1%feature("docstring") OT::SpecFunc::BesselI0 2"Modified first kind Bessel function of order 0. 3 4.. math:: 5 6 \forall x \in \Rset, \quad 7 \mathrm{I}_0(x) = \sum_{m=0}^\infty\frac{1}{m!^2}\left(\frac{x}{2}\right)^{2m} 8 9Parameters 10---------- 11x : float 12 13Returns 14------- 15result : float" 16 17// --------------------------------------------------------------------- 18 19%feature("docstring") OT::SpecFunc::LogBesselI0 20"Logarithm of the modified first kind Bessel function of order 0. 21 22.. math:: 23 24 \forall x \in \Rset, \quad 25 LogBesselI0(x) = \log (\mathrm{I}_0(x)) 26 27See also 28-------- 29SpecFunc_BesselI0 30 31Parameters 32---------- 33x : float 34 35Returns 36------- 37result : float" 38 39// --------------------------------------------------------------------- 40 41%feature("docstring") OT::SpecFunc::BesselI1 42"Modified first kind Bessel function of order 1. 43 44.. math:: 45 46 \forall x \in \Rset, \quad 47 \mathrm{I}_1(x) = \sum_{m=0}^\infty\frac{1}{m!(m+1)!}\left(\frac{x}{2}\right)^{2m+1} 48 49Parameters 50---------- 51x : float 52 53Returns 54------- 55result : float" 56 57// --------------------------------------------------------------------- 58 59%feature("docstring") OT::SpecFunc::LogBesselI1 60"Logarithm of the modified first kind Bessel function of order 1. 61 62.. math:: 63 64 \forall x \in \Rset, \quad 65 LogBesselI1(x) = \log (\mathrm{I}_1(x)) 66 67See also 68-------- 69SpecFunc_BesselI1 70 71Parameters 72---------- 73x : float 74 75Returns 76------- 77result : float" 78 79// --------------------------------------------------------------------- 80 81%feature("docstring") OT::SpecFunc::BesselK 82"Modified second kind Bessel function of order :math:`\nu`. 83 84.. math:: 85 86 \forall x \in \Rset, \quad 87 \mathrm{K}_{\nu}(x) = \frac{\pi}{2}\frac{\mathrm{I}_{-\nu}(x)-\mathrm{I}_{\nu}(x)}{\sin{\nu\pi}} 88 89Parameters 90---------- 91nu : float 92x : float 93 94Returns 95------- 96result : float" 97 98// --------------------------------------------------------------------- 99 100%feature("docstring") OT::SpecFunc::LogBesselK 101"Logarithm of the modified second kind Bessel function of order :math:`\nu`. 102 103.. math:: 104 105 \forall x \in \Rset, \quad 106 LogBesselK(\nu, x) = \log(\mathrm{K}_{\nu}(x)) 107 108See also 109-------- 110SpecFunc_BesselK 111 112Parameters 113---------- 114nu : float 115x : float 116 117Returns 118------- 119result : float" 120 121// --------------------------------------------------------------------- 122 123%feature("docstring") OT::SpecFunc::Beta 124"Beta function :math:`\mathrm{B}`. 125 126.. math:: 127 128 \forall (a, b) > 0, \quad 129 \mathrm{B}(a, b) = \int_0^1 t^{a-1}(1-t)^{b-1}\di{t} 130 131Parameters 132---------- 133a, b : float :math:`\in \Rset^*_+` 134 135Returns 136------- 137result : float" 138 139// --------------------------------------------------------------------- 140 141%feature("docstring") OT::SpecFunc::LogBeta 142"Logarithm of the Beta function. 143 144.. math:: 145 146 \forall (a, b) > 0, \quad 147 LogBeta(a, b) = \log (\mathrm{B}(a, b)) 148 149See also 150-------- 151SpecFunc_Beta 152 153Parameters 154---------- 155a, b : float :math:`\in \Rset^*_+` 156 157Returns 158------- 159result : float" 160 161// --------------------------------------------------------------------- 162 163%feature("docstring") OT::SpecFunc::LnBeta 164"Logarithm of the Beta function. 