SUBROUTINE DVI0 (M, X, F, WORK, IWORK, INFO) C***BEGIN PROLOGUE DVI0 C***PURPOSE Computes the hyperbolic Bessel function of the first kind C of order zero (I0) for a vector of real arguments C***LIBRARY VFNLIB C***CATEGORY C10B1 C***TYPE DOUBLE PRECISION (VI0-S, DVI0-D) C***KEYWORDS BESSEL FUNCTION,FIRST KIND,HYPERBOLIC BESSEL FUNCTION, C MODIFIED BESSEL FUNCTION, ORDER ZERO, VECTORIZED C***AUTHOR SAUNDERS, B. V., (NIST) C COMPUTING AND APPLIED MATHEMATICS LABORATORY C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY C GAITHERSBURG, MD 20899 C BOISVERT, R. F., (NIST) C COMPUTING AND APPLIED MATHEMATICS LABORATORY C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY C GAITHERSBURG, MD 20899 C***DESCRIPTION C C DVI0 computes the modified (hyperbolic) Bessel function of the C first kind of order zero (I0) for real arguments using uniform C approximation by Chebyshev polynomials. C C C P A R A M E T E R S C C M (Input) Integer (M .GT. 0) C The number of arguments at which the function is to be C evaluated. C C X (Input) Double precision array of length M C The arguments at which the function is to be evaluated are C stored in X(1) to X(M) in any order. C C F (Output) Double precision array of length M C F(i) contains the value of the function at X(i), i=1,..,M. C C WORK (Work) Double precision vector of length 7*M C C IWORK (Work) Integer vector of length M C C INFO (Output) Integer C Indicates status of computed result. The following table C lists possible values and their meanings. If OK=Yes then C all F(i) have been set, otherwise none have been set. C C INFO OK Description C ------------------------------------------------------------ C 0 Yes Successfull execution. C 1 No Error: M .LE. 0 C 2 No Error: Some abs(X(i)) so big I0 overflows. C The index of the first offending argument is C returned in IWORK(1). C C C ********************************************************************* C This routine is a modification of the function DBESI0 developed by C W. Fullerton of LANL. C ********************************************************************* C C***REFERENCES Ronald F. Boisvert and Bonita V. Saunders, Portable C Vectorized Software for Bessel Function Evaluation, C ACM Transactions on Mathematical Software 18 (1992), C pp 456-469. C***ROUTINES CALLED DWI0 C***REVISION HISTORY (YYMMDD) C 910226 DATE WRITTEN C 930203 Minor modifications to prologue. C***END PROLOGUE DVI0 C C ---------- C PARAMETERS C ---------- C INTEGER INFO, IWORK, M DOUBLE PRECISION F, X, WORK C DIMENSION X(M), F(M), WORK(7*M), IWORK(M) C C --------------- C LOCAL VARIABLES C --------------- C INTEGER IWB0, IWB1, IWB2, IWY, IWTC, IWYC, IWZC, JIN C C***FIRST EXECUTABLE STATEMENT DVI0 C C ... PARTITION WORK ARRAYS C IWY = 1 IWTC = IWY + M IWYC = IWTC + M IWZC = IWYC + M IWB0 = IWZC + M IWB1 = IWB0 + M IWB2 = IWB1 + M C Total = IWB2 + M C JIN = 1 C Total = JIN + M C C ... DWI0 DOES ALL THE WORK C CALL DWI0(M,X,F,WORK(IWY),WORK(IWTC),WORK(IWYC),WORK(IWZC), + IWORK(JIN),WORK(IWB0),WORK(IWB1),WORK(IWB2),INFO) C RETURN END SUBROUTINE DWI0 (M, X, F, Y, TCMP, YCMP, ZCMP, INDX, B0, B1, B2, + INFO) C***BEGIN PROLOGUE DWI0 C***SUBSIDIARY C***PURPOSE Computes the hyperbolic Bessel function of the first kind C of order zero (I0) for a vector of arguments C***LIBRARY VFNLIB C***AUTHOR SAUNDERS, B. V., (NIST) C COMPUTING AND APPLIED MATHEMATICS LABORATORY C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY C GAITHERSBURG, MD 20899 C BOISVERT, R. F., (NIST) C COMPUTING AND APPLIED MATHEMATICS LABORATORY C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY C GAITHERSBURG, MD 20899 C***ROUTINES CALLED IDWCS, D1MACH, DWNGT, DWGTHR, DWGTLE, DWGT, DWLE, C DWSCTR, DWCS C***REVISION HISTORY (YYMMDD) C 910226 DATE WRITTEN C***END PROLOGUE DWI0 C C ---------- C PARAMETERS C ---------- C INTEGER INFO, INDX, M DOUBLE PRECISION B0, B1, B2, F, X, Y, TCMP, YCMP, ZCMP C DIMENSION B0(M), B1(M), B2(M), F(M), INDX(M), X(M), Y(M), + TCMP(M), YCMP(M), ZCMP(M) C C --------------- C LOCAL VARIABLES C --------------- C INTEGER LAI0, LAI02, LBI0 PARAMETER ( LAI0=46, LAI02=69, LBI0=18 ) C INTEGER I, IDWCS, J, KEY, N, NTI0, NTAI0, NTAI02 DOUBLE PRECISION AI0CS, AI02CS, BI0CS, EPMACH, EPS, D1MACH, XSML, + XMAX C DIMENSION AI0CS(LAI0), AI02CS(LAI02), BI0CS(LBI0) C SAVE AI0CS, AI02CS, BI0CS, N, NTAI0, NTAI02, NTI0, XSML, XMAX C C---------------------------------------------------------------------- C C Series for BI0 on the interval 0. to 9.00000D+00 C with weighted error 9.51E-34 C log weighted error 33.02 C significant figures required 33.31 C decimal places required 33.65 C DATA BI0 CS( 1) / -.7660547252 8391449510 8189497624 3285 D-1 / DATA BI0 CS( 2) / +.1927337953 9938082699 5240875088 1196 D+1 / DATA BI0 CS( 3) / +.2282644586 9203013389 3702929233 0415 D+0 / DATA BI0 CS( 4) / +.1304891466 7072904280 7933421069 1888 D-1 / DATA BI0 CS( 5) / +.4344270900 8164874513 7868268102 6107 D-3 / DATA BI0 CS( 6) / +.9422657686 0019346639 2317174411 8766 D-5 / DATA BI0 CS( 7) / +.1434006289 5106910799 6209187817 9957 D-6 / DATA BI0 CS( 8) / +.1613849069 6617490699 1541971999 4611 D-8 / DATA BI0 CS( 9) / +.1396650044 5356696994 9509270814 2522 D-10 / DATA BI0 CS( 10) / +.9579451725 5054453446 2752317189 3333 D-13 / DATA BI0 CS( 11) / +.5333981859 8625021310 1510774400 0000 D-15 / DATA BI0 CS( 12) / +.2458716088 4374707746 9678591999 9999 D-17 / DATA BI0 CS( 13) / +.9535680890 2487700269 4434133333 3333 D-20 / DATA BI0 CS( 14) / +.3154382039 7214273367 8933333333 3333 D-22 / DATA BI0 CS( 15) / +.9004564101 0946374314 6666666666 6666 D-25 / DATA BI0 CS( 16) / +.2240647369 1236700160 0000000000 0000 D-27 / DATA BI0 CS( 17) / +.4903034603 2428373333 3333333333 3333 D-30 / DATA BI0 CS( 18) / +.9508172606 1226666666 6666666666 6666 D-33 / C C------------------------------------------------------------------- C C Series for AI0 on the interval 1.25000D-01 to 3.33333D-01 C with weighted error 2.74E-32 C log weighted error 31.56 C significant figures required 30.15 C decimal places required 32.39 C DATA AI0 CS( 1) / +.7575994494 0237959427 2987203743 8 D-1 / DATA AI0 CS( 2) / +.7591380810 8233455072 9297873320 4 D-2 / DATA AI0 CS( 3) / +.4153131338 9237505018 6319749138 2 D-3 / DATA AI0 CS( 4) / +.1070076463 4390730735 8242970217 0 D-4 / DATA AI0 CS( 5) / -.7901179979 2128946607 5031948573 0 D-5 / DATA AI0 CS( 6) / -.7826143501 4387522697 8898980690 9 D-6 / DATA AI0 CS( 7) / +.2783849942 9488708063 8118538985 7 D-6 / DATA AI0 CS( 8) / +.8252472600 6120271919 6682913319 8 D-8 / DATA AI0 CS( 9) / -.1204463945 5201991790 5496089110 3 D-7 / DATA AI0 CS( 10) / +.1559648598 5060764436 1228752792 8 D-8 / DATA AI0 CS( 11) / +.2292556367 1033165434 7725480285 7 D-9 / DATA AI0 CS( 12) / -.1191622884 2790646036 7777423447 8 D-9 / DATA AI0 CS( 13) / +.1757854916 0324098302 1833124774 3 D-10 / DATA AI0 CS( 14) / +.1128224463 2189005171 4441135682 4 D-11 / DATA AI0 CS( 15) / -.1146848625 9272988777 2963387698 2 D-11 / DATA AI0 CS( 16) / +.2715592054 8036628726 4365192160 6 D-12 / DATA AI0 CS( 17) / -.2415874666 5626878384 4247572028 1 D-13 / DATA AI0 CS( 18) / -.6084469888 2551250646 0609963922 4 D-14 / DATA AI0 CS( 19) / +.3145705077 1754772937 0836026730 3 D-14 / DATA AI0 CS( 20) / -.7172212924 8711877179 6217505917 6 D-15 / DATA AI0 CS( 21) / +.7874493403 4541033960 8390960332 7 D-16 / DATA AI0 CS( 22) / +.1004802753 0094624023 4524457183 9 D-16 / DATA AI0 CS( 23) / -.7566895365 3505348534 2843588881 0 D-17 / DATA AI0 CS( 24) / +.2150380106 8761198878 1205128784 5 D-17 / DATA AI0 CS( 25) / -.3754858341 8308744291 5158445260 8 D-18 / DATA AI0 CS( 26) / +.2354065842 2269925769 0075710532 2 D-19 / DATA AI0 CS( 27) / +.1114667612 0479285302 2637335511 0 D-19 / DATA AI0 CS( 28) / -.5398891884 3969903786 9677932270 9 D-20 / DATA AI0 CS( 29) / +.1439598792 2407526770 4285840452 2 D-20 / DATA AI0 CS( 30) / -.2591916360 1110934064 6081840196 2 D-21 / DATA AI0 CS( 31) / +.2238133183 9985839074 3409229824 0 D-22 / DATA AI0 CS( 32) / +.5250672575 3647711727 7221683199 9 D-23 / DATA AI0 CS( 33) / -.3249904138 5332307841 7343228586 6 D-23 / DATA AI0 CS( 34) / +.9924214103 2050379278 5728471040 0 D-24 / DATA AI0 CS( 35) / -.2164992254 2446695231 4655429973 3 D-24 / DATA AI0 CS( 36) / +.3233609471 9435940839 7333299199 9 D-25 / DATA AI0 CS( 37) / -.1184620207 3967424898 2473386666 6 D-26 / DATA AI0 CS( 38) / -.1281671853 9504986505 4833868799 9 D-26 / DATA AI0 CS( 39) / +.5827015182 2793905116 0556885333 3 D-27 / DATA AI0 CS( 40) / -.1668222326 0261097193 6450150399 9 D-27 / DATA AI0 CS( 41) / +.3625309510 5415699757 0068480000 0 D-28 / DATA AI0 CS( 42) / -.5733627999 0557135899 4595839999 9 D-29 / DATA AI0 CS( 43) / +.3736796722 0630982296 4258133333 3 D-30 / DATA AI0 CS( 44) / +.1602073983 1568519633 6551253333 3 D-30 / DATA AI0 CS( 45) / -.8700424864 0572298845 2249599999 9 D-31 / DATA AI0 CS( 46) / +.2741320937 9374811456 0341333333 3 D-31 / C C------------------------------------------------------------------- C C Series for AI02 on the interval 0. to 1.25000D-01 C with weighted error 1.97E-32 C log weighted error 31.71 C significant figures required 30.15 C decimal places required 32.63 C DATA AI02CS( 1) / +.5449041101 4108831607 8960962268 0 D-1 / DATA