symplectic
% Modify expression to add input arguments.
% Example:
% a = [1 2 3; 4 5 6];
% foo(a);
symplectic
close all
symplectic
y
y =
Columns 1 through 4
1.0000 1.0932 1.1670 1.2127
1.0000 0.7809 0.5255 0.2423
1.0000 1.0932 1.1670 1.2127
Columns 5 through 8
1.2241 1.1997 1.1429 1.0609
-0.0546 -0.3483 -0.6227 -0.8655
1.2241 1.1997 1.1429 1.0609
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0.9629 0.8579 0.7531 0.6536
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0.5623 0.4806 0.4089 0.3467
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0.2932 0.2475 0.2087 0.1758
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0.1480 0.1246 0.1048 0.0881
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0.0741 0.0623 0.0524 0.0441
Columns 29 through 32
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0.0370 0.0311 0.0262 0.0220
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0.0185 0.0155 0.0131 0.0110
Columns 37 through 40
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0.0092 0.0078 0.0065 0.0055
Columns 41 through 44
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0.0046 0.0039 0.0033 0.0027
Columns 45 through 48
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0.0023 0.0019 0.0016 0.0014
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0.0011 0.0010 0.0008 0.0007
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Columns 61 through 64
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-1.7321 -1.7321 -1.7321 -1.7321
0.0000 0.0000 0.0000 0.0000
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Columns 97 through 100
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0.0000 0.0000 0.0000 0.0000
Columns 101 through 104
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Columns 105 through 108
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0.0000 0.0000 0.0000 0.0000
Columns 117 through 120
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Columns 121 through 124
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Columns 125 through 128
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Columns 129 through 132
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Columns 133 through 136
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Columns 137 through 140
0.0000 0.0000 0.0000 0.0000
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0.0000 0.0000 0.0000 0.0000
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Columns 145 through 148
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Columns 153 through 156
0.0000 0.0000 0.0000 0.0000
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Columns 157 through 160
0.0000 0.0000 0.0000 0.0000
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Columns 161 through 164
0.0000 0.0000 0.0000 0.0000
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-0.0000 -0.0000 -0.0000 -0.0000
Columns 165 through 168
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 169 through 172
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-1.7321 -1.7321 -1.7321 -1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 173 through 176
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-1.7321 -1.7321 -1.7321 -1.7321
-0.0001 -0.0001 -0.0001 -0.0001
Columns 177 through 180
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-1.7321 -1.7321 -1.7321 -1.7321
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Columns 181 through 184
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Columns 185 through 188
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-1.7321 -1.7321 -1.7321 -1.7321
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Columns 189 through 192
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-0.0009 -0.0010 -0.0012 -0.0015
Columns 193 through 196
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Columns 197 through 200
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-1.7320 -1.7320 -1.7320 -1.7320
-0.0035 -0.0042 -0.0049 -0.0059
Columns 201 through 204
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-1.7320 -1.7320 -1.7320 -1.7320
-0.0070 -0.0083 -0.0099 -0.0118
Columns 205 through 208
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-0.0140 -0.0167 -0.0198 -0.0236
Columns 209 through 212
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-0.0280 -0.0334 -0.0397 -0.0472
Columns 213 through 216
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-0.0562 -0.0668 -0.0794 -0.0944
Columns 217 through 220
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-0.1123 -0.1335 -0.1586 -0.1883
Columns 221 through 224
