Fixing a variable in JuMP / Julia - optimization

I have an AMPL code like this:
param N;
set R := 1..N;
set V := 1..N;
initializeSendPrepareReq{i in R, v in V}: SendPrepReq[1, i, v] = 0;
I need to write it in Julia using JuMP.
N = 10
R = 1:N
V = 1:N
?
I know I probably need to use JuMP.fix() but don't know how. Thank you


for i in R, v in V
fix(SendPrepReq[1, i, v], 0)
end
If SendPrepReq has other bounds, you need
for i in R, v in V
fix(SendPrepReq[1, i, v], 0; force = true)
end
Here is the relevant documentation: https://www.juliaopt.org/JuMP.jl/stable/variables/#JuMP.fix


Just use zeros() fonction
N=10
SendPrepReq=zeros(1,N,N) or SendPrepReq=zeros(Int,1,N,N)
Or if you really want to use for loop:
N=10
R = 1:N
V = 1:N
for r in R
for v in V
SendPrepReq[1,r,v]=0
end
end
If SendPrepReq is a variable:
for r in R
for v in V
#constraint(model, SendPrepReq[1,r,v] == 0 )
end
end

Related

Understanding issue in Scilab for my code

I am doing a projectile motion where i need to plot curves between position x and y for various angles but the scilab shows only one plot. I am confused.
My code below
function[H,R,T]=projectile(m,r,h,c,rho,theta,v0,x0,y0,t0)
g=9.8
A=%pi*r^2
k=c*rho*A/2;
i=1
t(i)=t0
x(i)=x0
y(i)=y0
for j=0:5
thetha=theta+j*15;
vx(i)=v0*cos(thetha*%pi/180);
vy(i)=v0*sin(thetha*%pi/180);
while (y(i)>=0)
v=sqrt(vx(i)^2+vy(i)^2);
t(i+1)=t(i)+h;
vx(i+1)=vx(i)-h*(k*v*vx(i)/m);
vy(i+1)=vy(i)-h*(g+k*v*vy(i)/m);
x(i+1)=x(i)+h*vx(i)
y(i+1)=y(i)+h*vy(i)
i=i+1;
end
plot(x(i),y(i),'.');
end
n=i-1
R=x(n)-x(1);
T=t(n);
H=max(y)
endfunction

You should use vectors to improve compacity and readability of your code. Here is my proposition of improved (and working) code:
function [H,R,T] = projectile(m,r,h,c,rho,theta0,v0,x0,y0,t0)
g = 9.81
A = %pi*r^2
k = c*rho*A/2;
for theta = theta0 + (0:15:75)
v = v0*[cos(theta*%pi/180); sin(theta*%pi/180)];
t = t0
xy = [x0;y0]
i = 1
while xy(2,i) >= 0
t(i+1) = t(i)+h;
v = v + h*([0;-g] - k*norm(v)*v/m);
xy(:,i+1) = xy(:,i) + h*v;
i = i+1;
end
plot(xy(1,:), xy(2,:));
end
R = xy(1,$) - xy(1,1);
T = t($);
H = max(xy(2,:))
endfunction
clf
[H,R,T] = projectile(1,0.1,0.001,2,1000,5,1,0,0,0)

CASE expression in WHERE clause for diferent and

Can I use case expression to build where like this?
select *
from table
where
case
when x=y then z= j and t=v
when x=k then q= p and s=l
end
;
I need change where clause depending on the value of x variable.

Use or:
select *
from table
where (x = y and z = j and t = v) or (x = k and q = p and s = l);

An alternative to using OR is to use nested CASE statements:
SELECT *
FROM table_name
WHERE CASE
WHEN x = y THEN CASE WHEN z = j AND t = v THEN 1 ELSE 0 END
WHEN x = k THEN CASE WHEN q = p AND s = l THEN 1 ELSE 0 END
ELSE 0
END = 1;
or you could simplify it to:
SELECT *
FROM table_name
WHERE CASE
WHEN x = y AND z = j AND t = v THEN 1
WHEN x = k AND q = p AND s = l THEN 1
ELSE 0
END = 1;
However, you should check whether Oracle can use column indexes or if a separate function-based index is required with these solutions.

How to find the value of integer k efficiently for which q divides b ^ k finitely?

We have given two integers b and q, and we want to find the minimum value of an integer 'k' for which q completely divides b^k or k does not exist. Can we find out the value of k efficiently? Not just iterating each value of k (0, 1, 2, 3, ...) and checking (b^k) % q == 0) where q <= k or q >= k.

