wscott@EN.ECN.PURDUE.EDU (Wayne H Scott) (02/26/90)
I have always used the symbolic matrix programs to compute Eigenvalues until
today when I discovered a fast and simple way to do it using the hp28
solver.
The solver can the zero of a function or even a program if it does not take a
number off the stack and returns one number to the stack.
Enter the following program into your HP.
<< A DUP IDN X * - DET >>
Now press STEQ and enter the solver.
A and X appear on the menus. Enter the matrix you want to have the Eigenvalues
of and press A. Now enter you first guess for X and press X. Press shift X
and the solver will come up with a value.
I don't know about you people but I was very exicited when I discovered how
easily the system that already exists allows you to solver this problem.
Note: Inital test show that this is much faster than using other Eigenvalue
programs.
_______________________________________________________________________________
Wayne Scott | INTERNET: wscott@en.ecn.purdue.edu
Electrical Engineering | BITNET: wscott%ea.ecn.purdue.edu@purccvm
Purdue University | UUCP: {purdue, pur-ee}!en.ecn.purdue.edu!wscottakcs.jwendel@hpcvbbs.UUCP (James G. Wendel) (12/20/90)
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
john%solvint@orstcs.UUCP (12/21/90)
> 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" where it was used to solve for the eigenvalues of matrix 'A', but since the 28 doesn't have the lambda character, L was used instead. To use it to find the characteristic polynomial of [[ 1 2 ][ 3 2 ]], do the following: \<< A I * - DET \>> [lshift] [SOLVE] [STEQ] [SOLVR] [[ 1 2 ][ 3 2 ]] [A] [[ 1 0 ][ 0 1 ]] [I] -100 [L] @ as a guess [lshift] [L] ==> L: -1 100 [L] @ as a guess [lshift] [L] ==> L: 4 To create the polynomial from these, subtract each from T and multiply: 'T' SWAP - SWAP 'T' SWAP - * This gives '(T+1)*(T-4). Expanding: EXPAN EXPAN COLCT gives '-4+T^2-3*T' -- John W. Loux | Solve and Integrate Corp solvint!john@orstcs.cs.orst.edu | PO Box 1928 john@solvint.uucp | Corvallis, OR 97339-1928 | (503) 754-1207
jacobsd@usenet@scion.CS.ORST.EDU (Dana Jacobsen) (12/22/90)
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" >where it was used to solve for the eigenvalues of matrix 'A', but 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'