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-0.2234 -0.2649 -0.3135 -0.3704
Columns 225 through 228
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-0.4363 -0.5120 -0.5976 -0.6924
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-0.7946 -0.9002 -1.0033 -1.0960
Columns 233 through 236
1.1690 1.2137 1.2239 1.1983
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-1.1690 -1.2137 -1.2239 -1.1983
Columns 237 through 240
1.1405 1.0578 0.9595 0.8544
0.6314 0.8730 1.0765 1.2410
-1.1405 -1.0578 -0.9595 -0.8544
Columns 241 through 244
0.7497 0.6504 0.5594 0.4781
1.3696 1.4676 1.5408 1.5946
-0.7497 -0.6504 -0.5594 -0.4781
Columns 245 through 248
0.4067 0.3448 0.2916 0.2461
1.6338 1.6620 1.6823 1.6967
-0.4067 -0.3448 -0.2916 -0.2461
Columns 249 through 252
0.2075 0.1748 0.1472 0.1239
1.7070 1.7143 1.7195 1.7232
-0.2075 -0.1748 -0.1472 -0.1239
Columns 253 through 256
0.1042 0.0876 0.0737 0.0620
1.7258 1.7276 1.7289 1.7298
-0.1042 -0.0876 -0.0737 -0.0620
Columns 257 through 260
0.0521 0.0438 0.0368 0.0310
1.7305 1.7309 1.7313 1.7315
-0.0521 -0.0438 -0.0368 -0.0310
Columns 261 through 264
0.0260 0.0219 0.0184 0.0155
1.7317 1.7318 1.7319 1.7319
-0.0260 -0.0219 -0.0184 -0.0155
Columns 265 through 268
0.0130 0.0109 0.0092 0.0077
1.7320 1.7320 1.7320 1.7320
-0.0130 -0.0109 -0.0092 -0.0077
Columns 269 through 272
0.0065 0.0055 0.0046 0.0039
1.7320 1.7320 1.7320 1.7320
-0.0065 -0.0055 -0.0046 -0.0039
Columns 273 through 276
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1.7320 1.7320 1.7320 1.7320
-0.0032 -0.0027 -0.0023 -0.0019
Columns 277 through 280
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1.7320 1.7320 1.7321 1.7321
-0.0016 -0.0014 -0.0011 -0.0010
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1.7321 1.7321 1.7321 1.7321
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Columns 285 through 288
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1.7321 1.7321 1.7321 1.7321
-0.0004 -0.0003 -0.0003 -0.0002
Columns 289 through 292
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1.7321 1.7321 1.7321 1.7321
-0.0002 -0.0002 -0.0001 -0.0001
Columns 293 through 296
0.0001 0.0001 0.0001 0.0001
1.7321 1.7321 1.7321 1.7321
-0.0001 -0.0001 -0.0001 -0.0001
Columns 297 through 300
0.0001 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
-0.0001 -0.0000 -0.0000 -0.0000
Columns 301 through 304
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 305 through 308
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 309 through 312
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1.7321 1.7321 1.7321 1.7321
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Columns 313 through 316
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 317 through 320
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 321 through 324
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 325 through 328
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1.7321 1.7321 1.7321 1.7321
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Columns 329 through 332
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1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 333 through 336
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1.7321 1.7321 1.7321 1.7321
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Columns 337 through 340
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1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
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1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 345 through 348
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1.7321 1.7321 1.7321 1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 349 through 352
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1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 353 through 356
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 357 through 360
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 361 through 364
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 365 through 368
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 369 through 372
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 373 through 376
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 377 through 380
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 381 through 384
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 385 through 388
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 389 through 392
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 393 through 396
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 397 through 400