165 166.. math:: 167 168 \forall (a, b) > 0,\quad 169 LnBeta(a, b) = \ln (\mathrm{B}(a, b)) = \log (\mathrm{B}(a, b)) 170 171See also 172-------- 173SpecFunc_Beta 174 175Parameters 176---------- 177a, b : float :math:`\in \Rset^*_+` 178 179Returns 180------- 181result : float" 182 183// --------------------------------------------------------------------- 184 185%feature("docstring") OT::SpecFunc::IncompleteBeta 186"Incomplete Beta function. 187 188.. math:: 189 190 \forall (a, b) > 0, t \in [0, 1], \quad 191 \mathrm{B}(x; a, b) = \int_0^x t^{a-1}(1-t)^{b-1}\di{t} 192 193Parameters 194---------- 195a, b : float :math:`\in \Rset^*_+` 196x : float 197tail : bool, optional 198 By default, *tail* is *False*. 199 200Returns 201------- 202result : float 203 - If *tail* is *False*: :math:`result = \mathrm{B}(x; a, b)`. 204 - If *tail* is *True*: :math:`result = \mathrm{B}(a, b) - \mathrm{B}(x; a, b)`." 205 206// --------------------------------------------------------------------- 207 208%feature("docstring") OT::SpecFunc::IncompleteBetaInverse 209"Inverse of the incomplete Beta function. 210 211.. math:: 212 213 \forall (a, b) > 0 \quad 214 IncompleteBetaInverse(x; a, b) = \mathrm{B}^{-1}(x/\mathrm{B}(a, b); a, b) 215 216See also 217-------- 218SpecFunc_IncompleteBeta, SpecFunc_RegularizedIncompleteBetaInverse 219 220Parameters 221---------- 222a, b : float :math:`\in \Rset^*_+` 223x : float 224tail : bool, optional 225 By default, *tail* is *False*. 226 227Returns 228------- 229result : float 230 - If *tail* is *False*: :math:`result = \mathrm{B}^{-1}(x/\mathrm{B}(a, b); a, b)`. 231 - If *tail* is *True*: :math:`result = 1 - \mathrm{B}^{-1}(x/\mathrm{B}(a, b); b, a)`." 232 233// --------------------------------------------------------------------- 234 235%feature("docstring") OT::SpecFunc::RegularizedIncompleteBeta 236"Regularized incomplete Beta function. 237 238.. math:: 239 240 \forall (a, b) > 0 \quad 241 \mathrm{I}(x; a, b) = \frac{\mathrm{B}(x; a, b)}{\mathrm{B}(a, b)} 242 = \frac{1}{\mathrm{B}(a, b)} \int_0^x t^{a-1}(1-t)^{b-1}\di{t} 243 244with :math:`B(a, b)` the Beta function and :math:`B(x; a, b)` the incomplete 245Beta function. 246 247See also 248-------- 249SpecFunc_IncompleteBeta, SpecFunc_Beta 250 251Parameters 252---------- 253a, b : float :math:`\in \Rset^*_+` 254x : float 255tail : bool, optional 256 By default, *tail* is *False*. 257 258Returns 259------- 260result : float 261 - If *tail* is *False*: :math:`result = \mathrm{I}(x; a, b)`. 262 - If *tail* is *True*: :math:`result = 1 - \mathrm{I}(x; a, b)`." 263 264// --------------------------------------------------------------------- 265 266%feature("docstring") OT::SpecFunc::RegularizedIncompleteBetaInverse 267"Inverse of the regularized incomplete Beta function. 268 269.. math:: 270 271 \forall (a, b) > 0, \quad 272 RegularizedIncompleteBetaInverse(x; a, b) = \mathrm{I}^{-1}(x; a, b) 273 274See also 275-------- 276SpecFunc_RegularizedIncompleteBeta 277 278Parameters 279---------- 280a, b : float :math:`\in \Rset^*_+` 281x : float 282tail : bool, optional 283 By default, *tail* is *False*. 284 285Returns 286------- 287result : float 288 - If *tail* is *False*: :math:`result = \mathrm{I}^{-1}(x; a, b)`. 