, checking "if X or Y" takes more time than checking "if X" but it is a constant factor. The extra time does not vary with the size of n.
In some languages you only check the second condition if the first fails. How do we account for that? The simplest solution is to realize that the upper bound of the number of comparisons will be 3, while the number of iterations can be potentially millions with a large n. But 3 is a constant number, so it adds at most a constant amount of work per iteration. You can go into nitty-gritty details and try to reason about the distribution of how often the first, second and third condition will be true or false, but often you don't really want to go down that road. Pretend that you always do all the comparisons.
So yes, adding the guards might be bad for your runtime if you do the same number of iterations as before. But sometimes adding extra work in each iteration can decrease the number of iterations needed.
How would I correctly make a recursive call within every if-statement to get the change of money? Im specifically focusing on the "change" variable.Thanks
TEST CASE 1-------------------------------------------------------------------------------
<>> [change,flag] = makeChangeRecursive(2,100)
change =
50
20
20
5
2
1
flag =
1
My code is the following
function [change,flag] = makeChangeRecursive(cost,paid)
if extra > 0
flag = true;
elseif extra == 0
change = 0;
flag = true;
return
elseif cost > paid;
flag = false;
change = [];
warning('That''s not enough to buy that item.');
return
end
if extra >= 100
change = [change; makeChangeRecursive(cost,paid - change )];
paid =paid-100;
elseif extra >= 50
change = [change; 50];
paid =paid-50;
elseif
This continues for all dollar values.
Let's take a look at your first case:
if extra >= 100
change = [change; makeChangeRecursive(cost,paid - change )];
paid =paid-100;
elseif ...
The first time we call your function, the variable change doesn't have anything in it. In fact, it will never have anything in it at the beginning of the function call because you don't pass it in as a parameter or give it a value prior to this line. So putting change on the right-hand side of the assignment will give you an error.
But that's okay, because that's not what you want to do anyway. You want to build change up from the beginning.
In addition, change is a list of values. We want to pass the recursive calls a single value, paid after updating its value.
Let's build this up step by step:
if extra >= 100
If this is true, we want subtract 100 from the amount paid (what we pass in to the recursive call) and add 100 to our list of change. Let's do the first part:
paid = paid - 100;
As I said, we want to update paid first because we're going to use this value in the recursive call, which happens next, along with adding our new change value to the list:
change = [100; makeChangeRecursive(cost, paid)];
elseif ...
And so on for the remainder of the change values. I'm sure you can take care of the rest of them now by yourself.
I also noticed that you didn't assign a value to extra. This might have been just a cut-and-paste error, but you need to make sure that you have that at the beginning of your function.
I'm doing analysis on binary data. Suppose I have two uint8 data values:
a = uint8(0xAB);
b = uint8(0xCD);
I want to take the lower two bits from a, and whole content from b, to make a 10 bit value. In C-style, it should be like:
(a[2:1] << 8) | b
I tried bitget:
bitget(a,2:-1:1)
But this just gave me separate [1, 1] logical type values, which is not a scalar, and cannot be used in the bitshift operation later.
My current solution is:
Make a|b (a or b):
temp1 = bitor(bitshift(uint16(a), 8), uint16(b));
Left shift six bits to get rid of the higher six bits from a:
temp2 = bitshift(temp1, 6);
Right shift six bits to get rid of lower zeros from the previous result:
temp3 = bitshift(temp2, -6);
Putting all these on one line:
result = bitshift(bitshift(bitor(bitshift(uint16(a), 8), uint16(b)), 6), -6);
This is doesn't seem efficient, right? I only want to get (a[2:1] << 8) | b, and it takes a long expression to get the value.
Please let me know if there's well-known solution for this problem.
