Solving Eigenvalues for a 3x3 matrix 4

[IJR]

Pals

anyone has or would like to type here a faster vb code for finding eigenvalues of a 3x3 matrix

respects
ijr

 

[cowski]

Faster than what?

 

[GregLocock]

Faster than using the built in functions?

Cheers

Greg Locock


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[IJR]

GregLocock

you mean to say there is a built in function. Why didnt you just say that?

thanks anyway
ijr

 

[IJR]

Didnt find any eigenvalue function in xls

 

[GregLocock]

No, there isn't one funcyion. There are three functions in excel that allow you to rapidly compute lambda, MINVERT, MDETERM and MMULT.

Cheers

Greg Locock


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[electricpete]

I can't think of any simple way to combine those functions to solve Lambda in
Ax = Lambda*x
where A is nxn, x is nx1, Lambda is scalar.

But I might be wrong. If there is can you outline it Greg?

=====================================
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[GregLocock]

Well I hadn't actually done it

http://people.revoledu.com/kardi/tutorial/Excel/EigenValue.html

OP still hasn't defined faster than what.





Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[IDS]

I have modified the spreadsheet in Greg's link to find the eigenvalues by solving a cubic polynomial, rather than using goalseek. That should be quicker.

Here's the code:

Public Function Eigen3x3(MatrixA As Variant) As Variant
Dim a As Double, b As Double, c As Double
Dim d As Double, e As Double, f As Double
Dim g As Double, h As Double, i As Double
Dim ac As Double, bc As Double, cc As Double, dc As Double

MatrixA = MatrixA.Value2

a = MatrixA(1, 1)
b = MatrixA(1, 2)
c = MatrixA(1, 3)
d = MatrixA(2, 1)
e = MatrixA(2, 2)
f = MatrixA(2, 3)
g = MatrixA(3, 1)
h = MatrixA(3, 2)
i = MatrixA(3, 3)

ac = -1
bc = a + e + i
cc = f * h + b * d + c * g - a * e - a * i - e * i
dc = b * f * g + c * d * h - a * f * h - b * d * i - c * e * g + a * e * i

Eigen3x3 = CubicC(ac, bc, cc, dc)

End Function

The function to solve the cubic is included in the attached file.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IJR]

GregLocock and IDS

Thanks for the great posts. This solves my problem. I can move on from here.

Sorry for keeping you busy with the word "fast". How can you make me so responsible for that pals? Anyway, let me explain. No standard calculator around me or excel does it easily, so anything that can make me enter a matrix and gets me eigenvalues and eigenvectors is "fast". The algorithm above gets me eigenvalues, thats helpful.

There are numerical analysis that explain this, but I just figured out pals here have a better way around that would save me from learning the power method etc.

respects
ijr

 

[GregLocock]

Hey we were just ribbing you. If you really want fast for large matrices don't use Excel. Matlab and Octave both have a function (eig) that will rip out eigenvalues for big matrices, very quickly, say <4 seconds for a 500x500 matrix.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[IJR]

That is another great bit of info GregoLocock

I am now going into Matlab.

Anyway, your posts and IDS's simplified life for now.

respects

IJR