From 9d8a0c1d45c07a3d6f1c4972ac6af43bc290ca0a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Thu, 12 Mar 2020 21:09:20 +0200 Subject: [PATCH] Replace Amos with zbessel (shared version) zbessel as shared library can be found e.g. here: https://github.com/texnokrates/zbessel Former-commit-id: 3cc66da970731e37a242459f8af3d4b68f362c75 --- CMakeLists.txt | 6 +- amos/CMakeLists.txt | 18 - amos/README.md | 31 -- amos/amos.h | 42 -- amos/d1mach.f | 209 ---------- amos/dgamln.f | 189 --------- amos/i1mach.f | 291 ------------- amos/xerror.f | 22 - amos/zabs.f | 29 -- amos/zacai.f | 99 ----- amos/zacon.f | 203 --------- amos/zairy.f | 393 ------------------ amos/zasyi.f | 165 -------- amos/zbesh.f | 348 ---------------- amos/zbesi.f | 269 ------------ amos/zbesj.f | 266 ------------ amos/zbesk.f | 281 ------------- amos/zbesy.f | 244 ----------- amos/zbinu.f | 110 ----- amos/zbiry.f | 364 ---------------- amos/zbknu.f | 568 ------------------------- amos/zbuni.f | 174 -------- amos/zbunk.f | 35 -- amos/zdiv.f | 19 - amos/zexp.f | 16 - amos/zkscl.f | 121 ------ amos/zlog.f | 41 -- amos/zmlri.f | 204 --------- amos/zmlt.f | 15 - amos/zrati.f | 132 ------ amos/zs1s2.f | 49 --- amos/zseri.f | 190 --------- amos/zshch.f | 22 - amos/zsqrt.f | 44 -- amos/zuchk.f | 28 -- amos/zunhj.f | 714 -------------------------------- amos/zuni1.f | 204 --------- amos/zuni2.f | 267 ------------ amos/zunik.f | 211 ---------- amos/zunk1.f | 426 ------------------- amos/zunk2.f | 505 ---------------------- amos/zuoik.f | 194 --------- amos/zwrsk.f | 94 ----- cmake-scripts/FindZBESSEL.cmake | 17 + qpms/CMakeLists.txt | 3 +- qpms/bessel.c | 20 +- 46 files changed, 30 insertions(+), 7862 deletions(-) delete mode 100644 amos/CMakeLists.txt delete mode 100644 amos/README.md delete mode 100644 amos/amos.h delete mode 100644 amos/d1mach.f delete mode 100644 amos/dgamln.f delete mode 100644 amos/i1mach.f delete mode 100644 amos/xerror.f delete mode 100644 amos/zabs.f delete mode 100644 amos/zacai.f delete mode 100644 amos/zacon.f delete mode 100644 amos/zairy.f delete mode 100644 amos/zasyi.f delete mode 100644 amos/zbesh.f delete mode 100644 amos/zbesi.f delete mode 100644 amos/zbesj.f delete mode 100644 amos/zbesk.f delete mode 100644 amos/zbesy.f delete mode 100644 amos/zbinu.f delete mode 100644 amos/zbiry.f delete mode 100644 amos/zbknu.f delete mode 100644 amos/zbuni.f delete mode 100644 amos/zbunk.f delete mode 100644 amos/zdiv.f delete mode 100644 amos/zexp.f delete mode 100644 amos/zkscl.f delete mode 100644 amos/zlog.f delete mode 100644 amos/zmlri.f delete mode 100644 amos/zmlt.f delete mode 100644 amos/zrati.f delete mode 100644 amos/zs1s2.f delete mode 100644 amos/zseri.f delete mode 100644 amos/zshch.f delete mode 100644 amos/zsqrt.f delete mode 100644 amos/zuchk.f delete mode 100644 amos/zunhj.f delete mode 100644 amos/zuni1.f delete mode 100644 amos/zuni2.f delete mode 100644 amos/zunik.f delete mode 100644 amos/zunk1.f delete mode 100644 amos/zunk2.f delete mode 100644 amos/zuoik.f delete mode 100644 amos/zwrsk.f create mode 100644 cmake-scripts/FindZBESSEL.cmake diff --git a/CMakeLists.txt b/CMakeLists.txt index 84410d3..2cfb492 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -1,5 +1,5 @@ cmake_minimum_required(VERSION 3.0.2) -include(CMakeAddFortranSubdirectory) +set (CMAKE_MODULE_PATH "${CMAKE_MODULE_PATH};${CMAKE_CURRENT_SOURCE_DIR}/cmake-scripts") include(version.cmake) include(GNUInstallDirs) @@ -22,10 +22,6 @@ set(CMAKE_POSITION_INDEPENDENT_CODE ON) set (QPMS_VERSION_MAJOR 0) #set (QPMS_VERSION_MINOR 3) -cmake_add_fortran_subdirectory (amos - PROJECT amos - LIBRARIES amos - NO_EXTERNAL_INSTALL) add_subdirectory (qpms) diff --git a/amos/CMakeLists.txt b/amos/CMakeLists.txt deleted file mode 100644 index 73d9107..0000000 --- a/amos/CMakeLists.txt +++ /dev/null @@ -1,18 +0,0 @@ -enable_language (Fortran) -include(FortranCInterface) - -FortranCInterface_HEADER(amos_mangling.h - MACRO_NAMESPACE "AMOS_" - SYMBOL_NAMESPACE "amos_" - SYMBOLS zbesj zbesy zbesh zbesi zbesk zsqrt - ) - -add_library(amos - dgamln.f zabs.f zasyi.f zbinu.f zdiv.f zmlri.f zshch.f zunhj.f zunk1.f - d1mach.f zacai.f zbesh.f zbknu.f zexp.f zmlt.f zsqrt.f zunik.f zunk2.f - i1mach.f zacon.f zbesj.f zbuni.f zkscl.f zrati.f zs1s2.f zuni1.f zuoik.f - xerror.f zairy.f zbesy.f zbunk.f zlog.f zseri.f zuchk.f zuni2.f zwrsk.f - ) - -target_include_directories (amos PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}) - diff --git a/amos/README.md b/amos/README.md deleted file mode 100644 index 95d7029..0000000 --- a/amos/README.md +++ /dev/null @@ -1,31 +0,0 @@ -# AMOS - -A Portable Package for Bessel Functions of a Complex Argument -and Nonnegative Order - -This algorithm is a package of subroutines for computing Bessel -functions and Airy functions. The routines are updated -versions of those routines found in TOMS algorithm 644. - -## Disclaimer - -``` -* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * -* ISSUED BY SANDIA LABORATORIES, -* A PRIME CONTRACTOR TO THE -* UNITED STATES DEPARTMENT OF ENERGY -* * * * * * * * * * * * * * NOTICE * * * * * * * * * * * * * * * -* THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY THE -* UNITED STATES GOVERNMENT. NEITHER THE UNITED STATES NOR THE -* UNITED STATES DEPARTMENT OF ENERGY, NOR ANY OF THEIR -* EMPLOYEES, NOR ANY OF THEIR CONTRACTORS, SUBCONTRACTORS, OR THEIR -* EMPLOYEES, MAKES ANY WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY -* LEGAL LIABILITY OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS -* OR USEFULNESS OF ANY INFORMATION, APPARATUS, PRODUCT OR PROCESS -* DISCLOSED, OR REPRESENTS THAT ITS USE WOULD NOT INFRINGE -* PRIVATELY OWNED RIGHTS. -* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * -* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * -* THIS CODE HAS BEEN APPROVED FOR UNLIMITED RELEASE. -* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * -``` diff --git a/amos/amos.h b/amos/amos.h deleted file mode 100644 index 854a28f..0000000 --- a/amos/amos.h +++ /dev/null @@ -1,42 +0,0 @@ -#ifndef AMOS_H -#define AMOS_H -#include "amos_mangling.h" - -#define INTEGER_t int -#define DOUBLE_PRECISION_t double - -void amos_zbesj(const DOUBLE_PRECISION_t *zr, - const DOUBLE_PRECISION_t *zi, - const DOUBLE_PRECISION_t *fnu, - const INTEGER_t *kode, - const INTEGER_t *n, - DOUBLE_PRECISION_t *cyr, - DOUBLE_PRECISION_t *cyi, - INTEGER_t *nz, - INTEGER_t *ierr); - -void amos_zbesy(const DOUBLE_PRECISION_t *zr, - const DOUBLE_PRECISION_t *zi, - const DOUBLE_PRECISION_t *fnu, - const INTEGER_t *kode, - const INTEGER_t *n, - DOUBLE_PRECISION_t *cyr, - DOUBLE_PRECISION_t *cyi, - INTEGER_t *nz, - DOUBLE_PRECISION_t *cwrkr, - DOUBLE_PRECISION_t *cwrki, - INTEGER_t *ierr); - -void amos_zbesh(const DOUBLE_PRECISION_t *zr, - const DOUBLE_PRECISION_t *zi, - const DOUBLE_PRECISION_t *fnu, - const INTEGER_t *kode, - const INTEGER_t *m, - const INTEGER_t *n, - DOUBLE_PRECISION_t *cyr, - DOUBLE_PRECISION_t *cyi, - INTEGER_t *nz, - INTEGER_t *ierr); - - -#endif diff --git a/amos/d1mach.f b/amos/d1mach.f deleted file mode 100644 index bda4529..0000000 --- a/amos/d1mach.f +++ /dev/null @@ -1,209 +0,0 @@ - DOUBLE PRECISION FUNCTION D1MACH(I) - INTEGER I -C -C DOUBLE-PRECISION MACHINE CONSTANTS -C D1MACH( 1) = B**(EMIN-1), THE SMALLEST POSITIVE MAGNITUDE. -C D1MACH( 2) = B**EMAX*(1 - B**(-T)), THE LARGEST MAGNITUDE. -C D1MACH( 3) = B**(-T), THE SMALLEST RELATIVE SPACING. -C D1MACH( 4) = B**(1-T), THE LARGEST RELATIVE SPACING. -C D1MACH( 5) = LOG10(B) -C - INTEGER SMALL(2) - INTEGER LARGE(2) - INTEGER RIGHT(2) - INTEGER DIVER(2) - INTEGER LOG10(2) - INTEGER SC, CRAY1(38), J - COMMON /D9MACH/ CRAY1 - SAVE SMALL, LARGE, RIGHT, DIVER, LOG10, SC - DOUBLE PRECISION DMACH(5) - EQUIVALENCE (DMACH(1),SMALL(1)) - EQUIVALENCE (DMACH(2),LARGE(1)) - EQUIVALENCE (DMACH(3),RIGHT(1)) - EQUIVALENCE (DMACH(4),DIVER(1)) - EQUIVALENCE (DMACH(5),LOG10(1)) -C THIS VERSION ADAPTS AUTOMATICALLY TO MOST CURRENT MACHINES. -C R1MACH CAN HANDLE AUTO-DOUBLE COMPILING, BUT THIS VERSION OF -C D1MACH DOES NOT, BECAUSE WE DO NOT HAVE QUAD CONSTANTS FOR -C MANY MACHINES YET. -C TO COMPILE ON OLDER MACHINES, ADD A C IN COLUMN 1 -C ON THE NEXT LINE - DATA SC/0/ -C AND REMOVE THE C FROM COLUMN 1 IN ONE OF THE SECTIONS BELOW. -C CONSTANTS FOR EVEN OLDER MACHINES CAN BE OBTAINED BY -C mail netlib@research.bell-labs.com -C send old1mach from blas -C PLEASE SEND CORRECTIONS TO dmg OR ehg@bell-labs.com. -C -C MACHINE CONSTANTS FOR THE HONEYWELL DPS 8/70 SERIES. -C DATA SMALL(1),SMALL(2) / O402400000000, O000000000000 / -C DATA LARGE(1),LARGE(2) / O376777777777, O777777777777 / -C DATA RIGHT(1),RIGHT(2) / O604400000000, O000000000000 / -C DATA DIVER(1),DIVER(2) / O606400000000, O000000000000 / -C DATA LOG10(1),LOG10(2) / O776464202324, O117571775714 /, SC/987/ -C -C MACHINE CONSTANTS FOR PDP-11 FORTRANS SUPPORTING -C 32-BIT INTEGERS. -C DATA SMALL(1),SMALL(2) / 8388608, 0 / -C DATA LARGE(1),LARGE(2) / 2147483647, -1 / -C DATA RIGHT(1),RIGHT(2) / 612368384, 0 / -C DATA DIVER(1),DIVER(2) / 620756992, 0 / -C DATA LOG10(1),LOG10(2) / 1067065498, -2063872008 /, SC/987/ -C -C MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES. -C DATA SMALL(1),SMALL(2) / O000040000000, O000000000000 / -C DATA LARGE(1),LARGE(2) / O377777777777, O777777777777 / -C DATA RIGHT(1),RIGHT(2) / O170540000000, O000000000000 / -C DATA DIVER(1),DIVER(2) / O170640000000, O000000000000 / -C DATA LOG10(1),LOG10(2) / O177746420232, O411757177572 /, SC/987/ -C -C ON FIRST CALL, IF NO DATA UNCOMMENTED, TEST MACHINE TYPES. - IF (SC .NE. 987) THEN - DMACH(1) = 1.D13 - IF ( SMALL(1) .EQ. 1117925532 - * .AND. SMALL(2) .EQ. -448790528) THEN -* *** IEEE BIG ENDIAN *** - SMALL(1) = 1048576 - SMALL(2) = 0 - LARGE(1) = 2146435071 - LARGE(2) = -1 - RIGHT(1) = 1017118720 - RIGHT(2) = 0 - DIVER(1) = 1018167296 - DIVER(2) = 0 - LOG10(1) = 1070810131 - LOG10(2) = 1352628735 - ELSE IF ( SMALL(2) .EQ. 1117925532 - * .AND. SMALL(1) .EQ. -448790528) THEN -* *** IEEE LITTLE ENDIAN *** - SMALL(2) = 1048576 - SMALL(1) = 0 - LARGE(2) = 2146435071 - LARGE(1) = -1 - RIGHT(2) = 1017118720 - RIGHT(1) = 0 - DIVER(2) = 1018167296 - DIVER(1) = 0 - LOG10(2) = 1070810131 - LOG10(1) = 1352628735 - ELSE IF ( SMALL(1) .EQ. -2065213935 - * .AND. SMALL(2) .EQ. 10752) THEN -* *** VAX WITH D_FLOATING *** - SMALL(1) = 128 - SMALL(2) = 0 - LARGE(1) = -32769 - LARGE(2) = -1 - RIGHT(1) = 9344 - RIGHT(2) = 0 - DIVER(1) = 9472 - DIVER(2) = 0 - LOG10(1) = 546979738 - LOG10(2) = -805796613 - ELSE IF ( SMALL(1) .EQ. 1267827943 - * .AND. SMALL(2) .EQ. 704643072) THEN -* *** IBM MAINFRAME *** - SMALL(1) = 1048576 - SMALL(2) = 0 - LARGE(1) = 2147483647 - LARGE(2) = -1 - RIGHT(1) = 856686592 - RIGHT(2) = 0 - DIVER(1) = 873463808 - DIVER(2) = 0 - LOG10(1) = 1091781651 - LOG10(2) = 1352628735 - ELSE IF ( SMALL(1) .EQ. 1120022684 - * .AND. SMALL(2) .EQ. -448790528) THEN -* *** CONVEX C-1 *** - SMALL(1) = 1048576 - SMALL(2) = 0 - LARGE(1) = 2147483647 - LARGE(2) = -1 - RIGHT(1) = 1019215872 - RIGHT(2) = 0 - DIVER(1) = 1020264448 - DIVER(2) = 0 - LOG10(1) = 1072907283 - LOG10(2) = 1352628735 - ELSE IF ( SMALL(1) .EQ. 815547074 - * .AND. SMALL(2) .EQ. 58688) THEN -* *** VAX G-FLOATING *** - SMALL(1) = 16 - SMALL(2) = 0 - LARGE(1) = -32769 - LARGE(2) = -1 - RIGHT(1) = 15552 - RIGHT(2) = 0 - DIVER(1) = 15568 - DIVER(2) = 0 - LOG10(1) = 1142112243 - LOG10(2) = 2046775455 - ELSE - DMACH(2) = 1.D27 + 1 - DMACH(3) = 1.D27 - LARGE(2) = LARGE(2) - RIGHT(2) - IF (LARGE(2) .EQ. 64 .AND. SMALL(2) .EQ. 0) THEN - CRAY1(1) = 67291416 - DO 10 J = 1, 20 - CRAY1(J+1) = CRAY1(J) + CRAY1(J) - 10 CONTINUE - CRAY1(22) = CRAY1(21) + 321322 - DO 20 J = 22, 37 - CRAY1(J+1) = CRAY1(J) + CRAY1(J) - 20 CONTINUE - IF (CRAY1(38) .EQ. SMALL(1)) THEN -* *** CRAY *** - CALL I1MCRY(SMALL(1), J, 8285, 8388608, 0) - SMALL(2) = 0 - CALL I1MCRY(LARGE(1), J, 24574, 16777215, 16777215) - CALL I1MCRY(LARGE(2), J, 0, 16777215, 16777214) - CALL I1MCRY(RIGHT(1), J, 16291, 8388608, 0) - RIGHT(2) = 0 - CALL I1MCRY(DIVER(1), J, 16292, 8388608, 0) - DIVER(2) = 0 - CALL I1MCRY(LOG10(1), J, 16383, 10100890, 8715215) - CALL I1MCRY(LOG10(2), J, 0, 16226447, 9001388) - ELSE - WRITE(*,9000) - STOP 779 - END IF - ELSE - WRITE(*,9000) - STOP 779 - END IF - END IF - SC = 987 - END IF -* SANITY CHECK - IF (DMACH(4) .GE. 1.0D0) STOP 778 - IF (I .LT. 1 .OR. I .GT. 5) THEN - WRITE(*,*) 'D1MACH(I): I =',I,' is out of bounds.' - STOP - END IF - D1MACH = DMACH(I) - RETURN - 9000 FORMAT(/' Adjust D1MACH by uncommenting data statements'/ - *' appropriate for your machine.') -* /* Standard C source for D1MACH -- remove the * in column 1 */ -*#include -*#include -*#include -*double d1mach_(long *i) -*{ -* switch(*i){ -* case 1: return DBL_MIN; -* case 2: return DBL_MAX; -* case 3: return DBL_EPSILON/FLT_RADIX; -* case 4: return DBL_EPSILON; -* case 5: return log10(FLT_RADIX); -* } -* fprintf(stderr, "invalid argument: d1mach(%ld)\n", *i); -* exit(1); return 0; /* some compilers demand return values */ -*} - END - SUBROUTINE I1MCRY(A, A1, B, C, D) -**** SPECIAL COMPUTATION FOR OLD CRAY MACHINES **** - INTEGER A, A1, B, C, D - A1 = 16777216*B + C - A = 16777216*A1 + D - END diff --git a/amos/dgamln.f b/amos/dgamln.f deleted file mode 100644 index 792014b..0000000 --- a/amos/dgamln.f +++ /dev/null @@ -1,189 +0,0 @@ - DOUBLE PRECISION FUNCTION DGAMLN(Z,IERR) -C***BEGIN PROLOGUE DGAMLN -C***DATE WRITTEN 830501 (YYMMDD) -C***REVISION DATE 830501 (YYMMDD) -C***CATEGORY NO. B5F -C***KEYWORDS GAMMA FUNCTION,LOGARITHM OF GAMMA FUNCTION -C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES -C***PURPOSE TO COMPUTE THE LOGARITHM OF THE GAMMA FUNCTION -C***DESCRIPTION -C -C **** A DOUBLE PRECISION ROUTINE **** -C DGAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR -C Z.GT.0. THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES -C GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION -C G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN. THE FUNCTION WAS MADE AS -C PORTABLE AS POSSIBLE BY COMPUTIMG ZMIN FROM THE NUMBER OF BASE -C 10 DIGITS IN A WORD, RLN=AMAX1(-ALOG10(R1MACH(4)),0.5E-18) -C LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY. -C -C SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100 -C VALUES IS USED FOR SPEED OF EXECUTION. -C -C DESCRIPTION OF ARGUMENTS -C -C INPUT Z IS D0UBLE PRECISION -C Z - ARGUMENT, Z.GT.0.0D0 -C -C OUTPUT DGAMLN IS DOUBLE PRECISION -C DGAMLN - NATURAL LOG OF THE GAMMA FUNCTION AT Z.NE.0.0D0 -C IERR - ERROR FLAG -C IERR=0, NORMAL RETURN, COMPUTATION COMPLETED -C IERR=1, Z.LE.0.0D0, NO COMPUTATION -C -C -C***REFERENCES COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C BY D. E. AMOS, SAND83-0083, MAY, 1983. -C***ROUTINES CALLED I1MACH,D1MACH -C***END PROLOGUE DGAMLN - DOUBLE PRECISION CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST, - * T1, WDTOL, Z, ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ, D1MACH - INTEGER I, IERR, I1M, K, MZ, NZ, I1MACH - DIMENSION CF(22), GLN(100) -C LNGAMMA(N), N=1,100 - DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7), - 1 GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14), - 2 GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20), - 3 GLN(21), GLN(22)/ - 4 0.00000000000000000D+00, 0.00000000000000000D+00, - 5 6.93147180559945309D-01, 1.79175946922805500D+00, - 6 3.17805383034794562D+00, 4.78749174278204599D+00, - 7 6.57925121201010100D+00, 8.52516136106541430D+00, - 8 1.06046029027452502D+01, 1.28018274800814696D+01, - 9 1.51044125730755153D+01, 1.75023078458738858D+01, - A 1.99872144956618861D+01, 2.25521638531234229D+01, - B 2.51912211827386815D+01, 2.78992713838408916D+01, - C 3.06718601060806728D+01, 3.35050734501368889D+01, - D 3.63954452080330536D+01, 3.93398841871994940D+01, - E 4.23356164607534850D+01, 4.53801388984769080D+01/ - DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28), - 1 GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34), - 2 GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40), - 3 GLN(41), GLN(42), GLN(43), GLN(44)/ - 4 4.84711813518352239D+01, 5.16066755677643736D+01, - 5 5.47847293981123192D+01, 5.80036052229805199D+01, - 6 6.12617017610020020D+01, 6.45575386270063311D+01, - 7 6.78897431371815350D+01, 7.12570389671680090D+01, - 8 7.46582363488301644D+01, 7.80922235533153106D+01, - 9 8.15579594561150372D+01, 8.50544670175815174D+01, - A 8.85808275421976788D+01, 9.21361756036870925D+01, - B 9.57196945421432025D+01, 9.93306124547874269D+01, - C 1.02968198614513813D+02, 1.06631760260643459D+02, - D 1.10320639714757395D+02, 1.14034211781461703D+02, - E 1.17771881399745072D+02, 1.21533081515438634D+02/ - DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50), - 1 GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56), - 2 GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62), - 3 GLN(63), GLN(64), GLN(65), GLN(66)/ - 4 1.25317271149356895D+02, 1.29123933639127215D+02, - 5 1.32952575035616310D+02, 1.36802722637326368D+02, - 6 1.40673923648234259D+02, 1.44565743946344886D+02, - 7 1.48477766951773032D+02, 1.52409592584497358D+02, - 8 1.56360836303078785D+02, 1.60331128216630907D+02, - 9 1.64320112263195181D+02, 1.68327445448427652D+02, - A 1.72352797139162802D+02, 1.76395848406997352D+02, - B 1.80456291417543771D+02, 1.84533828861449491D+02, - C 1.88628173423671591D+02, 1.92739047287844902D+02, - D 1.96866181672889994D+02, 2.01009316399281527D+02, - E 2.05168199482641199D+02, 2.09342586752536836D+02/ - DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72), - 1 GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78), - 2 GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84), - 3 GLN(85), GLN(86), GLN(87), GLN(88)/ - 4 2.13532241494563261D+02, 2.17736934113954227D+02, - 5 2.21956441819130334D+02, 2.26190548323727593D+02, - 6 2.30439043565776952D+02, 2.34701723442818268D+02, - 7 2.38978389561834323D+02, 2.43268849002982714D+02, - 8 2.47572914096186884D+02, 2.51890402209723194D+02, - 9 2.56221135550009525D+02, 2.60564940971863209D+02, - A 2.64921649798552801D+02, 2.69291097651019823D+02, - B 2.73673124285693704D+02, 2.78067573440366143D+02, - C 2.82474292687630396D+02, 2.86893133295426994D+02, - D 2.91323950094270308D+02, 2.95766601350760624D+02, - E 3.00220948647014132D+02, 3.04686856765668715D+02/ - DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94), - 1 GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/ - 2 3.09164193580146922D+02, 3.13652829949879062D+02, - 3 3.18152639620209327D+02, 3.22663499126726177D+02, - 4 3.27185287703775217D+02, 3.31717887196928473D+02, - 5 3.36261181979198477D+02, 3.40815058870799018D+02, - 6 3.45379407062266854D+02, 3.49954118040770237D+02, - 7 3.54539085519440809D+02, 3.59134205369575399D+02/ -C COEFFICIENTS OF ASYMPTOTIC EXPANSION - DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8), - 1 CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15), - 2 CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/ - 3 8.33333333333333333D-02, -2.77777777777777778D-03, - 4 7.93650793650793651D-04, -5.95238095238095238D-04, - 5 8.41750841750841751D-04, -1.91752691752691753D-03, - 6 6.41025641025641026D-03, -2.95506535947712418D-02, - 7 1.79644372368830573D-01, -1.39243221690590112D+00, - 8 1.34028640441683920D+01, -1.56848284626002017D+02, - 9 2.19310333333333333D+03, -3.61087712537249894D+04, - A 6.91472268851313067D+05, -1.52382215394074162D+07, - B 3.82900751391414141D+08, -1.08822660357843911D+10, - C 3.47320283765002252D+11, -1.23696021422692745D+13, - D 4.88788064793079335D+14, -2.13203339609193739D+16/ -C -C LN(2*PI) - DATA CON / 1.83787706640934548D+00/ -C -C***FIRST EXECUTABLE STATEMENT DGAMLN - IERR=0 - IF (Z.LE.0.0D0) GO TO 70 - IF (Z.GT.101.0D0) GO TO 10 - NZ = INT(SNGL(Z)) - FZ = Z - FLOAT(NZ) - IF (FZ.GT.0.0D0) GO TO 10 - IF (NZ.GT.100) GO TO 10 - DGAMLN = GLN(NZ) - RETURN - 10 CONTINUE - WDTOL = D1MACH(4) - WDTOL = DMAX1(WDTOL,0.5D-18) - I1M = I1MACH(14) - RLN = D1MACH(5)*FLOAT(I1M) - FLN = DMIN1(RLN,20.0D0) - FLN = DMAX1(FLN,3.0D0) - FLN = FLN - 3.0D0 - ZM = 1.8000D0 + 0.3875D0*FLN - MZ = INT(SNGL(ZM)) + 1 - ZMIN = FLOAT(MZ) - ZDMY = Z - ZINC = 0.0D0 - IF (Z.GE.ZMIN) GO TO 20 - ZINC = ZMIN - FLOAT(NZ) - ZDMY = Z + ZINC - 20 CONTINUE - ZP = 1.0D0/ZDMY - T1 = CF(1)*ZP - S = T1 - IF (ZP.LT.WDTOL) GO TO 40 - ZSQ = ZP*ZP - TST = T1*WDTOL - DO 30 K=2,22 - ZP = ZP*ZSQ - TRM = CF(K)*ZP - IF (DABS(TRM).LT.TST) GO TO 40 - S = S + TRM - 30 CONTINUE - 40 CONTINUE - IF (ZINC.NE.0.0D0) GO TO 50 - TLG = DLOG(Z) - DGAMLN = Z*(TLG-1.0D0) + 0.5D0*(CON-TLG) + S - RETURN - 50 CONTINUE - ZP = 1.0D0 - NZ = INT(SNGL(ZINC)) - DO 60 I=1,NZ - ZP = ZP*(Z+FLOAT(I-1)) - 60 CONTINUE - TLG = DLOG(ZDMY) - DGAMLN = ZDMY*(TLG-1.0D0) - DLOG(ZP) + 0.5D0*(CON-TLG) + S - RETURN -C -C - 70 CONTINUE - IERR=1 - RETURN - END diff --git a/amos/i1mach.f b/amos/i1mach.f deleted file mode 100644 index 1d6f7fc..0000000 --- a/amos/i1mach.f +++ /dev/null @@ -1,291 +0,0 @@ - INTEGER FUNCTION I1MACH(I) - INTEGER I -C -C I1MACH( 1) = THE STANDARD INPUT UNIT. -C I1MACH( 2) = THE STANDARD OUTPUT UNIT. -C I1MACH( 3) = THE STANDARD PUNCH UNIT. -C I1MACH( 4) = THE STANDARD ERROR MESSAGE UNIT. -C I1MACH( 5) = THE NUMBER OF BITS PER INTEGER STORAGE UNIT. -C I1MACH( 6) = THE NUMBER OF CHARACTERS PER CHARACTER STORAGE UNIT. -C INTEGERS HAVE FORM SIGN ( X(S-1)*A**(S-1) + ... + X(1)*A + X(0) ) -C I1MACH( 7) = A, THE BASE. -C I1MACH( 8) = S, THE NUMBER OF BASE-A DIGITS. -C I1MACH( 9) = A**S - 1, THE LARGEST MAGNITUDE. -C FLOATS HAVE FORM SIGN (B**E)*( (X(1)/B) + ... + (X(T)/B**T) ) -C WHERE EMIN .LE. E .LE. EMAX. -C I1MACH(10) = B, THE BASE. -C SINGLE-PRECISION -C I1MACH(11) = T, THE NUMBER OF BASE-B DIGITS. -C I1MACH(12) = EMIN, THE SMALLEST EXPONENT E. -C I1MACH(13) = EMAX, THE LARGEST EXPONENT E. -C DOUBLE-PRECISION -C I1MACH(14) = T, THE NUMBER OF BASE-B DIGITS. -C I1MACH(15) = EMIN, THE SMALLEST EXPONENT E. -C I1MACH(16) = EMAX, THE LARGEST EXPONENT E. -C - INTEGER IMACH(16), OUTPUT, SC, SMALL(2) - SAVE IMACH, SC - REAL RMACH - EQUIVALENCE (IMACH(4),OUTPUT), (RMACH,SMALL(1)) - INTEGER I3, J, K, T3E(3) - DATA T3E(1) / 9777664 / - DATA T3E(2) / 5323660 / - DATA T3E(3) / 46980 / -C THIS VERSION ADAPTS AUTOMATICALLY TO MOST CURRENT MACHINES, -C INCLUDING AUTO-DOUBLE COMPILERS. -C TO COMPILE ON OLDER MACHINES, ADD A C IN COLUMN 1 -C ON THE NEXT LINE - DATA SC/0/ -C AND REMOVE THE C FROM COLUMN 1 IN ONE OF THE SECTIONS BELOW. -C CONSTANTS FOR EVEN OLDER MACHINES CAN BE OBTAINED BY -C mail netlib@research.bell-labs.com -C send old1mach from blas -C PLEASE SEND CORRECTIONS TO dmg OR ehg@bell-labs.com. -C -C MACHINE CONSTANTS FOR THE HONEYWELL DPS 8/70 SERIES. -C -C DATA IMACH( 1) / 5 / -C DATA IMACH( 2) / 6 / -C DATA IMACH( 3) / 43 / -C DATA IMACH( 4) / 6 / -C DATA IMACH( 5) / 36 / -C DATA IMACH( 6) / 4 / -C DATA IMACH( 7) / 2 / -C DATA IMACH( 8) / 35 / -C DATA IMACH( 9) / O377777777777 / -C DATA IMACH(10) / 2 / -C DATA IMACH(11) / 27 / -C DATA IMACH(12) / -127 / -C DATA IMACH(13) / 127 / -C DATA IMACH(14) / 63 / -C DATA IMACH(15) / -127 / -C DATA IMACH(16) / 127 /, SC/987/ -C -C MACHINE CONSTANTS FOR PDP-11 FORTRANS SUPPORTING -C 32-BIT INTEGER ARITHMETIC. -C -C DATA IMACH( 1) / 5 / -C DATA IMACH( 2) / 6 / -C DATA IMACH( 3) / 7 / -C DATA IMACH( 4) / 6 / -C DATA IMACH( 5) / 32 / -C DATA IMACH( 6) / 4 / -C DATA IMACH( 7) / 2 / -C DATA IMACH( 8) / 31 / -C DATA IMACH( 9) / 2147483647 / -C DATA IMACH(10) / 2 / -C DATA IMACH(11) / 24 / -C DATA IMACH(12) / -127 / -C DATA IMACH(13) / 127 / -C DATA IMACH(14) / 56 / -C DATA IMACH(15) / -127 / -C DATA IMACH(16) / 127 /, SC/987/ -C -C MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES. -C -C NOTE THAT THE PUNCH UNIT, I1MACH(3), HAS BEEN SET TO 7 -C WHICH IS APPROPRIATE FOR THE UNIVAC-FOR SYSTEM. -C IF YOU HAVE THE UNIVAC-FTN SYSTEM, SET IT TO 1. -C -C DATA IMACH( 1) / 5 / -C DATA IMACH( 2) / 6 / -C DATA IMACH( 3) / 7 / -C DATA IMACH( 4) / 6 / -C DATA IMACH( 5) / 36 / -C DATA IMACH( 6) / 6 / -C DATA IMACH( 7) / 2 / -C DATA IMACH( 8) / 35 / -C DATA IMACH( 9) / O377777777777 / -C DATA IMACH(10) / 2 / -C DATA IMACH(11) / 27 / -C DATA IMACH(12) / -128 / -C DATA IMACH(13) / 127 / -C DATA IMACH(14) / 60 / -C DATA IMACH(15) /-1024 / -C DATA IMACH(16) / 1023 /, SC/987/ -C - IF (SC .NE. 987) THEN -* *** CHECK FOR AUTODOUBLE *** - SMALL(2) = 0 - RMACH = 1E13 - IF (SMALL(2) .NE. 0) THEN -* *** AUTODOUBLED *** - IF ( (SMALL(1) .EQ. 1117925532 - * .AND. SMALL(2) .EQ. -448790528) - * .OR. (SMALL(2) .EQ. 1117925532 - * .AND. SMALL(1) .EQ. -448790528)) THEN -* *** IEEE *** - IMACH(10) = 2 - IMACH(14) = 53 - IMACH(15) = -1021 - IMACH(16) = 1024 - ELSE IF ( SMALL(1) .EQ. -2065213935 - * .AND. SMALL(2) .EQ. 10752) THEN -* *** VAX WITH D_FLOATING *** - IMACH(10) = 2 - IMACH(14) = 56 - IMACH(15) = -127 - IMACH(16) = 127 - ELSE IF ( SMALL(1) .EQ. 1267827943 - * .AND. SMALL(2) .EQ. 704643072) THEN -* *** IBM MAINFRAME *** - IMACH(10) = 16 - IMACH(14) = 14 - IMACH(15) = -64 - IMACH(16) = 63 - ELSE - WRITE(*,9010) - STOP 777 - END IF - IMACH(11) = IMACH(14) - IMACH(12) = IMACH(15) - IMACH(13) = IMACH(16) - ELSE - RMACH = 1234567. - IF (SMALL(1) .EQ. 1234613304) THEN -* *** IEEE *** - IMACH(10) = 2 - IMACH(11) = 24 - IMACH(12) = -125 - IMACH(13) = 128 - IMACH(14) = 53 - IMACH(15) = -1021 - IMACH(16) = 1024 - SC = 987 - ELSE IF (SMALL(1) .EQ. -1271379306) THEN -* *** VAX *** - IMACH(10) = 2 - IMACH(11) = 24 - IMACH(12) = -127 - IMACH(13) = 127 - IMACH(14) = 56 - IMACH(15) = -127 - IMACH(16) = 127 - SC = 987 - ELSE IF (SMALL(1) .EQ. 1175639687) THEN -* *** IBM MAINFRAME *** - IMACH(10) = 16 - IMACH(11) = 6 - IMACH(12) = -64 - IMACH(13) = 63 - IMACH(14) = 14 - IMACH(15) = -64 - IMACH(16) = 63 - SC = 987 - ELSE IF (SMALL(1) .EQ. 1251390520) THEN -* *** CONVEX C-1 *** - IMACH(10) = 2 - IMACH(11) = 24 - IMACH(12) = -128 - IMACH(13) = 127 - IMACH(14) = 53 - IMACH(15) = -1024 - IMACH(16) = 1023 - ELSE - DO 10 I3 = 1, 3 - J = SMALL(1) / 10000000 - K = SMALL(1) - 10000000*J - IF (K .NE. T3E(I3)) GO TO 20 - SMALL(1) = J - 10 CONTINUE -* *** CRAY T3E *** - IMACH( 1) = 5 - IMACH( 2) = 6 - IMACH( 3) = 0 - IMACH( 4) = 0 - IMACH( 5) = 64 - IMACH( 6) = 8 - IMACH( 7) = 2 - IMACH( 8) = 63 - CALL I1MCR1(IMACH(9), K, 32767, 16777215, 16777215) - IMACH(10) = 2 - IMACH(11) = 53 - IMACH(12) = -1021 - IMACH(13) = 1024 - IMACH(14) = 53 - IMACH(15) = -1021 - IMACH(16) = 1024 - GO TO 35 - 20 CALL I1MCR1(J, K, 16405, 9876536, 0) - IF (SMALL(1) .NE. J) THEN - WRITE(*,9020) - STOP 777 - END IF -* *** CRAY 1, XMP, 2, AND 3 *** - IMACH(1) = 5 - IMACH(2) = 6 - IMACH(3) = 102 - IMACH(4) = 6 - IMACH(5) = 46 - IMACH(6) = 8 - IMACH(7) = 2 - IMACH(8) = 45 - CALL I1MCR1(IMACH(9), K, 0, 4194303, 16777215) - IMACH(10) = 2 - IMACH(11) = 47 - IMACH(12) = -8188 - IMACH(13) = 8189 - IMACH(14) = 94 - IMACH(15) = -8141 - IMACH(16) = 8189 - GO TO 35 - END IF - END IF - IMACH( 1) = 5 - IMACH( 2) = 6 - IMACH( 3) = 7 - IMACH( 4) = 6 - IMACH( 5) = 32 - IMACH( 6) = 4 - IMACH( 7) = 2 - IMACH( 8) = 31 - IMACH( 9) = 2147483647 - 35 SC = 987 - END IF - 9010 FORMAT(/' Adjust autodoubled I1MACH by uncommenting data'/ - * ' statements appropriate for your machine and setting'/ - * ' IMACH(I) = IMACH(I+3) for I = 11, 12, and 13.') - 9020 FORMAT(/' Adjust I1MACH by uncommenting data statements'/ - * ' appropriate for your machine.') - IF (I .LT. 1 .OR. I .GT. 16) GO TO 40 - I1MACH = IMACH(I) - RETURN - 40 WRITE(*,*) 'I1MACH(I): I =',I,' is out of bounds.' - STOP -* /* C source for I1MACH -- remove the * in column 1 */ -* /* Note that some values may need changing. */ -*#include -*#include -*#include -*#include -* -*long i1mach_(long *i) -*{ -* switch(*i){ -* case 1: return 5; /* standard input */ -* case 2: return 6; /* standard output */ -* case 3: return 7; /* standard punch */ -* case 4: return 0; /* standard error */ -* case 5: return 32; /* bits per integer */ -* case 6: return sizeof(int); -* case 7: return 2; /* base for integers */ -* case 8: return 31; /* digits of integer base */ -* case 9: return LONG_MAX; -* case 10: return FLT_RADIX; -* case 11: return FLT_MANT_DIG; -* case 12: return FLT_MIN_EXP; -* case 13: return FLT_MAX_EXP; -* case 14: return DBL_MANT_DIG; -* case 15: return DBL_MIN_EXP; -* case 16: return DBL_MAX_EXP; -* } -* fprintf(stderr, "invalid argument: i1mach(%ld)\n", *i); -* exit(1);return 0; /* some compilers demand return values */ -*} - END - SUBROUTINE I1MCR1(A, A1, B, C, D) -**** SPECIAL COMPUTATION FOR OLD CRAY MACHINES **** - INTEGER A, A1, B, C, D - A1 = 16777216*B + C - A = 16777216*A1 + D - END diff --git a/amos/xerror.f b/amos/xerror.f deleted file mode 100644 index baa5506..0000000 --- a/amos/xerror.f +++ /dev/null @@ -1,22 +0,0 @@ - SUBROUTINE XERROR(MESS,NMESS,L1,L2) -C -C THIS IS A DUMMY XERROR ROUTINE TO PRINT ERROR MESSAGES WITH NMESS -C CHARACTERS. L1 AND L2 ARE DUMMY PARAMETERS TO MAKE THIS CALL -C COMPATIBLE WITH THE SLATEC XERROR ROUTINE. THIS IS A FORTRAN 77 -C ROUTINE. -C - CHARACTER*(*) MESS - NN=NMESS/70 - NR=NMESS-70*NN - IF(NR.NE.0) NN=NN+1 - K=1 - PRINT 900 - 900 FORMAT(/) - DO 10 I=1,NN - KMIN=MIN0(K+69,NMESS) - PRINT *, MESS(K:KMIN) - K=K+70 - 10 CONTINUE - PRINT 900 - RETURN - END diff --git a/amos/zabs.f b/amos/zabs.f deleted file mode 100644 index 31514a2..0000000 --- a/amos/zabs.f +++ /dev/null @@ -1,29 +0,0 @@ - DOUBLE PRECISION FUNCTION AZABS(ZR, ZI) -C***BEGIN PROLOGUE AZABS -C***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY -C -C AZABS COMPUTES THE ABSOLUTE VALUE OR MAGNITUDE OF A DOUBLE -C PRECISION COMPLEX VARIABLE CMPLX(ZR,ZI) -C -C***ROUTINES CALLED (NONE) -C***END PROLOGUE AZABS - DOUBLE PRECISION ZR, ZI, U, V, Q, S - U = DABS(ZR) - V = DABS(ZI) - S = U + V -C----------------------------------------------------------------------- -C S*1.0D0 MAKES AN UNNORMALIZED UNDERFLOW ON CDC MACHINES INTO A -C TRUE FLOATING ZERO -C----------------------------------------------------------------------- - S = S*1.0D+0 - IF (S.EQ.0.0D+0) GO TO 20 - IF (U.GT.V) GO TO 10 - Q = U/V - AZABS = V*DSQRT(1.D+0+Q*Q) - RETURN - 10 Q = V/U - AZABS = U*DSQRT(1.D+0+Q*Q) - RETURN - 20 AZABS = 0.0D+0 - RETURN - END diff --git a/amos/zacai.f b/amos/zacai.f deleted file mode 100644 index 87eba88..0000000 --- a/amos/zacai.f +++ /dev/null @@ -1,99 +0,0 @@ - SUBROUTINE ZACAI(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, - * ELIM, ALIM) -C***BEGIN PROLOGUE ZACAI -C***REFER TO ZAIRY -C -C ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA -C -C K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN) -C MP=PI*MR*CMPLX(0.0,1.0) -C -C TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT -C HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1. -C ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND -C RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT IF ZACON -C IS CALLED FROM ZAIRY. -C -C***ROUTINES CALLED ZASYI,ZBKNU,ZMLRI,ZSERI,ZS1S2,D1MACH,AZABS -C***END PROLOGUE ZACAI -C COMPLEX CSGN,CSPN,C1,C2,Y,Z,ZN,CY - DOUBLE PRECISION ALIM, ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR, - * CSPNI, C1R, C1I, C2R, C2I, CYR, CYI, DFNU, ELIM, FMR, FNU, PI, - * RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI, D1MACH, AZABS - INTEGER INU, IUF, KODE, MR, N, NN, NW, NZ - DIMENSION YR(N), YI(N), CYR(2), CYI(2) - DATA PI / 3.14159265358979324D0 / - NZ = 0 - ZNR = -ZR - ZNI = -ZI - AZ = AZABS(ZR,ZI) - NN = N - DFNU = FNU + DBLE(FLOAT(N-1)) - IF (AZ.LE.2.0D0) GO TO 10 - IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20 - 10 CONTINUE -C----------------------------------------------------------------------- -C POWER SERIES FOR THE I FUNCTION -C----------------------------------------------------------------------- - CALL ZSERI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM) - GO TO 40 - 20 CONTINUE - IF (AZ.LT.RL) GO TO 30 -C----------------------------------------------------------------------- -C ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION -C----------------------------------------------------------------------- - CALL ZASYI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM, - * ALIM) - IF (NW.LT.0) GO TO 80 - GO TO 40 - 30 CONTINUE -C----------------------------------------------------------------------- -C MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION -C----------------------------------------------------------------------- - CALL ZMLRI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL) - IF(NW.LT.0) GO TO 80 - 40 CONTINUE -C----------------------------------------------------------------------- -C ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION -C----------------------------------------------------------------------- - CALL ZBKNU(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM) - IF (NW.NE.0) GO TO 80 - FMR = DBLE(FLOAT(MR)) - SGN = -DSIGN(PI,FMR) - CSGNR = 0.0D0 - CSGNI = SGN - IF (KODE.EQ.1) GO TO 50 - YY = -ZNI - CSGNR = -CSGNI*DSIN(YY) - CSGNI = CSGNI*DCOS(YY) - 50 CONTINUE -C----------------------------------------------------------------------- -C CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE -C WHEN FNU IS LARGE -C----------------------------------------------------------------------- - INU = INT(SNGL(FNU)) - ARG = (FNU-DBLE(FLOAT(INU)))*SGN - CSPNR = DCOS(ARG) - CSPNI = DSIN(ARG) - IF (MOD(INU,2).EQ.0) GO TO 60 - CSPNR = -CSPNR - CSPNI = -CSPNI - 60 CONTINUE - C1R = CYR(1) - C1I = CYI(1) - C2R = YR(1) - C2I = YI(1) - IF (KODE.EQ.1) GO TO 70 - IUF = 0 - ASCLE = 1.0D+3*D1MACH(1)/TOL - CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) - NZ = NZ + NW - 70 CONTINUE - YR(1) = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I - YI(1) = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R - RETURN - 80 CONTINUE - NZ = -1 - IF(NW.EQ.