Since you are using Octave, you can make use of bitpack and bitunpack:
octave> a = bitunpack (uint8 (0xAB))
a =
1 1 0 1 0 1 0 1
octave> B = bitunpack (uint8 (0xCD))
B =
1 0 1 1 0 0 1 1
Once you have them in this form, it's dead easy to do what you want:
octave> [B A(1:2)]
ans =
1 0 1 1 0 0 1 1 1 1
Then simply pad with zeros accordingly and pack it back into an integer:
octave> postpad ([B A(1:2)], 16, false)
ans =
1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0
octave> bitpack (ans, "uint16")
ans = 973
That or is equivalent to an addition when dealing with integers
result = bitshift(bi2de(bitget(a,1:2)),8) + b;
e.g
a = 01010111
b = 10010010
result = 00000011 100010010
= a[2]*2^9 + a[1]*2^8 + b
an alternative method could be
result = mod(a,2^x)*2^y + b;
where the x is the number of bits you want to extract from a and y is the number of bits of a and b, in your case:
result = mod(a,4)*256 + b;
an extra alternative solution close to the C solution:
result = bitor(bitshift(bitand(a,3), 8), b);
I think it is important to explain exactly what "(a[2:1] << 8) | b" is doing.
In assembly, referencing individual bits is a single operation. Assume all operations take the exact same time and "efficient" a[2:1] starts looking extremely inefficient.
The convenience statement actually does (a & 0x03).
If your compiler actually converts a uint8 to a uint16 based on how much it was shifted, this is not a 'free' operation, per se. Effectively, what your compiler will do is first clear the "memory" to the size of uint16 and then copy "a" into the location. This requires an extra step (clearing the "memory" (register)) that wouldn't normally be needed.
This means your statement actually is (uint16(a & 0x03) << 8) | uint16(b)
Now yes, because you're doing a power of two shift, you could just move a into AH, move b into AL, and AH by 0x03 and move it all out but that's a compiler optimization and not what your C code said to do.
The point is that directly translating that statement into matlab yields
bitor(bitshift(uint16(bitand(a,3)),8),uint16(b))
But, it should be noted that while it is not as TERSE as (a[2:1] << 8) | b, the number of "high level operations" is the same.
Note that all scripting languages are going to be very slow upon initiating each instruction, but will complete said instruction rapidly. The terse nature of Python isn't because "terse is better" but to create simple structures that the language can recognize so it can easily go into vectorized operations mode and start executing code very quickly.
The point here is that you have an "overhead" cost for calling bitand; but when operating on an array it will use SSE and that "overhead" is only paid once. The JIT (just in time) compiler, which optimizes script languages by reducing overhead calls and creating temporary machine code for currently executing sections of code MAY be able to recognize that the type checks for a chain of bitwise operations need only occur on the initial inputs, hence further reducing runtime.
Very high level languages are quite different (and frustrating) from high level languages such as C. You are giving up a large amount of control over code execution for ease of code production; whether matlab actually has implemented uint8 or if it is actually using a double and truncating it, you do not know. A bitwise operation on a native uint8 is extremely fast, but to convert from float to uint8, perform bitwise operation, and convert back is slow. (Historically, Matlab used doubles for everything and only rounded according to what 'type' you specified)
Even now, octave 4.0.3 has a compiled bitshift function that, for bitshift(ones('uint32'),-32) results in it wrapping back to 1. BRILLIANT! VHLL place you at the mercy of the language, it isn't about how terse or how verbose you write the code, it's how the blasted language decides to interpret it and execute machine level code. So instead of shifting, uint32(floor(ones / (2^32))) is actually FASTER and more accurate.
It's that time of the week where I realize just how little I understand in MATLAB. This week, we have homework on iteration, so using for-loops and while-loops. The problem I am currently experiencing difficulties with is one where I have to write a function that decides who to hire somebody. I'm given a list of names, a list of GPAs and a logical vector that tells me whether or not a student stayed to talk. What I have to output is the names of people to hire and the time they spent chatting with the recruiter.
function[candidates_hire, time_spent] = CFRecruiter(names, GPAs, stays_to_talk)
In order to be hired, a canidate must have a GPA that is higher than 2.5 (not inclusive). In order to be hired, the student must stick around to talk, if they don't talk, they don't get hired. The names are separated by a ', ' and the GPAs is a vector. The time spent talking is determined by:
Time in minutes = (GPA - 2.5) * 4;
My code so far:
function[candidates_hire, time_spent] = CFRecruiter(names, GPAs, stays_to_talk)
candidates = strsplit(names, ', ');
%// My attempt to split up the candidates names.
