matlab 7.r22. Самоучитель
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MATLAB 7.*/R2006/R2007
, 2008
32.973.26 018.2 004.438 93
........................................................................ 35
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. . MATLAB 7.*/R2006/R2007: . .: , 2008. 768 .: . ISBN 978 5 94074 424 5 MATLAB, , . MATLAB, (GUI). MATLAB 7.* ( R2006a, b R2007a, b), , . MATLAB , . , , . MATLAB and Simulink are registered trademark of The The MathWorks Inc. Blockset, Toolbox and it components are trademark of The The MathWorks Inc.
................. 40 1. MATLAB ........................................................................ 41 2. ........................................................ 91 3. ................ 151 4. .......................................................... 193 5. ......................................... 233 6. .............................................. 277 7. ................................... 341
32.973.26 018.2 004.438 . . , , . , . , .
ISBN 978 5 94074 424 5
. ., 2008 , , , 2008
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8. ....................................... 383 9. ............................................ 441 10. , ......................................... 493 11. ......................................... 531 12. GUI ................................ 591 13. MATLAB ..... 659 14. MATLAB ............ 717 ................................................ 743 ........................................ 747
........................................................................ 35 ................. 40 1. MATLAB ............ 411.1. MATLAB ... 421.1.1. ............................. 42 1.1.2. MATLAB ................ 43 1.1.3. ......................... 44 1.1.4. MATLAB 7 + Simulink 6 ........... 45 1.1.5. MATLAB ..................................... 45
1.2. MATLAB ...................................... 461.2.1. MATLAB ............. 46 1.2.2. MATLAB ......... 47 1.2.3. MATLAB ................ 48 1.2.4. ...................... 49 1.2.5. .................................... 49
1.3. MATLAB ........................... 501.3.1. MATLAB ...... 50 1.3.2. ............... 53 1.3.3. MATLAB ........................................................ 54
1.4. MATLAB .................................. 55
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1.4.1. ................... 55 1.4.2. .................... 55 1.4.3. ....................................................... 56 1.4.4. ....................... 57 1.4.5. .................... 58 1.4.6. .............. 58 1.4.7. .................. 59 1.4.8. MATLAB ............. 60 1.4.9. : () ...................... 62 1.4.10. .......................................... 63 1.4.11. ............................................................................. 64
1.6.6. ........ 73
1.7. ............................................................................... 741.7.1. ...... 74 1.7.2. ............................. 75 1.7.3. .................................... 76 1.7.4. ................................... 77 1.7.5. .................... 77
1.8. ....................................................... 781.8.1. ............ 78 1.8.2. ............. 79 1.8.3. e^pi pi^e?...................................... 80 1.8.4. ................................................ 81 1.8.5. m ................ 81
1.5. ..................... 661.5.1. ................................................................. 66 1.5.2. ...................................................................... 67 1.5.3. ........................................................................... 68 1.5.4. () ...................... 69 1.5.5. ......................... 70
1.9. MATLAB ..... 821.9.1. MATLAB .............. 82 1.9.2. ...................... 83 1.9.3. ............................................ 84 1.9.4. fplot ...................................... 85
1.6. , m ................................. 701.6.1. .......................... 70 1.6.2. ...................... 71 1.6.3. ................................................... 71 1.6.4. ........................... 72 1.6.5. m .............................. 73
1.10. MATLAB ............................................................................. 861.10.1. ........................ 86 1.10.2. .................................. 87 1.10.3. ................................. 88
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2. ............................................................... 912.1. MATLAB ................... 922.1.1. ............................... 92 2.1.2. ........................................ 93 2.1.3. who whos .............................................................................. 95 2.1.4. .................................. 96
2.4.5. ......................................................... 111 2.4.6. MATLAB ........................................ 114
2.5. ............................ 1152.5.1. .................. 115 2.5.2. .................... 117 2.5.3. Tools ..................................... 117 2.5.4. .................................. 117 2.5.5. ................................................. 118
2.2. ......................................................... 962.2.1. , ............................ 96 2.2.2. MATLAB ........................................... 97 2.2.3. File ................................................................. 97 2.2.4. ........... 98 2.2.5. .......................... 99 2.2.6. Edit ..... 99 2.2.7. ...................................... 100
2.6. .................. 1182.6.1. ................. 118 2.6.2. ......................... 118 2.6.3. Plot Tool ............................ 120 2.6.4. MATLAB .................. 120 2.6.5. ................................................................ 121 2.6.6. ....................................................... 123 2.6.7. ........................... 124 2.6.8. Tools ......................... 124 2.6.9. ... 125 2.6.10. ........................ 126 2.6.11. ... 127 2.6.12. 3D ............................. 128
2.3. m ... 1002.3.1. / m .......... 100 2.3.2. .. 102 2.3.3. .. 102 2.3.4. ........ 103
2.4. MATLAB ..... 1042.4.1. Graphics ............................... 104 2.4.2. 2D MATLAB ..................... 104 2.4.3. MATLAB .................. 105 2.4.4. ..................... 108
2.7. ................ 1302.7.1. ............... 130 2.7.2. ............................................................................ 132
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2.7.3. mat ................................ 133 2.7.4. ...................... 133 2.7.5. .............................................. 135
3.2. ........................................ 1563.2.1. .......................................... 156 3.2.2. ..................... 159
2.8. .................................................................... 1352.8.1. Help Desk .................. 136 2.8.2. ..... 137 2.8.3. ............ 139
3.3. ................... 1613.3.1. ............................ 161 3.3.2. ............................................. 162 3.3.3. ..................... 165
2.9. MATLAB R2007 .............................................................. 1402.9.1. MATLAB R2007a ............ 140 2.9.2. MATLAB R2007a............... 141 2.9.3. / MATLAB R2007a .............................................................. 143 2.9.4. MATLAB R2007a ....................................... 144 2.9.5. MATLAB R2007a,b................... 144 2.9.6. MATLAB R2007b ................... 145 2.9.7. MATLAB R2007b ......................... 146 2.9.8. MATLAB R2007a,b ............................................................ 148
3.4. ................ 1683.4.1. ......... 168 3.4.2. ........................................ 173 3.4.3. .............................................. 177
3.5. ............................................... 1803.5.1. ........................... 180 3.5.2. ...................... 181
3.6. .......... 1823.6.1. ....................................................... 182 3.6.2. .................................................. 183 3.6.3. ................................. 186 3.6.4. .................... 187 3.6.5. ................................................... 188 3.6.6. ................... 189 3.6.7. ............................... 189 3.6.8. ..................... 190 3.6.9. psi ......................................... 191
3. ........................... 1513.1. ........ 1523.1.1. ... 152 3.1.2. ............................................ 153 3.1.3. ........................ 155