289 - If *tail* is *True*: :math:`result = 1 - \mathrm{I}^{-1}(x; b, a)`." 290 291// --------------------------------------------------------------------- 292 293%feature("docstring") OT::SpecFunc::Dawson 294"Dawson function. 295 296.. math:: 297 298 \forall x \in \Cset, \quad 299 \mathrm{D}_+(x) = \exp(-x^2)\int_0^x \exp(t^2)\di{t} 300 301Parameters 302---------- 303x : float or complex 304 305Returns 306------- 307result : float or complex" 308 309// --------------------------------------------------------------------- 310 311%feature("docstring") OT::SpecFunc::Debye 312"Debye function of order :math:`n`. 313 314.. math:: 315 316 \forall x \in \Rset, \forall n \in \Nset^* \text{and} \, n \leq 20, \quad 317 \mathrm{D}_n(x) = \frac{n}{x^n} \int_0^x \frac{t^n}{\exp(t)-1}\di{t} 318 319Parameters 320---------- 321x : float 322n : int :math:`\in \{1, \cdots, 20\}` 323 324Returns 325------- 326result : float" 327 328// --------------------------------------------------------------------- 329 330%feature("docstring") OT::SpecFunc::Ei 331"Exponential integral function. 332 333.. math:: 334 335 \forall z \in \Cset, \quad 336 \mathrm{Ei}(z) = -\int_{-z}^{\infty} \frac{\exp(-t)}{t}\di{t} 337 338Parameters 339---------- 340z : float or complex 341 342Returns 343------- 344result : float or complex (same as z)" 345 346// --------------------------------------------------------------------- 347 348%feature("docstring") OT::SpecFunc::Faddeeva 349"Complex Faddeeva function. 350 351.. math:: 352 353 \forall x \in \Cset, \quad 354 \mathrm{W}(x) = \exp(-x^2)\mathrm{erfc}(-ix) 355 356with :math:`ErfC` the complementary error function. 357 358See also 359-------- 360SpecFunc_ErfC 361 362Parameters 363---------- 364x : float or complex 365 366Returns 367------- 368result : complex" 369 370// --------------------------------------------------------------------- 371 372%feature("docstring") OT::SpecFunc::FaddeevaIm 373"Imaginary part of the Faddeeva function. 374 375.. math:: 376 377 \forall x \in \Rset, \quad 378 FaddeevaIm(x) = \Im (\mathrm{W}(x)) 379 380See also 381-------- 382SpecFunc_Faddeeva 383 384Parameters 385---------- 386x : float 387 388Returns 389------- 390result : float" 391 392// --------------------------------------------------------------------- 393 394%feature("docstring") OT::SpecFunc::Gamma 395"Gamma function :math:`\Gamma`. 396 397.. math:: 398 399 \forall a \in \Cset, \quad 400 \Gamma(a) = \int_0^{\infty} t^{a-1}\exp(-t)\di{t} 401 402Parameters 403---------- 404a : float or complex 405 406Returns 407------- 408result : float or complex" 409 410// --------------------------------------------------------------------- 411 412%feature("docstring") OT::SpecFunc::LogGamma 413"Logarithm of the Gamma function. 414 415.. math:: 416 417 \forall a \in \Cset, \quad 418 LogGamma(a) = \log (\Gamma(a)) 419 420See also 421-------- 422SpecFunc_Gamma 423 424Parameters 425---------- 426a : float or complex 427 428Returns 429------- 430result : float or complex" 431 432// --------------------------------------------------------------------- 433 434%feature("docstring") OT::SpecFunc::LogGamma1p 435"LogGamma1p function. 436 437.. math:: 438 439 \forall a \in \Rset, \quad 440 LogGamma1p(a) = \log (\Gamma(1+a)) 441 442with :math:`\Gamma` the Gamma function. 