0.0000 0.0000 0.0000 0.0000
1.7321 1.7321 1.7321 1.7321
0.0000 0.0000 0.0000 0.0000
Columns 401 through 404
0.0001 0.0001 0.0001 0.0001
1.7321 1.7321 1.7321 1.7321
0.0001 0.0001 0.0001 0.0001
Columns 405 through 408
0.0001 0.0001 0.0002 0.0002
1.7321 1.7321 1.7321 1.7321
0.0001 0.0001 0.0002 0.0002
Columns 409 through 412
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1.7321 1.7321 1.7321 1.7321
0.0002 0.0003 0.0003 0.0004
Columns 413 through 416
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1.7321 1.7321 1.7321 1.7321
0.0005 0.0005 0.0007 0.0008
Columns 417 through 420
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1.7321 1.7321 1.7320 1.7320
0.0009 0.0011 0.0013 0.0016
Columns 421 through 424
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1.7320 1.7320 1.7320 1.7320
0.0019 0.0022 0.0026 0.0031
Columns 425 through 428
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1.7320 1.7320 1.7320 1.7320
0.0037 0.0044 0.0053 0.0062
Columns 429 through 432
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1.7320 1.7320 1.7320 1.7320
0.0074 0.0088 0.0105 0.0125
Columns 433 through 436
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1.7319 1.7319 1.7318 1.7317
0.0149 0.0177 0.0211 0.0251
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0.0298 0.0355 0.0422 0.0502
1.7315 1.7313 1.7310 1.7306
0.0298 0.0355 0.0422 0.0502
Columns 441 through 444
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1.7300 1.7291 1.7279 1.7262
0.0597 0.0710 0.0844 0.1004
Columns 445 through 448
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0.1193 0.1418 0.1685 0.2000
Columns 449 through 452
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Columns 453 through 456
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1.6041 1.5538 1.4853 1.3931
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1.1884 1.2214 1.2189 1.1813
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1.1137 1.0244 0.9228 0.8171
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0.1954 0.1645 0.1385 0.1165
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0.0980 0.0824 0.0693 0.0583
Columns 485 through 488
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0.0490 0.0412 0.0346 0.0291
Columns 489 through 492
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0.0245 0.0206 0.0173 0.0145
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0.0122 0.0103 0.0086 0.0073
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-1.7320 -1.7320 -1.7320 -1.7320
0.0061 0.0051 0.0043 0.0036
Columns 501 through 504
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-1.7320 -1.7320 -1.7320 -1.7320
0.0030 0.0026 0.0022 0.0018
Columns 505 through 508
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0.0015 0.0013 0.0011 0.0009
Columns 509 through 512
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0.0008 0.0006 0.0005 0.0005
Columns 513 through 516
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Columns 517 through 520
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Columns 521 through 524
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Columns 537 through 540
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-1.7321 -1.7321 -1.7321 -1.7321
0.0000 0.0000 0.0000 0.0000
Columns 557 through 560
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
0.0000 0.0000 0.0000 0.0000
Columns 561 through 564
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
0.0000 0.0000 0.0000 0.0000
Columns 565 through 568
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
0.0000 0.0000 0.0000 0.0000
Columns 569 through 572
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
0.0000 0.0000 0.0000 0.0000
Columns 573 through 576
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
0.0000 0.0000 -0.0000 -0.0000
Columns 577 through 580
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 581 through 584
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 585 through 588
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 589 through 592
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 593 through 596
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Columns 597 through 600
0.0000 0.0000 0.0000 0.0000
-1.7321 -1.7321 -1.7321 -1.7321
-0.0000 -0.0000 -0.0000 -0.0000
Column 601
0.0000
-1.7321
-0.0000
y(1,:).^2+y(2,:).^2+y(3,:).^2
ans =
Columns 1 through 4
3.0000 3.0000 3.0000 3.0000
Columns 5 through 8
3.0000 3.0000 3.0000 3.0000
Columns 9 through 12
3.0000 3.0000 3.0000 3.0000
Columns 13 through 16
3.0000 3.0000 3.0000 3.0000
Columns 17 through 20
3.0000 3.0000 3.0000 3.0000
Columns 21 through 24