(-2)) NZ=-2 - RETURN - END diff --git a/amos/zacon.f b/amos/zacon.f deleted file mode 100644 index b0dbb91..0000000 --- a/amos/zacon.f +++ /dev/null @@ -1,203 +0,0 @@ - SUBROUTINE ZACON(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, FNUL, - * TOL, ELIM, ALIM) -C***BEGIN PROLOGUE ZACON -C***REFER TO ZBESK,ZBESH -C -C ZACON APPLIES THE ANALYTIC CONTINUATION FORMULA -C -C K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN) -C MP=PI*MR*CMPLX(0.0,1.0) -C -C TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT -C HALF Z PLANE -C -C***ROUTINES CALLED ZBINU,ZBKNU,ZS1S2,D1MACH,AZABS,ZMLT -C***END PROLOGUE ZACON -C COMPLEX CK,CONE,CSCL,CSCR,CSGN,CSPN,CY,CZERO,C1,C2,RZ,SC1,SC2,ST, -C *S1,S2,Y,Z,ZN - DOUBLE PRECISION ALIM, ARG, ASCLE, AS2, AZN, BRY, BSCLE, CKI, - * CKR, CONER, CPN, CSCL, CSCR, CSGNI, CSGNR, CSPNI, CSPNR, - * CSR, CSRR, CSSR, CYI, CYR, C1I, C1M, C1R, C2I, C2R, ELIM, FMR, - * FN, FNU, FNUL, PI, PTI, PTR, RAZN, RL, RZI, RZR, SC1I, SC1R, - * SC2I, SC2R, SGN, SPN, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, - * YY, ZEROR, ZI, ZNI, ZNR, ZR, D1MACH, AZABS - INTEGER I, INU, IUF, KFLAG, KODE, MR, N, NN, NW, NZ - DIMENSION YR(N), YI(N), CYR(2), CYI(2), CSSR(3), CSRR(3), BRY(3) - DATA PI / 3.14159265358979324D0 / - DATA ZEROR,CONER / 0.0D0,1.0D0 / - NZ = 0 - ZNR = -ZR - ZNI = -ZI - NN = N - CALL ZBINU(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, FNUL, TOL, - * ELIM, ALIM) - IF (NW.LT.0) GO TO 90 -C----------------------------------------------------------------------- -C ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION -C----------------------------------------------------------------------- - NN = MIN0(2,N) - CALL ZBKNU(ZNR, ZNI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM) - IF (NW.NE.0) GO TO 90 - S1R = CYR(1) - S1I = CYI(1) - FMR = DBLE(FLOAT(MR)) - SGN = -DSIGN(PI,FMR) - CSGNR = ZEROR - CSGNI = SGN - IF (KODE.EQ.1) GO TO 10 - YY = -ZNI - CPN = DCOS(YY) - SPN = DSIN(YY) - CALL ZMLT(CSGNR, CSGNI, CPN, SPN, CSGNR, CSGNI) - 10 CONTINUE -C----------------------------------------------------------------------- -C CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE -C WHEN FNU IS LARGE -C----------------------------------------------------------------------- - INU = INT(SNGL(FNU)) - ARG = (FNU-DBLE(FLOAT(INU)))*SGN - CPN = DCOS(ARG) - SPN = DSIN(ARG) - CSPNR = CPN - CSPNI = SPN - IF (MOD(INU,2).EQ.0) GO TO 20 - CSPNR = -CSPNR - CSPNI = -CSPNI - 20 CONTINUE - IUF = 0 - C1R = S1R - C1I = S1I - C2R = YR(1) - C2I = YI(1) - ASCLE = 1.0D+3*D1MACH(1)/TOL - IF (KODE.EQ.1) GO TO 30 - CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) - NZ = NZ + NW - SC1R = C1R - SC1I = C1I - 30 CONTINUE - CALL ZMLT(CSPNR, CSPNI, C1R, C1I, STR, STI) - CALL ZMLT(CSGNR, CSGNI, C2R, C2I, PTR, PTI) - YR(1) = STR + PTR - YI(1) = STI + PTI - IF (N.EQ.1) RETURN - CSPNR = -CSPNR - CSPNI = -CSPNI - S2R = CYR(2) - S2I = CYI(2) - C1R = S2R - C1I = S2I - C2R = YR(2) - C2I = YI(2) - IF (KODE.EQ.1) GO TO 40 - CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) - NZ = NZ + NW - SC2R = C1R - SC2I = C1I - 40 CONTINUE - CALL ZMLT(CSPNR, CSPNI, C1R, C1I, STR, STI) - CALL ZMLT(CSGNR, CSGNI, C2R, C2I, PTR, PTI) - YR(2) = STR + PTR - YI(2) = STI + PTI - IF (N.EQ.2) RETURN - CSPNR = -CSPNR - CSPNI = -CSPNI - AZN = AZABS(ZNR,ZNI) - RAZN = 1.0D0/AZN - STR = ZNR*RAZN - STI = -ZNI*RAZN - RZR = (STR+STR)*RAZN - RZI = (STI+STI)*RAZN - FN = FNU + 1.0D0 - CKR = FN*RZR - CKI = FN*RZI -C----------------------------------------------------------------------- -C SCALE NEAR EXPONENT EXTREMES DURING RECURRENCE ON K FUNCTIONS -C----------------------------------------------------------------------- - CSCL = 1.0D0/TOL - CSCR = TOL - CSSR(1) = CSCL - CSSR(2) = CONER - CSSR(3) = CSCR - CSRR(1) = CSCR - CSRR(2) = CONER - CSRR(3) = CSCL - BRY(1) = ASCLE - BRY(2) = 1.0D0/ASCLE - BRY(3) = D1MACH(2) - AS2 = AZABS(S2R,S2I) - KFLAG = 2 - IF (AS2.GT.BRY(1)) GO TO 50 - KFLAG = 1 - GO TO 60 - 50 CONTINUE - IF (AS2.LT.BRY(2)) GO TO 60 - KFLAG = 3 - 60 CONTINUE - BSCLE = BRY(KFLAG) - S1R = S1R*CSSR(KFLAG) - S1I = S1I*CSSR(KFLAG) - S2R = S2R*CSSR(KFLAG) - S2I = S2I*CSSR(KFLAG) - CSR = CSRR(KFLAG) - DO 80 I=3,N - STR = S2R - STI = S2I - S2R = CKR*STR - CKI*STI + S1R - S2I = CKR*STI + CKI*STR + S1I - S1R = STR - S1I = STI - C1R = S2R*CSR - C1I = S2I*CSR - STR = C1R - STI = C1I - C2R = YR(I) - C2I = YI(I) - IF (KODE.EQ.1) GO TO 70 - IF (IUF.LT.0) GO TO 70 - CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) - NZ = NZ + NW - SC1R = SC2R - SC1I = SC2I - SC2R = C1R - SC2I = C1I - IF (IUF.NE.3) GO TO 70 - IUF = -4 - S1R = SC1R*CSSR(KFLAG) - S1I = SC1I*CSSR(KFLAG) - S2R = SC2R*CSSR(KFLAG) - S2I = SC2I*CSSR(KFLAG) - STR = SC2R - STI = SC2I - 70 CONTINUE - PTR = CSPNR*C1R - CSPNI*C1I - PTI = CSPNR*C1I + CSPNI*C1R - YR(I) = PTR + CSGNR*C2R - CSGNI*C2I - YI(I) = PTI + CSGNR*C2I + CSGNI*C2R - CKR = CKR + RZR - CKI = CKI + RZI - CSPNR = -CSPNR - CSPNI = -CSPNI - IF (KFLAG.GE.3) GO TO 80 - PTR = DABS(C1R) - PTI = DABS(C1I) - C1M = DMAX1(PTR,PTI) - IF (C1M.LE.BSCLE) GO TO 80 - KFLAG = KFLAG + 1 - BSCLE = BRY(KFLAG) - S1R = S1R*CSR - S1I = S1I*CSR - S2R = STR - S2I = STI - S1R = S1R*CSSR(KFLAG) - S1I = S1I*CSSR(KFLAG) - S2R = S2R*CSSR(KFLAG) - S2I = S2I*CSSR(KFLAG) - CSR = CSRR(KFLAG) - 80 CONTINUE - RETURN - 90 CONTINUE - NZ = -1 - IF(NW.EQ.(-2)) NZ=-2 - RETURN - END diff --git a/amos/zairy.f b/amos/zairy.f deleted file mode 100644 index 1563d1d..0000000 --- a/amos/zairy.f +++ /dev/null @@ -1,393 +0,0 @@ - SUBROUTINE ZAIRY(ZR, ZI, ID, KODE, AIR, AII, NZ, IERR) -C***BEGIN PROLOGUE ZAIRY -C***DATE WRITTEN 830501 (YYMMDD) -C***REVISION DATE 890801 (YYMMDD) -C***CATEGORY NO. B5K -C***KEYWORDS AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD -C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES -C***PURPOSE TO COMPUTE AIRY FUNCTIONS AI(Z) AND DAI(Z) FOR COMPLEX Z -C***DESCRIPTION -C -C ***A DOUBLE PRECISION ROUTINE*** -C ON KODE=1, ZAIRY COMPUTES THE COMPLEX AIRY FUNCTION AI(Z) OR -C ITS DERIVATIVE DAI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON -C KODE=2, A SCALING OPTION CEXP(ZTA)*AI(Z) OR CEXP(ZTA)* -C DAI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL DECAY IN -C -PI/3.LT.ARG(Z).LT.PI/3 AND THE EXPONENTIAL GROWTH IN -C PI/3.LT.ABS(ARG(Z)).LT.PI WHERE ZTA=(2/3)*Z*CSQRT(Z). -C -C WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTIC IN -C THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED -C FOR KODE=2 HAVE A CUT ALONG THE NEGATIVE REAL AXIS. -C DEFINITIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF -C MATHEMATICAL FUNCTIONS (REF. 1). -C -C INPUT ZR,ZI ARE DOUBLE PRECISION -C ZR,ZI - Z=CMPLX(ZR,ZI) -C ID - ORDER OF DERIVATIVE, ID=0 OR ID=1 -C KODE - A PARAMETER TO INDICATE THE SCALING OPTION -C KODE= 1 RETURNS -C AI=AI(Z) ON ID=0 OR -C AI=DAI(Z)/DZ ON ID=1 -C = 2 RETURNS -C AI=CEXP(ZTA)*AI(Z) ON ID=0 OR -C AI=CEXP(ZTA)*DAI(Z)/DZ ON ID=1 WHERE -C ZTA=(2/3)*Z*CSQRT(Z) -C -C OUTPUT AIR,AII ARE DOUBLE PRECISION -C AIR,AII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND -C KODE -C NZ - UNDERFLOW INDICATOR -C NZ= 0 , NORMAL RETURN -C NZ= 1 , AI=CMPLX(0.0D0,0.0D0) DUE TO UNDERFLOW IN -C -PI/3.LT.ARG(Z).LT.PI/3 ON KODE=1 -C IERR - ERROR FLAG -C IERR=0, NORMAL RETURN - COMPUTATION COMPLETED -C IERR=1, INPUT ERROR - NO COMPUTATION -C IERR=2, OVERFLOW - NO COMPUTATION, REAL(ZTA) -C TOO LARGE ON KODE=1 -C IERR=3, CABS(Z) LARGE - COMPUTATION COMPLETED -C LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION -C PRODUCE LESS THAN HALF OF MACHINE ACCURACY -C IERR=4, CABS(Z) TOO LARGE - NO COMPUTATION -C COMPLETE LOSS OF ACCURACY BY ARGUMENT -C REDUCTION -C IERR=5, ERROR - NO COMPUTATION, -C ALGORITHM TERMINATION CONDITION NOT MET -C -C***LONG DESCRIPTION -C -C AI AND DAI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE K BESSEL -C FUNCTIONS BY -C -C AI(Z)=C*SQRT(Z)*K(1/3,ZTA) , DAI(Z)=-C*Z*K(2/3,ZTA) -C C=1.0/(PI*SQRT(3.0)) -C ZTA=(2/3)*Z**(3/2) -C -C WITH THE POWER SERIES FOR CABS(Z).LE.1.0. -C -C IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- -C MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES -C OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF -C THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR), -C THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR -C FLAG IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS -C DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. -C ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN -C ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT -C FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE -C LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA -C MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, -C AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE -C PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE -C PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT- -C ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG- -C NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN -C DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN -C EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, -C NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE -C PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER -C MACHINES. -C -C THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX -C BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT -C ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- -C SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE -C ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), -C ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF -C CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY -C HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN -C ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY -C SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER -C THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, -C 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS -C THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER -C COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY -C BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER -C COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE -C MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, -C THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, -C OR -PI/2+P. -C -C***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ -C AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF -C COMMERCE, 1955. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 -C -C A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- -C 1018, MAY, 1985 -C -C A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. -C MATH. SOFTWARE, 1986 -C -C***ROUTINES CALLED ZACAI,ZBKNU,AZEXP,AZSQRT,I1MACH,D1MACH -C***END PROLOGUE ZAIRY -C COMPLEX AI,CONE,CSQ,CY,S1,S2,TRM1,TRM2,Z,ZTA,Z3 - DOUBLE PRECISION AA, AD, AII, AIR, AK, ALIM, ATRM, AZ, AZ3, BK, - * CC, CK, COEF, CONEI, CONER, CSQI, CSQR, CYI, CYR, C1, C2, DIG, - * DK, D1, D2, ELIM, FID, FNU, PTR, RL, R1M5, SFAC, STI, STR, - * S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I, TRM2R, TTH, ZEROI, - * ZEROR, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, D1MACH, AZABS, ALAZ, BB - INTEGER ID, IERR, IFLAG, K, KODE, K1, K2, MR, NN, NZ, I1MACH - DIMENSION CYR(1), CYI(1) - DATA TTH, C1, C2, COEF /6.66666666666666667D-01, - * 3.55028053887817240D-01,2.58819403792806799D-01, - * 1.83776298473930683D-01/ - DATA ZEROR, ZEROI, CONER, CONEI /0.0D0,0.0D0,1.0D0,0.0D0/ -C***FIRST EXECUTABLE STATEMENT ZAIRY - IERR = 0 - NZ=0 - IF (ID.LT.0 .OR. ID.GT.1) IERR=1 - IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 - IF (IERR.NE.0) RETURN - AZ = AZABS(ZR,ZI) - TOL = DMAX1(D1MACH(4),1.0D-18) - FID = DBLE(FLOAT(ID)) - IF (AZ.GT.1.0D0) GO TO 70 -C----------------------------------------------------------------------- -C POWER SERIES FOR CABS(Z).LE.1. -C----------------------------------------------------------------------- - S1R = CONER - S1I = CONEI - S2R = CONER - S2I = CONEI - IF (AZ.LT.TOL) GO TO 170 - AA = AZ*AZ - IF (AA.LT.TOL/AZ) GO TO 40 - TRM1R = CONER - TRM1I = CONEI - TRM2R = CONER - TRM2I = CONEI - ATRM = 1.0D0 - STR = ZR*ZR - ZI*ZI - STI = ZR*ZI + ZI*ZR - Z3R = STR*ZR - STI*ZI - Z3I = STR*ZI + STI*ZR - AZ3 = AZ*AA - AK = 2.0D0 + FID - BK = 3.0D0 - FID - FID - CK = 4.0D0 - FID - DK = 3.0D0 + FID + FID - D1 = AK*DK - D2 = BK*CK - AD = DMIN1(D1,D2) - AK = 24.0D0 + 9.0D0*FID - BK = 30.0D0 - 9.0D0*FID - DO 30 K=1,25 - STR = (TRM1R*Z3R-TRM1I*Z3I)/D1 - TRM1I = (TRM1R*Z3I+TRM1I*Z3R)/D1 - TRM1R = STR - S1R = S1R + TRM1R - S1I = S1I + TRM1I - STR = (TRM2R*Z3R-TRM2I*Z3I)/D2 - TRM2I = (TRM2R*Z3I+TRM2I*Z3R)/D2 - TRM2R = STR - S2R = S2R + TRM2R - S2I = S2I + TRM2I - ATRM = ATRM*AZ3/AD - D1 = D1 + AK - D2 = D2 + BK - AD = DMIN1(D1,D2) - IF (ATRM.LT.TOL*AD) GO TO 40 - AK = AK + 18.0D0 - BK = BK + 18.0D0 - 30 CONTINUE - 40 CONTINUE - IF (ID.EQ.1) GO TO 50 - AIR = S1R*C1 - C2*(ZR*S2R-ZI*S2I) - AII = S1I*C1 - C2*(ZR*S2I+ZI*S2R) - IF (KODE.EQ.1) RETURN - CALL AZSQRT(ZR, ZI, STR, STI) - ZTAR = TTH*(ZR*STR-ZI*STI) - ZTAI = TTH*(ZR*STI+ZI*STR) - CALL AZEXP(ZTAR, ZTAI, STR, STI) - PTR = AIR*STR - AII*STI - AII = AIR*STI + AII*STR - AIR = PTR - RETURN - 50 CONTINUE - AIR = -S2R*C2 - AII = -S2I*C2 - IF (AZ.LE.TOL) GO TO 60 - STR = ZR*S1R - ZI*S1I - STI = ZR*S1I + ZI*S1R - CC = C1/(1.0D0+FID) - AIR = AIR + CC*(STR*ZR-STI*ZI) - AII = AII + CC*(STR*ZI+STI*ZR) - 60 CONTINUE - IF (KODE.EQ.1) RETURN - CALL AZSQRT(ZR, ZI, STR, STI) - ZTAR = TTH*(ZR*STR-ZI*STI) - ZTAI = TTH*(ZR*STI+ZI*STR) - CALL AZEXP(ZTAR, ZTAI, STR, STI) - PTR = STR*AIR - STI*AII - AII = STR*AII + STI*AIR - AIR = PTR - RETURN -C----------------------------------------------------------------------- -C CASE FOR CABS(Z).GT.1.0 -C----------------------------------------------------------------------- - 70 CONTINUE - FNU = (1.0D0+FID)/3.0D0 -C----------------------------------------------------------------------- -C SET PARAMETERS RELATED TO MACHINE CONSTANTS. -C TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0D-18. -C ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. -C EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND -C EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR -C UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. -C RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. -C DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). -C----------------------------------------------------------------------- - K1 = I1MACH(15) - K2 = I1MACH(16) - R1M5 = D1MACH(5) - K = MIN0(IABS(K1),IABS(K2)) - ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) - K1 = I1MACH(14) - 1 - AA = R1M5*DBLE(FLOAT(K1)) - DIG = DMIN1(AA,18.0D0) - AA = AA*2.303D0 - ALIM = ELIM + DMAX1(-AA,-41.45D0) - RL = 1.2D0*DIG + 3.0D0 - ALAZ = DLOG(AZ) -C-------------------------------------------------------------------------- -C TEST FOR PROPER RANGE -C----------------------------------------------------------------------- - AA=0.5D0/TOL - BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 - AA=DMIN1(AA,BB) - AA=AA**TTH - IF (AZ.GT.AA) GO TO 260 - AA=DSQRT(AA) - IF (AZ.GT.AA) IERR=3 - CALL AZSQRT(ZR, ZI, CSQR, CSQI) - ZTAR = TTH*(ZR*CSQR-ZI*CSQI) - ZTAI = TTH*(ZR*CSQI+ZI*CSQR) -C----------------------------------------------------------------------- -C RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL -C----------------------------------------------------------------------- - IFLAG = 0 - SFAC = 1.0D0 - AK = ZTAI - IF (ZR.GE.0.0D0) GO TO 80 - BK = ZTAR - CK = -DABS(BK) - ZTAR = CK - ZTAI = AK - 80 CONTINUE - IF (ZI.NE.0.0D0) GO TO 90 - IF (ZR.GT.0.0D0) GO TO 90 - ZTAR = 0.0D0 - ZTAI = AK - 90 CONTINUE - AA = ZTAR - IF (AA.GE.0.0D0 .AND. ZR.GT.0.0D0) GO TO 110 - IF (KODE.EQ.2) GO TO 100 -C----------------------------------------------------------------------- -C OVERFLOW TEST -C----------------------------------------------------------------------- - IF (AA.GT.(-ALIM)) GO TO 100 - AA = -AA + 0.25D0*ALAZ - IFLAG = 1 - SFAC = TOL - IF (AA.GT.ELIM) GO TO 270 - 100 CONTINUE -C----------------------------------------------------------------------- -C CBKNU AND CACON RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2 -C----------------------------------------------------------------------- - MR = 1 - IF (ZI.LT.0.0D0) MR = -1 - CALL ZACAI(ZTAR, ZTAI, FNU, KODE, MR, 1, CYR, CYI, NN, RL, TOL, - * ELIM, ALIM) - IF (NN.LT.0) GO TO 280 - NZ = NZ + NN - GO TO 130 - 110 CONTINUE - IF (KODE.EQ.2) GO TO 120 -C----------------------------------------------------------------------- -C UNDERFLOW TEST -C----------------------------------------------------------------------- - IF (AA.LT.ALIM) GO TO 120 - AA = -AA - 0.25D0*ALAZ - IFLAG = 2 - SFAC = 1.0D0/TOL - IF (AA.LT.(-ELIM)) GO TO 210 - 120 CONTINUE - CALL ZBKNU(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, TOL, ELIM, - * ALIM) - 130 CONTINUE - S1R = CYR(1)*COEF - S1I = CYI(1)*COEF - IF (IFLAG.NE.0) GO TO 150 - IF (ID.EQ.1) GO TO 140 - AIR = CSQR*S1R - CSQI*S1I - AII = CSQR*S1I + CSQI*S1R - RETURN - 140 CONTINUE - AIR = -(ZR*S1R-ZI*S1I) - AII = -(ZR*S1I+ZI*S1R) - RETURN - 150 CONTINUE - S1R = S1R*SFAC - S1I = S1I*SFAC - IF (ID.EQ.1) GO TO 160 - STR = S1R*CSQR - S1I*CSQI - S1I = S1R*CSQI + S1I*CSQR - S1R = STR - AIR = S1R/SFAC - AII = S1I/SFAC - RETURN - 160 CONTINUE - STR = -(S1R*ZR-S1I*ZI) - S1I = -(S1R*ZI+S1I*ZR) - S1R = STR - AIR = S1R/SFAC - AII = S1I/SFAC - RETURN - 170 CONTINUE - AA = 1.0D+3*D1MACH(1) - S1R = ZEROR - S1I = ZEROI - IF (ID.EQ.1) GO TO 190 - IF (AZ.LE.AA) GO TO 180 - S1R = C2*ZR - S1I = C2*ZI - 180 CONTINUE - AIR = C1 - S1R - AII = -S1I - RETURN - 190 CONTINUE - AIR = -C2 - AII = 0.0D0 - AA = DSQRT(AA) - IF (AZ.LE.AA) GO TO 200 - S1R = 0.5D0*(ZR*ZR-ZI*ZI) - S1I = ZR*ZI - 200 CONTINUE - AIR = AIR + C1*S1R - AII = AII + C1*S1I - RETURN - 210 CONTINUE - NZ = 1 - AIR = ZEROR - AII = ZEROI - RETURN - 270 CONTINUE - NZ = 0 - IERR=2 - RETURN - 280 CONTINUE - IF(NN.EQ.(-1)) GO TO 270 - NZ=0 - IERR=5 - RETURN - 260 CONTINUE - IERR=4 - NZ=0 - RETURN - END diff --git a/amos/zasyi.f b/amos/zasyi.f deleted file mode 100644 index 578136f..0000000 --- a/amos/zasyi.f +++ /dev/null @@ -1,165 +0,0 @@ - SUBROUTINE ZASYI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, - * ALIM) -C***BEGIN PROLOGUE ZASYI -C***REFER TO ZBESI,ZBESK -C -C ZASYI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY -C MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE -C REGION CABS(Z).GT.MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL RETURN. -C NZ.LT.0 INDICATES AN OVERFLOW ON KODE=1. -C -C***ROUTINES CALLED D1MACH,AZABS,ZDIV,AZEXP,ZMLT,AZSQRT -C***END PROLOGUE ZASYI -C COMPLEX AK1,CK,CONE,CS1,CS2,CZ,CZERO,DK,EZ,P1,RZ,S2,Y,Z - DOUBLE PRECISION AA, AEZ, AK, AK1I, AK1R, ALIM, ARG, ARM, ATOL, - * AZ, BB, BK, CKI, CKR, CONEI, CONER, CS1I, CS1R, CS2I, CS2R, CZI, - * CZR, DFNU, DKI, DKR, DNU2, ELIM, EZI, EZR, FDN, FNU, PI, P1I, - * P1R, RAZ, RL, RTPI, RTR1, RZI, RZR, S, SGN, SQK, STI, STR, S2I, - * S2R, TOL, TZI, TZR, YI, YR, ZEROI, ZEROR, ZI, ZR, D1MACH, AZABS - INTEGER I, IB, IL, INU, J, JL, K, KODE, KODED, M, N, NN, NZ - DIMENSION YR(N), YI(N) - DATA PI, RTPI /3.14159265358979324D0 , 0.159154943091895336D0 / - DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / -C - NZ = 0 - AZ = AZABS(ZR,ZI) - ARM = 1.0D+3*D1MACH(1) - RTR1 = DSQRT(ARM) - IL = MIN0(2,N) - DFNU = FNU + DBLE(FLOAT(N-IL)) -C----------------------------------------------------------------------- -C OVERFLOW TEST -C----------------------------------------------------------------------- - RAZ = 1.0D0/AZ - STR = ZR*RAZ - STI = -ZI*RAZ - AK1R = RTPI*STR*RAZ - AK1I = RTPI*STI*RAZ - CALL AZSQRT(AK1R, AK1I, AK1R, AK1I) - CZR = ZR - CZI = ZI - IF (KODE.NE.2) GO TO 10 - CZR = ZEROR - CZI = ZI - 10 CONTINUE - IF (DABS(CZR).GT.ELIM) GO TO 100 - DNU2 = DFNU + DFNU - KODED = 1 - IF ((DABS(CZR).GT.ALIM) .AND. (N.GT.2)) GO TO 20 - KODED = 0 - CALL AZEXP(CZR, CZI, STR, STI) - CALL ZMLT(AK1R, AK1I, STR, STI, AK1R, AK1I) - 20 CONTINUE - FDN = 0.0D0 - IF (DNU2.GT.RTR1) FDN = DNU2*DNU2 - EZR = ZR*8.0D0 - EZI = ZI*8.0D0 -C----------------------------------------------------------------------- -C WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE -C FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE -C EXPANSION FOR THE IMAGINARY PART. -C----------------------------------------------------------------------- - AEZ = 8.0D0*AZ - S = TOL/AEZ - JL = INT(SNGL(RL+RL)) + 2 - P1R = ZEROR - P1I = ZEROI - IF (ZI.EQ.0.0D0) GO TO 30 -C----------------------------------------------------------------------- -C CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF -C SIGNIFICANCE WHEN FNU OR N IS LARGE -C----------------------------------------------------------------------- - INU = INT(SNGL(FNU)) - ARG = (FNU-DBLE(FLOAT(INU)))*PI - INU = INU + N - IL - AK = -DSIN(ARG) - BK = DCOS(ARG) - IF (ZI.LT.0.0D0) BK = -BK - P1R = AK - P1I = BK - IF (MOD(INU,2).EQ.0) GO TO 30 - P1R = -P1R - P1I = -P1I - 30 CONTINUE - DO 70 K=1,IL - SQK = FDN - 1.0D0 - ATOL = S*DABS(SQK) - SGN = 1.0D0 - CS1R = CONER - CS1I = CONEI - CS2R = CONER - CS2I = CONEI - CKR = CONER - CKI = CONEI - AK = 0.0D0 - AA = 1.0D0 - BB = AEZ - DKR = EZR - DKI = EZI - DO 40 J=1,JL - CALL ZDIV(CKR, CKI, DKR, DKI, STR, STI) - CKR = STR*SQK - CKI = STI*SQK - CS2R = CS2R + CKR - CS2I = CS2I + CKI - SGN = -SGN - CS1R = CS1R + CKR*SGN - CS1I = CS1I + CKI*SGN - DKR = DKR + EZR - DKI = DKI + EZI - AA = AA*DABS(SQK)/BB - BB = BB + AEZ - AK = AK + 8.0D0 - SQK = SQK - AK - IF (AA.LE.ATOL) GO TO 50 - 40 CONTINUE - GO TO 110 - 50 CONTINUE - S2R = CS1R - S2I = CS1I - IF (ZR+ZR.GE.ELIM) GO TO 60 - TZR = ZR + ZR - TZI = ZI + ZI - CALL AZEXP(-TZR, -TZI, STR, STI) - CALL ZMLT(STR, STI, P1R, P1I, STR, STI) - CALL ZMLT(STR, STI, CS2R, CS2I, STR, STI) - S2R = S2R + STR - S2I = S2I + STI - 60 CONTINUE - FDN = FDN + 8.0D0*DFNU + 4.0D0 - P1R = -P1R - P1I = -P1I - M = N - IL + K - YR(M) = S2R*AK1R - S2I*AK1I - YI(M) = S2R*AK1I + S2I*AK1R - 70 CONTINUE - IF (N.LE.2) RETURN - NN = N - K = NN - 2 - AK = DBLE(FLOAT(K)) - STR = ZR*RAZ - STI = -ZI*RAZ - RZR = (STR+STR)*RAZ - RZI = (STI+STI)*RAZ - IB = 3 - DO 80 I=IB,NN - YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2) - YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2) - AK = AK - 1.0D0 - K = K - 1 - 80 CONTINUE - IF (KODED.EQ.0) RETURN - CALL AZEXP(CZR, CZI, CKR, CKI) - DO 90 I=1,NN - STR = YR(I)*CKR - YI(I)*CKI - YI(I) = YR(I)*CKI + YI(I)*CKR - YR(I) = STR - 90 CONTINUE - RETURN - 100 CONTINUE - NZ = -1 - RETURN - 110 CONTINUE - NZ=-2 - RETURN - END diff --git a/amos/zbesh.f b/amos/zbesh.f deleted file mode 100644 index 5aacecf..0000000 --- a/amos/zbesh.f +++ /dev/null @@ -1,348 +0,0 @@ - SUBROUTINE ZBESH(ZR, ZI, FNU, KODE, M, N, CYR, CYI, NZ, IERR) -C***BEGIN PROLOGUE ZBESH -C***DATE WRITTEN 830501 (YYMMDD) -C***REVISION DATE 890801 (YYMMDD) -C***CATEGORY NO. B5K -C***KEYWORDS H-BESSEL FUNCTIONS,BESSEL FUNCTIONS OF COMPLEX ARGUMENT, -C BESSEL FUNCTIONS OF THIRD KIND,HANKEL FUNCTIONS -C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES -C***PURPOSE TO COMPUTE THE H-BESSEL FUNCTIONS OF A COMPLEX ARGUMENT -C***DESCRIPTION -C -C ***A DOUBLE PRECISION ROUTINE*** -C ON KODE=1, ZBESH COMPUTES AN N MEMBER SEQUENCE OF COMPLEX -C HANKEL (BESSEL) FUNCTIONS CY(J)=H(M,FNU+J-1,Z) FOR KINDS M=1 -C OR 2, REAL, NONNEGATIVE ORDERS FNU+J-1, J=1,...,N, AND COMPLEX -C Z.NE.CMPLX(0.0,0.0) IN THE CUT PLANE -PI.LT.ARG(Z).LE.PI. -C ON KODE=2, ZBESH RETURNS THE SCALED HANKEL FUNCTIONS -C -C CY(I)=EXP(-MM*Z*I)*H(M,FNU+J-1,Z) MM=3-2*M, I**2=-1. -C -C WHICH REMOVES THE EXPONENTIAL BEHAVIOR IN BOTH THE UPPER AND -C LOWER HALF PLANES. DEFINITIONS AND NOTATION ARE FOUND IN THE -C NBS HANDBOOK OF MATHEMATICAL FUNCTIONS (REF. 1). -C -C INPUT ZR,ZI,FNU ARE DOUBLE PRECISION -C ZR,ZI - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0), -C -PT.LT.ARG(Z).LE.PI -C FNU - ORDER OF INITIAL H FUNCTION, FNU.GE.0.0D0 -C KODE - A PARAMETER TO INDICATE THE SCALING OPTION -C KODE= 1 RETURNS -C CY(J)=H(M,FNU+J-1,Z), J=1,...,N -C = 2 RETURNS -C CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M)) -C J=1,...,N , I**2=-1 -C M - KIND OF HANKEL FUNCTION, M=1 OR 2 -C N - NUMBER OF MEMBERS IN THE SEQUENCE, N.GE.1 -C -C OUTPUT CYR,CYI ARE DOUBLE PRECISION -C CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS -C CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE -C CY(J)=H(M,FNU+J-1,Z) OR -C CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M)) J=1,...,N -C DEPENDING ON KODE, I**2=-1. -C NZ - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW, -C NZ= 0 , NORMAL RETURN -C NZ.GT.0 , FIRST NZ COMPONENTS OF CY SET TO ZERO DUE -C TO UNDERFLOW, CY(J)=CMPLX(0.0D0,0.0D0) -C J=1,...,NZ WHEN Y.GT.0.0 AND M=1 OR -C Y.LT.0.0 AND M=2. FOR THE COMPLMENTARY -C HALF PLANES, NZ STATES ONLY THE NUMBER -C OF UNDERFLOWS. -C IERR - ERROR FLAG -C IERR=0, NORMAL RETURN - COMPUTATION COMPLETED -C IERR=1, INPUT ERROR - NO COMPUTATION -C IERR=2, OVERFLOW - NO COMPUTATION, FNU TOO -C LARGE OR CABS(Z) TOO SMALL OR BOTH -C IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE -C BUT LOSSES OF SIGNIFCANCE BY ARGUMENT -C REDUCTION PRODUCE LESS THAN HALF OF MACHINE -C ACCURACY -C IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA- -C TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI- -C CANCE BY ARGUMENT REDUCTION -C IERR=5, ERROR - NO COMPUTATION, -C ALGORITHM TERMINATION CONDITION NOT MET -C -C***LONG DESCRIPTION -C -C THE COMPUTATION IS CARRIED OUT BY THE RELATION -C -C H(M,FNU,Z)=(1/MP)*EXP(-MP*FNU)*K(FNU,Z*EXP(-MP)) -C MP=MM*HPI*I, MM=3-2*M, HPI=PI/2, I**2=-1 -C -C FOR M=1 OR 2 WHERE THE K BESSEL FUNCTION IS COMPUTED FOR THE -C RIGHT HALF PLANE RE(Z).GE.0.0. THE K FUNCTION IS CONTINUED -C TO THE LEFT HALF PLANE BY THE RELATION -C -C K(FNU,Z*EXP(MP)) = EXP(-MP*FNU)*K(FNU,Z)-MP*I(FNU,Z) -C MP=MR*PI*I, MR=+1 OR -1, RE(Z).GT.0, I**2=-1 -C -C WHERE I(FNU,Z) IS THE I BESSEL FUNCTION. -C -C EXPONENTIAL DECAY OF H(M,FNU,Z) OCCURS IN THE UPPER HALF Z -C PLANE FOR M=1 AND THE LOWER HALF Z PLANE FOR M=2. EXPONENTIAL -C GROWTH OCCURS IN THE COMPLEMENTARY HALF PLANES. SCALING -C BY EXP(-MM*Z*I) REMOVES THE EXPONENTIAL BEHAVIOR IN THE -C WHOLE Z PLANE FOR Z TO INFINITY. -C -C FOR NEGATIVE ORDERS,THE FORMULAE -C -C H(1,-FNU,Z) = H(1,FNU,Z)*CEXP( PI*FNU*I) -C H(2,-FNU,Z) = H(2,FNU,Z)*CEXP(-PI*FNU*I) -C I**2=-1 -C -C CAN BE USED. -C -C IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- -C MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS -C LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. -C CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN -C LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG -C IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS -C DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. -C IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS -C LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS -C MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE -C INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS -C RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3 -C ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION -C ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION -C ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN -C THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT -C TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS -C IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC. -C SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES. -C -C THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX -C BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT -C ROUNDOFF,1.0D-18) IS THE NOMINAL PRECISION AND 10**S REPRE- -C SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE -C ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), -C ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF -C CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY -C HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN -C ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY -C SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER -C THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, -C 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS -C THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER -C COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY -C BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER -C COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE -C MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, -C THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, -C OR -PI/2+P. -C -C***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ -C AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF -C COMMERCE, 1955. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C BY D. E. AMOS, SAND83-0083, MAY, 1983. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 -C -C A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- -C 1018, MAY, 1985 -C -C A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. -C MATH. SOFTWARE, 1986 -C -C***ROUTINES CALLED ZACON,ZBKNU,ZBUNK,ZUOIK,AZABS,I1MACH,D1MACH -C***END PROLOGUE ZBESH -C -C COMPLEX CY,Z,ZN,ZT,CSGN - DOUBLE PRECISION AA, ALIM, ALN, ARG, AZ, CYI, CYR, DIG, ELIM, - * FMM, FN, FNU, FNUL, HPI, RHPI, RL, R1M5, SGN, STR, TOL, UFL, ZI, - * ZNI, ZNR, ZR, ZTI, D1MACH, AZABS, BB, ASCLE, RTOL, ATOL, STI, - * CSGNR, CSGNI - INTEGER I, IERR, INU, INUH, IR, K, KODE, K1, K2, M, - * MM, MR, N, NN, NUF, NW, NZ, I1MACH - DIMENSION CYR(N), CYI(N) -C - DATA HPI /1.57079632679489662D0/ -C -C***FIRST EXECUTABLE STATEMENT ZBESH - IERR = 0 - NZ=0 - IF (ZR.EQ.0.0D0 .AND. ZI.EQ.0.0D0) IERR=1 - IF (FNU.LT.0.0D0) IERR=1 - IF (M.LT.1 .OR. M.GT.2) IERR=1 - IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 - IF (N.LT.1) IERR=1 - IF (IERR.NE.0) RETURN - NN = N -C----------------------------------------------------------------------- -C SET PARAMETERS RELATED TO MACHINE CONSTANTS. -C TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. -C ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. -C EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND -C EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR -C UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. -C RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. -C DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). -C FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU -C----------------------------------------------------------------------- - TOL = DMAX1(D1MACH(4),1.0D-18) - K1 = I1MACH(15) - K2 = I1MACH(16) - R1M5 = D1MACH(5) - K = MIN0(IABS(K1),IABS(K2)) - ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) - K1 = I1MACH(14) - 1 - AA = R1M5*DBLE(FLOAT(K1)) - DIG = DMIN1(AA,18.0D0) - AA = AA*2.303D0 - ALIM = ELIM + DMAX1(-AA,-41.45D0) - FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0) - RL = 1.2D0*DIG + 3.0D0 - FN = FNU + DBLE(FLOAT(NN-1)) - MM = 3 - M - M - FMM = DBLE(FLOAT(MM)) - ZNR = FMM*ZI - ZNI = -FMM*ZR -C----------------------------------------------------------------------- -C TEST FOR PROPER RANGE -C----------------------------------------------------------------------- - AZ = AZABS(ZR,ZI) - AA = 0.5D0/TOL - BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 - AA = DMIN1(AA,BB) - IF (AZ.GT.AA) GO TO 260 - IF (FN.GT.AA) GO TO 260 - AA = DSQRT(AA) - IF (AZ.GT.AA) IERR=3 - IF (FN.GT.AA) IERR=3 -C----------------------------------------------------------------------- -C OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE -C----------------------------------------------------------------------- - UFL = D1MACH(1)*1.0D+3 - IF (AZ.LT.UFL) GO TO 230 - IF (FNU.GT.FNUL) GO TO 90 - IF (FN.LE.1.0D0) GO TO 70 - IF (FN.GT.2.0D0) GO TO 60 - IF (AZ.GT.TOL) GO TO 70 - ARG = 0.5D0*AZ - ALN = -FN*DLOG(ARG) - IF (ALN.GT.ELIM) GO TO 230 - GO TO 70 - 60 CONTINUE - CALL ZUOIK(ZNR, ZNI, FNU, KODE, 2, NN, CYR, CYI, NUF, TOL, ELIM, - * ALIM) - IF (NUF.LT.0) GO TO 230 - NZ = NZ + NUF - NN = NN - NUF -C----------------------------------------------------------------------- -C HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1 ON RETURN FROM CUOIK -C IF NUF=NN, THEN CY(I)=CZERO FOR ALL I -C----------------------------------------------------------------------- - IF (NN.EQ.0) GO TO 140 - 70 CONTINUE - IF ((ZNR.LT.0.0D0) .OR. (ZNR.EQ.0.0D0 .AND. ZNI.LT.0.0D0 .AND. - * M.EQ.2)) GO TO 80 -C----------------------------------------------------------------------- -C RIGHT HALF PLANE COMPUTATION, XN.GE.0. .AND. (XN.NE.0. .OR. -C YN.GE.0. .OR. M=1) -C----------------------------------------------------------------------- - CALL ZBKNU(ZNR, ZNI, FNU, KODE, NN, CYR, CYI, NZ, TOL, ELIM, ALIM) - GO TO 110 -C----------------------------------------------------------------------- -C LEFT HALF PLANE COMPUTATION -C----------------------------------------------------------------------- - 80 CONTINUE - MR = -MM - CALL ZACON(ZNR, ZNI, FNU, KODE, MR, NN, CYR, CYI, NW, RL, FNUL, - * TOL, ELIM, ALIM) - IF (NW.LT.0) GO TO 240 - NZ=NW - GO TO 110 - 90 CONTINUE -C----------------------------------------------------------------------- -C UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL -C----------------------------------------------------------------------- - MR = 0 - IF ((ZNR.GE.0.0D0) .AND. (ZNR.NE.0.0D0 .OR. ZNI.GE.0.0D0 .OR. - * M.NE.2)) GO TO 100 - MR = -MM - IF (ZNR.NE.0.0D0 .OR. ZNI.GE.0.0D0) GO TO 100 - ZNR = -ZNR - ZNI = -ZNI - 100 CONTINUE - CALL ZBUNK(ZNR, ZNI, FNU, KODE, MR, NN, CYR, CYI, NW, TOL, ELIM, - * ALIM) - IF (NW.LT.0) GO TO 240 - NZ = NZ + NW - 110 CONTINUE -C----------------------------------------------------------------------- -C H(M,FNU,Z) = -FMM*(I/HPI)*(ZT**FNU)*K(FNU,-Z*ZT) -C -C ZT=EXP(-FMM*HPI*I) = CMPLX(0.0,-FMM), FMM=3-2*M, M=1,2 -C----------------------------------------------------------------------- - SGN = DSIGN(HPI,-FMM) -C----------------------------------------------------------------------- -C CALCULATE EXP(FNU*HPI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE -C WHEN FNU IS LARGE -C----------------------------------------------------------------------- - INU = INT(SNGL(FNU)) - INUH = INU/2 - IR = INU - 2*INUH - ARG = (FNU-DBLE(FLOAT(INU-IR)))*SGN - RHPI = 1.0D0/SGN -C ZNI = RHPI*DCOS(ARG) -C ZNR = -RHPI*DSIN(ARG) - CSGNI = RHPI*DCOS(ARG) - CSGNR = -RHPI*DSIN(ARG) - IF (MOD(INUH,2).EQ.0) GO TO 120 -C ZNR = -ZNR -C ZNI = -ZNI - CSGNR = -CSGNR - CSGNI = -CSGNI - 120 CONTINUE - ZTI = -FMM - RTOL = 1.0D0/TOL - ASCLE = UFL*RTOL - DO 130 I=1,NN -C STR = CYR(I)*ZNR - CYI(I)*ZNI -C CYI(I) = CYR(I)*ZNI + CYI(I)*ZNR -C CYR(I) = STR -C STR = -ZNI*ZTI -C ZNI = ZNR*ZTI -C ZNR = STR - AA = CYR(I) - BB = CYI(I) - ATOL = 1.0D0 - IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 135 - AA = AA*RTOL - BB = BB*RTOL - ATOL = TOL - 135 CONTINUE - STR = AA*CSGNR - BB*CSGNI - STI = AA*CSGNI + BB*CSGNR - CYR(I) = STR*ATOL - CYI(I) = STI*ATOL - STR = -CSGNI*ZTI - CSGNI = CSGNR*ZTI - CSGNR = STR - 130 CONTINUE - RETURN - 140 CONTINUE - IF (ZNR.LT.0.0D0) GO TO 230 - RETURN - 230 CONTINUE - NZ=0 - IERR=2 - RETURN - 240 CONTINUE - IF(NW.EQ.