I want to find some numbers in Matlab (denominated below p11,..., p119) satisfying a bunch of inequalities (specifically, 16 inequalities). I want Matlab to keep searching until it finds such numbers. I thought about using while as below but it does no work. What is wrong? How can I proceed?
clear
rng default
%% SOME INITIAL VALUES
p11=0.3;
p12=0.4;
p13=0.1;
p14=0.2;
p15=0.2;
p16=0.2;
p17=0.06;
p18=0.03;
p19=0.02;
p110=0.04;
p111=0.07;
p112=50;
p113=0.02;
p114=0.03;
p115=0.01;
p116=0.08;
p117=0.01;
p118=0.1;
p119=0.07;
while ... %CONDITION THAT SHOULD BE SATISFIED (16 CONDITIONS)
((p11<=(p15+p19+p110+p111+p115+p116+p117+p119))+...
(p12<=(p16+p19+p112+p113+p115+p117+p118+p119))+...
(p13<=(p17+p110+p112+p114+p116+p117+p118+p119))+...
(p14<=(p18+p111+p113+p114+p115+p116+p118+p119))+...
(p11+p12<=(p15+p19+p110+p111+p115+p116+p117+p119+...
p16+p112+p113+p118))+...
(p11+p13<=(p15+p19+p110+p111+p115+p116+p117+p119+...
p17+p112+p114+p118))+...
(p11+p14<=(p15+p19+p110+p111+p115+p116+p117+p119+...
p18+p113+p114+p118))+...
(p12+p13<=(p16+p19+p112+p113+p115+p117+p118+p119+...
p17+p110+p114+p116))+...
(p12+p14<=(p16+p19+p112+p113+p115+p117+p118+p119+...
p18+p111+p114+p116))+...
(p13+p14<=(p17+p110+p112+p114+p116+p117+p118+p119+...
p18+p111+p113+p115))+...
(p11+p12+p13<=(p15+p19+p110+p111+p115+p116+p117+p119+...
p16+p112+p113+p118+...
p17+p114))+...
(p11+p12+p14<=(p15+p19+p110+p111+p115+p116+p117+p119+...
p16+p112+p113+p118+...
p18+p114))+...
(p11+p13+p14<=(p15+p19+p110+p111+p115+p116+p117+p119+...
p17+p112+p114+p118+...
p18+p113))+...
(p12+p13+p14<=(p16+p19+p112+p113+p115+p117+p118+p119+...
p17+p110+p114+p116+...
p18+p111))+...
(p11+p12+p13+p14==1)+...
(p15+p16+p17+p18+p19+p110+p111+p112+p113+p114+p115+p116+p117+p118+p119==1))~=15
% IF THE CONDITION IS NOT SATISFIED KEEP SEARCHING BY GUESSING
% OTHER NUMBERS
p11=unifrnd(0,1);
p12=unifrnd(0,1);
p13=unifrnd(0,1);
p14=unifrnd(0,1);
p15=unifrnd(0,1);
p16=unifrnd(0,1);
p17=unifrnd(0,1);
p18=unifrnd(0,1);
p19=unifrnd(0,1);
p110=unifrnd(0,1);
p111=unifrnd(0,1);
p112=unifrnd(0,1);
p113=unifrnd(0,1);
p114=unifrnd(0,1);
p115=unifrnd(0,1);
p116=unifrnd(0,1);
p117=unifrnd(0,1);
p118=unifrnd(0,1);
p119=unifrnd(0,1);
end
The while loop will run while the condition is true. If false it terminates. Your test conditions is while .... ~= 15. This is false as the initial guesses result in 15 out of 16 trues. Since 15 ~= 15 is false, the while loop doesn't run.
One way to fix the issue is to change from ~= to ==. This will run through and find a solution to that condition.
You could have seen this by creating a variable called tests and populated it like this:
tests = [(p11<=(p15+p19+p110+p111+p115+p116+p117+p119));...
... skipped a bunch of stuff ...
(p15+p16+p17+p18+p19+p110+p111+p112+p113+p114+p115+p116+p117+p118+p119==1)];
sum(tests)
ans = 15
Or any other way of tracking that value.
Related
I am new to Julia and trying to use the Julia package DifferentialEquations to simultaneously solve for several conditions of the same set of coupled ODEs. My system is a model of an experiment and in one of the conditions, I increase the amount of one of the dependent variables at mid-way through the process.
I would like to be able to adjust the condition of this single trajectory, however so far I am only able to adjust all the trajectories at once. Is it possible to access a single one using callbacks? If not, is there a better way to do this?
