scipy tutorial - Baustatik-Info-Server

More documents

Recommendations

Info

SciPy Reference Guide, Release 0.8.dev 0.56714329040978387299996866221035555 >>> w*exp(w) 1.0 Any branch gives a valid inverse: >>> w = lambertw(1, k=3) >>> w (-2.8535817554090378072068187234910812 + 17.113535539412145912607826671159289j) >>> w*exp(w) (1.0 + 3.5075477124212226194278700785075126e-36j) Applications to equation-solving The Lambert W function may be used to solve various kinds of equations, such as finding the value of the infinite power tower z^{z^{z^{ldots}}}: >>> def tower(z, n): ... if n == 0: ... return z ... return z ** tower(z, n-1) ... >>> tower(0.5, 100) 0.641185744504986 >>> -lambertw(log(0.5))/log(0.5) 0.6411857445049859844862004821148236665628209571911 Properties The Lambert W function grows roughly like the natural logarithm for large arguments: >>> lambertw(1000) 5.2496028524016 >>> log(1000) 6.90775527898214 >>> lambertw(10**100) 224.843106445119 >>> log(10**100) 230.258509299405 The principal branch of the Lambert W function has a rational Taylor series expansion around z = 0: >>> nprint(taylor(lambertw, 0, 6), 10) [0.0, 1.0, -1.0, 1.5, -2.666666667, 5.208333333, -10.8] Some special values and limits are: >>> lambertw(0) 0.0 >>> lambertw(1) 0.567143290409784 >>> lambertw(e) 1.0 >>> lambertw(inf) +inf >>> lambertw(0, k=-1) -inf >>> lambertw(0, k=3) -inf >>> lambertw(inf, k=3) (+inf + 18.8495559215388j) The k = 0 and k = -1 branches join at z = -1/e where W(z) = -1 for both branches. Since -1/e can only be represented approximately with mpmath numbers, evaluating the Lambert W function at this point only gives -1 approximately: >>> lambertw(-1/e, 0) -0.999999999999837133022867 >>> lambertw(-1/e, -1) -1.00000000000016286697718 If -1/e happens to round in the negative direction, there might be a small imaginary part: >>> lambertw(-1/e) (-1.0 + 8.22007971511612e-9j) zeta y=zeta(x,q) returns the Riemann zeta function of two arguments: sum((k+q)**(-x),k=0..inf) 446 Chapter 3. Reference
zetac y=zetac(x) returns 1.0 - the Riemann zeta function: sum(k**(-x), k=2..inf) Convenience Functions cbrt() y=cbrt(x) returns the real cube root of x. exp10() y=exp10(x) returns 10 raised to the x power. exp2() y=exp2(x) returns 2 raised to the x power. radian(x1, x2) y=radian(d,m,s) returns the angle given in (d)egrees, (m)inutes, and cosdg() y=cosdg(x) calculates the cosine of the angle x given in degrees. sindg() y=sindg(x) calculates the sine of the angle x given in degrees. tandg() y=tandg(x) calculates the tangent of the angle x given in degrees. cotdg() y=cotdg(x) calculates the cotangent of the angle x given in degrees. log1p() y=log1p(x) calculates log(1+x) for use when x is near zero. expm1() y=expm1(x) calculates exp(x) - 1 for use when x is near zero. cosm1() y=calculates cos(x) - 1 for use when x is near zero. round() y=Returns the nearest integer to x as a double precision cbrt y=cbrt(x) returns the real cube root of x. exp10 y=exp10(x) returns 10 raised to the x power. exp2 y=exp2(x) returns 2 raised to the x power. SciPy Reference Guide, Release 0.8.dev radian y=radian(d,m,s) returns the angle given in (d)egrees, (m)inutes, and (s)econds in radians. cosdg y=cosdg(x) calculates the cosine of the angle x given in degrees. sindg y=sindg(x) calculates the sine of the angle x given in degrees. tandg y=tandg(x) calculates the tangent of the angle x given in degrees. cotdg y=cotdg(x) calculates the cotangent of the angle x given in degrees. log1p y=log1p(x) calculates log(1+x) for use when x is near zero. expm1 y=expm1(x) calculates exp(x) - 1 for use when x is near zero. cosm1 y=calculates cos(x) - 1 for use when x is near zero. round y=Returns the nearest integer to x as a double precision floating point result. If x ends in 0.5 exactly, the nearest even integer is chosen. 3.18 Statistical functions (<strong>scipy</strong>.stats) This module contains a large number of probability distributions as well as a growing library of statistical functions. 3.18. Statistical functions (<strong>scipy</strong>.stats) 447