(-1)) GO TO 230 - NZ=0 - IERR=5 - RETURN - 260 CONTINUE - NZ=0 - IERR=4 - RETURN - END diff --git a/amos/zbesi.f b/amos/zbesi.f deleted file mode 100644 index a2ddd8c..0000000 --- a/amos/zbesi.f +++ /dev/null @@ -1,269 +0,0 @@ - SUBROUTINE ZBESI(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR) -C***BEGIN PROLOGUE ZBESI -C***DATE WRITTEN 830501 (YYMMDD) -C***REVISION DATE 890801 (YYMMDD) -C***CATEGORY NO. B5K -C***KEYWORDS I-BESSEL FUNCTION,COMPLEX BESSEL FUNCTION, -C MODIFIED BESSEL FUNCTION OF THE FIRST KIND -C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES -C***PURPOSE TO COMPUTE I-BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C***DESCRIPTION -C -C ***A DOUBLE PRECISION ROUTINE*** -C ON KODE=1, ZBESI COMPUTES AN N MEMBER SEQUENCE OF COMPLEX -C BESSEL FUNCTIONS CY(J)=I(FNU+J-1,Z) FOR REAL, NONNEGATIVE -C ORDERS FNU+J-1, J=1,...,N AND COMPLEX Z IN THE CUT PLANE -C -PI.LT.ARG(Z).LE.PI. ON KODE=2, ZBESI RETURNS THE SCALED -C FUNCTIONS -C -C CY(J)=EXP(-ABS(X))*I(FNU+J-1,Z) J = 1,...,N , X=REAL(Z) -C -C WITH THE EXPONENTIAL GROWTH REMOVED IN BOTH THE LEFT AND -C RIGHT HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION -C ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS -C (REF. 1). -C -C INPUT ZR,ZI,FNU ARE DOUBLE PRECISION -C ZR,ZI - Z=CMPLX(ZR,ZI), -PI.LT.ARG(Z).LE.PI -C FNU - ORDER OF INITIAL I FUNCTION, FNU.GE.0.0D0 -C KODE - A PARAMETER TO INDICATE THE SCALING OPTION -C KODE= 1 RETURNS -C CY(J)=I(FNU+J-1,Z), J=1,...,N -C = 2 RETURNS -C CY(J)=I(FNU+J-1,Z)*EXP(-ABS(X)), J=1,...,N -C N - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1 -C -C OUTPUT CYR,CYI ARE DOUBLE PRECISION -C CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS -C CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE -C CY(J)=I(FNU+J-1,Z) OR -C CY(J)=I(FNU+J-1,Z)*EXP(-ABS(X)) J=1,...,N -C DEPENDING ON KODE, X=REAL(Z) -C NZ - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW, -C NZ= 0 , NORMAL RETURN -C NZ.GT.0 , LAST NZ COMPONENTS OF CY SET TO ZERO -C TO UNDERFLOW, CY(J)=CMPLX(0.0D0,0.0D0) -C J = N-NZ+1,...,N -C IERR - ERROR FLAG -C IERR=0, NORMAL RETURN - COMPUTATION COMPLETED -C IERR=1, INPUT ERROR - NO COMPUTATION -C IERR=2, OVERFLOW - NO COMPUTATION, REAL(Z) TOO -C LARGE ON KODE=1 -C IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE -C BUT LOSSES OF SIGNIFCANCE BY ARGUMENT -C REDUCTION PRODUCE LESS THAN HALF OF MACHINE -C ACCURACY -C IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA- -C TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI- -C CANCE BY ARGUMENT REDUCTION -C IERR=5, ERROR - NO COMPUTATION, -C ALGORITHM TERMINATION CONDITION NOT MET -C -C***LONG DESCRIPTION -C -C THE COMPUTATION IS CARRIED OUT BY THE POWER SERIES FOR -C SMALL CABS(Z), THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z), -C THE MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN AND A -C NEUMANN SERIES FOR IMTERMEDIATE MAGNITUDES, AND THE -C UNIFORM ASYMPTOTIC EXPANSIONS FOR I(FNU,Z) AND J(FNU,Z) -C FOR LARGE ORDERS. BACKWARD RECURRENCE IS USED TO GENERATE -C SEQUENCES OR REDUCE ORDERS WHEN NECESSARY. -C -C THE CALCULATIONS ABOVE ARE DONE IN THE RIGHT HALF PLANE AND -C CONTINUED INTO THE LEFT HALF PLANE BY THE FORMULA -C -C I(FNU,Z*EXP(M*PI)) = EXP(M*PI*FNU)*I(FNU,Z) REAL(Z).GT.0.0 -C M = +I OR -I, I**2=-1 -C -C FOR NEGATIVE ORDERS,THE FORMULA -C -C I(-FNU,Z) = I(FNU,Z) + (2/PI)*SIN(PI*FNU)*K(FNU,Z) -C -C CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO INTEGERS, THE -C THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE POSITIVE -C INTEGER,THE MAGNITUDE OF I(-FNU,Z)=I(FNU,Z) IS A LARGE -C NEGATIVE POWER OF TEN. BUT WHEN FNU IS NOT AN INTEGER, -C K(FNU,Z) DOMINATES IN MAGNITUDE WITH A LARGE POSITIVE POWER OF -C TEN AND THE MOST THAT THE SECOND TERM CAN BE REDUCED IS BY -C UNIT ROUNDOFF FROM THE COEFFICIENT. THUS, WIDE CHANGES CAN -C OCCUR WITHIN UNIT ROUNDOFF OF A LARGE INTEGER FOR FNU. HERE, -C LARGE MEANS FNU.GT.CABS(Z). -C -C IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- -C MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS -C LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. -C CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN -C LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG -C IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS -C DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. -C IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS -C LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS -C MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE -C INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS -C RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3 -C ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION -C ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION -C ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN -C THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT -C TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS -C IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC. -C SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES. -C -C THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX -C BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT -C ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- -C SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE -C ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), -C ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF -C CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY -C HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN -C ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY -C SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER -C THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, -C 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS -C THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER -C COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY -C BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER -C COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE -C MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, -C THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, -C OR -PI/2+P. -C -C***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ -C AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF -C COMMERCE, 1955. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C BY D. E. AMOS, SAND83-0083, MAY, 1983. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 -C -C A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- -C 1018, MAY, 1985 -C -C A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. -C MATH. SOFTWARE, 1986 -C -C***ROUTINES CALLED ZBINU,I1MACH,D1MACH -C***END PROLOGUE ZBESI -C COMPLEX CONE,CSGN,CW,CY,CZERO,Z,ZN - DOUBLE PRECISION AA, ALIM, ARG, CONEI, CONER, CSGNI, CSGNR, CYI, - * CYR, DIG, ELIM, FNU, FNUL, PI, RL, R1M5, STR, TOL, ZI, ZNI, ZNR, - * ZR, D1MACH, AZ, BB, FN, AZABS, ASCLE, RTOL, ATOL, STI - INTEGER I, IERR, INU, K, KODE, K1,K2,N,NZ,NN, I1MACH - DIMENSION CYR(N), CYI(N) - DATA PI /3.14159265358979324D0/ - DATA CONER, CONEI /1.0D0,0.0D0/ -C -C***FIRST EXECUTABLE STATEMENT ZBESI - IERR = 0 - NZ=0 - IF (FNU.LT.0.0D0) IERR=1 - IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 - IF (N.LT.1) IERR=1 - IF (IERR.NE.0) RETURN -C----------------------------------------------------------------------- -C SET PARAMETERS RELATED TO MACHINE CONSTANTS. -C TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. -C ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. -C EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND -C EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR -C UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. -C RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. -C DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). -C FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU. -C----------------------------------------------------------------------- - TOL = DMAX1(D1MACH(4),1.0D-18) - K1 = I1MACH(15) - K2 = I1MACH(16) - R1M5 = D1MACH(5) - K = MIN0(IABS(K1),IABS(K2)) - ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) - K1 = I1MACH(14) - 1 - AA = R1M5*DBLE(FLOAT(K1)) - DIG = DMIN1(AA,18.0D0) - AA = AA*2.303D0 - ALIM = ELIM + DMAX1(-AA,-41.45D0) - RL = 1.2D0*DIG + 3.0D0 - FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0) -C----------------------------------------------------------------------------- -C TEST FOR PROPER RANGE -C----------------------------------------------------------------------- - AZ = AZABS(ZR,ZI) - FN = FNU+DBLE(FLOAT(N-1)) - AA = 0.5D0/TOL - BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 - AA = DMIN1(AA,BB) - IF (AZ.GT.AA) GO TO 260 - IF (FN.GT.AA) GO TO 260 - AA = DSQRT(AA) - IF (AZ.GT.AA) IERR=3 - IF (FN.GT.AA) IERR=3 - ZNR = ZR - ZNI = ZI - CSGNR = CONER - CSGNI = CONEI - IF (ZR.GE.0.0D0) GO TO 40 - ZNR = -ZR - ZNI = -ZI -C----------------------------------------------------------------------- -C CALCULATE CSGN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE -C WHEN FNU IS LARGE -C----------------------------------------------------------------------- - INU = INT(SNGL(FNU)) - ARG = (FNU-DBLE(FLOAT(INU)))*PI - IF (ZI.LT.0.0D0) ARG = -ARG - CSGNR = DCOS(ARG) - CSGNI = DSIN(ARG) - IF (MOD(INU,2).EQ.0) GO TO 40 - CSGNR = -CSGNR - CSGNI = -CSGNI - 40 CONTINUE - CALL ZBINU(ZNR, ZNI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, TOL, - * ELIM, ALIM) - IF (NZ.LT.0) GO TO 120 - IF (ZR.GE.0.0D0) RETURN -C----------------------------------------------------------------------- -C ANALYTIC CONTINUATION TO THE LEFT HALF PLANE -C----------------------------------------------------------------------- - NN = N - NZ - IF (NN.EQ.0) RETURN - RTOL = 1.0D0/TOL - ASCLE = D1MACH(1)*RTOL*1.0D+3 - DO 50 I=1,NN -C STR = CYR(I)*CSGNR - CYI(I)*CSGNI -C CYI(I) = CYR(I)*CSGNI + CYI(I)*CSGNR -C CYR(I) = STR - AA = CYR(I) - BB = CYI(I) - ATOL = 1.0D0 - IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 55 - AA = AA*RTOL - BB = BB*RTOL - ATOL = TOL - 55 CONTINUE - STR = AA*CSGNR - BB*CSGNI - STI = AA*CSGNI + BB*CSGNR - CYR(I) = STR*ATOL - CYI(I) = STI*ATOL - CSGNR = -CSGNR - CSGNI = -CSGNI - 50 CONTINUE - RETURN - 120 CONTINUE - IF(NZ.EQ.(-2)) GO TO 130 - NZ = 0 - IERR=2 - RETURN - 130 CONTINUE - NZ=0 - IERR=5 - RETURN - 260 CONTINUE - NZ=0 - IERR=4 - RETURN - END diff --git a/amos/zbesj.f b/amos/zbesj.f deleted file mode 100644 index afe588f..0000000 --- a/amos/zbesj.f +++ /dev/null @@ -1,266 +0,0 @@ - SUBROUTINE ZBESJ(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR) -C***BEGIN PROLOGUE ZBESJ -C***DATE WRITTEN 830501 (YYMMDD) -C***REVISION DATE 890801 (YYMMDD) -C***CATEGORY NO. B5K -C***KEYWORDS J-BESSEL FUNCTION,BESSEL FUNCTION OF COMPLEX ARGUMENT, -C BESSEL FUNCTION OF FIRST KIND -C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES -C***PURPOSE TO COMPUTE THE J-BESSEL FUNCTION OF A COMPLEX ARGUMENT -C***DESCRIPTION -C -C ***A DOUBLE PRECISION ROUTINE*** -C ON KODE=1, CBESJ COMPUTES AN N MEMBER SEQUENCE OF COMPLEX -C BESSEL FUNCTIONS CY(I)=J(FNU+I-1,Z) FOR REAL, NONNEGATIVE -C ORDERS FNU+I-1, I=1,...,N AND COMPLEX Z IN THE CUT PLANE -C -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESJ RETURNS THE SCALED -C FUNCTIONS -C -C CY(I)=EXP(-ABS(Y))*J(FNU+I-1,Z) I = 1,...,N , Y=AIMAG(Z) -C -C WHICH REMOVE THE EXPONENTIAL GROWTH IN BOTH THE UPPER AND -C LOWER HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION -C ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS -C (REF. 1). -C -C INPUT ZR,ZI,FNU ARE DOUBLE PRECISION -C ZR,ZI - Z=CMPLX(ZR,ZI), -PI.LT.ARG(Z).LE.PI -C FNU - ORDER OF INITIAL J FUNCTION, FNU.GE.0.0D0 -C KODE - A PARAMETER TO INDICATE THE SCALING OPTION -C KODE= 1 RETURNS -C CY(I)=J(FNU+I-1,Z), I=1,...,N -C = 2 RETURNS -C CY(I)=J(FNU+I-1,Z)EXP(-ABS(Y)), I=1,...,N -C N - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1 -C -C OUTPUT CYR,CYI ARE DOUBLE PRECISION -C CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS -C CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE -C CY(I)=J(FNU+I-1,Z) OR -C CY(I)=J(FNU+I-1,Z)EXP(-ABS(Y)) I=1,...,N -C DEPENDING ON KODE, Y=AIMAG(Z). -C NZ - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW, -C NZ= 0 , NORMAL RETURN -C NZ.GT.0 , LAST NZ COMPONENTS OF CY SET ZERO DUE -C TO UNDERFLOW, CY(I)=CMPLX(0.0D0,0.0D0), -C I = N-NZ+1,...,N -C IERR - ERROR FLAG -C IERR=0, NORMAL RETURN - COMPUTATION COMPLETED -C IERR=1, INPUT ERROR - NO COMPUTATION -C IERR=2, OVERFLOW - NO COMPUTATION, AIMAG(Z) -C TOO LARGE ON KODE=1 -C IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE -C BUT LOSSES OF SIGNIFCANCE BY ARGUMENT -C REDUCTION PRODUCE LESS THAN HALF OF MACHINE -C ACCURACY -C IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA- -C TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI- -C CANCE BY ARGUMENT REDUCTION -C IERR=5, ERROR - NO COMPUTATION, -C ALGORITHM TERMINATION CONDITION NOT MET -C -C***LONG DESCRIPTION -C -C THE COMPUTATION IS CARRIED OUT BY THE FORMULA -C -C J(FNU,Z)=EXP( FNU*PI*I/2)*I(FNU,-I*Z) AIMAG(Z).GE.0.0 -C -C J(FNU,Z)=EXP(-FNU*PI*I/2)*I(FNU, I*Z) AIMAG(Z).LT.0.0 -C -C WHERE I**2 = -1 AND I(FNU,Z) IS THE I BESSEL FUNCTION. -C -C FOR NEGATIVE ORDERS,THE FORMULA -C -C J(-FNU,Z) = J(FNU,Z)*COS(PI*FNU) - Y(FNU,Z)*SIN(PI*FNU) -C -C CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO INTEGERS, THE -C THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE POSITIVE -C INTEGER,THE MAGNITUDE OF J(-FNU,Z)=J(FNU,Z)*COS(PI*FNU) IS A -C LARGE NEGATIVE POWER OF TEN. BUT WHEN FNU IS NOT AN INTEGER, -C Y(FNU,Z) DOMINATES IN MAGNITUDE WITH A LARGE POSITIVE POWER OF -C TEN AND THE MOST THAT THE SECOND TERM CAN BE REDUCED IS BY -C UNIT ROUNDOFF FROM THE COEFFICIENT. THUS, WIDE CHANGES CAN -C OCCUR WITHIN UNIT ROUNDOFF OF A LARGE INTEGER FOR FNU. HERE, -C LARGE MEANS FNU.GT.CABS(Z). -C -C IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- -C MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS -C LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. -C CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN -C LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG -C IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS -C DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. -C IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS -C LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS -C MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE -C INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS -C RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3 -C ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION -C ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION -C ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN -C THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT -C TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS -C IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC. -C SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES. -C -C THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX -C BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT -C ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- -C SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE -C ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), -C ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF -C CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY -C HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN -C ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY -C SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER -C THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, -C 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS -C THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER -C COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY -C BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER -C COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE -C MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, -C THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, -C OR -PI/2+P. -C -C***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ -C AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF -C COMMERCE, 1955. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C BY D. E. AMOS, SAND83-0083, MAY, 1983. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 -C -C A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- -C 1018, MAY, 1985 -C -C A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. -C MATH. SOFTWARE, 1986 -C -C***ROUTINES CALLED ZBINU,I1MACH,D1MACH -C***END PROLOGUE ZBESJ -C -C COMPLEX CI,CSGN,CY,Z,ZN - DOUBLE PRECISION AA, ALIM, ARG, CII, CSGNI, CSGNR, CYI, CYR, DIG, - * ELIM, FNU, FNUL, HPI, RL, R1M5, STR, TOL, ZI, ZNI, ZNR, ZR, - * D1MACH, BB, FN, AZ, AZABS, ASCLE, RTOL, ATOL, STI - INTEGER I, IERR, INU, INUH, IR, K, KODE, K1, K2, N, NL, NZ, I1MACH - DIMENSION CYR(N), CYI(N) - DATA HPI /1.57079632679489662D0/ -C -C***FIRST EXECUTABLE STATEMENT ZBESJ - IERR = 0 - NZ=0 - IF (FNU.LT.0.0D0) IERR=1 - IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 - IF (N.LT.1) IERR=1 - IF (IERR.NE.0) RETURN -C----------------------------------------------------------------------- -C SET PARAMETERS RELATED TO MACHINE CONSTANTS. -C TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. -C ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. -C EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND -C EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR -C UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. -C RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. -C DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). -C FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU. -C----------------------------------------------------------------------- - TOL = DMAX1(D1MACH(4),1.0D-18) - K1 = I1MACH(15) - K2 = I1MACH(16) - R1M5 = D1MACH(5) - K = MIN0(IABS(K1),IABS(K2)) - ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) - K1 = I1MACH(14) - 1 - AA = R1M5*DBLE(FLOAT(K1)) - DIG = DMIN1(AA,18.0D0) - AA = AA*2.303D0 - ALIM = ELIM + DMAX1(-AA,-41.45D0) - RL = 1.2D0*DIG + 3.0D0 - FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0) -C----------------------------------------------------------------------- -C TEST FOR PROPER RANGE -C----------------------------------------------------------------------- - AZ = AZABS(ZR,ZI) - FN = FNU+DBLE(FLOAT(N-1)) - AA = 0.5D0/TOL - BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 - AA = DMIN1(AA,BB) - IF (AZ.GT.AA) GO TO 260 - IF (FN.GT.AA) GO TO 260 - AA = DSQRT(AA) - IF (AZ.GT.AA) IERR=3 - IF (FN.GT.AA) IERR=3 -C----------------------------------------------------------------------- -C CALCULATE CSGN=EXP(FNU*HPI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE -C WHEN FNU IS LARGE -C----------------------------------------------------------------------- - CII = 1.0D0 - INU = INT(SNGL(FNU)) - INUH = INU/2 - IR = INU - 2*INUH - ARG = (FNU-DBLE(FLOAT(INU-IR)))*HPI - CSGNR = DCOS(ARG) - CSGNI = DSIN(ARG) - IF (MOD(INUH,2).EQ.0) GO TO 40 - CSGNR = -CSGNR - CSGNI = -CSGNI - 40 CONTINUE -C----------------------------------------------------------------------- -C ZN IS IN THE RIGHT HALF PLANE -C----------------------------------------------------------------------- - ZNR = ZI - ZNI = -ZR - IF (ZI.GE.0.0D0) GO TO 50 - ZNR = -ZNR - ZNI = -ZNI - CSGNI = -CSGNI - CII = -CII - 50 CONTINUE - CALL ZBINU(ZNR, ZNI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, TOL, - * ELIM, ALIM) - IF (NZ.LT.0) GO TO 130 - NL = N - NZ - IF (NL.EQ.0) RETURN - RTOL = 1.0D0/TOL - ASCLE = D1MACH(1)*RTOL*1.0D+3 - DO 60 I=1,NL -C STR = CYR(I)*CSGNR - CYI(I)*CSGNI -C CYI(I) = CYR(I)*CSGNI + CYI(I)*CSGNR -C CYR(I) = STR - AA = CYR(I) - BB = CYI(I) - ATOL = 1.0D0 - IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 55 - AA = AA*RTOL - BB = BB*RTOL - ATOL = TOL - 55 CONTINUE - STR = AA*CSGNR - BB*CSGNI - STI = AA*CSGNI + BB*CSGNR - CYR(I) = STR*ATOL - CYI(I) = STI*ATOL - STR = -CSGNI*CII - CSGNI = CSGNR*CII - CSGNR = STR - 60 CONTINUE - RETURN - 130 CONTINUE - IF(NZ.EQ.(-2)) GO TO 140 - NZ = 0 - IERR = 2 - RETURN - 140 CONTINUE - NZ=0 - IERR=5 - RETURN - 260 CONTINUE - NZ=0 - IERR=4 - RETURN - END diff --git a/amos/zbesk.f b/amos/zbesk.f deleted file mode 100644 index cd8eeda..0000000 --- a/amos/zbesk.f +++ /dev/null @@ -1,281 +0,0 @@ - SUBROUTINE ZBESK(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR) -C***BEGIN PROLOGUE ZBESK -C***DATE WRITTEN 830501 (YYMMDD) -C***REVISION DATE 890801 (YYMMDD) -C***CATEGORY NO. B5K -C***KEYWORDS K-BESSEL FUNCTION,COMPLEX BESSEL FUNCTION, -C MODIFIED BESSEL FUNCTION OF THE SECOND KIND, -C BESSEL FUNCTION OF THE THIRD KIND -C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES -C***PURPOSE TO COMPUTE K-BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C***DESCRIPTION -C -C ***A DOUBLE PRECISION ROUTINE*** -C -C ON KODE=1, CBESK COMPUTES AN N MEMBER SEQUENCE OF COMPLEX -C BESSEL FUNCTIONS CY(J)=K(FNU+J-1,Z) FOR REAL, NONNEGATIVE -C ORDERS FNU+J-1, J=1,...,N AND COMPLEX Z.NE.CMPLX(0.0,0.0) -C IN THE CUT PLANE -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESK -C RETURNS THE SCALED K FUNCTIONS, -C -C CY(J)=EXP(Z)*K(FNU+J-1,Z) , J=1,...,N, -C -C WHICH REMOVE THE EXPONENTIAL BEHAVIOR IN BOTH THE LEFT AND -C RIGHT HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND -C NOTATION ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL -C FUNCTIONS (REF. 1). -C -C INPUT ZR,ZI,FNU ARE DOUBLE PRECISION -C ZR,ZI - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0), -C -PI.LT.ARG(Z).LE.PI -C FNU - ORDER OF INITIAL K FUNCTION, FNU.GE.0.0D0 -C N - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1 -C KODE - A PARAMETER TO INDICATE THE SCALING OPTION -C KODE= 1 RETURNS -C CY(I)=K(FNU+I-1,Z), I=1,...,N -C = 2 RETURNS -C CY(I)=K(FNU+I-1,Z)*EXP(Z), I=1,...,N -C -C OUTPUT CYR,CYI ARE DOUBLE PRECISION -C CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS -C CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE -C CY(I)=K(FNU+I-1,Z), I=1,...,N OR -C CY(I)=K(FNU+I-1,Z)*EXP(Z), I=1,...,N -C DEPENDING ON KODE -C NZ - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW. -C NZ= 0 , NORMAL RETURN -C NZ.GT.0 , FIRST NZ COMPONENTS OF CY SET TO ZERO DUE -C TO UNDERFLOW, CY(I)=CMPLX(0.0D0,0.0D0), -C I=1,...,N WHEN X.GE.0.0. WHEN X.LT.0.0 -C NZ STATES ONLY THE NUMBER OF UNDERFLOWS -C IN THE SEQUENCE. -C -C IERR - ERROR FLAG -C IERR=0, NORMAL RETURN - COMPUTATION COMPLETED -C IERR=1, INPUT ERROR - NO COMPUTATION -C IERR=2, OVERFLOW - NO COMPUTATION, FNU IS -C TOO LARGE OR CABS(Z) IS TOO SMALL OR BOTH -C IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE -C BUT LOSSES OF SIGNIFCANCE BY ARGUMENT -C REDUCTION PRODUCE LESS THAN HALF OF MACHINE -C ACCURACY -C IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA- -C TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI- -C CANCE BY ARGUMENT REDUCTION -C IERR=5, ERROR - NO COMPUTATION, -C ALGORITHM TERMINATION CONDITION NOT MET -C -C***LONG DESCRIPTION -C -C EQUATIONS OF THE REFERENCE ARE IMPLEMENTED FOR SMALL ORDERS -C DNU AND DNU+1.0 IN THE RIGHT HALF PLANE X.GE.0.0. FORWARD -C RECURRENCE GENERATES HIGHER ORDERS. K IS CONTINUED TO THE LEFT -C HALF PLANE BY THE RELATION -C -C K(FNU,Z*EXP(MP)) = EXP(-MP*FNU)*K(FNU,Z)-MP*I(FNU,Z) -C MP=MR*PI*I, MR=+1 OR -1, RE(Z).GT.0, I**2=-1 -C -C WHERE I(FNU,Z) IS THE I BESSEL FUNCTION. -C -C FOR LARGE ORDERS, FNU.GT.FNUL, THE K FUNCTION IS COMPUTED -C BY MEANS OF ITS UNIFORM ASYMPTOTIC EXPANSIONS. -C -C FOR NEGATIVE ORDERS, THE FORMULA -C -C K(-FNU,Z) = K(FNU,Z) -C -C CAN BE USED. -C -C CBESK ASSUMES THAT A SIGNIFICANT DIGIT SINH(X) FUNCTION IS -C AVAILABLE. -C -C IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- -C MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS -C LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. -C CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN -C LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG -C IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS -C DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. -C IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS -C LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS -C MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE -C INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS -C RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3 -C ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION -C ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION -C ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN -C THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT -C TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS -C IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC. -C SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES. -C -C THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX -C BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT -C ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- -C SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE -C ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), -C ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF -C CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY -C HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN -C ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY -C SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER -C THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, -C 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS -C THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER -C COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY -C BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER -C COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE -C MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, -C THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, -C OR -PI/2+P. -C -C***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ -C AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF -C COMMERCE, 1955. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C BY D. E. AMOS, SAND83-0083, MAY, 1983. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983. -C -C A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- -C 1018, MAY, 1985 -C -C A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. -C MATH. SOFTWARE, 1986 -C -C***ROUTINES CALLED ZACON,ZBKNU,ZBUNK,ZUOIK,AZABS,I1MACH,D1MACH -C***END PROLOGUE ZBESK -C -C COMPLEX CY,Z - DOUBLE PRECISION AA, ALIM, ALN, ARG, AZ, CYI, CYR, DIG, ELIM, FN, - * FNU, FNUL, RL, R1M5, TOL, UFL, ZI, ZR, D1MACH, AZABS, BB - INTEGER IERR, K, KODE, K1, K2, MR, N, NN, NUF, NW, NZ, I1MACH - DIMENSION CYR(N), CYI(N) -C***FIRST EXECUTABLE STATEMENT ZBESK - IERR = 0 - NZ=0 - IF (ZI.EQ.0.0E0 .AND. ZR.EQ.0.0E0) IERR=1 - IF (FNU.LT.0.0D0) IERR=1 - IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 - IF (N.LT.1) IERR=1 - IF (IERR.NE.0) RETURN - NN = N -C----------------------------------------------------------------------- -C SET PARAMETERS RELATED TO MACHINE CONSTANTS. -C TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. -C ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. -C EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND -C EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR -C UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. -C RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. -C DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). -C FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU -C----------------------------------------------------------------------- - TOL = DMAX1(D1MACH(4),1.0D-18) - K1 = I1MACH(15) - K2 = I1MACH(16) - R1M5 = D1MACH(5) - K = MIN0(IABS(K1),IABS(K2)) - ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) - K1 = I1MACH(14) - 1 - AA = R1M5*DBLE(FLOAT(K1)) - DIG = DMIN1(AA,18.0D0) - AA = AA*2.303D0 - ALIM = ELIM + DMAX1(-AA,-41.45D0) - FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0) - RL = 1.2D0*DIG + 3.0D0 -C----------------------------------------------------------------------------- -C TEST FOR PROPER RANGE -C----------------------------------------------------------------------- - AZ = AZABS(ZR,ZI) - FN = FNU + DBLE(FLOAT(NN-1)) - AA = 0.5D0/TOL - BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 - AA = DMIN1(AA,BB) - IF (AZ.GT.AA) GO TO 260 - IF (FN.GT.AA) GO TO 260 - AA = DSQRT(AA) - IF (AZ.GT.AA) IERR=3 - IF (FN.GT.AA) IERR=3 -C----------------------------------------------------------------------- -C OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE -C----------------------------------------------------------------------- -C UFL = DEXP(-ELIM) - UFL = D1MACH(1)*1.0D+3 - IF (AZ.LT.UFL) GO TO 180 - IF (FNU.GT.FNUL) GO TO 80 - IF (FN.LE.1.0D0) GO TO 60 - IF (FN.GT.2.0D0) GO TO 50 - IF (AZ.GT.TOL) GO TO 60 - ARG = 0.5D0*AZ - ALN = -FN*DLOG(ARG) - IF (ALN.GT.ELIM) GO TO 180 - GO TO 60 - 50 CONTINUE - CALL ZUOIK(ZR, ZI, FNU, KODE, 2, NN, CYR, CYI, NUF, TOL, ELIM, - * ALIM) - IF (NUF.LT.0) GO TO 180 - NZ = NZ + NUF - NN = NN - NUF -C----------------------------------------------------------------------- -C HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1 ON RETURN FROM CUOIK -C IF NUF=NN, THEN CY(I)=CZERO FOR ALL I -C----------------------------------------------------------------------- - IF (NN.EQ.0) GO TO 100 - 60 CONTINUE - IF (ZR.LT.0.0D0) GO TO 70 -C----------------------------------------------------------------------- -C RIGHT HALF PLANE COMPUTATION, REAL(Z).GE.0. -C----------------------------------------------------------------------- - CALL ZBKNU(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM) - IF (NW.LT.0) GO TO 200 - NZ=NW - RETURN -C----------------------------------------------------------------------- -C LEFT HALF PLANE COMPUTATION -C PI/2.LT.ARG(Z).LE.PI AND -PI.LT.ARG(Z).LT.