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An Extension for Stefan's Matrix Multi-Tool Program
Posted by Palmer O. Hanson, Jr. on 4 May 2008, 9:24 a.m.
In a thread starting on of November 2, 2007 Stefan Vorkoetter announced that a Matrix Multi-Tool program for the HP-35s was available at his site http://www.stefanv.com/calculators/hp35s_matrix_multitool.html . He noted that his program "... is a long way from being as powerful as the facilities provided by the 15C, 41C/Advantage, or 42s, but it does provide several useful matrix operations in one simple tool. It is loosely modelled after the Advantage Pac matrix program and provides an easy-to-use subset of the functionality of the matrix library. ..."
This program was written to work with Stefan's program and provide more of the matrix processing functions that one finds in machines such as the HP-28S and TI-86. This program relies on Stefan's program for entry and readout of data, and for solution of linear equations. Stefan's program uses one matrix (Matrix A) and one vector (Vector B) for input and output. His program also uses a second matrix (which I shall call Matrix C) during the linear equation solution. Matrix C is not directly accessible through Stefan's input and output routines. This program adds a storage matrix (which I shall call Matrix D). Additional matrix processing functions provided by this program include:
Calculation of Frobenius norm (ABS), the row norm, and the column norm of Matrix A.
Moving of matrices between Stefan's matrix A and either his matrix C or the added storage matrix D using store, recall and exchange commands. Moving of matrices directly between Matrix C and Matrix D is not provided.
Matrix mathematics including the product of Matrix A and Vector b, the product of Matrix A and Matrix C, and the sum or difference between Matrix A and Matrix C.
Special operations such as the dot product of Matrix A and Matrix C, the formation of an identity matrix in Matrix A, the filling Matrix A with a user-defind constant value, and the transpose of Matrix A..
This program uses a menu system similar to that used in Stefan's program. Like Stefan's program it saves labels by having all routines part of the main program label. At program entry and at the completion of each function the menu 1NRM 2MOV 3MTH 4OPS 5XXX appears in the display.
Selection the NRM option brings the menu 1ABS 2COL 3ROW to the display. Pressing any number key other than 1, 2, or 3 and pressing R/S returns the program to the entry menu.. Entering 1, 2, or 3 and pressing R/S brings the Frobenius norm (ABS), the column norm (COL) or the row norm (ROW) of contents of Matrix A to the display. Then pressing R/S returns the calculator to the entry menu. Matrix A is not disturbed by these operations.
Selection of th MOV option from the main menu brings the menu 1STOC 4STOD 2RCLC 5RCLD 3EXCC 6EXCD to the display. Note that there are two spaces between each option in the program listing. This avoids splitting the option nomenclature during display.
The STO commands copy the contents Matrix A into Matrix C or Matrix D.
The RCL commands copy the contents of Matrix C or Matrix D into Matrix A
The EXC commands exchange the contents of Matrix A with the contents of Matrix C or Matrix D.
Selection of the MTH option from the main menu brings the menu 1AxB 2AxC 3A+C 4A-C to the display.
The AxB command multiplies the contents of Matrix A by the contents of Vector B and places the result in Vector B and in the left hand column of Matrix C.
The AxC command multiplies the contents of Matrix A times the contents of Matrix C and places the result in Matrix A. The contents of Matrix A before the multiply are placed in Matrix C.
The A+C command adds the contents of Matrix A and Matrux C and places the result in Matrix A. Tjhe contents of Matrix A before the addition are placed in Matrix C.
The A-C command subtracts the contents of Matrix C from the contents of Matrix A and places the result in Matrix A. The contents of Matrix A before the subtracion are placed in Matrix C.
Selection of the OPS option from the main menu brings the menu 1DOT 2IDN 3FIL 4TRN to the display.
The DOT command calculated the dot product of the contents of Matrix A and Matrix C and delivers the result to the display.
The IDN command replaces the contents of Matrix A with an identity matrix.
The FIL command replaces the contents of Matrix A with a matrix which has all elements equal to a value selected by the user.
The TRN command replaces the contents of Matrix A with its transpose and leaves the matrix which was formerly in Matrix A in Matrix C.