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4. ............................................................... 1934.1. .... 1944.1.1. ............................... 194 4.1.2. ...... 194 4.1.3. .......... 195 4.1.4. .............................................................................. 195 4.1.5. .............................. 196 4.1.6. ... 196 4.1.7. ...................................................................... 198
4.3.3. ................................................. 208 4.3.4. .................................................. 208 4.3.5. ............................................... 209 4.3.6. ............................. 210 4.3.7. .................................................. 210 4.3.8. .................................................. 211 4.3.9. .................................................. 212 4.3.10. ........................................ 212 4.3.11. ........................................... 213
4.4. ......... 2134.4.1. .............................................. 213 4.4.2. ......................................................................... 215 4.4.3. ............................... 217 4.4.4. ................................. 217 4.4.5. ......................................................................... 218 4.4.6. ............................................................................ 219 4.4.7. ........................................................ 219 4.4.8. .................................. 220 4.4.9. .......................................... 220 4.4.10. inv, pinv ................ 221 4.4.11. LU QR .......................................... 222 4.4.12. ....................................................... 225 4.4.13. ................................................................ 227
4.2. ....................................... 1994.2.1. ............................................ 199 4.2.2. ............. 200 4.2.3. .......................... 201 4.2.4. .................................... 201 4.2.5. ..................... 203 4.2.6. ............................ 204 4.2.7. .................................................... 205 4.2.8. ................. 205 4.2.9. ........................... 206
4.3. ............................................................................ 2074.3.1. ................................... 207 4.3.2. ................................................ 207
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4.5. ... 2314.5.1. MATLAB ............................................................. 231 4.5.2. MATLAB 7.* ... 231
5.3.2. ................................................ 252 5.3.3. LU .................... 253 5.3.4. ...................................................... 255
5. ................................................. 2335.1. ........................................ 2345.1.1. ............... 234 5.1.2. .................. 234 5.1.3. .................. 237 5.1.4. ........................................................................... 240 5.1.5. spy .. 241 5.1.6. ...................................... 242
5.4. ....................................... 2555.4.1. ......................... 255 5.4.2. : .... 257 5.4.3. .... 258 5.4.4. .......................................................................... 258 5.4.5. , ................................................... 259 5.4.6. ones, zeros, rand randn .......................... 259 5.4.7. ................... 260 5.4.8. reshape ...................................... 261
5.2. .................... 2455.2.1. ................................... 245 5.2.2. bucky......................... 246 5.2.3. ........................................ 246 5.2.4. .............................................................. 247 5.2.5. , ................................................... 249 5.2.6. ...................................................... 250
5.5. .................. 2625.5.1. ............ 262 5.5.2. ................. 262 5.5.3. .............................. 263 5.5.4. ...................... 264
5.6. ....................................... 2645.6.1. ................................................ 264 5.6.2. ...... 265 5.6.3. ................................... 266 5.6.4. ........................... 266
5.3. ........................... 2505.3.1. , .................................................... 250
5.7. ...................................... 267
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5.7.1. ............................... 267 5.7.2. ... 267 5.7.3. ................ 268 5.7.4. ..................................................... 268 5.7.5. ............................ 268
6.1.6. ............................................. 286 6.1.7. ............................ 287 6.1.8. ................. 288
6.2. ...................................................................... 2896.2.1. ............... 289 6.2.2. ........................................... 290
5.8. ...................................................... 2695.8.1. ..................................... 269 5.8.2. cell ............... 270 5.8.3. ............................... 271 5.8.4. .............................................................................. 271 5.8.5. deal ................ 272 5.8.6. ...................... 273 5.8.7. ................ 273
6.3. ....................................... 2916.3.1. ................................................. 291 6.3.2. ............... 292
6.4. ............................. 2936.4.1. ............................................... 293 6.4.2. .......................................................................... 294 6.4.3. ...................................... 296 6.4.4. .......................................... 297 6.4.5. 3D .......................... 298 6.4.6. 3D ..................... 301 6.4.7. ..................... 301
5.9. ............................ 2745.9.1. ................ 274 5.9.2. .................................... 275
6. ..................................................... 2776.1. ................................. 2786.1.1. .............. 278 6.1.2. ................ 282 6.1.3. ......... 283 6.1.4. ........................................ 284 6.1.5. ......................................................... 285
6.5. 3D ................................................................... 3026.5.1. ..................... 302 6.5.2. ................ 305 6.5.3. .................. 306 6.5.4. ............................................................................. 307
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6.5.5. .. 308 6.5.6. ............. 310 6.5.7. ............................ 310
6.8.9. ....... 334 6.8.10. ............ 335 6.8.11. ..................................................................... 335
6.6. ..................... 3126.6.1. ................................ 312 6.6.2. .................................. 312 6.6.3. ...................... 312 6.6.4. ......... 315
6.9. ............................ 3366.9.1. ........................................... 336 6.9.2. ................................................ 337 6.9.3. 3D ............. 338
6.7. ................................ 3166.7.1. .................................. 316 6.7.2. ... 319 6.7.3. ................ 319 6.7.4. ............................. 321 6.7.5. ....................... 322 6.7.6. ............................... 324 6.7.7. .............................. 324
7. ........................................... 3417.1. ....................................... 3427.1.1. ................................ 342 7.1.2. ............................ 342 7.1.3. ............................... 344 7.1.4. MATLAB ................... 344 7.1.5. ............................ 345
6.8. ............................... 3276.8.1. ..................................... 327 6.8.2. ............................................... 328 6.8.3. .......................................... 328 6.8.4. .......................... 329 6.8.5. .............. 330 6.8.6. ........................ 331 6.8.7. ............................................. 332 6.8.8. ................. 333
7.2. ....................... 3477.2.1. .......................... 347 7.2.2. ...... 347 7.2.3. ... 348 7.2.4. .......................................................................... 348 7.2.5. .......................................... 348 7.2.6. ............... 350 7.2.7. get .......................... 351 7.2.8. set ............ 352
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7.2.9. ................................................. 352 7.2.10. ....................... 353 7.2.11. ....... 356 7.2.12. .................... 357