-PI/2. -C----------------------------------------------------------------------- - 70 CONTINUE - IF (NZ.NE.0) GO TO 180 - MR = 1 - IF (ZI.LT.0.0D0) MR = -1 - CALL ZACON(ZR, ZI, FNU, KODE, MR, NN, CYR, CYI, NW, RL, FNUL, - * TOL, ELIM, ALIM) - IF (NW.LT.0) GO TO 200 - NZ=NW - RETURN -C----------------------------------------------------------------------- -C UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL -C----------------------------------------------------------------------- - 80 CONTINUE - MR = 0 - IF (ZR.GE.0.0D0) GO TO 90 - MR = 1 - IF (ZI.LT.0.0D0) MR = -1 - 90 CONTINUE - CALL ZBUNK(ZR, ZI, FNU, KODE, MR, NN, CYR, CYI, NW, TOL, ELIM, - * ALIM) - IF (NW.LT.0) GO TO 200 - NZ = NZ + NW - RETURN - 100 CONTINUE - IF (ZR.LT.0.0D0) GO TO 180 - RETURN - 180 CONTINUE - NZ = 0 - IERR=2 - RETURN - 200 CONTINUE - IF(NW.EQ.(-1)) GO TO 180 - NZ=0 - IERR=5 - RETURN - 260 CONTINUE - NZ=0 - IERR=4 - RETURN - END diff --git a/amos/zbesy.f b/amos/zbesy.f deleted file mode 100644 index 05ec40b..0000000 --- a/amos/zbesy.f +++ /dev/null @@ -1,244 +0,0 @@ - SUBROUTINE ZBESY(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, CWRKR, CWRKI, - * IERR) -C***BEGIN PROLOGUE ZBESY -C***DATE WRITTEN 830501 (YYMMDD) -C***REVISION DATE 890801 (YYMMDD) -C***CATEGORY NO. B5K -C***KEYWORDS Y-BESSEL FUNCTION,BESSEL FUNCTION OF COMPLEX ARGUMENT, -C BESSEL FUNCTION OF SECOND KIND -C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES -C***PURPOSE TO COMPUTE THE Y-BESSEL FUNCTION OF A COMPLEX ARGUMENT -C***DESCRIPTION -C -C ***A DOUBLE PRECISION ROUTINE*** -C -C ON KODE=1, CBESY COMPUTES AN N MEMBER SEQUENCE OF COMPLEX -C BESSEL FUNCTIONS CY(I)=Y(FNU+I-1,Z) FOR REAL, NONNEGATIVE -C ORDERS FNU+I-1, I=1,...,N AND COMPLEX Z IN THE CUT PLANE -C -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESY RETURNS THE SCALED -C FUNCTIONS -C -C CY(I)=EXP(-ABS(Y))*Y(FNU+I-1,Z) I = 1,...,N , Y=AIMAG(Z) -C -C WHICH REMOVE THE EXPONENTIAL GROWTH IN BOTH THE UPPER AND -C LOWER HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION -C ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS -C (REF. 1). -C -C INPUT ZR,ZI,FNU ARE DOUBLE PRECISION -C ZR,ZI - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0), -C -PI.LT.ARG(Z).LE.PI -C FNU - ORDER OF INITIAL Y FUNCTION, FNU.GE.0.0D0 -C KODE - A PARAMETER TO INDICATE THE SCALING OPTION -C KODE= 1 RETURNS -C CY(I)=Y(FNU+I-1,Z), I=1,...,N -C = 2 RETURNS -C CY(I)=Y(FNU+I-1,Z)*EXP(-ABS(Y)), I=1,...,N -C WHERE Y=AIMAG(Z) -C N - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1 -C CWRKR, - DOUBLE PRECISION WORK VECTORS OF DIMENSION AT -C CWRKI AT LEAST N -C -C OUTPUT CYR,CYI ARE DOUBLE PRECISION -C CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS -C CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE -C CY(I)=Y(FNU+I-1,Z) OR -C CY(I)=Y(FNU+I-1,Z)*EXP(-ABS(Y)) I=1,...,N -C DEPENDING ON KODE. -C NZ - NZ=0 , A NORMAL RETURN -C NZ.GT.0 , NZ COMPONENTS OF CY SET TO ZERO DUE TO -C UNDERFLOW (GENERALLY ON KODE=2) -C IERR - ERROR FLAG -C IERR=0, NORMAL RETURN - COMPUTATION COMPLETED -C IERR=1, INPUT ERROR - NO COMPUTATION -C IERR=2, OVERFLOW - NO COMPUTATION, FNU IS -C TOO LARGE OR CABS(Z) IS TOO SMALL OR BOTH -C IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE -C BUT LOSSES OF SIGNIFCANCE BY ARGUMENT -C REDUCTION PRODUCE LESS THAN HALF OF MACHINE -C ACCURACY -C IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA- -C TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI- -C CANCE BY ARGUMENT REDUCTION -C IERR=5, ERROR - NO COMPUTATION, -C ALGORITHM TERMINATION CONDITION NOT MET -C -C***LONG DESCRIPTION -C -C THE COMPUTATION IS CARRIED OUT BY THE FORMULA -C -C Y(FNU,Z)=0.5*(H(1,FNU,Z)-H(2,FNU,Z))/I -C -C WHERE I**2 = -1 AND THE HANKEL BESSEL FUNCTIONS H(1,FNU,Z) -C AND H(2,FNU,Z) ARE CALCULATED IN CBESH. -C -C FOR NEGATIVE ORDERS,THE FORMULA -C -C Y(-FNU,Z) = Y(FNU,Z)*COS(PI*FNU) + J(FNU,Z)*SIN(PI*FNU) -C -C CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO HALF ODD -C INTEGERS THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE -C POSITIVE HALF ODD INTEGER,THE MAGNITUDE OF Y(-FNU,Z)=J(FNU,Z)* -C SIN(PI*FNU) IS A LARGE NEGATIVE POWER OF TEN. BUT WHEN FNU IS -C NOT A HALF ODD INTEGER, Y(FNU,Z) DOMINATES IN MAGNITUDE WITH A -C LARGE POSITIVE POWER OF TEN AND THE MOST THAT THE SECOND TERM -C CAN BE REDUCED IS BY UNIT ROUNDOFF FROM THE COEFFICIENT. THUS, -C WIDE CHANGES CAN OCCUR WITHIN UNIT ROUNDOFF OF A LARGE HALF -C ODD INTEGER. HERE, LARGE MEANS FNU.GT.CABS(Z). -C -C IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- -C MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS -C LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. -C CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN -C LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG -C IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS -C DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. -C IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS -C LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS -C MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE -C INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS -C RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3 -C ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION -C ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION -C ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN -C THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT -C TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS -C IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC. -C SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES. -C -C THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX -C BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT -C ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- -C SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE -C ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), -C ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF -C CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY -C HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN -C ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY -C SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER -C THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, -C 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS -C THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER -C COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY -C BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER -C COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE -C MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, -C THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, -C OR -PI/2+P. -C -C***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ -C AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF -C COMMERCE, 1955. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C BY D. E. AMOS, SAND83-0083, MAY, 1983. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 -C -C A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- -C 1018, MAY, 1985 -C -C A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. -C MATH. SOFTWARE, 1986 -C -C***ROUTINES CALLED ZBESH,I1MACH,D1MACH -C***END PROLOGUE ZBESY -C -C COMPLEX CWRK,CY,C1,C2,EX,HCI,Z,ZU,ZV - DOUBLE PRECISION CWRKI, CWRKR, CYI, CYR, C1I, C1R, C2I, C2R, - * ELIM, EXI, EXR, EY, FNU, HCII, STI, STR, TAY, ZI, ZR, DEXP, - * D1MACH, ASCLE, RTOL, ATOL, AA, BB, TOL - INTEGER I, IERR, K, KODE, K1, K2, N, NZ, NZ1, NZ2, I1MACH - DIMENSION CYR(N), CYI(N), CWRKR(N), CWRKI(N) -C***FIRST EXECUTABLE STATEMENT ZBESY - IERR = 0 - NZ=0 - IF (ZR.EQ.0.0D0 .AND. ZI.EQ.0.0D0) IERR=1 - IF (FNU.LT.0.0D0) IERR=1 - IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 - IF (N.LT.1) IERR=1 - IF (IERR.NE.0) RETURN - HCII = 0.5D0 - CALL ZBESH(ZR, ZI, FNU, KODE, 1, N, CYR, CYI, NZ1, IERR) - IF (IERR.NE.0.AND.IERR.NE.3) GO TO 170 - CALL ZBESH(ZR, ZI, FNU, KODE, 2, N, CWRKR, CWRKI, NZ2, IERR) - IF (IERR.NE.0.AND.IERR.NE.3) GO TO 170 - NZ = MIN0(NZ1,NZ2) - IF (KODE.EQ.2) GO TO 60 - DO 50 I=1,N - STR = CWRKR(I) - CYR(I) - STI = CWRKI(I) - CYI(I) - CYR(I) = -STI*HCII - CYI(I) = STR*HCII - 50 CONTINUE - RETURN - 60 CONTINUE - TOL = DMAX1(D1MACH(4),1.0D-18) - K1 = I1MACH(15) - K2 = I1MACH(16) - K = MIN0(IABS(K1),IABS(K2)) - R1M5 = D1MACH(5) -C----------------------------------------------------------------------- -C ELIM IS THE APPROXIMATE EXPONENTIAL UNDER- AND OVERFLOW LIMIT -C----------------------------------------------------------------------- - ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) - EXR = DCOS(ZR) - EXI = DSIN(ZR) - EY = 0.0D0 - TAY = DABS(ZI+ZI) - IF (TAY.LT.ELIM) EY = DEXP(-TAY) - IF (ZI.LT.0.0D0) GO TO 90 - C1R = EXR*EY - C1I = EXI*EY - C2R = EXR - C2I = -EXI - 70 CONTINUE - NZ = 0 - RTOL = 1.0D0/TOL - ASCLE = D1MACH(1)*RTOL*1.0D+3 - DO 80 I=1,N -C STR = C1R*CYR(I) - C1I*CYI(I) -C STI = C1R*CYI(I) + C1I*CYR(I) -C STR = -STR + C2R*CWRKR(I) - C2I*CWRKI(I) -C STI = -STI + C2R*CWRKI(I) + C2I*CWRKR(I) -C CYR(I) = -STI*HCII -C CYI(I) = STR*HCII - AA = CWRKR(I) - BB = CWRKI(I) - ATOL = 1.0D0 - IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 75 - AA = AA*RTOL - BB = BB*RTOL - ATOL = TOL - 75 CONTINUE - STR = (AA*C2R - BB*C2I)*ATOL - STI = (AA*C2I + BB*C2R)*ATOL - AA = CYR(I) - BB = CYI(I) - ATOL = 1.0D0 - IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 85 - AA = AA*RTOL - BB = BB*RTOL - ATOL = TOL - 85 CONTINUE - STR = STR - (AA*C1R - BB*C1I)*ATOL - STI = STI - (AA*C1I + BB*C1R)*ATOL - CYR(I) = -STI*HCII - CYI(I) = STR*HCII - IF (STR.EQ.0.0D0 .AND. STI.EQ.0.0D0 .AND. EY.EQ.0.0D0) NZ = NZ - * + 1 - 80 CONTINUE - RETURN - 90 CONTINUE - C1R = EXR - C1I = EXI - C2R = EXR*EY - C2I = -EXI*EY - GO TO 70 - 170 CONTINUE - NZ = 0 - RETURN - END diff --git a/amos/zbinu.f b/amos/zbinu.f deleted file mode 100644 index c76846a..0000000 --- a/amos/zbinu.f +++ /dev/null @@ -1,110 +0,0 @@ - SUBROUTINE ZBINU(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, - * TOL, ELIM, ALIM) -C***BEGIN PROLOGUE ZBINU -C***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZAIRY,ZBIRY -C -C ZBINU COMPUTES THE I FUNCTION IN THE RIGHT HALF Z PLANE -C -C***ROUTINES CALLED AZABS,ZASYI,ZBUNI,ZMLRI,ZSERI,ZUOIK,ZWRSK -C***END PROLOGUE ZBINU - DOUBLE PRECISION ALIM, AZ, CWI, CWR, CYI, CYR, DFNU, ELIM, FNU, - * FNUL, RL, TOL, ZEROI, ZEROR, ZI, ZR, AZABS - INTEGER I, INW, KODE, N, NLAST, NN, NUI, NW, NZ - DIMENSION CYR(N), CYI(N), CWR(2), CWI(2) - DATA ZEROR,ZEROI / 0.0D0, 0.0D0 / -C - NZ = 0 - AZ = AZABS(ZR,ZI) - NN = N - DFNU = FNU + DBLE(FLOAT(N-1)) - IF (AZ.LE.2.0D0) GO TO 10 - IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20 - 10 CONTINUE -C----------------------------------------------------------------------- -C POWER SERIES -C----------------------------------------------------------------------- - CALL ZSERI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM) - INW = IABS(NW) - NZ = NZ + INW - NN = NN - INW - IF (NN.EQ.0) RETURN - IF (NW.GE.0) GO TO 120 - DFNU = FNU + DBLE(FLOAT(NN-1)) - 20 CONTINUE - IF (AZ.LT.RL) GO TO 40 - IF (DFNU.LE.1.0D0) GO TO 30 - IF (AZ+AZ.LT.DFNU*DFNU) GO TO 50 -C----------------------------------------------------------------------- -C ASYMPTOTIC EXPANSION FOR LARGE Z -C----------------------------------------------------------------------- - 30 CONTINUE - CALL ZASYI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, RL, TOL, ELIM, - * ALIM) - IF (NW.LT.0) GO TO 130 - GO TO 120 - 40 CONTINUE - IF (DFNU.LE.1.0D0) GO TO 70 - 50 CONTINUE -C----------------------------------------------------------------------- -C OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM -C----------------------------------------------------------------------- - CALL ZUOIK(ZR, ZI, FNU, KODE, 1, NN, CYR, CYI, NW, TOL, ELIM, - * ALIM) - IF (NW.LT.0) GO TO 130 - NZ = NZ + NW - NN = NN - NW - IF (NN.EQ.0) RETURN - DFNU = FNU+DBLE(FLOAT(NN-1)) - IF (DFNU.GT.FNUL) GO TO 110 - IF (AZ.GT.FNUL) GO TO 110 - 60 CONTINUE - IF (AZ.GT.RL) GO TO 80 - 70 CONTINUE -C----------------------------------------------------------------------- -C MILLER ALGORITHM NORMALIZED BY THE SERIES -C----------------------------------------------------------------------- - CALL ZMLRI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL) - IF(NW.LT.0) GO TO 130 - GO TO 120 - 80 CONTINUE -C----------------------------------------------------------------------- -C MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN -C----------------------------------------------------------------------- -C----------------------------------------------------------------------- -C OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN -C----------------------------------------------------------------------- - CALL ZUOIK(ZR, ZI, FNU, KODE, 2, 2, CWR, CWI, NW, TOL, ELIM, - * ALIM) - IF (NW.GE.0) GO TO 100 - NZ = NN - DO 90 I=1,NN - CYR(I) = ZEROR - CYI(I) = ZEROI - 90 CONTINUE - RETURN - 100 CONTINUE - IF (NW.GT.0) GO TO 130 - CALL ZWRSK(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, CWR, CWI, TOL, - * ELIM, ALIM) - IF (NW.LT.0) GO TO 130 - GO TO 120 - 110 CONTINUE -C----------------------------------------------------------------------- -C INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD -C----------------------------------------------------------------------- - NUI = INT(SNGL(FNUL-DFNU)) + 1 - NUI = MAX0(NUI,0) - CALL ZBUNI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, NUI, NLAST, FNUL, - * TOL, ELIM, ALIM) - IF (NW.LT.0) GO TO 130 - NZ = NZ + NW - IF (NLAST.EQ.0) GO TO 120 - NN = NLAST - GO TO 60 - 120 CONTINUE - RETURN - 130 CONTINUE - NZ = -1 - IF(NW.EQ.(-2)) NZ=-2 - RETURN - END diff --git a/amos/zbiry.f b/amos/zbiry.f deleted file mode 100644 index e0b6b77..0000000 --- a/amos/zbiry.f +++ /dev/null @@ -1,364 +0,0 @@ - SUBROUTINE ZBIRY(ZR, ZI, ID, KODE, BIR, BII, IERR) -C***BEGIN PROLOGUE ZBIRY -C***DATE WRITTEN 830501 (YYMMDD) -C***REVISION DATE 890801 (YYMMDD) -C***CATEGORY NO. B5K -C***KEYWORDS AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD -C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES -C***PURPOSE TO COMPUTE AIRY FUNCTIONS BI(Z) AND DBI(Z) FOR COMPLEX Z -C***DESCRIPTION -C -C ***A DOUBLE PRECISION ROUTINE*** -C ON KODE=1, CBIRY COMPUTES THE COMPLEX AIRY FUNCTION BI(Z) OR -C ITS DERIVATIVE DBI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON -C KODE=2, A SCALING OPTION CEXP(-AXZTA)*BI(Z) OR CEXP(-AXZTA)* -C DBI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL BEHAVIOR IN -C BOTH THE LEFT AND RIGHT HALF PLANES WHERE -C ZTA=(2/3)*Z*CSQRT(Z)=CMPLX(XZTA,YZTA) AND AXZTA=ABS(XZTA). -C DEFINITIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF -C MATHEMATICAL FUNCTIONS (REF. 1). -C -C INPUT ZR,ZI ARE DOUBLE PRECISION -C ZR,ZI - Z=CMPLX(ZR,ZI) -C ID - ORDER OF DERIVATIVE, ID=0 OR ID=1 -C KODE - A PARAMETER TO INDICATE THE SCALING OPTION -C KODE= 1 RETURNS -C BI=BI(Z) ON ID=0 OR -C BI=DBI(Z)/DZ ON ID=1 -C = 2 RETURNS -C BI=CEXP(-AXZTA)*BI(Z) ON ID=0 OR -C BI=CEXP(-AXZTA)*DBI(Z)/DZ ON ID=1 WHERE -C ZTA=(2/3)*Z*CSQRT(Z)=CMPLX(XZTA,YZTA) -C AND AXZTA=ABS(XZTA) -C -C OUTPUT BIR,BII ARE DOUBLE PRECISION -C BIR,BII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND -C KODE -C IERR - ERROR FLAG -C IERR=0, NORMAL RETURN - COMPUTATION COMPLETED -C IERR=1, INPUT ERROR - NO COMPUTATION -C IERR=2, OVERFLOW - NO COMPUTATION, REAL(Z) -C TOO LARGE ON KODE=1 -C IERR=3, CABS(Z) LARGE - COMPUTATION COMPLETED -C LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION -C PRODUCE LESS THAN HALF OF MACHINE ACCURACY -C IERR=4, CABS(Z) TOO LARGE - NO COMPUTATION -C COMPLETE LOSS OF ACCURACY BY ARGUMENT -C REDUCTION -C IERR=5, ERROR - NO COMPUTATION, -C ALGORITHM TERMINATION CONDITION NOT MET -C -C***LONG DESCRIPTION -C -C BI AND DBI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE I BESSEL -C FUNCTIONS BY -C -C BI(Z)=C*SQRT(Z)*( I(-1/3,ZTA) + I(1/3,ZTA) ) -C DBI(Z)=C * Z * ( I(-2/3,ZTA) + I(2/3,ZTA) ) -C C=1.0/SQRT(3.0) -C ZTA=(2/3)*Z**(3/2) -C -C WITH THE POWER SERIES FOR CABS(Z).LE.1.0. -C -C IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- -C MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES -C OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF -C THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR), -C THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR -C FLAG IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS -C DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. -C ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN -C ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT -C FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE -C LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA -C MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, -C AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE -C PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE -C PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT- -C ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG- -C NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN -C DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN -C EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, -C NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE -C PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER -C MACHINES. -C -C THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX -C BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT -C ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- -C SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE -C ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), -C ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF -C CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY -C HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN -C ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY -C SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER -C THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, -C 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS -C THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER -C COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY -C BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER -C COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE -C MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, -C THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, -C OR -PI/2+P. -C -C***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ -C AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF -C COMMERCE, 1955. -C -C COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT -C AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 -C -C A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- -C 1018, MAY, 1985 -C -C A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX -C ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. -C MATH. SOFTWARE, 1986 -C -C***ROUTINES CALLED ZBINU,AZABS,ZDIV,AZSQRT,D1MACH,I1MACH -C***END PROLOGUE ZBIRY -C COMPLEX BI,CONE,CSQ,CY,S1,S2,TRM1,TRM2,Z,ZTA,Z3 - DOUBLE PRECISION AA, AD, AK, ALIM, ATRM, AZ, AZ3, BB, BII, BIR, - * BK, CC, CK, COEF, CONEI, CONER, CSQI, CSQR, CYI, CYR, C1, C2, - * DIG, DK, D1, D2, EAA, ELIM, FID, FMR, FNU, FNUL, PI, RL, R1M5, - * SFAC, STI, STR, S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I, - * TRM2R, TTH, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, D1MACH, AZABS - INTEGER ID, IERR, K, KODE, K1, K2, NZ, I1MACH - DIMENSION CYR(2), CYI(2) - DATA TTH, C1, C2, COEF, PI /6.66666666666666667D-01, - * 6.14926627446000736D-01,4.48288357353826359D-01, - * 5.77350269189625765D-01,3.14159265358979324D+00/ - DATA CONER, CONEI /1.0D0,0.0D0/ -C***FIRST EXECUTABLE STATEMENT ZBIRY - IERR = 0 - NZ=0 - IF (ID.LT.0 .OR. ID.GT.1) IERR=1 - IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 - IF (IERR.NE.0) RETURN - AZ = AZABS(ZR,ZI) - TOL = DMAX1(D1MACH(4),1.0D-18) - FID = DBLE(FLOAT(ID)) - IF (AZ.GT.1.0E0) GO TO 70 -C----------------------------------------------------------------------- -C POWER SERIES FOR CABS(Z).LE.1. -C----------------------------------------------------------------------- - S1R = CONER - S1I = CONEI - S2R = CONER - S2I = CONEI - IF (AZ.LT.TOL) GO TO 130 - AA = AZ*AZ - IF (AA.LT.TOL/AZ) GO TO 40 - TRM1R = CONER - TRM1I = CONEI - TRM2R = CONER - TRM2I = CONEI - ATRM = 1.0D0 - STR = ZR*ZR - ZI*ZI - STI = ZR*ZI + ZI*ZR - Z3R = STR*ZR - STI*ZI - Z3I = STR*ZI + STI*ZR - AZ3 = AZ*AA - AK = 2.0D0 + FID - BK = 3.0D0 - FID - FID - CK = 4.0D0 - FID - DK = 3.0D0 + FID + FID - D1 = AK*DK - D2 = BK*CK - AD = DMIN1(D1,D2) - AK = 24.0D0 + 9.0D0*FID - BK = 30.0D0 - 9.0D0*FID - DO 30 K=1,25 - STR = (TRM1R*Z3R-TRM1I*Z3I)/D1 - TRM1I = (TRM1R*Z3I+TRM1I*Z3R)/D1 - TRM1R = STR - S1R = S1R + TRM1R - S1I = S1I + TRM1I - STR = (TRM2R*Z3R-TRM2I*Z3I)/D2 - TRM2I = (TRM2R*Z3I+TRM2I*Z3R)/D2 - TRM2R = STR - S2R = S2R + TRM2R - S2I = S2I + TRM2I - ATRM = ATRM*AZ3/AD - D1 = D1 + AK - D2 = D2 + BK - AD = DMIN1(D1,D2) - IF (ATRM.LT.TOL*AD) GO TO 40 - AK = AK + 18.0D0 - BK = BK + 18.0D0 - 30 CONTINUE - 40 CONTINUE - IF (ID.EQ.1) GO TO 50 - BIR = C1*S1R + C2*(ZR*S2R-ZI*S2I) - BII = C1*S1I + C2*(ZR*S2I+ZI*S2R) - IF (KODE.EQ.1) RETURN - CALL AZSQRT(ZR, ZI, STR, STI) - ZTAR = TTH*(ZR*STR-ZI*STI) - ZTAI = TTH*(ZR*STI+ZI*STR) - AA = ZTAR - AA = -DABS(AA) - EAA = DEXP(AA) - BIR = BIR*EAA - BII = BII*EAA - RETURN - 50 CONTINUE - BIR = S2R*C2 - BII = S2I*C2 - IF (AZ.LE.TOL) GO TO 60 - CC = C1/(1.0D0+FID) - STR = S1R*ZR - S1I*ZI - STI = S1R*ZI + S1I*ZR - BIR = BIR + CC*(STR*ZR-STI*ZI) - BII = BII + CC*(STR*ZI+STI*ZR) - 60 CONTINUE - IF (KODE.EQ.1) RETURN - CALL AZSQRT(ZR, ZI, STR, STI) - ZTAR = TTH*(ZR*STR-ZI*STI) - ZTAI = TTH*(ZR*STI+ZI*STR) - AA = ZTAR - AA = -DABS(AA) - EAA = DEXP(AA) - BIR = BIR*EAA - BII = BII*EAA - RETURN -C----------------------------------------------------------------------- -C CASE FOR CABS(Z).GT.1.0 -C----------------------------------------------------------------------- - 70 CONTINUE - FNU = (1.0D0+FID)/3.0D0 -C----------------------------------------------------------------------- -C SET PARAMETERS RELATED TO MACHINE CONSTANTS. -C TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. -C ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. -C EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND -C EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR -C UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. -C RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. -C DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). -C FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU. -C----------------------------------------------------------------------- - K1 = I1MACH(15) - K2 = I1MACH(16) - R1M5 = D1MACH(5) - K = MIN0(IABS(K1),IABS(K2)) - ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) - K1 = I1MACH(14) - 1 - AA = R1M5*DBLE(FLOAT(K1)) - DIG = DMIN1(AA,18.0D0) - AA = AA*2.303D0 - ALIM = ELIM + DMAX1(-AA,-41.45D0) - RL = 1.2D0*DIG + 3.0D0 - FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0) -C----------------------------------------------------------------------- -C TEST FOR RANGE -C----------------------------------------------------------------------- - AA=0.5D0/TOL - BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 - AA=DMIN1(AA,BB) - AA=AA**TTH - IF (AZ.GT.AA) GO TO 260 - AA=DSQRT(AA) - IF (AZ.GT.AA) IERR=3 - CALL AZSQRT(ZR, ZI, CSQR, CSQI) - ZTAR = TTH*(ZR*CSQR-ZI*CSQI) - ZTAI = TTH*(ZR*CSQI+ZI*CSQR) -C----------------------------------------------------------------------- -C RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL -C----------------------------------------------------------------------- - SFAC = 1.0D0 - AK = ZTAI - IF (ZR.GE.0.0D0) GO TO 80 - BK = ZTAR - CK = -DABS(BK) - ZTAR = CK - ZTAI = AK - 80 CONTINUE - IF (ZI.NE.0.0D0 .OR. ZR.GT.0.0D0) GO TO 90 - ZTAR = 0.0D0 - ZTAI = AK - 90 CONTINUE - AA = ZTAR - IF (KODE.EQ.2) GO TO 100 -C----------------------------------------------------------------------- -C OVERFLOW TEST -C----------------------------------------------------------------------- - BB = DABS(AA) - IF (BB.LT.ALIM) GO TO 100 - BB = BB + 0.25D0*DLOG(AZ) - SFAC = TOL - IF (BB.GT.ELIM) GO TO 190 - 100 CONTINUE - FMR = 0.0D0 - IF (AA.GE.0.0D0 .AND. ZR.GT.0.0D0) GO TO 110 - FMR = PI - IF (ZI.LT.0.0D0) FMR = -PI - ZTAR = -ZTAR - ZTAI = -ZTAI - 110 CONTINUE -C----------------------------------------------------------------------- -C AA=FACTOR FOR ANALYTIC CONTINUATION OF I(FNU,ZTA) -C KODE=2 RETURNS EXP(-ABS(XZTA))*I(FNU,ZTA) FROM CBESI -C----------------------------------------------------------------------- - CALL ZBINU(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, RL, FNUL, TOL, - * ELIM, ALIM) - IF (NZ.LT.0) GO TO 200 - AA = FMR*FNU - Z3R = SFAC - STR = DCOS(AA) - STI = DSIN(AA) - S1R = (STR*CYR(1)-STI*CYI(1))*Z3R - S1I = (STR*CYI(1)+STI*CYR(1))*Z3R - FNU = (2.0D0-FID)/3.0D0 - CALL ZBINU(ZTAR, ZTAI, FNU, KODE, 2, CYR, CYI, NZ, RL, FNUL, TOL, - * ELIM, ALIM) - CYR(1) = CYR(1)*Z3R - CYI(1) = CYI(1)*Z3R - CYR(2) = CYR(2)*Z3R - CYI(2) = CYI(2)*Z3R -C----------------------------------------------------------------------- -C BACKWARD RECUR ONE STEP FOR ORDERS -1/3 OR -2/3 -C----------------------------------------------------------------------- - CALL ZDIV(CYR(1), CYI(1), ZTAR, ZTAI, STR, STI) - S2R = (FNU+FNU)*STR + CYR(2) - S2I = (FNU+FNU)*STI + CYI(2) - AA = FMR*(FNU-1.0D0) - STR = DCOS(AA) - STI = DSIN(AA) - S1R = COEF*(S1R+S2R*STR-S2I*STI) - S1I = COEF*(S1I+S2R*STI+S2I*STR) - IF (ID.EQ.1) GO TO 120 - STR = CSQR*S1R - CSQI*S1I - S1I = CSQR*S1I + CSQI*S1R - S1R = STR - BIR = S1R/SFAC - BII = S1I/SFAC - RETURN - 120 CONTINUE - STR = ZR*S1R - ZI*S1I - S1I = ZR*S1I + ZI*S1R - S1R = STR - BIR = S1R/SFAC - BII = S1I/SFAC - RETURN - 130 CONTINUE - AA = C1*(1.0D0-FID) + FID*C2 - BIR = AA - BII = 0.0D0 - RETURN - 190 CONTINUE - IERR=2 - NZ=0 - RETURN - 200 CONTINUE - IF(NZ.EQ.(-1)) GO TO 190 - NZ=0 - IERR=5 - RETURN - 260 CONTINUE - IERR=4 - NZ=0 - RETURN - END diff --git a/amos/zbknu.f b/amos/zbknu.f deleted file mode 100644 index a8eb50d..0000000 --- a/amos/zbknu.f +++ /dev/null @@ -1,568 +0,0 @@ - SUBROUTINE ZBKNU(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, - * ALIM) -C***BEGIN PROLOGUE ZBKNU -C***REFER TO ZBESI,ZBESK,ZAIRY,ZBESH -C -C ZBKNU COMPUTES THE K BESSEL FUNCTION IN THE RIGHT HALF Z PLANE. -C -C***ROUTINES CALLED DGAMLN,I1MACH,D1MACH,ZKSCL,ZSHCH,ZUCHK,AZABS,ZDIV, -C AZEXP,AZLOG,ZMLT,AZSQRT -C***END PROLOGUE ZBKNU -C - DOUBLE PRECISION AA, AK, ALIM, ASCLE, A1, A2, BB, BK, BRY, CAZ, - * CBI, CBR, CC, CCHI, CCHR, CKI, CKR, COEFI, COEFR, CONEI, CONER, - * CRSCR, CSCLR, CSHI, CSHR, CSI, CSR, CSRR, CSSR, CTWOR, - * CZEROI, CZEROR, CZI, CZR, DNU, DNU2, DPI, ELIM, ETEST, FC, FHS, - * FI, FK, FKS, FMUI, FMUR, FNU, FPI, FR, G1, G2, HPI, PI, PR, PTI, - * PTR, P1I, P1R, P2I, P2M, P2R, QI, QR, RAK, RCAZ, RTHPI, RZI, - * RZR, R1, S, SMUI, SMUR, SPI, STI, STR, S1I, S1R, S2I, S2R, TM, - * TOL, TTH, T1, T2, YI, YR, ZI, ZR, DGAMLN, D1MACH, AZABS, ELM, - * CELMR, ZDR, ZDI, AS, ALAS, HELIM, CYR, CYI - INTEGER I, IFLAG, INU, K, KFLAG, KK, KMAX, KODE, KODED, N, NZ, - * IDUM, I1MACH, J, IC, INUB, NW - DIMENSION YR(N), YI(N), CC(8), CSSR(3), CSRR(3), BRY(3), CYR(2), - * CYI(2) -C COMPLEX Z,Y,A,B,RZ,SMU,FU,FMU,F,FLRZ,CZ,S1,S2,CSH,CCH -C COMPLEX CK,P,Q,COEF,P1,P2,CBK,PT,CZERO,CONE,CTWO,ST,EZ,CS,DK -C - DATA KMAX / 30 / - DATA CZEROR,CZEROI,CONER,CONEI,CTWOR,R1/ - 1 0.0D0 , 0.0D0 , 1.0D0 , 0.0D0 , 2.0D0 , 2.0D0 / - DATA DPI, RTHPI, SPI ,HPI, FPI, TTH / - 1 3.14159265358979324D0, 1.25331413731550025D0, - 2 1.90985931710274403D0, 1.57079632679489662D0, - 3 1.89769999331517738D0, 6.66666666666666666D-01/ - DATA CC(1), CC(2), CC(3), CC(4), CC(5), CC(6), CC(7), CC(8)/ - 1 5.77215664901532861D-01, -4.20026350340952355D-02, - 2 -4.21977345555443367D-02, 7.21894324666309954D-03, - 3 -2.15241674114950973D-04, -2.01348547807882387D-05, - 4 1.13302723198169588D-06, 6.11609510448141582D-09/ -C - CAZ = AZABS(ZR,ZI) - CSCLR = 1.0D0/TOL - CRSCR = TOL - CSSR(1) = CSCLR - CSSR(2) = 1.0D0 - CSSR(3) = CRSCR - CSRR(1) = CRSCR - CSRR(2) = 1.0D0 - CSRR(3) = CSCLR - BRY(1) = 1.0D+3*D1MACH(1)/TOL - BRY(2) = 1.0D0/BRY(1) - BRY(3) = D1MACH(2) - NZ = 0 - IFLAG = 0 - KODED = KODE - RCAZ = 1.0D0/CAZ - STR = ZR*RCAZ - STI = -ZI*RCAZ - RZR = (STR+STR)*RCAZ - RZI = (STI+STI)*RCAZ - INU = INT(SNGL(FNU+0.5D0)) - DNU = FNU - DBLE(FLOAT(INU)) - IF (DABS(DNU).EQ.0.5D0) GO TO 110 - DNU2 = 0.0D0 - IF (DABS(DNU).GT.TOL) DNU2 = DNU*DNU - IF (CAZ.GT.R1) GO TO 110 -C----------------------------------------------------------------------- -C SERIES FOR CABS(Z).LE.R1 -C----------------------------------------------------------------------- - FC = 1.0D0 - CALL AZLOG(RZR, RZI, SMUR, SMUI, IDUM) - FMUR = SMUR*DNU - FMUI = SMUI*DNU - CALL ZSHCH(FMUR, FMUI, CSHR, CSHI, CCHR, CCHI) - IF (DNU.EQ.0.0D0) GO TO 10 - FC = DNU*DPI - FC = FC/DSIN(FC) - SMUR = CSHR/DNU - SMUI = CSHI/DNU - 10 CONTINUE - A2 = 1.0D0 + DNU -C----------------------------------------------------------------------- -C GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU), T2=1/GAM(1+DNU) -C----------------------------------------------------------------------- - T2 = DEXP(-DGAMLN(A2,IDUM)) - T1 = 1.0D0/(T2*FC) - IF (DABS(DNU).GT.0.1D0) GO TO 40 -C----------------------------------------------------------------------- -C SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU) -C----------------------------------------------------------------------- - AK = 1.0D0 - S = CC(1) - DO 20 K=2,8 - AK = AK*DNU2 - TM = CC(K)*AK - S = S + TM - IF (DABS(TM).LT.TOL) GO TO 30 - 20 CONTINUE - 30 G1 = -S - GO TO 50 - 40 CONTINUE - G1 = (T1-T2)/(DNU+DNU) - 50 CONTINUE - G2 = (T1+T2)*0.5D0 - FR = FC*(CCHR*G1+SMUR*G2) - FI = FC*(CCHI*G1+SMUI*G2) - CALL AZEXP(FMUR, FMUI, STR, STI) - PR = 0.5D0*STR/T2 - PI = 0.5D0*STI/T2 - CALL ZDIV(0.5D0, 0.0D0, STR, STI, PTR, PTI) - QR = PTR/T1 - QI = PTI/T1 - S1R = FR - S1I = FI - S2R = PR - S2I = PI - AK = 1.0D0 - A1 = 1.0D0 - CKR = CONER - CKI = CONEI - BK = 1.0D0 - DNU2 - IF (INU.GT.0 .OR. N.GT.1) GO TO 80 -C----------------------------------------------------------------------- -C GENERATE K(FNU,Z), 0.0D0 .LE. FNU .LT. 0.5D0 AND N=1 -C----------------------------------------------------------------------- - IF (CAZ.LT.TOL) GO TO 70 - CALL ZMLT(ZR, ZI, ZR, ZI, CZR, CZI) - CZR = 0.25D0*CZR - CZI = 0.25D0*CZI - T1 = 0.25D0*CAZ*CAZ - 60 CONTINUE - FR = (FR*AK+PR+QR)/BK - FI = (FI*AK+PI+QI)/BK - STR = 1.0D0/(AK-DNU) - PR = PR*STR - PI = PI*STR - STR = 1.0D0/(AK+DNU) - QR = QR*STR - QI = QI*STR - STR = CKR*CZR - CKI*CZI - RAK = 1.0D0/AK - CKI = (CKR*CZI+CKI*CZR)*RAK - CKR = STR*RAK - S1R = CKR*FR - CKI*FI + S1R - S1I = CKR*FI + CKI*FR + S1I - A1 = A1*T1*RAK - BK = BK + AK + AK + 1.0D0 - AK = AK + 1.0D0 - IF (A1.GT.TOL) GO TO 60 - 70 CONTINUE - YR(1) = S1R - YI(1) = S1I - IF (KODED.EQ.1) RETURN - CALL AZEXP(ZR, ZI, STR, STI) - CALL ZMLT(S1R, S1I, STR, STI, YR(1), YI(1)) - RETURN -C----------------------------------------------------------------------- -C GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE -C----------------------------------------------------------------------- - 80 CONTINUE - IF (CAZ.LT.TOL) GO TO 100 - CALL ZMLT(ZR, ZI, ZR, ZI, CZR, CZI) - CZR = 0.25D0*CZR - CZI = 0.25D0*CZI - T1 = 0.25D0*CAZ*CAZ - 90 CONTINUE - FR = (FR*AK+PR+QR)/BK - FI = (FI*AK+PI+QI)/BK - STR = 1.0D0/(AK-DNU) - PR = PR*STR - PI = PI*STR - STR = 1.0D0/(AK+DNU) - QR = QR*STR - QI = QI*STR - STR = CKR*CZR - CKI*CZI - RAK = 1.0D0/AK - CKI = (CKR*CZI+CKI*CZR)*RAK - CKR = STR*RAK - S1R = CKR*FR - CKI*FI + S1R - S1I = CKR*FI + CKI*FR + S1I - STR = PR - FR*AK - STI = PI - FI*AK - S2R = CKR*STR - CKI*STI + S2R - S2I = CKR*STI + CKI*STR + S2I - A1 = A1*T1*RAK - BK = BK + AK + AK + 1.0D0 - AK = AK + 1.0D0 - IF (A1.GT.TOL) GO TO 90 - 100 CONTINUE - KFLAG = 2 - A1 = FNU + 1.0D0 - AK = A1*DABS(SMUR) - IF (AK.GT.ALIM) KFLAG = 3 - STR = CSSR(KFLAG) - P2R = S2R*STR - P2I = S2I*STR - CALL ZMLT(P2R, P2I, RZR, RZI, S2R, S2I) - S1R = S1R*STR - S1I = S1I*STR - IF (KODED.EQ.1) GO TO 210 - CALL AZEXP(ZR, ZI, FR, FI) - CALL ZMLT(S1R, S1I, FR, FI, S1R, S1I) - CALL ZMLT(S2R, S2I, FR, FI, S2R, S2I) - GO TO 210 -C----------------------------------------------------------------------- -C IFLAG=0 MEANS NO UNDERFLOW OCCURRED -C IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH -C KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD -C RECURSION -C----------------------------------------------------------------------- - 110 CONTINUE - CALL AZSQRT(ZR, ZI, STR, STI) - CALL ZDIV(RTHPI, CZEROI, STR, STI, COEFR, COEFI) - KFLAG = 2 - IF (KODED.EQ.2) GO TO 120 - IF (ZR.GT.ALIM) GO TO 290 -C BLANK LINE - STR = DEXP(-ZR)*CSSR(KFLAG) - STI = -STR*DSIN(ZI) - STR = STR*DCOS(ZI) - CALL ZMLT(COEFR, COEFI, STR, STI, COEFR, COEFI) - 120 CONTINUE - IF (DABS(DNU).EQ.0.5D0) GO TO 300 -C----------------------------------------------------------------------- -C MILLER ALGORITHM FOR CABS(Z).GT.R1 -C----------------------------------------------------------------------- - AK = DCOS(DPI*DNU) - AK = DABS(AK) - IF (AK.EQ.CZEROR) GO TO 300 - FHS = DABS(0.25D0-DNU2) - IF (FHS.EQ.CZEROR) GO TO 300 -C----------------------------------------------------------------------- -C COMPUTE