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From: handhelds@gac.edu
Subject: Re: Eigenvalues
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Newsgroups: comp.sys.handhelds
Subject: Re: Eigenvalues
Message-ID: <1990Dec22.002458.26290@usenet@scion.CS.ORST.EDU>
From: jacobsd@usenet@scion.CS.ORST.EDU (Dana Jacobsen)
Date: 22 Dec 90 00:24:58 GMT
References: <9012201714.AA26392@CS.ORST.EDU>
Organization: Oregon State University, Computer Science Dept
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In <9012201714.AA26392@CS.ORST.EDU> john%solvint@orstcs.UUCP writes:

>> Someone posted a message containing the program
>> \<<A I L * - DET \>> (where I = Identity matrix)
>> for finding the characteristic polynomial of a matrrix A.
>> I can't make it work because the 48 doesn't seem to permit
>> symbolic entries in arrayse, as was also the case with the 28s
>> Can someone give me the reference to this message?
>> Thanks...jim_wendel@ub.cc.umich.edu or jwendel@isdmnl.wr.usgs.gov
>> 
>> 

>Symbollic entries in arrays is not the point.

>One uses this program by making it the current SOLVER equation, putting a
square
>array in 'A', the square identity in 'I' and solving for 'L', the eigenvalue.
>This program looks like it was taken from the "Easy Course in Using the
HP-28S"
since the 28
>doesn't have the lambda character, L was used instead.

  The HP-28 solution book "Matrices & Vectors" has a more elegant solution that
is probably faster and works better in that you don't have to call the solver.
I wrote a plug-and-chug program around this.  Enter the matrix, press the key,
and you get back the eigenvalues.
  It works by finding the characteristic polynomial, then solving for that.
I posted this a while ago, but some peopl seem to have missed it, and I also 
left out the root-finding programs.  This program needs some way of solving an
arbitrary degree polynomial.  The program "BAIRS" which came by the net a
while back seems to do the job well.  I don't remember who wrote this though
(Wayne Scott?).   
  All the programs are available via anonymous FTP from scion.cs.orst.edu
(128.193.32.25):~ftp/pub/jacobsd/{hp.eig,hp.proot}.

%%HP: T(3)A(R)F(.);
      EIGVAL
        \<< DUP DUP
SIZE 1 GET \-> t g n
          \<< { } 1 n
            START 0
1 n
              FOR i
t i DUP 2 \->LIST GET
+
              NEXT
1 \->LIST + 't' g
STO*
            NEXT \->
b
            \<< { 1 }
1 n
              FOR i
\-> s
\<< 0 1 i
  FOR j b j GET s i
j - 1 + GET * -
  NEXT i / 1 \->LIST
s SWAP +
\>>
              NEXT
            \>>
          \>> PROOT
        \>>

  This is my eigenvalue program.  PROOT is a program that will solve f(x)=0
for a polynomial.  It takes a list of numbers which are coefficients for the
polynomial (i.e. "4 * x^2 + 3 * x - 3" would be { 4 3 -2 } ).  Programs for
this are available on the net, or I could send mine to you.  (Or you can
anonymous ftp it from scion.cs.orst.edu:pub/jacobsd/proot & math)  The 
files aren't in great shape (^M's at the end of each line) but it's there.

    Start:     An n x n matrix in level 1
    Stop:      n real or complex values on the stack.  These are the 
	       eigenvalues.

%%HP: T(3)A(R)F(.);
PROOT
\<< DUP SIZE \-> n
  \<<
    IF n 3 >
    THEN DUP { HOME
MATH POLY BAIRS }
RCL EVAL SWAP OVER
{ HOME MATH POLY
PDIV } RCL EVAL
DROP2 \-> a b
      \<< a PROOT b
PROOT
      \>>
    ELSE
      IF n 2 >
      THEN { HOME
MATH POLY QUD } RCL
EVAL
      ELSE LIST\->
DROP NEG SWAP /
      END
    END
  \>>
\>>

BAIRS
\<< LIST\-> 1 1
\-> n R S
  \<<
    DO 0 n
1 + PICK 0 0 0 4
PICK 5 n + 7
    FOR J
J PICK R 7 PICK * +
S 8 PICK * + 7 ROLL
DROP DUP 6 ROLLD R
3 PICK * + S 4 PICK
* + 5 ROLL DROP -1
    STEP
3 PICK SQ 3 PICK 6
PICK * -
      IF
DUP 0 ==
      THEN
DROP 1 1
      ELSE
6 PICK 6 PICK * 5
PICK 9 PICK * -
OVER / 4 PICK 9
PICK * 8 PICK 7
PICK * - ROT /
      END
DUP 'S' STO+ SWAP
DUP 'R' STO+
    UNTIL
R\->C ABS .000000001
< 7 ROLLD 6 DROPN
    END n
DROPN 1 R NEG S NEG
3 \->LIST
  \>>
\>>

QUD
\<< LIST\->
\->ARRY DUP 1 GET /
ARRY\-> DROP ROT DROP
SWAP 2 / NEG DUP SQ
ROT - \v/ DUP2 + 3
ROLLD -
\>>


  That's it.  Hope everything works fine -- I don't have a cable to transfer
the stuff, so got a friend to do the transfer..
--
Dana Jacobsen                       Oregon State University
jacobsd@cs.orst.edu                   Computer Science
..!hplabs!hp-pcd!orstcs!jacobsd
Dana_Jacobsen@RPITSMTS.BITNET            `Once a daemon, always a daemon'