C ALGORITHM 796, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 25,NO. 3, September, 1999, P. 306--315. #! /bin/sh # This is a shell archive, meaning: # 1. Remove everything above the #! /bin/sh line. # 2. Save the resulting text in a file. # 3. Execute the file with /bin/sh (not csh) to create the files: # d1mach.f # database.f # invltf.f # main.f # res # This archive created: Tue Feb 8 11:53:37 2000 export PATH; PATH=/bin:$PATH if test -f 'd1mach.f' then echo shar: will not over-write existing file "'d1mach.f'" else cat << SHAR_EOF > 'd1mach.f' DOUBLE PRECISION FUNCTION D1MACH(I) C C DOUBLE-PRECISION MACHINE CONSTANTS C C D1MACH( 1) = B**(EMIN-1), THE SMALLEST POSITIVE MAGNITUDE. C C D1MACH( 2) = B**EMAX*(1 - B**(-T)), THE LARGEST MAGNITUDE. C C D1MACH( 3) = B**(-T), THE SMALLEST RELATIVE SPACING. C C D1MACH( 4) = B**(1-T), THE LARGEST RELATIVE SPACING. C C D1MACH( 5) = LOG10(B) C C TO ALTER THIS FUNCTION FOR A PARTICULAR ENVIRONMENT, C THE DESIRED SET OF DATA STATEMENTS SHOULD BE ACTIVATED BY C REMOVING THE C FROM COLUMN 1. C C FOR IEEE-ARITHMETIC MACHINES (BINARY STANDARD), ONE OF THE FIRST C TWO SETS OF CONSTANTS BELOW SHOULD BE APPROPRIATE. C C WHERE POSSIBLE, DECIMAL, OCTAL OR HEXADECIMAL CONSTANTS ARE USED C TO SPECIFY THE CONSTANTS EXACTLY. SOMETIMES THIS REQUIRES USING C EQUIVALENT INTEGER ARRAYS. IF YOUR COMPILER USES HALF-WORD C INTEGERS BY DEFAULT (SOMETIMES CALLED INTEGER*2), YOU MAY NEED TO C CHANGE INTEGER TO INTEGER*4 OR OTHERWISE INSTRUCT YOUR COMPILER C TO USE FULL-WORD INTEGERS IN THE NEXT 5 DECLARATIONS. C C C C .. Scalar Arguments .. INTEGER I C .. C .. Local Scalars .. INTEGER SC C .. C .. Local Arrays .. DOUBLE PRECISION DMACH(5) INTEGER DIVER(2),LARGE(2),LOG10(2),RIGHT(2),SMALL(2) C .. C .. Equivalences .. 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 .. C .. Data statements .. C C MACHINE CONSTANTS FOR IEEE ARITHMETIC MACHINES, SUCH AS THE AT&T C 3B SERIES AND MOTOROLA 68000 BASED MACHINES (E.G. SUN 3 AND AT&T C PC 7300), IN WHICH THE MOST SIGNIFICANT BYTE IS STORED FIRST. C DATA SMALL(1),SMALL(2)/1048576,0/ DATA LARGE(1),LARGE(2)/2146435071,-1/ DATA RIGHT(1),RIGHT(2)/1017118720,0/ DATA DIVER(1),DIVER(2)/1018167296,0/ DATA LOG10(1),LOG10(2)/1070810131,1352628735/,SC/987/ C .. C C MACHINE CONSTANTS FOR IEEE ARITHMETIC MACHINES AND 8087-BASED C MICROS, SUCH AS THE IBM PC AND AT&T 6300, IN WHICH THE LEAST C SIGNIFICANT BYTE IS STORED FIRST. C C DATA SMALL(1),SMALL(2) / 0, 1048576 / C DATA LARGE(1),LARGE(2) / -1, 2146435071 / C DATA RIGHT(1),RIGHT(2) / 0, 1017118720 / C DATA DIVER(1),DIVER(2) / 0, 1018167296 / C DATA LOG10(1),LOG10(2) / 1352628735, 1070810131 /, SC/987/ C C MACHINE CONSTANTS FOR AMDAHL MACHINES. C C DATA SMALL(1),SMALL(2) / 1048576, 0 / C DATA LARGE(1),LARGE(2) / 2147483647, -1 / C DATA RIGHT(1),RIGHT(2) / 856686592, 0 / C DATA DIVER(1),DIVER(2) / 873463808, 0 / C DATA LOG10(1),LOG10(2) / 1091781651, 1352628735 /, SC/987/ C C MACHINE CONSTANTS FOR THE BURROUGHS 1700 SYSTEM. C C DATA SMALL(1) / ZC00800000 / C DATA SMALL(2) / Z000000000 / C C DATA LARGE(1) / ZDFFFFFFFF / C DATA LARGE(2) / ZFFFFFFFFF / C C DATA RIGHT(1) / ZCC5800000 / C DATA RIGHT(2) / Z000000000 / C C DATA DIVER(1) / ZCC6800000 / C DATA DIVER(2) / Z000000000 / C C DATA LOG10(1) / ZD00E730E7 / C DATA LOG10(2) / ZC77800DC0 /, SC/987/ C C MACHINE CONSTANTS FOR THE BURROUGHS 5700 SYSTEM. C C DATA SMALL(1) / O1771000000000000 / C DATA SMALL(2) / O0000000000000000 / C C DATA LARGE(1) / O0777777777777777 / C DATA LARGE(2) / O0007777777777777 / C C DATA RIGHT(1) / O1461000000000000 / C DATA RIGHT(2) / O0000000000000000 / C C DATA DIVER(1) / O1451000000000000 / C DATA DIVER(2) / O0000000000000000 / C C DATA LOG10(1) / O1157163034761674 / C DATA LOG10(2) / O0006677466732724 /, SC/987/ C C MACHINE CONSTANTS FOR THE BURROUGHS 6700/7700 SYSTEMS. C C DATA SMALL(1) / O1771000000000000 / C DATA SMALL(2) / O7770000000000000 / C C DATA LARGE(1) / O0777777777777777 / C DATA LARGE(2) / O7777777777777777 / C C DATA RIGHT(1) / O1461000000000000 / C DATA RIGHT(2) / O0000000000000000 / C C DATA DIVER(1) / O1451000000000000 / C DATA DIVER(2) / O0000000000000000 / C C DATA LOG10(1) / O1157163034761674 / C DATA LOG10(2) / O0006677466732724 /, SC/987/ C C MACHINE CONSTANTS FOR FTN4 ON THE CDC 6000/7000 SERIES. C C DATA SMALL(1) / 00564000000000000000B / C DATA SMALL(2) / 00000000000000000000B / C C DATA LARGE(1) / 37757777777777777777B / C DATA LARGE(2) / 37157777777777777774B / C C DATA RIGHT(1) / 15624000000000000000B / C DATA RIGHT(2) / 00000000000000000000B / C C DATA DIVER(1) / 15634000000000000000B / C DATA DIVER(2) / 00000000000000000000B / C C DATA LOG10(1) / 17164642023241175717B / C DATA LOG10(2) / 16367571421742254654B /, SC/987/ C C MACHINE CONSTANTS FOR FTN5 ON THE CDC 6000/7000 SERIES. C C DATA SMALL(1) / O"00564000000000000000" / C DATA SMALL(2) / O"00000000000000000000" / C C DATA LARGE(1) / O"37757777777777777777" / C DATA LARGE(2) / O"37157777777777777774" / C C DATA RIGHT(1) / O"15624000000000000000" / C DATA RIGHT(2) / O"00000000000000000000" / C C DATA DIVER(1) / O"15634000000000000000" / C DATA DIVER(2) / O"00000000000000000000" / C C DATA LOG10(1) / O"17164642023241175717" / C DATA LOG10(2) / O"16367571421742254654" /, SC/987/ C C MACHINE CONSTANTS FOR CONVEX C-1 C C DATA SMALL(1),SMALL(2) / '00100000'X, '00000000'X / C DATA LARGE(1),LARGE(2) / '7FFFFFFF'X, 'FFFFFFFF'X / C DATA RIGHT(1),RIGHT(2) / '3CC00000'X, '00000000'X / C DATA DIVER(1),DIVER(2) / '3CD00000'X, '00000000'X / C DATA LOG10(1),LOG10(2) / '3FF34413'X, '509F79FF'X /, SC/987/ C C MACHINE CONSTANTS FOR THE CRAY 1, XMP, 2, AND 3. C C DATA SMALL(1) / 201354000000000000000B / C DATA SMALL(2) / 000000000000000000000B / C C DATA LARGE(1) / 577767777777777777777B / C DATA LARGE(2) / 000007777777777777776B / C C DATA RIGHT(1) / 376434000000000000000B / C DATA RIGHT(2) / 000000000000000000000B / C C DATA DIVER(1) / 376444000000000000000B / C DATA DIVER(2) / 000000000000000000000B / C C DATA LOG10(1) / 377774642023241175717B / C DATA LOG10(2) / 000007571421742254654B /, SC/987/ C C MACHINE CONSTANTS FOR THE DATA GENERAL ECLIPSE S/200 C C NOTE - IT MAY BE APPROPRIATE TO INCLUDE THE FOLLOWING LINE - C STATIC DMACH(5) C C DATA SMALL/20K,3*0/,LARGE/77777K,3*177777K/ C DATA RIGHT/31420K,3*0/,DIVER/32020K,3*0/ C DATA LOG10/40423K,42023K,50237K,74776K/, SC/987/ C C MACHINE CONSTANTS FOR THE HARRIS SLASH 6 AND SLASH 7 C C DATA SMALL(1),SMALL(2) / '20000000, '00000201 / C DATA LARGE(1),LARGE(2) / '37777777, '37777577 / C DATA RIGHT(1),RIGHT(2) / '20000000, '00000333 / C DATA DIVER(1),DIVER(2) / '20000000, '00000334 / C DATA LOG10(1),LOG10(2) / '23210115, '10237777 /, SC/987/ C C MACHINE CONSTANTS FOR THE HONEYWELL DPS 8/70 SERIES. C 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 THE IBM 360/370 SERIES, C THE XEROX SIGMA 5/7/9 AND THE SEL SYSTEMS 85/86. C C DATA SMALL(1),SMALL(2) / Z00100000, Z00000000 / C DATA LARGE(1),LARGE(2) / Z7FFFFFFF, ZFFFFFFFF / C DATA RIGHT(1),RIGHT(2) / Z33100000, Z00000000 / C DATA DIVER(1),DIVER(2) / Z34100000, Z00000000 / C DATA LOG10(1),LOG10(2) / Z41134413, Z509F79FF /, SC/987/ C C MACHINE CONSTANTS FOR THE INTERDATA 8/32 C WITH THE UNIX SYSTEM FORTRAN 77 COMPILER. C C FOR THE INTERDATA FORTRAN VII COMPILER REPLACE C THE Z'S SPECIFYING HEX CONSTANTS WITH Y'S. C C DATA SMALL(1),SMALL(2) / Z'00100000', Z'00000000' / C DATA LARGE(1),LARGE(2) / Z'7EFFFFFF', Z'FFFFFFFF' / C DATA RIGHT(1),RIGHT(2) / Z'33100000', Z'00000000' / C DATA DIVER(1),DIVER(2) / Z'34100000', Z'00000000' / C DATA LOG10(1),LOG10(2) / Z'41134413', Z'509F79FF' /, SC/987/ C C MACHINE CONSTANTS FOR THE PDP-10 (KA PROCESSOR). C C DATA SMALL(1),SMALL(2) / "033400000000, "000000000000 / C DATA LARGE(1),LARGE(2) / "377777777777, "344777777777 / C DATA RIGHT(1),RIGHT(2) / "113400000000, "000000000000 / C DATA DIVER(1),DIVER(2) / "114400000000, "000000000000 / C DATA LOG10(1),LOG10(2) / "177464202324, "144117571776 /, SC/987/ C C MACHINE CONSTANTS FOR THE PDP-10 (KI PROCESSOR). C C DATA SMALL(1),SMALL(2) / "000400000000, "000000000000 / C DATA LARGE(1),LARGE(2) / "377777777777, "377777777777 / C DATA RIGHT(1),RIGHT(2) / "103400000000, "000000000000 / C DATA DIVER(1),DIVER(2) / "104400000000, "000000000000 / C DATA LOG10(1),LOG10(2) / "177464202324, "047674776746 /, SC/987/ C C MACHINE CONSTANTS FOR PDP-11 FORTRANS SUPPORTING C 32-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL). C 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 DATA SMALL(1),SMALL(2) / O00040000000, O00000000000 / C DATA LARGE(1),LARGE(2) / O17777777777, O37777777777 / C DATA RIGHT(1),RIGHT(2) / O04440000000, O00000000000 / C DATA DIVER(1),DIVER(2) / O04500000000, O00000000000 / C DATA LOG10(1),LOG10(2) / O07746420232, O20476747770 /, SC/987/ C C MACHINE CONSTANTS FOR PDP-11 FORTRANS SUPPORTING C 16-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL). C C DATA SMALL(1),SMALL(2) / 128, 0 / C DATA SMALL(3),SMALL(4) / 0, 0 / C C DATA LARGE(1),LARGE(2) / 32767, -1 / C DATA LARGE(3),LARGE(4) / -1, -1 / C C DATA RIGHT(1),RIGHT(2) / 9344, 0 / C DATA RIGHT(3),RIGHT(4) / 0, 0 / C C DATA DIVER(1),DIVER(2) / 9472, 0 / C DATA DIVER(3),DIVER(4) / 0, 0 / C C DATA LOG10(1),LOG10(2) / 16282, 8346 / C DATA LOG10(3),LOG10(4) / -31493, -12296 /, SC/987/ C C DATA SMALL(1),SMALL(2) / O000200, O000000 / C DATA SMALL(3),SMALL(4) / O000000, O000000 / C C DATA LARGE(1),LARGE(2) / O077777, O177777 / C DATA LARGE(3),LARGE(4) / O177777, O177777 / C C DATA RIGHT(1),RIGHT(2) / O022200, O000000 / C DATA RIGHT(3),RIGHT(4) / O000000, O000000 / C C DATA DIVER(1),DIVER(2) / O022400, O000000 / C DATA DIVER(3),DIVER(4) / O000000, O000000 / C C DATA LOG10(1),LOG10(2) / O037632, O020232 / C DATA LOG10(3),LOG10(4) / O102373, O147770 /, SC/987/ C C MACHINE CONSTANTS FOR THE PRIME 50 SERIES SYSTEMS C WITH 32-BIT INTEGERS AND 64V MODE INSTRUCTIONS, C SUPPLIED BY IGOR BRAY. C C DATA SMALL(1),SMALL(2) / :10000000000, :00000100001 / C DATA LARGE(1),LARGE(2) / :17777777777, :37777677775 / C DATA RIGHT(1),RIGHT(2) / :10000000000, :00000000122 / C DATA DIVER(1),DIVER(2) / :10000000000, :00000000123 / C DATA LOG10(1),LOG10(2) / :11504046501, :07674600177 /, SC/987/ C C MACHINE CONSTANTS FOR THE SEQUENT BALANCE 8000 C C DATA SMALL(1),SMALL(2) / $00000000, $00100000 / C DATA LARGE(1),LARGE(2) / $FFFFFFFF, $7FEFFFFF / C DATA RIGHT(1),RIGHT(2) / $00000000, $3CA00000 / C DATA DIVER(1),DIVER(2) / $00000000, $3CB00000 / C DATA LOG10(1),LOG10(2) / $509F79FF, $3FD34413 /, SC/987/ C C MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES. C 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 MACHINE CONSTANTS FOR THE VAX UNIX F77 COMPILER C C DATA SMALL(1),SMALL(2) / 128, 0 / C DATA LARGE(1),LARGE(2) / -32769, -1 / C DATA RIGHT(1),RIGHT(2) / 9344, 0 / C DATA DIVER(1),DIVER(2) / 9472, 0 / C DATA LOG10(1),LOG10(2) / 546979738, -805796613 /, SC/987/ C C MACHINE CONSTANTS FOR THE VAX-11 WITH C FORTRAN IV-PLUS COMPILER C C DATA SMALL(1),SMALL(2) / Z00000080, Z00000000 / C DATA LARGE(1),LARGE(2) / ZFFFF7FFF, ZFFFFFFFF / C DATA RIGHT(1),RIGHT(2) / Z00002480, Z00000000 / C DATA DIVER(1),DIVER(2) / Z00002500, Z00000000 / C DATA LOG10(1),LOG10(2) / Z209A3F9A, ZCFF884FB /, SC/987/ C C MACHINE CONSTANTS FOR VAX/VMS VERSION 2.2 C C DATA SMALL(1),SMALL(2) / '80'X, '0'X / C DATA LARGE(1),LARGE(2) / 'FFFF7FFF'X, 'FFFFFFFF'X / C DATA RIGHT(1),RIGHT(2) / '2480'X, '0'X / C DATA DIVER(1),DIVER(2) / '2500'X, '0'X / C DATA LOG10(1),LOG10(2) / '209A3F9A'X, 'CFF884FB'X /, SC/987/ C C *** ISSUE STOP 779 IF ALL DATA STATEMENTS ARE COMMENTED... IF (SC.NE.987) STOP 779 C/6S C IF (I .LT. 1 .OR. I .GT. 5) C 1 CALL SETERR(24HD1MACH - I OUT OF BOUNDS,24,1,2) C/7S C D1MACH = DMACH(I) RETURN C END SHAR_EOF fi # end of overwriting check if test -f 'database.f' then echo shar: will not over-write existing file "'database.f'" else cat << SHAR_EOF > 'database.f' C *********************************************** C ** C FUNCTION FZ CALLED BY THE INVERSION SOFTWARE ** C ** C *********************************************** COMPLEX*16 FUNCTION FZ(Z) C *********************************************** C ************************************************ C .. Scalar Arguments .. DOUBLE COMPLEX Z