Maple solves the following problem incorrectly when using ShowSolution function which is in student.calculus1 package. It's works fine when the power of x variable is odd or when I write sin(n*x) but when I wrote x^(even number)cos(nx) it's calculated incorrectly. Or when I put a number instead of n it's calculated correctly. Do I miss something? :|
It looks like a bug (and I have submitted a bug report), going wrong at the first step.
As workaround, you could do this as a first step,
restart;
with(Student:-Calculus1):
ee := Int( x^2*cos(n*x), x=-Pi..Pi ):
new := rhs( Rule[parts, x^2, sin(n*x)/n]( ee ) ) assuming n::integer;
-(Int(2*sin(n*x)*x/n, x = -Pi .. Pi))
ShowSolution( new ) assuming n::integer;
which produces 4*(-1)^n*Pi/n^2 at the final step.
Or do those steps without the assumptions on n, and then simplify the final result under assuming n::integer.
Related
I am using Gurobi through the JuMP package in Julia to solve a mixed-integer program.
I would like to obtain a graph
like this one, where also a solution based on Python is provided (which was also addressed on
Gurobi community form).
However, I have not found working solutions for Julia calling Gurobi through JuMP.
I understand that callback functions have to be used (such as this suggestion or even the main documentation here), but I do not fully understand how they work and what is essential to achieve my goal.
Any help is much appreciated, as well as a possible description of what the callback function is doing at each step.
If it helps, I am using Gurobi (v.9.0.0), JuMP (v0.20.1), MathOptInterface (v0.9.22) and Julia (v.1.3.0).
You need to use the C API. Here is a translation of Eli's answer on the Gurobi forum:
using JuMP, Gurobi
model = direct_model(Gurobi.Optimizer())
N = 30
#variable(model, x[1:N], Bin)
#constraint(model, rand(N)' * x <= 10)
#objective(model, Max, rand(N)' * x)
data = Any[]
start_time = 0.0
function my_callback_function(cb_data, cb_where::Cint)
#show cb_where
if cb_where == GRB_CB_MIP
objbst = Ref{Cdouble}()
GRBcbget(cb_data, cb_where, GRB_CB_MIP_OBJBST, objbst)
objbnd = Ref{Cdouble}()
GRBcbget(cb_data, cb_where, GRB_CB_MIP_OBJBND, objbnd)
push!(data, (time() - start_time, objbst[], objbnd[]))
end
return
end
MOI.set(model, Gurobi.CallbackFunction(), my_callback_function)
start_time = time()
optimize!(model)
open("data.csv", "w") do io
for x in data
println(io, join(x, ", "))
end
end
p.s. please update to Julia 1.6 and JuMP 0.22. I have not tested whether this works on the older version.
I want to run around 100 simulations with my model changing two parameters f and TLoadand track the changes on the phase currents currentSensor.i[1] etc.
Now I'm stuck with the documentation on the Wolfram website because there is no definite explanation on how to use scripting with the SystemModeler. I found for example this link on the Wolfram site with some code but no explanation in which commandline I should use it.
I downloaded the WolframScript program and tried to open my model with wolframscript -file SMPM_VoltageSource_Inverter.mo but it says ToExpression::sntx: Invalid syntax in or before ... eventhouh my model simulates totally fine and without any errors in the SimulationCenter.
Can someone explain to me:
Is it possible to write scripts ?
If Yes:
How can I simulate my model?
How can I do a parameter sweep of f and TLoad? Is it as described in the link?
Is it possible to export data of currentSensor.i[1] as a csv-file? And how to?
Thank you for any help!
I don't know about wolfram sorry, but for OpenModelica the following works:
// to load Model from file use
// loadFile("fileName.mo");
loadString("
model M
parameter Real a = 1;
Real x;
equation
x = a * sin(time);
end M;
"); getErrorString();
buildModel(M); getErrorString();
for a in {1,2,3,4} loop
str_a := String(a); getErrorString();
system("./M -override a=" + str_a); getErrorString();
// for windows use
//system("M.exe -override a=" + str_a); getErrorString();
system("mv M_res.mat " + "M_" + str_a + ".mat");
end for;
Put this in a file named for example model.mos and call it from terminal or command line, depending on your os, with omc model.mos if you have OpenModelica installed. this should generate a csv.
