I've been able to use the polyRoots function since day one, but all of a sudden it stopped working and it keeps returning an empty result,does someone know what is happening? Thank you in advance! This is the return I get, I´ve put a very simple one so that I know it's not an input problem
The function polyRoots only returns the real-valued zeros of a polynomial. Instead, you can use cPolyRoots to include complex-valued zeros, which will -- in your case -- look something like this:
cPolyRoots(3*x^2+4*x+5,x)
{-2/3-sqrt(11)/3*i,-2/3+sqrt(11)/3*i}
In case you're not familiar with complex numbers, here's a Wikipedia article regarding them. Basically, i=sqrt(-1), which is a number that isn't present anywhere on the real number line; the real number line only includes negative infinity through positive infinity.
Related
everyone!
I've posted a similar problem, initially on Stackexchange; it was moved here and can be found at the link: Declaring a functional recursive sequence in Matlab I'm trying to do something similar in this post, but I've figured that Matlab isn't the place to do it. I'll have to use Pari-GP; and at this point there's no two ways about it.
This is essentially a coding project I've made for myself; which is to effectively numerically evaluate a certain construction of the Tetration function. I've been able to code it fairly well in MatLab; the trouble is, as we are dealing with large numbers like e^e^e^e^e^e^e; these short circuit in MatLab. Pari-GP has a much better understanding of numbers which would usually cause overflows; and I'm now fully realizing why it's used consistently by the Tetration community.
Nonetheless, the Matlab code works for small numbers and numbers with a niceness to them (well placed imaginary argument). For completeness of this question; the github repository for the matlab code is https://github.com/JmsNxn92/Recursive_Tetration This isn't the code we want though; I've optimized it further; this isn't up to date totally. But for the purpose of this question, it's enough.
Now, I'm not the best programmer. I haven't programmed since '09, maybe; but I still know my way around. But it's more that I have the framework of coding; and less the actual syntax. Imagine being well acquainted with french philosophy and french writing; but stumbling your words when ordering a cafe.
As to that, I'll stop beating around the bush, and get to the question.
If I define a function beta_function in Pari-GP and write it as,
beta_function(z,l,n) =
{
out = 0;
for(i=0,n-1,
out = exp(out)/(exp(l*(n-i-z)) +1));
out;
}
Everything is good, and it works. Now the code for beta_function in MatLab isn't very different. There's nothing more complex being added. As I originally asked for MatLab, I'm asking again for Pari-GP. This is how to code a function tau_K(z,l,n,k); which is perfectly doable. I'm just missing something obvious.
The code for tau_K(z,l,n,k) in MatLab is attached below. A friendly person on here explained how to do this in MatLab; for those of you interested, I wasn't really defining the recursion properly beforehand. Here is the current MatLab code I'm using,
function f = tau_K(z,l,n,k)
if k == 1
f = -log(1+exp(-l*z));
return
end
f = log(1 + tau_K(z+1,l,n,k-1)./beta_function(z+1,l,n)) - log(1+exp(-l*z));
end
The question is simple. How would one define this recursion in Pari-GP; how do you code this in Pari-GP?
Everything seems to be collapsing towards a return value at 0, when I try to directly translate this code. And honest to god; I know it's just because I'm making some syntax error in how I'm calling the output into the next iteration. I've tried everything I could think of. And the tutorials, they don't seem to be helping. I've tried next to everything. And at this point, I know I'm missing something stupid syntactically.
I'm just hoping someone here would be so helpful as to explain this to me like I'm in kindergarten. I've heard that tail recursion is important here. And if so, how would I code this in? Simply add in a variable which keeps track of everything?
Again, thanks if you got this far into the question.
When asking questions, it would help if you would provide expected output for some specified given arguments, otherwise it is hard to test. I don't know MATLAB, but your functions could be written in PARI:
beta_function(z,l,n)={
my(out = 0);
for(i=0,n-1,
out = exp(out)/(exp(l*(n-i-z)) +1));
out;
}
tau_K(z,l,n,k)={
if(k == 1,
-log(1+exp(-l*z)),
log(1 + tau_K(z+1,l,n,k-1)/beta_function(z+1,l,n)) - log(1+exp(-l*z))
)
}
In the beta_function, it is important to put my() around out = 0. This keeps the variable local to the function. Failure to do this, means that out will be a global variable, and many subtle bugs can arise.