7.6.4. ...................................... 375 7.6.5. ...................... 377 7.6.6. ................. 378 7.6.7. ... 379 7.6.8. .................................................. 381
7.3. ............................ 3577.3.1. ................................................... 357 7.3.2. ................. 359
7.4. GUI .... 3627.4.1. GUI .................... 362 7.4.2. GUI ............... 364 7.4.3. GUI .......................... 365 7.4.4. ........................................................ 366 7.4.5. ........................................................................... 367
8. ................................................ 3838.1. () .... 3848.1.1. ........................................ 384 8.1.2. ............................................................ 386 8.1.3. .......................................... 387
8.2. ..... 3888.2.1. , ............................................. 388 8.2.2. .... 390 8.2.3. .................... 392 8.2.4. ............................ 392 8.2.5. ..... 393 8.2.6. ............ 393 8.2.7. qmr ........... 394
7.5. .......................... 3697.5.1. OpenGL ................................. 369 7.5.2. ........................................................................ 370 7.5.3. .......................................... 370
7.6. ................................................................... 3727.6.1. Path ......................................... 372 7.6.2. ...... 373 7.6.3. ........................................................................ 375
8.3. ............................. 3948.3.1. ... 394 8.3.2. ......................................................................... 395
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8.3.3. fsolve solve ..... 396 8.3.4. ............... 397
8.8. () ........................................................... 4168.8.1. ................................................. 416 8.8.2. ....................................................... 417 8.8.3. ................. 419
8.4. ..................... 3988.4.1. ............ 398 8.4.2. ......................................................... 398 8.4.3. ........ 400 8.4.4. .................................................. 400
8.9. ...................................................................... 4228.9.1. ........ 422 8.9.2. .... 423 8.9.3. ............................................... 426 8.9.4. ....................................................................... 427 8.9.5. ....................................... 429 8.9.6. ...................... 431 8.9.7. ......................................................................... 432 8.9.8. ......................... 433 8.9.9. ....................................... 435 8.9.10. ................................................... 437
8.5. ............................ 4038.5.1. .................................. 403 8.5.2. .................................................................... 404 8.5.3. ............................ 407
8.6. ................................ 4088.6.1. ...................... 408 8.6.2. ..................... 409 8.6.3. .......... 410
8.7. ...... 4118.7.1. ....................................... 411 8.7.2. .......................... 412 8.7.3. ......................................... 412 8.7.4. ............................... 414 8.7.5. ..................... 415 8.7.6. ...................................................................... 415 8.7.7. ............ 416
9. ................................................... 4419.1. .............................. 442
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9.1.1. ........................................................ 442 9.1.2. ............................ 443 9.1.3. .......... 445 9.1.4. .................. 447 9.1.5. .............. 447 9.1.6. ......................... 448
9.5. ......... 4659.5.1. .................................. 465 9.5.2. ...... 467 9.5.3. ................ 467 9.5.4. ................... 469 9.5.5. ..................... 470 9.5.6. .................... 472 9.5.7. N ....................... 473 9.5.8. ..................... 474
9.2. ........................ 4499.2.1. ............................................ 449 9.2.2. ............................ 450 9.2.3. ............................. 451 9.2.4. .............. 452 9.2.5. ......................... 453
9.6. ..................... 4759.6.1. ................................................................... 475 9.6.2. ........................................................................ 478 9.6.3. ..................... 479 9.6.4. 3D .......... 479 9.6.5. .................. 482
9.3. ....................................... 4549.3.1. ......................................... 454 9.3.2. ............................................................................. 455 9.3.3. ....... 457 9.3.4. ................................... 458 9.3.5. ............................................................................. 459
9.7. ........... 4849.7.1. ........................................................ 484 9.7.2. ... 485 9.7.3. .................... 487 9.7.4. ............................................................................ 488 9.7.5. ........................................................ 490 9.7.6. ................................................................. 492
9.4. .................... 4609.4.1. ................................... 460 9.4.2. ................................ 461 9.4.3. .................... 461 9.4.4. ......................................... 464 9.4.5. ..................................... 464
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10. , ................................................ 49310.1. .......................... 49410.1.1. .................... 494 10.1.2. ...................................... 496 10.1.3. ...................... 500 10.1.4. ....... 502 10.1.5. ...................... 503
11.1.1. MATLAB .... 532 11.1.2. .............. 533 11.1.3. ........................................ 533 11.1.4. .................................... 535 11.1.5. , ... 536 11.1.6. ...................................... 537 11.1.7. .................... 538
11.2. M ....................... 53811.2.1. ............ 538 11.2.2. M ............................... 540 11.2.3. ............................ 541 11.2.4. global .......... 543 11.2.5. ................................ 543 11.2.6. ................................................ 544
10.2. ............................................... 50410.2.1. .............................. 505 10.2.2. ......................... 507 10.2.3. ....... 510 10.2.4. ................................... 514 10.2.5. ............................... 517
11.3. ................. 545 10.3. ...................... 51810.3.1. imfinfo........ 518 10.3.2. imread ............... 520 10.3.3. imwrite .................. 522 11.3.1. ............................. 545 11.3.2. lasterr .................... 546 11.3.3. ...................................................... 547
10.4. ........................ 52610.4.1. .......................... 526 10.4.2. MATLAB 6.1/6.5 .......................... 526 10.4.3. ... 527
11.4. .................................................................... 54711.4.1. ................... 547 11.4.2. varargin varargout .......................... 549
11.5. m ................ 550
11. ................................................ 53111.1. .......... 532
11.5.1. m ......................... 550 11.5.2. P ............................................... 551
11.6. ................................... 552
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11.6.1. ................................................. 552 11.6.2. ifelseifelseend .............. 553 11.6.3. forend ............................................. 554 11.6.4. whileend ......................................... 556 11.6.5. switchcaseend ... 558 11.6.6. trycatchend ................................ 559 11.6.7. break, continue return ....................... 560 11.6.8. if while ................. 561 11.6.9. ........................... 561
11.9.4. , .................................................................... 569 11.9.5. m ..................... 570 11.9.6. ................................. 570 11.9.7. m ................................ 571 11.9.8. ................................. 572 11.9.9. ............................. 574 11.9.10. .................. 574
11.10. MATLAB 7 ...... 57511.10.1. Profiler ..................................................................... 575 11.10.2. ................ 576 11.10.3. ..................................................................... 577 11.10.4. ........................................................ 577