AI02CS( 2) / +.3369116478 2556940898 9785662979 9 D-2 / DATA AI02CS( 3) / +.6889758346 9168239842 6263914301 1 D-4 / DATA AI02CS( 4) / +.2891370520 8347564829 6692402323 2 D-5 / DATA AI02CS( 5) / +.2048918589 4690637418 2760534093 1 D-6 / DATA AI02CS( 6) / +.2266668990 4981780645 9327743136 1 D-7 / DATA AI02CS( 7) / +.3396232025 7083863451 5084396952 3 D-8 / DATA AI02CS( 8) / +.4940602388 2249695891 0482449783 5 D-9 / DATA AI02CS( 9) / +.1188914710 7846438342 4084525196 3 D-10 / DATA AI02CS( 10) / -.3149916527 9632413645 3864862961 9 D-10 / DATA AI02CS( 11) / -.1321581184 0447713118 7540739926 7 D-10 / DATA AI02CS( 12) / -.1794178531 5068061177 7943574026 9 D-11 / DATA AI02CS( 13) / +.7180124451 3836662336 7106429346 9 D-12 / DATA AI02CS( 14) / +.3852778382 7421427011 4089801777 6 D-12 / DATA AI02CS( 15) / +.1540086217 5214098269 1325823339 7 D-13 / DATA AI02CS( 16) / -.4150569347 2872220866 2689972015 6 D-13 / DATA AI02CS( 17) / -.9554846698 8283076487 0214494312 5 D-14 / DATA AI02CS( 18) / +.3811680669 3526224207 4605535511 8 D-14 / DATA AI02CS( 19) / +.1772560133 0565263836 0493266675 8 D-14 / DATA AI02CS( 20) / -.3425485619 6772191346 1924790328 2 D-15 / DATA AI02CS( 21) / -.2827623980 5165834849 4205593759 4 D-15 / DATA AI02CS( 22) / +.3461222867 6974610930 9706250813 4 D-16 / DATA AI02CS( 23) / +.4465621420 2967599990 1042054284 3 D-16 / DATA AI02CS( 24) / -.4830504485 9441820712 5525403795 4 D-17 / DATA AI02CS( 25) / -.7233180487 8747539545 6227240924 5 D-17 / DATA AI02CS( 26) / +.9921475412 1736985988 8046093981 0 D-18 / DATA AI02CS( 27) / +.1193650890 8459820855 0439949924 2 D-17 / DATA AI02CS( 28) / -.2488709837 1508072357 2054491660 2 D-18 / DATA AI02CS( 29) / -.1938426454 1609059289 8469781132 6 D-18 / DATA AI02CS( 30) / +.6444656697 3734438687 8301949394 9 D-19 / DATA AI02CS( 31) / +.2886051596 2892243264 8171383073 4 D-19 / DATA AI02CS( 32) / -.1601954907 1749718070 6167156200 7 D-19 / DATA AI02CS( 33) / -.3270815010 5923147208 9193567485 9 D-20 / DATA AI02CS( 34) / +.3686932283 8264091811 4600723939 3 D-20 / DATA AI02CS( 35) / +.1268297648 0309501530 1359529710 9 D-22 / DATA AI02CS( 36) / -.7549825019 3772739076 9636664410 1 D-21 / DATA AI02CS( 37) / +.1502133571 3778353496 3712789053 4 D-21 / DATA AI02CS( 38) / +.1265195883 5096485349 3208799248 3 D-21 / DATA AI02CS( 39) / -.6100998370 0836807086 2940891600 2 D-22 / DATA AI02CS( 40) / -.1268809629 2601282643 6872095924 2 D-22 / DATA AI02CS( 41) / +.1661016099 8907414578 4038487490 5 D-22 / DATA AI02CS( 42) / -.1585194335 7658855793 7970504881 4 D-23 / DATA AI02CS( 43) / -.3302645405 9682178009 5381766755 6 D-23 / DATA AI02CS( 44) / +.1313580902 8392397817 4039623117 4 D-23 / DATA AI02CS( 45) / +.3689040246 6711567933 1425637280 4 D-24 / DATA AI02CS( 46) / -.4210141910 4616891492 1978247249 9 D-24 / DATA AI02CS( 47) / +.4791954591 0828657806 3171401373 0 D-25 / DATA AI02CS( 48) / +.8459470390 2218217952 9971707412 4 D-25 / DATA AI02CS( 49) / -.4039800940 8728324931 4607937181 0 D-25 / DATA AI02CS( 50) / -.6434714653 6504313473 0100850469 5 D-26 / DATA