This program includes a dummy option in the main menu which is labeled 5XXX . I have been considering adding an I/O routine so that the user didn't have to move back and forth between Stefan's program and this program, but I haven't done it yet. Including the dummy option means that if I decide to do it later I will simply have to replace the XXX with an appropriate nomeclature and proceed to enter the new option beginning at step N427 of the existing program. The result will be that I will not have to modify existing GTO addresses in the documentation of the present program when and if I decide to make an addition.
The functions of this program assume that the order of the matrix is in N. Any other control variables are calculated inside each individual function. This results in a substantial amount of duplicate code. Furthemore, since I was also trying to expand my programming skill on the HP35s I used different methods of calculating the same control variables.
This program uses a subroutine starting at M389 from Stefan's original Matrix Multi-Tool program. If you are using the revision dated April 3, 2008 then you must change the commands at locations N244 and N289 from XEQ M389 to XEQ M403.
N001 LBL N N002 SF 10 N003 EQN 1NRM 2MOV 3MTH 4OPS 5XXX N004 CF 10 N005 1 N006 x=y? N007 GTO N025 N008 x<>y N009 2 N010 x=y? N011 GTO N119 N012 x<>y N013 3 N014 x=y? N015 GTO N222 N016 x<>y N017 4 N018 x=y? N019 GTO N324 N020 x<>y N021 5 N022 x=y? N023 GTO N427 N024 GTO N002 N025 SF 10 N026 EQN 1ABS 2COL 3ROW N027 CF 10 N028 1 N029 x=y? N030 GTO N040 N031 x<>y N032 2 N033 x=y? N034 GTO N057 N035 x<>y N036 3 N037 x=y? N038 GTO N084 N039 GTO N002 N040 RCL N N041 x^2 N042 1 N043 - N044 1000 N045 / N046 STO I N047 0 N048 RCL (I) N049 x^2 N050 + N051 ISG I N052 GTO N048 N053 SQRTx N054 STO A N055 VIEW A N056 GTO N002 N057 RCL N N058 1 N059 - N060 1000 N061 / N062 STO I N063 STO J N064 CLx N065 ENTER N066 0 N067 RCL (I) N068 ABS N069 + N070 ISG I N071 GTO N067 N072 x<y? N073 x<>y N074 RCL N N075 1000 N076 / N077 STO+ I N078 x<>y N079 ISG J N080 GTO N066 N081 STO C N082 VIEW C N083 GTO N002 N084 RCL N N085 STO I N086 1 N087 - N088 1000 N089 / N090 STOx I N091 STO J N092 RCL N N093 100000 N094 / N095 STO+ I N096 CLx N097 ENTER N098 0 N099 RCL (I) N100 ABS N101 + N102 ISG I N103 GTO N099 N104 x<y? N105 x<>y N106 RCL N N107 x^2 N108 1 N109 - N110 STO- I N111 0.001 N112 STO+ I N113 REGZ N114 ISG J N115 GTO N098 N116 STO R N117 VIEW R N118 GTO N002 N119 SF 10 N120 EQN 1STOC 4STOD 2RCLC 5RCLD 3EXCC 6EXCD 2 spaces between each N121 CF 10 N122 1 N123 x=y? N124 GTO N146 N125 x<>y N126 2 N127 x=y? N128 GTO N163 N129 x<>y N130 3 N131 x=y? N132 GTO N180 N133 x<>y N134 4 N135 x=y? N136 GTO N198 N137 x<>y N138 5 N139 x=y? N140 GTO N206 N141 x<>y N142 6 N143 x=y? N144 GTO N214 N145 GTO N002 N146 0 N147 STO J N148 RCL N N149 x^2 N150 STO+ J N151 1 N152 - N153 1000 N154 / N155 STO I N156 RCL (I) N157 STO (J) N158 1 N159 STO+ J N160 ISG I N161 GTO N156 N162 GTO N002 N163 0 N164 STO J N165 RCL N N166 x^2 N167 STO+ J N168 1 N169 - N170 1000 N171 / N172 STO I N173 RCL (J) N174 STO (I) N175 1 N176 STO+ J N177 ISG I N178 GTO N173 N179 GTO N002 N180 0 N181 STO J N182 RCL N N183 x^2 N184 