I know similar questions have been answered before but none of the answers I could find were specific to .NET.
Does the VB.NET compiler optimize expressions like:
x = y / 4
by compiling:
x = y * 0.25
And before anyone says don't worry the difference is small, i already know that but this will be executed a lot and choosing one over the other could make a useful difference in total execution time and will be much easier to do than a more major refactoring exercise.
Perhaps I should have mentioned for the benefit of those who live in an environment of total freedom: I am not at liberty to change to a different language. If I were I would probably have written this code in Fortran.
As suggested here is a simple comparison:
Dim y = 1234.567
Dim x As Double
Dim c = 10000000000.0
Dim ds As Date
Dim df As Date
ds = Now
For i = 1 To c
x = y / 4
Next
df = Now
Console.WriteLine("divide " & (df - ds).ToString)
ds = Now
For i = 1 To c
x = y * 0.25
Next
df = Now
Console.WriteLine("multiply " & (df - ds).ToString)
The output is:
divide 00:00:52.7452740
multiply 00:00:47.2607256
So divide does appear to be slower by about 10%. But this difference is so small that I suspected it to be accidental. Another two runs give:
divide 00:00:45.1280000
multiply 00:00:45.9540000
divide 00:00:45.9895985
multiply 00:00:46.8426838
Suggesting that in fact the optimization is made or that the arithmetic operations are a vanishingly small part of the total time.
In either case it means that I don't need to care which is used.
In fact ildasm shows that the IL uses div in the first loop and mul in the second. So it doesn't make the subsitution after all. Unless the JIT compiler does.
Related
I have 4 non negative real variable that are A, B, C and X. Based on the current problem that I have, I notice that the variable X must belong to the interval of [B,C] and the relation will be a bunch of if-else conditions like this:
If A < B:
x = B
elseif A > C:
x = C
elseif B<=A<=C:
x = A
As you can see, it quite difficult to reformulate as a Mixed Integer Programming problem with corresponding decision variable (d1, d2 and d3). I have try reading some instructions regarding if-then formulation using big M method at this site:
https://www.math.cuhk.edu.hk/course_builder/1415/math3220/L2%20(without%20solution).pdf but it seem that this problem is more challenging than their tutorial.
Could you kindly provide me with a formulation for this situation ?
Thank you very much !
Suppose we have N (in this example N = 3) events that can happen depending on some variables. Each of them can generate certain profit or loses (event1 = 300, event2 = -100, event3 = 200), they are constrained by rules when they happen.
event 1 happens only when x > 5,
event 2 happens only when x = 2 and y = 3
event 3 happens only when x is odd.
The problem is to know the maximum profit.
Assume x, y are integer numbers >= 0
In the real problem there are many events and many dimensions.
(the solution should not be specific)
My question is:
Is this linear programming problem? If yes please provide solution to the example problem using this approach. If no please suggest some algorithms to optimize such problem.
This can be formulated as a mixed integer linear program. This is a linear program where some of the variables are constrained to be integer. Contrary to linear programs, solving the general integer program is NP-hard. However, there are many commercial or open source solvers that can solve efficiently large-scale problems. For up to 300 variables and constraints, you can use excel's solver.
Here is a way to formulate the above constraints:
If you go down this route, you might find this document useful.
the last constraint in an interesting one. I am assuming that x has to be integer, but if x can be either integer or continuous I will edit the answer accordingly.
I hope this helps!
Edit: L and U above should be interpreted as L1 and U1.
Edit 2: z2 needs to changed to (1-z2) on the 3rd and 4th constraint.
A specific answer:
seems more like a mathematical calculation than a programming problem, can't you just run a loop for x= 1->1000 to see what results occur?
for the example:
as x = 2 or 3 = -200 then x > 2 or 3, and if x < 5 doesn't get the 300, so all that is really happening is x > 5 and x = odd = maximum results.
x = 7 = 300 + 200 . = maximum profit for x
A general answer:
I don't see how to answer the question without seeing what the events are and how the events effect X ? Weather it's a linear or functional (mathematical) answer seems rather beside the point of finding the desired solution.
I have the following line of code:
SomeDouble= constant1/ ((a * b) * (Math.Asin((c- a) / (a * d)) + constant2))
The two constants are different and calculated out of the loops, a - d are variables that change each time.