C .. C .. Scalars in Common .. INTEGER NFUN C .. C .. Local Scalars .. DOUBLE COMPLEX B,CI,CVAR,ARG,Z2,Z4,A1,A2,BB DOUBLE PRECISION R,C C .. C .. External Functions .. INTRINSIC CDEXP,CDLOG,CDSQRT C .. C .. Common blocks .. COMMON /NF/NFUN C .. GOTO(1,2,3,4,5,6,7,8,10,11,12,13,14,15, * 16,17,18,19,20, * 21,22,23,24,25,26,27,28,29,30,31,32, * 33,34,35,36,37,38) NFUN C ************************************************ C FUNCTIONS ORDER AND NUMBERING REFLECT FUNCTIONS C ORDER AND NUMBERING AS IN THE PAPER: C C D'AMORE L., LACCETTI G., MURLI A., - C C "ALGORITHM XXX: A FORTRAN SOFTWARE C PACKAGE FOR THE NUMERICAL INVERSION OF THE C LAPLACE TRANSFORM BASE ON FOURIER SERIES' METHOD" C C ACM TRANS. MATH. SOFTWARE, VOL. ##, C NO. #, MONTH YEAR, PP. ##-##. C ******************************************************* 1 FZ = (1.D0,0.D0)/Z GO TO 350 C C ************************************************ 2 FZ = (2.D0,0.D0)* (CDSQRT(Z+ (1.D0,0.D0))-CDSQRT(Z)) GO TO 350 C ************************************************ 3 FZ = (1.D0,0.D0)/CDSQRT(Z) GO TO 350 C ************************************************ C 4 FZ = (Z*Z- (1.D0,0.D0))/ ((Z*Z+ (1.D0,0.D0))**2) GO TO 350 C ************************************************ C 5 FZ = (1.D0,0.D0)/ (Z+ (1.D0,0.D0))**2 GO TO 350 C ************************************************ C 6 FZ = (1.D0,0.D0)/ (Z**2) GO TO 350 C ************************************************ C 7 FZ = (1.D0,0.D0)/ (Z**2+ (1.D0,0.D0)) GO TO 350 C ************************************************ C 8 FZ = (1.D0,0.D0)/ (Z+ (0.5D0,0.D0)) GO TO 350 C ************************************************ C 9 FZ = 1.D0/CDSQRT(Z*Z+ (1.D0,0.D0)) GO TO 350 C ************************************************ C 10 FZ = CDEXP((-1.D0,0.D0)/Z)/CDSQRT(Z) GO TO 350 C ************************************************ C 11 FZ = CDEXP((-4.D0,0.D0)*CDSQRT(Z)) GO TO 350 C************************************************* C 12 CI = (0.D0,1.D0) CVAR = 1.D0/ (2* (0.D0,1.D0)) FZ = CVAR*CDLOG((Z+CI)/ (Z-CI)) GO TO 350 C ************************************************* C 13 FZ = (1.D0,0.D0)/ ((Z+.2)**2+ (1.D0,0.D0)) GO TO 350 C ************************************************ C 14 FZ = 1.d0/Z**3 GO TO 350 C ************************************************ C 15 FZ = CDEXP(-2*Z)/Z GO TO 350 C ************************************************* C 16 FZ = (1.D0,0.D0)/ (Z* ((1.D0,0.D0)+CDEXP(-Z))) GO TO 350 C ************************************************ 17 FZ = (1.D0,0.D0)/ (Z*Z+Z+ (1.D0,0.D0)) GO TO 350 C ************************************************* C 18 FZ = (3.D0,0.D0)/ (Z**2- (9.D0,0.D0)) GO TO 350 C C ************************************************* C 19 FZ = (120.D0,0.D0)/Z**6 GO TO 350 C C ************************************************ C 20 FZ = Z/ (Z**2+ (1.D0,0.D0))**2 GO TO 350 C C ************************************************ C 21 FZ = (1.D0,0.D0)/ (Z+ (1.D0,0.D0)) - + (1.D0,0.D0)/ (Z+ (1000.D0,0.D0)) GO TO 350 C C ************************************************ C 22 FZ = Z/ (Z*Z+ (1.D0,0.D0)) GO TO 350 C ************************************************ C 23 FZ = (1.D0,0.D0)/ ((Z- (0.25D0,0.D0))**2) GO TO 350 C ************************************************ C 24 FZ = (1.D0,0.D0)/ (Z*CDSQRT(Z)) GO TO 350 C ************************************************ C 25 FZ = (1.D0,0.D0)/CDSQRT(Z+ (1.D0,0.D0)) GO TO 350 C ************************************************ C 26 FZ = (Z+ (2.D0,0.D0))/ (Z*CDSQRT(Z)) GO TO 350 C ************************************************ C 27 FZ = (1.D0,0.D0)/ ((Z*Z+ (1.D0,0.D0))**2) GO TO 350 C ************************************************ C 28 FZ = (1.D0,0.D0)/ (Z* (Z+ (1.D0,0.D0))**2) GO TO 350 C ************************************************ C 29 FZ = (1.D0,0.D0)/ (Z**3- (8.D0,0.D0)) GO TO 350 C ************************************************ C 30 FZ = CDLOG((Z*Z+ (1.D0,0.D0))/ (Z*Z+ (4.D0,0.D0))) GO TO 350 C C ************************************************ C 31 FZ = CDLOG((Z+ (1.D0,0.D0))/Z) GO TO 350 C ************************************************ 32 FZ= CDLOG(Z)/Z GO TO 350 C ************************************************ C 33 FZ = ((1.D0,0.D0)-CDEXP(-Z))/ (Z*Z) GO TO 350 C ************************************************ C 34 FZ = (1.D0,0.D0)/ (Z* ((1.D0,0.D0)+CDEXP(Z))) GO TO 350 C C ************************************************* C 35 B = (1.D0,0.D0)/ (2.*Z) - (CDEXP(-2.*Z)/ (1.-CDEXP(-2.*Z))) FZ = (1./ (Z*Z+Z))*B GO TO 350 C C ************************************************** 36 R=0.5D0 C=0.4D0 B=-R*CDSQRT((Z*(1+Z))/(1+C*Z)) FZ=1./Z*CDEXP(B) GO TO 350 C ************************************************** 37 CONTINUE C C FZ=CDEXP(-2.*PSI)/Z C C COSH(PSI)= SQRT(1+Z**2+((Z**4)/16)) C Z2=Z*Z Z4=Z2*Z2 ARG=1.d0+Z2+Z4/16 A1=CDSQRT(ARG) A2=(Z/4.d0)*CDSQRT(16.d0+Z2) FZ=1.d0/(Z*(A1+A2)**2) GO TO 350 C ************************************************** 38 continue B=Z-CDSQRT(Z*Z-1.d0) BB=CDSQRT(Z)*CDSQRT(Z*Z-1.D0)*CDSQRT(Z-0.5D0*(CDSQRT(Z*Z-1.D0))) FZ=B/BB GOTO 350 C ************************************************** 350 RETURN END c ********************************************************************* c C C FZ's COMPANION FUNCTION FEX TO COMPUTE THE EXACT VALUE OF THE ** C INVERSE TRANSFORM ** C c c ********************************************************************* DOUBLE PRECISION FUNCTION FEX(X) C C C C .. Scalar Arguments .. DOUBLE PRECISION X C .. C .. Scalars in Common .. INTEGER NFUN C .. C .. Local Scalars .. DOUBLE PRECISION A,B,PI,PI2,SUM,T DOUBLE PRECISION U1,U2,PARTE1,DUFFY6,COMX,EULERO INTEGER K,N LOGICAL TROV C .. Intrinsic Functions .. INTRINSIC DATAN,DCOS,DEXP,DSIN,DSINH,DSQRT,DFLOAT C .. C .. INTEGER LW, LIW PARAMETER (LW=1500,LIW=LW/4) INTEGER NOUT PARAMETER (NOUT=6) INTEGER KOUNT DOUBLE PRECISION ABSERR, EPSABS, EPSREL, RESULT INTEGER IFAIL, INF DOUBLE PRECISION W(LW) INTEGER IW(LIW) DOUBLE PRECISION FST3,FST4,FST52,FST51 EXTERNAL FST3,FST4,FST52,FST51 C .. Common blocks .. COMMON /NF/NFUN COMMON /TELNUM/COMX,KOUNT PI = 4.D0*DATAN(1.D0) COMX=X EULERO = .5772156D0 GOTO(1,2,3,4,5,6,7,8,10,11,12,13,14, + 15,16,17,18,19,20,21,22, + 23,24,25,26,27,28,29,30,31,32,33,34, c + 35,36,37,38)NFUN + 35)NFUN C ******************************************************************** C FUNCTIONS ORDER AND NUMBERING REFLECT FUNCTIONS C ORDER AND NUMBERING AS IN THE PAPER: C C D'AMORE L., LACCETTI G., MURLI A., - C C "ALGORITHM XXX: A FORTRAN SOFTWARE C PACKAGE FOR THE NUMERICAL INVERSION OF THE C LAPLACE TRANSFORM BASE ON FOURIER SERIES' METHOD" C C ACM TRANS. MATH. SOFTWARE, VOL. ##, C NO. #, MONTH YEAR, PP. ##-##. C ******************************************************************** C 1 FEX = 1.D0 GO TO 380 C ******************************************************************** C 2 FEX = (1.D0-DEXP(-X))/ (X*DSQRT(PI*X)) GO TO 380 C ******************************************************************** C 3 FEX = 1.D0/DSQRT(PI*X) GO TO 380 C ******************************************************************** C 4 FEX = X*DCOS(X) GO TO 380 C ******************************************************************** C 5 FEX = X*DEXP(-X) GO TO 380 C ******************************************************************** C 6 FEX = X GO TO 380 C C ******************************************************************** C 7 FEX = DSIN(X) GO TO 380 C **************************************************** C 8 FEX = DEXP(-.5D0*X) GO TO 380 C ******************************************************************** C Such inverse function is the Bessel function J_0. C Actually we compute it by using the Nag library. That's why C it does not appear here . C c 9 FEX = S17AEF(X,IFAIL) c GO TO 380 C ******************************************************************** C 10 FEX = DCOS(2.D0*DSQRT(X))/DSQRT(PI*X) GO TO 380 C C ******************************************************************** C 11 FEX = 2.D0*DEXP(-4.D0/X)/ (X*DSQRT(PI*X)) GO TO 380 C **************************************************************** C 12 FEX = DSIN(X)/X GO TO 380 C **************************************************** C 13 FEX = DEXP(-.2D0*X)*DSIN(X) GO TO 380 C ******************************************************************** C 14 FEX = 0.5d0 * X**2 GO TO 380 C ******************************************************************** C 15 IF (X.GT.2.D0) THEN FEX = 1.D0 ELSE IF (X.LT.2.D0) THEN FEX = 0.D0 ELSE FEX = 0.5D0 END IF GO TO 380 C **************************************************************** C 16 TROV = .FALSE. K = 0 310 CONTINUE IF (X.GT.2*K .AND. X.LT.2*K+1) THEN FEX = 1.D0 TROV = .TRUE. ELSE IF (X.GT.2*K+1 .AND. X.LT.2*K+2) THEN FEX = 0.D0 TROV = .TRUE. END IF IF (X.EQ.DFLOAT(K)) THEN FEX = 0.5D0 TROV = .TRUE. END IF K = K + 1 IF (.NOT.TROV .AND. K.LE.49) GO TO 310 GO TO 380 C C ******************************************************************** C 17 FEX = 2.D0/DSQRT(3.D0)*DEXP(-X/2.D0)*DSIN(X*DSQRT(3.D0)/2.D0) GO TO 380 C C ***************************************************** C 18 FEX = DSINH(3.D0*X) GO TO 380 C **************************************************** C 19 FEX = X**5 GO TO 380 C ******************************************************************** C 20 FEX = X/2.D0*DSIN(X) GO TO 380 C C ******************************************************************** C 21 FEX = DEXP(-X) - DEXP(-1000.D0*X) GO TO 380 C C ******************************************************************** C 22 FEX = DCOS(X) GO TO 380 C ******************************************************************** C 23 FEX = X*DEXP(X/4.) GO TO 380 C ******************************************************************** C 24 FEX = 2.D0*DSQRT(X/PI) GO TO 380 C ******************************************************************** C 25 FEX = DEXP(-X)/DSQRT(PI*X) GO TO 380 C ******************************************************************** C 26 FEX = (1.D0+4.D0*X)/DSQRT(PI*X) GO TO 380 C ******************************************************************** C 27 FEX = (DSIN(X)-X*DCOS(X))/2.D0 GO TO 380 C ******************************************************************** C 28 FEX = 1 - DEXP(-X)* (1+X) GO TO 380 C **************************************************************** C 29 FEX = DEXP(-X)/12.D0* (DEXP(3.D0*X)-DCOS(DSQRT(3.D0)*X)- + DSQRT(3.D0)*DSIN(DSQRT(3.D0)*X)) GO TO 380 c ******************************************************************** C 30 FEX = 2.D0* (DCOS(2.D0*X)-DCOS(X))/X GO TO 380 C ******************************************************************** C 31 FEX = (1-DEXP(-X))/X GO TO 380 c ******************************************************************* 32 FEX=-EULERO - DLOG(X) GO TO 380 c ******************************************************************* C 33 IF (X.GE.0.D0 .AND. X.LE.1.D0) THEN FEX = X ELSE FEX = 1.D0 END IF GO TO 380 C ******************************************************************** C 34 TROV = .FALSE. K = 0 210 CONTINUE IF (X.GT.2*K .AND. X.LT.2*K+1) THEN FEX = 0.D0 TROV = .TRUE. ELSE IF (X.GT.2*K+1 .AND. X.LT.2*K+2) THEN FEX = 1.D0 TROV = .TRUE. END IF IF (X.EQ.DFLOAT(K)) THEN FEX = 0.5D0 TROV = .TRUE. END IF K = K + 1 IF (.NOT.TROV .AND. K.LE.49) GO TO 210 GO TO 380 C ******************************************************************* C 35 T = X PI2 = PI*PI A = (0.5D0- (DEXP(2.D0)/ (DEXP(2.D0)-1.))*DEXP(-T)) + 0.5D0 N = 0.D0 SUM = 0.D0 370 CONTINUE N = N + 1.D0 B = DSIN((N*PI*T)-DATAN(N*PI)) B = B/ (N* (DSQRT((N*N*PI2)+1.D0))) SUM = SUM + B IF (N.LT.2.D+4) GO TO 370 SUM = SUM/PI SUM = SUM*DEXP(-T) FEX = A - SUM GO TO 380 C ****************************************************** C36 EPSABS = 0.0D0 C EPSREL = 1.0D-04 C A = 0.0D0 C INF = 1 C KOUNT = 0 C IFAIL = -1 C CALL D01AMF(FST3,A,INF,EPSABS,EPSREL,RESULT,ABSERR,W,LW,IW,LIW, C + IFAIL) C IF (IFAIL.NE.0) WRITE (NOUT,99996) 'IFAIL = ', IFAIL C FEX=(RESULT/PI)+0.5d0 C goto 380 C99996 FORMAT (1X,A,I4) C ***************************************************** C C C37 EPSABS = 0.0D0 C EPSREL = 1.0D-04 C U1=2.*DSQRT(2.D0-DSQRT(3.D0)) C U2=2.