3.0000 3.0000 3.0000 3.0000
Columns 25 through 28
3.0000 3.0000 3.0000 3.0000
Columns 29 through 32
3.0000 3.0000 3.0000 3.0000
Columns 33 through 36
3.0000 3.0000 3.0000 3.0000
Columns 37 through 40
3.0000 3.0000 3.0000 3.0000
Columns 41 through 44
3.0000 3.0000 3.0000 3.0000
Columns 45 through 48
3.0000 3.0000 3.0000 3.0000
Columns 49 through 52
3.0000 3.0000 3.0000 3.0000
Columns 53 through 56
3.0000 3.0000 3.0000 3.0000
Columns 57 through 60
3.0000 3.0000 3.0000 3.0000
Columns 61 through 64
3.0000 3.0000 3.0000 3.0000
Columns 65 through 68
3.0000 3.0000 3.0000 3.0000
Columns 69 through 72
3.0000 3.0000 3.0000 3.0000
Columns 73 through 76
3.0000 3.0000 3.0000 3.0000
Columns 77 through 80
3.0000 3.0000 3.0000 3.0000
Columns 81 through 84
3.0000 3.0000 3.0000 3.0000
Columns 85 through 88
3.0000 3.0000 3.0000 3.0000
Columns 89 through 92
3.0000 3.0000 3.0000 3.0000
Columns 93 through 96
3.0000 3.0000 3.0000 3.0000
Columns 97 through 100
3.0000 3.0000 3.0000 3.0000
Columns 101 through 104
3.0000 3.0000 3.0000 3.0000
Columns 105 through 108
3.0000 3.0000 3.0000 3.0000
Columns 109 through 112
3.0000 3.0000 3.0000 3.0000
Columns 113 through 116
3.0000 3.0000 3.0000 3.0000
Columns 117 through 120
3.0000 3.0000 3.0000 3.0000
Columns 121 through 124
3.0000 3.0000 3.0000 3.0000
Columns 125 through 128
3.0000 3.0000 3.0000 3.0000
Columns 129 through 132
3.0000 3.0000 3.0000 3.0000
Columns 133 through 136
3.0000 3.0000 3.0000 3.0000
Columns 137 through 140
3.0000 3.0000 3.0000 3.0000
Columns 141 through 144
3.0000 3.0000 3.0000 3.0000
Columns 145 through 148
3.0000 3.0000 3.0000 3.0000
Columns 149 through 152
3.0000 3.0000 3.0000 3.0000
Columns 153 through 156
3.0000 3.0000 3.0000 3.0000
Columns 157 through 160
3.0000 3.0000 3.0000 3.0000
Columns 161 through 164
3.0000 3.0000 3.0000 3.0000
Columns 165 through 168
3.0000 3.0000 3.0000 3.0000
Columns 169 through 172
3.0000 3.0000 3.0000 3.0000
Columns 173 through 176
3.0000 3.0000 3.0000 3.0000
Columns 177 through 180
3.0000 3.0000 3.0000 3.0000
Columns 181 through 184
3.0000 3.0000 3.0000 3.0000
Columns 185 through 188
3.0000 3.0000 3.0000 3.0000
Columns 189 through 192
3.0000 3.0000 3.0000 3.0000
Columns 193 through 196
3.0000 3.0000 3.0000 3.0000
Columns 197 through 200
3.0000 3.0000 3.0000 3.0000
Columns 201 through 204
3.0000 3.0000 3.0000 3.0000
Columns 205 through 208
3.0000 3.0000 3.0000 3.0000
Columns 209 through 212
3.0000 3.0000 3.0000 3.0000
Columns 213 through 216
3.0000 3.0000 3.0000 3.0000
Columns 217 through 220
3.0000 3.0000 3.0000 3.0000
Columns 221 through 224
3.0000 3.0000 3.0000 3.0000
Columns 225 through 228
3.0000 3.0000 3.0000 3.0000
Columns 229 through 232
3.0000 3.0000 3.0000 3.0000
Columns 233 through 236
3.0000 3.0000 3.0000 3.0000
Columns 237 through 240
3.0000 3.0000 3.0000 3.0000
Columns 241 through 244
3.0000 3.0000 3.0000 3.0000
Columns 245 through 248
3.0000 3.0000 3.0000 3.0000
Columns 249 through 252
3.0000 3.0000 3.0000 3.0000
Columns 253 through 256
3.0000 3.0000 3.0000 3.0000
Columns 257 through 260
3.0000 3.0000 3.0000 3.0000
Columns 261 through 264
3.0000 3.0000 3.0000 3.0000
Columns 265 through 268
3.0000 3.0000 3.0000 3.0000
Columns 269 through 272
3.0000 3.0000 3.0000 3.0000
Columns 273 through 276
3.0000 3.0000 3.0000 3.0000
Columns 277 through 280
3.0000 3.0000 3.0000 3.0000
Columns 281 through 284
3.0000 3.0000 3.0000 3.0000
Columns 285 through 288
3.0000 3.0000 3.0000 3.0000
Columns 289 through 292
3.0000 3.0000 3.0000 3.0000
Columns 293 through 296
3.0000 3.0000 3.0000 3.0000
Columns 297 through 300
3.0000 3.0000 3.0000 3.0000
Columns 301 through 304
3.0000 3.0000 3.0000 3.0000
Columns 305 through 308
3.0000 3.0000 3.0000 3.0000
Columns 309 through 312
3.0000 3.0000 3.0000 3.0000
Columns 313 through 316
3.0000 3.0000 3.0000 3.0000
Columns 317 through 320
3.0000 3.0000 3.0000 3.0000
Columns 321 through 324
3.0000 3.0000 3.0000 3.0000
Columns 325 through 328
3.0000 3.0000 3.0000 3.0000
Columns 329 through 332
3.0000 3.0000 3.0000 3.0000
Columns 333 through 336
3.0000 3.0000 3.0000 3.0000
Columns 337 through 340
3.0000 3.0000 3.0000 3.0000
Columns 341 through 344
3.0000 3.0000 3.0000 3.0000
Columns 345 through 348
3.0000 3.0000 3.0000 3.0000
Columns 349 through 352
3.0000 3.0000 3.0000 3.0000
Columns 353 through 356
3.0000 3.0000 3.0000 3.0000
Columns 357 through 360
3.0000 3.0000 3.0000 3.0000
Columns 361 through 364
3.0000 3.0000 3.0000 3.0000
Columns 365 through 368
3.0000 3.0000 3.0000 3.0000
Columns 369 through 372
3.0000 3.0000 3.0000 3.0000
Columns 373 through 376