First of all, k will never equal zero unless q=1. k will never equal one unless q=b.
Next, if you can factorize q and b, then you can reason about them.
If there are any prime factors of b that are not factors of q at all, then k does not exist. Otherwise, k has to be large enough so that every factor of b^k is represented in q.
Here's some pseudo-code:
if (q==1) return 0;
if (q==b) return 1;
// qfactors and bfactors are arrays, one element per factor
let qfactors = prime_factorization(q);
let bfactors = prime_factorization(b);
let kmin=0;
foreach (f in bfactors.unique) {
let bcount = bfactors.count(f);
let qcount = qfactors.count(f);
if (qcount==0 || qcount < bcount) return -1; // k does not exist
kmin_f = ceiling(bcount/qcount);
if (kmin_f > kmin) let kmin = kmin_f;
}
return kmin;

If q = 1 ; k = 0
If b = q ; k = 1
If b > q and factors ; k = 1
If b < q and factors ; k != I
If b != q and not factors ; k != I
We know,
Dividend = Divisor x Quotient + Reminder
=> Dividend = Divisor x Quotient [Here, Reminder = 0]
Now go for calculation of Maxima and Minima as lower the value of Quotient is lower the value of 'k'.
If you consider the Quotient as 1 (lowest but spl case) then your formula for 'k' becomes,
k = log q/log b

I found a solution-
If q divides pow(b,k) then all prime factors of q are prime factors of b. Now we can do iterations q = q ÷ gcd(b,q) while gcd(q,b)≠1. If q≠1 after iterations, there are prime factors of q which are not prime factors of b then k doesn't exist else k = no of iteration.

