Downhill Simplex Method (Nelder Mead) for WP-34S « Next Oldest | Next Newest »

 ▼ Marcel Samek Member Posts: 189 Threads: 39 Joined: Nov 2011 07-07-2013, 03:05 AM Over the years I have found the Downhill Simplex method very useful in all sorts of very varied applications. It may have its flaws and quirks, but with a little bit of massaging, I have found it an extremely reliable tool. So, for the first time, instead of writing application specific C code, I decided to put a version on my WP-34S. The code supports 8 dimensions but no more. You will need to write a function called 'FUN'. As it is implemented, you cannot pass the name of the function to the routine. The tolerance that needs to be met is hardcoded into the code and should probably be passed in, but I don't feel like making that change right now. The maximum number of iterations is also in the code and should also be changed to be a parameter. And, I don't feel like doing that either. This code is based on the Amoeba routines found in Numerical Recipes. I have not documented the code particularly well, however I am including a link to a version of the code that has corresponding C code inline as documentation. ------------- User Program ------------------ ```/* Nelder Mead (Downhill Simplex) Method Multi-dimensional Minimization Limitations: The code supports up to 8 dimensions, but you will probably not be able to use that many because of memory restrictions. It depends on the size of your evaluation function, register allocations, etc. Global Register required: N^2 + N + 20 Stack: Requires a stack size of 8 Local Registers: (20 at deepest point) + (your eval function) Prerequisite: You need to have a global function called 'FUN' which evaluates your function. The parameters to FUN are all passed on the stack. FUN needs to return one value (the evaluated function) in X. Input: (X) Number of dimensions Output: R03: F(x1, x2, x3....) at minimum R04: x1 R05: x2 R06: X3 ... Configuration: This algorithm is known for getting stuck, especially if the function has lots of local minima or discontinuities. There is a configuration value that defines the maximum number of times it shall adjust the simplex before giving up. It defaults to 10000. If you wish to adjust this value, it is assigned to local register .06 right at the beginning of NMS. The initial guess is aribrarily picked to be between 0 and 1 on all dimensions. If you wish to change the initial values, simply change the initValues function at LBL 31. Make sure that when that function returns it has valid values in the Y array for the simplex vertices you have chosen as the starting point. Algorithm: This is a direct derivative of the Downhill Simplex method as described and implemented in Numerical Recipes. Please see that text for a description of how the algorithm works. */ 0001 LBL'NMS' 0002 LocR 007 0003 REGS 100 0004 SSIZE8 0005 CLREGS 0006 STO 00 0007 1 0008 SDL 004 0009 STO .06 0010 XEQ 31 0011 XEQ 30 0012 0 0013 STO .02 0014 0 0015 XEQ 20 0016 1 0017 XEQ 20 0018 x=]? Y 0044 SKIP 005 0045 RCL 02 0046 STO .03 0047 RCL .00 0048 STO 02 0049 SKIP 011 0050 RCL .00 0051 XEQ 20 0052 RCL .03 0053 XEQ 20 0054 x[>=]? Y 0055 