11.7. ...................................................... 56111.7.1. ............................................... 561 11.7.2. ................................................. 562 11.7.3. .............................. 563 11.7.4. ......................................................... 564 11.7.5. ......................................................... 564
11.11. MATLAB .. 57911.11.1. ............................................... 579 11.11.2. !, dos, unix vms ................. 580 11.11.3. .... 580 11.11.4. ............................... 581
11.8. Handle inline .................................... 56511.8.1. handle ..................................... 565 11.8.2. handle ......... 566 11.8.3. Inline ..................................................... 566 11.8.4. handle inline ............ 567
11.12. Java ................................................ 58211.12.1. Java ......... 582 11.12.2. Java ..................................................... 582 11.12.3. Java ............. 584 11.12.4. Java .................................................... 586
11.9. .............................................. 56711.9.1. m .............. 567 11.9.2. ................................ 568 11.9.3. m ...................................... 568
11.13. MATLAB .................... 58711.13.1. MATLAB .... 587
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11.13.2. MATLAB Compiler ......................................................................... 587 11.13.3. m ......................... 588 11.13.4. ........... 589
12.3.7. GUI ... 622 12.3.8. GUI ........................................................... 629 12.3.9. .................... 634 12.3.10. ............ 639 12.3.11. GUI ............................................................................... 641
12. GUI ................................................................................... 59112.1. GUIDE .............................................................................. 59212.1.1. GUIDE .............................................. 592 12.1.2. GUIDE ...................... 593 12.1.3. GUI ............. 594 12.1.4. GUI ........................................ 597 12.1.5. .................................... 600 12.1.6. ...................................................................... 602
12.4. MATLAB ......... 64212.4.1. ....................................... 642 12.4.2. ....... 643 12.4.3. ............ 644 12.4.4. ............... 645 12.4.5. ................. 647 12.4.6. ...... 649 12.4.7. .... 650 12.4.8. ...................................... 654
12.2. ...................... 60412.2.1. ..... 604 12.2.2. ......... 609
13. MATLAB ........... 65913.1. MATLAB ............................ 66013.1.1. MATLAB+Simulink ............................................................ 660 13.1.2. Simulink 5/6 .............. 660
12.3. GUIDE ..... 61212.3.1. ..................... 612 12.3.2. File ............................................... 614 12.3.3. .............. 615 12.3.4. ............................. 618 12.3.5. .............................. 619 12.3.6. Tools ............................ 620
13.2. Simulink .............................. 66213.2.1. ... 662 13.2.2. Nonlinear Control Design Blockset ......................... 663 13.2.3. Digital Signal Processing (DSP) Blockset ................ 665 13.2.4. Fixed Point Blockset ................ 667
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13.2.5. Stateflow ................................ 667 13.2.6. SimPower System ................... 668 13.2.7. Report Generator MATLAB Simulink ............... 669 13.2.8. Real Time Windows Target WorkShop ................... 670
13.7. ........... 69913.7.1. Financial Toolbox .................................................. 699 13.7.2. Mapping Toolbox .................................................. 700 13.7.3. Data Acquisition Toolbox Instrument Control Toolbox ........................................................................... 701 13.7.4. Database toolbox .................................................. 703 13.7.5. Excel Link ............................................................. 703 13.7.6. Virtual Reality Toolbox............................................ 703 13.7.7. MATLAB Compiler ................................................. 704
13.3. .............. 67013.3.1. Symbolic Math Toolbox.......................................... 671 13.3.2. NAG Foundation Toolbox ....................................... 671 13.3.3. Spline Toolbox ...................................................... 672 13.3.4. Statistics Toolbox .................................................. 673 13.3.5. Optimization Toolbox ............................................. 674 13.3.6. Partial Differential Equations Toolbox ...................... 675 13.3.7. Fuzzy Logic Toolbox .............................................. 677 13.3.8. Neural Networks Toolbox ....................................... 678
13.8. MATLAB 6.5 ..................... 70413.8.1. Curve Fitting Toolbox ............................................. 704 13.8.2. Instrument Control Toolbox .................................... 706 13.8.3. Developers Kit for Texas Instruments DSP .............. 707 13.8.4. Dials & Gauges Blockset ........................................ 708 13.8.5. Mechanical System Blockset.................................. 708
13.4. .. 68013.4.1. Control System Toolbox ......................................... 680 13.4.2. Robust Control Toolbox ......................................... 682 13.4.3. Model Predictive Control Toolbox ........................... 684 13.4.4. Communications Toolbox ....................................... 685 13.4.5. m Analysis and Synthesis ....................................... 685 13.4.6. Quantitative Feedback Theory Toolbox .................... 686 13.4.7. LMI Control Toolbox .............................................. 686
13.9. MATLAB 7+Simulink 6 .................................................... 70913.9.1. Bioinformatics Toolbox ..................................................... 709 13.9.2. Genetic Algorithm and Direct Search Toolbox ................................................................ 711 13.9.3. Video and Image Processing Blockset .......................................................................... 713
13.5. .......................... 687 13.6. .............................................................. 68913.6.1. Signal Processing Toolbox ..................................... 689 13.6.2. Image Processing Toolbox ..................................... 691 13.6.3. Wavelet Toolbox .................................................... 695
14. MATLAB ........................ 71714.1. MATLAB ..................................................... 718
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14.1.1. ............... 718 14.1.2. .................................................. 719
[1], , MATLAB. MATLAB ( MATLAB R2007a,b 82) , . 3 . . MATLAB [2, 3] . 64 , Intel Core 2 Duo Quad, . MATLAB , . , , , IBM PC, AT Macintosh, UNIX . MATLAB , . MATLAB ( The MathWorks, Inc.) , , , , . Simulink, . MATLAB . . MATLAB + Simulink (. 0.1) Toolboxes MATLAB Bloksets Simulink. MATLAB + Simulink. MATLAB
14.2. ............................................................ 72114.2.1. USB ................................................................. 721 14.2.2. MATLAB Instrument Control Toolbox ............................................... 722 14.2.3. ............................ 723 14.2.4. MATLAB ............................................................ 724 14.2.5. MATLAB ... 728 14.2.6. MATLAB ........................................................................ 732
14.3. MATLAB .................................... 73514.3.1. .................................................. 735 14.3.2. AFG3000 MATLAB ........................................................ 736
14.4. MATLAB .... 739 14.5. MATLAB , ................... 741
................................................ 743 ........................................ 747
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. 0.1. MATLAB + Simulink
. , , , , , , , , . . MATLAB [4], 1993 . [549]. , Web The The MathWorks, Inc., , 1000 . (. 0.2), The The MathWorks, Inc. ( The MathWorks). , MATLAB Simulink. 1997 . MATLAB [443]. [1315] MATLAB 6.* MATLAB 6.5 () MATLAB 7.0 [1620]. MATLAB 7.*, MATLAB 7.5 MATLAB R2007b. , MATLAB 7.* , , . , MATLAB , . , c MATLAB 7.0 ( ) 1100 [28] 750 [29] . MATLAB 2800 [16 20] , , . , .
