I have a variable which is a Modulus of Congruence x=y(mod 360),which means y varies from 0 - 360 and if the value is greater than 360 it again comes to 0. For example x=5 for y = 365 .
I wrote this function to stabilize y , so if the difference between x and previousx is greater than 5 then i get x otherwise previousx .
float stabilize(float x,float previous){
if(fabs(x-previousx)<5)
{
return previousx;
}
else
{
return x;
}
}
This works fine between 0 to 360 But this fails on the boundary condition of 360 and 0 .How can i stabilize the value when y is a value near 0 such as 0.3 and previous y is near 360 such as 359. So the difference calculated here is 359 - .3 = 358.7 . but i want it to be the modulo 360 difference which is 1.3 .
What about something like if(fabs(x-previousx)<5 || fabs(x-previousx)>355)? Given that the input data is mod 360, if the difference is big enough it means that both values are close enough to the border.
You could subtract the original numbers and take modulo 360 of the fabs(result):
for example:
359 - 720.3 = -361.3
fabs(-361.3) = 361.3
361.3 % 360 = 1.3
Related
Greeting,
I'm trying to find a formula to convert a range where:
min = -100db and max = -30db
to:
min = 0 and max = 255
for example: -60db = ?
Seems easy but it makes my head spin.
Assuming you mean the result to stay in terms of db, you're asking for a simple linear interpolation:
f(x) = ymin + (x - xmin)*(ymax - ymin)/(xmax - xmin)
or in your case,
f(x) = 0 + (x + 100)*(255 - 0)/(-30 + 100)
f(-60 db) = 145.714
If instead you're talking about converting db to a scale factor with which to multiply an audio signal, then it's a bit more complex. For example, to multiply an audio signal by 0 is negative infinity db. So (at the very least) you'd have to special case that.
I need to quantize my vector and generate directional code words from 0 to 15. So I had implemented following code line using C++ to achieve that. Just pass 2 points and calculate atan() value using that points. But it's only return just 0 to 7. other values are not return. Also sometimes it's return very large numbers like 42345. How can I modify this to return directional code words from 0 to 15
double angle = abs(atan((acc.y - acc.lastY)/(acc.x - acc.lastX))/(20*3.14159/180));
That's what the std::atan2 function is for.
Since tan function is periodic over just half circle. Logically, if you negate both coordinates, the expression in the argument comes out the same, so you can't tell the two cases apart. So you have to first look at which quadrant you are in by checking the signs and than adding 180 if you are in the negative half-space. The std::atan2 function will do it for you.
double angle = std::atan2(acc.y - acc.lastY, acc.x - acc.lastX) * (8 / PI);
It has the added benefit of actually working when acc.x == acc.lastX, while your expression will signal division by zero.
Additionally, the use of abs is wrong. If you get angle between -π and π you want to get angle between 0 and 2π, you need to write:
double angle = std::atan2(acc.y - acc.lastY, acc.x - acc.lastX); // keep it in radians
if(angle < 0)
angle += 2 * PI;
return angle * (8 / PI); // convert to <0, 16)
With abs you are unifying the cases with oposite sign of y, but same x.
Additionally if you want to round the values so that 0 represents directions along x axis slightly off to either side, you'll need to modify the rounding by adding half of the interval width and you'll have to do before normalizing to the ⟨0, 2π) range. You'd start with:
double angle = std::atan2(acc.y - acc.lastY, acc.x - acc.lastX) + PI/16;
I'd like to know if there's any way in C++ to calculate a proportion involving possibily negative values in both vars and extremes.
My goal is to sync a float text input widget with fixed extremes ( eg the user can input any double value between A (min) and B (max) with A,B=any_constant_real_number ) with a slider who can only slide between 0 and 100 ( to simplify ).
If A and B are positive everything is trivial. as
val_slider = ((val_textin-A)*100)/(B-A)
but as A and B can be assumed real it looks to me the only possibility is to use several if/cases, or huge formulas involving a lot of abs() and checks over 0-divisions, whose are quite error prone and very cost intense compared to such an easy task.