3.0000 3.0000 3.0000 3.0000
Columns 377 through 380
3.0000 3.0000 3.0000 3.0000
Columns 381 through 384
3.0000 3.0000 3.0000 3.0000
Columns 385 through 388
3.0000 3.0000 3.0000 3.0000
Columns 389 through 392
3.0000 3.0000 3.0000 3.0000
Columns 393 through 396
3.0000 3.0000 3.0000 3.0000
Columns 397 through 400
3.0000 3.0000 3.0000 3.0000
Columns 401 through 404
3.0000 3.0000 3.0000 3.0000
Columns 405 through 408
3.0000 3.0000 3.0000 3.0000
Columns 409 through 412
3.0000 3.0000 3.0000 3.0000
Columns 413 through 416
3.0000 3.0000 3.0000 3.0000
Columns 417 through 420
3.0000 3.0000 3.0000 3.0000
Columns 421 through 424
3.0000 3.0000 3.0000 3.0000
Columns 425 through 428
3.0000 3.0000 3.0000 3.0000
Columns 429 through 432
3.0000 3.0000 3.0000 3.0000
Columns 433 through 436
3.0000 3.0000 3.0000 3.0000
Columns 437 through 440
3.0000 3.0000 3.0000 3.0000
Columns 441 through 444
3.0000 3.0000 3.0000 3.0000
Columns 445 through 448
3.0000 3.0000 3.0000 3.0000
Columns 449 through 452
3.0000 3.0000 3.0000 3.0000
Columns 453 through 456
3.0000 3.0000 3.0000 3.0000
Columns 457 through 460
3.0000 3.0000 3.0000 3.0000
Columns 461 through 464
3.0000 3.0000 3.0000 3.0000
Columns 465 through 468
3.0000 3.0000 3.0000 3.0000
Columns 469 through 472
3.0000 3.0000 3.0000 3.0000
Columns 473 through 476
3.0000 3.0000 3.0000 3.0000
Columns 477 through 480
3.0000 3.0000 3.0000 3.0000
Columns 481 through 484
3.0000 3.0000 3.0000 3.0000
Columns 485 through 488
3.0000 3.0000 3.0000 3.0000
Columns 489 through 492
3.0000 3.0000 3.0000 3.0000
Columns 493 through 496
3.0000 3.0000 3.0000 3.0000
Columns 497 through 500
3.0000 3.0000 3.0000 3.0000
Columns 501 through 504
3.0000 3.0000 3.0000 3.0000
Columns 505 through 508
3.0000 3.0000 3.0000 3.0000
Columns 509 through 512
3.0000 3.0000 3.0000 3.0000
Columns 513 through 516
3.0000 3.0000 3.0000 3.0000
Columns 517 through 520
3.0000 3.0000 3.0000 3.0000
Columns 521 through 524
3.0000 3.0000 3.0000 3.0000
Columns 525 through 528
3.0000 3.0000 3.0000 3.0000
Columns 529 through 532
3.0000 3.0000 3.0000 3.0000
Columns 533 through 536
3.0000 3.0000 3.0000 3.0000
Columns 537 through 540
3.0000 3.0000 3.0000 3.0000
Columns 541 through 544
3.0000 3.0000 3.0000 3.0000
Columns 545 through 548
3.0000 3.0000 3.0000 3.0000
Columns 549 through 552
3.0000 3.0000 3.0000 3.0000
Columns 553 through 556
3.0000 3.0000 3.0000 3.0000
Columns 557 through 560
3.0000 3.0000 3.0000 3.0000
Columns 561 through 564
3.0000 3.0000 3.0000 3.0000
Columns 565 through 568
3.0000 3.0000 3.0000 3.0000
Columns 569 through 572
3.0000 3.0000 3.0000 3.0000
Columns 573 through 576
3.0000 3.0000 3.0000 3.0000
Columns 577 through 580
3.0000 3.0000 3.0000 3.0000
Columns 581 through 584
3.0000 3.0000 3.0000 3.0000
Columns 585 through 588
3.0000 3.0000 3.0000 3.0000
Columns 589 through 592
3.0000 3.0000 3.0000 3.0000
Columns 593 through 596
3.0000 3.0000 3.0000 3.0000
Columns 597 through 600
3.0000 3.0000 3.0000 3.0000
Column 601
3.0000
format long e
y(1,:).^2+y(2,:).^2+y(3,:).^2
ans =
Column 1
3.000000000000000e+00
Column 2
3.000000000000000e+00
Column 3
3.000000000000000e+00
Column 4
3.000000000000000e+00
Column 5
3.000000000000001e+00
Column 6
3.000000000000001e+00
Column 7
3.000000000000001e+00
Column 8
3.000000000000001e+00
Column 9
3.000000000000001e+00
Column 10
3.000000000000001e+00
Column 11
3.000000000000001e+00
Column 12
3.000000000000001e+00
Column 13
3.000000000000001e+00
Column 14
3.000000000000001e+00
Column 15
3.000000000000001e+00
Column 16
3.000000000000001e+00
Column 17
3.000000000000001e+00
Column 18
3.000000000000001e+00
Column 19
3.000000000000001e+00
Column 20
3.000000000000001e+00
Column 21
3.000000000000001e+00
Column 22
3.000000000000001e+00
Column 23
3.000000000000001e+00
Column 24
3.000000000000000e+00
Column 25
3.000000000000000e+00
Column 26
3.000000000000000e+00
Column 27
3.000000000000000e+00
Column 28
3.000000000000000e+00
Column 29
3.000000000000001e+00
Column 30
3.000000000000000e+00
Column 31
3.000000000000000e+00
Column 32
3.000000000000000e+00
Column 33
3.000000000000000e+00
Column 34
3.000000000000000e+00
Column 35
3.000000000000000e+00
Column 36
3.000000000000000e+00
Column 37
3.000000000000000e+00
Column 38
3.000000000000000e+00
Column 39
3.000000000000000e+00
Column 40
3.000000000000000e+00
Column 41
3.000000000000000e+00
Column 42
2.999999999999999e+00
Column 43
3.000000000000000e+00
Column 44
3.000000000000000e+00
Column 45
2.999999999999999e+00
Column 46
2.999999999999999e+00
Column 47
2.999999999999999e+00
Column 48
2.999999999999999e+00
Column 49
2.999999999999999e+00