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The The MathWorks, Inc., Courtney Esposito, Naomi Fernandes Meg Vulliez. MATLAB MATLAB . , MATLAB, , . , , . (www.keytown.com) , The MathWorks, Inc., MATLAB . (vpdyak@keytown.com). , . , , . , : 214000, . , . , 4, . , . The MathWorks , www.mathworks.com. : The The MathWorks, Inc. 3 Apple Hill Drive Natick, MA, 01760 2098 USA Tel: 508 647 7000 Fax: 508 647 7101 E mail: info@The MathWorks.com
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52
MATLAB
MATLAB>> sin(V) ans = 0.8415 0.9093 0.1411 -0.7568 >> 3*V ans = 3 6 9 12 >> V^2 ??? Error using ==> ^ Matrix must be square. >> V.^2 ans = 1 4 9 16 >> V+2 ans = 3 4 5 6 >>
53
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1.3.2. MATLAB. , , . . , ans = 3 ans = 3 4 4 5 6 5 6
, MATLAB . , . , MATLAB :To get started, select "MATLAB Help" from the Help menu. >> 2+3 ans = 5 >> sin(1) ans = 0.8415 >> type sin sin is a built-in function. >> help sin SIN Sine. SIN(X) is the sine of the elements of X. Overloaded methods help sym/sin.m >> V=[1 2 3 4] V = 1 2 3 4
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56
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MATLABformat format format format format short short e long long e bank 1.3333 1.3333E+000 1.333333333333338 1.333333333333338E+000 1.33 0.0000 1.2345E-006 0.000001234500000 1.234500000000000E-006 0.00
57
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1.4.4. , (). (, 1, 2 1.23) . MATLAB , , , , . , MATLAB, : i j ( 1); pi p = 3,1415926; eps (252); realmin (21022); realmax (21023) inf ; ans , ; NaN (Not a Number). :>> 2*pi ans = 6.2832 >> eps ans = 2.2204e-016 >> realmin ans = 2.2251e-308 >> realmax ans = 1.7977e+308 >> 1/0 Warning: Divide by zero. ans = Inf >> 0/0 Warning: Divide by zero. ans = NaN
real(z) , Re(z), imag(z) , Im(z). abs(z), angle(Z). :>> i ans = 0 + 1.0000i >> j ans = 0 + 1.0000i >> z=2+3i z = 2.0000 + 3.0000i >> abs(z) ans = 3.6056 >> real(z) ans = 2 >> imag(z) ans = 3 >> angle(z) ans = 0.9828
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58
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61
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or variable 'V'.
or variable 'x'. or variable 'M'.
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1.4.8. MATLAB . , +, -, * /. . , 2+3 + , 2 3 . . , , . , * / , . , \ , .* ./ , , . :>> V1=[2 4 6 8] V1 = 2 4 6 >> V2=[1 2 3 4] V2 = 1 2 3 >> V1/V2 ans = 2 >> V1.*V2 ans = 2 8 18 32 >> V1./V2 ans = 2 2 2 2 8 4
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62
MATLAB
MATLAB>> sin(x)./x Warning: Divide by zero. ans = NaN 0.8415 0.4546
63
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, . , x = 0 sin(x)/x 0/0 1. , , MATLAB 0 . NaN, , 0/0 . : . , 0 5 0,5:>> bessel(0:1:5,1/2) ans = 0.9385 0.2423 0.0306 0.0026 0.0002 0.0000
0 5 1:>> bessel(0,0:1:5) ans = 1.0000 0.7652 0.2239 -0.2601 -0.3971 -0.1776
4.7124 0.4000
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1.4.10. MATLAB 1000 ( , ), . MATLAB . inline, , . sin(x) cos(y):>> sc2=inline('sin(x).^2+cos(y)^.2') sc2 = Inline function: sc2(x,y) = sin(x).^2+cos(y).^2
, MATLAB , , . :>> x=0:5 x = 0 1 >> cos(x) ans = 1.0000 >> sin(x)/x ans = -0.0862 2 0.5403 3 4 -0.4161 5 -0.9900 -0.6536 0.2837
. sin(x)/x , , ! , / , . , , . sin(x)/x, ./. :
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64>> type sc2 function y=sc2(x,y) y=sin(x).^2+cos(y).^2
MATLAB
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65
, , r. T, ENTER. :>> sqrt(2) ans = 1.4142
, , sc2(x,y), x y . :>> sc2(1,2) ans = 0.8813 >> sc2(2,1) y = 1.1187 ans = 1.1187
handle ( ) @:>> fh=@sc2;
feval(fh,x,y):>> feval(fh,1,2) y = 0.8813 ans = 0.8813 >> feval(fh,2,1) y = 1.1187 ans = 1.1187
, Tab . . MATLAB , . . , .m. , , () :>> hsin(1) ??? Undefined function or variable 'hsin'. >> sinh(1) ans = 1.1752
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ENTER. :??? Undefined function or variable 'sqr'.