Is there any faster and shorter way to achieve the same in c/c++/stl?
Pardon my bad english. Any hint? Thank you.
Your formula should work fine with negative values of A and B as well, as log as A < B.
Example, if you want the user to be able to enter values from -100 to 100, and map these to a slider which goes from 0 - 100, when the user enters -90 you get:
((-90 - A) * 100) / (B - A) = ((-90 - (-100)) * 100) / (100 - (-100))
= 10 * 100 / 200
= 5
An input value of 50 results in a slider value of:
((50 - A) * 100) / (B - A) = ((50 - (-100)) * 100) / (100 - (-100))
= 150 * 100 / 200
= 75
I don't know C++, but I do know Math, so try:
val_slider = 100 * ( val_textin - A ) / ( B - A )
Hey wait. That's exactly what you have. Test case..
A=-200, B=+200, val_texin = 100 (75% of bar, right?)
val_slider = 100 * ( 100 - -200 ) / ( 200 - - 200 )
= ( 300 ) / ( 400 ) * 100
= 75
See, you got it right. The only thing that COULD happen is B==A, but that can't be accounted for with math and requires a single IF. If they are equal, val_slider is exactly B (or A, as they are equal).
So i'm implementing a heuristic algorithm, and i've come across this function.
I have an array of 1 to n (0 to n-1 on C, w/e). I want to choose a number of elements i'll copy to another array. Given a parameter y, (0 < y <= 1), i want to have a distribution of numbers whose average is (y * n). That means that whenever i call this function, it gives me a number, between 0 and n, and the average of these numbers is y*n.
According to the author, "l" is a random number: 0 < l < n . On my test code its currently generating 0 <= l <= n. And i had the right code, but i'm messing with this for hours now, and i'm lazy to code it back.
So i coded the first part of the function, for y <= 0.5
I set y to 0.2, and n to 100. That means it had to return a number between 0 and 99, with average 20.
And the results aren't between 0 and n, but some floats. And the bigger n is, smaller this float is.
This is the C test code. "x" is the "l" parameter.
//hate how code tag works, it's not even working now
int n = 100;
float y = 0.2;
float n_copy;
for(int i = 0 ; i < 20 ; i++)
{
float x = (float) (rand()/(float)RAND_MAX); // 0 <= x <= 1
x = x * n; // 0 <= x <= n
float p1 = (1 - y) / (n*y);
float p2 = (1 - ( x / n ));
float exp = (1 - (2*y)) / y;
p2 = pow(p2, exp);
n_copy = p1 * p2;
printf("%.5f\n", n_copy);
}
And here are some results (5 decimals truncated):
0.03354
0.00484
0.00003
0.00029
0.00020
0.00028
0.00263
0.01619
0.00032
0.00000
0.03598
0.03975
0.00704
0.00176
0.00001
0.01333
0.03396
0.02795
0.00005
0.00860
The article is:
http://www.scribd.com/doc/3097936/cAS-The-Cunning-Ant-System
pages 6 and 7.
or search "cAS: cunning ant system" on google.
So what am i doing wrong? i don't believe the author is wrong, because there are more than 5 papers describing this same function.
all my internets to whoever helps me. This is important to my work.
Thanks :)
You may misunderstand what is expected of you.
Given a (properly normalized) PDF, and wanting to throw a random distribution consistent with it, you form the Cumulative Probability Distribution (CDF) by integrating the PDF, then invert the CDF, and use a uniform random predicate as the argument of the inverted function.
A little more detail.
f_s(l) is the PDF, and has been normalized on [0,n).
Now you integrate it to form the CDF
g_s(l') = \int_0^{l'} dl f_s(l)
Note that this is a definite integral to an unspecified endpoint which I have called l'. The CDF is accordingly a function of l'. Assuming we have the normalization right, g_s(N) = 1.0. If this is not so we apply a simple coefficient to fix it.
Next invert the CDF and call the result G^{-1}(x). For this you'll probably want to choose a particular value of gamma.