443 444See also 445-------- 446SpecFunc_Gamma 447 448Parameters 449---------- 450a : float 451 452Returns 453------- 454result : float" 455 456// --------------------------------------------------------------------- 457 458%feature("docstring") OT::SpecFunc::LnGamma 459"Logarithm of the Gamma function. 460 461.. math:: 462 463 \forall a \in \Rset, \quad 464 LnGamma(a) = \ln (\Gamma(a)) 465 466See also 467-------- 468SpecFunc_Gamma 469 470Parameters 471---------- 472a : float 473 474Returns 475------- 476result : float" 477 478// --------------------------------------------------------------------- 479 480%feature("docstring") OT::SpecFunc::IncompleteGamma 481"Incomplete Gamma function. 482 483.. math:: 484 485 \forall x \in \Rset, \quad 486 \gamma(a, x) = \int_0^x t^{a-1}\exp(-t)\di{t} 487 488Parameters 489---------- 490a : float :math:`\in \Rset^*_+` 491x : float 492tail : bool, optional 493 By default, *tail* is *False*. 494 495Returns 496------- 497result : float 498 - If *tail* is *False*: :math:`result = \gamma(a, x)`. 499 - If *tail* is *True*: :math:`result = \Gamma(a) - \gamma(a, x)`." 500 501// --------------------------------------------------------------------- 502 503%feature("docstring") OT::SpecFunc::IncompleteGammaInverse 504"Inverse of the incomplete Gamma function with respect to :math:`x`. 505 506.. math:: 507 508 IncompleteGammaInverse(a, x) = \gamma^{-1}(a, x) 509 510See also 511-------- 512SpecFunc_IncompleteGamma 513 514Parameters 515---------- 516a : float :math:`\in \Rset^*_+` 517x : float 518tail : bool, optional 519 By default, *tail* is *False*. 520 521Returns 522------- 523result : float 524 - If *tail* is *False*: :math:`result = \mathrm{P}^{-1}(a, x/\Gamma(a))`. 525 - If *tail* is *True*: :math:`result = \mathrm{P}^{-1}(a, (1-x)/\Gamma(a))`." 526 527// --------------------------------------------------------------------- 528 529%feature("docstring") OT::SpecFunc::RegularizedIncompleteGamma 530"Regularized incomplete Gamma function. 531 532.. math:: 533 534 \forall x \in \Rset, \quad 535 \mathrm{P}(a, x) = \frac{\gamma(a, x)}{\Gamma(a)} 536 = \frac{1}{\Gamma(a)}\int_0^x t^{a-1}\exp(-t)\di{t} 537 538See also 539-------- 540SpecFunc_Gamma, SpecFunc_IncompleteGamma 541 542Parameters 543---------- 544a : float :math:`\in \Rset^*_+` 545x : float 546tail : bool, optional 547 By default, *tail* is *False*. 548 549Returns 550------- 551result : float 552 - If *tail* is *False*: :math:`result = \mathrm{P}(a, x)`. 553 - If *tail* is *True*: :math:`result = \Gamma(a) - \mathrm{P}(a, x)`." 554 555// --------------------------------------------------------------------- 556 557%feature("docstring") OT::SpecFunc::RegularizedIncompleteGammaInverse 558"Inverse of the regularized incomplete Gamma function. 559 560.. math:: 561 562 \forall x \in \Rset, \quad 563 RegularizedIncompleteGammaInverse(a, x) = \mathrm{P}^{-1}(a, x) 564 565See also 566-------- 567SpecFunc_Gamma, SpecFunc_RegularizedIncompleteGamma 568 569Parameters 570---------- 571a : float :math:`\in \Rset^*_+` 572x : float :math:`\in [0, 1]` 573tail : bool, optional 574 By default, *tail* is *False*. 575 576Returns 577------- 578result : float 579 - If *tail* is *False*: :math:`result = \mathrm{P}^{-1}(a, x)`. 580 - If *tail* is *True*: :math:`result = \mathrm{P}^{-1}(a, 1-x)`." 