Threaded Mode | Linear Mode

mbrethen · 04-11-2015, 03:12 PM

I'm learning to program on the HP 35s; most of my experience programming an HP calculator is with the 41 series. I wrote a program to Solve Linear Systems. Its objective is to reduce the matrix on the upper right to a diagonal form with only ones in the diagonal. The determinant of this matrix is also computed and stored in named variable D.

Given a system of equations, for example:

2x + 3y + 5z + 4t = 39
-4x + 2y + z + 3t = 15
3x - y + 2z + 3t = 19
5x + 7y - 3z + 2t = 18

is re-written

39 = 2x + 3y + 5z + 4t
15 = -4x + 2y + z + 3t
19 = 3x - y + 2z + 3t
18 = 5x + 7y - 3z + 2t

storing these 20 numbers column-wise in R01 thru R20.

-If flag F00 is clear the pivots smaller than E-7 ( line 60 ) is regarded as zero
-If flag F00 is set, only zero is regarded as zero
-CF 01 = partial pivoting , SF 01 = no pivoting

There are 4 rows and 5 columns,

CF 00 CF 01
4 ENTER
5 XEQ "L" ENTER

Det A = 840 = Named Variable D

Registers R05 thru R16 now contain the unit matrix and registers R01 thru R04 contain the solution x = 1 , y = 2 , z = 3 , t = 4

When the program stops, D = det A.

Code:

L001 LBL "L"

L002 X<>Y

L003 .1

L004 %

L005 +

L006 STO N

L007 *

L008 LASTX

L009 FP

L010 -

L011 STO O

L012 1

L013 STO D       

L014 LASTX

L015 %

L016 REGZ

L017 IP

L018 +

L019 STO M

L020 FS? 1

L021 GTO L059

L022 IP

L023 RCL O

L024 FP

L025 +

L026 STO I

L027 0

L028 RCL(I)

L029 ABS 

L030 X<Y?

L031 GTO L036

L032 X<>Y

L033 CLX

L034 RCL I

L035 STO J

L036 RDN

L037 DSE I

L038 GTO L028

L039 RCL M

L040 STO I

L041 ENTER

L042 FP

L043 RCL J

L044 IP

L045 +

L046 STO J

L047 X=Y?

L048 GTO L059

L049 RCL(J)

L050 X<>(I)

L051 STO(J)

L052 DSE J

L053 RDN

L054 DSE I

L055 GTO L049

L056 RCL D

L057 +/-

L058 STO D

L059 CLX

L060 FS? 0

L061 GTO L063

L062 E-7

L063 RCL M

L064 STO I

L065 CLX

L066 RCL(I)

L067 STO* D

L068 ABS

L069 X<=Y?

L070 CLX

L071 X=0?

L072 STO D

L073 X=0?

L074 GTO L100

L075 LASTX

L076 ST/(I)

L077 DSE I

L078 GTO L076

L079 RCL O

L080 STO P

L081 RCL M

L082 STO I

L083 ENTER

L084 FP

L085 RCL P

L086 IP

L087 +

L088 X=Y?

L089 GTO L098

L090 STO J

L091 RCL(I)

L092 RCL*(J)

L093 STO-(J)

L094 DSE J

L095 RDN

L096 DSE I

L097 GTO L091

L098 DSE P

L099 GTO L081

L100 RCL N

L101 STO- O

L102 RCL O

L103 RCL M

L104 1

L105 -

L106 STO M

L107 X<=Y?

L108 CLX

L109 DSE M

L110 GTO L113

L111 RCL D

L112 RTN

L113 RCL M

L114 GTO L020

Program Notes:

Lines 28-38 Find the largest element of a column above the diagonal
Lines 49-55 Swap rows
Lines 59-78 Divides all the row by the pivot so this diagonal element becomes 1
Then this row is used to replace by 0 all the other elements of this column using linear combinations of rows.