PARI is a functional programming language which means you often don't need to assign things explicitly to temporary variables. For example if will return a value and this can be returned from your tau_K function (in your MATLAB code you assign to a temporary variable f, but in PARI this is not necessary).
There are no issues with calling a function recursively. In this case, tau_K can just call itself as needed.
In the MATLAB program you have ./. I don't know what this means - I have replaced by / which is just the normal division operator.
Before running you will need to set some precision for the numeric operations. The easiest way to achieve this is to enter \p100 at the PARI-GP prompt. (or \p1000 if you need a 1000 decimal digits of precision). It is possible to control precision dynamically, if you need some part of the calculation performed at high precision and other parts at a lower precision or if the precision needs to be dependent on n.
push button callback to convert to Morse
Hi, I have a problem, I'm supposed to create a GUI in MATLAB which converts letter & numbers into Morse code but my code wouldn't run, the attached image link above is for the push button callback. Also it says that the 'Morse' underlined in red needs to be preallocated for speed as it changes size every loop iteration. How should I approach this? Thanks..
Also, should I include anything under my edit1 and edit2 callbacks? Since edit1 is just for entering the input of numbers and letters and edit2 is just to output the Morse code. Thanks again!
edit1 & edit2 callbacks
"Morse" changes size every loop iteration. First of all, let's define 2 variables.
Morse_1 = [];
Morse_2 = zeros(1,100);
(I'm taking the liberty of defining matrices instead of strings, but that's easier to explain this concept). You are basically saying that Morse_1 is a blank variable that can be filled, while Morse_2 has fixed dimensions. The dimensions of blank variables like Morse_1 (pardon me if I'm not using the correct names, but I think blank variable explains it quite well) are flexible. This means that doing
Morse_1(1,101) = 1
will work (Morse_1 will be a 101-dimensional vector with 100 zeros and a 1 at the 101st position). Doing
Morse_2(1,101) = 1
will work as well, but you might end up with too many unused elements if you largely overestimate the dimensions (e.g. zeros(1,1000) but your message actually only reaches a few hundred).
In your case, I'd use a blank variable, since you don't really know beforehand how long your coded message is going to be (even if you knew the number of characters in your original string, the coded message would be 5 times longer if it were all '9's than all 'e's). This warning is really useful when dealing with 1000x1000 matrices, but for processing strings I'd ignore it.
To sum it up, I'd use a blank variable if you have no idea how long it'll get, or if your code can't handle a variable length, or if you don't want to worry about calculating exactly how many elements are needed. On the other hand, I'd use fixed dimensions if your code needs a properly dimensioned array, or if you're working with very large arrays. For a lot of cases, though, you really won't notice the speed difference (filling a blank array might take 0.01s, while filling a fixed dimension one might take 0.001s. Unless you're doing this a thousand times (why??), it's literally unnoticeable).
Personally, I'd change the way this loop works using strrep() like this:
for i=1:length(alphabet) %alphabet = 26 letters+10 numbers+space, 37 characters in total
original_message = strrep(original_message,alphabet{i},morse_alphabet{i});
end
strrep(a,b,c) finds the substrings b inside a and replaces it with c. In your case, alphabet is the same as the dictionary chars, and morse_alphabet is the same as the dictionary code.
As for the callbacks, I don't really know about it, so I can't help you with that.
I think this is a simple question, but I could not find an answer by googling.
Let's say that I have a code like this:
y1=1:0.01:2;
This creates 1x101 long cell, with numbers 1, 1.01, 1.02, 1.03, 1.04, etc.
Now I want to have an array of numbers which goes like 1, 1+0.01i, 1+0.02i, 1+0.03i, 1+0.04i, 1+0.05i, 1+0.06i, 1+0.07i, 1+0.08i, etc. I thought that the code 1:0.01i:2; will give the answer, but I am getting a warning
Warning: Colon operands must be real scalars.