581 582// --------------------------------------------------------------------- 583 584%feature("docstring") OT::SpecFunc::DiGamma 585"Digamma function. 586 587.. math:: 588 589 \Psi(x) = \frac{1}{\Gamma(x)}\frac{\mathrm{d} \Gamma(x)}{\mathrm{d}x} 590 591with :math:`\Gamma` the Gamma function. 592 593See also 594-------- 595SpecFunc_Gamma 596 597Parameters 598---------- 599x : float :math:`\in \Rset^*_+` 600 601Returns 602------- 603result : float" 604 605// --------------------------------------------------------------------- 606 607%feature("docstring") OT::SpecFunc::Psi 608"Psi function. 609 610.. math:: 611 612 \Psi(x) = \frac{1}{\Gamma(x)}\frac{\mathrm{d} \Gamma(x)}{\mathrm{d}x} 613 614with :math:`\Gamma` the Gamma function. 615 616See also 617-------- 618SpecFunc_Gamma 619 620Parameters 621---------- 622x : float :math:`\in \Rset^*_+` 623 624Returns 625------- 626result : float" 627 628// --------------------------------------------------------------------- 629 630%feature("docstring") OT::SpecFunc::DiGammaInv 631"Inverse of the DiGamma function. 632 633.. math:: 634 635 DiGammaInv(x) = \Psi^{-1} (x) 636 637See also 638-------- 639SpecFunc_DiGamma 640 641Parameters 642---------- 643x : float 644 645Returns 646------- 647result : float" 648 649// --------------------------------------------------------------------- 650 651%feature("docstring") OT::SpecFunc::TriGamma 652"TriGamma function. 653 654.. math:: 655 656 \Psi_1(x) = \frac{1}{\Gamma(x)}\frac{\mathrm{d}^2 \Gamma(x)}{\mathrm{d}x^2} 657 658with :math:`\Gamma` the Gamma function. 659 660See also 661-------- 662SpecFunc_Gamma 663 664Parameters 665---------- 666x : float :math:`\in \Rset^*_+` 667 668Returns 669------- 670result : float" 671 672// --------------------------------------------------------------------- 673 674%feature("docstring") OT::SpecFunc::IGamma1pm1 675"IGamma1pm1 function. 676 677.. math:: 678 679 \forall x \in \Rset, \quad 680 IGamma1pm1(a, x) = \int_0^x t^{a-1}\exp(-t)\di{t} 681 682Parameters 683---------- 684x : float 685 686Returns 687------- 688result : float" 689 690// --------------------------------------------------------------------- 691 692%feature("docstring") OT::SpecFunc::GammaCorrection 693"GammaCorrection function. 694 695.. math:: 696 697 \forall x \in \Rset^*_+, \quad 698 GammaCorrection(a) = \log (\Gamma(a)) - \log (\sqrt{2\Pi}) + a - (a - 0.5) \log(a) 699 700with :math:`\Gamma` the Gamma function. 701 702See also 703-------- 704SpecFunc_Gamma 705 706Parameters 707---------- 708a : float :math:`\in \Rset^*_+` 709 710Returns 711------- 712result : float" 713 714// --------------------------------------------------------------------- 715 716%feature("docstring") OT::SpecFunc::HyperGeom_1_1 717"Hypergeometric function of type (1,1). 718 719.. math:: 720 721 {}_1F_1(p_1, q_1, x) = \sum_{n=0}^{\infty} 722 \left[ 723 \prod_{k=0}^{n-1} \frac{(p_1 + k)}{(q_1 + k)} 724 \right] \frac{x^n}{n!} 725 726Parameters 727---------- 728p1, q1 : float 729x : float or complex 730 731Returns 732------- 733result : float or complex" 734 735// --------------------------------------------------------------------- 736 737%feature("docstring") OT::SpecFunc::HyperGeom_2_1 738"Hypergeometric function of type (2,1). 