Re: MuPad 3.0 extraction of individual eigenvectors

From: John O'Flaherty (quiasmox_at_yahoo.com)
Date: 11/11/04

  • Next message: Tony King: "Mathematica digit handling query" 
    Date: Thu, 11 Nov 2004 09:56:16 -0600

    Ralf Hillebrand wrote:

    > Hi Brad,
    >
    > Brad Cooper wrote:
    >
    >> In MuPad 3.0 I can find eigenvectors as follows:
    >>
    >> A := matrix([[1, 1, 1], [1, 1, 1], [1, 1, 1]]):
    >> S := linalg::eigenvectors(A);
    >>
    >> I now want to extract the eigenvectors from S
    >> to use linalg::orthog(S) to orthogonalise these
    >> eigenvectors.
    >
    >
    > Torsten provided a solution in his posting, here is a less
    > verbose one.
    >
    > Use map with op to extract the 3rd operands of the resulting
    > list:
    >
    > >> map(S, op, 3) // or map(S, x -> op(x, 3))
    >
    > -- -- +- -+ +- -+ -- -- +- -+ -- --
    > | | | -1 | | -1 | | | | 1 | | |
    > | | | | | | | | | | | |
    > | | | 1 |, | 0 | |, | | 1 | | |
    > | | | | | | | | | | | |
    > | | | 0 | | 1 | | | | 1 | | |
    > -- -- +- -+ +- -+ -- -- +- -+ -- --
    >
    > And since you want a flat list of vectors another op will do.
    > The command below is equivalent to 'map(S, x -> op(op(x, 3)))'
    > but even shorter and more efficient:
    >
    > >> map(S, op@op, 3)
    >
    > -- +- -+ +- -+ +- -+ --
    > | | -1 | | -1 | | 1 | |
    > | | | | | | | |
    > | | 1 |, | 0 |, | 1 | |
    > | | | | | | | |
    > | | 0 | | 1 | | 1 | |
    > -- +- -+ +- -+ +- -+ --
    >
    > This is a valid input for linalg::orthog:
    >
    > >> linalg::orthog(map(S, op@op, 3))
    >
    > -- +- -+ +- -+ +- -+ --
    > | | -1 | | -1/2 | | 1 | |
    > | | | | | | | |
    > | | 1 |, | -1/2 |, | 1 | |
    > | | | | | | | |
    > | | 0 | | 1 | | 1 | |
    > -- +- -+ +- -+ +- -+ --
    >
    >
    >
    >> I have found the problem I usually have with MuPad
    >> is taking the output from a command and making further
    >> use of that output as input to another command. Just
    >> a general observation.
    >
    >
    > Thats a point. If you find such problems, please tell us.
    > Our bug tracking system (http://www.mupad.de/bugs.shtml) is
    > not only for there for sending bug reports, but also for making
    > suggestions for improvements.
    >
    > We can't fix problems that we don't know of. So, please help
    > us to improve MuPAD by providing suggestions for improvements.
    > A note about problems you find will do, too. Maybe we find a
    > solution. I have just added a suggestion for this problem under
    > the bug number 1542.

    It's often tedious to see how many nested op's,? are needed to get the
    nugget desired. The magical solution would be to select the desired part
    with a mouse, press the F_whatever key, and have the correct expression
    appear on the next line. 

    --
john
  • Next message: Tony King: "Mathematica digit handling query"

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