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66
MATLAB
>> (2, 2) ans = 5
67
1.5. 1.5.1. MATLAB , , . , , . . , X=1, , X , 1, 11. , , . , , >> V=[1 2 3] V = 1 2 3
5. M(i, j) x, M(ij)=x
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2 100 8
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68
MATLAB
69
( 1). , :>> i=sqrt(-1); >> CM = [1 2; 3 4] + i*[5 6; 7 8]
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>> CM = [1+5*i 2+6*i; 3+7*i 4+8*i]
1.5.4. () . , 33:>> A=magic(3) A = 8 1 3 5 4 9
:CM = 1.0000 + 5.0000i 3.0000 + 7.0000i 2.0000 + 6.0000i 4.0000 + 8.0000i
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6 7 2
1.5.3. , , . . , * , .* . , M , M.*2 , 2. , M*2 M.*2 . . , magic(n) nn, , :>> M=magic(4) M = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 >> sum(M) ans = 34 34 34 34 >> sum(M) ans = 34 34 34 34 >> sum(diag(M)) ans = 34 >> M(1,2)+M(2,2)+M(3,2)+M(4,2) ans = 34
, :>> B=[A A+16;A+32 A+16] B = 8 1 6 3 5 7 4 9 2 40 33 38 35 37 39 36 41 34 >> sum(B) ans = 126
24 19 20 24 19 20
17 21 25 17 21 25
22 23 18 22 23 18
66. :126 126 126 126 126
, . >> sum(B.') ans = 78 78 78 174 174 174
B.' B, . . , B . :>> D=magic(6) D = 35 1 3 32 31 9 8 28 30 5 4 36 >> sum(D) ans = 111 111 >> sum(D.') ans = 111 111
6 7 2 33 34 29 111 111
26 21 22 17 12 13 111 111
19 23 27 10 14 18 111 111
24 25 20 15 16 11 111 111
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70
MATLAB
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71
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1.6.2. MATLAB .mat. save, : save fname fname.mat; save fname X X; save fname X Y Z X, Y Z. save , : -mat MAT , ; -ascii ASCII (8 ); -ascii -double ASCII (16 ); -ascii -double -tabs ; V4 MAT MATLAB 4; -append MAT . save , , :save('fname','var1','var2')
, : ():>> M(:,2)=[ ] M = 1 3 4 6 7 9
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1.6. , m 1.6.1. MATLAB , . . . , , . ( , ) pack, . ,
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72>> diary off >> 2+3 ans = 5 >> diary on >> sin(1) ans = 0.8415 >> diary off
MATLAB
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73
, 1 + 2 = 3 myfile.m, 2 + 3 = 5 , sin(1) = 0,8415 . , Script :1+2 ans = 3 diary off sin(1) ans = 0.8415 diary off
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, , . :>> myfile ??? ans = Missing variable or function. Error in ==> C:\MATLAB\bin\myfile.m On line 3 ==> ans =
, , , MATLAB , ans =. type :>> type myfile 1+2 ans = 3 diary off sin(1) ans = 0.8415 diary off
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74
MATLAB
Elementary matrices and matrix manipulation. Matlab\elfun Elementary math functions. Matlab\specfun Specialized math functions. ................................................ Matlab\elmat
75
, m , , MATLAB. . MATLAB. , , MATLAB, . , .
1.7.2. >> help
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>> doc
quit, exit Ctrl+Q. (, ) , save . load , .
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, , hsin m . :>> help sinh SINH Hyperbolic sine. SINH(X) is the hyperbolic sine of the elements of X. Overloaded methods help sym/sinh.m
General purpose commands. Operators and special characters. Programming language constructs.
sinh. , X. MATLAB () , () . . , .
76
MATLAB
77
MATLAB. :>> help pi PI 3.1415926535897 PI = 4*atan(1) = imag(log(-1)) = 3.1415926535897
1.7.4. MATLAB m m . lookfor
help . , , MS DOS. doc HTML.
lookfor ' '
1.7.3. MATLAB , , . MATLAB. timefun:>> help timefun Time and dates. Current date and time. Now Current date and time as date number. Date Current date as date string. Clock Current date and time as date vector. Basic functions. Datenum Serial date number. Datestr String representation of date. Datevec Date components. Date functions. Calendar Calendar. Weekday Day of week. Eomday End of month. Datetick Date formatted tick labels. Timing functions. Cputime CPU time in seconds. Tic Start stopwatch timer. Toc Stop stopwatch timer. Etime Elapsed time. Pause Wait in seconds.
m , , . , . lookfor. :>> lookfor 'inverse sin' ASIN Inverse sine. IS2RC Convert inverse sine parameters to reflection coefficients. RC2IS Convert reflection coefficients to inverse sine parameters. ASIN Symbolic inverse sine.
'inverse sin', . , ( ) MATLAB. , Windows 95/98/Me/2000/NT4/XP/Vista .
1.7.5. : computer , MATLAB; help script m (Script ); help function m ; info MathWorks ; subscribe ;
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78
MATLAB
79
ver MATLAB ; version MATLAB; version java MATLAB (Java); what ; what name , name; whatsnew name readme name ; which name . , , ver MATLAB . version. , MATLAB R2007a:>> version ans = 7.4.0.287 (R2007a)
. MATLAB . MATLAB.
1.8.2. MATLAB. >> wernerboy
, . 1.7 . , . .
1.8. 1.8.1. . MATLAB . demos :>> help demos Examples and demonstrations. Type 'demo' at the command line to browse more demos of MATLAB, the Toolboxes, and Simulink. demo Run demonstrations. Mathematics. intro Basic Matrix Operations inverter Inverses of Matrices buckydem Graphs and Matrices sparsity Sparse Matrices matmanip Matrix Manipulation integerMath Integer Arithmetic Examples ...............................................
. 1.7.
80
MATLAB
>> e^pi>pi^e ans = 1
81
1.8.3. e^pi pi^e? , , e^pi pi^e? >> e2pi
1.8.4. MATLAB , . , knot, (. 1.9). , . , MATLAB 7 SP2 . .
x^y y^x . 1.8. . , :>> e=exp(1) e = 2.7183 >> e^pi ans = 23.1407 >> pi^e ans = 22.4592
1.8.5. m MATLAB . m , , , m , , type _M-
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82
MATLAB
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83
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1.9.2. MATLAB . . , MATLAB ( ) , , . x 0 10 0,1. x=0:0.1:15, plot(sin(x)). , :x=0:0.1:15; y=sin(x); plot(x,y)
help, .
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84
MATLAB
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sin(x), x . , . 100 , 1020 .
1.9.3. . : sin(x), cos(x) sin(x)/x. , , y(x):>> y1=sin(x); y2=cos(x); y3=sin(x)/x;
, x. plot:plot(a1,f1,a2,f2,a3,f3,...),
a1, a2, a3, ( x), f1, f2, f3, , . :>> plot(x,y1,x,y2,x,y3)
. 1.11.
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1.9.4. fplot, MATLAB , sin(x)/x, . , , , fplot:fplot('f(x)', [xmin xmax])
f(x), , x xmin xmax x. . 1.12. ( 0) , , x=0 sin(x)/x=1. : clear () grid on () , . . 1.12 Insert () . , , . . . 1.12 Colorbar.
86
MATLAB
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87
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88
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92
MATLAB
93
MATLAB . . MATLAB 2006b MATLAB, . ( ) MATLAB MATLAB R2007a,b.
2.1. MATLAB MATLAB . 1 . GUI (Graphics User Interface). GUI Windows, , MATLAB [16, 44, 45]. ( GUI 12).
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94
MATLAB
95
. 2.1. MATLAB R2006b
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2.1.3. who whos , , Workspace Browser. who , whos . : .>> x=1.234; >> V=[1 2 3 4 5]; >> M=magic(4); >> who Your variables are: M V x >> whos Name Size Bytes Class M 4x4 128 double V 1x5 40 double X 1x1 8 double Grand total is 22 elements using
array array array 176 bytes
. 2.2.