Page 1:
SciPy Reference Guide Release 0.8.d
Page 4 and 5:
Bibliography 699 Index 703 ii
Page 6 and 7:
SciPy Reference Guide, Release 0.8.
Page 8 and 9:
Page 10 and 11:
Page 12 and 13:
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
Page 268 and 269:
Page 270 and 271:
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
Page 286 and 287:
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
Page 320 and 321:
Page 322 and 323:
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
Page 352 and 353:
Page 354 and 355:
Page 356 and 357:
Page 358 and 359:
Page 360 and 361:
Page 362 and 363:
Page 364 and 365:
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
Page 372 and 373:
Page 374 and 375:
Page 376 and 377:
Page 378 and 379:
Page 380 and 381:
Page 382 and 383:
Page 384 and 385:
Page 386 and 387:
Page 388 and 389:
Page 390 and 391:
Page 392 and 393:
Page 394 and 395:
Page 396 and 397:
Page 398 and 399:
Page 400 and 401: SciPy Reference Guide, Release 0.8.
Page 500 and 501:
Page 502 and 503:
Page 504 and 505:
Page 506 and 507:
Page 508 and 509:
Page 510 and 511:
Page 512 and 513:
Page 514 and 515:
Page 516 and 517:
Page 518 and 519:
Page 520 and 521:
Page 522 and 523:
Page 524 and 525:
Page 526 and 527:
Page 528 and 529:
Page 530 and 531:
Page 532 and 533:
Page 534 and 535:
Page 536 and 537:
Page 538 and 539:
Page 540 and 541:
Page 542 and 543:
Page 544 and 545:
Page 546 and 547:
Page 548 and 549:
Page 550 and 551:
Page 552 and 553:
Page 554 and 555:
Page 556 and 557:
Page 558 and 559:
Page 560 and 561:
Page 562 and 563:
Page 564 and 565:
Page 566 and 567:
Page 568 and 569:
Page 570 and 571:
Page 572 and 573:
Page 574 and 575:
Page 576 and 577:
Page 578 and 579:
Page 580 and 581:
Page 582 and 583:
Page 584 and 585:
Page 586 and 587:
Page 588 and 589:
Page 590 and 591:
Page 592 and 593:
Page 594 and 595:
Page 596 and 597:
Page 598 and 599:
Page 600 and 601:
Page 602 and 603:
Page 604 and 605:
Page 606 and 607:
Page 608 and 609:
Page 610 and 611:
Page 612 and 613:
Page 614 and 615:
Page 616 and 617:
Page 618 and 619:
Page 620 and 621:
Page 622 and 623:
Page 624 and 625:
Page 626 and 627:
Page 628 and 629:
Page 630 and 631:
Page 632 and 633:
Page 634 and 635:
Page 636 and 637:
Page 638 and 639:
Page 640 and 641:
Page 642 and 643:
Page 644 and 645:
Page 646 and 647:
Page 648 and 649:
Page 650 and 651:
Page 652 and 653:
Page 654 and 655:
Page 656 and 657:
Page 658 and 659:
Page 660 and 661:
Page 662 and 663:
Page 664 and 665:
Page 666 and 667:
Page 668 and 669:
Page 670 and 671:
Page 672 and 673:
Page 674 and 675:
Page 676 and 677:
Page 678 and 679:
Page 680 and 681:
Page 682 and 683:
Page 684 and 685:
Page 686 and 687:
Page 688 and 689:
Page 690 and 691:
Page 692 and 693:
Page 694 and 695:
Page 696 and 697:
Page 698 and 699:
Page 700 and 701:
Page 702 and 703:
Page 704 and 705:
Page 706 and 707:
Page 708 and 709:
Page 710 and 711:
Page 712 and 713:
Page 714 and 715:
Page 716 and 717:
Page 718 and 719:
Page 720 and 721:
Page 722:
show all

scipy tutorial - Baustatik-Info-Server

Create successful ePaper yourself

Delete template?

Save as template?