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Harry Garst

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How can I plot the eigenvectors in the 3...

Harry Garst 259 Maple
pointplot3d plotting eigenvector
April 29 2020
1 2

I have been using Alex Potapchik & & Alec Mihailovs' procedure for generating a multivariate sample

https://www.mapleprimes.com/questions/37539-Generate-Data-From-A-Multivariate-Normal

How can I plot the eigenvectors in the 3D scatterplot?

``

> 

restart
> 

kernelopts(version); interface(version)

`Maple 2019.2, X86 64 WINDOWS, Nov 26 2019, Build ID 1435526`

  

`Standard Worksheet Interface, Maple 2019.2, Windows 10, November 26 2019 Build ID 1435526`

 (1)
> 

with(LinearAlgebra); with(Statistics); with(plots)
> 

MultivariateNormalSample := proc (Sigma, V, N) local d; d := LinearAlgebra:-Dimension(V); LinearAlgebra:-LUDecomposition(Matrix(Sigma, datatype = float[8]), 'method' = 'Cholesky').ArrayTools:-Alias(Statistics:-Sample(Normal(0, 1), d*N), [d, N])+ArrayTools:-Replicate(Vector[column](V, datatype = float[8]), 1, N) end proc
> 

Cov := Matrix([[4, 2.5, .4], [2.5, 2, .2], [.4, .2, .5]])
> 

Cor := simplify(MatrixPower(DiagonalMatrix(Diagonal(Cov)), -1/2).Cov.MatrixPower(DiagonalMatrix(Diagonal(Cov)), -1/2))
> 

S := MultivariateNormalSample(Cov, `<,>`(0, 0, 0), 1000); Statistics:-CovarianceMatrix(S^%T); map(Statistics:-Mean, [S[1], S[2]])
> 

Determinant(Cov)

.795

 (2)
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Z := Scale(S^%T)
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E, V := Eigenvectors(Cor)
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E := Re(E); V := Re(V)

Vector(3, {(1) = 2.0005950859349144, (2) = .11194337607751015, (3) = .8874615374875758})

  

Matrix(%id = 18446746188592589870)

 (3)
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plots:-pointplot3d(Z, axes = normal, thickness = 1, symbol = circle, axis[1] = [color = black], axis[2] = [color = blue], axis[3] = [color = green], color = "DarkRed", orientation = [30, 75], viewpoint = "circleright", symbolsize = 1)

 

NULL

 

Download Plot_eigenvectors_in_3d_scatterplot.mw

simplification using the power rule for ...

Harry Garst 259 Maple
simplify simplification power
March 05 2020
2 0

I had expected that applying the power rule for exponents would lead to an answer of zero. Maple refuses to give the desired answer, but using a procedure it works as expected.

Did I miss something?
 

``

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restart
> 

kernelopts(version)

`Maple 2019.2, X86 64 WINDOWS, Nov 26 2019, Build ID 1435526`

 (1)
> 

interface(version)

`Standard Worksheet Interface, Maple 2019.2, Windows 10, November 26 2019 Build ID 1435526`

 (2)
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simplify(exp(k*(ln(t)+ln(a)))-(exp(ln(t)+ln(a)))^k, symbolic)

exp(k*(ln(t)+ln(a)))-t^k*a^k

 (3)
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W := proc (m, n) local r; r := simplify(exp(m*n)-(exp(m))^n, symbolic); return r end proc
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W(n, k)

0

 (4)
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subs(n = ln(t)+ln(a), W(n, k))

0

 (5)
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V := proc (m, n) local r; r := simplify((exp(m))^n, symbolic); return r end proc
> 

V(n, k)

exp(k*n)

 (6)
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V(ln(t)+ln(a), k)

t^k*a^k

 (7)

``


 

Download mapleprimes.mw

principal components in 3d with projecti...

Harry Garst 259 Maple
statistics 3d projection
April 28 2019
1 1

 

Did someone already made a Pointplot3d for a Principal Components Analysis with projections for some data points on the eigenvectors?

I like this example very much:

http://www.joyofdata.de/public/pca-3d/

but I want to add projections on the three eigenvectors for some data points. I think it has to do something with the dot product, but I do not know how to do it in Maple. 

Hopefully someone already did this and is willing to share it.

kind regards,

Harry

 

Statistical procedures?...

Harry Garst 259 Maple
statistics correlation
March 19 2019
1 4

For a statistical course I will give next year, I would like to demonstrate the calculation of tetrachoric and polychoric correlations. Furthermore, it would be nice to show the students how the expectation-maximization algorithm works.

Has anyone already programmed this in Maple?

best regards,

Harry

 

combinations on subsets...

Harry Garst 259 Maple
combinatorics
February 19 2019
2 1

This works fine, but I was wondering whether it could be done in a simple way.
 

``

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restart; kernelopts(version); interface(version)

`Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973`

  

`Standard Worksheet Interface, Maple 2018.2, Windows 10, November 16 2018 Build ID 1362973`

 (1)
> 

kollect := proc (p::`+`, y) local x; subs(x = y, collect(subs(y = x, p), x)) end proc
> 

kollect(kollect(kollect(kollect(expand(add(mul(k)*add(k), `in`(k, combinat:-choose([i1, i2, i3, i4], 3)))), i1^2), i2^2), i3^2), i4^2)

(i1*i2+i1*i3+i2*i3)*i4^2+(i1*i2+i1*i4+i2*i4)*i3^2+(i1*i3+i1*i4+i3*i4)*i2^2+(i2*i3+i2*i4+i3*i4)*i1^2

 (2)

``


thanks in advance,

Harry

Download nested_comb.mw

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