739 740.. math:: 741 742 {}_2F_1(p_1, p_2, q_1, x) = \sum_{n=0}^{\infty} 743 \left[ 744 \prod_{k=0}^{n-1} \frac{(p_1 + k)(p_2 + k)}{(q_1 + k)} 745 \right] \frac{x^n}{n!} 746 747Parameters 748---------- 749p1, p2, q1, x : float 750 751Returns 752------- 753result : float" 754 755// --------------------------------------------------------------------- 756 757%feature("docstring") OT::SpecFunc::HyperGeom_2_2 758"Hypergeometric function of type (2,2). 759 760.. math:: 761 762 {}_2F_2(p_1, p_2, q_1, q_2, x) = \sum_{n=0}^{\infty} 763 \left[ 764 \prod_{k=0}^{n-1} \frac{(p_1 + k)(p_2 + k)}{(q_1 + k) (q_2 + k)} 765 \right] \frac{x^n}{n!} 766 767Parameters 768---------- 769p1, p2, q1, q2, x : float 770 771Returns 772------- 773result : float" 774 775// --------------------------------------------------------------------- 776 777%feature("docstring") OT::SpecFunc::Erf 778"Error function Erf. 779 780.. math:: 781 782 \forall x \in \Cset, \quad 783 Erf(x) = \frac{2}{\sqrt{\pi}} \int_0^x \exp(-t^2)\di{t} 784 785Parameters 786---------- 787x : float or complex 788 789Returns 790------- 791result : float or complex" 792 793// --------------------------------------------------------------------- 794 795%feature("docstring") OT::SpecFunc::ErfC 796"Complementary error function ErfC. 797 798.. math:: 799 800 \forall x \in \Cset, \quad 801 ErfC(x) = 1 - Erf(x) 802 803with :math:`Erf` the error function. 804 805See also 806-------- 807SpecFunc_Erf 808 809Parameters 810---------- 811x : float or complex 812 813Returns 814------- 815result : float or complex" 816 817// --------------------------------------------------------------------- 818 819%feature("docstring") OT::SpecFunc::ErfInverse 820"Inverse of the error function Erf. 821 822.. math:: 823 824 \forall x \in \Cset, \quad 825 ErfInverse(x) = Erf^{-1} (x) 826 827See also 828-------- 829SpecFunc_Erf 830 831Parameters 832---------- 833x : float 834 835Returns 836------- 837result : float" 838 839// --------------------------------------------------------------------- 840 841%feature("docstring") OT::SpecFunc::ErfCX 842"ErfCX function. 843 844.. math:: 845 846 \forall x \in \Cset, \quad 847 ErfCX(x) = \exp(x^2).ErfC(x) 848 849with :math:`ErfC` the complementary error function. 850 851See also 852-------- 853SpecFunc_ErfC 854 855Parameters 856---------- 857x : float or complex 858 859Returns 860------- 861result : float or complex" 862 863// --------------------------------------------------------------------- 864 865%feature("docstring") OT::SpecFunc::ErfI 866"Imaginary error function ErfI. 867 868.. math:: 869 870 \forall x \in \Cset, \quad 871 ErfI(x) = -i Erf(ix) 872 873with :math:`Erf` the error function. 874 875See also 876-------- 877SpecFunc_Erf 878 879Parameters 880---------- 881x : float or complex 882 883Returns 884------- 885result : float or complex" 886 887// --------------------------------------------------------------------- 888 889%feature("docstring") OT::SpecFunc::Log1MExp 890"Log1MExp function. 891 892.. math:: 893 894 \forall x \in \Rset^+, \quad 895 Log1MExp(x) = \log (1-\exp(-x)) 896 897Parameters 898---------- 899x : float :math:`\in \Rset^*_+` 900 901Returns 902------- 903result : complex" 904 905// --------------------------------------------------------------------- 906 907%feature("docstring") OT::SpecFunc::Expm1 908"Expm1 function. 