Here is a simplified example using the lorentz equations for what I want to be doing:
#Differential Equations setup
function lorentz!(du,u,p,t)
a,r,b=p
du[1]= a*(u[2]-u[1])
du[2]=u[1]*(r-u[3])-u[2]
du[3]=u[1]*u[2]-b*u[3];
end
#function to cycle through inital conditions
function prob_func(prob,i,repeat)
remake(prob; u0 = u0_arr[i]);
end
#inputs
t_span=[(0.0,100.0),(0.0,100.0)];
u01=[0.0;1.0;0.0];
u02=[0.0;1.0;0.0];
u0_arr = [u01,u02];
p=[10.,28.,8/3];
#initialising the Ensemble Problem
prob = ODEProblem(lorentz!,u0_arr[1],t_span[1],p);
CombinedProblem = EnsembleProblem(prob,
prob_func = prob_func, #-> (prob),#repeat is a count for how many times the trajectories had been repeated
safetycopy = true # determines whether a safetly deepcopy is called on the prob before the prob_func (sounds best to leave as true for user-given prob_func)
);
#introducing callback
function condition(u,t,repeat)
return 50 .-t
end
function affect!(repeat)
repeat.u[1]=repeat.u[1] +50
end
callback = DifferentialEquations.ContinuousCallback(condition, affect!)
#solving
sim=solve(CombinedProblem,Rosenbrock23(),EnsembleSerial(),trajectories=2,callback=callback);
# Plotting for ease of understanding example
plot(sim[1].t,sim[1][1,:])
plot!(sim[2].t,sim[2][1,:])
I want to produce something like this:
Example_desired_outcome
But this code produces:
Example_current_outcome
Thank you for your help!
You can make that callback dependent on a parameter and make the parameter different between problems. For example:
function f(du,u,p,t)
if p == 0
du[1] = 2u[1]
else
du[1] = -2u[1]
end
du[2] = -u[2]
end
condition(t,u,integrator) = u[2] - 0.5
affect!(integrator) = integrator.prob.p = 1
For more information, check out the FAQ on this topic: https://diffeq.sciml.ai/stable/basics/faq/#Switching-ODE-functions-in-the-middle-of-integration
I have the following code that generates a matrix of 15 blocks that will then be used in a Montecarlo approach as multiple starting points. How can I get the same exact result in a smarter way?
assume that J=15*100 are the total simulation and paramNum the number of parameters
[10^-10*ones(paramNum,round(J/15)) 10^-9*ones(paramNum,round(J/15)) 10^-8*ones(paramNum,round(J/15)) 10^-7*ones(paramNum,round(J/15)) 10^-6*ones(paramNum,round(J/15)) 10^-5*ones(paramNum,round(J/15)) rand*10^-5*ones(paramNum,round(J/15)) 10^-4*ones(paramNum,round(J/15)) rand*10^-4*ones(paramNum,round(J/15)) 10^-3*ones(paramNum,round(J/15)) 10^-2*ones(paramNum,round(J/15)) 10^-1*ones(paramNum,round(J/15)) 10^-abs(randn/2)*ones(paramNum,round(J/15))];
you could do
v = 10.^[-10:-5 rand*10^-5 -4:-1 10^-abs(randn/2)];
repmat(repelem(v, 1, round(J/15)), paramNum) .* ...
repmat(ones(paramNum,round(J/15)), numel(v))
Or mimic the repmat/repelem functionality with a for loop. The first is shorter, the later is more understandable.
By the way... it's less than 15 blocks...
options = optimset('Display','iter','MaxIter',3,'OutputFcn',#outfun);
[x,fval,~,output] = fminsearch(#(param) esm6(param,identi),result(k,1:end-1),options);
This code will find the local Minimum of my esm6 function and due to the 'Display' Option it will Output strings like this
Iteration Func-count min f(x) Procedure
0 1 36.9193
1 5 35.9815 initial simplex
2 7 35.4924 contract inside
3 9 35.4924 contract inside
4 11 33.0085 expand
So in the command window, i get the function Count for each Iteration step. The structure output, which is created by fminsearch has only the total amount of func-count in it. Is there a way to receive all the Information, that is outputed in the command window also in the Output-structure?
EDIT:
I think i'm pretty Close to the solution. I wrote this outputfunction:
function stop = outfun(x,optimvalues,state);
stop = false;
if state == 'iter'
history = evalin('base','history');
history = [history; optimvalues.iteration optimvalues.funcCount];
assignin('base','history',history);
end
end
due to http://de.mathworks.com/help/matlab/math/output-functions.html this should work, but in fact, matlab tells me,
??? Reference to non-existent field 'funcCount'.
any idea, why this happens?
I have the following codes which I wish to have an output matrix Rpp of (10201,3). I run this code (which takes a bit long) then I check the matrix size of Rpp and I see (1,3), I tried so many things I couldn't find any proper way. The logic of the codes is to take the 6 values (contain 4 constant values and 2 variable values (chosen from 101 values)) and make the calculation for 3 different i1 and store every output vector of 3 in a matrix with (101*101 (pairs of those 2 variable values)) rows and 3 (for each i1) columns.