R2=F(E). IF CABS(Z).GE.R2, USE FORWARD RECURRENCE TO -C DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT LINE ON -C 12.LE.E.LE.60. E IS COMPUTED FROM 2**(-E)=B**(1-I1MACH(14))= -C TOL WHERE B IS THE BASE OF THE ARITHMETIC. -C----------------------------------------------------------------------- - T1 = DBLE(FLOAT(I1MACH(14)-1)) - T1 = T1*D1MACH(5)*3.321928094D0 - T1 = DMAX1(T1,12.0D0) - T1 = DMIN1(T1,60.0D0) - T2 = TTH*T1 - 6.0D0 - IF (ZR.NE.0.0D0) GO TO 130 - T1 = HPI - GO TO 140 - 130 CONTINUE - T1 = DATAN(ZI/ZR) - T1 = DABS(T1) - 140 CONTINUE - IF (T2.GT.CAZ) GO TO 170 -C----------------------------------------------------------------------- -C FORWARD RECURRENCE LOOP WHEN CABS(Z).GE.R2 -C----------------------------------------------------------------------- - ETEST = AK/(DPI*CAZ*TOL) - FK = CONER - IF (ETEST.LT.CONER) GO TO 180 - FKS = CTWOR - CKR = CAZ + CAZ + CTWOR - P1R = CZEROR - P2R = CONER - DO 150 I=1,KMAX - AK = FHS/FKS - CBR = CKR/(FK+CONER) - PTR = P2R - P2R = CBR*P2R - P1R*AK - P1R = PTR - CKR = CKR + CTWOR - FKS = FKS + FK + FK + CTWOR - FHS = FHS + FK + FK - FK = FK + CONER - STR = DABS(P2R)*FK - IF (ETEST.LT.STR) GO TO 160 - 150 CONTINUE - GO TO 310 - 160 CONTINUE - FK = FK + SPI*T1*DSQRT(T2/CAZ) - FHS = DABS(0.25D0-DNU2) - GO TO 180 - 170 CONTINUE -C----------------------------------------------------------------------- -C COMPUTE BACKWARD INDEX K FOR CABS(Z).LT.R2 -C----------------------------------------------------------------------- - A2 = DSQRT(CAZ) - AK = FPI*AK/(TOL*DSQRT(A2)) - AA = 3.0D0*T1/(1.0D0+CAZ) - BB = 14.7D0*T1/(28.0D0+CAZ) - AK = (DLOG(AK)+CAZ*DCOS(AA)/(1.0D0+0.008D0*CAZ))/DCOS(BB) - FK = 0.12125D0*AK*AK/CAZ + 1.5D0 - 180 CONTINUE -C----------------------------------------------------------------------- -C BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM -C----------------------------------------------------------------------- - K = INT(SNGL(FK)) - FK = DBLE(FLOAT(K)) - FKS = FK*FK - P1R = CZEROR - P1I = CZEROI - P2R = TOL - P2I = CZEROI - CSR = P2R - CSI = P2I - DO 190 I=1,K - A1 = FKS - FK - AK = (FKS+FK)/(A1+FHS) - RAK = 2.0D0/(FK+CONER) - CBR = (FK+ZR)*RAK - CBI = ZI*RAK - PTR = P2R - PTI = P2I - P2R = (PTR*CBR-PTI*CBI-P1R)*AK - P2I = (PTI*CBR+PTR*CBI-P1I)*AK - P1R = PTR - P1I = PTI - CSR = CSR + P2R - CSI = CSI + P2I - FKS = A1 - FK + CONER - FK = FK - CONER - 190 CONTINUE -C----------------------------------------------------------------------- -C COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR BETTER -C SCALING -C----------------------------------------------------------------------- - TM = AZABS(CSR,CSI) - PTR = 1.0D0/TM - S1R = P2R*PTR - S1I = P2I*PTR - CSR = CSR*PTR - CSI = -CSI*PTR - CALL ZMLT(COEFR, COEFI, S1R, S1I, STR, STI) - CALL ZMLT(STR, STI, CSR, CSI, S1R, S1I) - IF (INU.GT.0 .OR. N.GT.1) GO TO 200 - ZDR = ZR - ZDI = ZI - IF(IFLAG.EQ.1) GO TO 270 - GO TO 240 - 200 CONTINUE -C----------------------------------------------------------------------- -C COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR SCALING -C----------------------------------------------------------------------- - TM = AZABS(P2R,P2I) - PTR = 1.0D0/TM - P1R = P1R*PTR - P1I = P1I*PTR - P2R = P2R*PTR - P2I = -P2I*PTR - CALL ZMLT(P1R, P1I, P2R, P2I, PTR, PTI) - STR = DNU + 0.5D0 - PTR - STI = -PTI - CALL ZDIV(STR, STI, ZR, ZI, STR, STI) - STR = STR + 1.0D0 - CALL ZMLT(STR, STI, S1R, S1I, S2R, S2I) -C----------------------------------------------------------------------- -C FORWARD RECURSION ON THE THREE TERM RECURSION WITH RELATION WITH -C SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3 -C----------------------------------------------------------------------- - 210 CONTINUE - STR = DNU + 1.0D0 - CKR = STR*RZR - CKI = STR*RZI - IF (N.EQ.1) INU = INU - 1 - IF (INU.GT.0) GO TO 220 - IF (N.GT.1) GO TO 215 - S1R = S2R - S1I = S2I - 215 CONTINUE - ZDR = ZR - ZDI = ZI - IF(IFLAG.EQ.1) GO TO 270 - GO TO 240 - 220 CONTINUE - INUB = 1 - IF(IFLAG.EQ.1) GO TO 261 - 225 CONTINUE - P1R = CSRR(KFLAG) - ASCLE = BRY(KFLAG) - DO 230 I=INUB,INU - STR = S2R - STI = S2I - S2R = CKR*STR - CKI*STI + S1R - S2I = CKR*STI + CKI*STR + S1I - S1R = STR - S1I = STI - CKR = CKR + RZR - CKI = CKI + RZI - IF (KFLAG.GE.3) GO TO 230 - P2R = S2R*P1R - P2I = S2I*P1R - STR = DABS(P2R) - STI = DABS(P2I) - P2M = DMAX1(STR,STI) - IF (P2M.LE.ASCLE) GO TO 230 - KFLAG = KFLAG + 1 - ASCLE = BRY(KFLAG) - S1R = S1R*P1R - S1I = S1I*P1R - S2R = P2R - S2I = P2I - STR = CSSR(KFLAG) - S1R = S1R*STR - S1I = S1I*STR - S2R = S2R*STR - S2I = S2I*STR - P1R = CSRR(KFLAG) - 230 CONTINUE - IF (N.NE.1) GO TO 240 - S1R = S2R - S1I = S2I - 240 CONTINUE - STR = CSRR(KFLAG) - YR(1) = S1R*STR - YI(1) = S1I*STR - IF (N.EQ.1) RETURN - YR(2) = S2R*STR - YI(2) = S2I*STR - IF (N.EQ.2) RETURN - KK = 2 - 250 CONTINUE - KK = KK + 1 - IF (KK.GT.N) RETURN - P1R = CSRR(KFLAG) - ASCLE = BRY(KFLAG) - DO 260 I=KK,N - P2R = S2R - P2I = S2I - S2R = CKR*P2R - CKI*P2I + S1R - S2I = CKI*P2R + CKR*P2I + S1I - S1R = P2R - S1I = P2I - CKR = CKR + RZR - CKI = CKI + RZI - P2R = S2R*P1R - P2I = S2I*P1R - YR(I) = P2R - YI(I) = P2I - IF (KFLAG.GE.3) GO TO 260 - STR = DABS(P2R) - STI = DABS(P2I) - P2M = DMAX1(STR,STI) - IF (P2M.LE.ASCLE) GO TO 260 - KFLAG = KFLAG + 1 - ASCLE = BRY(KFLAG) - S1R = S1R*P1R - S1I = S1I*P1R - S2R = P2R - S2I = P2I - STR = CSSR(KFLAG) - S1R = S1R*STR - S1I = S1I*STR - S2R = S2R*STR - S2I = S2I*STR - P1R = CSRR(KFLAG) - 260 CONTINUE - RETURN -C----------------------------------------------------------------------- -C IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON UNDERFLOW -C----------------------------------------------------------------------- - 261 CONTINUE - HELIM = 0.5D0*ELIM - ELM = DEXP(-ELIM) - CELMR = ELM - ASCLE = BRY(1) - ZDR = ZR - ZDI = ZI - IC = -1 - J = 2 - DO 262 I=1,INU - STR = S2R - STI = S2I - S2R = STR*CKR-STI*CKI+S1R - S2I = STI*CKR+STR*CKI+S1I - S1R = STR - S1I = STI - CKR = CKR+RZR - CKI = CKI+RZI - AS = AZABS(S2R,S2I) - ALAS = DLOG(AS) - P2R = -ZDR+ALAS - IF(P2R.LT.(-ELIM)) GO TO 263 - CALL AZLOG(S2R,S2I,STR,STI,IDUM) - P2R = -ZDR+STR - P2I = -ZDI+STI - P2M = DEXP(P2R)/TOL - P1R = P2M*DCOS(P2I) - P1I = P2M*DSIN(P2I) - CALL ZUCHK(P1R,P1I,NW,ASCLE,TOL) - IF(NW.NE.0) GO TO 263 - J = 3 - J - CYR(J) = P1R - CYI(J) = P1I - IF(IC.EQ.(I-1)) GO TO 264 - IC = I - GO TO 262 - 263 CONTINUE - IF(ALAS.LT.HELIM) GO TO 262 - ZDR = ZDR-ELIM - S1R = S1R*CELMR - S1I = S1I*CELMR - S2R = S2R*CELMR - S2I = S2I*CELMR - 262 CONTINUE - IF(N.NE.1) GO TO 270 - S1R = S2R - S1I = S2I - GO TO 270 - 264 CONTINUE - KFLAG = 1 - INUB = I+1 - S2R = CYR(J) - S2I = CYI(J) - J = 3 - J - S1R = CYR(J) - S1I = CYI(J) - IF(INUB.LE.INU) GO TO 225 - IF(N.NE.1) GO TO 240 - S1R = S2R - S1I = S2I - GO TO 240 - 270 CONTINUE - YR(1) = S1R - YI(1) = S1I - IF(N.EQ.1) GO TO 280 - YR(2) = S2R - YI(2) = S2I - 280 CONTINUE - ASCLE = BRY(1) - CALL ZKSCL(ZDR,ZDI,FNU,N,YR,YI,NZ,RZR,RZI,ASCLE,TOL,ELIM) - INU = N - NZ - IF (INU.LE.0) RETURN - KK = NZ + 1 - S1R = YR(KK) - S1I = YI(KK) - YR(KK) = S1R*CSRR(1) - YI(KK) = S1I*CSRR(1) - IF (INU.EQ.1) RETURN - KK = NZ + 2 - S2R = YR(KK) - S2I = YI(KK) - YR(KK) = S2R*CSRR(1) - YI(KK) = S2I*CSRR(1) - IF (INU.EQ.2) RETURN - T2 = FNU + DBLE(FLOAT(KK-1)) - CKR = T2*RZR - CKI = T2*RZI - KFLAG = 1 - GO TO 250 - 290 CONTINUE -C----------------------------------------------------------------------- -C SCALE BY DEXP(Z), IFLAG = 1 CASES -C----------------------------------------------------------------------- - KODED = 2 - IFLAG = 1 - KFLAG = 2 - GO TO 120 -C----------------------------------------------------------------------- -C FNU=HALF ODD INTEGER CASE, DNU=-0.5 -C----------------------------------------------------------------------- - 300 CONTINUE - S1R = COEFR - S1I = COEFI - S2R = COEFR - S2I = COEFI - GO TO 210 -C -C - 310 CONTINUE - NZ=-2 - RETURN - END diff --git a/amos/zbuni.f b/amos/zbuni.f deleted file mode 100644 index 965eddf..0000000 --- a/amos/zbuni.f +++ /dev/null @@ -1,174 +0,0 @@ - SUBROUTINE ZBUNI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NUI, NLAST, - * FNUL, TOL, ELIM, ALIM) -C***BEGIN PROLOGUE ZBUNI -C***REFER TO ZBESI,ZBESK -C -C ZBUNI COMPUTES THE I BESSEL FUNCTION FOR LARGE CABS(Z).GT. -C FNUL AND FNU+N-1.LT.FNUL. THE ORDER IS INCREASED FROM -C FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING -C ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z) -C ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2 -C -C***ROUTINES CALLED ZUNI1,ZUNI2,AZABS,D1MACH -C***END PROLOGUE ZBUNI -C COMPLEX CSCL,CSCR,CY,RZ,ST,S1,S2,Y,Z - DOUBLE PRECISION ALIM, AX, AY, CSCLR, CSCRR, CYI, CYR, DFNU, - * ELIM, FNU, FNUI, FNUL, GNU, RAZ, RZI, RZR, STI, STR, S1I, S1R, - * S2I, S2R, TOL, YI, YR, ZI, ZR, AZABS, ASCLE, BRY, C1R, C1I, C1M, - * D1MACH - INTEGER I, IFLAG, IFORM, K, KODE, N, NL, NLAST, NUI, NW, NZ - DIMENSION YR(N), YI(N), CYR(2), CYI(2), BRY(3) - NZ = 0 - AX = DABS(ZR)*1.7321D0 - AY = DABS(ZI) - IFORM = 1 - IF (AY.GT.AX) IFORM = 2 - IF (NUI.EQ.0) GO TO 60 - FNUI = DBLE(FLOAT(NUI)) - DFNU = FNU + DBLE(FLOAT(N-1)) - GNU = DFNU + FNUI - IF (IFORM.EQ.2) GO TO 10 -C----------------------------------------------------------------------- -C ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN -C -PI/3.LE.ARG(Z).LE.PI/3 -C----------------------------------------------------------------------- - CALL ZUNI1(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL, - * ELIM, ALIM) - GO TO 20 - 10 CONTINUE -C----------------------------------------------------------------------- -C ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU -C APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I -C AND HPI=PI/2 -C----------------------------------------------------------------------- - CALL ZUNI2(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL, - * ELIM, ALIM) - 20 CONTINUE - IF (NW.LT.0) GO TO 50 - IF (NW.NE.0) GO TO 90 - STR = AZABS(CYR(1),CYI(1)) -C---------------------------------------------------------------------- -C SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED -C---------------------------------------------------------------------- - BRY(1)=1.0D+3*D1MACH(1)/TOL - BRY(2) = 1.0D0/BRY(1) - BRY(3) = BRY(2) - IFLAG = 2 - ASCLE = BRY(2) - CSCLR = 1.0D0 - IF (STR.GT.BRY(1)) GO TO 21 - IFLAG = 1 - ASCLE = BRY(1) - CSCLR = 1.0D0/TOL - GO TO 25 - 21 CONTINUE - IF (STR.LT.BRY(2)) GO TO 25 - IFLAG = 3 - ASCLE=BRY(3) - CSCLR = TOL - 25 CONTINUE - CSCRR = 1.0D0/CSCLR - S1R = CYR(2)*CSCLR - S1I = CYI(2)*CSCLR - S2R = CYR(1)*CSCLR - S2I = CYI(1)*CSCLR - RAZ = 1.0D0/AZABS(ZR,ZI) - STR = ZR*RAZ - STI = -ZI*RAZ - RZR = (STR+STR)*RAZ - RZI = (STI+STI)*RAZ - DO 30 I=1,NUI - STR = S2R - STI = S2I - S2R = (DFNU+FNUI)*(RZR*STR-RZI*STI) + S1R - S2I = (DFNU+FNUI)*(RZR*STI+RZI*STR) + S1I - S1R = STR - S1I = STI - FNUI = FNUI - 1.0D0 - IF (IFLAG.GE.3) GO TO 30 - STR = S2R*CSCRR - STI = S2I*CSCRR - C1R = DABS(STR) - C1I = DABS(STI) - C1M = DMAX1(C1R,C1I) - IF (C1M.LE.ASCLE) GO TO 30 - IFLAG = IFLAG+1 - ASCLE = BRY(IFLAG) - S1R = S1R*CSCRR - S1I = S1I*CSCRR - S2R = STR - S2I = STI - CSCLR = CSCLR*TOL - CSCRR = 1.0D0/CSCLR - S1R = S1R*CSCLR - S1I = S1I*CSCLR - S2R = S2R*CSCLR - S2I = S2I*CSCLR - 30 CONTINUE - YR(N) = S2R*CSCRR - YI(N) = S2I*CSCRR - IF (N.EQ.1) RETURN - NL = N - 1 - FNUI = DBLE(FLOAT(NL)) - K = NL - DO 40 I=1,NL - STR = S2R - STI = S2I - S2R = (FNU+FNUI)*(RZR*STR-RZI*STI) + S1R - S2I = (FNU+FNUI)*(RZR*STI+RZI*STR) + S1I - S1R = STR - S1I = STI - STR = S2R*CSCRR - STI = S2I*CSCRR - YR(K) = STR - YI(K) = STI - FNUI = FNUI - 1.0D0 - K = K - 1 - IF (IFLAG.GE.3) GO TO 40 - C1R = DABS(STR) - C1I = DABS(STI) - C1M = DMAX1(C1R,C1I) - IF (C1M.LE.ASCLE) GO TO 40 - IFLAG = IFLAG+1 - ASCLE = BRY(IFLAG) - S1R = S1R*CSCRR - S1I = S1I*CSCRR - S2R = STR - S2I = STI - CSCLR = CSCLR*TOL - CSCRR = 1.0D0/CSCLR - S1R = S1R*CSCLR - S1I = S1I*CSCLR - S2R = S2R*CSCLR - S2I = S2I*CSCLR - 40 CONTINUE - RETURN - 50 CONTINUE - NZ = -1 - IF(NW.EQ.(-2)) NZ=-2 - RETURN - 60 CONTINUE - IF (IFORM.EQ.2) GO TO 70 -C----------------------------------------------------------------------- -C ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN -C -PI/3.LE.ARG(Z).LE.PI/3 -C----------------------------------------------------------------------- - CALL ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL, - * ELIM, ALIM) - GO TO 80 - 70 CONTINUE -C----------------------------------------------------------------------- -C ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU -C APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I -C AND HPI=PI/2 -C----------------------------------------------------------------------- - CALL ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL, - * ELIM, ALIM) - 80 CONTINUE - IF (NW.LT.0) GO TO 50 - NZ = NW - RETURN - 90 CONTINUE - NLAST = N - RETURN - END diff --git a/amos/zbunk.f b/amos/zbunk.f deleted file mode 100644 index b20b79f..0000000 --- a/amos/zbunk.f +++ /dev/null @@ -1,35 +0,0 @@ - SUBROUTINE ZBUNK(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, - * ALIM) -C***BEGIN PROLOGUE ZBUNK -C***REFER TO ZBESK,ZBESH -C -C ZBUNK COMPUTES THE K BESSEL FUNCTION FOR FNU.GT.FNUL. -C ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR K(FNU,Z) -C IN ZUNK1 AND THE EXPANSION FOR H(2,FNU,Z) IN ZUNK2 -C -C***ROUTINES CALLED ZUNK1,ZUNK2 -C***END PROLOGUE ZBUNK -C COMPLEX Y,Z - DOUBLE PRECISION ALIM, AX, AY, ELIM, FNU, TOL, YI, YR, ZI, ZR - INTEGER KODE, MR, N, NZ - DIMENSION YR(N), YI(N) - NZ = 0 - AX = DABS(ZR)*1.7321D0 - AY = DABS(ZI) - IF (AY.GT.AX) GO TO 10 -C----------------------------------------------------------------------- -C ASYMPTOTIC EXPANSION FOR K(FNU,Z) FOR LARGE FNU APPLIED IN -C -PI/3.LE.ARG(Z).LE.PI/3 -C----------------------------------------------------------------------- - CALL ZUNK1(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM) - GO TO 20 - 10 CONTINUE -C----------------------------------------------------------------------- -C ASYMPTOTIC EXPANSION FOR H(2,FNU,Z*EXP(M*HPI)) FOR LARGE FNU -C APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I -C AND HPI=PI/2 -C----------------------------------------------------------------------- - CALL ZUNK2(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM) - 20 CONTINUE - RETURN - END diff --git a/amos/zdiv.f b/amos/zdiv.f deleted file mode 100644 index f897f4e..0000000 --- a/amos/zdiv.f +++ /dev/null @@ -1,19 +0,0 @@ - SUBROUTINE ZDIV(AR, AI, BR, BI, CR, CI) -C***BEGIN PROLOGUE ZDIV -C***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY -C -C DOUBLE PRECISION COMPLEX DIVIDE C=A/B. -C -C***ROUTINES CALLED AZABS -C***END PROLOGUE ZDIV - DOUBLE PRECISION AR, AI, BR, BI, CR, CI, BM, CA, CB, CC, CD - DOUBLE PRECISION AZABS - BM = 1.0D0/AZABS(BR,BI) - CC = BR*BM - CD = BI*BM - CA = (AR*CC+AI*CD)*BM - CB = (AI*CC-AR*CD)*BM - CR = CA - CI = CB - RETURN - END diff --git a/amos/zexp.f b/amos/zexp.f deleted file mode 100644 index 8a34276..0000000 --- a/amos/zexp.f +++ /dev/null @@ -1,16 +0,0 @@ - SUBROUTINE AZEXP(AR, AI, BR, BI) -C***BEGIN PROLOGUE AZEXP -C***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY -C -C DOUBLE PRECISION COMPLEX EXPONENTIAL FUNCTION B=EXP(A) -C -C***ROUTINES CALLED (NONE) -C***END PROLOGUE AZEXP - DOUBLE PRECISION AR, AI, BR, BI, ZM, CA, CB - ZM = DEXP(AR) - CA = ZM*DCOS(AI) - CB = ZM*DSIN(AI) - BR = CA - BI = CB - RETURN - END diff --git a/amos/zkscl.f b/amos/zkscl.f deleted file mode 100644 index 90df795..0000000 --- a/amos/zkscl.f +++ /dev/null @@ -1,121 +0,0 @@ - SUBROUTINE ZKSCL(ZRR,ZRI,FNU,N,YR,YI,NZ,RZR,RZI,ASCLE,TOL,ELIM) -C***BEGIN PROLOGUE ZKSCL -C***REFER TO ZBESK -C -C SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE -C ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN -C RETURN WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL. -C -C***ROUTINES CALLED ZUCHK,AZABS,AZLOG -C***END PROLOGUE ZKSCL -C COMPLEX CK,CS,CY,CZERO,RZ,S1,S2,Y,ZR,ZD,CELM - DOUBLE PRECISION ACS, AS, ASCLE, CKI, CKR, CSI, CSR, CYI, - * CYR, ELIM, FN, FNU, RZI, RZR, STR, S1I, S1R, S2I, - * S2R, TOL, YI, YR, ZEROI, ZEROR, ZRI, ZRR, AZABS, - * ZDR, ZDI, CELMR, ELM, HELIM, ALAS - INTEGER I, IC, IDUM, KK, N, NN, NW, NZ - DIMENSION YR(N), YI(N), CYR(2), CYI(2) - DATA ZEROR,ZEROI / 0.0D0 , 0.0D0 / -C - NZ = 0 - IC = 0 - NN = MIN0(2,N) - DO 10 I=1,NN - S1R = YR(I) - S1I = YI(I) - CYR(I) = S1R - CYI(I) = S1I - AS = AZABS(S1R,S1I) - ACS = -ZRR + DLOG(AS) - NZ = NZ + 1 - YR(I) = ZEROR - YI(I) = ZEROI - IF (ACS.LT.(-ELIM)) GO TO 10 - CALL AZLOG(S1R, S1I, CSR, CSI, IDUM) - CSR = CSR - ZRR - CSI = CSI - ZRI - STR = DEXP(CSR)/TOL - CSR = STR*DCOS(CSI) - CSI = STR*DSIN(CSI) - CALL ZUCHK(CSR, CSI, NW, ASCLE, TOL) - IF (NW.NE.0) GO TO 10 - YR(I) = CSR - YI(I) = CSI - IC = I - NZ = NZ - 1 - 10 CONTINUE - IF (N.EQ.1) RETURN - IF (IC.GT.1) GO TO 20 - YR(1) = ZEROR - YI(1) = ZEROI - NZ = 2 - 20 CONTINUE - IF (N.EQ.2) RETURN - IF (NZ.EQ.0) RETURN - FN = FNU + 1.0D0 - CKR = FN*RZR - CKI = FN*RZI - S1R = CYR(1) - S1I = CYI(1) - S2R = CYR(2) - S2I = CYI(2) - HELIM = 0.5D0*ELIM - ELM = DEXP(-ELIM) - CELMR = ELM - ZDR = ZRR - ZDI = ZRI -C -C FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE RECURRENCE IF -C S2 GETS LARGER THAN EXP(ELIM/2) -C - DO 30 I=3,N - KK = I - CSR = S2R - CSI = S2I - S2R = CKR*CSR - CKI*CSI + S1R - S2I = CKI*CSR + CKR*CSI + S1I - S1R = CSR - S1I = CSI - CKR = CKR + RZR - CKI = CKI + RZI - AS = AZABS(S2R,S2I) - ALAS = DLOG(AS) - ACS = -ZDR + ALAS - NZ = NZ + 1 - YR(I) = ZEROR - YI(I) = ZEROI - IF (ACS.LT.(-ELIM)) GO TO 25 - CALL AZLOG(S2R, S2I, CSR, CSI, IDUM) - CSR = CSR - ZDR - CSI = CSI - ZDI - STR = DEXP(CSR)/TOL - CSR = STR*DCOS(CSI) - CSI = STR*DSIN(CSI) - CALL ZUCHK(CSR, CSI, NW, ASCLE, TOL) - IF (NW.NE.0) GO TO 25 - YR(I) = CSR - YI(I) = CSI - NZ = NZ - 1 - IF (IC.EQ.KK-1) GO TO 40 - IC = KK - GO TO 30 - 25 CONTINUE - IF(ALAS.LT.HELIM) GO TO 30 - ZDR = ZDR - ELIM - S1R = S1R*CELMR - S1I = S1I*CELMR - S2R = S2R*CELMR - S2I = S2I*CELMR - 30 CONTINUE - NZ = N - IF(IC.EQ.N) NZ=N-1 - GO TO 45 - 40 CONTINUE - NZ = KK - 2 - 45 CONTINUE - DO 50 I=1,NZ - YR(I) = ZEROR - YI(I) = ZEROI - 50 CONTINUE - RETURN - END diff --git a/amos/zlog.f b/amos/zlog.f deleted file mode 100644 index 403d8be..0000000 --- a/amos/zlog.f +++ /dev/null @@ -1,41 +0,0 @@ - SUBROUTINE AZLOG(AR, AI, BR, BI, IERR) -C***BEGIN PROLOGUE AZLOG -C***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY -C -C DOUBLE PRECISION COMPLEX LOGARITHM B=CLOG(A) -C IERR=0,NORMAL RETURN IERR=1, Z=CMPLX(0.0,0.0) -C***ROUTINES CALLED AZABS -C***END PROLOGUE AZLOG - DOUBLE PRECISION AR, AI, BR, BI, ZM, DTHETA, DPI, DHPI - DOUBLE PRECISION AZABS - DATA DPI , DHPI / 3.141592653589793238462643383D+0, - 1 1.570796326794896619231321696D+0/ -C - IERR=0 - IF (AR.EQ.0.0D+0) GO TO 10 - IF (AI.EQ.0.0D+0) GO TO 20 - DTHETA = DATAN(AI/AR) - IF (DTHETA.LE.0.0D+0) GO TO 40 - IF (AR.LT.0.0D+0) DTHETA = DTHETA - DPI - GO TO 50 - 10 IF (AI.EQ.0.0D+0) GO TO 60 - BI = DHPI - BR = DLOG(DABS(AI)) - IF (AI.LT.0.0D+0) BI = -BI - RETURN - 20 IF (AR.GT.0.0D+0) GO TO 30 - BR = DLOG(DABS(AR)) - BI = DPI - RETURN - 30 BR = DLOG(AR) - BI = 0.0D+0 - RETURN - 40 IF (AR.LT.0.0D+0) DTHETA = DTHETA + DPI - 50 ZM = AZABS(AR,AI) - BR = DLOG(ZM) - BI = DTHETA - RETURN - 60 CONTINUE - IERR=1 - RETURN - END diff --git a/amos/zmlri.f b/amos/zmlri.f deleted file mode 100644 index 5bc8d77..0000000 --- a/amos/zmlri.f +++ /dev/null @@ -1,204 +0,0 @@ - SUBROUTINE ZMLRI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL) -C***BEGIN PROLOGUE ZMLRI -C***REFER TO ZBESI,ZBESK -C -C ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE -C MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES. -C -C***ROUTINES CALLED DGAMLN,D1MACH,AZABS,AZEXP,AZLOG,ZMLT -C***END PROLOGUE ZMLRI -C COMPLEX CK,CNORM,CONE,CTWO,CZERO,PT,P1,P2,RZ,SUM,Y,Z - DOUBLE PRECISION ACK, AK, AP, AT, AZ, BK, CKI, CKR, CNORMI, - * CNORMR, CONEI, CONER, FKAP, FKK, FLAM, FNF, FNU, PTI, PTR, P1I, - * P1R, P2I, P2R, RAZ, RHO, RHO2, RZI, RZR, SCLE, STI, STR, SUMI, - * SUMR, TFNF, TOL, TST, YI, YR, ZEROI, ZEROR, ZI, ZR, DGAMLN, - * D1MACH, AZABS - INTEGER I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, KODE, M, N, NZ - DIMENSION YR(N), YI(N) - DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / - SCLE = D1MACH(1)/TOL - NZ=0 - AZ = AZABS(ZR,ZI) - IAZ = INT(SNGL(AZ)) - IFNU = INT(SNGL(FNU)) - INU = IFNU + N - 1 - AT = DBLE(FLOAT(IAZ)) + 1.0D0 - RAZ = 1.0D0/AZ - STR = ZR*RAZ - STI = -ZI*RAZ - CKR = STR*AT*RAZ - CKI = STI*AT*RAZ - RZR = (STR+STR)*RAZ - RZI = (STI+STI)*RAZ - P1R = ZEROR - P1I = ZEROI - P2R = CONER - P2I = CONEI - ACK = (AT+1.0D0)*RAZ - RHO = ACK + DSQRT(ACK*ACK-1.0D0) - RHO2 = RHO*RHO - TST = (RHO2+RHO2)/((RHO2-1.0D0)*(RHO-1.0D0)) - TST = TST/TOL -C----------------------------------------------------------------------- -C COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES -C----------------------------------------------------------------------- - AK = AT - DO 10 I=1,80 - PTR = P2R - PTI = P2I - P2R = P1R - (CKR*PTR-CKI*PTI) - P2I = P1I - (CKI*PTR+CKR*PTI) - P1R = PTR - P1I = PTI - CKR = CKR + RZR - CKI = CKI + RZI - AP = AZABS(P2R,P2I) - IF (AP.GT.TST*AK*AK) GO TO 20 - AK = AK + 1.0D0 - 10 CONTINUE - GO TO 110 - 20 CONTINUE - I = I + 1 - K = 0 - IF (INU.LT.IAZ) GO TO 40 -C----------------------------------------------------------------------- -C COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS -C----------------------------------------------------------------------- - P1R = ZEROR - P1I = ZEROI - P2R = CONER - P2I = CONEI - AT = DBLE(FLOAT(INU)) + 1.0D0 - STR = ZR*RAZ - STI = -ZI*RAZ - CKR = STR*AT*RAZ - CKI = STI*AT*RAZ - ACK = AT*RAZ - TST = DSQRT(ACK/TOL) - ITIME = 1 - DO 30 K=1,80 - PTR = P2R - PTI = P2I - P2R = P1R - (CKR*PTR-CKI*PTI) - P2I = P1I - (CKR*PTI+CKI*PTR) - P1R = PTR - P1I = PTI - CKR = CKR + RZR - CKI = CKI + RZI - AP = AZABS(P2R,P2I) - IF (AP.LT.TST) GO TO 30 - IF (ITIME.EQ.2) GO TO 40 - ACK = AZABS(CKR,CKI) - FLAM = ACK + DSQRT(ACK*ACK-1.0D0) - FKAP = AP/AZABS(P1R,P1I) - RHO = DMIN1(FLAM,FKAP) - TST = TST*DSQRT(RHO/(RHO*RHO-1.0D0)) - ITIME = 2 - 30 CONTINUE - GO TO 110 - 40 CONTINUE -C----------------------------------------------------------------------- -C BACKWARD RECURRENCE AND SUM NORMALIZING RELATION -C----------------------------------------------------------------------- - K = K + 1 - KK = MAX0(I+IAZ,K+INU) - FKK = DBLE(FLOAT(KK)) - P1R = ZEROR - P1I = ZEROI -C----------------------------------------------------------------------- -C SCALE P2 AND SUM BY SCLE -C----------------------------------------------------------------------- - P2R = SCLE - P2I = ZEROI - FNF = FNU - DBLE(FLOAT(IFNU)) - TFNF = FNF + FNF - BK = DGAMLN(FKK+TFNF+1.0D0,IDUM) - DGAMLN(FKK+1.0D0,IDUM) - - * DGAMLN(TFNF+1.0D0,IDUM) - BK = DEXP(BK) - SUMR = ZEROR - SUMI = ZEROI - KM = KK - INU - DO 50 I=1,KM - PTR = P2R - PTI = P2I - P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) - P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI) - P1R = PTR - P1I = PTI - AK = 1.0D0 - TFNF/(FKK+TFNF) - ACK = BK*AK - SUMR = SUMR + (ACK+BK)*P1R - SUMI = SUMI + (ACK+BK)*P1I - BK = ACK - FKK = FKK - 1.0D0 - 50 CONTINUE - YR(N) = P2R - YI(N) = P2I - IF (N.EQ.1) GO TO 70 - DO 60 I=2,N - PTR = P2R - PTI = P2I - P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) - P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI) - P1R = PTR - P1I = PTI - AK = 1.0D0 - TFNF/(FKK+TFNF) - ACK = BK*AK - SUMR = SUMR + (ACK+BK)*P1R - SUMI = SUMI + (ACK+BK)*P1I - BK = ACK - FKK = FKK - 1.0D0 - M = N - I + 1 - YR(M) = P2R - YI(M) = P2I - 60 CONTINUE - 70 CONTINUE - IF (IFNU.LE.0) GO TO 90 - DO 80 I=1,IFNU - PTR = P2R - PTI = P2I - P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) - P2I = P1I + (FKK+FNF)*(RZR*PTI+RZI*PTR) - P1R = PTR - P1I = PTI - AK = 1.0D0 - TFNF/(FKK+TFNF) - ACK = BK*AK - SUMR = SUMR + (ACK+BK)*P1R - SUMI = SUMI + (ACK+BK)*P1I - BK = ACK - FKK = FKK - 1.0D0 - 80 CONTINUE - 90 CONTINUE - PTR = ZR - PTI = ZI - IF (KODE.EQ.2) PTR = ZEROR - CALL AZLOG(RZR, RZI, STR, STI, IDUM) - P1R = -FNF*STR + PTR - P1I = -FNF*STI + PTI - AP = DGAMLN(1.0D0+FNF,IDUM) - PTR = P1R - AP - PTI = P1I -C----------------------------------------------------------------------- -C THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW -C IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES -C----------------------------------------------------------------------- - P2R = P2R + SUMR - P2I = P2I + SUMI - AP = AZABS(P2R,P2I) - P1R = 1.0D0/AP - CALL AZEXP(PTR, PTI, STR, STI) - CKR = STR*P1R - CKI = STI*P1R - PTR = P2R*P1R - PTI = -P2I*P1R - CALL ZMLT(CKR, CKI, PTR, PTI, CNORMR, CNORMI) - DO 100 I=1,N - STR = YR(I)*CNORMR - YI(I)*CNORMI - YI(I) = YR(I)*CNORMI + YI(I)*CNORMR - YR(I) = STR - 100 CONTINUE - RETURN - 110 CONTINUE - NZ=-2 - RETURN - END diff --git a/amos/zmlt.f b/amos/zmlt.f deleted file mode 100644 index 3bde7d3..0000000 --- a/amos/zmlt.f +++ /dev/null @@ -1,15 +0,0 @@ - SUBROUTINE ZMLT(AR, AI, BR, BI, CR, CI) -C***BEGIN PROLOGUE ZMLT -C***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY -C -C DOUBLE PRECISION COMPLEX MULTIPLY, C=A*B. -C -C***ROUTINES CALLED (NONE) -C***END PROLOGUE ZMLT - DOUBLE PRECISION AR, AI, BR, BI, CR, CI, CA, CB - CA = AR*BR - AI*BI - CB = AR*BI + AI*BR - CR = CA - CI = CB - RETURN - END diff --git a/amos/zrati.f b/amos/zrati.f deleted file mode 100644 index d8ab777..0000000 --- a/amos/zrati.f +++ /dev/null @@ -1,132 +0,0 @@ - SUBROUTINE ZRATI(ZR, ZI, FNU, N, CYR, CYI, TOL) -C***BEGIN PROLOGUE ZRATI -C***REFER TO ZBESI,ZBESK,ZBESH -C -C ZRATI COMPUTES RATIOS OF I BESSEL FUNCTIONS BY BACKWARD -C RECURRENCE. THE STARTING INDEX IS DETERMINED BY FORWARD -C RECURRENCE AS DESCRIBED IN J. RES. OF NAT. BUR. OF STANDARDS-B, -C MATHEMATICAL SCIENCES, VOL 77B, P111-114, SEPTEMBER, 1973, -C BESSEL FUNCTIONS I AND J OF COMPLEX ARGUMENT AND INTEGER ORDER, -C BY D. J. SOOKNE. -C -C***ROUTINES CALLED AZABS,ZDIV -C***END PROLOGUE ZRATI -C COMPLEX Z,CY(1),CONE,CZERO,P1,P2,T1,RZ,PT,CDFNU - DOUBLE PRECISION AK, AMAGZ, AP1, AP2, ARG, AZ, CDFNUI, CDFNUR, - * CONEI, CONER, CYI, CYR, CZEROI, CZEROR, DFNU, FDNU, FLAM, FNU, - * FNUP, PTI, PTR, P1I, P1R, P2I, P2R, RAK, RAP1, RHO, RT2, RZI, - * RZR, TEST, TEST1, TOL, TTI, TTR, T1I, T1R, ZI, ZR, AZABS - INTEGER I, ID, IDNU, INU, ITIME, K, KK, MAGZ, N - DIMENSION CYR(N), CYI(N) - DATA CZEROR,CZEROI,CONER,CONEI,RT2/ - 1 0.0D0, 0.0D0, 1.0D0, 0.0D0, 1.41421356237309505D0 / - AZ = AZABS(ZR,ZI) - INU = INT(SNGL(FNU)) - IDNU = INU + N - 1 - MAGZ = INT(SNGL(AZ)) - AMAGZ = DBLE(FLOAT(MAGZ+1)) - FDNU = DBLE(FLOAT(IDNU)) - FNUP = DMAX1(AMAGZ,FDNU) - ID = IDNU - MAGZ - 1 - ITIME = 1 - K = 1 - PTR = 1.0D0/AZ - RZR = PTR*(ZR+ZR)*PTR - RZI = -PTR*(ZI+ZI)*PTR - T1R = RZR*FNUP - T1I = RZI*FNUP - P2R = -T1R - P2I = -T1I - P1R = CONER - P1I = CONEI - T1R = T1R + RZR - T1I = T1I + RZI - IF (ID.GT.0) ID = 0 - AP2 = AZABS(P2R,P2I) - AP1 = AZABS(P1R,P1I) -C----------------------------------------------------------------------- -C THE OVERFLOW TEST ON K(FNU+I-1,Z) BEFORE THE CALL TO CBKNU -C GUARANTEES THAT P2 IS ON SCALE. SCALE TEST1 AND ALL SUBSEQUENT -C P2 VALUES BY AP1 TO ENSURE THAT AN OVERFLOW DOES NOT OCCUR -C PREMATURELY. -C----------------------------------------------------------------------- - ARG = (AP2+AP2)/(AP1*TOL) - TEST1 = DSQRT(ARG) - TEST = TEST1 - RAP1 = 1.0D0/AP1 - P1R = P1R*RAP1 - P1I = P1I*RAP1 - P2R = P2R*RAP1 - P2I = P2I*RAP1 - AP2 = AP2*RAP1 - 10 CONTINUE - K = K + 1 - AP1 = AP2 - PTR = P2R - PTI = P2I - P2R = P1R - (T1R*PTR-T1I*PTI) - P2I = P1I - (T1R*PTI+T1I*PTR) - P1R = PTR - P1I = PTI - T1R = T1R + RZR - T1I = T1I + RZI - AP2 = AZABS(P2R,P2I) - IF (AP1.LE.TEST) GO TO 10 - IF (ITIME.EQ.2) GO TO 20 - AK = AZABS(T1R,T1I)*0.5D0 - FLAM = AK + DSQRT(AK*AK-1.0D0) - RHO = DMIN1(AP2/AP1,FLAM) - TEST = TEST1*DSQRT(RHO/(RHO*RHO-1.0D0)) - ITIME = 2 - GO TO 10 - 20 CONTINUE - KK = K + 1 - ID - AK = DBLE(FLOAT(KK)) - T1R = AK - T1I = CZEROI - DFNU = FNU + DBLE(FLOAT(N-1)) - P1R = 1.0D0/AP2 - P1I = CZEROI - P2R = CZEROR - P2I = CZEROI - DO 30 I=1,KK - PTR = P1R - PTI = P1I - RAP1 = DFNU + T1R - TTR = RZR*RAP1 - TTI = RZI*RAP1 - P1R = (PTR*TTR-PTI*TTI) + P2R - P1I = (PTR*TTI+PTI*TTR) + P2I - P2R = PTR - P2I = PTI - T1R = T1R - CONER - 30 CONTINUE - IF (P1R.NE.CZEROR .OR. P1I.NE.CZEROI) GO TO 40 - P1R = TOL - P1I = TOL - 40 CONTINUE - CALL ZDIV(P2R, P2I, P1R, P1I, CYR(N), CYI(N)) - IF (N.EQ.1) RETURN - K = N - 1 - AK = DBLE(FLOAT(K)) - T1R = AK - T1I = CZEROI - CDFNUR = FNU*RZR - CDFNUI = FNU*RZI - DO 60 I=2,N - PTR = CDFNUR + (T1R*RZR-T1I*RZI) + CYR(K+1) - PTI = CDFNUI + (T1R*RZI+T1I*RZR) + CYI(K+1) - AK = AZABS(PTR,PTI) - IF (AK.NE.CZEROR) GO TO 50 - PTR = TOL - PTI = TOL - AK = TOL*RT2 - 50 CONTINUE - RAK = CONER/AK - CYR(K) = RAK*PTR*RAK - CYI(K) = -RAK*PTI*RAK - T1R = T1R - CONER - K = K - 1 - 60 CONTINUE - RETURN - END diff --git a/amos/zs1s2.f b/amos/zs1s2.f deleted file mode 100644 index 194be44..0000000 --- a/amos/zs1s2.f +++ /dev/null @@ -1,49 +0,0 @@ - SUBROUTINE ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NZ, ASCLE, ALIM, - * IUF) -C***BEGIN PROLOGUE ZS1S2 -C***REFER TO ZBESK,ZAIRY -C -C ZS1S2 TESTS FOR A POSSIBLE UNDERFLOW RESULTING FROM THE -C ADDITION OF THE I AND K FUNCTIONS IN THE ANALYTIC CON- -C TINUATION FORMULA WHERE S1=K FUNCTION AND S2=I FUNCTION. -C ON KODE=1 THE I AND K FUNCTIONS ARE DIFFERENT ORDERS OF -C MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER -C OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE -C PRECISION ABOVE THE UNDERFLOW LIMIT. -C -C***ROUTINES CALLED AZABS,AZEXP,AZLOG -C***END PROLOGUE ZS1S2 -C COMPLEX CZERO,C1,S1,S1D,S2,ZR - DOUBLE PRECISION AA, ALIM, ALN, ASCLE, AS1, AS2, C1I, C1R, S1DI, - * S1DR, S1I, S1R, S2I, S2R, ZEROI, ZEROR, ZRI, ZRR, AZABS - INTEGER IUF, IDUM, NZ - DATA ZEROR,ZEROI / 0.0D0 , 0.0D0 / - NZ = 0 - AS1 = AZABS(S1R,S1I) - AS2 = AZABS(S2R,S2I) - IF (S1R.EQ.0.0D0 .AND. S1I.EQ.0.0D0) GO TO 10 - IF (AS1.EQ.0.0D0) GO TO 10 - ALN = -ZRR - ZRR + DLOG(AS1) - S1DR = S1R - S1DI = S1I - S1R = ZEROR - S1I = ZEROI - AS1 = ZEROR - IF (ALN.LT.(-ALIM)) GO TO 10 - CALL AZLOG(S1DR, S1DI, C1R, C1I, IDUM) - C1R = C1R - ZRR - ZRR - C1I = C1I - ZRI - ZRI - CALL AZEXP(C1R, C1I, S1R, S1I) - AS1 = AZABS(S1R,S1I) - IUF = IUF + 1 - 10 CONTINUE - AA = DMAX1(AS1,AS2) - IF (AA.GT.ASCLE) RETURN - S1R = ZEROR - S1I = ZEROI - S2R = ZEROR - S2I = ZEROI - NZ = 1 - IUF = 0 - RETURN - END diff --git a/amos/zseri.f b/amos/zseri.f deleted file mode 100644 index 4c487f0..0000000 --- a/amos/zseri.f +++ /dev/null @@ -1,190 +0,0 @@ - SUBROUTINE ZSERI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, - * ALIM) -C***BEGIN PROLOGUE ZSERI -C***REFER TO ZBESI,ZBESK -C -C ZSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY -C MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE -C REGION CABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN. -C NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO -C DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE -C CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE -C COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ). -C -C***ROUTINES CALLED DGAMLN,D1MACH,ZUCHK,AZABS,ZDIV,AZLOG,ZMLT -C***END PROLOGUE ZSERI -C COMPLEX AK1,CK,COEF,CONE,CRSC,CSCL,CZ,CZERO,HZ,RZ,S1,S2,Y,Z - DOUBLE PRECISION AA, ACZ, AK, AK1I, AK1R, ALIM, ARM, ASCLE, ATOL, - * AZ, CKI, CKR, COEFI, COEFR, CONEI, CONER, CRSCR, CZI, CZR, DFNU, - * ELIM, FNU, FNUP, HZI, HZR, RAZ, RS, RTR1, RZI, RZR, S, SS, STI, - * STR, S1I, S1R, S2I, S2R, TOL, YI, YR, WI, WR, ZEROI, ZEROR, ZI, - * ZR, DGAMLN, D1MACH, AZABS - INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NZ, NW - DIMENSION YR(N), YI(N), WR(2), WI(2) - DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / -C - NZ = 0 - AZ = AZABS(ZR,ZI) - IF (AZ.EQ.0.0D0) GO TO 160 - ARM = 1.0D+3*D1MACH(1) - RTR1 = DSQRT(ARM) - CRSCR = 1.0D0 - IFLAG = 0 - IF (AZ.LT.ARM) GO TO 150 - HZR = 0.5D0*ZR - HZI = 0.5D0*ZI - CZR = ZEROR - CZI = ZEROI - IF (AZ.LE.RTR1) GO TO 10 - CALL ZMLT(HZR, HZI, HZR, HZI, CZR, CZI) - 10 CONTINUE - ACZ = AZABS(CZR,CZI) - NN = N - CALL AZLOG(HZR, HZI, CKR, CKI, IDUM) - 20 CONTINUE - DFNU = FNU + DBLE(FLOAT(NN-1)) - FNUP = DFNU + 1.0D0 -C----------------------------------------------------------------------- -C UNDERFLOW TEST -C----------------------------------------------------------------------- - AK1R = CKR*DFNU - AK1I = CKI*DFNU - AK = DGAMLN(FNUP,IDUM) - AK1R = AK1R - AK - IF (KODE.EQ.2) AK1R = AK1R - ZR - IF (AK1R.GT.(-ELIM)) GO TO 40 - 30 CONTINUE - NZ = NZ + 1 - YR(NN) = ZEROR - YI(NN) = ZEROI - IF (ACZ.GT.DFNU) GO TO 190 - NN = NN - 1 - IF (NN.EQ.0) RETURN - GO TO 20 - 40 CONTINUE - IF (AK1R.GT.