Column 50
2.999999999999999e+00
Column 51
3.000000000000000e+00
Column 52
3.000000000000000e+00
Column 53
3.000000000000000e+00
Column 54
3.000000000000000e+00
Column 55
3.000000000000000e+00
Column 56
3.000000000000000e+00
Column 57
3.000000000000000e+00
Column 58
3.000000000000000e+00
Column 59
3.000000000000000e+00
Column 60
3.000000000000000e+00
Column 61
3.000000000000000e+00
Column 62
3.000000000000000e+00
Column 63
3.000000000000000e+00
Column 64
3.000000000000000e+00
Column 65
3.000000000000000e+00
Column 66
3.000000000000000e+00
Column 67
3.000000000000000e+00
Column 68
3.000000000000000e+00
Column 69
3.000000000000000e+00
Column 70
3.000000000000000e+00
Column 71
3.000000000000000e+00
Column 72
3.000000000000001e+00
Column 73
3.000000000000000e+00
Column 74
3.000000000000000e+00
Column 75
3.000000000000000e+00
Column 76
3.000000000000001e+00
Column 77
3.000000000000000e+00
Column 78
3.000000000000000e+00
Column 79
3.000000000000000e+00
Column 80
3.000000000000000e+00
Column 81
3.000000000000000e+00
Column 82
3.000000000000000e+00
Column 83
3.000000000000000e+00
Column 84
3.000000000000000e+00
Column 85
2.999999999999970e+00
Column 86
2.999999999999949e+00
Column 87
2.999999999999934e+00
Column 88
2.999999999999923e+00
Column 89
2.999999999999915e+00
Column 90
2.999999999999909e+00
Column 91
2.999999999999905e+00
Column 92
2.999999999999902e+00
Column 93
2.999999999999901e+00
Column 94
2.999999999999899e+00
Column 95
2.999999999999897e+00
Column 96
2.999999999999897e+00
Column 97
2.999999999999897e+00
Column 98
2.999999999999897e+00
Column 99
2.999999999999897e+00
Column 100
2.999999999999897e+00
Column 101
2.999999999999897e+00
Column 102
2.999999999999896e+00
Column 103
2.999999999999895e+00
Column 104
2.999999999999895e+00
Column 105
2.999999999999896e+00
Column 106
2.999999999999896e+00
Column 107
2.999999999999896e+00
Column 108
2.999999999999896e+00
Column 109
2.999999999999896e+00
Column 110
2.999999999999896e+00
Column 111
2.999999999999896e+00
Column 112
2.999999999999896e+00
Column 113
2.999999999999896e+00
Column 114
2.999999999999896e+00
Column 115
2.999999999999895e+00
Column 116
2.999999999999895e+00
Column 117
2.999999999999895e+00
Column 118
2.999999999999895e+00
Column 119
2.999999999999895e+00
Column 120
2.999999999999895e+00
Column 121
2.999999999999895e+00
Column 122
2.999999999999895e+00
Column 123
2.999999999999895e+00
Column 124
2.999999999999895e+00
Column 125
2.999999999999896e+00
Column 126
2.999999999999896e+00
Column 127
2.999999999999896e+00
Column 128
2.999999999999896e+00
Column 129
2.999999999999896e+00
Column 130
2.999999999999895e+00
Column 131
2.999999999999895e+00
Column 132
2.999999999999896e+00
Column 133
2.999999999999896e+00
Column 134
2.999999999999896e+00
Column 135
2.999999999999896e+00
Column 136
2.999999999999896e+00
Column 137
2.999999999999896e+00
Column 138
2.999999999999896e+00
Column 139
2.999999999999896e+00
Column 140
2.999999999999896e+00
Column 141
2.999999999999896e+00
Column 142
2.999999999999896e+00
Column 143
2.999999999999897e+00
Column 144
2.999999999999897e+00
Column 145
2.999999999999897e+00
Column 146
2.999999999999898e+00
Column 147
2.999999999999900e+00
Column 148
2.999999999999902e+00
Column 149
2.999999999999905e+00
Column 150
2.999999999999909e+00
Column 151
2.999999999999915e+00
Column 152
2.999999999999924e+00
Column 153
2.999999999999937e+00
Column 154
2.999999999999955e+00
Column 155
2.999999999999980e+00
Column 156
2.999999999999979e+00
Column 157
2.999999999999980e+00
Column 158
2.999999999999979e+00
Column 159
2.999999999999980e+00
Column 160
2.999999999999980e+00
Column 161
2.999999999999979e+00
Column 162
2.999999999999979e+00
Column 163
2.999999999999979e+00
Column 164
2.999999999999979e+00
Column 165
2.999999999999978e+00
Column 166
2.999999999999978e+00
Column 167
2.999999999999978e+00
Column 168
2.999999999999978e+00
Column 169
2.999999999999979e+00
Column 170
2.999999999999978e+00
Column 171
2.999999999999978e+00
Column 172
2.999999999999978e+00
Column 173
2.999999999999978e+00
Column 174
2.999999999999978e+00
Column 175
2.999999999999978e+00
Column 176
2.999999999999978e+00
Column 177
2.999999999999978e+00
Column 178
2.999999999999978e+00
Column 179
2.999999999999978e+00
Column 180
2.999999999999978e+00
Column 181
2.999999999999978e+00
Column 182
2.999999999999978e+00
Column 183
2.999999999999978e+00
Column 184
2.999999999999977e+00
Column 185
2.999999999999978e+00
Column 186
2.999999999999977e+00
Column 187
2.999999999999977e+00
Column 188
2.999999999999977e+00
Column 189
2.999999999999977e+00