*DSQRT(2.D0+DSQRT(3.D0)) C A = .0D0 C B =U1 C KOUNT = 0 C IFAIL = -1 C CALL D01AKF(FST4,A,B,EPSABS,EPSREL,RESULT,ABSERR,W,LW,IW,LIW, C * IFAIL) C IF (IFAIL.NE.0) WRITE (NOUT,99996) 'IFAIL = ', IFAIL C DUFFY6=RESULT C A=U2 C B=4.D0 C IFAIL=-1 C KOUNT=0 C CALL D01AKF(FST4,A,B,EPSABS,EPSREL,RESULT,ABSERR,W,LW,IW,LIW, C * IFAIL) C IF (IFAIL.NE.0) WRITE (NOUT,99996) 'IFAIL = ', IFAIL C FEX=(-DUFFY6+RESULT)/PI +1.D0 C GO TO 380 C ****************************************************** C C38 EPSABS = 0.0D0 C EPSREL = 1.0D-04 C A = 0.0D0 C B = (1.-0.5d0)/0.5d0 C KOUNT = 0 C IFAIL = -1 C CALL D01AJF(FST51,A,B,EPSABS,EPSREL,RESULT,ABSERR,W,LW,IW,LIW, C * IFAIL) C IF (IFAIL.NE.0) WRITE (NOUT,99996) 'IFAIL = ', IFAIL C PARTE1=RESULT C A=0.d0 C B=DSQRT((1.-0.5d0)/1.5d0) C KOUNT=0 C IFAIL=-1 C CALL D01AJF(FST52,A,B,EPSABS,EPSREL,RESULT,ABSERR,W,LW,IW,LIW, C * IFAIL) C FEX=(RESULT+PARTE1)*(2.D0/PI) C ****************************************************** 380 RETURN C ****************************************************** END C ****************************************************** C ****************************************************** DOUBLE PRECISION FUNCTION FST51(U) DOUBLE PRECISION U,N,C,B DOUBLE PRECISION COMX, R INTEGER KOUNT INTRINSIC SIN, SQRT COMMON /TELNUM/COMX,KOUNT KOUNT = KOUNT + 1 N=0.5D0 C=(1.-N)/N B=DSQRT((1.-N)/(1.+N)) R=DSQRT(U*U + N*N*(C*C-U*U)) FST51 = DCOSH(COMX*U)* * ((U*DSQRT((R+U)/2))+ * DSQRT(C**2-U**2)*DSQRT( * (R-U)/2))/ * (R*DSQRT(C**2-U**2) * *DSQRT(U)) RETURN END C ****************************************************** DOUBLE PRECISION FUNCTION FST52(u) DOUBLE PRECISION U,N,C,B DOUBLE PRECISION COMX INTEGER KOUNT INTRINSIC SIN, SQRT COMMON /TELNUM/COMX,KOUNT KOUNT = KOUNT + 1 N=0.5d0 C=(1.-N)/N B=DSQRT((1.-N)/(1.+N)) FST52=DCOS(COMX*U)*((U-DSQRT(C**2+U**2))/(DSQRT(U)* * DSQRT(C**2+U**2)*DSQRT(N*DSQRT(C**2+U**2)-U))) RETURN END C ****************************************************** DOUBLE PRECISION FUNCTION FST3(U) DOUBLE PRECISION M,COMX,THETA,ARG1,ARG2,R,C,U INTEGER KOUNT INTRINSIC SQRT COMMON /TELNUM/COMX,KOUNT KOUNT = KOUNT + 1 R=0.5d0 c=0.4d0 M=(1.D0+U*U)/(1.D0+C*C*U*U) M=M**0.25 THETA=ATAN(U)-ATAN(U*C) THETA=THETA/2 ARG1=-R*M*DSQRT(U/2)*(DCOS(THETA)-DSIN(THETA)) ARG2=COMX*u-R*M*DSQRT(U/2)*(DCOS(THETA)+DSIN(THETA)) FST3=DEXP(ARG1)*DSIN(ARG2)/u RETURN END C ****************************************************** DOUBLE PRECISION FUNCTION FST4(U) DOUBLE PRECISION COMX,U,U1,U2,K INTEGER KOUNT INTRINSIC SIN, SQRT,ACOS COMMON /TELNUM/comx,KOUNT KOUNT = KOUNT + 1 U1=4.*(2.D0-DSQRT(3.D0)) U2=4.*(2.D0+DSQRT(3.D0)) IF((U1 - U**2 )*( U2 - U**2) .GE. 0.D0) THEN K=ACOS(.25D0*DSQRT((U1-U**2)*(U2-U**2))) FST4=(DSIN(U*COMX+2.*K)-DSIN(U*COMX-2*K))/U endif RETURN END C ****************************************************** SHAR_EOF fi # end of overwriting check if test -f 'invltf.f' then echo shar: will not over-write existing file "'invltf.f'" else cat << SHAR_EOF > 'invltf.f' SUBROUTINE INVLTF(TOL,VALT,FZ,SIGMA0,SSBAR,NMAX,FZINV,ERROR, + IFZEVAL,WORK,IFAIL) C C ********************************************************************* C C PURPOSE: C ======= C THIS ROUTINE COMPUTES AN APPROXIMATE VALUE OF AN INVERSE LAPLACE C TRANSFORM, BY MEANS OF AN EXPANSION IN SINE AND COSINE C FOURIER SERIES. C THE METHOD WHICH THIS SOFTWARE IS BASED ON UTILIZES THE Q-D C ALGORITHM TO ACCELERATE THE CONVERGENCE OF THE SERIES. c THE SUMMATION OF SUCCESSIVE TERMS IS TRUNCATED WHEN THE C ESTIMATED TRUNCATION ERROR IS LESS OR EQUAL THAN AN INPUT C PROVIDED TOLERANCE. THE DISCRETIZATION ERROR IS MADE LESS OR C EQUAL THAN THIS TOLERANCE BY SUITABLY CHOOSING SOME METHOD'S C PARAMETERS. C C C THE CALLING SEQUENCE IS C ======================= C C CALL INVLTF(TOL,VALT,FZ,SIGMA0,SSBAR,NMAX,FZINV,ERROR, C + IFZEVAL,WORK,IFAIL) C C C C C C INPUT PARAMETERS C ================ C C C TOL: DOUBLE PRECISION. C ON ENTRY TOL CONTAINS THE RELATIVE C REQUIRED ACCURACY. C C VALT: DOUBLE PRECISION. C ON ENTRY, VALT CONTAINS A POSITIVE VALUE OF T C FOR WHICH THE INVERSE LAPLACE TRANSFORM IS REQUIRED. C VALT HAS TO BE GREATER THAN ZERO. C C FZ: COMPLEX*16 (DOUBLE PRECISION COMPLEX). C NAME OF THE FUNCTION SUBPROGRAMS FOR THE COMPLEX C VALUED LAPLACE TRANSFORM TO BE INVERTED. C ITS SPECIFICATION IS: C COMPLEX*16 FUNCTION FZ(Z) C COMPLEX*16 Z C C Z: COMPLEX*16. ON ENTRY, Z MUST SPECIFY THE POINT AT C WHICH THE LAPLACE TRANSFORM FUNCTION VALUE IS C REQUIRED. C C FZ MUST BE DECLARED AS EXTERNAL IN THE PROGRAM C FROM WHICH INVLTF IS C CALLED. C C SIGMA0: DOUBLE PRECISION. C ON ENTRY, SIGMA0 CONTAINS THE VALUE OF THE C ABSCISSA OF CONVERGENCE OF C THE LAPLACE TRANSFORM FUNCTION TO C BE INVERTED OR AN UPPER BOUND OF THIS. C IT IS RECOMMENDED THAT A CORRECT VALUE TO SIGMA0 C OR A CORRECT UPPER BOUND TO SIGMA0 IS PROVIDED. C IF AN INCORRECT VALUE IS USED THE ROUTINE APPEARS TO C WORK WELL BUT CONVERGES TO COMPLETELY WRONG RESULTS. C THERE IS NO WAY IN WHICH THE ROUNTINE CAN DETECT THIS. C C SSBAR: DOUBLE PRECISION. C ON ENTRY, IT SPECIFIES THE VALUE OF THE C PARAMETER SS (GREATER THAN 2) TO BE USED IN C CALCULATING THE PARAMETER D*T. C TO OBTAIN DEFAULT OPTION (SS=4.1d0) ONE C MAY SET SSBAR = 0. C C NMAX: INTEGER. C ON ENTRY, NMAX SPECIFIES THE MAXIMUM C NUMBER OF FZ EVALUATIONS ALLOWED. C C C OUTPUT PARAMETERS C ================= C C FZINV: DOUBLE PRECISION. C ON EXIT, FZINV CONTAINS THE APPROXIMATION C OF THE INVERSE LAPLACE TRANSFORM AT THE POINT VALT. C C ERROR: DOUBLE PRECISION ARRAY OF DIMENSION 3. C ON EXIT, ERROR(1) CONTAINS AN ESTIMATE OF THE RELATIVE ERROR C WHICH SHOULD BE AN UPPER BOUND FOR C C ABS(TRUEVALUE AT VALT - FZINV)/ABS(TRUEVALUE AT VALT) C C ON EXIT, ERROR(2) CONTAINS AN ESTIMATE OF THE ABSOLUTE ERROR C WHICH SHOULD BE AN UPPER BOUND FOR C C ABS(TRUEVALUE AT VALT - FZINV) C C ON EXIT, ERROR(3) CONTAINS AN ESTIMATE OF THE TRUNCATION ERROR C MADE IN CALCULATING FZINV. C C IFZEVAL: INTEGER. C ON EXIT, IFZEVAL CONTAINS THE C NUMBER OF EVALUATIONS OF FZ USED TO OBTAIN FZINV. C C IFAIL: INTEGER. C ON EXIT, A DIAGNOSTIC. C = 0 ALL INPUTS WITHIN LIMITS. C ALGORITHM APPERENTLY WORKED C PROPERLY. C = 1 TOL IS EQUAL OR GREATER THAN 1. C = 2 VALT NOT POSITIVE. C = -1 ACCURACY NOT REACHED AFTER NMAX FUNCTION EVALUATIONS. C = -2 ALGORITHM DID NOT APPEAR TO BE CONVERGIING, C POSSIBLY DUE TO AN C UNSUITABLE VALUE OF PARAMETER SSBAR. C C WORK : DOUBLE COMPLEX ARRAY OF DIMENSION(2,0:2*NMAX). WORKSPACE AREA. C C C SUBROUTINES OR FUNCTIONS NEEDED C C FZ : USER PROVIDED FUNCTION C QDACC : Q-D ALGORITHM C BACKCF : COMPUTATION OF THE CONTINUED FRACTION C D1MACH : PROVIDES MACHINE EPSILON C C *************************************************************************** C C .. Scalar Arguments .. DOUBLE PRECISION SIGMA0,SS,TOL,SSBAR,VALT,FZINV INTEGER IFAIL,NMAX,IFZEVAL C .. C .. Array Arguments .. DOUBLE COMPLEX WORK(2,0:NMAX) DOUBLE PRECISION ERROR(3) C .. C .. Function Arguments .. DOUBLE COMPLEX FZ EXTERNAL FZ C .. C .. Local Scalars .. DOUBLE PRECISION PI,GAMMA,ALPHA,DT,ERR1,ERR2,FA3,PART2, + PART0,PART1,RELP,T,TOL1,TOLL,D1MACH INTEGER MA,MP LOGICAL FIRST C .. C .. External Subroutines .. EXTERNAL QDACC,BACKCF,D1MACH C .. C .. Intrinsic Functions .. INTRINSIC ABS,DATAN,DLOG C .. C .. Common blocks .. COMMON /PARAM/FIRST,MA,MP COMMON /PARAM1/GAMMA,PI C .. C ERROR(1) = 0.0D0 ERROR(2) = 0.0D0 ERROR(3) = 0.0D0 C SS= SSBAR + 4.1D0 C **************************************************************************** C C INPUT DATA CHECK C C **************************************************************************** IFAIL = 0 IF (TOL .GE. 1) THEN IFAIL = 1 RETURN END IF IF (VALT.LT.0) THEN IFAIL = 2 RETURN END IF C C C ************************************************************************ C SETTING THE PARAMETERS : ALPHA, TOL1, RELP C THE PRODUCT D*T IS COMPUTED IN SUCH A WAY THAT C THE ERROR IS LESS THAN TOL C ************************************************************************ C RELP = D1MACH(4) C RELP = X02AJF() C RELP =0.222044d-15 C FOR AN IBM 6000 RISC STATION MOD. 32H IF (TOL.LT.RELP) TOL = RELP TOL1 = TOL/10.D0 ALPHA = 1.4D0 c DT = -DLOG(TOL1*2*DATAN(1.D0))/ (SS-DLOG(10.D0)) c DT = DT*ALPHA GAMMA = DT/VALT + SIGMA0 T = SS/2.D0*VALT IFZEVAL = 0 PI = 4.D0*DATAN(1.D0)/T FIRST = .TRUE. MA = 2 MP = MA - 1 C *********************************************************************** C C CALL TO THE Q-D ALGORITHM C C *********************************************************************** 10 CONTINUE IF (IFAIL .NE. 0) RETURN CALL QDACC(FZ,IFZEVAL,IFAIL,WORK,NMAX,PART0,PART1,PART2) IF (IFAIL .NE. 0) RETURN CALL BACKCF(VALT,WORK,NMAX,PART2) C C C C********************************************************************** C C FZINV IS THE APPROXIMATED VALUE OF THE INVERSE LAPLACE TRANSFORM C C ********************************************************************* FA3 = DEXP(DT)/T FZINV = DEXP(SIGMA0*VALT)*FA3*PART2 C C C C ********************************************************************* C C COMPUTATION OF THE TRUNCATION ERROR C C ERR1 IS THE DIFFERENCE BETWEEN THE LAST APPROXIMATION AND THE PREVIOUS C ONE, C WHILE ERR2 IS THE DIFFERENCE BETWEEN THE LAST APPROXIMATION C AND THE LAST-THIRD C C *************************************************************************** C ERR1 = FA3*ABS(PART2-PART1) ERR2 = FA3*ABS(PART2-PART0) ERROR(2) = TOL1*ABS(FA3*PART2) TOLL = TOL1*ABS(FA3*PART2) + RELP*ABS(FA3*PART2) IF (TOLL.EQ.0.D0) TOLL = RELP C C **************************************************************************** C C STOPPING CRITERION C C THE ALGORITHM STOPS WHEN BOTH ERR1 AND ERR2 ARE LESS THAN RELP C OR C THE NUMBER OF FUNCTION EVALUATIONS, OF COURSE, IS GREATER OR EQUAL TO NMAX C C ***************************************************************************** C IF (IFZEVAL.LT.NMAX) THEN IF (ERR1.NE.0.D0 .AND. ERR2.NE.0.D0) THEN IF (ERR1.GT.RELP .AND. ERR2.GT.RELP) THEN IF (ERR1.GT.TOLL .OR. ERR2.GT.TOLL) GO TO 10 END IF ELSE IF (ERR1.EQ.0.D0 .AND. ERR2.NE.0.D0) THEN IF (ERR2.GT.RELP .OR. ERR2.GT.TOLL) THEN GO TO 10 ELSE IF (ERR2.EQ.0.D0 .AND. ERR1.NE.0.D0) THEN IF (ERR1.GT.RELP .OR. ERR1.GT.TOLL) GO TO 10 END IF END IF ELSE IF (ERR1.NE.0.D0 .AND. ERR2.NE.0.D0) THEN IF (ERR1.GT.RELP .AND. ERR2.GT.RELP) THEN IF (ERR1.GT.TOLL .OR. ERR2.GT.TOLL) THEN IFAIL = - 1 END IF END IF ELSE IF (ERR1.EQ.0.D0 .AND. ERR2.NE.0.D0) THEN IF (ERR2.GT.RELP .OR. ERR2.GT.TOLL) THEN IFAIL = -1 ELSE IF (ERR2.EQ.0.D0 .AND. ERR1.NE.0.D0) THEN IF (ERR1.GT.RELP .OR. ERR1.GT.TOLL) THEN IFAIL = -1 END IF END IF END IF END IF C **************************************************************************** C C ESTIMATION OF THE ABSOLUTE ERROR, TRUNCATION ERROR AND THE SUM OF THEM C C **************************************************************************** ERROR(2) = ERROR(2) + (ERR1+ERR2) IF (PART2.NE.0.D0) THEN ERROR(3) = (ERR1+ERR2)/ABS(FA3*PART2) ELSE ERROR(3) = ERR1 + ERR2 END IF ERROR(1) = TOL1 + ERROR(3) RETURN END C C **************************************************************** C SUBROUTINE QDACC(FZ,IFV,IFAIL,WORK,NMAX,PART0,PART1,PART2) C C **************************************************************** C PURPOSE: C ======= C THIS SUBROUTINE IMPLEMENTS A COLUMN-VERSION OF THE Q-D ALGORITHM. C THE QD SCHEME IS BUILT UP PROCEEDING FROM LEFT TO RIGHT ALONG THE C DIAGONAL DIRECTION. THE ELEMENTS OF EACH DIAGONALS ARE COMPUTED C PROCEEDING BOTTOM-UP IN THE TABLE. THE LAST ELEMENT COMPUTED IN C EACH DIAGONAL IS THE COEFFICIENT OF THE CONTINUED FRACTION. C C DESCRIPTION OF PARAMETERS: C ========================= C C INPUT PARAMETERS: C C FZ: COMPLEX*16 (DOUBLE PRECISION COMPLEX) FUNCTION, SUPPLIED BY C THE USER. C FZ MUST RETURN THE VALUE OF THE LAPLACE TRANSFORM FUNCTION TO C BE INVERTED, AT A GIVEN POINT. ITS SPECIFICATION IS: C COMPLEX*16 FUNCTION FZ(Z) C COMPLEX*16 Z C C Z: COMPLEX*16. ON ENTRY, Z MUST SPECIFY THE POINT AT C WHICH THE LAPLACE TRANSFORM FUNCTION VALUE IS C REQUIRED. C C FZ MUST BE DECLARED AS EXTERNAL IN THE PROGRAM FROM WHICH INVLTF IS C CALLED. C C IFV : INTEGER. ON EXIT, IFV CONTAINS THE C NUMBER OF EVALUATIONS OF FZ USED TO OBTAIN PART2. C C IFAIL: INTEGER. ON EXIT, IFAIL CONTAINS POSSIBLE ERRORS DETECTED C C WORK : DOUBLE COMPLEX ARRAY OF DIMENSION(2,0:2*NMAX). WORKSPACE AREAS. C C PART0: DOUBLE PRECISION. ON EXIT PART0 CONTAINS THE APPROXIMATION C OF THE LAST-THIRD ACCELERATED TERM. C C PART1: DOUBLE PRECISION. ON EXIT PART1 CONTAINS THE APPROXIMATION C OF THE LAST-SECOND ACCELERATED TERM. C C PART2: DOUBLE PRECISION. ON EXIT PART2 CONTAINS