Mo_Jalal

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These are questions asked by Mo_Jalal

howca i determine the range of gains if g(x)=1/(x+x^2+x^3+2)

the answer is like closed loop

This is the same example in previous post,

But here my question is how to produce smother plot of date. I tried the interpolation package but it not working.. 
 

restart:

with(LinearAlgebra): with(CurveFitting): with(Interpolation): with(plots): with(Statistics):
Omega:=0.1:no:=0:Delta:=0:tau0:=1:c:=0:gamma1:=0:
j:=1:k1:=0:t:=1:xr:=1:Gamma:=0.1:

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received Interpolation

 


for i from -10 to 10 do
d[i]:=i:
b:=sum(-gamma1*tau0+I*tau0*Delta-2*a*(k-1)*xr,k=0..1):
a:=1+I*c;
c1:=sqrt(conjugate(a))/tau0:
c2:=0.5*((conjugate(b)/sqrt(conjugate(a)))):
lambda1[i]:=2*(Gamma-I*d[i])*(t-k1)/j+(Gamma-I*d[i])^2:
lambda2[i]:=t*(1-j)-k1/j+1/sqrt(2)*(Gamma-I*d[i]):
lambda3[i]:=c1*(t-k1)/j+c1*(Gamma-I*d[i])+c2:
J1[i]:=sqrt(Pi)/sqrt(2)*(1-erf(lambda2[i]));
J1mod[i]:=(Re(J1[i]))^2+(Im(J1[i]))^2:

g1[i]:=0.5*sqrt(Pi)*tau0*exp(c2^2)
    *exp(-conjugate(a)*((k-1)*xr)^2)/(sqrt(conjugate(a)));

F2[i]:=map(fnormal,evalf(sqrt(2)*Int(unapply(exp(-x^2)*erf(-sqrt(2)*c1*x+lambda3[i]),x),-lambda2[i]..5,epsilon=1e-5)));

J2[i]:=sum(g1[i]*J1[i]+g1[i]*F2[i],k=1..1);

J2mod[i]:=abs(J2[i])^2:
h1[i]:=map(fnormal,evalf(exp(-d[i]^2))):
f[d[i]]:=map(fnormal, evalf(h1[i]*(no*J1mod[i]+Omega^2*J2mod[i]))):
#f[d[i]]:=-d[i]^2*log(exp(1))+2*log(Omega)+log(J2mod[i]):
#map(simplify~, %[2], zero):
end do:

with(CurveFitting):
ptsN1 := CodeTools:-Usage(
           [seq([d[i], evalf(f[d[i]])], i = -10 .. 10)]
                         ):

memory used=3.44KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns, gc time=0ns

 

 

P1:=plot(ptsN1, color = black, linestyle = solid, thickness = 2,
     color = black, axes = boxed, labelfont = ["HELVETICA", 14],
     labels = ["d", "S_M(d)"]);

 

         
 

points := [seq(x, x = -10 .. 10, 1)]:
data   := [seq(evalf(f[d[i]]), i = -10 .. 10, 1)]:
f := Interpolate(points, data):
plot(f,-10..10);

Error, (in plot) procedure expected, as range contains no plotting variable

 

``

``


I noticed this package is not introduced in Maple 17.. what is the alternative way to produce smother curve

Download interploation.mw

Hi 

The integration in (F2) is not work properly.

My tyr is below:

restart:with(plots):
assume(d,real):

b:=-gamma1*tau0+I*tau0*Delta-2*a*(k-1)*xr:
a:=1+I*c;
c1:=sqrt(conjugate(a))/tau0:
c2:=0.5*((conjugate(b)/sqrt(conjugate(a)))):
lambda1:=2*(1-I*d)*(t-k1)/j+(1-I*d)^2:
lambda2:=t*(1-j)*k1/j+1/sqrt(2)*(1-I*d):
lambda3:=c1*(t-k1)/j+c1*(1-I*d)+c2:
J1:=sqrt(Pi)/sqrt(2)*(1-erf(lambda2)):
J1mod:=(Re(J1))^2+(Im(J1))^2:
g1:=0.5*sqrt(Pi)*tau0*exp(c2^2)*exp(-conjugate(a)*((k-1)*xr)^2)/(sqrt(conjugate(a))):

                       
F2:=-sqrt(2)*int(exp(-x^2)*erf(sqrt(2)*c1*x+lambda3),x=-lambda2..infty);
Warning,  computation interrupted
J2:=sum(g1*J1+g1*F2,k=1..1);
J2mod:=(((Re(J2))^2+(Im(J2))^2)):
W:= unapply(no*J1mod+Omega^2*J2mod,d):
Omega:=0.01:no:=1:Delta:=0:tau0:=1:c:=0:gamma1:=0:j:=1:k1:=0:t:=2*Pi:xr:=1:
P1:=plot(W,-50..50,axes=boxed,title=tit,color=black,font=[2,3,18],thickness=2,tickmarks=[3,2],titlefont=[SYMBOL,14],font=[1,1,18],linestyle=1);

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