909 910.. math:: 911 912 \forall x \in \Cset, \quad 913 Expm1(x) = \exp(x)-1 914 915Parameters 916---------- 917x : float or complex 918 919Returns 920------- 921result : complex" 922 923// --------------------------------------------------------------------- 924 925%feature("docstring") OT::SpecFunc::Log1p 926"Log1p function. 927 928.. math:: 929 930 \forall x \in \Cset, \quad 931 Log1p(x) = \log (1+x) 932 933Parameters 934---------- 935x : float or complex 936 937Returns 938------- 939result : complex" 940 941// --------------------------------------------------------------------- 942 943%feature("docstring") OT::SpecFunc::DiLog 944"Dilogarithm function. 945 946.. math:: 947 948 \forall x \in ]-\infty, 1[, \quad 949 Li_2(x) = -\int_0^x \frac{\log (1-t)}{t}\di{t} 950 951Parameters 952---------- 953x : float :math:`\in ]-\infty, 1[` 954 955Returns 956------- 957result : float" 958 959// --------------------------------------------------------------------- 960 961%feature("docstring") OT::SpecFunc::IPow 962"Raise the given :math:`x` to the integral power :math:`n`. 963 964.. math:: 965 966 IPow(x, n) = x^n 967 968Parameters 969---------- 970n : int 971x : float 972 973Returns 974------- 975result : foat 976 977Examples 978-------- 979>>> import openturns as ot 980>>> ot.SpecFunc.IPow(-2.5, 3) 981-15.625" 982 983// --------------------------------------------------------------------- 984 985%feature("docstring") OT::SpecFunc::IRoot 986"Extract the :math:`n` integral root of the given :math:`x`. 987 988.. math:: 989 990 IRoot(x, n) = \sqrt[n]{x} 991 992Parameters 993---------- 994n : int 995x : float 996 997Returns 998------- 999result : foat 1000 1001Examples 1002-------- 1003>>> import openturns as ot 1004>>> ot.SpecFunc.IRoot(-15.625, 3) 1005-2.5" 1006 1007// --------------------------------------------------------------------- 1008 1009%feature("docstring") OT::SpecFunc::NextPowerOfTwo 1010"Smallest power of two greater or equal to the given :math:`n`. 1011 1012.. math:: 1013 1014 NextPowerOfTwo(n) = 2^{\lceil \log_2(n)\rceil} 1015 1016Parameters 1017---------- 1018n : positive int 1019 1020Returns 1021------- 1022result : positive int 1023 1024Examples 1025-------- 1026>>> import openturns as ot 1027>>> int(ot.SpecFunc.NextPowerOfTwo(42)) 102864" 1029 1030// --------------------------------------------------------------------- 1031 1032%feature("docstring") OT::SpecFunc::Log2 1033"Integer base 2 logarithm of :math:`n`. 1034 1035.. math:: 1036 1037 Log2(n) = \log_2(n) 1038 1039Parameters 1040---------- 1041n : positive int 1042 1043Returns 1044------- 1045result : positive int 1046 1047Examples 1048-------- 1049>>> import openturns as ot 1050>>> int(ot.SpecFunc.Log2(42)) 10515" 1052 1053// --------------------------------------------------------------------- 1054 1055%feature("docstring") OT::SpecFunc::BitCount 1056"Compute the number of bits set to 1 in an integer. 1057 1058Parameters 1059---------- 1060n : positive int 1061 1062Returns 1063------- 1064result : positive int 1065 1066Examples 1067-------- 1068>>> import openturns as ot 1069>>> int(ot.SpecFunc.BitCount(42)) 10703" 1071 1072// --------------------------------------------------------------------- 1073 1074%feature("docstring") OT::SpecFunc::LambertW 1075"Lambert W function. 