A Third Order Complex Linear Equation Solver for the hp 33s

[Palmer O. Hanson, Jr.]

In response to publication of my "Sixth Order Linear Equation Solver for the hp 33s" (Article No. 676) correspondent Gerson W. Barbosa wrote "... Now, a fourth or even a third order Complex Linear Equation Solver would be great, but that would be asking too much, I recognize."

I have written a third order complex linear equation solver for the hp 33s. It is much too long to be in the Forum so it has been posted as Article 722.

So far, I have only tested the program with three problems:

1. The test problem in Article 722.

2. The test problem in Article 722 modified to cause a determinant of zero which will trigger the "DIVIDE BY ZERO" abort.

2. The Simultaneous Equation problem from page 15-18 of the hp 33s User's Guide to demonstrate the capability to solve third order linear equations with real coefficients.

[Gerson W. Barbosa]

Quote:

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In response to publication of my "Sixth Order Linear Equation Solver for the hp 33s" (Article No. 676) correspondent Gerson W. Barbosa wrote "... Now, a fourth or even a third order Complex Linear Equation Solver would be great, but that would be asking too much, I recognize."

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Hey, thank you very much Sir!

Of course, when I said "asking too much" I didn't mean this was not feasible. I meant it was a difficult task to ask to someone who'd already given us a sixth order linear equation solver (and later even an eighth order one!). I am glad you have written this, even if it might not be so useful to you as it may be to some of us here. When I needed to solve complex linear systems at college, I relied on an HP-28S, but then I did write a program for the SHARP PC-1211 for a colleague, but the task was way easier in BASIC than it is in RPN keystroke programming.

Quote:

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So far, I have only tested the program with three problems

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I will try it later with a real problem I once had to solve at work.

Best regards,

Gerson.

[Palmer O. Hanson, Jr.]

I listed the command at step M0058 incorrectly as STO (I) which, of course, is not a valid command. The command should be STO (i) .

[Gerson W. Barbosa]

For a problem this long, perhaps it should be useful if you include a length and checksum table in your article, so that the user has an easy way to check if everything was keyed in correctly:

LABEL  LENGTH  CHECKSUM

------------------------

  L      45      C89C

  M     432      A45A

  D     210      038E

  V     150      9987

  X      27      6AB0

A preference for roman numerals when choosing the labels or just a coincidence? I haven't checked your program with other problems, so the table should be checked against your own.

By the way, my n-order complex equation solver for the CASIO PB-700 finds the same answers to your test problem in 14.5 seconds.

Best regards,

Gerson.

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	  10 CLS :CLEAR :INP		T=R(L,J):R(L,J)=R(I,		D=I(I,I):GOSUB 290

	UT "Order: ",N:N=N-1		J):R(I,J)=T		 	 210 R(I,N+1)=X:I(I,

	:DIM R(N,N+1),I(N,N+		 100 T=I(L,J):I(L,J)		N+1)=Y:NEXT I:BEEP :

	1)				=I(I,J):I(I,J)=T:NEX		FOR I=0 TO N:CLS

	  20 FOR I=0 TO N:FO		T J		 		 220 PRINT "XR(";I+1

	R J=0 TO N+1		 	 110 FOR J=I+1 TO N		;"):";USING"#####.##

	  30 CLS :PRINT "R("		 120 A=R(J,I):B=I(J,		####";R(I,N+1);:LOCA

	;I+1;",";J+1;"):";:L		I):C=P:D=Q:GOSUB 290		TE 0,2

	OCATE 0,2:PRINT "I("		:F=X:G=Y		 	 230 PRINT "XI(";I+1

	;I+1;",";J+1;"):";		 130 FOR K=I+1 TO N+		;"):";USING"#####.##

	  40 LOCATE 12,0:INP		1:A=F:B=G:C=R(I,K):D		####";I(I,N+1);

	UT "",R(I,J):LOCATE 		=I(I,K):GOSUB 280		 240 X$=INKEY$:IF X$

	12,2:INPUT "",I(I,J)		 140 R(J,K)=R(J,K)-X		="" THEN 240 ELSE NE

	:NEXT J:NEXT I			:I(J,K)=I(J,K)-Y:NEX		XT I

	  50 CLS :PRINT "Wai		T K:NEXT J:NEXT I		 250 IF X$=" " THEN

	t...":FOR I=0 TO N-1		 150 A=R(N,N):B=I(N,		10 ELSE CLS :END

	:P=R(I,I):Q=I(I,I):L		N):GOSUB 300:IF M<1E		 260 CLS :BEEP :BEEP

	=0				-10 THEN 260		 	:PRINT "No solution

	  60 FOR J=I+1 TO N:		 160 FOR I=N TO 0 ST		!"

	A=R(J,I):B=I(J,I):GO		EP -1:R=0:S=0:J=I		 270 X$=INKEY$:IF X$

	SUB 300:T=M:A=P:B=Q		 170 IF J>N-1 THEN 2		="" THEN 270 ELSE 25

	  70 GOSUB 300:IF T>		00				0

	M THEN P=R(J,I):Q=I(		 180 J=J+1:A=R(I,J):		 280 X=A*C-B*D:Y=A*D

	J,I):L=J			B=I(I,J):C=R(J,N+1):		+B*C:RETURN

	  80 NEXT J:A=P:B=Q:		D=I(J,N+1)		 	 290 M=C*C+D*D:X=(A*

	GOSUB 300:IF M<1E-10 		 190 GOSUB 280:R=R+X		C+B*D)/M:Y=(B*C-A*D)

	 THEN 260 ELSE IF L=		:S=S+Y:GOTO 170			/M:RETURN

	0 THEN 110		 	 200 A=R(I,N+1)-R:B=		 300 M=A*A+B*B:RETUR

	  90 FOR J=I TO N+1:		I(I,N+1)-S:C=R(I,I):		N

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 1 < N < 30 (with all three 4KB memory packs in place)

_{Edited to correct a typo in line 130.}

Edited: 5 July 2007, 5:05 p.m.

[Palmer O. Hanson, Jr.]

Gerson:

You wrote:

Quote:

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A preference for roman numerals when choosing the labels or just a coincidence? I haven't checked your program with other problems, so the table should be checked against your own.

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I used the labels I did because those were the ones which were available with two other programs on the machine. That may mean that I have a distaste for roman numerals, but I don't think so.

I match your lengths for all five programs. Unfortunately, I had to move my 33s programs around and had to use Label P instead of Label D. That means that the checksums for M and P are different.

I devised the original test problems with pencil and paper so using integers was an easy way to do it. But, I am always a little nervous until I have also run a program such as this with non integers. I was using my HP-28s for another problem when I belatedly discovered that it can divide a complex vector by a complex matrix. I have subsequently run several problems with values other than integers and the HP-28s results and the HP-33s results agree.

Edited: 7 July 2007, 3:03 a.m.