AI02CS( 51) / +.1225743398 8756659903 4464736990 5 D-25 / DATA AI02CS( 52) / -.2934391316 0257089231 9879821175 4 D-26 / DATA AI02CS( 53) / -.1961311309 1949829262 0371205728 9 D-26 / DATA AI02CS( 54) / +.1503520374 8221934241 6229900309 8 D-26 / DATA AI02CS( 55) / -.9588720515 7448265520 3386388206 9 D-28 / DATA AI02CS( 56) / -.3483339380 8170454863 9441108511 4 D-27 / DATA AI02CS( 57) / +.1690903610 2630436730 6244960725 6 D-27 / DATA AI02CS( 58) / +.1982866538 7356030438 9400115718 8 D-28 / DATA AI02CS( 59) / -.5317498081 4918162145 7583002528 4 D-28 / DATA AI02CS( 60) / +.1803306629 8883929462 3501450390 1 D-28 / DATA AI02CS( 61) / +.6213093341 4548931758 8405311242 2 D-29 / DATA AI02CS( 62) / -.7692189292 7721618632 0072806673 0 D-29 / DATA AI02CS( 63) / +.1858252826 1117025426 2556016596 3 D-29 / DATA AI02CS( 64) / +.1237585142 2813957248 9927154554 1 D-29 / DATA AI02CS( 65) / -.1102259120 4092238032 1779478779 2 D-29 / DATA AI02CS( 66) / +.1886287118 0397044900 7787447943 1 D-30 / DATA AI02CS( 67) / +.2160196872 2436589131 4903141406 0 D-30 / DATA AI02CS( 68) / -.1605454124 9197432005 8446594965 5 D-30 / DATA AI02CS( 69) / +.1965352984 5942906039 3884807331 8 D-31 / C C------------------------------------------------------------------- C DATA NTI0 / 0 / C C***FIRST EXECUTABLE STATEMENT DWI0 C IF (M .LE. 0) GO TO 910 C IF (NTI0.EQ.0) THEN EPMACH = D1MACH(3) EPS = 0.10D0*EPMACH NTI0 = IDWCS(BI0CS, LBI0, EPS) NTAI0 = IDWCS(AI0CS, LAI0, EPS) NTAI02 = IDWCS(AI02CS, LAI02, EPS) XSML = SQRT(4.0D0*EPMACH) XMAX = LOG(D1MACH(2)) ENDIF C DO 10 I=1,M Y(I) = ABS(X(I)) 10 CONTINUE C CALL DWNGT(M,Y,XMAX,KEY) IF (KEY .NE. 0) GO TO 920 C C ---------------- C CASE Y .LE. XSML C ---------------- C DO 15 I=1,M F(I) = 1.0D0 15 CONTINUE C C -------------------------- C CASE XSML .LT. Y .LE. 3.0 C -------------------------- C CALL DWGTLE(M,Y,XSML,3.0D0,N,INDX) IF (N .GT. 0) THEN CALL DWGTHR(N,Y,INDX,YCMP) DO 20 J=1,N TCMP(J) = YCMP(J)**2/4.50D0 - 1.0D0 20 CONTINUE CALL DWCS(N,TCMP,BI0CS,NTI0,ZCMP,B0,B1,B2) DO 30 J=1,N ZCMP(J) = 2.750D0 + ZCMP(J) 30 CONTINUE CALL DWSCTR(N,ZCMP,INDX,F) ENDIF C C ------------------------- C CASE 3.0 .LT. Y .LE. 8.0 C ------------------------- C CALL DWGTLE(M,Y,3.0D0,8.0D0,N,INDX) IF (N .GT. 0) THEN CALL DWGTHR(N,Y,INDX,YCMP) DO 50 J=1,N TCMP(J) = (48.0D0/YCMP(J) - 11.0D0)/5.0D0 50 CONTINUE CALL DWCS(N,TCMP,AI0CS,NTAI0,ZCMP,B0,B1,B2) DO 60 J=1,N ZCMP(J) = EXP(YCMP(J))*(0.3750D0+ZCMP(J))/SQRT(YCMP(J)) 60 CONTINUE CALL DWSCTR(N,ZCMP,INDX,F) ENDIF C C ---------------- C CASE Y .GT. 8.0 C ---------------- C CALL DWGT(M,Y,8.0D0,N,INDX) IF (N .GT. 0) THEN CALL DWGTHR(N,Y,INDX,YCMP) DO 80 J=1,N TCMP(J) = 16.0D0/YCMP(J) - 1.0D0 80 CONTINUE CALL DWCS(N,TCMP,AI02CS,NTAI02,ZCMP,B0,B1,B2) DO 90 J=1,N ZCMP(J) = EXP(YCMP(J))*(0.3750D0+ZCMP(J))/SQRT(YCMP(J)) 90 CONTINUE CALL DWSCTR(N,ZCMP,INDX,F) ENDIF C C ----- C EXITS C ----- C C ... NORMAL C INFO = 0 GO TO 999 C C ... M .LE. 0 C 910 CONTINUE INFO = 1 GO TO 999 C C ... ABS(X) SO LARGE I0 OVERFLOWS C 920 CONTINUE INFO = 2 INDX(1) = KEY GO TO 999 C 999 CONTINUE RETURN END