%// I get a 1x3 cell array though
for i = 1:length(GPAs)
%// This is where I ran into trouble, I need to separate the GPAs
student_GPA = (GPAs(1:length(GPAs)));
%// The length is unknown, but this isn't working out quite yet.
%// Not too sure how to fix that
return
end
time_spent = (student_GPA - 2.5) * 4; %My second output
while stays_to_talk == 1 %// My first attempt at a while-loop!
if student_GPA > 2.5
%// If the student has a high enough GPA and talks, yay for them
student = 'hired';
else
student = 'nothired'; %If not, sadface
return
end
end
hired = 'hired';
%// Here was my attempt to get it to realize how was hired, but I need
%// to concatenate the names that qualify into a string for the end
nothired = 'nothired';
canidates_hire = [hired];
What my main issue is here is figuring out how to let the function know them names(1) has the GPA of GPAs(1). It was recommended that I start a counter, and that I had to make sure my loops kept the names with them. Any suggestions with this problem? Please and thank you :)
Test Codes
[Names, Time] = CFRecruiter('Jack, Rose, Tom', [3.9, 2.3, 3.3],...
[false true true])
=> Name = 'Tom'
Time = 3.2000
[Names, Time] = CFRecruiter('Vatech, George Burdell, Barnes Noble',...
[4.0, 2.5, 3.6], [true true true])
=> Name = 'Vatech, Barnes Noble'
Time = 10.4000
I'm going to do away with for and while loops for this particular problem, mainly because you can solve this problem very elegantly in (I kid you not) three lines of code... well four if you count returning the candidate names. Also, the person who is teaching you MATLAB (absolutely no offense intended) hasn't the faintest idea of what they're talking about. The #1 rule in MATLAB is that if you can vectorize your code, do it. However, there are certain situations where a for loop is very suitable due to the performance enhancements of the JIT (Just-In-Time) accelerator. If you're curious, you can check out this link for more details on what JIT is about. However, I can guarantee that using loops in this case will be slow.
We can decompose your problem into three steps:
Determine who stuck around to talk.
For those who stuck around to talk, check their GPAs to see if they are > 2.5.
For those that have satisfied (1) and (2), determine the total time spent on talking by using the formula in your post for each person and add up the times.
We can use a logical vector to generate a Boolean array that simultaneously checks steps #1 and #2 so that we can index into our GPA array that you are specifying. Once we do this, we simply apply the formula to the filtered GPAs, then sum up the time spent. Therefore, your code is very simply:
function [candidates_hire, time_spent] = CFRecruiter(names, GPAs, stays_to_talk)
%// Pre-processing - split up the names
candidates = strsplit(names, ', ');
%// Steps #1 and #2
filtered_candidates = GPAs > 2.5 & stays_to_talk;
%// Return candidates who are hired
candidates_hire = strjoin(candidates(filtered_candidates), ', ');
%// Step #3
time_spent = sum((GPAs(filtered_candidates) - 2.5) * 4);
You had the right idea to split up the names based on the commas. strsplit splits up a string that has the token you're looking for (which is , in your case) into separate strings inside a cell array. As such, you will get a cell array where each element has the name of the person to be interviewed. Now, I combined steps #1 and #2 into a single step where I have a logical vector calculated that tells you which candidates satisfied the requirements. I then use this to index into our candidates cell array, then use strjoin to join all of the names together in a single string, where each name is separated by , as per your example output.
The final step would be to use the logical vector to index into the GPAs vector, grab those GPAs from those candidates who are successful, then apply the formula to each of these elements and sum them up. With this, here are the results using your sample inputs:
>> [Names, Time] = CFRecruiter('Jack, Rose, Tom', [3.9, 2.3, 3.3],...
[false true true])
Names =
Tom
Time =
3.2000
>> [Names, Time] = CFRecruiter('Vatech, George Burdell, Barnes Noble',...
[4.0, 2.5, 3.6], [true true true])
Names =
Vatech, Barnes Noble
Time =
10.4000
To satisfy the masses...