Then throw uniform random number on [0,n), and use those as the argument, x, to G^{-1}. The result should lie between [0,1), and should be distributed according to f_s.
Like Justin said, you can use a computer algebra system for the math.
dmckee is actually correct, but I thought that I would elaborate more and try to explain away some of the confusion here. I could definitely fail. f_s(l), the function you have in your pretty formula above, is the probability distribution function. It tells you, for a given input l between 0 and n, the probability that l is the segment length. The sum (integral) for all values between 0 and n should be equal to 1.
The graph at the top of page 7 confuses this point. It plots l vs. f_s(l), but you have to watch out for the stray factors it puts on the side. You notice that the values on the bottom go from 0 to 1, but there is a factor of x n on the side, which means that the l values actually go from 0 to n. Also, on the y-axis there is a x 1/n which means these values don't actually go up to about 3, they go to 3/n.
So what do you do now? Well, you need to solve for the cumulative distribution function by integrating the probability distribution function over l which actually turns out to be not too bad (I did it with the Wolfram Mathematica Online Integrator by using x for l and using only the equation for y <= .5). That however was using an indefinite integral and you are really integration along x from 0 to l. If we set the resulting equation equal to some variable (z for instance), the goal now is to solve for l as a function of z. z here is a random number between 0 and 1. You can try using a symbolic solver for this part if you would like (I would). Then you have not only achieved your goal of being able to pick random ls from this distribution, you have also achieved nirvana.
A little more work done
I'll help a little bit more. I tried doing what I said about for y <= .5, but the symbolic algebra system I was using wasn't able to do the inversion (some other system might be able to). However, then I decided to try using the equation for .5 < y <= 1. This turns out to be much easier. If I change l to x in f_s(l) I get
y / n / (1 - y) * (x / n)^((2 * y - 1) / (1 - y))
Integrating this over x from 0 to l I got (using Mathematica's Online Integrator):
(l / n)^(y / (1 - y))
It doesn't get much nicer than that with this sort of thing. If I set this equal to z and solve for l I get:
l = n * z^(1 / y - 1) for .5 < y <= 1
One quick check is for y = 1. In this case, we get l = n no matter what z is. So far so good. Now, you just generate z (a random number between 0 and 1) and you get an l that is distributed as you desired for .5 < y <= 1. But wait, looking at the graph on page 7 you notice that the probability distribution function is symmetric. That means that we can use the above result to find the value for 0 < y <= .5. We just change l -> n-l and y -> 1-y and get
n - l = n * z^(1 / (1 - y) - 1)
l = n * (1 - z^(1 / (1 - y) - 1)) for 0 < y <= .5
Anyway, that should solve your problem unless I made some error somewhere. Good luck.
Given that for any values l, y, n as described, the terms you call p1 and p2 are both in [0,1) and exp is in [1,..) making pow(p2, exp) also in [0,1) thus I don't see how you'd ever get an output with the range [0,n)
I'm in a strange situation where I have a value of 0.5 and I want to convert the values from 0.5 to 1 to be a percentage and from 0.5 to 0 to be a negative percentage.
As it says in the title 0.4 should be -20%, 0.3 should be -40% and 0.1 should be -80%.
I'm sure this is a simple problem, but my mind is just refusing to figure it out :)
Can anyone help? :)
What we want to do is to scale the range (0; 1) to (-100; 100):
percentage = (value - 0.5) * 200;
The subtraction transforms the value so that it's in the range (-0.5; 0.5), and the multiplication scales it to the range of (-100; 100).
percent = ((value - 0.5) / 0.5) * 100
This will generate from -100 to 100. You want to subtract your zero value (0.5) from the given value, and divide by the range that should give 100% (also 0.5 in your example). Then multiply by 100 to convert to percentage.
Normalize it, and you're done:
// Assuming x is in the range (0,1)
x *= 2.0; // x is in the range (0,2)
x -= 1.0; // (-1,1)
x *= 100; // (-100,100)