LU decomposition

[hoshang]

Hi all,
I wonder why LU for this matrix retrieves such LU decomposition result.
M=
-0.5 -1 0
-1 -1 -1
0 -1 -0.5

L=
1 0 0
0 1 0
0.5 0.5 1

U=
-1 -1 -1
0 -1 -0.5
0 0 0.75



While it should be:

L=
1 0 0
2 1 0
0 -1 1

 

[hoshang]

I can't help with Mathcad,

Your original post has one questioned that has been answered in detail.

You're just going to have to do your own LU decomposition.

My original post has one question that hasn't been answered.
Is there any workaround in Mathcad so that I can get hoshang results?

 

[IRstuff]

That question has been answered several times now, both explicitly and implicitly

You're just going to have to do your own LU decomposition.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

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[IDS]

The question in the OP was:

I wonder why LU for this matrix retrieves such LU decomposition result.

to which the answer is:

there is more than one way to decompose a matrix.

The link previously posted:

https://courses.physics.illinois.edu/cs357/sp2020/notes/ref-9-linsys.html

has a good clear explanation of how to do LU decomposition, with and without pivoting, and why it is a good idea to use pivoting for general use, to avoid problems if there are any zeros on the leading diagonal. It also has Python code which will generate the unpivoted matrices (after applying corrections as posted above).

You haven't told us why you have to use the unpivoted matrices, or why it has to be done in Mathcad, but if both are essential for some reason, and if Mathcad doesn't have that as an option, it shouldn't be too hard to convert the Python code to Mathcad, or you could look at using:

https://pypi.org/project/MathcadPy/

or something similar.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

I have now posted full Python code for solving with LU decomposition, with and without pivoting, at:

https://newtonexcelbach.com/2023/05/26/lu-decomposition-with-python-and-scipy/

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IRstuff]

Full code to link the Scipy linear algebra functions, and the code above, to Excel via pyxll will be posted in the near future.

Thanks, do you know when you'll be posting the actual code?

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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[IDS]

IRstuff - it should be in the next few days. There will also be functions to call the Scipy linear algebra functions from Excel.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IRstuff]

Awesome, thanks

TTFN (ta ta for now)
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[IDS]

The Python code used in my posts in this thread, together with code to call the Scipy linear algebra functions from Excel, and a sample spreadsheet can be download from:

https://newtonexcelbach.com/2023/05/30/scipy-linear-algebra-functions-in-excel/

Note that calling the Python code from Excel requires the pyxll add-in.



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IRstuff]

Thanks!

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

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[PNachtwey]

There is python library for LU decomposition.

https://stackoverflow.com/questions/69241952/to-find-an-inverse-matrix-of-a-with-lu-decomposition

It will probably run much faster than code you write yourself because scipy is really compiled C or Fortran code with a python wrapper.



Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

IFPS Hall of Fame Member

 

[IDS]

There is python library for LU decomposition.

The great majority of the code in my link is for calling the Scipy linear algebra functions from Excel, including the LU decomposition functions.

The Python routines were written purely so I (and others) can see how the process works, in response to the question in the first post of this thread.

Also note that the download file includes links to the pyPardiso library which is very much faster than the Scipy LU functions.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[hoshang]

Hi all
Any workaround using Mathcad.

 

[IDS]

As said on 22nd May:

You haven't told us why you have to use the unpivoted matrices, or why it has to be done in Mathcad, but if both are essential for some reason, and if Mathcad doesn't have that as an option, it shouldn't be too hard to convert the Python code to Mathcad, or you could look at using:

https://pypi.org/project/MathcadPy/

or something similar.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IRstuff]

You're just going to have to do your own LU decomposition.

You CAN do this in Mathcad, albeit, a bit, or more, painfully

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

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