@goli Just for interest's sake, here is what you can get for that data.

Note the I used s3[1..-5]  which is all of s3 except the last 4 points. Those 4 points are shown as lying on the ellipse that fits the green (middle, s2) set. So if the full s3 is used to fit an ellipse it would get distorted by those 4 points. I don't know what you code is doing, so I have no idea whether those points are correct.

K1:=Statistics:-Fit(a*(x-x0)^2-b*(x-x0)*(y-y0)+c*(y-y0)^2-1,
                   Matrix(s1), Vector(nops(s1)),[x,y],
                   initialvalues=[a=0,b=0,c=0,x0=0.26,y0=0.0]):

ellK1:=plots:-implicitplot(K1,x=0.21..0.32,y=-0.025..0.02):
#plots:-display(s11,ellK1);

K2:=Statistics:-Fit(a*(x-x0)^2-b*(x-x0)*(y-y0)+c*(y-y0)^2-1,
                   Matrix(s2), Vector(nops(s2)),[x,y],
                   initialvalues=[a=0,b=0,c=0,x0=0.26,y0=0.0]):

ellK2:=plots:-implicitplot(K2,x=0.21..0.32,y=-0.025..0.02):
#plots:-display(s22,ellK2);

K3:=Statistics:-Fit(a*(x-x0)^2-b*(x-x0)*(y-y0)+c*(y-y0)^2-1,
                   Matrix(s3[1..-5]), Vector(nops(s3[1..-5])),[x,y],
                   initialvalues=[a=0,b=0,c=0,x0=0.26,y0=0.0]):

ellK3:=plots:-implicitplot(K3,x=0.21..0.32,y=-0.025..0.02):
#plots:-display(s33,ellK3);

plots:-display(s11,s22,s33,ellK1,ellK2,ellK3);

Anyway, this was just an experiment. Perhaps you really do want three hulls, with s3 being treated in full for that.

@okoolo If you've adjusted interface(rtablesize) as suggested above, then simply entering the Matrix or Vector name and hitting return/enter should print it in full.

An alternative is to right-click on the Matrix output (including the short-form summary that you see if rtablesize is not big enough) and choose the context-menu item "Browse". That should launch a pop-up window with some nice views of the data.

@okoolo If you've adjusted interface(rtablesize) as suggested above, then simply entering the Matrix or Vector name and hitting return/enter should print it in full.

An alternative is to right-click on the Matrix output (including the short-form summary that you see if rtablesize is not big enough) and choose the context-menu item "Browse". That should launch a pop-up window with some nice views of the data.

@goli 

Trying appending the first point as a duplicate, as one way to closeout the hull.

a:=simplex[convexhull](B00,output=[hull]);

plot( [op(a),a[1]] );

@goli 

Trying appending the first point as a duplicate, as one way to closeout the hull.

a:=simplex[convexhull](B00,output=[hull]);

plot( [op(a),a[1]] );

@goli I made two plots. One, named `P1`, is just a point plot (the black points). The other, `ellK`, is the red ellipse.

Then I displayed both together, using the plots:-display command. You don't have to plot them together. They may be displayed separately. Just remove whichever you want, from that plots:-display call.

Also note that `K` is assigned a formula for the ellipse, in case you want that for some reason other than plotting.

I'm not sure why you got an error message about the initial values. Could you say which version number of Maple you are using?  Also helpful might be if you could upload your attemptin a worksheet, so that we may check the syntax, etc, and know that there is no misunderstanding in the code entry.

As far as what I did goes, it isn't as complicated as it looks at first. I took a general (curve) formula for an ellipse, with variables x and y and several parameters (a,b,c,x0,y0). I supplied it to the Statistics:-Fit command, also passing your point data. That routine works by computing values for the parameters which make the curve formula a "good fit" to the point data.

@goli I made two plots. One, named `P1`, is just a point plot (the black points). The other, `ellK`, is the red ellipse.

Then I displayed both together, using the plots:-display command. You don't have to plot them together. They may be displayed separately. Just remove whichever you want, from that plots:-display call.

Also note that `K` is assigned a formula for the ellipse, in case you want that for some reason other than plotting.

I'm not sure why you got an error message about the initial values. Could you say which version number of Maple you are using?  Also helpful might be if you could upload your attemptin a worksheet, so that we may check the syntax, etc, and know that there is no misunderstanding in the code entry.

As far as what I did goes, it isn't as complicated as it looks at first. I took a general (curve) formula for an ellipse, with variables x and y and several parameters (a,b,c,x0,y0). I supplied it to the Statistics:-Fit command, also passing your point data. That routine works by computing values for the parameters which make the curve formula a "good fit" to the point data.

@okoolo The angle-brackets are a shortcut syntax for the Vector and Matrix commands.

By default, only small Vectors and Matrices get printed in full. (For the Standard GUI, the default cutoff is size 10,and for the commandline interface the cutoff is 25.)

You can control this with the interface(rtablesize) setting.

For example, you could put this early on in your worksheet,

interface(rtablesize=100):

FYI, these `interface` setting commands are a little funny, and sometime take getting used to. Their return value (ie. what prints out after you call them) is the old value, even though the new value one specifies gets stored and used.

@okoolo The angle-brackets are a shortcut syntax for the Vector and Matrix commands.

By default, only small Vectors and Matrices get printed in full. (For the Standard GUI, the default cutoff is size 10,and for the commandline interface the cutoff is 25.)

You can control this with the interface(rtablesize) setting.

For example, you could put this early on in your worksheet,

interface(rtablesize=100):

FYI, these `interface` setting commands are a little funny, and sometime take getting used to. Their return value (ie. what prints out after you call them) is the old value, even though the new value one specifies gets stored and used.

@okoolo Are you using an older version of Maple?

If your version predates the (new as of Maple 13) syntax for elementwise operation, then you could replace

ln~(p)

with

map(ln,p)

and so on.

But maybe this is not the problem, since in Maple 12 trying to apply ln~ to a list or Vector normally results in an error message like "Error, missing operator or `;`".

Could you let us know the version. But also upload your Worksheet/Document here, using the green up-arrow on the menu of the editing window? The failure of copy and paste, on your tilde, makes me wonder whether it might be some 2D Math or localization issue, and we'd likely need the poke around the sheet to find out for sure.

@okoolo Are you using an older version of Maple?

If your version predates the (new as of Maple 13) syntax for elementwise operation, then you could replace

ln~(p)

with

map(ln,p)

and so on.

But maybe this is not the problem, since in Maple 12 trying to apply ln~ to a list or Vector normally results in an error message like "Error, missing operator or `;`".

Could you let us know the version. But also upload your Worksheet/Document here, using the green up-arrow on the menu of the editing window? The failure of copy and paste, on your tilde, makes me wonder whether it might be some 2D Math or localization issue, and we'd likely need the poke around the sheet to find out for sure.

Sorry if I missed something, but is the call to with(Units) necessary?

Also, I notice that you did not load Units:-Standard, and instead call `simplify` to combine units in results. Is that because things misbehave, if you do? (I'm thinking about some unit cancellation by Units:-Standard:-`=`, but maybe I misremember.)

acer

@okoolo You forgot the tilde (~) after the `ln`, when doing ln~(p).

The tilde makes the action be applied elementwise, similar in this case to issuing map(ln,p).

@okoolo You forgot the tilde (~) after the `ln`, when doing ln~(p).

The tilde makes the action be applied elementwise, similar in this case to issuing map(ln,p).

@Christopher2222 Robert's suggestion is to produce a variation on `RandomArray` which would use whatever values of mu and sigma happen to be (not as local names or parameters of that procedure). That would allow you to produce Arrays with variations on the normal distribution, on the fly.

But it would be better to have such a new routine be named something else entirely, since as Robert mentioned you'd otherwise be in danger of breaking some other routine's dependence on `RandomArray`. Better to call it `myRandomArray` or something else, and not to unprotect and change the original at all.

But in your comment immediately above you've also implied having replaced 'Normal(0,1)' with some other literal numeric parameters such as 'Normal(0,3)', rather that Robert's suggestion of using unassigned names `mu` and `sigma`. Note that repeatedly reconstructing the entire procedure and its body via `subs` and `eval`, just to mimic the behaviour of dynamicaly changing parameters, is a particularly unnecessarily inefficient way to program. Whatever you do, don't devise a work flow wherein you repeatedly recreate the entire procedure instantiated with new literal numeric parameters in the body.

I feel compelled to mention once more, sorry: doing this is inferior to just using Statistics:-Sample to obtain an Array with random float enntries in modern Maple.