Trying to do a gaussian bell in Scilab

I'm trying to do a Gaussian bell using the data I am obtaining from a matrix but everytime I try to run the program I obtain this message:
"Error: syntax error, unexpected identifier, expecting end"
The data used to obtain the gaussina bell is a matrix which includes the last point of every n displacements, which are the last position of a particle. I want to know if there is an easier way to obtain the gaussian bell in scilab because I have to also do a fit with an histogram using the same data.
function bla7()
t=4000
n=1000
l=0.067
p=%pi*2
w1=zeros(t,1);
w2=zeros(t,1);
for I=1:t
a=(grand(n,1,"unf",0,p));
x=l*cos(a)
y=l*sin(a)
z1=zeros(n,1);
z2=zeros(n,1);
for i=2:n
z1(i)=z1(i-1)+x(i);
z2(i)=z2(i-1)+y(i);
end
w1(I)=z1($)
w2(I)=z2($)
end
n=10000
w10=zeros(t,1);
w20=zeros(t,1);
for I=1:t
a=(grand(n,1,"unf",0,p));
x=l*cos(a)
y=l*sin(a)
z1=zeros(n,1);
z2=zeros(n,1);
for i=2:n
z1(i)=z1(i-1)+x(i);
z2(i)=z2(i-1)+y(i);
end
w10(I)=z1($)
w20(I)=z2($)
end
n=100
w100=zeros(t,1);
w200=zeros(t,1);
for I=1:t
a=(grand(n,1,"unf",0,p));
x=l*cos(a)
y=l*sin(a)
z1=zeros(n,1);
z2=zeros(n,1);
for i=2:n
z1(i)=z1(i-1)+x(i);
z2(i)=z2(i-1)+y(i);
end
w100(I)=z1($)
w200(I)=z2($)
end
k=70
v=12/k
c1=zeros(k,1)
for r=1:t
c=w1(r)
m=-6+v
n=-6
for g=1:k
if (c<m & c>=n) then
c1(g)=c1(g)+1
m=m+v
n=n+v
else
m=m+v
n=n+v
end
end
end
c2=zeros(k,1)
c2(1)=-6+(6/k)
for b=2:k
c2(b)=c2(b-1)+v
end
y = stdev(w1)
normal1=zeros(k,1)
normal2=zeros(k,1)
bb=-6
bc=-6+v
for wa=1:k
bd=(bb+bc)/2
gauss1=(1/(y*sqrt(2*%pi)))exp(-0.5(bb/y)^2)
gauss2=(1/(y*sqrt(2*%pi)))exp(-0.5(bc/y)^2)
gauss3=(1/(y*sqrt(2*%pi)))exp(-0.5(bd/y)^2)
gauss4=((bc-bb)/6)*(gauss1+gauss2+4*gauss3)
bb=bb+v
bc=bc+v
normal2(wa,1)=gauss4
end
normal3=normal2*4000
k=100
v=24/k
c10=zeros(k,1)
for r=1:t
c=w10(r)
m=-12+v
n=-12
for g=1:k
if (c<m & c>=n) then
c10(g)=c10(g)+1
m=m+v
n=n+v
else
m=m+v
n=n+v
end
end
end
c20=zeros(k,1)
c20(1)=-12+(12/k)
for b=2:k
c20(b)=c20(b-1)+v
end
y = stdev(w10)
normal10=zeros(k,1)
normal20=zeros(k,1)
bb=-12
bc=-12+v
for wa=1:k
bd=(bb+bc)/2
gauss10=(1/(y*sqrt(2*%pi)))exp(-0.5(bb/y)^2)
gauss20=(1/(y*sqrt(2*%pi)))exp(-0.5(bc/y)^2)
gauss30=(1/(y*sqrt(2*%pi)))exp(-0.5(bd/y)^2)
gauss40=((bc-bb)/6)*(gauss10+gauss20+4*gauss30)
bb=bb+v
bc=bc+v
normal20(wa,1)=gauss40
end
normal30=normal20*4000
k=70
v=12/k
c100=zeros(k,1)
for r=1:t
c=w100(r)
m=-6+v
n=-6
for g=1:k
if (c<m & c>=n) then
c100(g)=c100(g)+1
m=m+v
n=n+v
else
m=m+v
n=n+v
end
end
end
c200=zeros(k,1)
c200(1)=-6+(6/k)
for b=2:k
c200(b)=c200(b-1)+v
end
y = stdev(w100)
normal100=zeros(k,1)
normal200=zeros(k,1)
bb=-6
bc=-6+v
for wa=1:k
bd=(bb+bc)/2
gauss100=(1/(y*sqrt(2*%pi)))exp(-0.5(bb/y)^2)
gauss200=(1/(y*sqrt(2*%pi)))exp(-0.5(bc/y)^2)
gauss300=(1/(y*sqrt(2*%pi)))exp(-0.5(bd/y)^2)
gauss400=((bc-bb)/6)*(gauss100+gauss200+4*gauss300)
bb=bb+v
bc=bc+v
normal200(wa,1)=gauss400
end
normal300=normal200*4000
bar(c20,c10,1.0,'white')
plot(c20, normal30, 'b-')
bar(c2,c1,1.0,'white')
plot(c2, normal3, 'r-')
bar(c200,c100,1.0,'white')
plot(c200, normal300, 'm-')
poly1.thickness=3;
xlabel(["x / um"]);
ylabel("molecules");
gcf().axes_size=[500,500]
a=gca();
a.zoom_box=[-12,12;0,600];
a.font_size=4;
a.labels_font_size=5;
a.x_label.font_size = 5;
a.y_label.font_size = 5;
ticks = a.x_ticks
ticks.labels =["-12";"-10";"-8";"-6";"-4";"-2";"0";"2";"4";"6";"8";"10";"12"]
ticks.locations = [-12;-10;-8;-6;-4;-2;0;2;4;6;8;10;12]
a.x_ticks = ticks
endfunction