, M, whos M. , (Workspace Browser) .
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2.2. 2.2.1. , . (Enter). ,
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Redo () Undo; Cut () ; Copy () ; Paste () ; Paste to Workspace ( ); Clear () ; Select All () ; Delete () ; Find () ( ); Find files ( ); Clear Command Windows ( ) ( ); Clear Command History ( ) ; Clear Workspace . . , Clear Command Window . , , . , cl, . ( ) .
. 2.6. MATLAB R2006b
2.2.7. MATLAB . , . Desktop. . Desktop Layout Default Desktop . MATLAB R2006b . 2.6.
2.3. m 2.3.1. / m MATLAB m . , m ( MATLAB R2006a,b/R2007a )
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Annotations (, , , . .). , , z , sin(x)./x. Annotations, , , . 2.10. , , . , Reverse Direction . . 2.11.
. 2.9. MATLAB Graphics
. 2.11. 2D
. 2.10. 2D
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. 2.13.
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111
. 2.14. 3D Surface
. 2.16. surfc
, . . 2.17. .
2.4.5. . . Figure Palette. . 2.18 , . , . 2.19. , . , . Add Data, , , (. 2.20) ,
. 2.15. surfc
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113
. 2.17.
. 2.19.
. 2.18.
. 2.20.
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115
. ( ). Add Data to Axes. , . , sin(x)^3, x , y sin(x).^3. OK, . . 2.21.
. 2.22. MATLAB
. 2.22 Current Directory. , . , . .
2.5. . 2.21.
2.5.1. (. . 2.36) Show M code M , . M . . 2.38 . MATLAB . 2.23. Windows . MATLAB . MATLAB. . Edit : Copy Figure ( ) ( ); Copy Options ( ) ; Figure Properties ( ) ;
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. MATLAB .
2.5.2. MATLAB 6.0 (3D) . ( . 2.23 ) View Camera Toolbar. ( ), . , . .
2.5.3. Tools Tools (). , MATLAB 6.0, . : Edit Plot ( ) ; Zoom In () ; Zoom Out () ; Rotate 3D ( 3D) ; Move Camera ( ) ; Camera Motion ( ) ; Camera Axes ( ) ; Camera Reset ( ) ; Basic Fitting ; Data Statistics . ( ) .
. 2.23. MATLAB
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, (, ), , , . . , MATLAB 7.
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, . 2.24, Inspec tor. .
2.6.3. Plot Tool . , x, y z. . , : Data cursor ; Insert Color Bar ; Insert Legends ; Hide Plot Tools ; Show Plot Tools . . : , . . , , . 1.16 Insert .
. 2.25.
2.6.4. MATLAB MATLAB. M , . , Graphics MATLAB. . 2.25. Figure Palette New Subplots, ( ) . Variables. . . 2.25 . Annotations , , . Plot Browser. , . , ,
. . .
2.6.5. . . 2.26. ( ) , . . x, 15 +15 0,1. , . . 2.27, , . , . ,
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. , , , . . .
2.6.6. , . :>> x=-6:.1:6; >> plot(x,sin(x),x,sin(x).^3,x,sin(x).^5);
. 2.26.
2.28 , . . , . 2.28 . , , . sin(x)^2 cos(x)^2 , x . .^ , .
. 2.27.
. 2.28.
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2.6.7. . , ( ) , (. 2.29), .
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, , . . , ( Scale), (X, , Z), ( Grid Show), ( Style ()), ( Label ()) .
2.6.9. A. . . 2.31 . . , ^ ( ). . 2.31, , , . ,
2.6.8. Tools Tools () . . 2.30.
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. 2.31.
. 2.32.
. ( ).
2.6.11. (. Tools ( ) Zoom In () Zoom Out ()), ( Rotate 3D), ( Add) , , . . 1.11. , . , ( ). . . 1.12 . 2.23. , , , . , text(x,y, 'legend') 'legend' , (x,y). \leftarrow, () , . \rightarrow
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2.6.12. 3D (2D) , . 3D :>> Z=peaks(40); >> mesh(Z);
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MATLAB . . , . . 2.33 , Camera (). , 3D , ,
. 2.34.
. 2.33. 3D
. () . 2.35, . ( ), . () . , , MATLAB, . .
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. 2.36. Import . 2.35.
2.7. 2.7.1. MATLAB . Import Wizard. . Import Data File Import . 2.36. , . , . , Import Wizard. . 2.37 canoe.tif, , TIF. : , , . , . , (, , , . .) .
. 2.37. Import Wizard Wizard
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2.7.2. : Image Preview ( , ); dvp dvp ( ). Show Image. Image Viewer. , . , . . , . . 2.37. . . Finish, . , , , . 2.38. , , ( ), ,
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2.7.3. mat MATLAB mat . . . 2.39 logo.mat, MATLAB.
. 2.39. logo.mat
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2.7.4. . 2.38. colormap,
. . 2.41 . license.txt.
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, . Next, . 2.42. , . .
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. 2.42. license.txt
2.7.5. , MATLAB, . . , , , , . MATLAB , .
2.8. . 2.41. license.txt
, MATLAB , , , . ,
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2.8.2. , MATLAB , . ? MATLAB . . 2.43 MATLAB Functions Alfabetical List:. . 2.44 .
2.8.1. Help Desk Full Product Family Help Help. , . 2.43.
. 2.44. MATLAB 7
. 2.43. MATLAB 7 (R14)
( ), HTML .
, . 2.45 abs, . ( ) , MATLAB . ( ) Evaluate Selection .
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. 2.45. abs
. 2.46. , abs
, : Contents ( ); Index ( ); Search . , Favorite MATLAB 7 . , MATLAB . , Microsoft Internet Explorer Opera. , . , Search , , . . 2.46. , , abs. , , MATLAB.
MATLAB. . Help , , .
2.8.3. Help Demos, MATLAB. MATLAB Demo Window, . 2.47. demo Demos . MATLAB 7 . . MATLAB 7
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MATLAB R2007
141
. 2.47.
. 2.48.
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2.9. MATLAB R20072.9.1. MATLAB R2007a MATLAB . MathWorks 23 . ,
(, MATLAB 7.*) . ( ) MATLAB R2007a,b. MATLAB R2007a, (Default), . 2.49. Command Window, , , Current Directory, Workspace Command History. , m About MATLAB. . 2.49 . 1.1 , . About MATLAB ( MATLAB 2007a 2007 .).