THE APPROXIMATION C OF THE LAST ACCELERATED. C **************************************************************** C .. Scalar Arguments .. DOUBLE PRECISION GAMMA,PART2,PI INTEGER IFAIL,IFV,MA,NMAX LOGICAL FIRST C .. C .. Array Arguments .. DOUBLE COMPLEX WORK(2,0:2*NMAX) C .. C .. Function Arguments .. DOUBLE COMPLEX FZ EXTERNAL FZ C .. C .. Local Scalars .. DOUBLE COMPLEX AUX1,AUX2,AUX3,H,MX DOUBLE PRECISION PART0,PART1,TOLL INTEGER IBEGIN,I,J,K,MM,MP,UL LOGICAL RIV C .. C .. Intrinsic Functions .. INTRINSIC ABS,DCMPLX,DEXP,DREAL,CDEXP,CDSQRT C .. C .. Common blocks .. COMMON /PARAM/FIRST,MA,MP COMMON /PARAM1/GAMMA,PI C ********************************************************** C INITIALIZATION STEP C ********************************************************** IBEGIN = 2*MP MM = 2*MA IF (FIRST) THEN H = FZ(DCMPLX(GAMMA,0.D0))/ (2.D0,0.D0) IFV = IFV + 1 MX = H WORK(2,0) = H C ************************************************************** C INITIALIZE THE WORKSPACE AREA: THE ARRAYS Q and D OF C THE COLUMN VERSION OF THE QD ALGORITHM C THE VECTOR Q HAS BEEN STORED IN THE FIRST ROW OF THE ARRAY WORK C THE VECTOR D HAS BEEN STORED IN THE SECOND ROW OF THE ARRAY WORK C *************************************************************** DO 20 K = 0,1 WORK(1,K) = MX MX = FZ(DCMPLX(GAMMA,PI* (K+1))) IFV = IFV + 1 WORK(1,K) = MX/ WORK(1,K) WORK(2,K+1) = WORK(1,K) 20 CONTINUE AUX1 = WORK(1,1) WORK(1,1) = WORK(1,1) - WORK(1,0) WORK(2,2) = - WORK(1,1) WORK(1,0) = AUX1 WORK(2,1) = -WORK(2,1) WORK(1,2) = 0.D0 END IF UL = MM - 1 C DO 15 K = 3, UL C WORK(1,K) = 0.0D0 C15 CONTINUE C C ***************************************************************** C COMPUTATION OF THE COEFFICIENTS NEEDED IN THE QD ALGORITHM C ***************************************************************** IFAIL = 0 I= IBEGIN 25 CONTINUE RIV = .TRUE. AUX1 = WORK(1,0) WORK(1,0) = MX MX = FZ(DCMPLX(GAMMA,PI* (I+1))) IFV = IFV + 1 WORK(1,0) = MX/WORK(1,0) AUX2 = WORK(1,1) WORK(1,1) = WORK(1,0) - AUX1 J=2 30 CONTINUE IF (J .EQ. I) WORK(1,J) = 0.D0 AUX3 = WORK(1,J) IF (RIV) THEN IF (AUX2.NE. (0.D0,0.D0)) THEN WORK(1,J) = AUX1*WORK(1,J-1)/AUX2 ELSE IFAIL = -2 END IF ELSE WORK(1,J) = WORK(1,J-1) - AUX2 + AUX1 END IF AUX1 = AUX2 AUX2 = AUX3 RIV = .NOT. RIV J=J+1 IF(J .LE.I .AND. IFAIL .EQ. 0) GOTO 30 WORK(2,I+1) = -WORK(1,I) I = I+1 IF (I .LE. UL .AND. IFAIL .EQ. 0 ) GOTO 25 IF (.NOT.FIRST) THEN IBEGIN = IBEGIN + 1 END IF IF (FIRST) THEN PART0 = 0.D0 PART1 = 0.D0 ELSE PART0 = PART1 PART1 = PART2 END IF C *************************************************************************** C ************* END OF THE QD ALGORITHM ************************************* C *************************************************************************** RETURN END C ***************************************************************************** SUBROUTINE BACKCF(TV,WORK,NMAX,PART2) C ***************************************************************************** C COMPUTATION OF THE CONTINUED FRACTION BY THE BACKWARD FORMULA C ***************************************************************************** INTEGER MA,MM,MP,NMAX,I DOUBLE COMPLEX WORK(2,0:2*NMAX),CC,Z,H2M,R2M DOUBLE PRECISION PART2,GAMMA,PI,TV LOGICAL FIRST COMMON /PARAM/FIRST,MA,MP COMMON /PARAM1/ GAMMA,PI MM=2*MA Z = CDEXP(DCMPLX(0.D0,PI*TV)) H2M = ((WORK(2,MM-1)-WORK(2,MM))*Z+ (1.D0,0.D0))/ (2.D0,0.D0) R2M = CDSQRT((WORK(2,MM)*Z/ (H2M*H2M))+ (1.D0,0.D0)) R2M = (1.D0,0.D0) - R2M R2M = -H2M*R2M CC = (R2M*Z) DO 50 I = MM - 1,1,-1 CC = (WORK(2,I)*Z)/ ((1.D0,0.D0)+CC) 50 CONTINUE CC = WORK(2,0)/ ((1.D0,0.D0)+CC) PART2 = DREAL(CC) MP = MA MA = MA + 1 FIRST = .FALSE. RETURN END SHAR_EOF fi # end of overwriting check if test -f 'main.f' then echo shar: will not over-write existing file "'main.f'" else cat << SHAR_EOF > 'main.f' C DRIVER PROGRAM FOR TESTING SOFTWARE INVLTF IMPLEMENTING C C FOURIER BASED METHOD FOR THE NUMERICAL INVERSION C C OF LAPLACE TRANSFORMS C C C C C JANUARY , 1998 C C C AUTHORS: D'AMORE LUISA, GIULIANO LACCETTI, ALMERICO MURLI C C C C C C REFERENCES C ========== C C C C C C C C C C C REFERENCES C ========== C C D'AMORE L., LACCETTI G., MURLI A., - "ALGORITHM XXX: A FORTRAN C SOFTWARE PACKAGE FOR THE NUMERICAL INVERSION OF THE C LAPLACE TRANSFORM BASE ON FOURIER SERIES' METHOD" C PROGRAM MAIN C *********************************************************** C DRIVER PROGRAM TO TEST THE ROUTINE INVLTF C FOR THE INVERSION OF A LAPLACE TRANSFORM FUNCTION. C THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION C OPERATIONS. C THE MAIN PROGRAM ALLOWS THE INVERSION OF A SET OF LAPLACE C TRANSFORM FUNCTIONS WHICH CAN BE ADDRESSED BY A NATURAL C NUMBER BETWEEN 1 AND 34. C FOR THE COMPLETE LIST SEE THE TABLE IN THE COMPANION PAPER. C C THIS IS A SELF-CONTAINED DRIVER FOR THE INVLTF ROUTINE C COMPRISING A MAIN PROGRAM AND SUBPROGRAMS QDACC, BACKCF, C AND THE LAPLACE TRANSFORM PAIRS FZ AND FEX C C THIS DRIVER ALLOWS TO OBTAIN UP TO 50 VALUES OF THE C INVERSE LAPLACE FUNCTION C C ************************************************************ C C C C .. Parameters .. INTEGER NMAX,FMAX,LASTFN PARAMETER (NMAX=550,FMAX=50,LASTFN=34) C .. C .. Scalars in Common .. INTEGER NFUN C .. C .. Local Scalars .. DOUBLE PRECISION EXF,SIGMA0,TOL,SSBAR INTEGER I,NT CHARACTER*100 AA,BB LOGICAL STOP C .. C .. Local Arrays .. DOUBLE COMPLEX WORK(2,0:2*NMAX) DOUBLE PRECISION DIFABS(FMAX),DIFREL(FMAX),FZINV(FMAX), + TARRAY(FMAX),ERROR(3,FMAX),ERR(3) INTEGER IFAIL(FMAX),IFZEVAL(FMAX) C .. C .. External Functions .. DOUBLE COMPLEX FZ DOUBLE PRECISION FEX EXTERNAL FZ,FEX C .. C .. External Subroutines .. EXTERNAL INVLTF C .. C .. Intrinsic Functions .. INTRINSIC ABS C .. C .. Common blocks .. COMMON /NF/NFUN C .. C ***************************************************************** C SET UP THE OUTPUT C ***************************************************************** C C Loop through all the tests C DO 50 NFUN = 1,LASTFN C C Skip the tests that require the use of NAG library routines C C Commented out lines need to be reintroduced in the routines C FZ and FEX after labels 9, 36, 37, 38 C IF (NFUN.EQ.9 .OR. NFUN.EQ.36 .OR. NFUN.EQ.37 .OR. + NFUN.EQ.38) GO TO 50 AA = +'***************************************************************** +***********************' BB = + '<><><><><><><><><><><><><><><><><><><><><><><><><><><><><>' WRITE (*,FMT=9000) AA,AA,AA,AA WRITE (*,FMT=9090) C READ (*,FMT=*) NFUN WRITE (*,FMT=9050) NFUN WRITE (*,FMT=9110) C READ (*,FMT=*) SIGMA0 SIGMA0 = 0.0 WRITE (*,FMT=9120) SIGMA0 IF (NFUN .EQ. 18) SIGMA0 = 3.0 IF (NFUN .EQ. 23) SIGMA0 = 0.25D0 IF (NFUN .EQ. 29) SIGMA0 = 2.D0 WRITE (*,FMT=9080) BB,BB,BB,BB C ***************************************************************** C NOW, SET INPUT PARAMETERS FOR INVLTF C ***************************************************************** C C NT IS THE NUMBER OF T-VALUES USED HERE FOR THE TEST FUNCTIONS. C THE MAXIMUM ALLOWED IS THE DIMENSION OF THE ARRAY TVAL C ***************************************************************** C C IN THIS TEST PROGRAM THE INVERSE FUNCTION IS REQUESTED IN THE C FOLLOWING VALUES OF T: C T=1,20, STEP=0.5 AND T=20,65 STEP=5 C REMARK: C ====== C FOR T SMALL, THAT IS FOR T=1,20, STEP=0.5, ALL THE RESULTS ARE C QUITE ACCURATE, WHILE FOR T LARGE, THAT IS FOR T=20,65 STEP=5, C IN SOME CASES THE RESULTS COULDN'T BE ACCURATE. IN SUCH CASES C THE AUTHORS SUGGEST TO USE AN ASYMPTOTIC INVERSION METHOD. C ***************************************************************** NT = 44 DO 10 I = 1,39 TARRAY(I) =1.D0 + (I-1)*0.5D0 10 CONTINUE TARRAY(40) = 30. DO 20 I = 41,44 TARRAY(I) = 30.D0 + 5.D0* (I-40) 20 CONTINUE TOL = .1D-5 SSBAR=0.d0 WRITE (*,FMT=9010) AA,AA WRITE (*,FMT=9030) AA,AA WRITE (*,FMT=9020) TOL C C ************************************************************ C CALL OF THE ROUTINE INVLTF C ************************************************************ C C DO 2 I=1,NT CALL INVLTF(TOL,TARRAY(I),FZ,SIGMA0,SSBAR,NMAX,FZINV(I),ERR, + IFZEVAL(I),WORK,IFAIL(I)) ERROR(1,I)= ERR(1) ERROR(2,I)= ERR(2) ERROR(3,I)= ERR(3) 2 CONTINUE C C C WRITE (*,FMT=9040) AA,AA DO 30 I = 1,NT STOP= .FALSE. IF (IFAIL(I).NE. 0 )THEN WRITE (*,FMT=9100) I,IFAIL(I) STOP=.TRUE. ENDIF IF (.NOT. STOP) THEN C EXF = FEX(TARRAY(I)) DIFABS(I) = ABS(EXF-FZINV(I)) IF (EXF.NE.0.D0) THEN DIFREL(I) = DIFABS(I)/ABS(EXF) ELSE DIFREL(I) = DIFABS(I) END IF EXF = FEX(TARRAY(I)) IF (IFAIL(I).NE.-2) THEN WRITE (*,FMT=9070) TARRAY(I),FZINV(I),EXF,ERROR(1,I), + DIFREL(I),ERROR(3,I),ERROR(2,I),DIFABS(I),IFZEVAL(I), + IFAIL(I) ELSE WRITE (*,FMT=9060) TARRAY(I),IFAIL(I) END IF END IF 30 CONTINUE 50 CONTINUE STOP C 9000 FORMAT (1X,A45,A45,/,/,15X, + ' SUBROUTINE INVLTF ',/,15X, + 'NUMERICAL INVERSION OF A LAPLACE TRANSFORM:',/,15X, + ' THIS VERSION USES BOTH REAL AND COMPLEX',/,15X, + ' DOUBLE PRECISION OPERATIONS',/,/,1X,A45,A45,/) 9010 FORMAT (/,A45,A45,/,/,16X,' OUTPUT',/) 9020 FORMAT (/,1X,'TOLL --> ',E15.7) 9030 FORMAT (1X,'T : POINT AT WHICH THE INVERSE TRANSFORM IS', + ' COMPUTED;',/,/,1X, + 'FEX : EXACT VALUE OF THE INVERSE TRANSFORM;',/,/,1X, + 'FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM;',/,/,1X, + 'ESTREL : ESTIMATED RELATIVE ERROR;',/,/,1X, + 'RELERR : ACTUAL RELATIVE ERROR;',/,/,1X, + 'ESTABS : ESTIMATED ABSOLUTE ERROR ;',/,/,1X, + 'ABSERR : ACTUAL ABSOLUTE ERROR;',/,/,1X, + 'N : # OF FUNCTION EVALUATIONS;',/,/,1X, + 'IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN', + ' (ACCURACY REACHED AND IFZEVAL= 1,',/,10X, + '= 2 VALT LESS THAN ZERO,',/,10X, + '= -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;,',/,10X, + '= -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL;',/,10X, + ' IN SUCH A CASE THE USER MAY SLIGHTLY',/,10X, + ' CHANGE THE DEFAULT VALUE;',/,/,A45,A45,/,/) 9040 FORMAT (/,A86,/,' T',9X,'FCAL',9X,'FEX',8X,' ESTREL',3X, + 'RELERR',2X,'TRUNERR',2X,'ESTABS',3X,'ABSERR',3X,'N',2X, + 'IFAIL',/,A100,/,/) 9050 FORMAT (/,' TEST FUNCTION -----> ',I2,/) 9060 FORMAT (F5.1,90X,I2) 9070 FORMAT (F5.1,1X,E14.8,1X,E14.8,1X,E8.3,1X,E8.3,1X,E8.3,1X,E8.3,1X, + E8.3,1X,I3,3X,I2) 9080 FORMAT (/,/,1X,A45,A45,/,/,2X, + ' THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20' + ,' STEP=0.5 AND T=20,100 STEP=10.',/,/,1X,A45,A45) 9090 FORMAT (1X,'TEST FUNCTION : ') 9100 FORMAT (/,1X,'ERROR DETECTED , I = ', I3, ' IFAIL=',I3) 9110 FORMAT (/,' ABSCISSA OF CONVERGENCE ---> ',/) 9120 FORMAT (/,' ABSCISSA OF CONVERGENCE ---> ',F5.1,/) END SHAR_EOF fi # end of overwriting check if test -f 'res' then echo shar: will not over-write existing file "'res'" else cat << SHAR_EOF > 'res' ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 1 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.10000000E+01 0.10000000E+01 .107E-06 .716E-09 .689E-08 .107E-06 .716E-09 25 0 1.5 0.10000000E+01 0.10000000E+01 .108E-06 .213E-09 .811E-08 .108E-06 .213E-09 25 0 2.0 0.10000000E+01 0.10000000E+01 .107E-06 .716E-09 .689E-08 .107E-06 .716E-09 25 0 2.5 0.10000000E+01 0.10000000E+01 .108E-06 .642E-09 .828E-08 .108E-06 .642E-09 25 0 3.0 0.10000000E+01 0.10000000E+01 .108E-06 .213E-09 .811E-08 .108E-06 .213E-09 25 0 3.5 0.10000000E+01 0.10000000E+01 .109E-06 .663E-09 .863E-08 .109E-06 .663E-09 25 0 4.0 0.10000000E+01 0.10000000E+01 .107E-06 .716E-09 .689E-08 .107E-06 .716E-09 25 0 4.5 0.10000000E+01 0.10000000E+01 .108E-06 .671E-09 .784E-08 .108E-06 .671E-09 25 0 5.0 0.10000000E+01 0.10000000E+01 .108E-06 .642E-09 .828E-08 .108E-06 .642E-09 25 0 5.5 0.10000000E+01 0.10000000E+01 .107E-06 .684E-09 .732E-08 .107E-06 .684E-09 25 0 6.0 0.10000000E+01 0.10000000E+01 .108E-06 .213E-09 .811E-08 .108E-06 .213E-09 25 0 6.5 0.10000000E+01 0.10000000E+01 .108E-06 .668E-09 .763E-08 .108E-06 .668E-09 25 0 7.0 0.10000000E+01 0.10000000E+01 .109E-06 .663E-09 .863E-08 .109E-06 .663E-09 25 0 7.5 0.10000000E+01 0.10000000E+01 .107E-06 .910E-09 .716E-08 .107E-06 .910E-09 25 0 8.0 0.10000000E+01 0.10000000E+01 .107E-06 .716E-09 .689E-08 .107E-06 .716E-09 25 0 8.5 0.10000000E+01 0.10000000E+01 .107E-06 .630E-09 .743E-08 .107E-06 .630E-09 25 0 9.0 0.10000000E+01 0.10000000E+01 .108E-06 .671E-09 .784E-08 .108E-06 .671E-09 25 0 9.5 0.10000000E+01 0.10000000E+01 .107E-06 .633E-09 .726E-08 .107E-06 .633E-09 25 0 10.0 0.10000000E+01 0.10000000E+01 .108E-06 .642E-09 .828E-08 .108E-06 .642E-09 25 0 10.5 0.10000000E+01 0.10000000E+01 .108E-06 .210E-09 .821E-08 .108E-06 .210E-09 25 0 11.0 0.10000000E+01 0.10000000E+01 .107E-06 .684E-09 .732E-08 .107E-06 .684E-09 25 0 11.5 0.10000000E+01 0.10000000E+01 .107E-06 .670E-09 .747E-08 .107E-06 .670E-09 25 0 12.0 0.10000000E+01 0.10000000E+01 .108E-06 .213E-09 .811E-08 .108E-06 .213E-09 25 0 12.5 0.10000000E+01 0.10000000E+01 .108E-06 .565E-09 .792E-08 .108E-06 .565E-09 25 0 13.0 0.10000000E+01 0.10000000E+01 .108E-06 .668E-09 .763E-08 .108E-06 .668E-09 25 0 13.5 0.10000000E+01 0.10000000E+01 .110E-06 .672E-09 .989E-08 .110E-06 .672E-09 25 0 14.0 0.10000000E+01 0.10000000E+01 .109E-06 .663E-09 .863E-08 .109E-06 .663E-09 25 0 14.5 0.10000000E+01 0.10000000E+01 .107E-06 .618E-09 .736E-08 .107E-06 .618E-09 25 0 15.0 0.10000000E+01 0.10000000E+01 .107E-06 .910E-09 .716E-08 .107E-06 .910E-09 25 0 15.5 0.10000000E+01 0.10000000E+01 .109E-06 .268E-09 .876E-08 .109E-06 .268E-09 25 0 16.0 0.10000000E+01 0.10000000E+01 .107E-06 .716E-09 .689E-08 .107E-06 .716E-09 25 0 16.5 0.10000000E+01 0.10000000E+01 .108E-06 .382E-09 .847E-08 .108E-06 .382E-09 25 0 17.0 0.10000000E+01 0.10000000E+01 .107E-06 .630E-09 .743E-08 .107E-06 .630E-09 25 0 17.5 0.10000000E+01 0.10000000E+01 .110E-06 .500E-09 .977E-08 .110E-06 .500E-09 25 0 18.0 0.10000000E+01 0.10000000E+01 .108E-06 .671E-09 .784E-08 .108E-06 .671E-09 25 0 18.5 0.10000000E+01 0.10000000E+01 .108E-06 .528E-09 .820E-08 .108E-06 .528E-09 25 0 19.0 0.10000000E+01 0.10000000E+01 .107E-06 .633E-09 .726E-08 .107E-06 .633E-09 25 0 19.5 0.10000000E+01 0.10000000E+01 .108E-06 .743E-09 .780E-08 .108E-06 .743E-09 25 0 20.0 0.10000000E+01 0.10000000E+01 .108E-06 .642E-09 .828E-08 .108E-06 .642E-09 25 0 30.0 0.10000000E+01 0.10000000E+01 .107E-06 .910E-09 .716E-08 .107E-06 .910E-09 25 0 35.0 0.10000000E+01 0.10000000E+01 .110E-06 .500E-09 .977E-08 .110E-06 .500E-09 25 0 40.0 0.10000000E+01 0.10000000E+01 .108E-06 .642E-09 .828E-08 .108E-06 .642E-09 25 0 45.0 0.10000000E+01 0.10000000E+01 .107E-06 .436E-09 .750E-08 .107E-06 .436E-09 25 0 50.0 0.10000000E+01 0.10000000E+01 .108E-06 .565E-09 .792E-08 .108E-06 .565E-09 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 2 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.35663584E+00 0.35663583E+00 .201E-06 .240E-07 .101E-06 .718E-07 .854E-08 27 0 1.5 0.23858132E+00 0.23858132E+00 .122E-06 .374E-08 .225E-07 .292E-07 .892E-09 27 0 2.0 0.17247566E+00 0.17247566E+00 .167E-06 .121E-07 .667E-07 .288E-07 .209E-08 27 0 2.5 0.13101394E+00 0.13101394E+00 .123E-06 .140E-09 .225E-07 .161E-07 .184E-10 29 0 3.0 0.10317254E+00 0.10317254E+00 .151E-06 .202E-08 .509E-07 .156E-07 .208E-09 25 0 3.5 0.83561523E-01 0.83561523E-01 .104E-06 .885E-08 .352E-08 .865E-08 .740E-09 27 0 4.0 0.69232010E-01 0.69232011E-01 .160E-06 .239E-07 .600E-07 .111E-07 .165E-08 25 0 4.5 0.58445991E-01 0.58445990E-01 .104E-06 .110E-07 .426E-08 .609E-08 .640E-09 27 0 5.0 0.50122634E-01 0.50122636E-01 .214E-06 .435E-07 .114E-06 .107E-07 .218E-08 25 0 5.5 0.43561470E-01 0.43561470E-01 .231E-06 .147E-07 .131E-06 .101E-07 .639E-09 27 0 6.0 0.38293085E-01 0.38293084E-01 .140E-06 .197E-07 .397E-07 .535E-08 .756E-09 25 0 6.5 0.33993947E-01 0.33993948E-01 .160E-06 .141E-07 .602E-07 .545E-08 .478E-09 27 0 7.0 0.30435595E-01 0.30435595E-01 .160E-06 .245E-08 .601E-07 .487E-08 .745E-10 27 0 7.5 0.27453195E-01 0.27453195E-01 .174E-06 .639E-08 .741E-07 .478E-08 .175E-09 27 0 8.0 0.24925528E-01 0.24925528E-01 .113E-06 .303E-08 .134E-07 .283E-08 .756E-10 31 0 8.5 0.22761889E-01 0.22761889E-01 .230E-06 .660E-08 .130E-06 .524E-08 .150E-09 25 0 9.0 0.20893332E-01 0.20893332E-01 .108E-06 .247E-07 .849E-08 .227E-08 .516E-09 25 0 9.5 0.19266692E-01 0.19266692E-01 .144E-06 .635E-08 .442E-07 .278E-08 .122E-09 27 0 10.0 0.17840431E-01 0.17840431E-01 .129E-06 .109E-08 .293E-07 .231E-08 .195E-10 27 0 10.5 0.16581704E-01 0.16581704E-01 .141E-06 .295E-09 .415E-07 .235E-08 .489E-11 27 0 11.0 0.15464249E-01 0.15464247E-01 .206E-06 .141E-06 .106E-06 .319E-08 .218E-08 25 0 11.5 0.14466848E-01 0.14466848E-01 .137E-06 .155E-08 .367E-07 .198E-08 .224E-10 27 0 12.0 0.13572209E-01 0.13572209E-01 .122E-06 .506E-08 .216E-07 .165E-08 .687E-10 27 0 12.5 0.12766105E-01 0.12766105E-01 .160E-06 .101E-07 .596E-07 .204E-08 .129E-09 27 0 13.0 0.12036745E-01 0.12036745E-01 .163E-06 .807E-08 .630E-07 .196E-08 .971E-10 27 0 13.5 0.11374277E-01 0.11374277E-01 .136E-06 .405E-08 .364E-07 .155E-08 .461E-10 27 0 14.0 0.10770420E-01 0.10770420E-01 .165E-06 .300E-08 .646E-07 .177E-08 .323E-10 27 0 14.5 0.10218164E-01 0.10218163E-01 .136E-06 .248E-07 .359E-07 .139E-08 .253E-09 25 0 15.0 0.97115386E-02 0.97115386E-02 .151E-06 .155E-08 .508E-07 .146E-08 .151E-10 27 0 15.5 0.92454371E-02 0.92454368E-02 .104E-06 .249E-07 .355E-08 .957E-09 .230E-09 27 0 16.0 0.88154614E-02 0.88154613E-02 .191E-06 .181E-07 .913E-07 .169E-08 .160E-09 25 0 16.5 0.84178099E-02 0.84178100E-02 .157E-06 .352E-08 .567E-07 .132E-08 .296E-10 27 0 17.0 0.80491804E-02 0.80491804E-02 .132E-06 .877E-08 .319E-07 .106E-08 .706E-10 27 0 17.5 0.77066916E-02 0.77066916E-02 .248E-06 .412E-08 .148E-06 .191E-08 .318E-10 27 0 18.0 0.73878199E-02 0.73878199E-02 .168E-06 .407E-08 .676E-07 .124E-08 .301E-10 27 0 18.5 0.70903466E-02 0.70903466E-02 .161E-06 .386E-08 .612E-07 .114E-08 .274E-10 27 0 19.0 0.68123138E-02 0.68123140E-02 .173E-06 .299E-07 .734E-07 .118E-08 .203E-09 25 0 19.5 0.65519888E-02 0.65519888E-02 .133E-06 .893E-08 .335E-07 .874E-09 .585E-10 27 0 20.0 0.63078313E-02 0.63078313E-02 .181E-06 .547E-08 .807E-07 .114E-08 .345E-10 27 0 30.0 0.34335485E-02 0.34335485E-02 .167E-06 .621E-08 .666E-07 .572E-09 .213E-10 27 0 35.0 0.27247270E-02 0.27247270E-02 .133E-06 .335E-08 .330E-07 .362E-09 .913E-11 27 0 40.0 0.22301551E-02 0.22301551E-02 .134E-06 .791E-08 .341E-07 .299E-09 .176E-10 27 0 45.0 0.18689871E-02 0.18689871E-02 .227E-06 .162E-08 .127E-06 .425E-09 .303E-11 27 0 50.0 0.15957691E-02 0.15957691E-02 .216E-06 .130E-07 .116E-06 .345E-09 .208E-10 27 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 3 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.56418958E+00 0.56418958E+00 .129E-06 .442E-09 .288E-07 .727E-07 .250E-09 25 0 1.5 0.46065887E+00 0.46065887E+00 .128E-06 .836E-09 .285E-07 .592E-07 .385E-09 25 0 2.0 0.39894228E+00 0.39894228E+00 .136E-06 .179E-08 .364E-07 .544E-07 .715E-09 25 0 2.5 0.35682482E+00 0.35682482E+00 .130E-06 .463E-09 .298E-07 .463E-07 .165E-09 25 0 3.0 0.32573501E+00 0.32573501E+00 .149E-06 .795E-10 .493E-07 .486E-07 .259E-10 25 0 3.5 0.30157202E+00 0.30157202E+00 .131E-06 .117E-09 .312E-07 .396E-07 .353E-10 25 0 4.0 0.28209479E+00 0.28209479E+00 .129E-06 .442E-09 .288E-07 .363E-07 .125E-09 25 0 4.5 0.26596152E+00 0.26596152E+00 .125E-06 .232E-08 .255E-07 .334E-07 .618E-09 25 0 5.0 0.25231325E+00 0.25231325E+00 .130E-06 .193E-08 .303E-07 .329E-07 .486E-09 25 0 5.5 0.24057125E+00 0.24057125E+00 .134E-06 .422E-09 .339E-07 .322E-07 .102E-09 25 0 6.0 0.23032943E+00 0.23032943E+00 .128E-06 .836E-09 .285E-07 .296E-07 .193E-09 25 0 6.5 0.22129336E+00 0.22129336E+00 .143E-06 .978E-09 .427E-07 .316E-07 .216E-09 25 0 7.0 0.21324362E+00 0.21324362E+00 .144E-06 .687E-09 .442E-07 .308E-07 .146E-09 25 0 7.5 0.20601291E+00 0.20601291E+00 .101E-06 .131E-09 .111E-08 .208E-07 .269E-10 29 0 8.0 0.19947114E+00 0.19947114E+00 .136E-06 .179E-08 .364E-07 .272E-07 .357E-09 25 0 8.5 0.19351543E+00 0.19351543E+00 .138E-06 .116E-08 .380E-07 .267E-07 .225E-09 25 0 9.0 0.18806319E+00 0.18806319E+00 .126E-06 .293E-09 .258E-07 .236E-07 .552E-10 25 0 9.5 0.18304727E+00 0.18304727E+00 .127E-06 .144E-08 .270E-07 .232E-07 .263E-09 25 0 10.0 0.17841241E+00 0.17841241E+00 .130E-06 .463E-09 .298E-07 .232E-07 .826E-10 25 0 10.5 0.17411269E+00 0.17411269E+00 .138E-06 .341E-09 .376E-07 .240E-07 .593E-10 25 0 11.0 0.17010956E+00 0.17010956E+00 .131E-06 .165E-09 .311E-07 .223E-07 .280E-10 25 0 11.5 0.16637043E+00 0.16637043E+00 .126E-06 .239E-09 .259E-07 .209E-07 .398E-10 25 0 12.0 0.16286750E+00 0.16286750E+00 .149E-06 .795E-10 .493E-07 .243E-07 .130E-10 25 0 12.5 0.15957691E+00 0.15957691E+00 .137E-06 .105E-08 .375E-07 .219E-07 .168E-09 25 0 13.0 0.15647804E+00 0.15647804E+00 .159E-06 .687E-09 .593E-07 .249E-07 .107E-09 25 0 13.5 0.15355296E+00 0.15355296E+00 .147E-06 .321E-08 .474E-07 .226E-07 .492E-09 25 0 14.0 0.15078601E+00 0.15078601E+00 .128E-06 .653E-09 .282E-07 .193E-07 .984E-10 25 0 14.5 0.14816344E+00 0.14816344E+00 .140E-06 .291E-10 .396E-07 .207E-07 .431E-11 25 0 15.0 0.14567312E+00 0.14567312E+00 .130E-06 .191E-08 .297E-07 .189E-07 .279E-09 25 0 15.5 0.14330430E+00 0.14330430E+00 .134E-06 .147E-08 .335E-07 .191E-07 .210E-09 25 0 16.0 0.14104740E+00 0.14104740E+00 .165E-06 .236E-09 .649E-07 .233E-07 .332E-10 25 0 16.5 0.13889387E+00 0.13889387E+00 .140E-06 .337E-09 .405E-07 .195E-07 .469E-10 25 0 17.0 0.13683607E+00 0.13683607E+00 .141E-06 .769E-08 .414E-07 .194E-07 .105E-08 25 0 17.5 0.13486711E+00 0.13486711E+00 .135E-06 .144E-09 .349E-07 .182E-07 .194E-10 25 0 18.0 0.13298076E+00 0.13298076E+00 .141E-06 .565E-09 .411E-07 .188E-07 .751E-10 25 0 18.5 0.13117141E+00 0.13117141E+00 .127E-06 .348E-09 .268E-07 .166E-07 .456E-10 25 0 19.0 0.12943397E+00 0.12943397E+00 .136E-06 .829E-09 .364E-07 .177E-07 .107E-09 25 0 19.5 0.12776378E+00 0.12776378E+00 .207E-06 .186E-10 .107E-06 .265E-07 .238E-11 25 0 20.0 0.12615663E+00 0.12615663E+00 .128E-06 .443E-09 .281E-07 .162E-07 .558E-10 25 0 30.0 0.10300645E+00 0.10300645E+00 .136E-06 .184E-08 .361E-07 .140E-07 .189E-09 25 0 35.0 0.95365445E-01 0.95365445E-01 .136E-06 .931E-09 .362E-07 .130E-07 .888E-10 25 0 40.0 0.89206206E-01 0.89206206E-01 .142E-06 .911E-09 .423E-07 .127E-07 .812E-10 25 0 45.0 0.84104417E-01 0.84104417E-01 .134E-06 .512E-08 .344E-07 .113E-07 .431E-09 25 0 50.0 0.79788456E-01 0.79788456E-01 .137E-06 .105E-08 .375E-07 .110E-07 .840E-10 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 4 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.54030231E+00 0.54030231E+00 .141E-06 .897E-10 .410E-07 .762E-07 .485E-10 25 0 1.5 0.10610580E+00 0.10610580E+00 .122E-06 .104E-08 .216E-07 .129E-07 .111E-09 27 0 2.0 -.83229367E+00 -.83229367E+00 .105E-06 .899E-10 .483E-08 .873E-07 .748E-10 27 0 2.5 -.20028590E+01 -.20028590E+01 .104E-06 .133E-09 .357E-08 .207E-06 .266E-09 27 0 3.0 -.29699775E+01 -.29699775E+01 .104E-06 .186E-09 .384E-08 .308E-06 .553E-09 27 0 3.5 -.32775984E+01 -.32775984E+01 .105E-06 .188E-09 .490E-08 .344E-06 .615E-09 27 0 4.0 -.26145745E+01 -.26145745E+01 .108E-06 .319E-10 .823E-08 .283E-06 .834E-10 27 0 4.5 -.94858110E+00 -.94858110E+00 .118E-06 .116E-09 .182E-07 .112E-06 .110E-09 27 0 5.0 0.14183109E+01 0.14183109E+01 .135E-06 .456E-09 .349E-07 .191E-06 .647E-09 27 0 5.5 0.38976838E+01 0.38976838E+01 .152E-06 .648E-09 .518E-07 .592E-06 .253E-08 27 0 6.0 0.57610217E+01 0.57610217E+01 .203E-06 .128E-08 .103E-06 .117E-05 .739E-08 27 0 6.5 0.63478196E+01 0.63478196E+01 .125E-06 .937E-10 .254E-07 .796E-06 .595E-09 29 0 7.0 0.52773158E+01 0.52773158E+01 .162E-06 .195E-09 .620E-07 .855E-06 .103E-08 29 0 7.5 0.25997649E+01 0.25997649E+01 .113E-06 .898E-10 .132E-07 .294E-06 .233E-09 31 0 8.0 -.11640003E+01 -.11640003E+01 .153E-06 .314E-09 .532E-07 .178E-06 .365E-09 31 0 8.5 -.51171012E+01 -.51171012E+01 .125E-06 .536E-09 .246E-07 .638E-06 .274E-08 31 0 9.0 -.82001724E+01 -.82001724E+01 .128E-06 .499E-09 .283E-07 .105E-05 .409E-08 31 0 9.5 -.94731355E+01 -.94731355E+01 .137E-06 .321E-09 .366E-07 .129E-05 .304E-08 31 0 10.0 -.83907153E+01 -.83907153E+01 .162E-06 .825E-09 .621E-07 .136E-05 .693E-08 31 0 10.5 -.49931377E+01 -.49931377E+01 .105E-06 .138E-08 .487E-08 .524E-06 .688E-08 33 0 11.0 0.48682678E-01 0.48682678E-01 .118E-06 .147E-08 .180E-07 .575E-08 .717E-10 39 0 11.5 0.55580047E+01 0.55580047E+01 .165E-06 .202E-08 .654E-07 .919E-06 .112E-07 33 0 12.0 0.10126247E+02 0.10126248E+02 .202E-06 .783E-09 .102E-06 .205E-05 .793E-08 33 0 12.5 0.12472478E+02 0.12472478E+02 .115E-06 .594E-10 .152E-07 .144E-05 .741E-09 35 0 13.0 0.11796808E+02 0.11796808E+02 .134E-06 .282E-09 .344E-07 .159E-05 .333E-08 35 0 13.5 0.80314290E+01 0.80314290E+01 .205E-06 .124E-09 .105E-06 .165E-05 .994E-09 35 0 14.0 0.19143211E+01 0.19143211E+01 .172E-06 .333E-09 .715E-07 .328E-06 .637E-09 37 0 14.5 -.51464019E+01 -.51464019E+01 .123E-06 .346E-09 .234E-07 .635E-06 .178E-08 37 0 15.0 -.11395319E+02 -.11395319E+02 .137E-06 .408E-08 .368E-07 .156E-05 .465E-07 37 0 15.5 -.15166029E+02 -.15166029E+02 .120E-06 .894E-10 .196E-07 .181E-05 .136E-08 37 0 16.0 -.15322552E+02 -.15322552E+02 .174E-06 .959E-09 .744E-07 .267E-05 .147E-07 37 0 16.5 -.11589551E+02 -.11589551E+02 .115E-06 .540E-10 .155E-07 .134E-05 .626E-09 39 0 17.0 -.46777768E+01 -.46777767E+01 .207E-06 .275E-08 .107E-06 .967E-06 .129E-07 39 0 17.5 0.38401993E+01 0.38401994E+01 .275E-06 .501E-08 .175E-06 .106E-05 .192E-07 39 0 18.0 0.11885701E+02 0.11885701E+02 .188E-06 .139E-08 .878E-07 .223E-05 .165E-07 39 0 18.5 0.17381211E+02 0.17381211E+02 .109E-06 .447E-09 .865E-08 .189E-05 .777E-08 41 0 19.0 0.18785388E+02 0.18785388E+02 .173E-06 .119E-08 .730E-07 .325E-05 .224E-07 41 0 19.5 0.15518392E+02 0.15518392E+02 .109E-06 .162E-09 .938E-08 .170E-05 .252E-08 43 0 20.0 0.81616412E+01 0.81616412E+01 .135E-06 .162E-08 .353E-07 .110E-05 .133E-07 43 0 30.0 0.46275435E+01 0.46275435E+01 .163E-06 .981E-08 .632E-07 .755E-06 .454E-07 55 0 35.0 -.31629228E+02 -.31629227E+02 .130E-06 .347E-07 .302E-07 .412E-05 .110E-05 61 0 40.0 -.26677517E+02 -.26677522E+02 .100E-06 .189E-06 .000E+00 .267E-05 .505E-05 67 0 45.0 0.23634836E+02 0.23639489E+02 .100E-06 .197E-03 .000E+00 .236E-05 .465E-02 71 0 50.0 0.48258980E+02 0.48248301E+02 .100E-06 .221E-03 .000E+00 .483E-05 .107E-01 77 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 5 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.36787944E+00 0.36787944E+00 .125E-06 .815E-10 .255E-07 .462E-07 .300E-10 25 0 1.5 0.33469524E+00 0.33469524E+00 .126E-06 .850E-10 .259E-07 .421E-07 .285E-10 25 0 2.0 0.27067057E+00 0.27067057E+00 .117E-06 .593E-09 .171E-07 .317E-07 .161E-09 25 0 2.5 0.20521250E+00 0.20521250E+00 .122E-06 .432E-10 .222E-07 .251E-07 .887E-11 25 0 3.0 0.14936121E+00 0.14936121E+00 .178E-06 .188E-08 .784E-07 .266E-07 .281E-09 25 0 3.5 0.10569084E+00 0.10569084E+00 .120E-06 .508E-09 .197E-07 .126E-07 .537E-10 27 0 4.0 0.73262556E-01 0.73262556E-01 .116E-06 .978E-09 .158E-07 .849E-08 .717E-10 27 0 4.5 0.49990485E-01 0.49990484E-01 .107E-06 .187E-08 .694E-08 .535E-08 .933E-10 27 0 5.0 0.33689735E-01 0.33689735E-01 .130E-06 .170E-08 .302E-07 .438E-08 .571E-10 27 0 5.5 0.22477243E-01 0.22477243E-01 .126E-06 .700E-09 .258E-07 .283E-08 .157E-10 27 0 6.0 0.14872513E-01 0.14872513E-01 .209E-06 .157E-07 .109E-06 .311E-08 .233E-09 25 0 6.5 0.97723548E-02 0.97723548E-02 .107E-06 .322E-09 .689E-08 .104E-08 .315E-11 29 0 7.0 0.63831738E-02 0.63831738E-02 .138E-06 .161E-08 .381E-07 .882E-09 .103E-10 29 0 7.5 0.41481328E-02 0.41481328E-02 .211E-06 .411E-08 .111E-06 .877E-09 .170E-10 29 0 8.0 0.26837010E-02 0.26837010E-02 .211E-06 .704E-08 .111E-06 .566E-09 .189E-10 29 0 8.5 0.17294813E-02 0.17294811E-02 .168E-06 .861E-07 .676E-07 .290E-09 .149E-09 27 0 9.0 0.11106882E-02 0.11106882E-02 .146E-06 .387E-08 .456E-07 .162E-09 .430E-11 31 0 9.5 0.71109239E-03 0.71109238E-03 .187E-06 .119E-07 .866E-07 .133E-09 .844E-11 31 0 10.0 0.45399930E-03 0.45399930E-03 .220E-06 .293E-08 .120E-06 .998E-10 .133E-11 33 0 10.5 0.28913272E-03 0.28913272E-03 .231E-06 .232E-08 .131E-06 .668E-10 .670E-12 33 0 11.0 0.18371871E-03 0.18371871E-03 .210E-06 .175E-07 .110E-06 .385E-10 .321E-11 35 0 11.5 0.11649607E-03 0.11649608E-03 .465E-06 .861E-07 .365E-06 .542E-10 .100E-10 31 0 12.0 0.73730523E-04 0.73730548E-04 .110E-05 .343E-06 .997E-06 .809E-10 .253E-10 31 0 12.5 0.46583166E-04 0.46583165E-04 .120E-06 .259E-07 .199E-07 .559E-11 .120E-11 37 0 13.0 0.29384284E-04 0.29384282E-04 .194E-06 .559E-07 .942E-07 .571E-11 .164E-11 33 0 13.5 0.18507949E-04 0.18507948E-04 .199E-06 .476E-07 .990E-07 .368E-11 .882E-12 39 0 14.0 0.11641402E-04 0.11641402E-04 .204E-06 .170E-07 .104E-06 .238E-11 .197E-12 41 0 14.5 0.73130395E-05 0.73130411E-05 .100E-06 .220E-06 .000E+00 .731E-12 .161E-11 47 0 15.0 0.45885359E-05 0.45885348E-05 .230E-06 .246E-06 .130E-06 .106E-11 .113E-11 39 0 15.5 0.28758573E-05 0.28758566E-05 .100E-06 .224E-06 .000E+00 .288E-12 .644E-12 45 0 16.0 0.18005627E-05 0.18005628E-05 .263E-06 .603E-07 .163E-06 .474E-12 .108E-12 37 0 16.5 0.11262246E-05 0.11262246E-05 .100E-06 .711E-08 .000E+00 .113E-12 .801E-14 41 0 17.0 0.70378791E-06 0.70378941E-06 .100E-06 .213E-05 .000E+00 .704E-13 .150E-11 53 0 17.5 0.43942470E-06 0.43942485E-06 .531E-05 .355E-06 .521E-05 .233E-11 .156E-12 43 0 18.0 0.27413885E-06 0.27413964E-06 .100E-06 .288E-05 .000E+00 .274E-13 .789E-12 49 0 18.5 0.17089371E-06 0.17089282E-06 .100E-06 .519E-05 .000E+00 .171E-13 .887E-12 41 0 19.0 0.10645313E-06 0.10645313E-06 .100E-06 .110E-07 .000E+00 .106E-13 .117E-14 43 0 19.5 0.66265649E-07 0.66266222E-07 .427E-05 .866E-05 .417E-05 .283E-12 .574E-12 37 0 20.0 0.41223902E-07 0.41223072E-07 .674E-05 .201E-04 .664E-05 .278E-12 .829E-12 49 0 30.0 0.29612971E-11 0.28072869E-11 .769E-01 .549E-01 .769E-01 .228E-12 .154E-12 37 0 35.0 -.12542153E-11 0.22067909E-13 .833E+00 .578E+02 .833E+00 .105E-11 .128E-11 27 0 40.0 0.11568466E-11 0.16993417E-15 .333E+00 .681E+04 .333E+00 .386E-12 .116E-11 29 0 45.0 -.21447726E-11 0.12881334E-17 .108E+01 .167E+07 .108E+01 .232E-11 .214E-11 23 0 50.0 0.00000000E+00 0.96437492E-20 .100E-06 .100E+01 .000E+00 .000E+00 .964E-20 33 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 6 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.10000000E+01 0.10000000E+01 .152E-06 .640E-09 .515E-07 .152E-06 .640E-09 23 0 1.5 0.15000000E+01 0.15000000E+01 .152E-06 .766E-09 .516E-07 .227E-06 .115E-08 23 0 2.0 0.20000000E+01 0.20000000E+01 .152E-06 .640E-09 .515E-07 .303E-06 .128E-08 23 0 2.5 0.25000000E+01 0.25000000E+01 .152E-06 .729E-09 .517E-07 .379E-06 .182E-08 23 0 3.0 0.30000000E+01 0.30000000E+01 .152E-06 .766E-09 .516E-07 .455E-06 .230E-08 23 0 3.5 0.35000000E+01 0.35000000E+01 .152E-06 .712E-09 .516E-07 .531E-06 .249E-08 23 0 4.0 0.40000000E+01 0.40000000E+01 .152E-06 .640E-09 .515E-07 .606E-06 .256E-08 23 0 4.5 0.45000000E+01 0.45000000E+01 .152E-06 .801E-09 .517E-07 .683E-06 .361E-08 23 0 5.0 0.50000000E+01 0.50000000E+01 .152E-06 .729E-09 .517E-07 .758E-06 .365E-08 23 0 5.5 0.55000000E+01 0.55000000E+01 .152E-06 .709E-09 .516E-07 .834E-06 .390E-08 23 0 6.0 0.60000000E+01 0.60000000E+01 .152E-06 .766E-09 .516E-07 .909E-06 .460E-08 23 0 6.5 0.65000000E+01 0.65000000E+01 .152E-06 .733E-09 .517E-07 .986E-06 .476E-08 23 0 7.0 0.70000000E+01 0.70000000E+01 .152E-06 .712E-09 .516E-07 .106E-05 .498E-08 23 0 7.5 0.75000000E+01 0.75000000E+01 .152E-06 .712E-09 .516E-07 .114E-05 .534E-08 23 0 8.0 0.80000000E+01 0.80000000E+01 .152E-06 .640E-09 .515E-07 .121E-05 .512E-08 23 0 8.5 0.85000000E+01 0.85000000E+01 .152E-06 .693E-09 .516E-07 .129E-05 .589E-08 23 0 9.0 0.90000000E+01 0.90000000E+01 .152E-06 .801E-09 .517E-07 .137E-05 .721E-08 23 0 9.5 0.95000000E+01 0.95000000E+01 .152E-06 .741E-09 .516E-07 .144E-05 .704E-08 23 0 10.0 0.10000000E+02 0.10000000E+02 .152E-06 .729E-09 .517E-07 .152E-05 .729E-08 23 0 10.5 0.10500000E+02 0.10500000E+02 .152E-06 .728E-09 .517E-07 .159E-05 .764E-08 23 0 11.0 0.11000000E+02 0.11000000E+02 .152E-06 .709E-09 .516E-07 .167E-05 .780E-08 23 0 11.5 0.11500000E+02 0.11500000E+02 .152E-06 .758E-09 .517E-07 .174E-05 .872E-08 23 0 12.0 0.12000000E+02 0.12000000E+02 .152E-06 .766E-09 .516E-07 .182E-05 .919E-08 23 0 12.5 0.12500000E+02 0.12500000E+02 .152E-06 .750E-09 .516E-07 .190E-05 .938E-08 23 0 13.0 0.13000000E+02 0.13000000E+02 .152E-06 .733E-09 .517E-07 .197E-05 .952E-08 23 0 13.5 0.13500000E+02 0.13500000E+02 .152E-06 .776E-09 .517E-07 .205E-05 .105E-07 23 0 14.0 0.14000000E+02 0.14000000E+02 .152E-06 .712E-09 .516E-07 .212E-05 .997E-08 23 0 14.5 0.14500000E+02 0.14500000E+02 .152E-06 .728E-09 .516E-07 .220E-05 .106E-07 23 0 15.0 0.15000000E+02 0.15000000E+02 .152E-06 .712E-09 .516E-07 .227E-05 .107E-07 23 0 15.5 0.15500000E+02 0.15500000E+02 .152E-06 .744E-09 .516E-07 .235E-05 .115E-07 23 0 16.0 0.16000000E+02 0.16000000E+02 .152E-06 .640E-09 .515E-07 .242E-05 .102E-07 23 0 16.5 0.16500000E+02 0.16500000E+02 .152E-06 .777E-09 .517E-07 .250E-05 .128E-07 23 0 17.0 0.17000000E+02 0.17000000E+02 .152E-06 .693E-09 .516E-07 .258E-05 .118E-07 23 0 17.5 0.17500000E+02 0.17500000E+02 .152E-06 .745E-09 .516E-07 .265E-05 .130E-07 23 0 18.0 0.18000000E+02 0.18000000E+02 .152E-06 .801E-09 .517E-07 .273E-05 .144E-07 23 0 18.5 0.18500000E+02 0.18500000E+02 .152E-06 .709E-09 .516E-07 .280E-05 .131E-07 23 0 19.0 0.19000000E+02 0.19000000E+02 .152E-06 .741E-09 .516E-07 .288E-05 .141E-07 23 0 19.5 0.19500000E+02 0.19500000E+02 .152E-06 .679E-09 .515E-07 .295E-05 .132E-07 23 0 20.0 0.20000000E+02 0.20000000E+02 .152E-06 .729E-09 .517E-07 .303E-05 .146E-07 23 0 30.0 0.30000000E+02 0.30000000E+02 .152E-06 .712E-09 .516E-07 .455E-05 .214E-07 23 0 35.0 0.35000000E+02 0.35000000E+02 .152E-06 .745E-09 .516E-07 .531E-05 .261E-07 23 0 40.0 0.40000000E+02 0.40000000E+02 .152E-06 .729E-09 .517E-07 .607E-05 .292E-07 23 0 45.0 0.45000000E+02 0.45000000E+02 .152E-06 .714E-09 .516E-07 .682E-05 .321E-07 23 0 50.0 0.50000000E+02 0.50000000E+02 .152E-06 .750E-09 .516E-07 .758E-05 .375E-07 23 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 7 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.84147098E+00 0.84147098E+00 .214E-06 .886E-09 .114E-06 .180E-06 .746E-09 23 0 1.5 0.99749499E+00 0.99749499E+00 .129E-06 .113E-09 .294E-07 .129E-06 .112E-09 25 0 2.0 0.90929743E+00 0.90929743E+00 .157E-06 .225E-09 .570E-07 .143E-06 .205E-09 25 0 2.5 0.59847214E+00 0.59847214E+00 .106E-06 .163E-09 .593E-08 .634E-07 .975E-10 27 0 3.0 0.14112001E+00 0.14112001E+00 .127E-06 .252E-08 .273E-07 .180E-07 .355E-09 27 0 3.5 -.35078323E+00 -.35078323E+00 .116E-06 .617E-09 .159E-07 .407E-07 .217E-09 27 0 4.0 -.75680250E+00 -.75680250E+00 .107E-06 .124E-09 .670E-08 .808E-07 .935E-10 27 0 4.5 -.97753012E+00 -.97753012E+00 .103E-06 .200E-08 .292E-08 .101E-06 .195E-08 27 0 5.0 -.95892428E+00 -.95892427E+00 .122E-06 .495E-09 .219E-07 .117E-06 .475E-09 27 0 5.5 -.70554033E+00 -.70554033E+00 .187E-06 .719E-09 .869E-07 .132E-06 .507E-09 27 0 6.0 -.27941550E+00 -.27941550E+00 .172E-06 .162E-09 .717E-07 .480E-07 .452E-10 29 0 6.5 0.21511999E+00 0.21511999E+00 .105E-06 .748E-10 .512E-08 .226E-07 .161E-10 31 0 7.0 0.65698660E+00 0.65698660E+00 .196E-06 .345E-09 .964E-07 .129E-06 .227E-09 29 0 7.5 0.93799998E+00 0.93799998E+00 .105E-06 .187E-09 .517E-08 .987E-07 .176E-09 31 0 8.0 0.98935825E+00 0.98935825E+00 .110E-06 .244E-09 .101E-07 .109E-06 .241E-09 31 0 8.5 0.79848711E+00 0.79848711E+00 .126E-06 .539E-09 .257E-07 .100E-06 .431E-09 31 0 9.0 0.41211849E+00 0.41211849E+00 .195E-06 .208E-08 .953E-07 .805E-07 .859E-09 31 0 9.5 -.75151120E-01 -.75151120E-01 .128E-06 .880E-09 .278E-07 .961E-08 .661E-10 35 0 10.0 -.54402111E+00 -.54402111E+00 .132E-06 .310E-08 .323E-07 .720E-07 .168E-08 31 0 10.5 -.87969575E+00 -.87969576E+00 .130E-06 .682E-08 .304E-07 .115E-06 .600E-08 31 0 11.0 -.99999021E+00 -.99999021E+00 .118E-06 .297E-10 .178E-07 .118E-06 .297E-10 33 0 11.5 -.87545217E+00 -.87545217E+00 .210E-06 .336E-10 .110E-06 .184E-06 .294E-10 33 0 12.0 -.53657292E+00 -.53657292E+00 .101E-06 .829E-10 .875E-09 .541E-07 .445E-10 37 0 12.5 -.66321897E-01 -.66321897E-01 .114E-06 .839E-09 .135E-07 .753E-08 .556E-10 37 0 13.0 0.42016704E+00 0.42016704E+00 .196E-06 .158E-08 .961E-07 .824E-07 .662E-09 35 0 13.5 0.80378443E+00 0.80378443E+00 .119E-06 .264E-08 .186E-07 .953E-07 .212E-08 35 0 14.0 0.99060735E+00 0.99060736E+00 .151E-06 .121E-08 .508E-07 .149E-06 .120E-08 35 0 14.5 0.93489506E+00 0.93489506E+00 .144E-06 .906E-09 .437E-07 .134E-06 .847E-09 37 0 15.0 0.65028784E+00 0.65028784E+00 .141E-06 .621E-08 .406E-07 .915E-07 .404E-08 37 0 15.5 0.20646748E+00 0.20646748E+00 .190E-06 .152E-08 .896E-07 .391E-07 .313E-09 39 0 16.0 -.28790332E+00 -.28790332E+00 .104E-06 .882E-11 .357E-08 .298E-07 .254E-11 43 0 16.5 -.71178534E+00 -.71178534E+00 .103E-06 .192E-09 .304E-08 .733E-07 .137E-09 41 0 17.0 -.96139749E+00 -.96139749E+00 .109E-06 .516E-09 .857E-08 .104E-06 .496E-09 41 0 17.5 -.97562601E+00 -.97562601E+00 .108E-06 .421E-09 .849E-08 .106E-06 .411E-09 41 0 18.0 -.75098725E+00 -.75098725E+00 .179E-06 .185E-08 .788E-07 .134E-06 .139E-08 