(-ALIM)) GO TO 50 - IFLAG = 1 - SS = 1.0D0/TOL - CRSCR = TOL - ASCLE = ARM*SS - 50 CONTINUE - AA = DEXP(AK1R) - IF (IFLAG.EQ.1) AA = AA*SS - COEFR = AA*DCOS(AK1I) - COEFI = AA*DSIN(AK1I) - ATOL = TOL*ACZ/FNUP - IL = MIN0(2,NN) - DO 90 I=1,IL - DFNU = FNU + DBLE(FLOAT(NN-I)) - FNUP = DFNU + 1.0D0 - S1R = CONER - S1I = CONEI - IF (ACZ.LT.TOL*FNUP) GO TO 70 - AK1R = CONER - AK1I = CONEI - AK = FNUP + 2.0D0 - S = FNUP - AA = 2.0D0 - 60 CONTINUE - RS = 1.0D0/S - STR = AK1R*CZR - AK1I*CZI - STI = AK1R*CZI + AK1I*CZR - AK1R = STR*RS - AK1I = STI*RS - S1R = S1R + AK1R - S1I = S1I + AK1I - S = S + AK - AK = AK + 2.0D0 - AA = AA*ACZ*RS - IF (AA.GT.ATOL) GO TO 60 - 70 CONTINUE - S2R = S1R*COEFR - S1I*COEFI - S2I = S1R*COEFI + S1I*COEFR - WR(I) = S2R - WI(I) = S2I - IF (IFLAG.EQ.0) GO TO 80 - CALL ZUCHK(S2R, S2I, NW, ASCLE, TOL) - IF (NW.NE.0) GO TO 30 - 80 CONTINUE - M = NN - I + 1 - YR(M) = S2R*CRSCR - YI(M) = S2I*CRSCR - IF (I.EQ.IL) GO TO 90 - CALL ZDIV(COEFR, COEFI, HZR, HZI, STR, STI) - COEFR = STR*DFNU - COEFI = STI*DFNU - 90 CONTINUE - IF (NN.LE.2) RETURN - K = NN - 2 - AK = DBLE(FLOAT(K)) - RAZ = 1.0D0/AZ - STR = ZR*RAZ - STI = -ZI*RAZ - RZR = (STR+STR)*RAZ - RZI = (STI+STI)*RAZ - IF (IFLAG.EQ.1) GO TO 120 - IB = 3 - 100 CONTINUE - DO 110 I=IB,NN - YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2) - YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2) - AK = AK - 1.0D0 - K = K - 1 - 110 CONTINUE - RETURN -C----------------------------------------------------------------------- -C RECUR BACKWARD WITH SCALED VALUES -C----------------------------------------------------------------------- - 120 CONTINUE -C----------------------------------------------------------------------- -C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE -C UNDERFLOW LIMIT = ASCLE = D1MACH(1)*SS*1.0D+3 -C----------------------------------------------------------------------- - S1R = WR(1) - S1I = WI(1) - S2R = WR(2) - S2I = WI(2) - DO 130 L=3,NN - CKR = S2R - CKI = S2I - S2R = S1R + (AK+FNU)*(RZR*CKR-RZI*CKI) - S2I = S1I + (AK+FNU)*(RZR*CKI+RZI*CKR) - S1R = CKR - S1I = CKI - CKR = S2R*CRSCR - CKI = S2I*CRSCR - YR(K) = CKR - YI(K) = CKI - AK = AK - 1.0D0 - K = K - 1 - IF (AZABS(CKR,CKI).GT.ASCLE) GO TO 140 - 130 CONTINUE - RETURN - 140 CONTINUE - IB = L + 1 - IF (IB.GT.NN) RETURN - GO TO 100 - 150 CONTINUE - NZ = N - IF (FNU.EQ.0.0D0) NZ = NZ - 1 - 160 CONTINUE - YR(1) = ZEROR - YI(1) = ZEROI - IF (FNU.NE.0.0D0) GO TO 170 - YR(1) = CONER - YI(1) = CONEI - 170 CONTINUE - IF (N.EQ.1) RETURN - DO 180 I=2,N - YR(I) = ZEROR - YI(I) = ZEROI - 180 CONTINUE - RETURN -C----------------------------------------------------------------------- -C RETURN WITH NZ.LT.0 IF CABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE -C THE CALCULATION IN CBINU WITH N=N-IABS(NZ) -C----------------------------------------------------------------------- - 190 CONTINUE - NZ = -NZ - RETURN - END diff --git a/amos/zshch.f b/amos/zshch.f deleted file mode 100644 index 168e62e..0000000 --- a/amos/zshch.f +++ /dev/null @@ -1,22 +0,0 @@ - SUBROUTINE ZSHCH(ZR, ZI, CSHR, CSHI, CCHR, CCHI) -C***BEGIN PROLOGUE ZSHCH -C***REFER TO ZBESK,ZBESH -C -C ZSHCH COMPUTES THE COMPLEX HYPERBOLIC FUNCTIONS CSH=SINH(X+I*Y) -C AND CCH=COSH(X+I*Y), WHERE I**2=-1. -C -C***ROUTINES CALLED (NONE) -C***END PROLOGUE ZSHCH -C - DOUBLE PRECISION CCHI, CCHR, CH, CN, CSHI, CSHR, SH, SN, ZI, ZR, - * DCOSH, DSINH - SH = DSINH(ZR) - CH = DCOSH(ZR) - SN = DSIN(ZI) - CN = DCOS(ZI) - CSHR = SH*CN - CSHI = CH*SN - CCHR = CH*CN - CCHI = SH*SN - RETURN - END diff --git a/amos/zsqrt.f b/amos/zsqrt.f deleted file mode 100644 index 43ba617..0000000 --- a/amos/zsqrt.f +++ /dev/null @@ -1,44 +0,0 @@ - SUBROUTINE AZSQRT(AR, AI, BR, BI) -C***BEGIN PROLOGUE AZSQRT -C***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY -C -C DOUBLE PRECISION COMPLEX SQUARE ROOT, B=CSQRT(A) -C -C***ROUTINES CALLED AZABS -C***END PROLOGUE AZSQRT - DOUBLE PRECISION AR, AI, BR, BI, ZM, DTHETA, DPI, DRT - DOUBLE PRECISION AZABS - DATA DRT , DPI / 7.071067811865475244008443621D-1, - 1 3.141592653589793238462643383D+0/ - ZM = AZABS(AR,AI) - ZM = DSQRT(ZM) - IF (AR.EQ.0.0D+0) GO TO 10 - IF (AI.EQ.0.0D+0) GO TO 20 - DTHETA = DATAN(AI/AR) - IF (DTHETA.LE.0.0D+0) GO TO 40 - IF (AR.LT.0.0D+0) DTHETA = DTHETA - DPI - GO TO 50 - 10 IF (AI.GT.0.0D+0) GO TO 60 - IF (AI.LT.0.0D+0) GO TO 70 - BR = 0.0D+0 - BI = 0.0D+0 - RETURN - 20 IF (AR.GT.0.0D+0) GO TO 30 - BR = 0.0D+0 - BI = DSQRT(DABS(AR)) - RETURN - 30 BR = DSQRT(AR) - BI = 0.0D+0 - RETURN - 40 IF (AR.LT.0.0D+0) DTHETA = DTHETA + DPI - 50 DTHETA = DTHETA*0.5D+0 - BR = ZM*DCOS(DTHETA) - BI = ZM*DSIN(DTHETA) - RETURN - 60 BR = ZM*DRT - BI = ZM*DRT - RETURN - 70 BR = ZM*DRT - BI = -ZM*DRT - RETURN - END diff --git a/amos/zuchk.f b/amos/zuchk.f deleted file mode 100644 index d15dc84..0000000 --- a/amos/zuchk.f +++ /dev/null @@ -1,28 +0,0 @@ - SUBROUTINE ZUCHK(YR, YI, NZ, ASCLE, TOL) -C***BEGIN PROLOGUE ZUCHK -C***REFER TO ZSERI,ZUOIK,ZUNK1,ZUNK2,ZUNI1,ZUNI2,ZKSCL -C -C Y ENTERS AS A SCALED QUANTITY WHOSE MAGNITUDE IS GREATER THAN -C EXP(-ALIM)=ASCLE=1.0E+3*D1MACH(1)/TOL. THE TEST IS MADE TO SEE -C IF THE MAGNITUDE OF THE REAL OR IMAGINARY PART WOULD UNDERFLOW -C WHEN Y IS SCALED (BY TOL) TO ITS PROPER VALUE. Y IS ACCEPTED -C IF THE UNDERFLOW IS AT LEAST ONE PRECISION BELOW THE MAGNITUDE -C OF THE LARGEST COMPONENT; OTHERWISE THE PHASE ANGLE DOES NOT HAVE -C ABSOLUTE ACCURACY AND AN UNDERFLOW IS ASSUMED. -C -C***ROUTINES CALLED (NONE) -C***END PROLOGUE ZUCHK -C -C COMPLEX Y - DOUBLE PRECISION ASCLE, SS, ST, TOL, WR, WI, YR, YI - INTEGER NZ - NZ = 0 - WR = DABS(YR) - WI = DABS(YI) - ST = DMIN1(WR,WI) - IF (ST.GT.ASCLE) RETURN - SS = DMAX1(WR,WI) - ST = ST/TOL - IF (SS.LT.ST) NZ = 1 - RETURN - END diff --git a/amos/zunhj.f b/amos/zunhj.f deleted file mode 100644 index e56e43c..0000000 --- a/amos/zunhj.f +++ /dev/null @@ -1,714 +0,0 @@ - SUBROUTINE ZUNHJ(ZR, ZI, FNU, IPMTR, TOL, PHIR, PHII, ARGR, ARGI, - * ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) -C***BEGIN PROLOGUE ZUNHJ -C***REFER TO ZBESI,ZBESK -C -C REFERENCES -C HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A. -C STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9. -C -C ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC -C PRESS, N.Y., 1974, PAGE 420 -C -C ABSTRACT -C ZUNHJ COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) = -C J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU -C BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION -C -C C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) ) -C -C FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS -C AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE. -C -C (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2, -C -C ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING -C PURPOSES IN AIRY FUNCTIONS FROM CAIRY OR CBIRY. -C -C MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND -C MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR= -C 1 COMPUTES ALL EXCEPT ASUM AND BSUM. -C -C***ROUTINES CALLED AZABS,ZDIV,AZLOG,AZSQRT,D1MACH -C***END PROLOGUE ZUNHJ -C COMPLEX ARG,ASUM,BSUM,CFNU,CONE,CR,CZERO,DR,P,PHI,PRZTH,PTFN, -C *RFN13,RTZTA,RZTH,SUMA,SUMB,TFN,T2,UP,W,W2,Z,ZA,ZB,ZC,ZETA,ZETA1, -C *ZETA2,ZTH - DOUBLE PRECISION ALFA, ANG, AP, AR, ARGI, ARGR, ASUMI, ASUMR, - * ATOL, AW2, AZTH, BETA, BR, BSUMI, BSUMR, BTOL, C, CONEI, CONER, - * CRI, CRR, DRI, DRR, EX1, EX2, FNU, FN13, FN23, GAMA, GPI, HPI, - * PHII, PHIR, PI, PP, PR, PRZTHI, PRZTHR, PTFNI, PTFNR, RAW, RAW2, - * RAZTH, RFNU, RFNU2, RFN13, RTZTI, RTZTR, RZTHI, RZTHR, STI, STR, - * SUMAI, SUMAR, SUMBI, SUMBR, TEST, TFNI, TFNR, THPI, TOL, TZAI, - * TZAR, T2I, T2R, UPI, UPR, WI, WR, W2I, W2R, ZAI, ZAR, ZBI, ZBR, - * ZCI, ZCR, ZEROI, ZEROR, ZETAI, ZETAR, ZETA1I, ZETA1R, ZETA2I, - * ZETA2R, ZI, ZR, ZTHI, ZTHR, AZABS, AC, D1MACH - INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR, - * LRP1, L1, L2, M, IDUM - DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30), - * AP(30), PR(30), PI(30), UPR(14), UPI(14), CRR(14), CRI(14), - * DRR(14), DRI(14) - DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7), AR(8), - 1 AR(9), AR(10), AR(11), AR(12), AR(13), AR(14)/ - 2 1.00000000000000000D+00, 1.04166666666666667D-01, - 3 8.35503472222222222D-02, 1.28226574556327160D-01, - 4 2.91849026464140464D-01, 8.81627267443757652D-01, - 5 3.32140828186276754D+00, 1.49957629868625547D+01, - 6 7.89230130115865181D+01, 4.74451538868264323D+02, - 7 3.20749009089066193D+03, 2.40865496408740049D+04, - 8 1.98923119169509794D+05, 1.79190200777534383D+06/ - DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7), BR(8), - 1 BR(9), BR(10), BR(11), BR(12), BR(13), BR(14)/ - 2 1.00000000000000000D+00, -1.45833333333333333D-01, - 3 -9.87413194444444444D-02, -1.43312053915895062D-01, - 4 -3.17227202678413548D-01, -9.42429147957120249D-01, - 5 -3.51120304082635426D+00, -1.57272636203680451D+01, - 6 -8.22814390971859444D+01, -4.92355370523670524D+02, - 7 -3.31621856854797251D+03, -2.48276742452085896D+04, - 8 -2.04526587315129788D+05, -1.83844491706820990D+06/ - DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), - 1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), - 2 C(19), C(20), C(21), C(22), C(23), C(24)/ - 3 1.00000000000000000D+00, -2.08333333333333333D-01, - 4 1.25000000000000000D-01, 3.34201388888888889D-01, - 5 -4.01041666666666667D-01, 7.03125000000000000D-02, - 6 -1.02581259645061728D+00, 1.84646267361111111D+00, - 7 -8.91210937500000000D-01, 7.32421875000000000D-02, - 8 4.66958442342624743D+00, -1.12070026162229938D+01, - 9 8.78912353515625000D+00, -2.36408691406250000D+00, - A 1.12152099609375000D-01, -2.82120725582002449D+01, - B 8.46362176746007346D+01, -9.18182415432400174D+01, - C 4.25349987453884549D+01, -7.36879435947963170D+00, - D 2.27108001708984375D-01, 2.12570130039217123D+02, - E -7.65252468141181642D+02, 1.05999045252799988D+03/ - DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), - 1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), - 2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ - 3 -6.99579627376132541D+02, 2.18190511744211590D+02, - 4 -2.64914304869515555D+01, 5.72501420974731445D-01, - 5 -1.91945766231840700D+03, 8.06172218173730938D+03, - 6 -1.35865500064341374D+04, 1.16553933368645332D+04, - 7 -5.30564697861340311D+03, 1.20090291321635246D+03, - 8 -1.08090919788394656D+02, 1.72772750258445740D+00, - 9 2.02042913309661486D+04, -9.69805983886375135D+04, - A 1.92547001232531532D+05, -2.03400177280415534D+05, - B 1.22200464983017460D+05, -4.11926549688975513D+04, - C 7.10951430248936372D+03, -4.93915304773088012D+02, - D 6.07404200127348304D+00, -2.42919187900551333D+05, - E 1.31176361466297720D+06, -2.99801591853810675D+06/ - DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), - 1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), - 2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ - 3 3.76327129765640400D+06, -2.81356322658653411D+06, - 4 1.26836527332162478D+06, -3.31645172484563578D+05, - 5 4.52187689813627263D+04, -2.49983048181120962D+03, - 6 2.43805296995560639D+01, 3.28446985307203782D+06, - 7 -1.97068191184322269D+07, 5.09526024926646422D+07, - 8 -7.41051482115326577D+07, 6.63445122747290267D+07, - 9 -3.75671766607633513D+07, 1.32887671664218183D+07, - A -2.78561812808645469D+06, 3.08186404612662398D+05, - B -1.38860897537170405D+04, 1.10017140269246738D+02, - C -4.93292536645099620D+07, 3.25573074185765749D+08, - D -9.39462359681578403D+08, 1.55359689957058006D+09, - E -1.62108055210833708D+09, 1.10684281682301447D+09/ - DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), - 1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), - 2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ - 3 -4.95889784275030309D+08, 1.42062907797533095D+08, - 4 -2.44740627257387285D+07, 2.24376817792244943D+06, - 5 -8.40054336030240853D+04, 5.51335896122020586D+02, - 6 8.14789096118312115D+08, -5.86648149205184723D+09, - 7 1.86882075092958249D+10, -3.46320433881587779D+10, - 8 4.12801855797539740D+10, -3.30265997498007231D+10, - 9 1.79542137311556001D+10, -6.56329379261928433D+09, - A 1.55927986487925751D+09, -2.25105661889415278D+08, - B 1.73951075539781645D+07, -5.49842327572288687D+05, - C 3.03809051092238427D+03, -1.46792612476956167D+10, - D 1.14498237732025810D+11, -3.99096175224466498D+11, - E 8.19218669548577329D+11, -1.09837515608122331D+12/ - DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), - 1 C(105)/ - 2 1.00815810686538209D+12, -6.45364869245376503D+11, - 3 2.87900649906150589D+11, -8.78670721780232657D+10, - 4 1.76347306068349694D+10, -2.16716498322379509D+09, - 5 1.43157876718888981D+08, -3.87183344257261262D+06, - 6 1.82577554742931747D+04/ - DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5), ALFA(6), - 1 ALFA(7), ALFA(8), ALFA(9), ALFA(10), ALFA(11), ALFA(12), - 2 ALFA(13), ALFA(14), ALFA(15), ALFA(16), ALFA(17), ALFA(18), - 3 ALFA(19), ALFA(20), ALFA(21), ALFA(22)/ - 4 -4.44444444444444444D-03, -9.22077922077922078D-04, - 5 -8.84892884892884893D-05, 1.65927687832449737D-04, - 6 2.46691372741792910D-04, 2.65995589346254780D-04, - 7 2.61824297061500945D-04, 2.48730437344655609D-04, - 8 2.32721040083232098D-04, 2.16362485712365082D-04, - 9 2.00738858762752355D-04, 1.86267636637545172D-04, - A 1.73060775917876493D-04, 1.61091705929015752D-04, - B 1.50274774160908134D-04, 1.40503497391269794D-04, - C 1.31668816545922806D-04, 1.23667445598253261D-04, - D 1.16405271474737902D-04, 1.09798298372713369D-04, - E 1.03772410422992823D-04, 9.82626078369363448D-05/ - DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26), ALFA(27), ALFA(28), - 1 ALFA(29), ALFA(30), ALFA(31), ALFA(32), ALFA(33), ALFA(34), - 2 ALFA(35), ALFA(36), ALFA(37), ALFA(38), ALFA(39), ALFA(40), - 3 ALFA(41), ALFA(42), ALFA(43), ALFA(44)/ - 4 9.32120517249503256D-05, 8.85710852478711718D-05, - 5 8.42963105715700223D-05, 8.03497548407791151D-05, - 6 7.66981345359207388D-05, 7.33122157481777809D-05, - 7 7.01662625163141333D-05, 6.72375633790160292D-05, - 8 6.93735541354588974D-04, 2.32241745182921654D-04, - 9 -1.41986273556691197D-05, -1.16444931672048640D-04, - A -1.50803558053048762D-04, -1.55121924918096223D-04, - B -1.46809756646465549D-04, -1.33815503867491367D-04, - C -1.19744975684254051D-04, -1.06184319207974020D-04, - D -9.37699549891194492D-05, -8.26923045588193274D-05, - E -7.29374348155221211D-05, -6.44042357721016283D-05/ - DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48), ALFA(49), ALFA(50), - 1 ALFA(51), ALFA(52), ALFA(53), ALFA(54), ALFA(55), ALFA(56), - 2 ALFA(57), ALFA(58), ALFA(59), ALFA(60), ALFA(61), ALFA(62), - 3 ALFA(63), ALFA(64), ALFA(65), ALFA(66)/ - 4 -5.69611566009369048D-05, -5.04731044303561628D-05, - 5 -4.48134868008882786D-05, -3.98688727717598864D-05, - 6 -3.55400532972042498D-05, -3.17414256609022480D-05, - 7 -2.83996793904174811D-05, -2.54522720634870566D-05, - 8 -2.28459297164724555D-05, -2.05352753106480604D-05, - 9 -1.84816217627666085D-05, -1.66519330021393806D-05, - A -1.50179412980119482D-05, -1.35554031379040526D-05, - B -1.22434746473858131D-05, -1.10641884811308169D-05, - C -3.54211971457743841D-04, -1.56161263945159416D-04, - D 3.04465503594936410D-05, 1.30198655773242693D-04, - E 1.67471106699712269D-04, 1.70222587683592569D-04/ - DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70), ALFA(71), ALFA(72), - 1 ALFA(73), ALFA(74), ALFA(75), ALFA(76), ALFA(77), ALFA(78), - 2 ALFA(79), ALFA(80), ALFA(81), ALFA(82), ALFA(83), ALFA(84), - 3 ALFA(85), ALFA(86), ALFA(87), ALFA(88)/ - 4 1.56501427608594704D-04, 1.36339170977445120D-04, - 5 1.14886692029825128D-04, 9.45869093034688111D-05, - 6 7.64498419250898258D-05, 6.07570334965197354D-05, - 7 4.74394299290508799D-05, 3.62757512005344297D-05, - 8 2.69939714979224901D-05, 1.93210938247939253D-05, - 9 1.30056674793963203D-05, 7.82620866744496661D-06, - A 3.59257485819351583D-06, 1.44040049814251817D-07, - B -2.65396769697939116D-06, -4.91346867098485910D-06, - C -6.72739296091248287D-06, -8.17269379678657923D-06, - D -9.31304715093561232D-06, -1.02011418798016441D-05, - E -1.08805962510592880D-05, -1.13875481509603555D-05/ - DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92), ALFA(93), ALFA(94), - 1 ALFA(95), ALFA(96), ALFA(97), ALFA(98), ALFA(99), ALFA(100), - 2 ALFA(101), ALFA(102), ALFA(103), ALFA(104), ALFA(105), - 3 ALFA(106), ALFA(107), ALFA(108), ALFA(109), ALFA(110)/ - 4 -1.17519675674556414D-05, -1.19987364870944141D-05, - 5 3.78194199201772914D-04, 2.02471952761816167D-04, - 6 -6.37938506318862408D-05, -2.38598230603005903D-04, - 7 -3.10916256027361568D-04, -3.13680115247576316D-04, - 8 -2.78950273791323387D-04, -2.28564082619141374D-04, - 9 -1.75245280340846749D-04, -1.25544063060690348D-04, - A -8.22982872820208365D-05, -4.62860730588116458D-05, - B -1.72334302366962267D-05, 5.60690482304602267D-06, - C 2.31395443148286800D-05, 3.62642745856793957D-05, - D 4.58006124490188752D-05, 5.24595294959114050D-05, - E 5.68396208545815266D-05, 5.94349820393104052D-05/ - DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114), ALFA(115), - 1 ALFA(116), ALFA(117), ALFA(118), ALFA(119), ALFA(120), - 2 ALFA(121), ALFA(122), ALFA(123), ALFA(124), ALFA(125), - 3 ALFA(126), ALFA(127), ALFA(128), ALFA(129), ALFA(130)/ - 4 6.06478527578421742D-05, 6.08023907788436497D-05, - 5 6.01577894539460388D-05, 5.89199657344698500D-05, - 6 5.72515823777593053D-05, 5.52804375585852577D-05, - 7 5.31063773802880170D-05, 5.08069302012325706D-05, - 8 4.84418647620094842D-05, 4.60568581607475370D-05, - 9 -6.91141397288294174D-04, -4.29976633058871912D-04, - A 1.83067735980039018D-04, 6.60088147542014144D-04, - B 8.75964969951185931D-04, 8.77335235958235514D-04, - C 7.49369585378990637D-04, 5.63832329756980918D-04, - D 3.68059319971443156D-04, 1.88464535514455599D-04/ - DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134), ALFA(135), - 1 ALFA(136), ALFA(137), ALFA(138), ALFA(139), ALFA(140), - 2 ALFA(141), ALFA(142), ALFA(143), ALFA(144), ALFA(145), - 3 ALFA(146), ALFA(147), ALFA(148), ALFA(149), ALFA(150)/ - 4 3.70663057664904149D-05, -8.28520220232137023D-05, - 5 -1.72751952869172998D-04, -2.36314873605872983D-04, - 6 -2.77966150694906658D-04, -3.02079514155456919D-04, - 7 -3.12594712643820127D-04, -3.12872558758067163D-04, - 8 -3.05678038466324377D-04, -2.93226470614557331D-04, - 9 -2.77255655582934777D-04, -2.59103928467031709D-04, - A -2.39784014396480342D-04, -2.20048260045422848D-04, - B -2.00443911094971498D-04, -1.81358692210970687D-04, - C -1.63057674478657464D-04, -1.45712672175205844D-04, - D -1.29425421983924587D-04, -1.14245691942445952D-04/ - DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154), ALFA(155), - 1 ALFA(156), ALFA(157), ALFA(158), ALFA(159), ALFA(160), - 2 ALFA(161), ALFA(162), ALFA(163), ALFA(164), ALFA(165), - 3 ALFA(166), ALFA(167), ALFA(168), ALFA(169), ALFA(170)/ - 4 1.92821964248775885D-03, 1.35592576302022234D-03, - 5 -7.17858090421302995D-04, -2.58084802575270346D-03, - 6 -3.49271130826168475D-03, -3.46986299340960628D-03, - 7 -2.82285233351310182D-03, -1.88103076404891354D-03, - 8 -8.89531718383947600D-04, 3.87912102631035228D-06, - 9 7.28688540119691412D-04, 1.26566373053457758D-03, - A 1.62518158372674427D-03, 1.83203153216373172D-03, - B 1.91588388990527909D-03, 1.90588846755546138D-03, - C 1.82798982421825727D-03, 1.70389506421121530D-03, - D 1.55097127171097686D-03, 1.38261421852276159D-03/ - DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174), ALFA(175), - 1 ALFA(176), ALFA(177), ALFA(178), ALFA(179), ALFA(180)/ - 2 1.20881424230064774D-03, 1.03676532638344962D-03, - 3 8.71437918068619115D-04, 7.16080155297701002D-04, - 4 5.72637002558129372D-04, 4.42089819465802277D-04, - 5 3.24724948503090564D-04, 2.20342042730246599D-04, - 6 1.28412898401353882D-04, 4.82005924552095464D-05/ - DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5), BETA(6), - 1 BETA(7), BETA(8), BETA(9), BETA(10), BETA(11), BETA(12), - 2 BETA(13), BETA(14), BETA(15), BETA(16), BETA(17), BETA(18), - 3 BETA(19), BETA(20), BETA(21), BETA(22)/ - 4 1.79988721413553309D-02, 5.59964911064388073D-03, - 5 2.88501402231132779D-03, 1.80096606761053941D-03, - 6 1.24753110589199202D-03, 9.22878876572938311D-04, - 7 7.14430421727287357D-04, 5.71787281789704872D-04, - 8 4.69431007606481533D-04, 3.93232835462916638D-04, - 9 3.34818889318297664D-04, 2.88952148495751517D-04, - A 2.52211615549573284D-04, 2.22280580798883327D-04, - B 1.97541838033062524D-04, 1.76836855019718004D-04, - C 1.59316899661821081D-04, 1.44347930197333986D-04, - D 1.31448068119965379D-04, 1.20245444949302884D-04, - E 1.10449144504599392D-04, 1.01828770740567258D-04/ - DATA BETA(23), BETA(24), BETA(25), BETA(26), BETA(27), BETA(28), - 1 BETA(29), BETA(30), BETA(31), BETA(32), BETA(33), BETA(34), - 2 BETA(35), BETA(36), BETA(37), BETA(38), BETA(39), BETA(40), - 3 BETA(41), BETA(42), BETA(43), BETA(44)/ - 4 9.41998224204237509D-05, 8.74130545753834437D-05, - 5 8.13466262162801467D-05, 7.59002269646219339D-05, - 6 7.09906300634153481D-05, 6.65482874842468183D-05, - 7 6.25146958969275078D-05, 5.88403394426251749D-05, - 8 -1.49282953213429172D-03, -8.78204709546389328D-04, - 9 -5.02916549572034614D-04, -2.94822138512746025D-04, - A -1.75463996970782828D-04, -1.04008550460816434D-04, - B -5.96141953046457895D-05, -3.12038929076098340D-05, - C -1.26089735980230047D-05, -2.42892608575730389D-07, - D 8.05996165414273571D-06, 1.36507009262147391D-05, - E 1.73964125472926261D-05, 1.98672978842133780D-05/ - DATA BETA(45), BETA(46), BETA(47), BETA(48), BETA(49), BETA(50), - 1 BETA(51), BETA(52), BETA(53), BETA(54), BETA(55), BETA(56), - 2 BETA(57), BETA(58), BETA(59), BETA(60), BETA(61), BETA(62), - 3 BETA(63), BETA(64), BETA(65), BETA(66)/ - 4 2.14463263790822639D-05, 2.23954659232456514D-05, - 5 2.28967783814712629D-05, 2.30785389811177817D-05, - 6 2.30321976080909144D-05, 2.28236073720348722D-05, - 7 2.25005881105292418D-05, 2.20981015361991429D-05, - 8 2.16418427448103905D-05, 2.11507649256220843D-05, - 9 2.06388749782170737D-05, 2.01165241997081666D-05, - A 1.95913450141179244D-05, 1.90689367910436740D-05, - B 1.85533719641636667D-05, 1.80475722259674218D-05, - C 5.52213076721292790D-04, 4.47932581552384646D-04, - D 2.79520653992020589D-04, 1.52468156198446602D-04, - E 6.93271105657043598D-05, 1.76258683069991397D-05/ - DATA BETA(67), BETA(68), BETA(69), BETA(70), BETA(71), BETA(72), - 1 BETA(73), BETA(74), BETA(75), BETA(76), BETA(77), BETA(78), - 2 BETA(79), BETA(80), BETA(81), BETA(82), BETA(83), BETA(84), - 3 BETA(85), BETA(86), BETA(87), BETA(88)/ - 4 -1.35744996343269136D-05, -3.17972413350427135D-05, - 5 -4.18861861696693365D-05, -4.69004889379141029D-05, - 6 -4.87665447413787352D-05, -4.87010031186735069D-05, - 7 -4.74755620890086638D-05, -4.55813058138628452D-05, - 8 -4.33309644511266036D-05, -4.09230193157750364D-05, - 9 -3.84822638603221274D-05, -3.60857167535410501D-05, - A -3.37793306123367417D-05, -3.15888560772109621D-05, - B -2.95269561750807315D-05, -2.75978914828335759D-05, - C -2.58006174666883713D-05, -2.41308356761280200D-05, - D -2.25823509518346033D-05, -2.11479656768912971D-05, - E -1.98200638885294927D-05, -1.85909870801065077D-05/ - DATA BETA(89), BETA(90), BETA(91), BETA(92), BETA(93), BETA(94), - 1 BETA(95), BETA(96), BETA(97), BETA(98), BETA(99), BETA(100), - 2 BETA(101), BETA(102), BETA(103), BETA(104), BETA(105), - 3 BETA(106), BETA(107), BETA(108), BETA(109), BETA(110)/ - 4 -1.74532699844210224D-05, -1.63997823854497997D-05, - 5 -4.74617796559959808D-04, -4.77864567147321487D-04, - 6 -3.20390228067037603D-04, -1.61105016119962282D-04, - 7 -4.25778101285435204D-05, 3.44571294294967503D-05, - 8 7.97092684075674924D-05, 1.03138236708272200D-04, - 9 1.12466775262204158D-04, 1.13103642108481389D-04, - A 1.08651634848774268D-04, 1.01437951597661973D-04, - B 9.29298396593363896D-05, 8.40293133016089978D-05, - C 7.52727991349134062D-05, 6.69632521975730872D-05, - D 5.92564547323194704D-05, 5.22169308826975567D-05, - E 4.58539485165360646D-05, 4.01445513891486808D-05/ - DATA BETA(111), BETA(112), BETA(113), BETA(114), BETA(115), - 1 BETA(116), BETA(117), BETA(118), BETA(119), BETA(120), - 2 BETA(121), BETA(122), BETA(123), BETA(124), BETA(125), - 3 BETA(126), BETA(127), BETA(128), BETA(129), BETA(130)/ - 4 3.50481730031328081D-05, 3.05157995034346659D-05, - 5 2.64956119950516039D-05, 2.29363633690998152D-05, - 6 1.97893056664021636D-05, 1.70091984636412623D-05, - 7 1.45547428261524004D-05, 1.23886640995878413D-05, - 8 1.04775876076583236D-05, 8.79179954978479373D-06, - 9 7.36465810572578444D-04, 8.72790805146193976D-04, - A 6.22614862573135066D-04, 2.85998154194304147D-04, - B 3.84737672879366102D-06, -1.87906003636971558D-04, - C -2.97603646594554535D-04, -3.45998126832656348D-04, - D -3.53382470916037712D-04, -3.35715635775048757D-04/ - DATA BETA(131), BETA(132), BETA(133), BETA(134), BETA(135), - 1 BETA(136), BETA(137), BETA(138), BETA(139), BETA(140), - 2 BETA(141), BETA(142), BETA(143), BETA(144), BETA(145), - 3 BETA(146), BETA(147), BETA(148), BETA(149), BETA(150)/ - 4 -3.04321124789039809D-04, -2.66722723047612821D-04, - 5 -2.27654214122819527D-04, -1.89922611854562356D-04, - 6 -1.55058918599093870D-04, -1.23778240761873630D-04, - 7 -9.62926147717644187D-05, -7.25178327714425337D-05, - 8 -5.22070028895633801D-05, -3.50347750511900522D-05, - 9 -2.06489761035551757D-05, -8.70106096849767054D-06, - A 1.13698686675100290D-06, 9.16426474122778849D-06, - B 1.56477785428872620D-05, 2.08223629482466847D-05, - C 2.48923381004595156D-05, 2.80340509574146325D-05, - D 3.03987774629861915D-05, 3.21156731406700616D-05/ - DATA BETA(151), BETA(152), BETA(153), BETA(154), BETA(155), - 1 BETA(156), BETA(157), BETA(158), BETA(159), BETA(160), - 2 BETA(161), BETA(162), BETA(163), BETA(164), BETA(165), - 3 BETA(166), BETA(167), BETA(168), BETA(169), BETA(170)/ - 4 -1.80182191963885708D-03, -2.43402962938042533D-03, - 5 -1.83422663549856802D-03, -7.62204596354009765D-04, - 6 2.39079475256927218D-04, 9.49266117176881141D-04, - 7 1.34467449701540359D-03, 1.48457495259449178D-03, - 8 1.44732339830617591D-03, 1.30268261285657186D-03, - 9 1.10351597375642682D-03, 8.86047440419791759D-04, - A 6.73073208165665473D-04, 4.77603872856582378D-04, - B 3.05991926358789362D-04, 1.60315694594721630D-04, - C 4.00749555270613286D-05, -5.66607461635251611D-05, - D -1.32506186772982638D-04, -1.90296187989614057D-04/ - DATA BETA(171), BETA(172), BETA(173), BETA(174), BETA(175), - 1 BETA(176), BETA(177), BETA(178), BETA(179), BETA(180), - 2 BETA(181), BETA(182), BETA(183), BETA(184), BETA(185), - 3 BETA(186), BETA(187), BETA(188), BETA(189), BETA(190)/ - 4 -2.32811450376937408D-04, -2.62628811464668841D-04, - 5 -2.82050469867598672D-04, -2.93081563192861167D-04, - 6 -2.97435962176316616D-04, -2.96557334239348078D-04, - 7 -2.91647363312090861D-04, -2.83696203837734166D-04, - 8 -2.73512317095673346D-04, -2.61750155806768580D-04, - 9 6.38585891212050914D-03, 9.62374215806377941D-03, - A 7.61878061207001043D-03, 2.83219055545628054D-03, - B -2.09841352012720090D-03, -5.73826764216626498D-03, - C -7.70804244495414620D-03, -8.21011692264844401D-03, - D -7.65824520346905413D-03, -6.47209729391045177D-03/ - DATA BETA(191), BETA(192), BETA(193), BETA(194), BETA(195), - 1 BETA(196), BETA(197), BETA(198), BETA(199), BETA(200), - 2 BETA(201), BETA(202), BETA(203), BETA(204), BETA(205), - 3 BETA(206), BETA(207), BETA(208), BETA(209), BETA(210)/ - 4 -4.99132412004966473D-03, -3.45612289713133280D-03, - 5 -2.01785580014170775D-03, -7.59430686781961401D-04, - 6 2.84173631523859138D-04, 1.10891667586337403D-03, - 7 1.72901493872728771D-03, 2.16812590802684701D-03, - 8 2.45357710494539735D-03, 2.61281821058334862D-03, - 9 2.67141039656276912D-03, 2.65203073395980430D-03, - A 2.57411652877287315D-03, 2.45389126236094427D-03, - B 2.30460058071795494D-03, 2.13684837686712662D-03, - C 1.95896528478870911D-03, 1.77737008679454412D-03, - D 1.59690280765839059D-03, 1.42111975664438546D-03/ - DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5), GAMA(6), - 1 GAMA(7), GAMA(8), GAMA(9), GAMA(10), GAMA(11), GAMA(12), - 2 GAMA(13), GAMA(14), GAMA(15), GAMA(16), GAMA(17), GAMA(18), - 3 GAMA(19), GAMA(20), GAMA(21), GAMA(22)/ - 4 6.29960524947436582D-01, 2.51984209978974633D-01, - 5 1.54790300415655846D-01, 1.10713062416159013D-01, - 6 8.57309395527394825D-02, 6.97161316958684292D-02, - 7 5.86085671893713576D-02, 5.04698873536310685D-02, - 8 4.42600580689154809D-02, 3.93720661543509966D-02, - 9 3.54283195924455368D-02, 3.21818857502098231D-02, - A 2.94646240791157679D-02, 2.71581677112934479D-02, - B 2.51768272973861779D-02, 2.34570755306078891D-02, - C 2.19508390134907203D-02, 2.06210828235646240D-02, - D 1.94388240897880846D-02, 1.83810633800683158D-02, - E 1.74293213231963172D-02, 1.65685837786612353D-02/ - DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26), GAMA(27), GAMA(28), - 1 GAMA(29), GAMA(30)/ - 2 1.57865285987918445D-02, 1.50729501494095594D-02, - 3 1.44193250839954639D-02, 1.38184805735341786D-02, - 4 1.32643378994276568D-02, 1.27517121970498651D-02, - 5 1.22761545318762767D-02, 1.18338262398482403D-02/ - DATA EX1, EX2, HPI, GPI, THPI / - 1 3.33333333333333333D-01, 6.66666666666666667D-01, - 2 1.57079632679489662D+00, 3.14159265358979324D+00, - 3 4.71238898038468986D+00/ - DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / -C - RFNU = 1.0D0/FNU -C----------------------------------------------------------------------- -C OVERFLOW TEST (Z/FNU TOO SMALL) -C----------------------------------------------------------------------- - TEST = D1MACH(1)*1.0D+3 - AC = FNU*TEST - IF (DABS(ZR).GT.AC .OR. DABS(ZI).GT.AC) GO TO 15 - ZETA1R = 2.0D0*DABS(DLOG(TEST))+FNU - ZETA1I = 0.0D0 - ZETA2R = FNU - ZETA2I = 0.0D0 - PHIR = 1.0D0 - PHII = 0.0D0 - ARGR = 1.0D0 - ARGI = 0.0D0 - RETURN - 15 CONTINUE - ZBR = ZR*RFNU - ZBI = ZI*RFNU - RFNU2 = RFNU*RFNU -C----------------------------------------------------------------------- -C COMPUTE IN THE FOURTH QUADRANT -C----------------------------------------------------------------------- - FN13 = FNU**EX1 - FN23 = FN13*FN13 - RFN13 = 1.0D0/FN13 - W2R = CONER - ZBR*ZBR + ZBI*ZBI - W2I = CONEI - ZBR*ZBI - ZBR*ZBI - AW2 = AZABS(W2R,W2I) - IF (AW2.GT.0.25D0) GO TO 130 -C----------------------------------------------------------------------- -C POWER SERIES FOR CABS(W2).LE.0.25D0 -C----------------------------------------------------------------------- - K = 1 - PR(1) = CONER - PI(1) = CONEI - SUMAR = GAMA(1) - SUMAI = ZEROI - AP(1) = 1.0D0 - IF (AW2.LT.TOL) GO TO 20 - DO 10 K=2,30 - PR(K) = PR(K-1)*W2R - PI(K-1)*W2I - PI(K) = PR(K-1)*W2I + PI(K-1)*W2R - SUMAR = SUMAR + PR(K)*GAMA(K) - SUMAI = SUMAI + PI(K)*GAMA(K) - AP(K) = AP(K-1)*AW2 - IF (AP(K).LT.TOL) GO TO 20 - 10 CONTINUE - K = 30 - 20 CONTINUE - KMAX = K - ZETAR = W2R*SUMAR - W2I*SUMAI - ZETAI = W2R*SUMAI + W2I*SUMAR - ARGR = ZETAR*FN23 - ARGI = ZETAI*FN23 - CALL AZSQRT(SUMAR, SUMAI, ZAR, ZAI) - CALL AZSQRT(W2R, W2I, STR, STI) - ZETA2R = STR*FNU - ZETA2I = STI*FNU - STR = CONER + EX2*(ZETAR*ZAR-ZETAI*ZAI) - STI = CONEI + EX2*(ZETAR*ZAI+ZETAI*ZAR) - ZETA1R = STR*ZETA2R - STI*ZETA2I - ZETA1I = STR*ZETA2I + STI*ZETA2R - ZAR = ZAR + ZAR - ZAI = ZAI + ZAI - CALL AZSQRT(ZAR, ZAI, STR, STI) - PHIR = STR*RFN13 - PHII = STI*RFN13 - IF (IPMTR.EQ.1) GO TO 120 -C----------------------------------------------------------------------- -C SUM SERIES FOR ASUM AND BSUM -C----------------------------------------------------------------------- - SUMBR = ZEROR - SUMBI = ZEROI - DO 30 K=1,KMAX - SUMBR = SUMBR + PR(K)*BETA(K) - SUMBI = SUMBI + PI(K)*BETA(K) - 30 CONTINUE - ASUMR = ZEROR - ASUMI = ZEROI - BSUMR = SUMBR - BSUMI = SUMBI - L1 = 0 - L2 = 30 - BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI)) - ATOL = TOL - PP = 1.0D0 - IAS = 0 - IBS = 0 - IF (RFNU2.LT.TOL) GO TO 110 - DO 100 IS=2,7 - ATOL = ATOL/RFNU2 - PP = PP*RFNU2 - IF (IAS.EQ.1) GO TO 60 - SUMAR = ZEROR - SUMAI = ZEROI - DO 40 K=1,KMAX - M = L1 + K - SUMAR = SUMAR + PR(K)*ALFA(M) - SUMAI = SUMAI + PI(K)*ALFA(M) - IF (AP(K).LT.ATOL) GO TO 50 - 40 CONTINUE - 50 CONTINUE - ASUMR = ASUMR + SUMAR*PP - ASUMI = ASUMI + SUMAI*PP - IF (PP.LT.TOL) IAS = 1 - 60 CONTINUE - IF (IBS.EQ.1) GO TO 90 - SUMBR = ZEROR - SUMBI = ZEROI - DO 70 K=1,KMAX - M = L2 + K - SUMBR = SUMBR + PR(K)*BETA(M) - SUMBI = SUMBI + PI(K)*BETA(M) - IF (AP(K).LT.ATOL) GO TO 80 - 70 CONTINUE - 80 CONTINUE - BSUMR = BSUMR + SUMBR*PP - BSUMI = BSUMI + SUMBI*PP - IF (PP.LT.BTOL) IBS = 1 - 90 CONTINUE - IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 110 - L1 = L1 + 30 - L2 = L2 + 30 - 100 CONTINUE - 110 CONTINUE - ASUMR = ASUMR + CONER - PP = RFNU*RFN13 - BSUMR = BSUMR*PP - BSUMI = BSUMI*PP - 120 CONTINUE - RETURN -C----------------------------------------------------------------------- -C CABS(W2).GT.0.25D0 -C----------------------------------------------------------------------- - 130 CONTINUE - CALL AZSQRT(W2R, W2I, WR, WI) - IF (WR.LT.0.0D0) WR = 0.0D0 - IF (WI.LT.0.0D0) WI = 0.0D0 - STR = CONER + WR - STI = WI - CALL ZDIV(STR, STI, ZBR, ZBI, ZAR, ZAI) - CALL AZLOG(ZAR, ZAI, ZCR, ZCI, IDUM) - IF (ZCI.LT.0.0D0) ZCI = 0.0D0 - IF (ZCI.GT.HPI) ZCI = HPI - IF (ZCR.LT.0.0D0) ZCR = 0.0D0 - ZTHR = (ZCR-WR)*1.5D0 - ZTHI = (ZCI-WI)*1.5D0 - ZETA1R = ZCR*FNU - ZETA1I = ZCI*FNU - ZETA2R = WR*FNU - ZETA2I = WI*FNU - AZTH = AZABS(ZTHR,ZTHI) - ANG = THPI - IF (ZTHR.GE.0.0D0 .AND. ZTHI.LT.0.0D0) GO TO 140 - ANG = HPI - IF (ZTHR.EQ.0.0D0) GO TO 140 - ANG = DATAN(ZTHI/ZTHR) - IF (ZTHR.LT.0.0D0) ANG = ANG + GPI - 140 CONTINUE - PP = AZTH**EX2 - ANG = ANG*EX2 - ZETAR = PP*DCOS(ANG) - ZETAI = PP*DSIN(ANG) - IF (ZETAI.LT.0.0D0) ZETAI = 0.0D0 - ARGR = ZETAR*FN23 - ARGI = ZETAI*FN23 - CALL ZDIV(ZTHR, ZTHI, ZETAR, ZETAI, RTZTR, RTZTI) - CALL ZDIV(RTZTR, RTZTI, WR, WI, ZAR, ZAI) - TZAR = ZAR + ZAR - TZAI = ZAI + ZAI - CALL AZSQRT(TZAR, TZAI, STR, STI) - PHIR = STR*RFN13 - PHII = STI*RFN13 - IF (IPMTR.EQ.1) GO TO 120 - RAW = 1.0D0/DSQRT(AW2) - STR = WR*RAW - STI = -WI*RAW - TFNR = STR*RFNU*RAW - TFNI = STI*RFNU*RAW - RAZTH = 1.0D0/AZTH - STR = ZTHR*RAZTH - STI = -ZTHI*RAZTH - RZTHR = STR*RAZTH*RFNU - RZTHI = STI*RAZTH*RFNU - ZCR = RZTHR*AR(2) - ZCI = RZTHI*AR(2) - RAW2 = 1.0D0/AW2 - STR = W2R*RAW2 - STI = -W2I*RAW2 - T2R = STR*RAW2 - T2I = STI*RAW2 - STR = T2R*C(2) + C(3) - STI = T2I*C(2) - UPR(2) = STR*TFNR - STI*TFNI - UPI(2) = STR*TFNI + STI*TFNR - BSUMR = UPR(2) + ZCR - BSUMI = UPI(2) + ZCI - ASUMR = ZEROR - ASUMI = ZEROI - IF (RFNU.LT.TOL) GO TO 220 - PRZTHR = RZTHR - PRZTHI = RZTHI - PTFNR = TFNR - PTFNI = TFNI - UPR(1) = CONER - UPI(1) = CONEI - PP = 1.0D0 - BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI)) - KS = 0 - KP1 = 2 - L = 3 - IAS = 0 - IBS = 0 - DO 210 LR=2,12,2 - LRP1 = LR + 1 -C----------------------------------------------------------------------- -C COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE TERMS IN -C NEXT SUMA AND SUMB -C----------------------------------------------------------------------- - DO 160 K=LR,LRP1 - KS = KS + 1 - KP1 = KP1 + 1 - L = L + 1 - ZAR = C(L) - ZAI = ZEROI - DO 150 J=2,KP1 - L = L + 1 - STR = ZAR*T2R - T2I*ZAI + C(L) - ZAI = ZAR*T2I + ZAI*T2R - ZAR = STR - 150 CONTINUE - STR = PTFNR*TFNR - PTFNI*TFNI - PTFNI = PTFNR*TFNI + PTFNI*TFNR - PTFNR = STR - UPR(KP1) = PTFNR*ZAR - PTFNI*ZAI - UPI(KP1) = PTFNI*ZAR + PTFNR*ZAI - CRR(KS) = PRZTHR*BR(KS+1) - CRI(KS) = PRZTHI*BR(KS+1) - STR = PRZTHR*RZTHR - PRZTHI*RZTHI - PRZTHI = PRZTHR*RZTHI + PRZTHI*RZTHR - PRZTHR = STR - DRR(KS) = PRZTHR*AR(KS+2) - DRI(KS) = PRZTHI*AR(KS+2) - 160 CONTINUE - PP = PP*RFNU2 - IF (IAS.EQ.1) GO TO 180 - SUMAR = UPR(LRP1) - SUMAI = UPI(LRP1) - JU = LRP1 - DO 170 JR=1,LR - JU = JU - 1 - SUMAR = SUMAR + CRR(JR)*UPR(JU) - CRI(JR)*UPI(JU) - SUMAI = SUMAI + CRR(JR)*UPI(JU) + CRI(JR)*UPR(JU) - 170 CONTINUE - ASUMR = ASUMR + SUMAR - ASUMI = ASUMI + SUMAI - TEST = DABS(SUMAR) + DABS(SUMAI) - IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1 - 180 CONTINUE - IF (IBS.EQ.1) GO TO 200 - SUMBR = UPR(LR+2) + UPR(LRP1)*ZCR - UPI(LRP1)*ZCI - SUMBI = UPI(LR+2) + UPR(LRP1)*ZCI + UPI(LRP1)*ZCR - JU = LRP1 - DO 190 JR=1,LR - JU = JU - 1 - SUMBR = SUMBR + DRR(JR)*UPR(JU) - DRI(JR)*UPI(JU) - SUMBI = SUMBI + DRR(JR)*UPI(JU) + DRI(JR)*UPR(JU) - 190 CONTINUE - BSUMR = BSUMR + SUMBR - BSUMI = BSUMI + SUMBI - TEST = DABS(SUMBR) + DABS(SUMBI) - IF (PP.LT.BTOL .AND. TEST.LT.BTOL) IBS = 1 - 200 CONTINUE - IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 220 - 210 CONTINUE - 220 CONTINUE - ASUMR = ASUMR + CONER - STR = -BSUMR*RFN13 - STI = -BSUMI*RFN13 - CALL ZDIV(STR, STI, RTZTR, RTZTI, BSUMR, BSUMI) - GO TO 120 - END diff --git a/amos/zuni1.f b/amos/zuni1.f deleted file mode 100644 index c7173b3..0000000 --- a/amos/zuni1.f +++ /dev/null @@ -1,204 +0,0 @@ - SUBROUTINE ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL, - * TOL, ELIM, ALIM) -C***BEGIN PROLOGUE ZUNI1 -C***REFER TO ZBESI,ZBESK -C -C ZUNI1 COMPUTES I(FNU,Z) BY MEANS OF THE UNIFORM ASYMPTOTIC -C EXPANSION FOR I(FNU,Z) IN -PI/3.LE.ARG Z.LE.PI/3. -C -C FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC -C EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. -C NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER -C FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. -C Y(I)=CZERO FOR I=NLAST+1,N -C -C***ROUTINES CALLED ZUCHK,ZUNIK,ZUOIK,D1MACH,AZABS -C***END PROLOGUE ZUNI1 -C COMPLEX CFN,CONE,CRSC,CSCL,CSR,CSS,CWRK,CZERO,C1,C2,PHI,RZ,SUM,S1, -C *S2,Y,Z,ZETA1,ZETA2 - DOUBLE PRECISION ALIM, APHI, ASCLE, BRY, CONER, CRSC, - * CSCL, CSRR, CSSR, CWRKI, CWRKR, C1R, C2I, C2M, C2R, ELIM, FN, - * FNU, FNUL, PHII, PHIR, RAST, RS1, RZI, RZR, STI, STR, SUMI, - * SUMR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, - * ZETA1R, ZETA2I, ZETA2R, ZI, ZR, CYR, CYI, D1MACH, AZABS - INTEGER I, IFLAG, INIT, K, KODE, M, N, ND, NLAST, NN, NUF, NW, NZ - DIMENSION BRY(3), YR(N), YI(N), CWRKR(16), CWRKI(16), CSSR(3), - * CSRR(3), CYR(2), CYI(2) - DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 / -C - NZ = 0 - ND = N - NLAST = 0 -C----------------------------------------------------------------------- -C COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- -C NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, -C EXP(ALIM)=EXP(ELIM)*TOL -C----------------------------------------------------------------------- - CSCL = 1.0D0/TOL - CRSC = TOL - CSSR(1) = CSCL - CSSR(2) = CONER - CSSR(3) = CRSC - CSRR(1) = CRSC - CSRR(2) = CONER - CSRR(3) = CSCL - BRY(1) = 1.0D+3*D1MACH(1)/TOL -C----------------------------------------------------------------------- -C CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER -C----------------------------------------------------------------------- - FN = DMAX1(FNU,1.0D0) - INIT = 0 - CALL ZUNIK(ZR, ZI, FN, 1, 1, TOL, INIT, PHIR, PHII, ZETA1R, - * ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) - IF (KODE.EQ.1) GO TO 10 - STR = ZR + ZETA2R - STI = ZI + ZETA2I - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = -ZETA1R + STR - S1I = -ZETA1I + STI - GO TO 20 - 10 CONTINUE - S1R = -ZETA1R + ZETA2R - S1I = -ZETA1I + ZETA2I - 20 CONTINUE - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 130 - 30 CONTINUE - NN = MIN0(2,ND) - DO 80 I=1,NN - FN = FNU + DBLE(FLOAT(ND-I)) - INIT = 0 - CALL ZUNIK(ZR, ZI, FN, 1, 0, TOL, INIT, PHIR, PHII, ZETA1R, - * ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) - IF (KODE.EQ.1) GO TO 40 - STR = ZR + ZETA2R - STI = ZI + ZETA2I - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = -ZETA1R + STR - S1I = -ZETA1I + STI + ZI - GO TO 50 - 40 CONTINUE - S1R = -ZETA1R + ZETA2R - S1I = -ZETA1I + ZETA2I - 50 CONTINUE -C----------------------------------------------------------------------- -C TEST FOR UNDERFLOW AND OVERFLOW -C----------------------------------------------------------------------- - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 110 - IF (I.EQ.1) IFLAG = 2 - IF (DABS(RS1).LT.ALIM) GO TO 60 -C----------------------------------------------------------------------- -C REFINE TEST AND SCALE -C----------------------------------------------------------------------- - APHI = AZABS(PHIR,PHII) - RS1 = RS1 + DLOG(APHI) - IF (DABS(RS1).GT.ELIM) GO TO 110 - IF (I.EQ.1) IFLAG = 1 - IF (RS1.LT.0.0D0) GO TO 60 - IF (I.EQ.1) IFLAG = 3 - 60 CONTINUE -C----------------------------------------------------------------------- -C SCALE S1 IF CABS(S1).LT.ASCLE -C----------------------------------------------------------------------- - S2R = PHIR*SUMR - PHII*SUMI - S2I = PHIR*SUMI + PHII*SUMR - STR = DEXP(S1R)*CSSR(IFLAG) - S1R = STR*DCOS(S1I) - S1I = STR*DSIN(S1I) - STR = S2R*S1R - S2I*S1I - S2I = S2R*S1I + S2I*S1R - S2R = STR - IF (IFLAG.NE.1) GO TO 70 - CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) - IF (NW.NE.0) GO TO 110 - 70 CONTINUE - CYR(I) = S2R - CYI(I) = S2I - M = ND - I + 1 - YR(M) = S2R*CSRR(IFLAG) - YI(M) = S2I*CSRR(IFLAG) - 80 CONTINUE - IF (ND.LE.2) GO TO 100 - RAST = 1.0D0/AZABS(ZR,ZI) - STR = ZR*RAST - STI = -ZI*RAST - RZR = (STR+STR)*RAST - RZI = (STI+STI)*RAST - BRY(2) = 1.0D0/BRY(1) - BRY(3) = D1MACH(2) - S1R = CYR(1) - S1I = CYI(1) - S2R = CYR(2) - S2I = CYI(2) - C1R = CSRR(IFLAG) - ASCLE = BRY(IFLAG) - K = ND - 2 - FN = DBLE(FLOAT(K)) - DO 90 I=3,ND - C2R = S2R - C2I = S2I - S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I) - S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R) - S1R = C2R - S1I = C2I - C2R = S2R*C1R - C2I = S2I*C1R - YR(K) = C2R - YI(K) = C2I - K = K - 1 - FN = FN - 1.0D0 - IF (IFLAG.GE.3) GO TO 90 - STR = DABS(C2R) - STI = DABS(C2I) - C2M = DMAX1(STR,STI) - IF (C2M.LE.ASCLE) GO TO 90 - IFLAG = IFLAG + 1 - ASCLE = BRY(IFLAG) - S1R = S1R*C1R - S1I = S1I*C1R - S2R = C2R - S2I = C2I - S1R = S1R*CSSR(IFLAG) - S1I = S1I*CSSR(IFLAG) - S2R = S2R*CSSR(IFLAG) - S2I = S2I*CSSR(IFLAG) - C1R = CSRR(IFLAG) - 90 CONTINUE - 100 CONTINUE - RETURN -C----------------------------------------------------------------------- -C SET UNDERFLOW AND UPDATE PARAMETERS -C----------------------------------------------------------------------- - 110 CONTINUE - IF (RS1.GT.0.0D0) GO TO 120 - YR(ND) = ZEROR - YI(ND) = ZEROI - NZ = NZ + 1 - ND = ND - 1 - IF (ND.EQ.0) GO TO 100 - CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM) - IF (NUF.LT.0) GO TO 120 - ND = ND - NUF - NZ = NZ + NUF - IF (ND.EQ.0) GO TO 100 - FN = FNU + DBLE(FLOAT(ND-1)) - IF (FN.GE.FNUL) GO TO 30 - NLAST = ND - RETURN - 120 CONTINUE - NZ = -1 - RETURN - 130 CONTINUE - IF (RS1.GT.0.0D0) GO TO 120 - NZ = N - DO 140 I=1,N - YR(I) = ZEROR - YI(I) = ZEROI - 140 CONTINUE - RETURN - END diff --git a/amos/zuni2.f b/amos/zuni2.f deleted file mode 100644 index 49061cb..0000000 --- a/amos/zuni2.f +++ /dev/null @@ -1,267 +0,0 @@ - SUBROUTINE ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL, - * TOL, ELIM, ALIM) -C***BEGIN PROLOGUE ZUNI2 -C***REFER TO ZBESI,ZBESK -C -C ZUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF -C UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I -C OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO. -C -C FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC -C EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. -C NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER -C FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. -C Y(I)=CZERO FOR I=NLAST+1,N -C -C***ROUTINES CALLED ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,AZABS -C***END PROLOGUE ZUNI2 -C COMPLEX AI,ARG,ASUM,BSUM,CFN,CI,CID,CIP,CONE,CRSC,CSCL,CSR,CSS, -C *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN - DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGI, - * ARGR, ASCLE, ASUMI, ASUMR, BRY, BSUMI, BSUMR, CIDI, CIPI, CIPR, - * CONER, CRSC, CSCL, CSRR, CSSR, C1R, C2I, C2M, C2R, DAII, - * DAIR, ELIM, FN, FNU, FNUL, HPI, PHII, PHIR, RAST, RAZ, RS1, RZI, - * RZR, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZBI, ZBR, ZEROI, - * ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, ZNI, ZNR, ZR, CYR, - * CYI, D1MACH, AZABS, CAR, SAR - INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST, - * NN, NUF, NW, NZ, IDUM - DIMENSION BRY(3), YR(N), YI(N), CIPR(4), CIPI(4), CSSR(3), - * CSRR(3), CYR(2), CYI(2) - DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 / - DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4), - * CIPI(4)/ 1.0D0,0.0D0, 0.0D0,1.0D0, -1.0D0,0.0D0, 0.0D0,-1.0D0/ - DATA HPI, AIC / - 1 1.57079632679489662D+00, 1.265512123484645396D+00/ -C - NZ = 0 - ND = N - NLAST = 0 -C----------------------------------------------------------------------- -C COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- -C NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, -C EXP(ALIM)=EXP(ELIM)*TOL -C----------------------------------------------------------------------- - CSCL = 1.0D0/TOL - CRSC = TOL - CSSR(1) = CSCL - CSSR(2) = CONER - CSSR(3) = CRSC - CSRR(1) = CRSC - CSRR(2) = CONER - CSRR(3) = CSCL - BRY(1) = 1.0D+3*D1MACH(1)/TOL -C----------------------------------------------------------------------- -C ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI -C----------------------------------------------------------------------- - ZNR = ZI - ZNI = -ZR - ZBR = ZR - ZBI = ZI - CIDI = -CONER - INU = INT(SNGL(FNU)) - ANG = HPI*(FNU-DBLE(FLOAT(INU))) - C2R = DCOS(ANG) - C2I = DSIN(ANG) - CAR = C2R - SAR = C2I - IN = INU + N - 1 - IN = MOD(IN,4) + 1 - STR = C2R*CIPR(IN) - C2I*CIPI(IN) - C2I = C2R*CIPI(IN) + C2I*CIPR(IN) - C2R = STR - IF (ZI.GT.0.0D0) GO TO 10 - ZNR = -ZNR - ZBI = -ZBI - CIDI = -CIDI - C2I = -C2I - 10 CONTINUE -C----------------------------------------------------------------------- -C CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER -C----------------------------------------------------------------------- - FN = DMAX1(FNU,1.0D0) - CALL ZUNHJ(ZNR, ZNI, FN, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, - * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) - IF (KODE.EQ.1) GO TO 20 - STR = ZBR + ZETA2R - STI = ZBI + ZETA2I - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = -ZETA1R + STR - S1I = -ZETA1I + STI - GO TO 30 - 20 CONTINUE - S1R = -ZETA1R + ZETA2R - S1I = -ZETA1I + ZETA2I - 30 CONTINUE - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 150 - 40 CONTINUE - NN = MIN0(2,ND) - DO 90 I=1,NN - FN = FNU + DBLE(FLOAT(ND-I)) - CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR, PHII, ARGR, ARGI, - * ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) - IF (KODE.EQ.1) GO TO 50 - STR = ZBR + ZETA2R - STI = ZBI + ZETA2I - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = -ZETA1R + STR - S1I = -ZETA1I + STI + DABS(ZI) - GO TO 60 - 50 CONTINUE - S1R = -ZETA1R + ZETA2R - S1I = -ZETA1I + ZETA2I - 60 CONTINUE -C----------------------------------------------------------------------- -C TEST FOR UNDERFLOW AND OVERFLOW -C----------------------------------------------------------------------- - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 120 - IF (I.EQ.1) IFLAG = 2 - IF (DABS(RS1).LT.ALIM) GO TO 70 -C----------------------------------------------------------------------- -C REFINE TEST AND SCALE -C----------------------------------------------------------------------- -C----------------------------------------------------------------------- - APHI = AZABS(PHIR,PHII) - AARG = AZABS(ARGR,ARGI) - RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC - IF (DABS(RS1).GT.ELIM) GO TO 120 - IF (I.EQ.1) IFLAG = 1 - IF (RS1.LT.0.0D0) GO TO 70 - IF (I.EQ.1) IFLAG = 3 - 70 CONTINUE -C----------------------------------------------------------------------- -C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR -C EXPONENT EXTREMES -C----------------------------------------------------------------------- - CALL ZAIRY(ARGR, ARGI, 0, 2, AIR, AII, NAI, IDUM) - CALL ZAIRY(ARGR, ARGI, 1, 2, DAIR, DAII, NDAI, IDUM) - STR = DAIR*BSUMR - DAII*BSUMI - STI = DAIR*BSUMI + DAII*BSUMR - STR = STR + (AIR*ASUMR-AII*ASUMI) - STI = STI + (AIR*ASUMI+AII*ASUMR) - S2R = PHIR*STR - PHII*STI - S2I = PHIR*STI + PHII*STR - STR = DEXP(S1R)*CSSR(IFLAG) - S1R = STR*DCOS(S1I) - S1I = STR*DSIN(S1I) - STR = S2R*S1R - S2I*S1I - S2I = S2R*S1I + S2I*S1R - S2R = STR - IF (IFLAG.NE.1) GO TO 80 - CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) - IF (NW.NE.0) GO TO 120 - 80 CONTINUE - IF (ZI.LE.0.0D0) S2I = -S2I - STR = S2R*C2R - S2I*C2I - S2I = S2R*C2I + S2I*C2R - S2R = STR - CYR(I) = S2R - CYI(I) = S2I - J = ND - I + 1 - YR(J) = S2R*CSRR(IFLAG) - YI(J) = S2I*CSRR(IFLAG) - STR = -C2I*CIDI - C2I = C2R*CIDI - C2R = STR - 90 CONTINUE - IF (ND.LE.2) GO TO 110 - RAZ = 1.0D0/AZABS(ZR,ZI) - STR = ZR*RAZ - STI = -ZI*RAZ - RZR = (STR+STR)*RAZ - RZI = (STI+STI)*RAZ - BRY(2) = 1.0D0/BRY(1) - BRY(3) = D1MACH(2) - S1R = CYR(1) - S1I = CYI(1) - S2R = CYR(2) - S2I = CYI(2) - C1R = CSRR(IFLAG) - ASCLE = BRY(IFLAG) - K = ND - 2 - FN = DBLE(FLOAT(K)) - DO 100 I=3,ND - C2R = S2R - C2I = S2I - S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I) - S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R) - S1R = C2R - S1I = C2I - C2R = S2R*C1R - C2I = S2I*C1R - YR(K) = C2R - YI(K) = C2I - K = K - 1 - FN = FN - 1.0D0 - IF (IFLAG.GE.3) GO TO 100 - STR = DABS(C2R) - STI = DABS(C2I) - C2M = DMAX1(STR,STI) - IF (C2M.LE.ASCLE) GO TO 100 - IFLAG = IFLAG + 1 - ASCLE = BRY(IFLAG) - S1R = S1R*C1R - S1I = S1I*C1R - S2R = C2R - S2I = C2I - S1R = S1R*CSSR(IFLAG) - S1I = S1I*CSSR(IFLAG) - S2R = S2R*CSSR(IFLAG) - S2I = S2I*CSSR(IFLAG) - C1R = CSRR(IFLAG) - 100 CONTINUE - 110 CONTINUE - RETURN - 120 CONTINUE - IF (RS1.GT.0.0D0) GO TO 140 -C----------------------------------------------------------------------- -C SET UNDERFLOW AND UPDATE PARAMETERS -C----------------------------------------------------------------------- - YR(ND) = ZEROR - YI(ND) = ZEROI - NZ = NZ + 1 - ND = ND - 1 - IF (ND.EQ.0) GO TO 110 - CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM) - IF (NUF.LT.0) GO TO 140 - ND = ND - NUF - NZ = NZ + NUF - IF (ND.EQ.0) GO TO 110 - FN = FNU + DBLE(FLOAT(ND-1)) - IF (FN.LT.FNUL) GO TO 130 -C FN = CIDI -C J = NUF + 1 -C K = MOD(J,4) + 1 -C S1R = CIPR(K) -C S1I = CIPI(K) -C IF (FN.LT.0.0D0) S1I = -S1I -C STR = C2R*S1R - C2I*S1I -C C2I = C2R*S1I + C2I*S1R -C C2R = STR - IN = INU + ND - 1 - IN = MOD(IN,4) + 1 - C2R = CAR*CIPR(IN) - SAR*CIPI(IN) - C2I = CAR*CIPI(IN) + SAR*CIPR(IN) - IF (ZI.LE.0.0D0) C2I = -C2I - GO TO 40 - 130 CONTINUE - NLAST = ND - RETURN - 140 CONTINUE - NZ = -1 - RETURN - 150 CONTINUE - IF (RS1.GT.0.0D0) GO TO 140 - NZ = N - DO 160 I=1,N - YR(I) = ZEROR - YI(I) = ZEROI - 160 CONTINUE - RETURN - END diff --git a/amos/zunik.f b/amos/zunik.f deleted file mode 100644 index 7f297c3..0000000 --- a/amos/zunik.f +++ /dev/null @@ -1,211 +0,0 @@ - SUBROUTINE ZUNIK(ZRR, ZRI, FNU, IKFLG, IPMTR, TOL, INIT, PHIR, - * PHII, ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) -C***BEGIN PROLOGUE ZUNIK -C***REFER TO ZBESI,ZBESK -C -C ZUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC -C EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2 -C RESPECTIVELY BY -C -C W(FNU,ZR) = PHI*EXP(ZETA)*SUM -C -C WHERE ZETA=-ZETA1 + ZETA2 OR -C ZETA1 - ZETA2 -C -C THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE -C SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG= -C 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK -C ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI, -C ZETA1,ZETA2. -C -C***ROUTINES CALLED ZDIV,AZLOG,AZSQRT,D1MACH -C***END PROLOGUE ZUNIK -C COMPLEX CFN,CON,CONE,CRFN,CWRK,CZERO,PHI,S,SR,SUM,T,T2,ZETA1, -C *ZETA2,ZN,ZR - DOUBLE PRECISION AC, C, CON, CONEI, CONER, CRFNI, CRFNR, CWRKI, - * CWRKR, FNU, PHII, PHIR, RFN, SI, SR, SRI, SRR, STI, STR, SUMI, - * SUMR, TEST, TI, TOL, TR, T2I, T2R, ZEROI, ZEROR, ZETA1I, ZETA1R, - * ZETA2I, ZETA2R, ZNI, ZNR, ZRI, ZRR, D1MACH - INTEGER I, IDUM, IKFLG, INIT, IPMTR, J, K, L - DIMENSION C(120), CWRKR(16), CWRKI(16), CON(2) - DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / - DATA CON(1), CON(2) / - 1 3.98942280401432678D-01, 1.25331413731550025D+00 / - DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), - 1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), - 2 C(19), C(20), C(21), C(22), C(23), C(24)/ - 3 1.00000000000000000D+00, -2.08333333333333333D-01, - 4 1.25000000000000000D-01, 3.34201388888888889D-01, - 5 -4.01041666666666667D-01, 7.03125000000000000D-02, - 6 -1.02581259645061728D+00, 1.84646267361111111D+00, - 7 -8.91210937500000000D-01, 7.32421875000000000D-02, - 8 4.66958442342624743D+00, -1.12070026162229938D+01, - 9 8.78912353515625000D+00, -2.36408691406250000D+00, - A 1.12152099609375000D-01, -2.82120725582002449D+01, - B 8.46362176746007346D+01, -9.18182415432400174D+01, - C 4.25349987453884549D+01, -7.36879435947963170D+00, - D 2.27108001708984375D-01, 2.12570130039217123D+02, - E -7.65252468141181642D+02, 1.05999045252799988D+03/ - DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), - 1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), - 2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ - 3 -6.99579627376132541D+02, 2.18190511744211590D+02, - 4 -2.64914304869515555D+01, 5.72501420974731445D-01, - 5 -1.91945766231840700D+03, 8.06172218173730938D+03, - 6 -1.35865500064341374D+04, 1.16553933368645332D+04, - 7 -5.30564697861340311D+03, 1.20090291321635246D+03, - 8 -1.08090919788394656D+02, 1.72772750258445740D+00, - 9 2.02042913309661486D+04, -9.69805983886375135D+04, - A 1.92547001232531532D+05, -2.03400177280415534D+05, - B 1.22200464983017460D+05, -4.11926549688975513D+04, - C 7.10951430248936372D+03, -4.93915304773088012D+02, - D 6.07404200127348304D+00, -2.42919187900551333D+05, - E 1.31176361466297720D+06, -2.99801591853810675D+06/ - DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), - 1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), - 2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ - 3 3.76327129765640400D+06, -2.81356322658653411D+06, - 4 1.26836527332162478D+06, -3.31645172484563578D+05, - 5 4.52187689813627263D+04, -2.49983048181120962D+03, - 6 2.43805296995560639D+01, 3.28446985307203782D+06, - 7 -1.97068191184322269D+07, 5.09526024926646422D+07, - 8 -7.41051482115326577D+07, 6.63445122747290267D+07, - 9 -3.75671766607633513D+07, 1.32887671664218183D+07, - A -2.78561812808645469D+06, 3.08186404612662398D+05, - B -1.38860897537170405D+04, 1.10017140269246738D+02, - C -4.93292536645099620D+07, 3.25573074185765749D+08, - D -9.39462359681578403D+08, 1.55359689957058006D+09, - E -1.62108055210833708D+09, 1.10684281682301447D+09/ - DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), - 1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), - 2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ - 3 -4.95889784275030309D+08, 1.42062907797533095D+08, - 4 -2.44740627257387285D+07, 2.24376817792244943D+06, - 5 -8.40054336030240853D+04, 5.51335896122020586D+02, - 6 8.14789096118312115D+08, -5.86648149205184723D+09, - 7 1.86882075092958249D+10, -3.46320433881587779D+10, - 8 4.12801855797539740D+10, -3.30265997498007231D+10, - 9 1.79542137311556001D+10, -6.56329379261928433D+09, - A 1.55927986487925751D+09, -2.25105661889415278D+08, - B 1.73951075539781645D+07, -5.49842327572288687D+05, - C 3.03809051092238427D+03, -1.46792612476956167D+10, - D 1.14498237732025810D+11, -3.99096175224466498D+11, - E 8.19218669548577329D+11, -1.09837515608122331D+12/ - DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), - 1 C(105), C(106), C(107), C(108), C(109), C(110), C(111), - 2 C(112), C(113), C(114), C(115), C(116), C(117), C(118)/ - 3 1.00815810686538209D+12, -6.45364869245376503D+11, - 4 2.87900649906150589D+11, -8.78670721780232657D+10, - 5 1.76347306068349694D+10, -2.16716498322379509D+09, - 6 1.43157876718888981D+08, -3.87183344257261262D+06, - 7 1.82577554742931747D+04, 2.86464035717679043D+11, - 8 -2.40629790002850396D+12, 9.10934118523989896D+12, - 9 -2.05168994109344374D+13, 3.05651255199353206D+13, - A -3.16670885847851584D+13, 2.33483640445818409D+13, - B -1.23204913055982872D+13, 4.61272578084913197D+12, - C -1.19655288019618160D+12, 2.05914503232410016D+11, - D -2.18229277575292237D+10, 1.24700929351271032D+09/ - DATA C(119), C(120)/ - 1 -2.91883881222208134D+07, 1.18838426256783253D+05/ -C - IF (INIT.NE.0) GO TO 40 -C----------------------------------------------------------------------- -C INITIALIZE ALL VARIABLES -C----------------------------------------------------------------------- - RFN = 1.0D0/FNU -C----------------------------------------------------------------------- -C OVERFLOW TEST (ZR/FNU TOO SMALL) -C----------------------------------------------------------------------- - TEST = D1MACH(1)*1.0D+3 - AC = FNU*TEST - IF (DABS(ZRR).GT.AC .OR. DABS(ZRI).GT.AC) GO TO 15 - ZETA1R = 2.0D0*DABS(DLOG(TEST))+FNU - ZETA1I = 0.0D0 - ZETA2R = FNU - ZETA2I = 0.0D0 - PHIR = 1.0D0 - PHII = 0.0D0 - RETURN - 15 CONTINUE - TR = ZRR*RFN - TI = ZRI*RFN - SR = CONER + (TR*TR-TI*TI) - SI = CONEI + (TR*TI+TI*TR) - CALL AZSQRT(SR, SI, SRR, SRI) - STR = CONER + SRR - STI = CONEI + SRI - CALL ZDIV(STR, STI, TR, TI, ZNR, ZNI) - CALL AZLOG(ZNR, ZNI, STR, STI, IDUM) - ZETA1R = FNU*STR - ZETA1I = FNU*STI - ZETA2R = FNU*SRR - ZETA2I = FNU*SRI - CALL ZDIV(CONER, CONEI, SRR, SRI, TR, TI) - SRR = TR*RFN - SRI = TI*RFN - CALL AZSQRT(SRR, SRI, CWRKR(16), CWRKI(16)) - PHIR = CWRKR(16)*CON(IKFLG) - PHII = CWRKI(16)*CON(IKFLG) - IF (IPMTR.NE.0) RETURN - CALL ZDIV(CONER, CONEI, SR, SI, T2R, T2I) - CWRKR(1) = CONER - CWRKI(1) = CONEI - CRFNR = CONER - CRFNI = CONEI - AC = 1.0D0 - L = 1 - DO 20 K=2,15 - SR = ZEROR - SI = ZEROI - DO 10 J=1,K - L = L + 1 - STR = SR*T2R - SI*T2I + C(L) - SI = SR*T2I + SI*T2R - SR = STR - 10 CONTINUE - STR = CRFNR*SRR - CRFNI*SRI - CRFNI = CRFNR*SRI + CRFNI*SRR - CRFNR = STR - CWRKR(K) = CRFNR*SR - CRFNI*SI - CWRKI(K) = CRFNR*SI + CRFNI*SR - AC = AC*RFN - TEST = DABS(CWRKR(K)) + DABS(CWRKI(K)) - IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30 - 20 CONTINUE - K = 15 - 30 CONTINUE - INIT = K - 40 CONTINUE - IF (IKFLG.EQ.2) GO TO 60 -C----------------------------------------------------------------------- -C COMPUTE SUM FOR THE I FUNCTION -C----------------------------------------------------------------------- - SR = ZEROR - SI = ZEROI - DO 50 I=1,INIT - SR = SR + CWRKR(I) - SI = SI + CWRKI(I) - 50 CONTINUE - SUMR = SR - SUMI = SI - PHIR = CWRKR(16)*CON(1) - PHII = CWRKI(16)*CON(1) - RETURN - 60 CONTINUE -C----------------------------------------------------------------------- -C COMPUTE SUM FOR THE K FUNCTION -C----------------------------------------------------------------------- - SR = ZEROR - SI = ZEROI - TR = CONER - DO 70 I=1,INIT - SR = SR + TR*CWRKR(I) - SI = SI + TR*CWRKI(I) - TR = -TR - 70 CONTINUE - SUMR = SR - SUMI = SI - PHIR = CWRKR(16)*CON(2) - PHII = CWRKI(16)*CON(2) - RETURN - END diff --git a/amos/zunk1.f b/amos/zunk1.f deleted file mode 100644 index 5457d07..0000000 --- a/amos/zunk1.f +++ /dev/null @@ -1,426 +0,0 @@ - SUBROUTINE ZUNK1(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, - * ALIM) -C***BEGIN PROLOGUE ZUNK1 -C***REFER TO ZBESK -C -C ZUNK1 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE -C RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE -C UNIFORM ASYMPTOTIC EXPANSION. -C MR INDICATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION. -C NZ=-1 MEANS AN OVERFLOW WILL OCCUR -C -C***ROUTINES CALLED ZKSCL,ZS1S2,ZUCHK,ZUNIK,D1MACH,AZABS -C***END PROLOGUE ZUNK1 -C COMPLEX CFN,CK,CONE,CRSC,CS,CSCL,CSGN,CSPN,CSR,CSS,CWRK,CY,CZERO, -C *C1,C2,PHI,PHID,RZ,SUM,SUMD,S1,S2,Y,Z,ZETA1,ZETA1D,ZETA2,ZETA2D,ZR - DOUBLE PRECISION ALIM, ANG, APHI, ASC, ASCLE, BRY, CKI, CKR, - * CONER, CRSC, CSCL, CSGNI, CSPNI, CSPNR, CSR, CSRR, CSSR, - * CWRKI, CWRKR, CYI, CYR, C1I, C1R, C2I, C2M, C2R, ELIM, FMR, FN, - * FNF, FNU, PHIDI, PHIDR, PHII, PHIR, PI, RAST, RAZR, RS1, RZI, - * RZR, SGN, STI, STR, SUMDI, SUMDR, SUMI, SUMR, S1I, S1R, S2I, - * S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, - * ZET1DI, ZET1DR, ZET2DI, ZET2DR, ZI, ZR, ZRI, ZRR, D1MACH, AZABS - INTEGER I, IB, IFLAG, IFN, IL, INIT, INU, IUF, K, KDFLG, KFLAG, - * KK, KODE, MR, N, NW, NZ, INITD, IC, IPARD, J - DIMENSION BRY(3), INIT(2), YR(N), YI(N), SUMR(2), SUMI(2), - * ZETA1R(2), ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2), - * CWRKR(16,3), CWRKI(16,3), CSSR(3), CSRR(3), PHIR(2), PHII(2) - DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 / - DATA PI / 3.14159265358979324D0 / -C - KDFLG = 1 - NZ = 0 -C----------------------------------------------------------------------- -C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN -C THE UNDERFLOW LIMIT -C----------------------------------------------------------------------- - CSCL = 1.0D0/TOL - CRSC = TOL - CSSR(1) = CSCL - CSSR(2) = CONER - CSSR(3) = CRSC - CSRR(1) = CRSC - CSRR(2) = CONER - CSRR(3) = CSCL - BRY(1) = 1.0D+3*D1MACH(1)/TOL - BRY(2) = 1.0D0/BRY(1) - BRY(3) = D1MACH(2) - ZRR = ZR - ZRI = ZI - IF (ZR.GE.0.0D0) GO TO 10 - ZRR = -ZR - ZRI = -ZI - 10 CONTINUE - J = 2 - DO 70 I=1,N -C----------------------------------------------------------------------- -C J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J -C----------------------------------------------------------------------- - J = 3 - J - FN = FNU + DBLE(FLOAT(I-1)) - INIT(J) = 0 - CALL ZUNIK(ZRR, ZRI, FN, 2, 0, TOL, INIT(J), PHIR(J), PHII(J), - * ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), SUMR(J), SUMI(J), - * CWRKR(1,J), CWRKI(1,J)) - IF (KODE.EQ.1) GO TO 20 - STR = ZRR + ZETA2R(J) - STI = ZRI + ZETA2I(J) - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = ZETA1R(J) - STR - S1I = ZETA1I(J) - STI - GO TO 30 - 20 CONTINUE - S1R = ZETA1R(J) - ZETA2R(J) - S1I = ZETA1I(J) - ZETA2I(J) - 30 CONTINUE - RS1 = S1R -C----------------------------------------------------------------------- -C TEST FOR UNDERFLOW AND OVERFLOW -C----------------------------------------------------------------------- - IF (DABS(RS1).GT.ELIM) GO TO 60 - IF (KDFLG.EQ.1) KFLAG = 2 - IF (DABS(RS1).LT.ALIM) GO TO 40 -C----------------------------------------------------------------------- -C REFINE TEST AND SCALE -C----------------------------------------------------------------------- - APHI = AZABS(PHIR(J),PHII(J)) - RS1 = RS1 + DLOG(APHI) - IF (DABS(RS1).GT.ELIM) GO TO 60 - IF (KDFLG.EQ.1) KFLAG = 1 - IF (RS1.LT.0.0D0) GO TO 40 - IF (KDFLG.EQ.1) KFLAG = 3 - 40 CONTINUE -C----------------------------------------------------------------------- -C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR -C EXPONENT EXTREMES -C----------------------------------------------------------------------- - S2R = PHIR(J)*SUMR(J) - PHII(J)*SUMI(J) - S2I = PHIR(J)*SUMI(J) + PHII(J)*SUMR(J) - STR = DEXP(S1R)*CSSR(KFLAG) - S1R = STR*DCOS(S1I) - S1I = STR*DSIN(S1I) - STR = S2R*S1R - S2I*S1I - S2I = S1R*S2I + S2R*S1I - S2R = STR - IF (KFLAG.NE.1) GO TO 50 - CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) - IF (NW.NE.0) GO TO 60 - 50 CONTINUE - CYR(KDFLG) = S2R - CYI(KDFLG) = S2I - YR(I) = S2R*CSRR(KFLAG) - YI(I) = S2I*CSRR(KFLAG) - IF (KDFLG.EQ.2) GO TO 75 - KDFLG = 2 - GO TO 70 - 60 CONTINUE - IF (RS1.GT.0.0D0) GO TO 300 -C----------------------------------------------------------------------- -C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW -C----------------------------------------------------------------------- - IF (ZR.LT.0.0D0) GO TO 300 - KDFLG = 1 - YR(I)=ZEROR - YI(I)=ZEROI - NZ=NZ+1 - IF (I.EQ.1) GO TO 70 - IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 70 - YR(I-1)=ZEROR - YI(I-1)=ZEROI - NZ=NZ+1 - 70 CONTINUE - I = N - 75 CONTINUE - RAZR = 1.0D0/AZABS(ZRR,ZRI) - STR = ZRR*RAZR - STI = -ZRI*RAZR - RZR = (STR+STR)*RAZR - RZI = (STI+STI)*RAZR - CKR = FN*RZR - CKI = FN*RZI - IB = I + 1 - IF (N.LT.IB) GO TO 160 -C----------------------------------------------------------------------- -C TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO -C ON UNDERFLOW. -C----------------------------------------------------------------------- - FN = FNU + DBLE(FLOAT(N-1)) - IPARD = 1 - IF (MR.NE.0) IPARD = 0 - INITD = 0 - CALL ZUNIK(ZRR, ZRI, FN, 2, IPARD, TOL, INITD, PHIDR, PHIDI, - * ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI, CWRKR(1,3), - * CWRKI(1,3)) - IF (KODE.EQ.1) GO TO 80 - STR = ZRR + ZET2DR - STI = ZRI + ZET2DI - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = ZET1DR - STR - S1I = ZET1DI - STI - GO TO 90 - 80 CONTINUE - S1R = ZET1DR - ZET2DR - S1I = ZET1DI - ZET2DI - 90 CONTINUE - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 95 - IF (DABS(RS1).LT.ALIM) GO TO 100 -C---------------------------------------------------------------------------- -C REFINE ESTIMATE AND TEST -C------------------------------------------------------------------------- - APHI = AZABS(PHIDR,PHIDI) - RS1 = RS1+DLOG(APHI) - IF (DABS(RS1).LT.ELIM) GO TO 100 - 95 CONTINUE - IF (DABS(RS1).GT.0.0D0) GO TO 300 -C----------------------------------------------------------------------- -C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW -C----------------------------------------------------------------------- - IF (ZR.LT.0.0D0) GO TO 300 - NZ = N - DO 96 I=1,N - YR(I) = ZEROR - YI(I) = ZEROI - 96 CONTINUE - RETURN -C--------------------------------------------------------------------------- -C FORWARD RECUR FOR REMAINDER OF THE SEQUENCE -C---------------------------------------------------------------------------- - 100 CONTINUE - S1R = CYR(1) - S1I = CYI(1) - S2R = CYR(2) - S2I = CYI(2) - C1R = CSRR(KFLAG) - ASCLE = BRY(KFLAG) - DO 120 I=IB,N - C2R = S2R - C2I = S2I - S2R = CKR*C2R - CKI*C2I + S1R - S2I = CKR*C2I + CKI*C2R + S1I - S1R = C2R - S1I = C2I - CKR = CKR + RZR - CKI = CKI + RZI - C2R = S2R*C1R - C2I = S2I*C1R - YR(I) = C2R - YI(I) = C2I - IF (KFLAG.GE.3) GO TO 120 - STR = DABS(C2R) - STI = DABS(C2I) - C2M = DMAX1(STR,STI) - IF (C2M.LE.ASCLE) GO TO 120 - KFLAG = KFLAG + 1 - ASCLE = BRY(KFLAG) - S1R = S1R*C1R - S1I = S1I*C1R - S2R = C2R - S2I = C2I - S1R = S1R*CSSR(KFLAG) - S1I = S1I*CSSR(KFLAG) - S2R = S2R*CSSR(KFLAG) - S2I = S2I*CSSR(KFLAG) - C1R = CSRR(KFLAG) - 120 CONTINUE - 160 CONTINUE - IF (MR.EQ.0) RETURN -C----------------------------------------------------------------------- -C ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0 -C----------------------------------------------------------------------- - NZ = 0 - FMR = DBLE(FLOAT(MR)) - SGN = -DSIGN(PI,FMR) -C----------------------------------------------------------------------- -C CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP. -C----------------------------------------------------------------------- - CSGNI = SGN - INU = INT(SNGL(FNU)) - FNF = FNU - DBLE(FLOAT(INU)) - IFN = INU + N - 1 - ANG = FNF*SGN - CSPNR = DCOS(ANG) - CSPNI = DSIN(ANG) - IF (MOD(IFN,2).EQ.0) GO TO 170 - CSPNR = -CSPNR - CSPNI = -CSPNI - 170 CONTINUE - ASC = BRY(1) - IUF = 0 - KK = N - KDFLG = 1 - IB = IB - 1 - IC = IB - 1 - DO 270 K=1,N - FN = FNU + DBLE(FLOAT(KK-1)) -C----------------------------------------------------------------------- -C LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K -C FUNCTION ABOVE -C----------------------------------------------------------------------- - M=3 - IF (N.GT.2) GO TO 175 - 172 CONTINUE - INITD = INIT(J) - PHIDR = PHIR(J) - PHIDI = PHII(J) - ZET1DR = ZETA1R(J) - ZET1DI = ZETA1I(J) - ZET2DR = ZETA2R(J) - ZET2DI = ZETA2I(J) - SUMDR = SUMR(J) - SUMDI = SUMI(J) - M = J - J = 3 - J - GO TO 180 - 175 CONTINUE - IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 180 - IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172 - INITD = 0 - 180 CONTINUE - CALL ZUNIK(ZRR, ZRI, FN, 1, 0, TOL, INITD, PHIDR, PHIDI, - * ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI, - * CWRKR(1,M), CWRKI(1,M)) - IF (KODE.EQ.1) GO TO 200 - STR = ZRR + ZET2DR - STI = ZRI + ZET2DI - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = -ZET1DR + STR - S1I = -ZET1DI + STI - GO TO 210 - 200 CONTINUE - S1R = -ZET1DR + ZET2DR - S1I = -ZET1DI + ZET2DI - 210 CONTINUE -C----------------------------------------------------------------------- -C TEST FOR UNDERFLOW AND OVERFLOW -C----------------------------------------------------------------------- - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 260 - IF (KDFLG.EQ.1) IFLAG = 2 - IF (DABS(RS1).LT.ALIM) GO TO 220 -C----------------------------------------------------------------------- -C REFINE TEST AND SCALE -C----------------------------------------------------------------------- - APHI = AZABS(PHIDR,PHIDI) - RS1 = RS1 + DLOG(APHI) - IF (DABS(RS1).GT.ELIM) GO TO 260 - IF (KDFLG.EQ.1) IFLAG = 1 - IF (RS1.LT.0.0D0) GO TO 220 - IF (KDFLG.EQ.1) IFLAG = 3 - 220 CONTINUE - STR = PHIDR*SUMDR - PHIDI*SUMDI - STI = PHIDR*SUMDI + PHIDI*SUMDR - S2R = -CSGNI*STI - S2I = CSGNI*STR - STR = DEXP(S1R)*CSSR(IFLAG) - S1R = STR*DCOS(S1I) - S1I = STR*DSIN(S1I) - STR = S2R*S1R - S2I*S1I - S2I = S2R*S1I + S2I*S1R - S2R = STR - IF (IFLAG.NE.1) GO TO 230 - CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) - IF (NW.EQ.0) GO TO 230 - S2R = ZEROR - S2I = ZEROI - 230 CONTINUE - CYR(KDFLG) = S2R - CYI(KDFLG) = S2I - C2R = S2R - C2I = S2I - S2R = S2R*CSRR(IFLAG) - S2I = S2I*CSRR(IFLAG) -C----------------------------------------------------------------------- -C ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N -C----------------------------------------------------------------------- - S1R = YR(KK) - S1I = YI(KK) - IF (KODE.EQ.1) GO TO 250 - CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF) - NZ = NZ + NW - 250 CONTINUE - YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R - YI(KK) = CSPNR*S1I + CSPNI*S1R + S2I - KK = KK - 1 - CSPNR = -CSPNR - CSPNI = -CSPNI - IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255 - KDFLG = 1 - GO TO 270 - 255 CONTINUE - IF (KDFLG.EQ.2) GO TO 275 - KDFLG = 2 - GO TO 270 - 260 CONTINUE - IF (RS1.GT.0.0D0) GO TO 300 - S2R = ZEROR - S2I = ZEROI - GO TO 230 - 270 CONTINUE - K = N - 275 CONTINUE - IL = N - K - IF (IL.EQ.0) RETURN -C----------------------------------------------------------------------- -C RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE -C K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP -C INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES. -C----------------------------------------------------------------------- - S1R = CYR(1) - S1I = CYI(1) - S2R = CYR(2) - S2I = CYI(2) - CSR = CSRR(IFLAG) - ASCLE = BRY(IFLAG) - FN = DBLE(FLOAT(INU+IL)) - DO 290 I=1,IL - C2R = S2R - C2I = S2I - S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I) - S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R) - S1R = C2R - S1I = C2I - FN = FN - 1.0D0 - C2R = S2R*CSR - C2I = S2I*CSR - CKR = C2R - CKI = C2I - C1R = YR(KK) - C1I = YI(KK) - IF (KODE.EQ.1) GO TO 280 - CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF) - NZ = NZ + NW - 280 CONTINUE - YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R - YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I - KK = KK - 1 - CSPNR = -CSPNR - CSPNI = -CSPNI - IF (IFLAG.GE.3) GO TO 290 - C2R = DABS(CKR) - C2I = DABS(CKI) - C2M = DMAX1(C2R,C2I) - IF (C2M.LE.ASCLE) GO TO 290 - IFLAG = IFLAG + 1 - ASCLE = BRY(IFLAG) - S1R = S1R*CSR - S1I = S1I*CSR - S2R = CKR - S2I = CKI - S1R = S1R*CSSR(IFLAG) - S1I = S1I*CSSR(IFLAG) - S2R = S2R*CSSR(IFLAG) - S2I = S2I*CSSR(IFLAG) - CSR = CSRR(IFLAG) - 290 CONTINUE - RETURN - 300 CONTINUE - NZ = -1 - RETURN - END diff --git a/amos/zunk2.f b/amos/zunk2.f deleted file mode 100644 index 932fe8e..0000000 --- a/amos/zunk2.f +++ /dev/null @@ -1,505 +0,0 @@ - SUBROUTINE ZUNK2(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, - * ALIM) -C***BEGIN PROLOGUE ZUNK2 -C***REFER TO ZBESK -C -C ZUNK2 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE -C RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE -C UNIFORM ASYMPTOTIC EXPANSIONS FOR H(KIND,FNU,ZN) AND J(FNU,ZN) -C WHERE ZN IS IN THE RIGHT HALF PLANE, KIND=(3-MR)/2, MR=+1 OR -C -1. HERE ZN=ZR*I OR -ZR*I WHERE ZR=Z IF Z IS IN THE RIGHT -C HALF PLANE OR ZR=-Z IF Z IS IN THE LEFT HALF PLANE. MR INDIC- -C ATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION. -C NZ=-1 MEANS AN OVERFLOW WILL OCCUR -C -C***ROUTINES CALLED ZAIRY,ZKSCL,ZS1S2,ZUCHK,ZUNHJ,D1MACH,AZABS -C***END PROLOGUE ZUNK2 -C COMPLEX AI,ARG,ARGD,ASUM,ASUMD,BSUM,BSUMD,CFN,CI,CIP,CK,CONE,CRSC, -C *CR1,CR2,CS,CSCL,CSGN,CSPN,CSR,CSS,CY,CZERO,C1,C2,DAI,PHI,PHID,RZ, -C *S1,S2,Y,Z,ZB,ZETA1,ZETA1D,ZETA2,ZETA2D,ZN,ZR - DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGDI, - * ARGDR, ARGI, ARGR, ASC, ASCLE, ASUMDI, ASUMDR, ASUMI, ASUMR, - * BRY, BSUMDI, BSUMDR, BSUMI, BSUMR, CAR, CIPI, CIPR, CKI, CKR, - * CONER, CRSC, CR1I, CR1R, CR2I, CR2R, CSCL, CSGNI, CSI, - * CSPNI, CSPNR, CSR, CSRR, CSSR, CYI, CYR, C1I, C1R, C2I, C2M, - * C2R, DAII, DAIR, ELIM, FMR, FN, FNF, FNU, HPI, PHIDI, PHIDR, - * PHII, PHIR, PI, PTI, PTR, RAST, RAZR, RS1, RZI, RZR, SAR, SGN, - * STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, YY, ZBI, ZBR, ZEROI, - * ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZET1DI, ZET1DR, ZET2DI, - * ZET2DR, ZI, ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, AZABS - INTEGER I, IB, IFLAG, IFN, IL, IN, INU, IUF, K, KDFLG, KFLAG, KK, - * KODE, MR, N, NAI, NDAI, NW, NZ, IDUM, J, IPARD, IC - DIMENSION BRY(3), YR(N), YI(N), ASUMR(2), ASUMI(2), BSUMR(2), - * BSUMI(2), PHIR(2), PHII(2), ARGR(2), ARGI(2), ZETA1R(2), - * ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2), CIPR(4), - * CIPI(4), CSSR(3), CSRR(3) - DATA ZEROR,ZEROI,CONER,CR1R,CR1I,CR2R,CR2I / - 1 0.0D0, 0.0D0, 1.0D0, - 1 1.0D0,1.73205080756887729D0 , -0.5D0,-8.66025403784438647D-01 / - DATA HPI, PI, AIC / - 1 1.57079632679489662D+00, 3.14159265358979324D+00, - 1 1.26551212348464539D+00/ - DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4), - * CIPI(4) / - 1 1.0D0,0.0D0 , 0.0D0,-1.0D0 , -1.0D0,0.0D0 , 0.0D0,1.0D0 / -C - KDFLG = 1 - NZ = 0 -C----------------------------------------------------------------------- -C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN -C THE UNDERFLOW LIMIT -C----------------------------------------------------------------------- - CSCL = 1.0D0/TOL - CRSC = TOL - CSSR(1) = CSCL - CSSR(2) = CONER - CSSR(3) = CRSC - CSRR(1) = CRSC - CSRR(2) = CONER - CSRR(3) = CSCL - BRY(1) = 1.0D+3*D1MACH(1)/TOL - BRY(2) = 1.0D0/BRY(1) - BRY(3) = D1MACH(2) - ZRR = ZR - ZRI = ZI - IF (ZR.GE.0.0D0) GO TO 10 - ZRR = -ZR - ZRI = -ZI - 10 CONTINUE - YY = ZRI - ZNR = ZRI - ZNI = -ZRR - ZBR = ZRR - ZBI = ZRI - INU = INT(SNGL(FNU)) - FNF = FNU - DBLE(FLOAT(INU)) - ANG = -HPI*FNF - CAR = DCOS(ANG) - SAR = DSIN(ANG) - C2R = HPI*SAR - C2I = -HPI*CAR - KK = MOD(INU,4) + 1 - STR = C2R*CIPR(KK) - C2I*CIPI(KK) - STI = C2R*CIPI(KK) + C2I*CIPR(KK) - CSR = CR1R*STR - CR1I*STI - CSI = CR1R*STI + CR1I*STR - IF (YY.GT.0.0D0) GO TO 20 - ZNR = -ZNR - ZBI = -ZBI - 20 CONTINUE -C----------------------------------------------------------------------- -C K(FNU,Z) IS COMPUTED FROM H(2,FNU,-I*Z) WHERE Z IS IN THE FIRST -C QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY -C CONJUGATION SINCE THE K FUNCTION IS REAL ON THE POSITIVE REAL AXIS -C----------------------------------------------------------------------- - J = 2 - DO 80 I=1,N -C----------------------------------------------------------------------- -C J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J -C----------------------------------------------------------------------- - J = 3 - J - FN = FNU + DBLE(FLOAT(I-1)) - CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR(J), PHII(J), ARGR(J), - * ARGI(J), ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), ASUMR(J), - * ASUMI(J), BSUMR(J), BSUMI(J)) - IF (KODE.EQ.1) GO TO 30 - STR = ZBR + ZETA2R(J) - STI = ZBI + ZETA2I(J) - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = ZETA1R(J) - STR - S1I = ZETA1I(J) - STI - GO TO 40 - 30 CONTINUE - S1R = ZETA1R(J) - ZETA2R(J) - S1I = ZETA1I(J) - ZETA2I(J) - 40 CONTINUE -C----------------------------------------------------------------------- -C TEST FOR UNDERFLOW AND OVERFLOW -C----------------------------------------------------------------------- - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 70 - IF (KDFLG.EQ.1) KFLAG = 2 - IF (DABS(RS1).LT.ALIM) GO TO 50 -C----------------------------------------------------------------------- -C REFINE TEST AND SCALE -C----------------------------------------------------------------------- - APHI = AZABS(PHIR(J),PHII(J)) - AARG = AZABS(ARGR(J),ARGI(J)) - RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC - IF (DABS(RS1).GT.ELIM) GO TO 70 - IF (KDFLG.EQ.1) KFLAG = 1 - IF (RS1.LT.0.0D0) GO TO 50 - IF (KDFLG.EQ.1) KFLAG = 3 - 50 CONTINUE -C----------------------------------------------------------------------- -C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR -C EXPONENT EXTREMES -C----------------------------------------------------------------------- - C2R = ARGR(J)*CR2R - ARGI(J)*CR2I - C2I = ARGR(J)*CR2I + ARGI(J)*CR2R - CALL ZAIRY(C2R, C2I, 0, 2, AIR, AII, NAI, IDUM) - CALL ZAIRY(C2R, C2I, 1, 2, DAIR, DAII, NDAI, IDUM) - STR = DAIR*BSUMR(J) - DAII*BSUMI(J) - STI = DAIR*BSUMI(J) + DAII*BSUMR(J) - PTR = STR*CR2R - STI*CR2I - PTI = STR*CR2I + STI*CR2R - STR = PTR + (AIR*ASUMR(J)-AII*ASUMI(J)) - STI = PTI + (AIR*ASUMI(J)+AII*ASUMR(J)) - PTR = STR*PHIR(J) - STI*PHII(J) - PTI = STR*PHII(J) + STI*PHIR(J) - S2R = PTR*CSR - PTI*CSI - S2I = PTR*CSI + PTI*CSR - STR = DEXP(S1R)*CSSR(KFLAG) - S1R = STR*DCOS(S1I) - S1I = STR*DSIN(S1I) - STR = S2R*S1R - S2I*S1I - S2I = S1R*S2I + S2R*S1I - S2R = STR - IF (KFLAG.NE.1) GO TO 60 - CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) - IF (NW.NE.0) GO TO 70 - 60 CONTINUE - IF (YY.LE.0.0D0) S2I = -S2I - CYR(KDFLG) = S2R - CYI(KDFLG) = S2I - YR(I) = S2R*CSRR(KFLAG) - YI(I) = S2I*CSRR(KFLAG) - STR = CSI - CSI = -CSR - CSR = STR - IF (KDFLG.EQ.2) GO TO 85 - KDFLG = 2 - GO TO 80 - 70 CONTINUE - IF (RS1.GT.0.0D0) GO TO 320 -C----------------------------------------------------------------------- -C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW -C----------------------------------------------------------------------- - IF (ZR.LT.0.0D0) GO TO 320 - KDFLG = 1 - YR(I)=ZEROR - YI(I)=ZEROI - NZ=NZ+1 - STR = CSI - CSI =-CSR - CSR = STR - IF (I.EQ.1) GO TO 80 - IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 80 - YR(I-1)=ZEROR - YI(I-1)=ZEROI - NZ=NZ+1 - 80 CONTINUE - I = N - 85 CONTINUE - RAZR = 1.0D0/AZABS(ZRR,ZRI) - STR = ZRR*RAZR - STI = -ZRI*RAZR - RZR = (STR+STR)*RAZR - RZI = (STI+STI)*RAZR - CKR = FN*RZR - CKI = FN*RZI - IB = I + 1 - IF (N.LT.IB) GO TO 180 -C----------------------------------------------------------------------- -C TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO -C ON UNDERFLOW. -C----------------------------------------------------------------------- - FN = FNU + DBLE(FLOAT(N-1)) - IPARD = 1 - IF (MR.NE.0) IPARD = 0 - CALL ZUNHJ(ZNR, ZNI, FN, IPARD, TOL, PHIDR, PHIDI, ARGDR, ARGDI, - * ZET1DR, ZET1DI, ZET2DR, ZET2DI, ASUMDR, ASUMDI, BSUMDR, BSUMDI) - IF (KODE.EQ.1) GO TO 90 - STR = ZBR + ZET2DR - STI = ZBI + ZET2DI - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = ZET1DR - STR - S1I = ZET1DI - STI - GO TO 100 - 90 CONTINUE - S1R = ZET1DR - ZET2DR - S1I = ZET1DI - ZET2DI - 100 CONTINUE - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 105 - IF (DABS(RS1).LT.ALIM) GO TO 120 -C---------------------------------------------------------------------------- -C REFINE ESTIMATE AND TEST -C------------------------------------------------------------------------- - APHI = AZABS(PHIDR,PHIDI) - RS1 = RS1+DLOG(APHI) - IF (DABS(RS1).LT.ELIM) GO TO 120 - 105 CONTINUE - IF (RS1.GT.0.0D0) GO TO 320 -C----------------------------------------------------------------------- -C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW -C----------------------------------------------------------------------- - IF (ZR.LT.0.0D0) GO TO 320 - NZ = N - DO 106 I=1,N - YR(I) = ZEROR - YI(I) = ZEROI - 106 CONTINUE - RETURN - 120 CONTINUE - S1R = CYR(1) - S1I = CYI(1) - S2R = CYR(2) - S2I = CYI(2) - C1R = CSRR(KFLAG) - ASCLE = BRY(KFLAG) - DO 130 I=IB,N - C2R = S2R - C2I = S2I - S2R = CKR*C2R - CKI*C2I + S1R - S2I = CKR*C2I + CKI*C2R + S1I - S1R = C2R - S1I = C2I - CKR = CKR + RZR - CKI = CKI + RZI - C2R = S2R*C1R - C2I = S2I*C1R - YR(I) = C2R - YI(I) = C2I - IF (KFLAG.GE.3) GO TO 130 - STR = DABS(C2R) - STI = DABS(C2I) - C2M = DMAX1(STR,STI) - IF (C2M.LE.ASCLE) GO TO 130 - KFLAG = KFLAG + 1 - ASCLE = BRY(KFLAG) - S1R = S1R*C1R - S1I = S1I*C1R - S2R = C2R - S2I = C2I - S1R = S1R*CSSR(KFLAG) - S1I = S1I*CSSR(KFLAG) - S2R = S2R*CSSR(KFLAG) - S2I = S2I*CSSR(KFLAG) - C1R = CSRR(KFLAG) - 130 CONTINUE - 180 CONTINUE - IF (MR.EQ.0) RETURN -C----------------------------------------------------------------------- -C ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0 -C----------------------------------------------------------------------- - NZ = 0 - FMR = DBLE(FLOAT(MR)) - SGN = -DSIGN(PI,FMR) -C----------------------------------------------------------------------- -C CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP. -C----------------------------------------------------------------------- - CSGNI = SGN - IF (YY.LE.0.0D0) CSGNI = -CSGNI - IFN = INU + N - 1 - ANG = FNF*SGN - CSPNR = DCOS(ANG) - CSPNI = DSIN(ANG) - IF (MOD(IFN,2).EQ.0) GO TO 190 - CSPNR = -CSPNR - CSPNI = -CSPNI - 190 CONTINUE -C----------------------------------------------------------------------- -C CS=COEFF OF THE J FUNCTION TO GET THE I FUNCTION. I(FNU,Z) IS -C COMPUTED FROM EXP(I*FNU*HPI)*J(FNU,-I*Z) WHERE Z IS IN THE FIRST -C QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY -C CONJUGATION SINCE THE I FUNCTION IS REAL ON THE POSITIVE REAL AXIS -C----------------------------------------------------------------------- - CSR = SAR*CSGNI - CSI = CAR*CSGNI - IN = MOD(IFN,4) + 1 - C2R = CIPR(IN) - C2I = CIPI(IN) - STR = CSR*C2R + CSI*C2I - CSI = -CSR*C2I + CSI*C2R - CSR = STR - ASC = BRY(1) - IUF = 0 - KK = N - KDFLG = 1 - IB = IB - 1 - IC = IB - 1 - DO 290 K=1,N - FN = FNU + DBLE(FLOAT(KK-1)) -C----------------------------------------------------------------------- -C LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K -C FUNCTION ABOVE -C----------------------------------------------------------------------- - IF (N.GT.2) GO TO 175 - 172 CONTINUE - PHIDR = PHIR(J) - PHIDI = PHII(J) - ARGDR = ARGR(J) - ARGDI = ARGI(J) - ZET1DR = ZETA1R(J) - ZET1DI = ZETA1I(J) - ZET2DR = ZETA2R(J) - ZET2DI = ZETA2I(J) - ASUMDR = ASUMR(J) - ASUMDI = ASUMI(J) - BSUMDR = BSUMR(J) - BSUMDI = BSUMI(J) - J = 3 - J - GO TO 210 - 175 CONTINUE - IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 210 - IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172 - CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIDR, PHIDI, ARGDR, - * ARGDI, ZET1DR, ZET1DI, ZET2DR, ZET2DI, ASUMDR, - * ASUMDI, BSUMDR, BSUMDI) - 210 CONTINUE - IF (KODE.EQ.1) GO TO 220 - STR = ZBR + ZET2DR - STI = ZBI + ZET2DI - RAST = FN/AZABS(STR,STI) - STR = STR*RAST*RAST - STI = -STI*RAST*RAST - S1R = -ZET1DR + STR - S1I = -ZET1DI + STI - GO TO 230 - 220 CONTINUE - S1R = -ZET1DR + ZET2DR - S1I = -ZET1DI + ZET2DI - 230 CONTINUE -C----------------------------------------------------------------------- -C TEST FOR UNDERFLOW AND OVERFLOW -C----------------------------------------------------------------------- - RS1 = S1R - IF (DABS(RS1).GT.ELIM) GO TO 280 - IF (KDFLG.EQ.1) IFLAG = 2 - IF (DABS(RS1).LT.ALIM) GO TO 240 -C----------------------------------------------------------------------- -C REFINE TEST AND SCALE -C----------------------------------------------------------------------- - APHI = AZABS(PHIDR,PHIDI) - AARG = AZABS(ARGDR,ARGDI) - RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC - IF (DABS(RS1).GT.ELIM) GO TO 280 - IF (KDFLG.EQ.1) IFLAG = 1 - IF (RS1.LT.0.0D0) GO TO 240 - IF (KDFLG.EQ.1) IFLAG = 3 - 240 CONTINUE - CALL ZAIRY(ARGDR, ARGDI, 0, 2, AIR, AII, NAI, IDUM) - CALL ZAIRY(ARGDR, ARGDI, 1, 2, DAIR, DAII, NDAI, IDUM) - STR = DAIR*BSUMDR - DAII*BSUMDI - STI = DAIR*BSUMDI + DAII*BSUMDR - STR = STR + (AIR*ASUMDR-AII*ASUMDI) - STI = STI + (AIR*ASUMDI+AII*ASUMDR) - PTR = STR*PHIDR - STI*PHIDI - PTI = STR*PHIDI + STI*PHIDR - S2R = PTR*CSR - PTI*CSI - S2I = PTR*CSI + PTI*CSR - STR = DEXP(S1R)*CSSR(IFLAG) - S1R = STR*DCOS(S1I) - S1I = STR*DSIN(S1I) - STR = S2R*S1R - S2I*S1I - S2I = S2R*S1I + S2I*S1R - S2R = STR - IF (IFLAG.NE.1) GO TO 250 - CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) - IF (NW.EQ.0) GO TO 250 - S2R = ZEROR - S2I = ZEROI - 250 CONTINUE - IF (YY.LE.0.0D0) S2I = -S2I - CYR(KDFLG) = S2R - CYI(KDFLG) = S2I - C2R = S2R - C2I = S2I - S2R = S2R*CSRR(IFLAG) - S2I = S2I*CSRR(IFLAG) -C----------------------------------------------------------------------- -C ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N -C----------------------------------------------------------------------- - S1R = YR(KK) - S1I = YI(KK) - IF (KODE.EQ.1) GO TO 270 - CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF) - NZ = NZ + NW - 270 CONTINUE - YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R - YI(KK) = S1R*CSPNI + S1I*CSPNR + S2I - KK = KK - 1 - CSPNR = -CSPNR - CSPNI = -CSPNI - STR = CSI - CSI = -CSR - CSR = STR - IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255 - KDFLG = 1 - GO TO 290 - 255 CONTINUE - IF (KDFLG.EQ.2) GO TO 295 - KDFLG = 2 - GO TO 290 - 280 CONTINUE - IF (RS1.GT.0.0D0) GO TO 320 - S2R = ZEROR - S2I = ZEROI - GO TO 250 - 290 CONTINUE - K = N - 295 CONTINUE - IL = N - K - IF (IL.EQ.0) RETURN -C----------------------------------------------------------------------- -C RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE -C K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP -C INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES. -C----------------------------------------------------------------------- - S1R = CYR(1) - S1I = CYI(1) - S2R = CYR(2) - S2I = CYI(2) - CSR = CSRR(IFLAG) - ASCLE = BRY(IFLAG) - FN = DBLE(FLOAT(INU+IL)) - DO 310 I=1,IL - C2R = S2R - C2I = S2I - S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I) - S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R) - S1R = C2R - S1I = C2I - FN = FN - 1.0D0 - C2R = S2R*CSR - C2I = S2I*CSR - CKR = C2R - CKI = C2I - C1R = YR(KK) - C1I = YI(KK) - IF (KODE.EQ.1) GO TO 300 - CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF) - NZ = NZ + NW - 300 CONTINUE - YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R - YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I - KK = KK - 1 - CSPNR = -CSPNR - CSPNI = -CSPNI - IF (IFLAG.GE.3) GO TO 310 - C2R = DABS(CKR) - C2I = DABS(CKI) - C2M = DMAX1(C2R,C2I) - IF (C2M.LE.ASCLE) GO TO 310 - IFLAG = IFLAG + 1 - ASCLE = BRY(IFLAG) - S1R = S1R*CSR - S1I = S1I*CSR - S2R = CKR - S2I = CKI - S1R = S1R*CSSR(IFLAG) - S1I = S1I*CSSR(IFLAG) - S2R = S2R*CSSR(IFLAG) - S2I = S2I*CSSR(IFLAG) - CSR = CSRR(IFLAG) - 310 CONTINUE - RETURN - 320 CONTINUE - NZ = -1 - RETURN - END diff --git a/amos/zuoik.f b/amos/zuoik.f deleted file mode 100644 index 5b05f96..0000000 --- a/amos/zuoik.f +++ /dev/null @@ -1,194 +0,0 @@ - SUBROUTINE ZUOIK(ZR, ZI, FNU, KODE, IKFLG, N, YR, YI, NUF, TOL, - * ELIM, ALIM) -C***BEGIN PROLOGUE ZUOIK -C***REFER TO ZBESI,ZBESK,ZBESH -C -C ZUOIK COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC -C EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM -C (IN LOGARITHMIC FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW -C WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING -C EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN -C THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER -C MULTIPLIERS (IN LOGARITHMIC FORM) IS MADE BASED ON ELIM. HERE -C EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)= -C EXP(-ELIM)/TOL -C -C IKFLG=1 MEANS THE I SEQUENCE IS TESTED -C =2 MEANS THE K SEQUENCE IS TESTED -C NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE -C =-1 MEANS AN OVERFLOW WOULD OCCUR -C IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO -C THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE -C IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO -C IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY -C ANOTHER ROUTINE -C -C***ROUTINES CALLED ZUCHK,ZUNHJ,ZUNIK,D1MACH,AZABS,AZLOG -C***END PROLOGUE ZUOIK -C COMPLEX ARG,ASUM,BSUM,CWRK,CZ,CZERO,PHI,SUM,Y,Z,ZB,ZETA1,ZETA2,ZN, -C *ZR - DOUBLE PRECISION AARG, AIC, ALIM, APHI, ARGI, ARGR, ASUMI, ASUMR, - * ASCLE, AX, AY, BSUMI, BSUMR, CWRKI, CWRKR, CZI, CZR, ELIM, FNN, - * FNU, GNN, GNU, PHII, PHIR, RCZ, STR, STI, SUMI, SUMR, TOL, YI, - * YR, ZBI, ZBR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, - * ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, AZABS - INTEGER I, IDUM, IFORM, IKFLG, INIT, KODE, N, NN, NUF, NW - DIMENSION YR(N), YI(N), CWRKR(16), CWRKI(16) - DATA ZEROR,ZEROI / 0.0D0, 0.0D0 / - DATA AIC / 1.265512123484645396D+00 / - NUF = 0 - NN = N - ZRR = ZR - ZRI = ZI - IF (ZR.GE.0.0D0) GO TO 10 - ZRR = -ZR - ZRI = -ZI - 10 CONTINUE - ZBR = ZRR - ZBI = ZRI - AX = DABS(ZR)*1.7321D0 - AY = DABS(ZI) - IFORM = 1 - IF (AY.GT.AX) IFORM = 2 - GNU = DMAX1(FNU,1.0D0) - IF (IKFLG.EQ.1) GO TO 20 - FNN = DBLE(FLOAT(NN)) - GNN = FNU + FNN - 1.0D0 - GNU = DMAX1(GNN,FNN) - 20 CONTINUE -C----------------------------------------------------------------------- -C ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE -C REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET -C THE SIGN OF THE IMAGINARY PART CORRECT. -C----------------------------------------------------------------------- - IF (IFORM.EQ.2) GO TO 30 - INIT = 0 - CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII, - * ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) - CZR = -ZETA1R + ZETA2R - CZI = -ZETA1I + ZETA2I - GO TO 50 - 30 CONTINUE - ZNR = ZRI - ZNI = -ZRR - IF (ZI.GT.0.0D0) GO TO 40 - ZNR = -ZNR - 40 CONTINUE - CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, - * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) - CZR = -ZETA1R + ZETA2R - CZI = -ZETA1I + ZETA2I - AARG = AZABS(ARGR,ARGI) - 50 CONTINUE - IF (KODE.EQ.1) GO TO 60 - CZR = CZR - ZBR - CZI = CZI - ZBI - 60 CONTINUE - IF (IKFLG.EQ.1) GO TO 70 - CZR = -CZR - CZI = -CZI - 70 CONTINUE - APHI = AZABS(PHIR,PHII) - RCZ = CZR -C----------------------------------------------------------------------- -C OVERFLOW TEST -C----------------------------------------------------------------------- - IF (RCZ.GT.ELIM) GO TO 210 - IF (RCZ.LT.ALIM) GO TO 80 - RCZ = RCZ + DLOG(APHI) - IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC - IF (RCZ.GT.ELIM) GO TO 210 - GO TO 130 - 80 CONTINUE -C----------------------------------------------------------------------- -C UNDERFLOW TEST -C----------------------------------------------------------------------- - IF (RCZ.LT.(-ELIM)) GO TO 90 - IF (RCZ.GT.(-ALIM)) GO TO 130 - RCZ = RCZ + DLOG(APHI) - IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC - IF (RCZ.GT.(-ELIM)) GO TO 110 - 90 CONTINUE - DO 100 I=1,NN - YR(I) = ZEROR - YI(I) = ZEROI - 100 CONTINUE - NUF = NN - RETURN - 110 CONTINUE - ASCLE = 1.0D+3*D1MACH(1)/TOL - CALL AZLOG(PHIR, PHII, STR, STI, IDUM) - CZR = CZR + STR - CZI = CZI + STI - IF (IFORM.EQ.1) GO TO 120 - CALL AZLOG(ARGR, ARGI, STR, STI, IDUM) - CZR = CZR - 0.25D0*STR - AIC - CZI = CZI - 0.25D0*STI - 120 CONTINUE - AX = DEXP(RCZ)/TOL - AY = CZI - CZR = AX*DCOS(AY) - CZI = AX*DSIN(AY) - CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL) - IF (NW.NE.0) GO TO 90 - 130 CONTINUE - IF (IKFLG.EQ.2) RETURN - IF (N.EQ.1) RETURN -C----------------------------------------------------------------------- -C SET UNDERFLOWS ON I SEQUENCE -C----------------------------------------------------------------------- - 140 CONTINUE - GNU = FNU + DBLE(FLOAT(NN-1)) - IF (IFORM.EQ.2) GO TO 150 - INIT = 0 - CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII, - * ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) - CZR = -ZETA1R + ZETA2R - CZI = -ZETA1I + ZETA2I - GO TO 160 - 150 CONTINUE - CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, - * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) - CZR = -ZETA1R + ZETA2R - CZI = -ZETA1I + ZETA2I - AARG = AZABS(ARGR,ARGI) - 160 CONTINUE - IF (KODE.EQ.1) GO TO 170 - CZR = CZR - ZBR - CZI = CZI - ZBI - 170 CONTINUE - APHI = AZABS(PHIR,PHII) - RCZ = CZR - IF (RCZ.LT.(-ELIM)) GO TO 180 - IF (RCZ.GT.(-ALIM)) RETURN - RCZ = RCZ + DLOG(APHI) - IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC - IF (RCZ.GT.(-ELIM)) GO TO 190 - 180 CONTINUE - YR(NN) = ZEROR - YI(NN) = ZEROI - NN = NN - 1 - NUF = NUF + 1 - IF (NN.EQ.0) RETURN - GO TO 140 - 190 CONTINUE - ASCLE = 1.0D+3*D1MACH(1)/TOL - CALL AZLOG(PHIR, PHII, STR, STI, IDUM) - CZR = CZR + STR - CZI = CZI + STI - IF (IFORM.EQ.1) GO TO 200 - CALL AZLOG(ARGR, ARGI, STR, STI, IDUM) - CZR = CZR - 0.25D0*STR - AIC - CZI = CZI - 0.25D0*STI - 200 CONTINUE - AX = DEXP(RCZ)/TOL - AY = CZI - CZR = AX*DCOS(AY) - CZI = AX*DSIN(AY) - CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL) - IF (NW.NE.0) GO TO 180 - RETURN - 210 CONTINUE - NUF = -1 - RETURN - END diff --git a/amos/zwrsk.f b/amos/zwrsk.f deleted file mode 100644 index 397340f..0000000 --- a/amos/zwrsk.f +++ /dev/null @@ -1,94 +0,0 @@ - SUBROUTINE ZWRSK(ZRR, ZRI, FNU, KODE, N, YR, YI, NZ, CWR, CWI, - * TOL, ELIM, ALIM) -C***BEGIN PROLOGUE ZWRSK -C***REFER TO ZBESI,ZBESK -C -C ZWRSK COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY -C NORMALIZING THE I FUNCTION RATIOS FROM ZRATI BY THE WRONSKIAN -C -C***ROUTINES CALLED D1MACH,ZBKNU,ZRATI,AZABS -C***END PROLOGUE ZWRSK -C COMPLEX CINU,CSCL,CT,CW,C1,C2,RCT,ST,Y,ZR - DOUBLE PRECISION ACT, ACW, ALIM, ASCLE, CINUI, CINUR, CSCLR, CTI, - * CTR, CWI, CWR, C1I, C1R, C2I, C2R, ELIM, FNU, PTI, PTR, RACT, - * STI, STR, TOL, YI, YR, ZRI, ZRR, AZABS, D1MACH - INTEGER I, KODE, N, NW, NZ - DIMENSION YR(N), YI(N), CWR(2), CWI(2) -C----------------------------------------------------------------------- -C I(FNU+I-1,Z) BY BACKWARD RECURRENCE FOR RATIOS -C Y(I)=I(FNU+I,Z)/I(FNU+I-1,Z) FROM CRATI NORMALIZED BY THE -C WRONSKIAN WITH K(FNU,Z) AND K(FNU+1,Z) FROM CBKNU. -C----------------------------------------------------------------------- - NZ = 0 - CALL ZBKNU(ZRR, ZRI, FNU, KODE, 2, CWR, CWI, NW, TOL, ELIM, ALIM) - IF (NW.NE.0) GO TO 50 - CALL ZRATI(ZRR, ZRI, FNU, N, YR, YI, TOL) -C----------------------------------------------------------------------- -C RECUR FORWARD ON I(FNU+1,Z) = R(FNU,Z)*I(FNU,Z), -C R(FNU+J-1,Z)=Y(J), J=1,...,N -C----------------------------------------------------------------------- - CINUR = 1.0D0 - CINUI = 0.0D0 - IF (KODE.EQ.1) GO TO 10 - CINUR = DCOS(ZRI) - CINUI = DSIN(ZRI) - 10 CONTINUE -C----------------------------------------------------------------------- -C ON LOW EXPONENT MACHINES THE K FUNCTIONS CAN BE CLOSE TO BOTH -C THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE -C SCALED TO PREVENT OVER OR UNDERFLOW. CUOIK HAS DETERMINED THAT -C THE RESULT IS ON SCALE. -C----------------------------------------------------------------------- - ACW = AZABS(CWR(2),CWI(2)) - ASCLE = 1.0D+3*D1MACH(1)/TOL - CSCLR = 1.0D0 - IF (ACW.GT.ASCLE) GO TO 20 - CSCLR = 1.0D0/TOL - GO TO 30 - 20 CONTINUE - ASCLE = 1.0D0/ASCLE - IF (ACW.LT.ASCLE) GO TO 30 - CSCLR = TOL - 30 CONTINUE - C1R = CWR(1)*CSCLR - C1I = CWI(1)*CSCLR - C2R = CWR(2)*CSCLR - C2I = CWI(2)*CSCLR - STR = YR(1) - STI = YI(1) -C----------------------------------------------------------------------- -C CINU=CINU*(CONJG(CT)/CABS(CT))*(1.0D0/CABS(CT) PREVENTS -C UNDER- OR OVERFLOW PREMATURELY BY SQUARING CABS(CT) -C----------------------------------------------------------------------- - PTR = STR*C1R - STI*C1I - PTI = STR*C1I + STI*C1R - PTR = PTR + C2R - PTI = PTI + C2I - CTR = ZRR*PTR - ZRI*PTI - CTI = ZRR*PTI + ZRI*PTR - ACT = AZABS(CTR,CTI) - RACT = 1.0D0/ACT - CTR = CTR*RACT - CTI = -CTI*RACT - PTR = CINUR*RACT - PTI = CINUI*RACT - CINUR = PTR*CTR - PTI*CTI - CINUI = PTR*CTI + PTI*CTR - YR(1) = CINUR*CSCLR - YI(1) = CINUI*CSCLR - IF (N.EQ.1) RETURN - DO 40 I=2,N - PTR = STR*CINUR - STI*CINUI - CINUI = STR*CINUI + STI*CINUR - CINUR = PTR - STR = YR(I) - STI = YI(I) - YR(I) = CINUR*CSCLR - YI(I) = CINUI*CSCLR - 40 CONTINUE - RETURN - 50 CONTINUE - NZ = -1 - IF(NW.EQ.(-2)) NZ=-2 - RETURN - END diff --git a/cmake-scripts/FindZBESSEL.cmake b/cmake-scripts/FindZBESSEL.cmake new file mode 100644 index 0000000..3997bfd --- /dev/null +++ b/cmake-scripts/FindZBESSEL.cmake @@ -0,0 +1,17 @@ +# Try to find the ZBESSEL librairies +# ZBESSEL_FOUND - system has ZBESSEL lib +# ZBESSEL_INCLUDE_DIR - the ZBESSEL include directory +# ZBESSEL_LIBRARIES - Libraries needed to use ZBESSEL + +if (ZBESSEL_INCLUDE_DIR AND ZBESSEL_LIBRARIES) + # Already in cache, be silent + set(ZBESSEL_FIND_QUIETLY TRUE) +endif (ZBESSEL_INCLUDE_DIR AND ZBESSEL_LIBRARIES) + +find_path(ZBESSEL_INCLUDE_DIR NAMES zbessel.h ) +find_library(ZBESSEL_LIBRARIES NAMES zbessel libzbessel) + +include(FindPackageHandleStandardArgs) +FIND_PACKAGE_HANDLE_STANDARD_ARGS(ZBESSEL DEFAULT_MSG ZBESSEL_INCLUDE_DIR ZBESSEL_LIBRARIES) + +mark_as_advanced(ZBESSEL_INCLUDE_DIR ZBESSEL_LIBRARIES) diff --git a/qpms/CMakeLists.txt b/qpms/CMakeLists.txt index 4a7f0cc..b3af0a6 100644 --- a/qpms/CMakeLists.txt +++ b/qpms/CMakeLists.txt @@ -2,6 +2,7 @@ find_package(GSL 2.0 REQUIRED) find_package(BLAS REQUIRED) find_package(LAPACK REQUIRED) +find_package(ZBESSEL REQUIRED) # disable an annoying warning that gives false positives probably due to a bug in gcc # and other not very relevant warnings @@ -25,7 +26,7 @@ target_link_libraries (qpms gsl lapack blas - amos + zbessel ) target_include_directories (qpms PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}) diff --git a/qpms/bessel.c b/qpms/bessel.c index 1d11805..4774c32 100644 --- a/qpms/bessel.c +++ b/qpms/bessel.c @@ -7,7 +7,7 @@ #include #include #include "qpms_error.h" -#include +#include #include #ifndef M_LN2 @@ -92,30 +92,30 @@ qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex doub else if (fpclassify(creal(x)) == FP_INFINITE) for(qpms_l_t l = 0; l <= lmax; ++l) res[l] = INFINITY + I * INFINITY; else { - const DOUBLE_PRECISION_t zr = creal(x), zi = cimag(x), fnu = 0.5; - const INTEGER_t n = lmax + 1, kode = 1 /* No exponential scaling */; - DOUBLE_PRECISION_t cyr[n], cyi[n]; - INTEGER_t ierr, nz; + const double zr = creal(x), zi = cimag(x), fnu = 0.5; + const int n = lmax + 1, kode = 1 /* No exponential scaling */; + double cyr[n], cyi[n]; + int ierr, nz; unsigned int kindchar; // Only for error output const complex double prefac = csqrt(M_PI_2/x); switch(typ) { case QPMS_BESSEL_REGULAR: kindchar = 'j'; - amos_zbesj(&zr, &zi, &fnu, &kode, &n, cyr, cyi, &nz, &ierr); + ierr = zbesj(zr, zi, fnu, kode, n, cyr, cyi, &nz); break; case QPMS_BESSEL_SINGULAR: kindchar = 'y'; { - DOUBLE_PRECISION_t cwrkr[lmax + 1], cwrki[lmax + 1]; - amos_zbesy(&zr, &zi, &fnu, &kode, &n, cyr, cyi, &nz, cwrkr, cwrki, &ierr); + double cwrkr[lmax+1], cwrki[lmax+1]; + ierr = zbesy(zr, zi, fnu, kode, n, cyr, cyi, &nz, cwrkr, cwrki); } break; case QPMS_HANKEL_PLUS: case QPMS_HANKEL_MINUS: kindchar = 'h'; { - const INTEGER_t m = (typ == QPMS_HANKEL_PLUS) ? 1 : 2; - amos_zbesh(&zr, &zi, &fnu, &kode, &m, &n, cyr, cyi, &nz, &ierr); + const int m = (typ == QPMS_HANKEL_PLUS) ? 1 : 2; + ierr = zbesh(zr, zi, fnu, kode, m, n, cyr, cyi, &nz); } break; default: