Quite right, we don't need printed manuals.

But please, don't say you stop printing manuals to help save the environment.

Stopping because it does not make sense economically is a good enough reason!

@STHence This appears to me to be the same problem raised earlier: There is no solution for X0 to Y0=C.X0.

But if you accept the next best to a solution, a leastsquare solution, then it is not surprising that with Y defined from the X we found based on that X0 by

Y:=C.X:
# we shall see a nonnegligible difference here:
(eval(Y,t=0)-convert(Y0,Vector))[1];

In your graph you have what you call the real solution. Where does that come from?

@STHence This appears to me to be the same problem raised earlier: There is no solution for X0 to Y0=C.X0.

But if you accept the next best to a solution, a leastsquare solution, then it is not surprising that with Y defined from the X we found based on that X0 by

Y:=C.X:
# we shall see a nonnegligible difference here:
(eval(Y,t=0)-convert(Y0,Vector))[1];

In your graph you have what you call the real solution. Where does that come from?

@STHence If X(0) is not known, but is just

X0:= <seq(x0[i],i=1..7)>;

then you can still compute E.X0, but then you are faced with having to solve Y = C.X w.r.t. X0 in some "best" way.

@STHence If X(0) is not known, but is just

X0:= <seq(x0[i],i=1..7)>;

then you can still compute E.X0, but then you are faced with having to solve Y = C.X w.r.t. X0 in some "best" way.

@STHence Somehow angular brackets often disappear when you paste them into the editor.

X was supposed to be
X:=<seq(x[i](t),i=1..7)>;

that is the same as

X:=Vector([seq(x[i](t),i=1..7)]);

which is safer with this editor, but not as convenient. I have corrected it above. I hope it stays OK.

@STHence Somehow angular brackets often disappear when you paste them into the editor.

X was supposed to be
X:=<seq(x[i](t),i=1..7)>;

that is the same as

X:=Vector([seq(x[i](t),i=1..7)]);

which is safer with this editor, but not as convenient. I have corrected it above. I hope it stays OK.

@STHence The LeastSquare solution minimizes the 2-norm of the residual A.X-Y. So in what sense do you expect a better solution than that?

X:=LinearAlgebra:-LeastSquares(A,Y);
A.X-Y:
LinearAlgebra:-Norm(%,2);
#Returns 0.1478777205
#LeastSquare does the same as the following (not codewise):
use LinearAlgebra in
   LinearSolve(Transpose(A).A,Transpose(A).Y)
end use;

@STHence The LeastSquare solution minimizes the 2-norm of the residual A.X-Y. So in what sense do you expect a better solution than that?

X:=LinearAlgebra:-LeastSquares(A,Y);
A.X-Y:
LinearAlgebra:-Norm(%,2);
#Returns 0.1478777205
#LeastSquare does the same as the following (not codewise):
use LinearAlgebra in
   LinearSolve(Transpose(A).A,Transpose(A).Y)
end use;

@acer You are quite right. The following splits a plot structure containing a single curve, so is less general than the evalindets idea in that respect. Also individual curve options (like thickness and color are gone):

restart;
u:=sqrt(x^2-5)+3;
plot(u,view=0..15,thickness=6); p:=%:
M:=plottools:-getdata(p)[-1];
S:=ListTools:-Split(hastype,convert(M,listlist),undefined):
plots:-display(plot~([S]),p);

You don't need the p in the last line except for keeping the view option.

#Here is an updated version that seems to work well:

R:=proc(p) local f;
   f:=proc(curve)
      evalindets(curve,Or(listlist,Matrix),m->ListTools:-Split(hastype,convert(m,listlist),undefined))
   end proc;
   evalindets(p,specfunc(anything,CURVES),f);
end proc;

R(p); #Returns the plot hoped for

@acer You are quite right. The following splits a plot structure containing a single curve, so is less general than the evalindets idea in that respect. Also individual curve options (like thickness and color are gone):

restart;
u:=sqrt(x^2-5)+3;
plot(u,view=0..15,thickness=6); p:=%:
M:=plottools:-getdata(p)[-1];
S:=ListTools:-Split(hastype,convert(M,listlist),undefined):
plots:-display(plot~([S]),p);

You don't need the p in the last line except for keeping the view option.

#Here is an updated version that seems to work well:

R:=proc(p) local f;
   f:=proc(curve)
      evalindets(curve,Or(listlist,Matrix),m->ListTools:-Split(hastype,convert(m,listlist),undefined))
   end proc;
   evalindets(p,specfunc(anything,CURVES),f);
end proc;

R(p); #Returns the plot hoped for

Here is another way of removing HFloat(undefined) (as unfortunately seems necessary in Maple 16.02):

restart;
u:=sqrt(75-3*x^2);
plot(u); p:=%:
evalindets(p,Matrix,m->remove(hastype,convert(m,listlist),undefined));

#Turning the data matrix into a listlist makes it easier to remove undefined elements.
#To catch cases where the data (or some of it) in fact is already a listlist as in
http://www.mapleprimes.com/questions/142416-Problems-With-DEplot
#we could do
evalindets(p,Or(Matrix,listlist),m->remove(hastype,convert(m,listlist),undefined));

Here is another way of removing HFloat(undefined) (as unfortunately seems necessary in Maple 16.02):

restart;
u:=sqrt(75-3*x^2);
plot(u); p:=%:
evalindets(p,Matrix,m->remove(hastype,convert(m,listlist),undefined));

#Turning the data matrix into a listlist makes it easier to remove undefined elements.
#To catch cases where the data (or some of it) in fact is already a listlist as in
http://www.mapleprimes.com/questions/142416-Problems-With-DEplot
#we could do
evalindets(p,Or(Matrix,listlist),m->remove(hastype,convert(m,listlist),undefined));

@Axel Vogt Amazingly simple! And thank you!

@Axel Vogt Amazingly simple! And thank you!