And on the face of it it's pretty fast 0.002ms on average (47,633.588s for 26,508,249 hits). The issue I'm having is it's going to be called billions of times, literally around 20 billion hits each time the software is run. So if I can cut this down to 0.001ms the difference will be substantial. I know that dividing is a very slow process and I expect calculating arcsin is also slow. If anyone can suggest if there's a faster method of calculating arcsin or any other help in speeding up this line of code that would be great. On a side note any advice on whether vb.net's built in math functions are optimised for speed would be great I've noticed that math.sqrt(somevalue) is quicker than (somevalue)^0.5.
Thanks in advanced!
I'd do some tests to make sure that the Math.Asin really is the slowest part of the formula. If it really is slow relative to the other multiplications and divisions, then you could try implementing your own lookup table for Math.Asin. In other words, calculate millions of Math.Asin values in advance, and code them into your program. This would trade the size of your program for speed, so if program size doesn't matter, it might help.
You can use the following approximation for Asin, in my tests it was just under twice as fast as Math.Asin (32bit, better if manually inlined, under 64bit it was slightly better than twice as fast) and it looked reasonably accurate, but you'd have to test whether the accuracy is acceptable.
static double Asin(double x)
{
double x2 = x * x;
double x3 = x2 * x;
const double piover2 = 1.5707963267948966;
const double a = 1.5707288;
const double b = -0.2121144;
const double c = 0.0742610;
const double d = -0.0187293;
return piover2 - Math.Sqrt(1 - x) * (a + b * x + c * x2 + d * x3);[]
}
(this is C# of course, but you can convert it I'm sure)
[EDIT]
Here is the VB version.
Shared Function Asin(ByVal x As Double) As Double
Dim x2 As Double = x * x
Dim x3 As Double = x2 * x
Const piover2 As Double = 1.5707963267948966
Const a As Double = 1.5707288
Const b As Double = -0.2121144
Const c As Double = 0.0742610
Const d As Double = -0.0187293
Return piover2 - Math.Sqrt(1 - x) * (a + b * x + c * x2 + d * x3)
End Function
You could try to implement the series expansion to whatever precision you require, and compare that against Stochastically's suggestion of a lookup table (which may well be how Math.asin ultimately calculates it) built to the precision required. It seems unlikely that you could enjoy the halving of processing time you'd like, however.
If the calculations aren't meaningfully dependent upon one another (or if the dependencies can be isolated into different batches), you might try to run them in parallel (whether on different systems or with different processors), but be wary -- I worked at a space physics lab, and we found that the precision we required generated really annoying anomalies when we ran tests on different systems.
(I also must say, I'm incredibly curious as to why you'd need to run billions of arc-sine calculations.)
I'm sorry the title is so confusingly worded, but it's hard to condense this problem down to a few words.
I'm trying to find the minimum value of a specific equation. At first I'm looping through the equation, which for our purposes here can be something like y = .245x^3-.67x^2+5x+12. I want to design a loop where the "steps" through the loop get smaller and smaller.
For example, the first time it loops through, it uses a step of 1. I will get about 30 values. What I need help on is how do I Use the three smallest values I receive from this first loop?
Here's an example of the values I might get from the first loop: (I should note this isn't supposed to be actual code at all. It's just a brief description of what's happening)
loop from x = 1 to 8 with step 1
results:
x = 1 -> y = 30
x = 2 -> y = 28
x = 3 -> y = 25
x = 4 -> y = 21
x = 5 -> y = 18
x = 6 -> y = 22
x = 7 -> y = 27
x = 8 -> y = 33
I want something that can detect the lowest three values and create a loop. From theses results, the values of x that get the smallest three results for y are x = 4, 5, and 6.
So my "guess" at this point would be x = 5. To get a better "guess" I'd like a loop that now does:
loop from x = 4 to x = 6 with step .5
I could keep this pattern going until I get an absurdly accurate guess for the minimum value of x.
Does anybody know of a way I can do this? I know the values I'm going to get are going to be able to be modeled by a parabola opening up, so this format will definitely work. I was thinking that the values could be put into a column. It wouldn't be hard to make something that returns the smallest value for y in that column, and the corresponding x-value.