Lines 81-89 Scans all the column to which belongs a given pivot ( = 1 now )
If the element of this column is the diagonal element ( line 88 X=Y? ) the process below is skipped ( GTO L098 ).

Lines 90-97 A linear combination of the rows is performed to replace the element of this column by 0.

The program isn't working quite right yet and I haven't been able to trace the error. Any help would be appreciated.

Thomas Klemm · 04-11-2015, 07:56 PM

You might find this program helpful:
A Matrix Multi-Tool for the HP 35s Programmable Calculator

Kind regards
Thomas

Jeff_Kearns · (This post was last modified: 04-12-2015 12:23 PM by Jeff_Kearns.)

(04-11-2015 03:12 PM)mbrethen Wrote: I'm learning to program on the HP 35s;

Based on this article, you have some experience with this calculator and Stephan's program.

Jeff

mbrethen · (This post was last modified: 04-13-2015 02:14 AM by mbrethen.)

That was my first try at programming the 35s. I made some minor modifications to an existing program written by Mr. Hanson and used it along with the other program from Stefan, already mentioned, for some engineering classes I was taking at the time.

So, yeah, I'm still learning. After spending a week debugging this program I traced the errors to lines L091-L114.

Code:

L001 LBL "L"

L002 X<>Y

L003 .1

L004 %

L005 +

L006 STO N

L007 *

L008 LASTX

L009 FP

L010 -

L011 STO O

L012 1

L013 STO D       

L014 LASTX

L015 %

L016 REGZ

L017 IP

L018 +

L019 STO M

L020 FS? 1

L021 GTO L059

L022 IP

L023 RCL O

L024 FP

L025 +

L026 STO I

L027 0

L028 RCL(I)

L029 ABS 

L030 X<Y?

L031 GTO L036

L032 X<>Y

L033 CLX

L034 RCL I

L035 STO J

L036 RDN

L037 DSE I

L038 GTO L028

L039 RCL M

L040 STO I

L041 ENTER

L042 FP

L043 RCL J

L044 IP

L045 +

L046 STO J

L047 X=Y?

L048 GTO L059

L049 RCL(J)

L050 X<>(I)

L051 STO(J)

L052 DSE J

L053 RDN

L054 DSE I

L055 GTO L049

L056 RCL D

L057 +/-

L058 STO D

L059 CLX

L060 FS? 0

L061 GTO L063

L062 E-7

L063 RCL M

L064 STO I

L065 CLX

L066 RCL(I)

L067 STO* D

L068 ABS

L069 X<=Y?

L070 CLX

L071 X=0?

L072 STO D

L073 X=0?

L074 GTO L103

L075 LASTX

L076 ST/(I)

L077 DSE I

L078 GTO L076

L079 RCL O

L080 STO P

L081 RCL M

L082 STO I

L083 ENTER

L084 FP

L085 RCL P

L086 IP

L087 +

L088 X=Y?

L089 GTO L098

L090 STO J

L091 RCL(J)

L092 ENTER

L093 ENTER

L094 ENTER

L095 RCL*(I)

L096 STO-(J)

L097 DSE J

L098 RDN

L099 DSE I

L100 GTO L095

L101 DSE P

L102 GTO L081

L103 RCL O

L104 RCL- N

L105 STO O

L106 RCL M

L107 1

L108 -

L109 X>Y?

L110 GTO L114

L111 CLX

L112 RCL D

L113 RTN

L114 STO M

L115 DSE M

L116 RCL M

L117 GTO L020

I decided to replace those menu-driven programs with a library of matrix programs that use a control-number format similar to the 41 Advantage module.

So far, I have added the following to my library:
1. Storing a Matrix (which can be found here).
2. Addition & Subtraction
3. Multiplication
4. Norm of a Matrix
5. Trace of a Square Matrix
6. Transpose
a) General case
b) Square Matrix
7. Copying a Matrix

They are translations of Jean-Marc Baillard's programs for the 41.