1076 1077The Lambert W function :math:`\mathrm{W}(x)` is defined by the relation: 1078 1079.. math:: 1080 1081 x = \mathrm{W}(x) \exp(\mathrm{W}(x)) 1082 1083Parameters 1084---------- 1085x : float 1086principal : bool, optional 1087 By default, *principal* is *True*. 1088 1089Returns 1090------- 1091result : float 1092 - If *principal* is *True* : :math:`result = \mathrm{W}_0(x)`. 1093 :math:`\mathrm{W}_0(x)` is referred to as the principal branch of the Lambert W 1094 function. It denotes the upper part of the function whose domain is 1095 :math:`[-1/e, +\infty[` and range :math:`[-1, +\infty[`. 1096 - If *principal* is *False* : :math:`result = \mathrm{W}_{-1}(x)`. 1097 :math:`\mathrm{W}_{-1}(x)` is the second real branch of the Lambert W function. 1098 It denotes the lower part of the function whose domain is 1099 :math:`[-1/e, 0[` and range :math:`]-\infty, -1]`." 1100 1101// --------------------------------------------------------------------- 1102 1103%feature("docstring") OT::SpecFunc::Cbrt 1104"Cubit root function. 1105 1106Parameters 1107---------- 1108x : float 1109 1110Returns 1111------- 1112result : float" 1113 1114// --------------------------------------------------------------------- 1115 1116%feature("docstring") OT::SpecFunc::BinomialCoefficient 1117"Binomial coefficient. 1118 1119Returns the value :math:`C_k^n = \binom{n}{k}` 1120 1121Parameters 1122---------- 1123n : int 1124k : int 1125 1126Returns 1127------- 1128result : int" 1129 1130// --------------------------------------------------------------------- 1131 1132%feature("docstring") OT::SpecFunc::IsNormal 1133"Check for non-NaN and non-Inf values. 1134 1135Parameters 1136---------- 1137v : float 1138 1139Returns 1140------- 1141result : bool" 1142 1143// --------------------------------------------------------------------- 1144 1145%feature("docstring") OT::SpecFunc::LogFactorial 1146"Logarithm of the factorial function. 1147 1148.. math:: 1149 1150 \forall n \in \Nset, \quad 1151 LogFactorial(n) = \log(n!) 1152 1153See also 1154-------- 1155SpecFunc_Stirlerr 1156 1157Parameters 1158---------- 1159n : int 1160 1161Returns 1162------- 1163result : float" 1164 1165// --------------------------------------------------------------------- 1166 1167%feature("docstring") OT::SpecFunc::Stirlerr 1168"Error of the Stirling approximation of the factorial logarithm. 1169 1170.. math:: 1171 1172 \forall n \in \Nset, \quad 1173 Stirlerr(n) = \log(n!) - \log\left(sqrt{2\pi n}\left(\dfrac{n}{e}\right)^n\right) 1174 1175See also 1176-------- 1177SpecFunc_LogFactorial 1178 1179Parameters 1180---------- 1181n : int 1182 1183Returns 1184------- 1185result : float" 1186 1187// --------------------------------------------------------------------- 1188 1189%feature("docstring") OT::SpecFunc::IsBoostAvailable 1190"Check for Boost availability. 1191 1192Returns 1193------- 1194result : bool" 1195 1196// --------------------------------------------------------------------- 1197 1198%feature("docstring") OT::SpecFunc::IsMPFRAvailable 1199"Check for MPFR availability. 1200 1201Returns 1202------- 1203result : bool" 1204 1205// --------------------------------------------------------------------- 1206 1207%feature("docstring") OT::SpecFunc::IsMPCAvailable 1208"Check for MPC availability. 1209 1210Returns 1211------- 1212result : bool" 1213 1214