2.9.2. MATLAB R2007a Desktop. . 2.50 MATLAB 2007a, , , ,
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MATLAB R2007
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. Desktop . . 2.50 . 1.2 , MATLAB R2006/R2007 , .
2.9.3. / MATLAB R2007a MATLAB, MATLAB R2007a / . , . 2.49, , , . 2.51.
. 2.49. MATLAB 2007a
. 2.51. / MATLAB 2007a
. 2.50. MATLAB 2007a
. 2.51 Debug (), . / 11. MATLAB.
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MATLAB R2007
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2.9.4. MATLAB R2007a MATLAB R2007a . . 2.52 Realize Note ( ). MATLAB .
Distributed MATLAB R2007b, ; , ; ToolboxGeneration ; .
2.9.6. MATLAB R2007b MATLAB MATLAB R2007b. . ver . . 2.53 MATLAB R2007b , ver. , . MATLAB Simulink ( Simulink 7).
. 2.52. MATLAB 2007a Realize Note
2.9.5. MATLAB R2007a,b , MATLAB R2007a,b : ( 82 ) , ; (Hyper Threading) ; (multicore) ; ; ;
. 2.53. MATLAB R2007b
146
MATLAB R2007
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MATLAB R2007b . 2.54. Distributed. : Select Configuration ( ) Manage Confiuration. Local , , . 2.4 .
. 2.55. MATLAB R2007b
. 2.54. MATLAB R2007b
MATLAB R2007b . 2.55. . , , MATLAB . Loading.
2.9.7. MATLAB R2007b MATLAB Prefe rences, File . . 2.56 MATLAB R2007b. MATLAB (. 2.5), , MATLAB , .
. 2.56. MATLAB R2007b
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MATLAB R2007
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( Multithreading). . 4 .
2.9.8. MATLAB R2007a,b . 2.57 Pentium 4 HT 2,6 MATLAB R2007a (MATLAB 7.4.0). . , ( , , ). MATLAB 2006b (. 1.5) , .
. 2.58. MATLAB 2007b Core 2 Quad
. 2.57. MATLAB 2007a
MATLAB R2007b . , . , MATLAB . , . , MATLAB ( ), . , , MATLAB 2007a/ R2007b), MATLAB R2006a,b . MATLAB .
, MATLAB 2007b (MATLAB 7.5.0) ? . 2.58,
3 3.1. ............ 3.2. ...... 3.3. .................................. 3.4. ........... 3.5. ............ 3.6. ........ 152 156 161 168 180 182
152
ans = 3 >> minus(B,A) ans = 3 >> A.^2 ans = 1 >> power(A,2) ans = 1 >> A.\B ans = 4.0000 >> ldivide(A,B) ans = 4.0000 >> rdivide(A,B) ans = 0.2500 3 3 4 4 2.5000 2.5000 0.4000 3 3 9 9 2.0000 2.0000 0.5000
153
MATLAB . . , , M . MATLAB .
3.1. 3.1.1. . MATLAB (. 3.1). .
3.1. MATLAB plus uplus minus uminus mtimes times mpower power mldivide mrdivide ldivide rdivide kron ( ) + + * .* ^ .^ \ / .\ ./ kron M1+M2 +M M1-M2 -M M1*M2 A1*A2 M1^x A1^x M1\M2 M1/M2 A1.\A2 A1./A2 kron(X,Y)
MATLAB . , . , MATLAB : 1) ; 2) ; 3) ( + , ~); 4) ; 5) ; 6) :; 7) ; 8) . . . .
3.1.2. . , . , x y, , . 3.2.
, . , * mtimes(M1,M2). , ( ans ):>> A=[1 2 3]; >> B=[4 5 6]; >> B-A
3.2. eq ne lt gt le ge == ~= < > = x==y x~=y xy x=y
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1 (True), , 0 (False) . , : , eq(2,2) 1, le(5,3) 0. , = . == ~= , , :>> (2+3i)>=(2+i) ans = 1 >> (2+3i)>(2+i) ans = 0 >> abs(2+3i)>abs(2+i) ans = 1 >> (2+3i)==(2+i) ans = 0 >> (2+3i)~=(2+i) ans = 1
, , ASCII . , . , (. 11).
3.1.3. (. 3.3). (. 11) .
3.3. MATLAB And Or Not Xor Any All
, :M = -1 1 >> M>=0 ans = 0 1 0 2
(AND) & (OR) | (NOT) ~ (EXCLUSIVE OR) , ,
:>> A=[1 2 3]; >> B=[1 0 0]; >> and(A,B) ans = 1 >> or(A,B) ans = 1 >> A&B ans = 1 >> A|B ans = 1 >> not(A) ans = 0 >> not(B) ans = 0 >> ~B ans = 0 >> xor(A,B) ans = 0 >> any(A) ans = 1 >> all([0 0 0]) ans = 0 >> all(B) ans = 0
1 1
0 1 0 1 0 1 1 1
0 1 0 1 0 1 1 1
:>> M>[0 1; 1 0] ans = 0 0
0 1
, MATLAB , , , , . :>> 'b'>'a' ans = 1 >> 'abc'=='abc' ans = 1 >> 'cba'> and('abc','012') ans = 1 1
, . , . : ASCII . MATLAB && || ( ). . , A&&B A , B , . A||B A , , .
3.2. 3.2.1. MATLAB . . . 3.4 .
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. : () . : MATLAB. : j:k , [j,j+1,,k]; j:k , j>k; j:i:k , [j,j+i,j+2i,,k]; j:i:k , i>0 j>k i> [str,maxsize] = computer str = PCWIN maxsize = 268435455
' ( ) , A' A. , . . ; .' () , A.' . ;
eps 1.0 , 1.0. eps pinv rank, . eps = 2^(52), 2.22e16. :
160
>> eps ans = 2.2204e-016
>> n = realmax n = 1.7977e+308
161
i j ( sqrt(1)), . i . j. :>> w=3+5i w = 3.0000 + 5.0000i
realmin , . . :>> n = realmin n = 2.2251e-308
i j , for. , . I J i j . Inf . , , , , , . :>> 4/0 Warning: Divide by zero. ans = Inf
varargin varargout : varargout = foo(n) foo; y = function bar(varargin) bar. varargin varargout m . , . 11.
3.3. 3.3.1. : bitand(A,B) A
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