STO+ J N185 1 N186 - N187 1000 N188 / N189 STO I N190 RCL (I) N191 x<>(J) N192 STO (I) N193 1 N194 STO+ J N195 ISG I N196 GTO N190 N197 GTO N002 N198 RCL N N199 ENTER N200 x^2 N201 + N202 1 N203 + N204 STO J N205 GTO N148 N206 RCL N N207 ENTER N208 x^2 N209 + N210 1 N211 + N212 STO J N213 GTO N165 N214 RCL N N215 ENTER N216 x^2 N217 + N218 1 N219 + N220 STO J N221 GTO N182 N222 SF 10 N223 EQN 1AxB 2AxC 3A+C 4A-C N224 CF10 N225 1 N226 x=y N227 GTO N241 N228 x<>y N229 2 N230 x=y? N231 GTO N252 N232 x<>y N233 3 N234 x=y? N235 GTO N301 N236 x<>y N237 4 N238 x=y? N239 GTO N303 N240 GTO N002 N241 RCL N N242 ENTER N243 x^2 N244 2 N245 x N246 + N247 STO E N248 XEQ M389 N249 CF 0 N250 CF 2 N251 GTO N002 N252 RCL N N253 ENTER N254 x^2 N255 x N256 4 N257 / N258 2 N259 + N260 INTG N261 STO T N262 VIEW T N263 RCL N N264 ENTER N265 x^2 N266 2 N267 x N268 + N269 STO E N270 RCL N N271 1 N272 - N273 1000 N274 / N275 STO V N276 RCL N N277 STO J N278 x^2 N279 STO+ J N280 STO+ J N281 STO I N282 STO+ I N283 1 N284 STO- J N285 STO- I N286 - N287 1000 N288 / N289 STO+ I N290 RCL (I) N291 STO (J) N292 DSE J N293 DSE I N294 GTO N290 N295 XEQ M389 N296 ISG V N297 GTO N276 N298 CF 0 N299 CF 2 N300 GTO N180 N301 1 N302 GTO N304 N303 -1 N304 STO S N305 RCL N N306 x^2 N307 STO J N308 1 N309 - N310 1000 N311 / N312 STO I N313 RCL (I) N314 RCL (J) N315 RCL S N316 x N317 + N318 STO (J) N319 1 N320 STO+ J N321 ISG I N322 GTO N313 N323 GTO N180 N324 SF 10 N325 EQN 1DOT 2IDN 3FIL 4TRN N326 CF 10 N327 1 N328 x=y? N329 GTO N343 N330 x<>y N331 2 N332 x=y? N333 GTO N366 N334 x<>y N335 3 N336 x=y? N337 GTO N389 N338 x<>y N339 4 N340 x=y? N341 GTO N401 N342 GTO N002 N343 RCL N N344 x^2 N345 STO J N346 1 N347 - N348 1000 N349 / N350 STO I N351 0 N352 RCL (I) N353 RCLx (J) N354 + N355 1 N356 STO+ J N357 R Down N358 ISG I N359 GTO N352 N360 ENTER N361 SF 10 N362 EQN DOT = N363 CF 10 N364 STOP N365 GTO N002 N366 RCL N N367 x^2 N368 1 N369 - N370 1000 N371 / N372 STO I N373 RCL I N374 INTG N375 RCL N N376 1 N377 + N378 / N379 FP N380 x=0? N381 GTO N384 N382 0 N383 GTO N385 N384 1 N385 STO (I) N386 ISG I N387 GTO N373 N388 GTO N002 N389 INPUT K N390 RCL N N391 x^2 N392 STO I N393 1 N394 STO- I N395 RCL K N396 STO (I) N397 RCL I N398 x not equal 0 ? N399 GTO N393 N400 GTO N002 N401 RCL N N402 x^2 N403 STO W N404 STO J N405 1 N406 - N407 1000 N408 / N409 STO I N410 RCL (I) N411 STO (J) N412 RCL N N413 STO+ J N414 x^2 N415 2 N416 x N417 RCL J N418 x<y? N419 GTO N424 N420 1 N421 STO+ W N422 RCL W N423 STO J N424 ISG I N425 GTO N410 N426 GTO N180 N427 GTO N002Since some users have reported the length and checksum may not be reliable I have provided some example problems which will demonstrate that the program has been properly entered. We will use three 3x3 matrices
Length = 1532; Checksum = 0AE0
HP33 HP15 ProductThe matrix at the left is from the demonstration of the Solutions of Simultaneous Equations program on page 1-18 of the hp33s user's guide. The matrix in the center is from the demonstration of a residual correction program on page 121 of the HP-15C Advanced Functions Handbook. The matrix on the right is the product of the matrix on the left and the matrix in the center; i.e., HP33xHP15