How to get around this?
Thanks in advance
As the warning message is trying to tell you, the : is meant to be used in only one dimension. It cannot keep the real part constant and only increase the imaginary part. Instead, do this:
y=0:.01:1;
z=1+i*y
and z will contain the values you want. Here is the relevant docs.
I've got a Subscripted assignment dimension mismatch problem.
I've already localized the issue, and know exactly what is going on, I just don't know why.
Here's the problematic piece of code:
mFrames(:,i) = vSignal(round(start:1:frameLength*samplingRate));
start=start+frameShift*samplingRate;
frameLength = frameLength+frameShift;
I've already checked what's going on in debugmode; usually my resulting column length of mFrames is 128, this stays the same until i=1004. Then, my column length changes to 127.
I've checked the values involved while in debug mode, and it simply does not make sense what is going on. At i==1004 start=32097 and frameLength*samplingRate=32224.
That's a difference of 127 meaning 128 points, that should work.
BUT when i assign a vector A=round(start:1:frameLength*samplingRate)
OR B=start:1:frameLength*samplingRate
In both cases I get a vector going from 32097 to 32223. This ALTHOUGH when I give in frameLength*samplingRate matlab is giving me 32224.
In other words, matlab is telling me it's using one number, but when I test I find it's using a different one.
Any help appreciated.
I suspect your 32224 is not actually 32224. MATLAB's default format only displays so many decimal places, so when dealing with floating point numbers, what is printed on screen is not necessarily the "exact" value.
Let's go back a step and look at how the synatx x = start:step:end works.
1:1:10 should give us numbers in steps of 1 from 1 to 10. Fair enough, that makes sense. What if we set the end value to something that's slightly above 10?
e.g.:
1:1:10.1
Well, it still gives us 1:1:10, (or 1:10, 1 being the default step) because we can't have values higher than the end-point, so 11 isn't a correct step.
So what about this:
1:1:9.99
Spoiler: it's the same as 1:9
And this?
1:1:9.9999999
Yep, still 1:9
But if we do this:
a = 9.9999999;
Then with default format, the value of a will be shown on the command line and in your list of workspace variables as 10.0000.
Now, if frameLength and samplingRate are both stored as floating point numbers, it's possible that the number you see as 32224 is not 32224 but very slightly below that. You can check this by changing your default format - e.g. format long at the command line - to show more decimal places.
The simplest solution is probably to do something like:
B=start:1:round(frameLength*samplingRate)
Or try to store the relevant values as integers (e.g., uint32).
%function [flag] =verify(area)
[FileName,PathName,FilterIndex]= uigetfile('*.tif','Select the signature file');
display(PathName)
m=[PathName,FileName];
area=nor_area(m);
%display(area)
%area=0.8707;
class(area)
flag=0;
extract=xlsread('D:\Project\Image_processing\important\best.xlsx', 'CW4:CW17');
c=numel(extract);
display(c)
l=extract(1);
class(l)
display(l)
for k = 1:c
%x=extract(k);
if (l==area && flag==0)
% display(extract(k));
flag=1;
display(flag)
end
end
display(flag)
The above is my code for verification, i am not able to compare "l==area", even if the values are same am not able to enter inside the loop. If i try passing the value assume l=0.9999 and the area that i obtain to be the same , if i sent l value explicitly it works..!! but if i try using some function and pass the same value it wont work. I have tried checking the type by using class, both returns double.
Can anyone please help me out with this and if this approach is not good, suggest any alternative that may be used.
It is not generally a good idea to compare floats like you are doing (with the == operator) since floats, unlike integer values are subject to round off. See here and here for a discussion on comparing floats in MATLAB.
Essentially you have to check that two floats are 'close enough' rather than exactly equal, which is what == checks for. MATLAB has a built in function eps for determining the floating point precision on your machine, so use that function when comparing floats. See its documentation for more information.
In most cases it is not wise to compare floating point numbers by a == b. Use abs(a-b)<epsilon where epsilonis some small tolerance like 1e-10 instead.