Column 190
2.999999999999977e+00
Column 191
2.999999999999976e+00
Column 192
2.999999999999976e+00
Column 193
2.999999999999977e+00
Column 194
2.999999999999977e+00
Column 195
2.999999999999977e+00
Column 196
2.999999999999977e+00
Column 197
2.999999999999977e+00
Column 198
2.999999999999976e+00
Column 199
2.999999999999977e+00
Column 200
2.999999999999977e+00
Column 201
2.999999999999977e+00
Column 202
2.999999999999976e+00
Column 203
2.999999999999976e+00
Column 204
2.999999999999976e+00
Column 205
2.999999999999976e+00
Column 206
2.999999999999975e+00
Column 207
2.999999999999975e+00
Column 208
2.999999999999975e+00
Column 209
2.999999999999975e+00
Column 210
2.999999999999975e+00
Column 211
2.999999999999975e+00
Column 212
2.999999999999975e+00
Column 213
2.999999999999974e+00
Column 214
2.999999999999974e+00
Column 215
2.999999999999974e+00
Column 216
2.999999999999975e+00
Column 217
2.999999999999974e+00
Column 218
2.999999999999974e+00
Column 219
2.999999999999974e+00
Column 220
2.999999999999974e+00
Column 221
2.999999999999974e+00
Column 222
2.999999999999974e+00
Column 223
2.999999999999974e+00
Column 224
2.999999999999974e+00
Column 225
2.999999999999975e+00
Column 226
2.999999999999975e+00
Column 227
2.999999999999975e+00
Column 228
2.999999999999975e+00
Column 229
2.999999999999975e+00
Column 230
2.999999999999974e+00
Column 231
2.999999999999975e+00
Column 232
2.999999999999975e+00
Column 233
2.999999999999975e+00
Column 234
2.999999999999976e+00
Column 235
2.999999999999976e+00
Column 236
2.999999999999976e+00
Column 237
2.999999999999975e+00
Column 238
2.999999999999975e+00
Column 239
2.999999999999976e+00
Column 240
2.999999999999975e+00
Column 241
2.999999999999976e+00
Column 242
2.999999999999975e+00
Column 243
2.999999999999975e+00
Column 244
2.999999999999975e+00
Column 245
2.999999999999974e+00
Column 246
2.999999999999975e+00
Column 247
2.999999999999975e+00
Column 248
2.999999999999975e+00
Column 249
2.999999999999975e+00
Column 250
2.999999999999975e+00
Column 251
2.999999999999974e+00
Column 252
2.999999999999974e+00
Column 253
2.999999999999974e+00
Column 254
2.999999999999974e+00
Column 255
2.999999999999974e+00
Column 256
2.999999999999974e+00
Column 257
2.999999999999975e+00
Column 258
2.999999999999975e+00
Column 259
2.999999999999976e+00
Column 260
2.999999999999975e+00
Column 261
2.999999999999975e+00
Column 262
2.999999999999975e+00
Column 263
2.999999999999975e+00
Column 264
2.999999999999975e+00
Column 265
2.999999999999975e+00
Column 266
2.999999999999975e+00
Column 267
2.999999999999975e+00
Column 268
2.999999999999975e+00
Column 269
2.999999999999975e+00
Column 270
2.999999999999975e+00
Column 271
2.999999999999976e+00
Column 272
2.999999999999975e+00
Column 273
2.999999999999976e+00
Column 274
2.999999999999976e+00
Column 275
2.999999999999976e+00
Column 276
2.999999999999976e+00
Column 277
2.999999999999976e+00
Column 278
2.999999999999976e+00
Column 279
2.999999999999976e+00
Column 280
2.999999999999976e+00
Column 281
2.999999999999976e+00
Column 282
2.999999999999976e+00
Column 283
2.999999999999976e+00
Column 284
2.999999999999976e+00
Column 285
2.999999999999976e+00
Column 286
2.999999999999976e+00
Column 287
2.999999999999976e+00
Column 288
2.999999999999976e+00
Column 289
2.999999999999976e+00
Column 290
2.999999999999976e+00
Column 291
2.999999999999976e+00
Column 292
2.999999999999976e+00
Column 293
2.999999999999976e+00
Column 294
2.999999999999976e+00
Column 295
2.999999999999976e+00
Column 296
2.999999999999976e+00
Column 297
2.999999999999976e+00
Column 298
2.999999999999976e+00
Column 299
2.999999999999976e+00
Column 300
2.999999999999976e+00
Column 301
2.999999999999976e+00
Column 302
2.999999999999976e+00
Column 303
2.999999999999976e+00
Column 304
2.999999999999976e+00
Column 305
2.999999999999976e+00
Column 306
2.999999999999976e+00
Column 307
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options.InitialStep=0.001
options =
InitialStep: 1.000000000000000e-03
options.AbsTol=1e-8
options =
InitialStep: 1.000000000000000e-03
AbsTol: 1.000000000000000e-08
(2)^(1/3)
ans =
1.259921049894873e+00
(-2)^(1/3)
ans =
6.299605249474367e-01 + 1.091123635971721e+00i
nthroot(-2,3)
ans =
-1.259921049894873e+00
nthroot(-2,4)
??? Error using ==> nthroot at 33
If X is negative, N must be an odd integer.
ese4rk23
time step rejected
time step rejected
time step rejected
time step rejected
time step rejected
time step rejected
time step rejected
time step rejected
time step rejected
time step rejected
help ode
ode not found.