I appreciate your help
Vp1=linspace(3000,3500,101);
Vp2=3850;
rho1=2390;
rho2=2510;
Vs1=linspace(1250,1750,101);
Vs2=2000;
i1=[10 25 40];
Rpp = zeros(length(Vp1)*length(Vs1),length (i1));
for n=1:length(Vp1)*length(Vs1)
for m=1:length (i1)
for l=1:length(Vp1)
for k=1:length(Vs1)
p=sin(i1)/Vp1(l);
i2=asin(p*Vp2);
j1=asin(p*Vs1(k));
j2=asin(p*Vs2);
a=rho2*(1-2*Vs2^2*p.^2)-rho1*(1-2*Vs1(k).^2*p.^2);
b=rho2*(1-2*Vs2^2*p.^2)+2*rho1*Vs1(k)^2*p.^2;
c=rho1*(1-2*Vs1(k)^2*p.^2)+2*rho2*Vs2^2*p.^2;
d=2*(rho2*Vs2^2-rho1*Vs1(k)^2);
E=b.*cos(i1)./Vp1(l)+c.*cos(i2)/Vp2;
F=b.*cos(j1)./Vs1(k)+c.*cos(j2)/Vs2;
G=a-d*(cos(i1)/Vp1(l)).*(cos(j2)/Vs2);
H=a-d*(cos(i2)/Vp2).*(cos(j1)/Vs1(k));
D=E.*F+G.*H.*p.^2;
Rpp=((b.*(cos(i1)/Vp1(l))-c.*cos((i2)/Vp2)).*F-(a+d*((cos(i1)/Vp1(l))).*(cos(j2)/Vs2)).*H.*p.^2)./D
end
end
end
end
Try this. You 2 outer loops didn't do anything. You never used m or n so I killed those 2 loops. Also you just kept overwriting Rpp on every loop so your initialization of Rpp didn't do anything. I added an index var to assign the results to the equation to what I think is the correct part of Rpp.
Vp1=linspace(3000,3500,101);
Vp2=3850;
rho1=2390;
rho2=2510;
Vs1=linspace(1250,1750,101);
Vs2=2000;
i1=[10 25 40];
Rpp = zeros(length(Vp1)*length(Vs1),length (i1));
index = 1;
for l=1:length(Vp1)
for k=1:length(Vs1)
p=sin(i1)/Vp1(l);
i2=asin(p*Vp2);
j1=asin(p*Vs1(k));
j2=asin(p*Vs2);
a=rho2*(1-2*Vs2^2*p.^2)-rho1*(1-2*Vs1(k).^2*p.^2);
b=rho2*(1-2*Vs2^2*p.^2)+2*rho1*Vs1(k)^2*p.^2;
c=rho1*(1-2*Vs1(k)^2*p.^2)+2*rho2*Vs2^2*p.^2;
d=2*(rho2*Vs2^2-rho1*Vs1(k)^2);
E=b.*cos(i1)./Vp1(l)+c.*cos(i2)/Vp2;
F=b.*cos(j1)./Vs1(k)+c.*cos(j2)/Vs2;
G=a-d*(cos(i1)/Vp1(l)).*(cos(j2)/Vs2);
H=a-d*(cos(i2)/Vp2).*(cos(j1)/Vs1(k));
D=E.*F+G.*H.*p.^2;
Rpp(index,:)=((b.*(cos(i1)/Vp1(l))-c.*cos((i2)/Vp2)).*F-(a+d*((cos(i1)/Vp1(l))).*(cos(j2)/Vs2)).*H.*p.^2)./D;
index = index+1;
end
end
Results:
>> size(Rpp)
ans =
10201 3
The way you use the for loop is wrong. You're running the calculation for length(Vp1)*length(Vs1) * length (i1) * length(Vp1) * length(Vs1) times. Here's the correct way. I changed l into lll just so I won't confuse it with the number 1. In each iteration of the first for loop, you're running length(Vs1) times, and you need to assign the result (a 1X3 array) to the Rpp by using a row number specified by k+(lll-1)*length(Vp1).
for lll=1:length(Vp1)
for k=1:length(Vs1)
p=sin(i1)/Vp1(lll);
i2=asin(p*Vp2);
j1=asin(p*Vs1(k));
j2=asin(p*Vs2);
a=rho2*(1-2*Vs2^2*p.^2)-rho1*(1-2*Vs1(k).^2*p.^2);
b=rho2*(1-2*Vs2^2*p.^2)+2*rho1*Vs1(k)^2*p.^2;
c=rho1*(1-2*Vs1(k)^2*p.^2)+2*rho2*Vs2^2*p.^2;
d=2*(rho2*Vs2^2-rho1*Vs1(k)^2);
E=b.*cos(i1)./Vp1(lll)+c.*cos(i2)/Vp2;
F=b.*cos(j1)./Vs1(k)+c.*cos(j2)/Vs2;
G=a-d*(cos(i1)/Vp1(lll)).*(cos(j2)/Vs2);
H=a-d*(cos(i2)/Vp2).*(cos(j1)/Vs1(k));
D=E.*F+G.*H.*p.^2;
Rpp(k+(lll-1)*length(Vp1),:)=((b.*(cos(i1)/Vp1(lll))-c.*cos((i2)/Vp2)).*F-(a+d*((cos(i1)/Vp1(lll))).*(cos(j2)/Vs2)).*H.*p.^2)./D;
end
end
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.