If I'm being too vague, just let me know, and I can answer any questions you might have.
nice question. Here's at least a start for what I think you should do for this:
Sub findMin()
Dim lowest As Integer
Dim middle As Integer
Dim highest As Integer
lowest = 999
middle = 999
hightest = 999
Dim i As Integer
i = 1
Do While i < 9
If (retVal(i) < retVal(lowest)) Then
highest = middle
middle = lowest
lowest = i
Else
If (retVal(i) < retVal(middle)) Then
highest = middle
middle = i
Else
If (retVal(i) < retVal(highest)) Then
highest = i
End If
End If
End If
i = i + 1
Loop
End Sub
Function retVal(num As Integer) As Double
retVal = 0.245 * Math.Sqr(num) * num - 0.67 * Math.Sqr(num) + 5 * num + 12
End Function
What I've done here is set three Integers as your three Min values: lowest, middle, and highest. You loop through the values you're plugging into the formula (here, the retVal function) and comparing the return value of retVal (hence the name) to the values of retVal(lowest), retVal(middle), and retVal(highest), replacing them as necessary. I'm just beginning with VBA so what I've done likely isn't very elegant, but it does at least identify the Integers that result in the lowest values of the function. You may have to play around with the values of lowest, middle, and highest a bit to make it work. I know this isn't EXACTLY what you're looking for, but it's something along the lines of what I think you should do.
There is no trivial way to approach this unless the problem domain is narrowed.
The example polynomial given in fact has no minimum, which is readily determined by observing y'>0 (hence, y is always increasing WRT x).
Given the wide interpretation of
[an] equation, which for our purposes here can be something like y =
.245x^3-.67x^2+5x+12
many conditions need to be checked, even assuming the domain is limited to polynomials.
The polynomial order is significant, and the order determines what conditions are necessary to check for how many solutions are possible, or whether any solution is possible at all.
Without taking this complexity into account, an iterative approach could yield an incorrect solution due to underflow error, or an unfortunate choice of iteration steps or bounds.
I'm not trying to be hard here, I think your idea is neat. In practice it is more complicated than you think.
How do I use Excel VBA to find the minimum value of an equation?
For example, if I have the equation y = 2x^2 + 14, and I want to make a loop that will slowly increase/decrease the value of x until it can find the smallest value possible for y, and then let me know what the corresponding value of x is, how would I go about doing that?
Is there a method that would work for much more complicated equations?
Thank you for your help!
Edit: more details
I'm trying to design a program that will find a certain constant needed to graph a nuclear decay. This constant is a part of an equation that gets me a calculated decay. I'm comparing this calculated decay against a measured decay. However, the constant changes very slightly as the decay happens, which means I have to use something called a residual-square to find the best constant to use that will fit the entire decay best to make my calculated decay as accurate as possible.
It works by doing (Measured Decay - Calculated Decay) ^2
You do that for the decay at several times, and add them all up. What I need my program to do is to slowly increase and decrease this constant until I can find a minimum value for the value I get when I add up the residual-squared results for all the times using this decay. The residual-squared that has the smallest value has the value of the constant that I want.
I already drafted a program that does all the calculations and such. I'm just not sure how to find this minimum value. I'm sure if a method works for something like y = x^2 + 1, I can adapt it to work for my needs.
Test the output while looping to look for the smallest output result.
Here's an Example:
Sub FormulaLoop()
Dim x As Double
Dim y As Double
Dim yBest As Double
x = 1
y = (x ^ 2) + 14
yBest = y
For x = 2 To 100
y = (x ^ 2) + 14
If y < yBest Then
yBest = y
End If
Next x
MsgBox "The smallest output of y was: " & yBest
End Sub
If you want to loop through all the possibilities of two variables that make up x then I'd recommend looping in this format:
Sub FormulaLoop_v2()
Dim MeasuredDecay As Double
Dim CalculatedDecay As Double
Dim y As Double
Dim yBest As Double
MeasuredDecay = 1
CalculatedDecay = 1
y = ((MeasuredDecay - CalculatedDecay) ^ 2) + 14
yBest = y
For MeasuredDecay = 2 To 100
For CalculatedDecay = 2 To 100
y = ((MeasuredDecay - CalculatedDecay) ^ 2) + 14
If y < yBest Then
yBest = y
End If
Next CalculatedDecay
Next MeasuredDecay
MsgBox "The smallest output of y was: " & yBest
End Sub