23 15 17 33 16 72 263 150 512
8 11 -6 -24 -10 -57 48 42 51
4 15 12 -8 -4 -17 -324 -134 -771
1. Use Stefan's program to enter HP15 into Matrix A..
2. Use the NRM functions of this program to calculate the Frobenius norm (ABS) of HP15 as 104.033648403, the row norm (ROW) as 121 and the column norm (COL) as 146 .
3. Use the STOC and STOD functions of this program to store HP15 into Matrix C and into Matrix D. This leaves HP15 in all three matrix locations.
4. Use Stefan's program to enter HP33 into Matrix A.
5. Use the DOT function of this program to calculate the dot product of HP33 and HP15 as 1967.
6. Use the AxC function of this program to calculate the product HP33xHP15. The execution time estimate will be 8 seconds. The product will be in Matrix A and HP33 will be in Matrix C.
7. Use the ABS function of this program to calculate the Frobenius norm of HP33xHP15 as 1,038.197958 .If this is correct you can be reasonably confident that the AxC function is working properly. You can verify the individual elements of the product by returning to Stefan's program.
8. Use the EXCC function of this program to exchange the contents of Matrix A and the contents of Matrix C. This places HP33 in Matrix A and the product in Matrix C.
9. Use the STOD function of this program to store the contents of Matrix A into Matrix D. This places HP33 in Marix D.
10. Use Stefan's program to enter the vector [ 31 17 14 ] in b. Solve and read the determinant of HP33 as 4,598. Read the solution vector X to the problem on page 15-18 of the hp33s user's guide from b as
9.30622009565E-1 7.94258373205E-1 -0.13636363636The inverse of HP33 will be in matrix A and in Matric C. HP33 will still be in Matrix D.
11. Use the RCLD function of this program to recall HP33 from Matrix D and place it into Matrix A . Use the AxB function of this program to multiply HP33 by the solution vector found in step 10. The product HP33xX will be in b and in the left hand column of Matrix C.
12. Use Stefan's program to read out the product HP33xX as
31 17 14.000000000113. Use the STO C function of this program to store the contents of Matrix A (HP33) into Matrix C. Use the IDN function of this program to place the 3x3 identity matrix in Matrix A. Use the A+C function of this program to place the sum HP33 and the identiity matrix in Matrix A. The identity matrix will still be in matrix C. Use the ABS function of this program to calculate the Frobenius norm of the sum of HP33 and the identity matrix as 41.7612260356. Again, if this is correct you can be reasonably confident that the IDN and A+C functions are working properly. You can verify the individual elements of the sum with Stefan's program to be
24 15 1714. Use the STOC function of this program to store the matrix in Matrix A into Matrix C. Use the FIL function of this program to place a matrix of all two's in Matrix A. Use the EXCC function of this program to exchange the matrices in Matrix A and Matrix C. Use the A-C function of this program to subtract the matrix of all two's from the matrix in Matrix A (which is thes sum of HP33 and the 3x3 identity matrix) in Matrix A.. Calculate the Frobenius norm of the result as 37.0405183549 . Once again, if this is correct you can be reasonably confident that the FIL and A-C functions are working properly. You can verify the individual elements of the difference with Stefan's program to be
8 12 -6
4 15 13
22 13 1515. Use the EXCD function of this program to bring HP33 to Matrix A. Use the TRN function of this program to place the transpose of HP-33 in Matrix A. Use Stefan's program to verify that the transpose of HP33 is in Matrix A.
6 10 -8
2 13 11
Some other subroutine capabilities of Stefan's program:
Entry at M328 will copy the contents of the temporary matrix into matrix A and stop with the contents of the D register in X.
Entry at M383 will stop with a time estimate in the display. When R/S is pressed the product of matrix A and vector B will be placed in the left hand column of the temporary matrix and in vector b. To avoid stopping for the time estimate enter at M389.
Entry at M415 will copy the contents of the left hand column of the temporary matrix into vector b.
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