41 0 18.5 -.34248062E+00 -.34248062E+00 .148E-06 .243E-08 .481E-07 .507E-07 .831E-09 41 0 19.0 0.14987721E+00 0.14987721E+00 .164E-06 .226E-08 .642E-07 .246E-07 .339E-09 43 0 19.5 0.60553987E+00 0.60553987E+00 .126E-06 .200E-08 .262E-07 .764E-07 .121E-08 43 0 20.0 0.91294525E+00 0.91294525E+00 .208E-06 .111E-08 .108E-06 .190E-06 .101E-08 41 0 30.0 -.98803162E+00 -.98803162E+00 .107E-06 .277E-09 .661E-08 .105E-06 .274E-09 57 0 35.0 -.42818267E+00 -.42818267E+00 .100E-06 .404E-08 .000E+00 .428E-07 .173E-08 65 0 40.0 0.74510911E+00 0.74511316E+00 .100E-06 .543E-05 .000E+00 .745E-07 .405E-05 69 0 45.0 0.85089266E+00 0.85090352E+00 .100E-06 .128E-04 .000E+00 .851E-07 .109E-04 73 0 50.0 -.26237883E+00 -.26237485E+00 .100E-06 .152E-04 .000E+00 .262E-07 .398E-05 79 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 8 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.60653066E+00 0.60653066E+00 .110E-06 .395E-09 .105E-07 .670E-07 .240E-09 25 0 1.5 0.47236655E+00 0.47236655E+00 .125E-06 .925E-09 .250E-07 .590E-07 .437E-09 25 0 2.0 0.36787944E+00 0.36787944E+00 .136E-06 .529E-09 .361E-07 .501E-07 .194E-09 25 0 2.5 0.28650480E+00 0.28650480E+00 .167E-06 .321E-09 .671E-07 .479E-07 .921E-10 25 0 3.0 0.22313016E+00 0.22313016E+00 .211E-06 .613E-08 .111E-06 .470E-07 .137E-08 23 0 3.5 0.17377394E+00 0.17377394E+00 .117E-06 .948E-09 .173E-07 .204E-07 .165E-09 27 0 4.0 0.13533528E+00 0.13533528E+00 .116E-06 .381E-09 .161E-07 .157E-07 .516E-10 27 0 4.5 0.10539922E+00 0.10539922E+00 .104E-06 .127E-08 .388E-08 .109E-07 .133E-09 27 0 5.0 0.82084998E-01 0.82084999E-01 .119E-06 .248E-08 .193E-07 .980E-08 .203E-09 27 0 5.5 0.63927861E-01 0.63927861E-01 .115E-06 .611E-09 .148E-07 .734E-08 .391E-10 27 0 6.0 0.49787068E-01 0.49787068E-01 .128E-06 .351E-09 .277E-07 .636E-08 .175E-10 27 0 6.5 0.38774208E-01 0.38774208E-01 .161E-06 .421E-08 .606E-07 .623E-08 .163E-09 27 0 7.0 0.30197383E-01 0.30197383E-01 .142E-06 .287E-08 .417E-07 .428E-08 .866E-10 27 0 7.5 0.23517746E-01 0.23517746E-01 .106E-06 .783E-11 .633E-08 .250E-08 .184E-12 31 0 8.0 0.18315639E-01 0.18315639E-01 .193E-06 .736E-08 .934E-07 .354E-08 .135E-09 27 0 8.5 0.14264234E-01 0.14264234E-01 .185E-06 .118E-07 .850E-07 .264E-08 .168E-09 27 0 9.0 0.11108997E-01 0.11108997E-01 .119E-06 .168E-08 .195E-07 .133E-08 .187E-10 29 0 9.5 0.86516952E-02 0.86516952E-02 .113E-06 .544E-08 .127E-07 .975E-09 .470E-10 29 0 10.0 0.67379470E-02 0.67379470E-02 .133E-06 .306E-08 .328E-07 .895E-09 .206E-10 29 0 10.5 0.52475185E-02 0.52475184E-02 .164E-06 .194E-07 .644E-07 .863E-09 .102E-09 27 0 11.0 0.40867713E-02 0.40867714E-02 .213E-06 .323E-07 .113E-06 .869E-09 .132E-09 29 0 11.5 0.31827809E-02 0.31827808E-02 .154E-06 .344E-07 .538E-07 .489E-09 .109E-09 29 0 12.0 0.24787523E-02 0.24787522E-02 .143E-06 .449E-07 .429E-07 .354E-09 .111E-09 29 0 12.5 0.19304541E-02 0.19304541E-02 .182E-06 .169E-07 .819E-07 .351E-09 .326E-10 29 0 13.0 0.15034392E-02 0.15034392E-02 .113E-06 .108E-07 .133E-07 .170E-09 .162E-10 31 0 13.5 0.11708796E-02 0.11708796E-02 .129E-06 .143E-07 .287E-07 .151E-09 .167E-10 31 0 14.0 0.91188197E-03 0.91188197E-03 .165E-06 .506E-08 .654E-07 .151E-09 .462E-11 31 0 14.5 0.71017438E-03 0.71017439E-03 .284E-06 .159E-07 .184E-06 .202E-09 .113E-10 31 0 15.0 0.55308437E-03 0.55308437E-03 .179E-06 .717E-08 .794E-07 .992E-10 .396E-11 31 0 15.5 0.43074254E-03 0.43074254E-03 .148E-06 .112E-07 .478E-07 .637E-10 .481E-11 33 0 16.0 0.33546263E-03 0.33546263E-03 .110E-06 .404E-08 .101E-07 .369E-10 .136E-11 35 0 16.5 0.26125853E-03 0.26125856E-03 .187E-06 .973E-07 .868E-07 .488E-10 .254E-10 31 0 17.0 0.20346837E-03 0.20346837E-03 .139E-06 .623E-08 .388E-07 .282E-10 .127E-11 35 0 17.5 0.15846132E-03 0.15846133E-03 .170E-06 .125E-07 .696E-07 .269E-10 .198E-11 31 0 18.0 0.12340981E-03 0.12340980E-03 .204E-06 .126E-07 .104E-06 .251E-10 .156E-11 33 0 18.5 0.96111655E-04 0.96111652E-04 .159E-06 .310E-07 .591E-07 .153E-10 .298E-11 35 0 19.0 0.74851840E-04 0.74851830E-04 .175E-06 .132E-06 .749E-07 .131E-10 .986E-11 33 0 19.5 0.58294664E-04 0.58294664E-04 .121E-06 .375E-08 .211E-07 .706E-11 .218E-12 37 0 20.0 0.45399935E-04 0.45399930E-04 .153E-06 .126E-06 .534E-07 .697E-11 .573E-11 37 0 30.0 0.30590293E-06 0.30590232E-06 .269E-04 .200E-05 .268E-04 .822E-11 .612E-12 35 0 35.0 0.25110147E-07 0.25109992E-07 .100E-06 .618E-05 .000E+00 .251E-14 .155E-12 43 0 40.0 0.20594638E-08 0.20611536E-08 .194E-03 .820E-03 .194E-03 .399E-12 .169E-11 33 0 45.0 0.16915085E-09 0.16918979E-09 .217E-02 .230E-03 .217E-02 .368E-12 .389E-13 35 0 50.0 0.13293768E-10 0.13887944E-10 .100E-06 .428E-01 .208E-14 .133E-17 .594E-12 37 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 10 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.20666985E-01 0.20666985E-01 .109E-06 .383E-10 .940E-08 .226E-08 .791E-12 25 0 1.5 0.42677557E-01 0.42677557E-01 .114E-06 .327E-10 .137E-07 .485E-08 .139E-11 25 0 2.0 0.53990966E-01 0.53990967E-01 .101E-06 .260E-09 .140E-08 .547E-08 .140E-10 25 0 2.5 0.57633351E-01 0.57633351E-01 .120E-06 .239E-09 .196E-07 .690E-08 .138E-10 25 0 3.0 0.57241877E-01 0.57241877E-01 .122E-06 .283E-09 .218E-07 .697E-08 .162E-10 25 0 3.5 0.54956168E-01 0.54956168E-01 .117E-06 .160E-08 .175E-07 .646E-08 .882E-10 25 0 4.0 0.51888437E-01 0.51888437E-01 .106E-06 .933E-09 .577E-08 .549E-08 .484E-10 25 0 4.5 0.48595578E-01 0.48595578E-01 .114E-06 .177E-10 .137E-07 .552E-08 .861E-12 25 0 5.0 0.45348661E-01 0.45348661E-01 .208E-06 .438E-08 .108E-06 .945E-08 .199E-09 23 0 5.5 0.42272749E-01 0.42272749E-01 .179E-06 .416E-08 .788E-07 .756E-08 .176E-09 23 0 6.0 0.39418358E-01 0.39418358E-01 .136E-06 .128E-08 .360E-07 .536E-08 .506E-10 25 0 6.5 0.36798226E-01 0.36798226E-01 .138E-06 .480E-10 .376E-07 .506E-08 .177E-11 25 0 7.0 0.34406439E-01 0.34406439E-01 .140E-06 .829E-10 .396E-07 .480E-08 .285E-11 25 0 7.5 0.32228452E-01 0.32228452E-01 .142E-06 .110E-08 .421E-07 .458E-08 .355E-10 25 0 8.0 0.30246341E-01 0.30246341E-01 .141E-06 .803E-09 .411E-07 .427E-08 .243E-10 25 0 8.5 0.28441520E-01 0.28441520E-01 .142E-06 .121E-08 .422E-07 .404E-08 .345E-10 25 0 9.0 0.26796096E-01 0.26796096E-01 .134E-06 .392E-08 .335E-07 .358E-08 .105E-09 25 0 9.5 0.25293493E-01 0.25293493E-01 .139E-06 .186E-08 .386E-07 .351E-08 .471E-10 25 0 10.0 0.23918683E-01 0.23918683E-01 .144E-06 .626E-09 .443E-07 .345E-08 .150E-10 25 0 10.5 0.22658210E-01 0.22658210E-01 .137E-06 .727E-09 .372E-07 .311E-08 .165E-10 25 0 11.0 0.21500114E-01 0.21500114E-01 .128E-06 .943E-09 .277E-07 .275E-08 .203E-10 25 0 11.5 0.20433810E-01 0.20433810E-01 .121E-06 .252E-08 .211E-07 .248E-08 .514E-10 25 0 12.0 0.19449944E-01 0.19449944E-01 .117E-06 .161E-08 .167E-07 .227E-08 .313E-10 25 0 12.5 0.18540259E-01 0.18540259E-01 .134E-06 .130E-08 .338E-07 .248E-08 .241E-10 25 0 13.0 0.17697461E-01 0.17697461E-01 .148E-06 .123E-08 .484E-07 .263E-08 .218E-10 25 0 13.5 0.16915100E-01 0.16915100E-01 .124E-06 .703E-09 .240E-07 .210E-08 .119E-10 25 0 14.0 0.16187466E-01 0.16187466E-01 .140E-06 .458E-09 .402E-07 .227E-08 .741E-11 25 0 14.5 0.15509496E-01 0.15509496E-01 .107E-06 .181E-08 .732E-08 .166E-08 .281E-10 25 0 15.0 0.14876690E-01 0.14876690E-01 .123E-06 .141E-08 .225E-07 .182E-08 .210E-10 25 0 15.5 0.14285042E-01 0.14285042E-01 .136E-06 .238E-08 .355E-07 .194E-08 .340E-10 25 0 16.0 0.13730978E-01 0.13730978E-01 .127E-06 .665E-09 .271E-07 .175E-08 .914E-11 25 0 16.5 0.13211302E-01 0.13211302E-01 .118E-06 .258E-09 .179E-07 .156E-08 .341E-11 25 0 17.0 0.12723153E-01 0.12723153E-01 .111E-06 .124E-08 .108E-07 .141E-08 .158E-10 25 0 17.5 0.12263959E-01 0.12263959E-01 .140E-06 .270E-08 .403E-07 .172E-08 .331E-10 25 0 18.0 0.11831408E-01 0.11831408E-01 .164E-06 .499E-08 .642E-07 .194E-08 .590E-10 25 0 18.5 0.11423415E-01 0.11423415E-01 .140E-06 .914E-09 .404E-07 .160E-08 .104E-10 25 0 19.0 0.11038098E-01 0.11038098E-01 .128E-06 .393E-08 .281E-07 .141E-08 .434E-10 25 0 19.5 0.10673752E-01 0.10673752E-01 .115E-06 .128E-08 .150E-07 .123E-08 .137E-10 25 0 20.0 0.10328831E-01 0.10328831E-01 .140E-06 .109E-08 .401E-07 .145E-08 .113E-10 25 0 30.0 0.60099000E-02 0.60099000E-02 .202E-06 .502E-08 .102E-06 .122E-08 .302E-10 25 0 35.0 0.48609295E-02 0.48609297E-02 .175E-06 .349E-07 .748E-07 .850E-09 .170E-09 23 0 40.0 0.40358555E-02 0.40358556E-02 .153E-06 .355E-07 .533E-07 .619E-09 .143E-09 23 0 45.0 0.34200491E-02 0.34200490E-02 .200E-06 .497E-08 .100E-06 .684E-09 .170E-10 25 0 50.0 0.29461611E-02 0.29461611E-02 .192E-06 .115E-07 .917E-07 .565E-09 .340E-10 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 11 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.84147099E+00 0.84147098E+00 .119E-06 .110E-08 .192E-07 .100E-06 .928E-09 25 0 1.5 0.66499666E+00 0.66499666E+00 .139E-06 .225E-08 .393E-07 .926E-07 .150E-08 25 0 2.0 0.45464871E+00 0.45464871E+00 .147E-06 .101E-08 .467E-07 .667E-07 .460E-09 25 0 2.5 0.23938886E+00 0.23938886E+00 .146E-06 .220E-08 .456E-07 .349E-07 .526E-09 27 0 3.0 0.47040003E-01 0.47040003E-01 .144E-06 .536E-08 .437E-07 .676E-08 .252E-09 29 0 3.5 -.10022378E+00 -.10022378E+00 .191E-06 .559E-08 .914E-07 .192E-07 .560E-09 27 0 4.0 -.18920062E+00 -.18920062E+00 .146E-06 .126E-08 .459E-07 .276E-07 .239E-09 27 0 4.5 -.21722891E+00 -.21722892E+00 .268E-06 .908E-08 .168E-06 .582E-07 .197E-08 27 0 5.0 -.19178485E+00 -.19178485E+00 .129E-06 .164E-09 .291E-07 .248E-07 .315E-10 29 0 5.5 -.12828006E+00 -.12828006E+00 .200E-06 .203E-07 .100E-06 .257E-07 .260E-08 29 0 6.0 -.46569250E-01 -.46569250E-01 .197E-06 .284E-08 .973E-07 .919E-08 .132E-09 29 0 6.5 0.33095383E-01 0.33095383E-01 .109E-06 .352E-08 .866E-08 .360E-08 .117E-09 33 0 7.0 0.93855228E-01 0.93855228E-01 .217E-06 .370E-09 .117E-06 .204E-07 .348E-10 31 0 7.5 0.12506667E+00 0.12506666E+00 .153E-06 .117E-07 .532E-07 .192E-07 .146E-08 29 0 8.0 0.12366978E+00 0.12366978E+00 .118E-06 .133E-08 .178E-07 .146E-07 .165E-09 33 0 8.5 0.93939661E-01 0.93939660E-01 .103E-06 .413E-08 .327E-08 .970E-08 .388E-09 33 0 9.0 0.45790943E-01 0.45790943E-01 .169E-06 .600E-08 .692E-07 .775E-08 .275E-09 33 0 9.5 -.79106442E-02 -.79106443E-02 .108E-06 .128E-08 .758E-08 .851E-09 .101E-10 37 0 10.0 -.54402112E-01 -.54402111E-01 .186E-06 .102E-07 .863E-07 .101E-07 .555E-09 33 0 10.5 -.83780549E-01 -.83780549E-01 .163E-06 .388E-08 .628E-07 .136E-07 .325E-09 35 0 11.0 -.90908200E-01 -.90908201E-01 .172E-06 .354E-08 .717E-07 .156E-07 .322E-09 35 0 11.5 -.76126276E-01 -.76126276E-01 .127E-06 .457E-08 .272E-07 .968E-08 .348E-09 35 0 12.0 -.44714410E-01 -.44714410E-01 .172E-06 .386E-09 .721E-07 .769E-08 .173E-10 35 0 12.5 -.53057519E-02 -.53057518E-02 .129E-06 .278E-07 .287E-07 .683E-09 .148E-09 39 0 13.0 0.32320541E-01 0.32320541E-01 .146E-06 .883E-09 .462E-07 .473E-08 .285E-10 39 0 13.5 0.59539587E-01 0.59539587E-01 .163E-06 .346E-08 .630E-07 .971E-08 .206E-09 37 0 14.0 0.70757668E-01 0.70757668E-01 .161E-06 .466E-09 .612E-07 .114E-07 .329E-10 39 0 14.5 0.64475521E-01 0.64475521E-01 .159E-06 .471E-08 .589E-07 .102E-07 .304E-09 37 0 15.0 0.43352522E-01 0.43352523E-01 .164E-06 .148E-07 .636E-07 .709E-08 .643E-09 37 0 15.5 0.13320483E-01 0.13320483E-01 .218E-06 .556E-08 .118E-06 .291E-08 .740E-10 41 0 16.0 -.17993957E-01 -.17993957E-01 .135E-06 .295E-08 .348E-07 .242E-08 .531E-10 43 0 16.5 -.43138506E-01 -.43138506E-01 .150E-06 .211E-08 .504E-07 .649E-08 .909E-10 41 0 17.0 -.56552794E-01 -.56552794E-01 .130E-06 .458E-09 .304E-07 .737E-08 .259E-10 43 0 17.5 -.55750057E-01 -.55750057E-01 .118E-06 .543E-08 .176E-07 .656E-08 .303E-09 43 0 18.0 -.41721513E-01 -.41721514E-01 .222E-06 .167E-07 .122E-06 .928E-08 .698E-09 41 0 18.5 -.18512466E-01 -.18512466E-01 .104E-06 .130E-09 .446E-08 .193E-08 .241E-11 47 0 19.0 0.78882742E-02 0.78882742E-02 .114E-06 .488E-08 .141E-07 .900E-09 .385E-10 47 0 19.5 0.31053327E-01 0.31053327E-01 .141E-06 .191E-07 .413E-07 .439E-08 .594E-09 43 0 20.0 0.45647263E-01 0.45647263E-01 .142E-06 .525E-08 .423E-07 .650E-08 .240E-09 45 0 30.0 -.32934388E-01 -.32934387E-01 .186E-06 .216E-08 .863E-07 .614E-08 .710E-10 59 0 35.0 -.12233791E-01 -.12233791E-01 .132E-06 .833E-09 .320E-07 .161E-08 .102E-10 65 0 40.0 0.18627827E-01 0.18627829E-01 .244E-06 .875E-07 .144E-06 .454E-08 .163E-08 71 0 45.0 0.18909015E-01 0.18908967E-01 .100E-06 .252E-05 .000E+00 .189E-08 .476E-07 79 0 