Now, if you're absolutely hell bent on using for loops, we can replace steps #1 and #2 by using a loop and an if condition, as well as a counter to keep track of the total amount of time spent so far. We will also need an additional cell array to keep track of those names that have passed the requirements. As such:
function [candidates_hire, time_spent] = CFRecruiter(names, GPAs, stays_to_talk)
%// Pre-processing - split up the names
candidates = strsplit(names, ', ');
final_names = [];
time_spent = 0;
for idx = 1 : length(candidates)
%// Steps #1 and #2
if GPAs(idx) > 2.5 && stays_to_talk(idx)
%// Step #3
time_spent = time_spent + (GPAs(idx) - 2.5)*4;
final_names = [final_names candidates(idx)];
end
end
%// Return candidates who are hired
candidates_hire = strjoin(final_names, ', ');
The trick with the above code is that we are keeping an additional cell array around that stores those candidates that have passed. We will then join all of the strings together with a , between each name as we did before. You'll also notice that there is a difference in checking for steps #1 and #2 between the two methods. In particular, there is a & in the first method and a && in the second method. The single & is for arrays and matrices while && is for single values. If you don't know what that symbol is, that is the symbol for logical AND. This means that something is true only if both the left side of the & and the right side of the & are both true. In your case, this means that someone who has a GPA of > 2.5 and stays to talk must both be true if they are to be hired.
In Python we have lru_cache as a function wrapper. Add it to your function and the function will only be evaluated once per different input argument.
Example (from Python docs):
#lru_cache(maxsize=None)
def fib(n):
if n < 2:
return n
return fib(n-1) + fib(n-2)
>>> [fib(n) for n in range(16)]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610]
>>> fib.cache_info()
CacheInfo(hits=28, misses=16, maxsize=None, currsize=16)
I wonder whether a similar thing exists in Matlab? At the moment I am using cache files, like so:
function result = fib(n):
% FIB example like the Python example. Don't implement it like that!
cachefile = ['fib_', n, '.mat'];
try
load(cachefile);
catch e
if n < 2
result = n;
else
result = fib(n-1) + fib(n-2);
end
save(cachefile, 'result');
end
end
The problem I have with doing it this way, is that if I change my function, I need to delete the cachefile.
Is there a way to do this with Matlab realising when I changed the function and the cache has become invalidated?
Since matlab 2017 this is available:
https://nl.mathworks.com/help/matlab/ref/memoizedfunction.html
a = memoized(#sin)
I've created something like this for my own personal use: a CACHE class. (I haven't documented the code yet though.) It appears to be more flexible than Python's lru_cache (I wasn't aware of that, thanks) in that it has several methods for adjusting exactly what gets cached (to save memory) and how the comparisons are made. It could still use some refinement (#Daniel's suggestion to use the containers.Map class is a good one – though it would limit compatibility with old Matlab versions). The code is on GitHub so you're welcome to fork and improve it.
Here is a basic example of how it can be used:
function Output1 = CacheDemo(Input1,Input2)
persistent DEMO_CACHE
if isempty(DEMO_CACHE)
% Initialize cache object on first run
CACHE_SIZE = 10; % Number of input/output patterns to cache
DEMO_CACHE = CACHE(CACHE_SIZE,Input1,Input2);
CACHE_IDX = 1;
else
% Check if input pattern corresponds something stored in cache
% If not, return next available CACHE_IDX
CACHE_IDX = DEMO_CACHE.IN([],Input1,Input2);
if ~isempty(CACHE_IDX) && DEMO_CACHE.OUT(CACHE_IDX) > 0
[~,Output1] = DEMO_CACHE.OUT(CACHE_IDX);
return;
end
end
% Perform computation
Output1 = rand(Input1,Input2);
% Save output to cache CACHE_IDX
DEMO_CACHE.OUT(CACHE_IDX,Output1);
I created this class to cache the results from time-consuming stochastic simulations and have since used it to good effect in a few other places. If there is interest, I might be willing to spend some time documenting the code sooner as opposed to later. It would be nice if there was a way to limit memory use as well (a big consideration in my own applications), but getting the size of arbitrary Matlab datatypes is not trivial. I like your idea of caching to a file, which might be a good idea for larger data. Also, it might be nice to create a "lite" version that does what Python's lru_cache does.