SKIP 005 0056 RCL 02 0057 RCL .00 0058 x=? Y 0059 SKIP 001 0060 STO .03 0061 DSL .00 0062 BACK 031 0063 RCL 02 0064 XEQ 20 0065 RCL .02 0066 XEQ 20 0067 - 0068 ABS 0069 RCL 02 0070 XEQ 20 0071 ABS 0072 RCL .02 0073 XEQ 20 0074 ABS 0075 + 0076 1 0077 SDR 010 0078 + 0079 / 0080 2 0081 [times] 0082 1 0083 SDR 003 0084 x[<=]? Y 0085 SKIP 016 0086 RCL .02 0087 XEQ 20 0088 STO 03 0089 RCL 00 0090 STO .00 0091 DEC .00 0092 RCL .02 0093 RCL .00 0094 XEQ 24 0095 4 0096 RCL+ .00 0097 x[<->] Y 0098 STO[->]Y 0099 DSL .00 0100 BACK 008 0101 GTO 99 0102 RCL 01 0103 x? Y 0139 SKIP 039 0140 RCL 00 0141 STO .00 0142 RCL .00 0143 x=? .02 0144 SKIP 027 0145 RCL 00 0146 STO .01 0147 DEC .01 0148 RCL .00 0149 RCL .01 0150 XEQ 24 0151 RCL .02 0152 RCL .01 0153 XEQ 24 0154 + 0155 2 0156 / 0157 RCL .01 0158 x[<->] Y 0159 XEQ 23 0160 RCL .00 0161 RCL .01 0162 RCL .01 0163 XEQ 22 0164 XEQ 25 0165 DSL .01 0166 BACK 018 0167 RCLS 12 0168 XEQ'FUN' 0169 RCL .00 0170 x[<->] Y 0171 XEQ 21 0172 DSL .00 0173 BACK 031 0174 RCL 00 0175 STO+ 01 0176 XEQ 30 0177 SKIP 001 0178 DEC 01 0179 BACK 167 0180 LBL 99 0181 STOP 0182 RTN 0183 LBL 00 0184 RCL[->]X 0185 x[<->] Y 0186 DROP 0187 RTN 0188 LBL 20 0189 3 0190 + 0191 XEQ 00 0192 RTN 0193 LBL 21 0194 x[<->] Y 0195 3 0196 + 0197 x[<->] Y 0198 STO[->]Y 0199 RTN 0200 LBL 22 0201 # 012 0202 + 0203 XEQ 00 0204 RTN 0205 LBL 23 0206 x[<->] Y 0207 # 012 0208 + 0209 x[<->] Y 0210 STO[->]Y 0211 RTN 0212 LBL 24 0213 x[<->] Y 0214 RCL[times] 00 0215 + 0216 # 020 0217 + 0218 XEQ 00 0219 RTN 0220 LBL 25 0221 [<->] ZYXT 0222 RCL[times] 00 0223 + 0224 # 020 0225 + 0226 x[<->] Y 0227 STO[->]Y 0228 RTN 0229 LBL 26 0230 LocR 013 0231 STO .04 0232 +/- 0233 1 0234 + 0235 RCL 00 0236 / 0237 STO .01 0238 RCL .04 0239 - 0240 STO .02 0241 RCL 00 0242 STO .00 0243 DEC .00 0244 RCL .00 0245 XEQ 22 0246 RCL .01 0247 [times] 0248 RCL 02 0249 RCL .00 0250 XEQ 24 0251 RCL .02 0252 [times] 0253 - 0254 RCL .00 0255 # 117 0256 + 0257 x[<->] Y 0258 STO[->]Y 0259 DSL .00 0260 BACK 016 0261 RCLS .05 0262 XEQ'FUN' 0263 STO .03 0264 RCL 02 0265 XEQ 20 0266 RCL .03 0267 x[>=]? Y 0268 SKIP 026 0269 RCL 02 0270 RCL .03 0271 XEQ 21 0272 RCL 00 0273 STO .00 0274 DEC .00 0275 RCL .00 0276 ENTER[^] 0277 XEQ 22 0278 # 117 0279 RCL+ .00 0280 XEQ 00 0281 + 0282 RCL 02 0283 RCL .00 0284 XEQ 24 0285 - 0286 XEQ 23 0287 RCL 02 0288 RCL .00 0289 # 117 0290 RCL+ .00 0291 XEQ 00 0292 XEQ 25 0293 DSL .00 0294 BACK 019 0295 RCL .03 0296 RTN 0297 LBL 30 0298 LocR 003 0299 RCL 00 0300 STO .01 0301 DEC .01 0302 0 0303 STO .02 0304 RCL 00 0305 STO .00 0306 RCL .00 0307 RCL .01 0308 XEQ 24 0309 STO+ .02 0310 DSL .00 0311 BACK 005 0312 RCL .01 0313 RCL .02 0314 XEQ 23 0315 DSL .01 0316 BACK 014 0317 RTN 0318 LBL 31 0319 LocR 010 0320 RCL 00 0321 STO .00 0322 RCL 00 0323 STO .01 0324 DEC .01 0325 RCL .01 0326 1 0327 + 0328 RCL .00 0329 0 0330 x[<->] Y 0331 x=? Z 0332 INC Y 0333 DROP 0334 RCL .01 0335 # 114 0336 + 0337 x[<->] Y 0338 STO[->]Y 0339 RCL .00 0340 RCL .01 0341 [<->] ZXYT 0342 XEQ 25 0343 DSL .01 0344 BACK 019 0345 RCLS .02 0346 XEQ'FUN' 0347 RCL .00 0348 x[<->] Y 0349 XEQ 21 0350 DSL .00 0351 BACK 029 0352 RTN 0353 END ```

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