Use the Help browser Search tab to search the documentation, or
type "help help" for help command options, such as help for methods.
help ode23
ODE23 Solve non-stiff differential equations, low order method.
[TOUT,YOUT] = ODE23(ODEFUN,TSPAN,Y0) with TSPAN = [T0 TFINAL] integrates
the system of differential equations y' = f(t,y) from time T0 to TFINAL
with initial conditions Y0. ODEFUN is a function handle. For a scalar T
and a vector Y, ODEFUN(T,Y) must return a column vector corresponding
to f(t,y). Each row in the solution array YOUT corresponds to a time
returned in the column vector TOUT. To obtain solutions at specific
times T0,T1,...,TFINAL (all increasing or all decreasing), use TSPAN =
[T0 T1 ... TFINAL].
[TOUT,YOUT] = ODE23(ODEFUN,TSPAN,Y0,OPTIONS) solves as above with default
integration properties replaced by values in OPTIONS, an argument created
with the ODESET function. See ODESET for details. Commonly used options
are scalar relative error tolerance 'RelTol' (1e-3 by default) and vector
of absolute error tolerances 'AbsTol' (all components 1e-6 by default).
If certain components of the solution must be non-negative, use
ODESET to set the 'NonNegative' property to the indices of these
components.
ODE23 can solve problems M(t,y)*y' = f(t,y) with mass matrix M that is
nonsingular. Use ODESET to set the 'Mass' property to a function handle
MASS if MASS(T,Y) returns the value of the mass matrix. If the mass matrix
is constant, the matrix can be used as the value of the 'Mass' option. If
the mass matrix does not depend on the state variable Y and the function
MASS is to be called with one input argument T, set 'MStateDependence' to
'none'. ODE15S and ODE23T can solve problems with singular mass matrices.
[TOUT,YOUT,TE,YE,IE] = ODE23(ODEFUN,TSPAN,Y0,OPTIONS) with the 'Events'
property in OPTIONS set to a function handle EVENTS, solves as above
while also finding where functions of (T,Y), called event functions,
are zero. For each function you specify whether the integration is
to terminate at a zero and whether the direction of the zero crossing
matters. These are the three column vectors returned by EVENTS:
[VALUE,ISTERMINAL,DIRECTION] = EVENTS(T,Y). For the I-th event function:
VALUE(I) is the value of the function, ISTERMINAL(I)=1 if the integration
is to terminate at a zero of this event function and 0 otherwise.
DIRECTION(I)=0 if all zeros are to be computed (the default), +1 if only
zeros where the event function is increasing, and -1 if only zeros where
the event function is decreasing. Output TE is a column vector of times
at which events occur. Rows of YE are the corresponding solutions, and
indices in vector IE specify which event occurred.
SOL = ODE23(ODEFUN,[T0 TFINAL],Y0...) returns a structure that can be
used with DEVAL to evaluate the solution or its first derivative at
any point between T0 and TFINAL. The steps chosen by ODE23 are returned
in a row vector SOL.x. For each I, the column SOL.y(:,I) contains
the solution at SOL.x(I). If events were detected, SOL.xe is a row vector
of points at which events occurred. Columns of SOL.ye are the corresponding
solutions, and indices in vector SOL.ie specify which event occurred.
Example
[t,y]=ode23(@vdp1,[0 20],[2 0]);
plot(t,y(:,1));
solves the system y' = vdp1(t,y), using the default relative error
tolerance 1e-3 and the default absolute tolerance of 1e-6 for each
component, and plots the first component of the solution.
Class support for inputs TSPAN, Y0, and the result of ODEFUN(T,Y):
float: double, single
See also
other ODE solvers: ode45, ode113, ode15s, ode23s, ode23t, ode23tb
implicit ODEs: ode15i
options handling: odeset, odeget
output functions: odeplot, odephas2, odephas3, odeprint
evaluating solution: deval
ODE examples: rigidode, ballode, orbitode
function handles: function_handle
NOTE:
The interpretation of the first input argument of the ODE solvers and
some properties available through ODESET have changed in MATLAB 6.0.
Although we still support the v5 syntax, any new functionality is
available only with the new syntax. To see the v5 help, type in
the command line
more on, type ode23, more off
Reference page in Help browser
doc ode23
doc ode23
opzioni
opzioni =
InitialStep: 1.000000000000000e-03
AbsTol: 1.000000000000000e-02
RelTol: 1.000000000000000e-02
clear opzioni
opzioni=odeset('AbsTol',1e-4,'InitialStep',0.1)
opzioni =
AbsTol: 1.000000000000000e-04
BDF: []
Events: []
InitialStep: 1.000000000000000e-01
Jacobian: []
JConstant: []
JPattern: []
Mass: []
MassConstant: []
MassSingular: []
MaxOrder: []
MaxStep: []
NonNegative: []
NormControl: []
OutputFcn: []
OutputSel: []
Refine: []
RelTol: []
Stats: []
Vectorized: []
MStateDependence: []
MvPattern: []
InitialSlope: []
edit ode23
edit ode45
diary off