Each and every one of your gauss variables are missing the multiplication operator in two places. Check every line at it will run. For example, this:
gauss1=(1/(y*sqrt(2*%pi)))exp(-0.5(bb/y)^2)
should be this:
gauss1=(1/(y*sqrt(2*%pi))) * exp(-0.5 * (bb/y)^2)
As for the Gaussian bell, there is no standard function in Scilab. However, you could define a new function to make things more clear in your case:
function x = myGauss(s,b_)
x = (1/(s*sqrt(2*%pi)))*exp(-0.5*(b_/s)^2)
endfunction
Actually, while we're at it, your whole code is really difficult to read. You should define functions instead of repeating code: it helps clarify what you mean, and if there is a mistake, you need to fix only one place. Also, I personally do not recommend that you enclose everything in a function like bla7() because it makes things harder to debug. Your example could be rewritten like this:
The myGauss function;
A function w_ to calculate w1, w2, w10, w20, w100 and w200;
A function c_ to calculate c1, c2, c10, c20, c100 and c200;
A function normal_ to calculate normal1, normal2, normal10, normal20, normal100 and normal200;
Call all four functions as many times as needed with different inputs for different results.
If you do that, your could will look like this:
function x = myGauss(s,b_)
x = (1 / (s * sqrt(2 * %pi))) * exp(-0.5 * (b_/s)^2);
endfunction
function [w1_,w2_] = w_(t_,l_,n_,p_)
w1_ = zeros(t_,1);
w2_ = zeros(t_,1);
for I = 1 : t_
a = (grand(n_,1,"unf",0,p_));
x = l_ * cos(a);
y = l_ * sin(a);
z1 = zeros(n_,1);
z2 = zeros(n_,1);
for i = 2 : n_
z1(i) = z1(i-1) + x(i);
z2(i) = z2(i-1) + y(i);
end
w1_(I) = z1($);
w2_(I) = z2($);
end
endfunction
function [c1_,c2_] = c_(t_,k_,v_,w1_,x_)
c1_ = zeros(k_,1)
for r = 1 : t_
c = w1_(r);
m = -x_ + v_;
n = -x_;
for g = 1 : k_
if (c < m & c >= n) then
c1_(g) = c1_(g) + 1;
m = m + v_;
n = n + v_;
else
m = m + v_;
n = n + v_;
end
end
end
c2_ = zeros(k_,1);
c2_(1) = -x_ + (x_/k_);
for b = 2 : k_
c2_(b) = c2_(b-1) + v_;
end
endfunction
function [normal1_,normal2_,normal3_] = normal_(k_,bb_,bc_,v_,w1_)
y = stdev(w1_);
normal1_ = zeros(k_,1);
normal2_ = zeros(k_,1);
for wa = 1 : k_
bd_ = (bb_ + bc_) / 2;
gauss1 = myGauss(y,bb_);
gauss2 = myGauss(y,bc_);
gauss3 = myGauss(y,bd_);
gauss4 = ((bc_ - bb_) / 6) * (gauss1 + gauss2 + 4 * gauss3);
bb_ = bb_ + v_;
bc_ = bc_ + v_;
normal2_(wa,1) = gauss4;
end
normal3_ = normal2_ * 4000;
endfunction
t = 4000;
l = 0.067;
p = 2 * %pi;
n = 1000;
k = 70;
v = 12 / k;
x = 6;
bb = -x;
bc = -x + v;
[w1,w2] = w_(t,l,n,p);
[c1,c2] = c_(t,k,v,w1,x);
[normal1,normal2,normal3] = normal_(k,bb,bc,v,w1);
bar(c2,c1,1.0,'white');
plot(c2, normal3, 'r-');
n = 10000;
k = 100;
v = 24 / k;
x = 12;
bb = -x;
bc = -x + v;
[w10,w20] = w_(t,l,n,p);
[c10,c20] = c_(t,k,v,w10,x);
[normal10,normal20,normal30] = normal_(k,bb,bc,v,w10);
bar(c20,c10,1.0,'white');
plot(c20, normal30, 'b-');
n = 100;
k = 70;
v = 12 / k;
x = 6;
bb = -x;
bc = -x + v;
[w100,w200] = w_(t,l,n,p);
[c100,c200] = c_(t,k,v,w100,x);
[normal100,normal200,normal300] = normal_(k,bb,bc,v,w100);
bar(c200,c100,1.0,'white');
plot(c200, normal300, 'm-');
poly1.thickness=3;
xlabel(["x / um"]);
ylabel("molecules");
gcf().axes_size=[500,500]
a=gca();
a.zoom_box=[-12,12;0,600];
a.font_size=4;
a.labels_font_size=5;
a.x_label.font_size = 5;
a.y_label.font_size = 5;
ticks = a.x_ticks
ticks.labels =["-12";"-10";"-8";"-6";"-4";"-2";"0";"2";"4";"6";"8";"10";"12"]
ticks.locations = [-12;-10;-8;-6;-4;-2;0;2;4;6;8;10;12]
a.x_ticks = ticks

Index was outside the bounds of the array VB

This is my code and when I run it appears index was outside the bounds of the array in line b = Asc(y(j + m)). I have tried Try and Catch and it didn't work out.
Public Function SMITH(x, y, SX, SY)
Dim a, b, j As Integer
result = 0
m = x.Length
n = y.Length
preBmBc(x)
preQsBc(x)
j = 0
While (j <= (n - m))
If (SX = SY.ToString.Substring(j, m)) Then
result = 1
End If
a = Asc(y(j + (m - 1)))
b = Asc(y(j + m))
j = j + Math.Max(bmBc(a), qsBc(b))
End While
Return result
End Function

Have you tried making m = "m-1" for b also? You really need to step through the code using breakpoints and the debugger to figure out when the program throws the OutOfRangeException.