EDIT: I realized the original just saves the last value of x, you might want the full output. Therefore i changed the .mos-file. Each different result will be saved in a different file, if you want to change it to csv you just have to change the generated xml.
I give a simple example of what I want to do in Matlabs MuPad
S := matrix([[0,S_1,S_2]]);
sum(S[k]*(k < 2)* S[k] * (TRUE), k=1..3)
should be: "S_1^2 + S_2"
however I get: Error: The first argument must be of type 'Type::Arithmetical'. [sum]
I understand the error, I just don't know how to succeed.
Advice appreciated. I'm looking for some kind of indicator function.
The question:
Start with the inner term. To have a valid number 0 or 1, I used the following expression:
piecewise([A[k]>a*B[l],1],[Otherwise,0])
The rest is straight forward:
sum(sum(A[k]*B[l]*piecewise([A[k]>a*B[l],1],[Otherwise,0]), l=1..L), k=1..K)
S := matrix([[0,S_1,S_2]]);
sum(S[k]^(4-k), k=1..3)
I'm to really sure what you are trying to do.
I've been looking throught the documentation, but can't seem to find the bit I want.
I have a for loop and I would like to be able to view every value in the for loop.
for example here is a part of my code:
for d = 1 : nb
%for loop performs blade by blade averaging and produces a column vector
for cc = navg : length(atbmat);
atb2 = (sum(atbmat((cc-(navg-1):cc),d)))/navg;
atbvec2(:,cc) = atb2;
end
%assigns column vector 'atbvec2' to the correct column of the matrix 'atbmat2'
atbmat2(d,1:length(atbvec2)) = atbvec2;
end
I would like to view every value of atb2. I'm a python user(new to MATLAB) and would normally use a simple print statement to find this.
I'm sure there is a way to do it, but I can't quite find how.
Thankyou in advance.
you can use disp in Matlab to print to the screen but you might want to use sprintf first to format it nicely. However for debugging you're better off using a break point and then inspect the variable in the workspace browser graphically. To me, this is one of Matlab's best features.
Have a look at the "Examine Values" section of this article
The simplest way to view it everywhere is to change this line:
atb2 = (sum(atbmat((cc-(navg-1):cc),d)))/navg;
Into this, without semicolon:
atb2 = (sum(atbmat((cc-(navg-1):cc),d)))/navg
That being said, given the nature of your calculation, you could get the information you need as well by simply storing every value of abt2 and observing them afterwards. This may be done in atbmat2 already?
If you want to look at each value at the time it happens, consider setting a breakpoint or conditional breakpoint after the line where abt2 is assigned.
I have problem with the following code:
.
.
.
a=zeros(1000,ctimes);
a1=zeros(1000,ctimes);
hold all
for i=num1:num2;
colors=Lines(i);
switch phantom
case 1
path=['E:\filename\'];
path1=['E:\filename2\'];
n=['S',num2str(emt),'_',num2str(i),'.m'];
d=load([path,name]);
a(:,i)=complex(d(:,2),d(:,3)));
n1=['S',num2str(emt),'_',num2str(i),'.m'];
d1=load([path1,name1]);
a1(:,i)=complex(d1(:,2),d1(:,3)));
the problem is that a(:,i) can not be defined. while there is no problem or with complex(d1(:,2),d1(:,3))) , can any expert body help me plz?!
thank you ...
Are you sure you are forming your file name correctly? You are doing something to create a variable n, but using a variable name when you form the path. Here are some recommended debugging steps:
1) make sure the file path is formed correctly:
filePath = fullfile(path, name);
disp(filePath);
The fullfile function concatenates elements of a file path & name, and takes care of using the right file path separator (good for portable code, stops you having to remember to add a / or \ to the end of a file path, etc).
2) check that d is loaded correctly:
clear d;
d = load(filePath);
disp(size(d));
3) check the size of the complex quantity you compute before assigning it to a(:,i):
temp = complex(d(:,2), d(:,3));
disp(size(temp));
By the time you have done these things, you should have found your problem (the dimensions of temp should be [1000 1] to match the size of a(:,i), of course).
As an aside, you should avoid using i as a variable name, especially when you are using complex numbers, since its built-in value is sqrt(-1). Thus, c = a + i * b; would create a complex number (a,b) and put it into c - until you change the meaning of i. A simple solution is to use ii. The same is true for j, by the way. It is one of the unfortunate design decisions in Matlab that you can overwrite built in values like that...