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These are replies submitted by mmcdara

@Carl Love 

Sorry Carl, the correct command is 
ff := convert([ seq(es(entries( f [i,..], nolist)), i=1..N^P) ], Matrix);

I probably changed the name of the vraiable ffd into f and saved without executing.

@Christian Wolinski 

More elegant than what I did.
By the way, in maple 2015 the command to use is R := RootOf(numtheory:-cyclotomic(N, x), x); 

Thanks for the tip

@Christian Wolinski 

probably too long to explain. But if you want to have a quick idea, it's related to the construction of "full factorial designs"

(here a "3^2 design).
There exist many ways to do that, all depending on some coding. Here I used a coding based on the roots of the 1.
The design is the 9x2 matrix named f.
It's 9x9 extension ff must be an orthogonal matrix relatively to an adhoc dot product.

Tell me if you are are intersted by more details.

@Christian Wolinski 

F being a matrix of complex I sould have used  LinearAlgebra[HermitianTranspose] instead of ^+

I was fooled by the fact that "." in the double loop gave me the result I expected (the identity matrix) and I didn't payed attention to use  LinearAlgebra[HermitianTranspose].

When I said I was blind !


Thank you.



Here is a screen capture of the assistant's sub menu in Maple 2015.2
There is no such Typesetiting Assistant: is my version too old?




Isn't it what I wrote in my reply and in ????
So I think your "but thank you:)" is particularly unwelcome.

I don't thank you for that


Here is a classical example of missing data in Statistics: you want to collect P informations on a sample of N individuals (practically tht whole information can be represesented by a NxP matrix). Unfortunately, it happens that for one reason or another some informations are not collected for some individuals; in other terms this matrix has "holes"... or "missing data".

I can't relate this to your question, so what do you mean exactly by "missing data"?


F(5) (the variable you want to plot?) depends on a, b, c, d, Re, N[1], G(0) and G(1): assuming you want to plot F(5) as a function of Re and N[1] alone, the first thing to do is to set a, b, c, d,G(0) and G(1) to some numerical values.

If you do not want to be bothered with Re, begin your worksheet by
local Re:


​​​​​​​You understood my question poperly.
Thanks for answer acer.


If I understand correctly you want do do this: 

  • You have a theoritical model B(T), ...H(T) which depends on 12 parameters (Ggamma, ..., xi) and 16 observations of a given quantity iV at times tV = 1, ..16.
  • You want to estimate the unknown values of these 12 parameters by minimizing some loss function of the form 
    add( (i(T)-iV[T])^2, T=1..16).

Am I right?

Because if I am your problem seems incorrectly posed.
In these kind of "parameter fitting" problems, the output of the model, let's say B(T), must be a theoritical, or a priori, model of the empirical observations iV.
More clearly, B(T) and iV must represent the same physical quantity.
But if it is the case, iV cannot be considered as the empirical observation of, let's say, C(T) or DD(T), ...

I would understant your problem if the data you want to adjust your model on were resumed by a 16 by 7 matrix (7 unknowns B(T), ...H(T)), not a single vector.
Can you clarify this point in order I might go forward?




Ok I think I understand. Now, what is the relation between i(T) and B(T), C(T), ... H(T) ?

I think that no progress can be obtain unless you give the reference of "the journal that i have been referred to"
Something about ta variant of the Falkner-Skan equation maybe?


When I'm at home I only have access to Maple 2015, but I will use valuesplit when back to the office (in 10 days).
Thanks for the tip.

I just found a trick to fix the issue but it seems a little like looking for noon at 2 PM...

A := Sample(Uniform(0, 1), [N, P]):
C := CorrelationMatrix(A);
X := < Vector[column](P, [1, -1, 0$(P-2)]) | C >:
  colorscheme=["blue", "white", "red"],   
  view=[default, 2..numelems(X[1,..])+1, default], 
  tickmarks=[[seq(i+1/2=A||i, i=1..P)], [seq(i+1/2=A||(i-1), i=1..P)], default], 
  title="Empirical Correlation Matrix" 


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