50.0 -.52473572E-02 -.52474971E-02 .618E-06 .267E-04 .518E-06 .325E-08 .140E-06 83 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 12 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.68893817E+00 0.68893817E+00 .122E-06 .302E-08 .218E-07 .839E-07 .208E-08 25 0 1.5 0.73896246E+00 0.73896246E+00 .136E-06 .416E-08 .363E-07 .101E-06 .308E-08 25 0 2.0 0.60952029E+00 0.60952029E+00 .169E-06 .662E-08 .686E-07 .103E-06 .403E-08 25 0 2.5 0.36299170E+00 0.36299170E+00 .102E-06 .754E-08 .174E-08 .369E-07 .274E-08 27 0 3.0 0.77448302E-01 0.77448303E-01 .122E-06 .105E-07 .224E-07 .948E-08 .810E-09 27 0 3.5 -.17419379E+00 -.17419380E+00 .141E-06 .956E-08 .411E-07 .246E-07 .166E-08 27 0 4.0 -.34005328E+00 -.34005328E+00 .234E-06 .833E-08 .134E-06 .796E-07 .283E-08 25 0 4.5 -.39743408E+00 -.39743409E+00 .179E-06 .129E-07 .787E-07 .710E-07 .514E-08 27 0 5.0 -.35276852E+00 -.35276853E+00 .116E-06 .143E-07 .164E-07 .410E-07 .505E-08 29 0 5.5 -.23485397E+00 -.23485397E+00 .117E-06 .168E-07 .173E-07 .275E-07 .395E-08 29 0 6.0 -.84158329E-01 -.84158331E-01 .181E-06 .167E-07 .814E-07 .153E-07 .141E-08 29 0 6.5 0.58627035E-01 0.58627036E-01 .161E-06 .204E-07 .608E-07 .943E-08 .120E-08 31 0 7.0 0.16201090E+00 0.16201090E+00 .132E-06 .276E-07 .320E-07 .214E-07 .448E-08 29 0 7.5 0.20929608E+00 0.20929609E+00 .167E-06 .208E-07 .671E-07 .350E-07 .434E-08 31 0 8.0 0.19974798E+00 0.19974799E+00 .125E-06 .236E-07 .245E-07 .249E-07 .471E-08 31 0 8.5 0.14587044E+00 0.14587044E+00 .107E-06 .260E-07 .714E-08 .156E-07 .379E-08 33 0 9.0 0.68122725E-01 0.68122727E-01 .151E-06 .300E-07 .510E-07 .103E-07 .205E-08 33 0 9.5 -.11240249E-01 -.11240249E-01 .177E-06 .350E-07 .767E-07 .199E-08 .394E-09 35 0 10.0 -.73625249E-01 -.73625251E-01 .137E-06 .308E-07 .373E-07 .101E-07 .227E-08 35 0 10.5 -.10772440E+00 -.10772440E+00 .207E-06 .490E-07 .107E-06 .223E-07 .527E-08 33 0 11.0 -.11080207E+00 -.11080207E+00 .139E-06 .325E-07 .393E-07 .154E-07 .360E-08 35 0 11.5 -.87771820E-01 -.87771823E-01 .123E-06 .344E-07 .233E-07 .108E-07 .302E-08 35 0 12.0 -.48676795E-01 -.48676797E-01 .111E-06 .339E-07 .110E-07 .540E-08 .165E-08 37 0 12.5 -.54440341E-02 -.54440329E-02 .226E-06 .233E-06 .126E-06 .123E-08 .127E-08 35 0 13.0 0.31207308E-01 0.31207309E-01 .175E-06 .381E-07 .746E-07 .545E-08 .119E-08 37 0 13.5 0.54018741E-01 0.54018745E-01 .232E-06 .701E-07 .132E-06 .125E-07 .378E-08 37 0 14.0 0.60238893E-01 0.60238895E-01 .116E-06 .418E-07 .158E-07 .697E-08 .252E-08 41 0 14.5 0.51440933E-01 0.51440936E-01 .192E-06 .678E-07 .918E-07 .987E-08 .349E-08 35 0 15.0 0.32375924E-01 0.32375925E-01 .114E-06 .439E-07 .143E-07 .370E-08 .142E-08 43 0 15.5 0.93011950E-02 0.93011954E-02 .138E-06 .434E-07 .383E-07 .129E-08 .404E-09 43 0 16.0 -.11735573E-01 -.11735574E-01 .146E-06 .481E-07 .464E-07 .172E-08 .565E-09 43 0 16.5 -.26252897E-01 -.26252898E-01 .137E-06 .499E-07 .366E-07 .359E-08 .131E-08 43 0 17.0 -.32084976E-01 -.32084978E-01 .157E-06 .489E-07 .573E-07 .505E-08 .157E-08 43 0 17.5 -.29461351E-01 -.29461353E-01 .214E-06 .494E-07 .114E-06 .630E-08 .145E-08 43 0 18.0 -.20519766E-01 -.20519767E-01 .177E-06 .547E-07 .772E-07 .364E-08 .112E-08 45 0 18.5 -.84673282E-02 -.84673286E-02 .133E-06 .479E-07 .326E-07 .112E-08 .405E-09 47 0 19.0 0.33528687E-02 0.33528689E-02 .125E-06 .520E-07 .250E-07 .419E-09 .174E-09 49 0 19.5 0.12257284E-01 0.12257284E-01 .121E-06 .617E-07 .208E-07 .148E-08 .757E-09 47 0 20.0 0.16721175E-01 0.16721176E-01 .187E-06 .595E-07 .871E-07 .313E-08 .994E-09 47 0 30.0 -.24490853E-02 -.24490855E-02 .185E-06 .901E-07 .854E-07 .454E-09 .221E-09 63 0 35.0 -.39045202E-03 -.39045205E-03 .118E-06 .954E-07 .183E-07 .462E-10 .372E-10 73 0 40.0 0.24995759E-03 0.24995762E-03 .150E-06 .134E-06 .498E-07 .374E-10 .335E-10 77 0 45.0 0.10500981E-03 0.10500984E-03 .159E-06 .252E-06 .595E-07 .167E-10 .264E-10 81 0 50.0 -.11911797E-04 -.11911800E-04 .134E-06 .271E-06 .342E-07 .160E-11 .323E-11 99 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 13 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.50000000E+00 0.50000000E+00 .195E-06 .680E-10 .955E-07 .977E-07 .340E-10 23 0 1.5 0.11250000E+01 0.11250000E+01 .195E-06 .720E-10 .955E-07 .220E-06 .810E-10 23 0 2.0 0.20000000E+01 0.20000000E+01 .195E-06 .680E-10 .955E-07 .391E-06 .136E-09 23 0 2.5 0.31250000E+01 0.31250000E+01 .195E-06 .710E-10 .955E-07 .611E-06 .222E-09 23 0 3.0 0.45000000E+01 0.45000000E+01 .195E-06 .720E-10 .955E-07 .880E-06 .324E-09 23 0 3.5 0.61250000E+01 0.61250000E+01 .195E-06 .686E-10 .955E-07 .120E-05 .420E-09 23 0 4.0 0.80000000E+01 0.80000000E+01 .195E-06 .680E-10 .955E-07 .156E-05 .544E-09 23 0 4.5 0.10125000E+02 0.10125000E+02 .195E-06 .704E-10 .955E-07 .198E-05 .713E-09 23 0 5.0 0.12500000E+02 0.12500000E+02 .195E-06 .710E-10 .955E-07 .244E-05 .888E-09 23 0 5.5 0.15125000E+02 0.15125000E+02 .195E-06 .748E-10 .955E-07 .296E-05 .113E-08 23 0 6.0 0.18000000E+02 0.18000000E+02 .195E-06 .720E-10 .955E-07 .352E-05 .130E-08 23 0 6.5 0.21125000E+02 0.21125000E+02 .195E-06 .695E-10 .955E-07 .413E-05 .147E-08 23 0 7.0 0.24500000E+02 0.24500000E+02 .195E-06 .686E-10 .955E-07 .479E-05 .168E-08 23 0 7.5 0.28125000E+02 0.28125000E+02 .195E-06 .680E-10 .955E-07 .550E-05 .191E-08 23 0 8.0 0.32000000E+02 0.32000000E+02 .195E-06 .680E-10 .955E-07 .626E-05 .218E-08 23 0 8.5 0.36125000E+02 0.36125000E+02 .195E-06 .672E-10 .955E-07 .706E-05 .243E-08 23 0 9.0 0.40500000E+02 0.40500000E+02 .195E-06 .704E-10 .955E-07 .792E-05 .285E-08 23 0 9.5 0.45125000E+02 0.45125000E+02 .195E-06 .713E-10 .955E-07 .882E-05 .322E-08 23 0 10.0 0.50000000E+02 0.50000000E+02 .195E-06 .710E-10 .955E-07 .977E-05 .355E-08 23 0 10.5 0.55125000E+02 0.55125000E+02 .195E-06 .707E-10 .955E-07 .108E-04 .390E-08 23 0 11.0 0.60500000E+02 0.60500000E+02 .195E-06 .748E-10 .955E-07 .118E-04 .453E-08 23 0 11.5 0.66125000E+02 0.66125000E+02 .195E-06 .678E-10 .955E-07 .129E-04 .449E-08 23 0 12.0 0.72000000E+02 0.72000000E+02 .195E-06 .720E-10 .955E-07 .141E-04 .519E-08 23 0 12.5 0.78125000E+02 0.78125000E+02 .195E-06 .708E-10 .955E-07 .153E-04 .553E-08 23 0 13.0 0.84500000E+02 0.84500000E+02 .195E-06 .695E-10 .955E-07 .165E-04 .588E-08 23 0 13.5 0.91125000E+02 0.91125000E+02 .195E-06 .747E-10 .955E-07 .178E-04 .681E-08 23 0 14.0 0.98000000E+02 0.98000000E+02 .195E-06 .686E-10 .955E-07 .192E-04 .672E-08 23 0 14.5 0.10512500E+03 0.10512500E+03 .196E-06 .634E-10 .955E-07 .206E-04 .666E-08 23 0 15.0 0.11250000E+03 0.11250000E+03 .195E-06 .680E-10 .955E-07 .220E-04 .765E-08 23 0 15.5 0.12012500E+03 0.12012500E+03 .195E-06 .797E-10 .955E-07 .235E-04 .957E-08 23 0 16.0 0.12800000E+03 0.12800000E+03 .195E-06 .680E-10 .955E-07 .250E-04 .870E-08 23 0 16.5 0.13612500E+03 0.13612500E+03 .195E-06 .757E-10 .955E-07 .266E-04 .103E-07 23 0 17.0 0.14450000E+03 0.14450000E+03 .195E-06 .672E-10 .955E-07 .282E-04 .970E-08 23 0 17.5 0.15312500E+03 0.15312500E+03 .196E-06 .667E-10 .955E-07 .299E-04 .102E-07 23 0 18.0 0.16200000E+03 0.16200000E+03 .195E-06 .704E-10 .955E-07 .317E-04 .114E-07 23 0 18.5 0.17112500E+03 0.17112500E+03 .195E-06 .662E-10 .955E-07 .335E-04 .113E-07 23 0 19.0 0.18050000E+03 0.18050000E+03 .195E-06 .713E-10 .955E-07 .353E-04 .129E-07 23 0 19.5 0.19012500E+03 0.19012500E+03 .196E-06 .653E-10 .955E-07 .372E-04 .124E-07 23 0 20.0 0.20000000E+03 0.20000000E+03 .195E-06 .710E-10 .955E-07 .391E-04 .142E-07 23 0 30.0 0.45000000E+03 0.45000000E+03 .195E-06 .680E-10 .955E-07 .880E-04 .306E-07 23 0 35.0 0.61250000E+03 0.61250000E+03 .196E-06 .667E-10 .955E-07 .120E-03 .409E-07 23 0 40.0 0.80000000E+03 0.80000000E+03 .195E-06 .710E-10 .955E-07 .156E-03 .568E-07 23 0 45.0 0.10125000E+04 0.10125000E+04 .195E-06 .775E-10 .955E-07 .198E-03 .785E-07 23 0 50.0 0.12500000E+04 0.12500000E+04 .195E-06 .708E-10 .955E-07 .244E-03 .885E-07 23 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 14 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 -.16779778E-17 0.00000000E+00 .670E+03 .168E-17 .670E+03 .112E-14 .168E-17 17 0 1.5 -.31396748E-15 0.00000000E+00 .257E+01 .314E-15 .257E+01 .808E-15 .314E-15 45 0 ERROR DETECTED , I = 3 IFAIL= -1 2.5 0.10000000E+01 0.10000000E+01 .121E-06 .334E-07 .213E-07 .121E-06 .334E-07 41 0 3.0 0.99999994E+00 0.10000000E+01 .214E-06 .585E-07 .114E-06 .214E-06 .585E-07 29 0 3.5 0.10000000E+01 0.10000000E+01 .111E-06 .942E-10 .114E-07 .111E-06 .942E-10 33 0 4.0 0.10000000E+01 0.10000000E+01 .147E-06 .147E-07 .466E-07 .147E-06 .147E-07 27 0 4.5 0.10000000E+01 0.10000000E+01 .130E-06 .376E-08 .305E-07 .130E-06 .376E-08 27 0 5.0 0.10000000E+01 0.10000000E+01 .201E-06 .134E-08 .101E-06 .201E-06 .134E-08 27 0 5.5 0.10000000E+01 0.10000000E+01 .117E-06 .195E-08 .167E-07 .117E-06 .195E-08 27 0 6.0 0.10000000E+01 0.10000000E+01 .148E-06 .370E-08 .482E-07 .148E-06 .370E-08 25 0 6.5 0.10000000E+01 0.10000000E+01 .155E-06 .397E-08 .553E-07 .155E-06 .397E-08 25 0 7.0 0.10000000E+01 0.10000000E+01 .192E-06 .258E-08 .923E-07 .192E-06 .258E-08 25 0 7.5 0.10000000E+01 0.10000000E+01 .181E-06 .500E-10 .813E-07 .181E-06 .500E-10 25 0 8.0 0.10000000E+01 0.10000000E+01 .163E-06 .501E-09 .633E-07 .163E-06 .501E-09 25 0 8.5 0.10000000E+01 0.10000000E+01 .145E-06 .217E-08 .455E-07 .145E-06 .217E-08 25 0 9.0 0.10000000E+01 0.10000000E+01 .101E-06 .422E-08 .144E-08 .101E-06 .422E-08 25 0 9.5 0.10000000E+01 0.10000000E+01 .117E-06 .162E-08 .170E-07 .117E-06 .162E-08 25 0 10.0 0.99999999E+00 0.10000000E+01 .200E-06 .797E-08 .100E-06 .200E-06 .797E-08 23 0 10.5 0.10000000E+01 0.10000000E+01 .148E-06 .779E-09 .479E-07 .148E-06 .779E-09 25 0 11.0 0.10000000E+01 0.10000000E+01 .144E-06 .150E-09 .438E-07 .144E-06 .150E-09 25 0 11.5 0.10000000E+01 0.10000000E+01 .151E-06 .437E-09 .508E-07 .151E-06 .437E-09 25 0 12.0 0.10000000E+01 0.10000000E+01 .151E-06 .405E-09 .509E-07 .151E-06 .405E-09 25 0 12.5 0.10000000E+01 0.10000000E+01 .150E-06 .878E-09 .500E-07 .150E-06 .878E-09 25 0 13.0 0.10000000E+01 0.10000000E+01 .151E-06 .377E-09 .507E-07 .151E-06 .377E-09 25 0 13.5 0.10000000E+01 0.10000000E+01 .141E-06 .144E-08 .407E-07 .141E-06 .144E-08 25 0 14.0 0.10000000E+01 0.10000000E+01 .142E-06 .130E-08 .419E-07 .142E-06 .130E-08 25 0 14.5 0.10000000E+01 0.10000000E+01 .138E-06 .609E-09 .380E-07 .138E-06 .609E-09 25 0 15.0 0.10000000E+01 0.10000000E+01 .130E-06 .149E-08 .300E-07 .130E-06 .149E-08 25 0 15.5 0.10000000E+01 0.10000000E+01 .127E-06 .406E-09 .269E-07 .127E-06 .406E-09 25 0 16.0 0.10000000E+01 0.10000000E+01 .119E-06 .479E-09 .186E-07 .119E-06 .479E-09 25 0 16.5 0.10000000E+01 0.10000000E+01 .121E-06 .199E-08 .212E-07 .121E-06 .199E-08 25 0 17.0 0.10000000E+01 0.10000000E+01 .110E-06 .165E-08 .988E-08 .110E-06 .165E-08 25 0 17.5 0.10000000E+01 0.10000000E+01 .113E-06 .890E-09 .128E-07 .113E-06 .890E-09 25 0 18.0 0.10000000E+01 0.10000000E+01 .103E-06 .133E-08 .294E-08 .103E-06 .133E-08 25 0 18.5 0.10000000E+01 0.10000000E+01 .103E-06 .446E-09 .319E-08 .103E-06 .446E-09 25 0 19.0 0.10000000E+01 0.10000000E+01 .107E-06 .102E-08 .713E-08 .107E-06 .102E-08 25 0 19.5 0.10000000E+01 0.10000000E+01 .107E-06 .984E-09 .662E-08 .107E-06 .984E-09 25 0 20.0 0.10000000E+01 0.10000000E+01 .109E-06 .690E-09 .937E-08 .109E-06 .690E-09 25 0 30.0 0.10000000E+01 0.10000000E+01 .131E-06 .365E-09 .313E-07 .131E-06 .365E-09 25 0 35.0 0.10000000E+01 0.10000000E+01 .137E-06 .352E-09 .369E-07 .137E-06 .352E-09 25 0 40.0 0.10000000E+01 0.10000000E+01 .136E-06 .756E-09 .359E-07 .136E-06 .756E-09 25 0 45.0 0.10000000E+01 0.10000000E+01 .130E-06 .117E-08 .300E-07 .130E-06 .117E-08 25 0 50.0 0.10000000E+01 0.10000000E+01 .132E-06 .815E-09 .325E-07 .132E-06 .815E-09 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 15 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** ERROR DETECTED , I = 1 IFAIL= -1 1.5 -.25151090E-11 0.00000000E+00 .500E+00 .252E-11 .500E+00 .126E-11 .252E-11 93 0 ERROR DETECTED , I = 3 IFAIL= -1 2.5 0.99999994E+00 0.10000000E+01 .123E-06 .595E-07 .232E-07 .123E-06 .595E-07 101 0 ERROR DETECTED , I = 5 IFAIL= -1 3.5 0.58961340E-11 0.00000000E+00 .400E+00 .590E-11 .400E+00 .236E-11 .590E-11 215 0 ERROR DETECTED , I = 7 IFAIL= -1 4.5 0.10000005E+01 0.10000000E+01 .138E-06 .478E-06 .376E-07 .138E-06 .478E-06 163 0 ERROR DETECTED , I = 9 IFAIL= -1 5.5 0.11705151E-10 0.00000000E+00 .727E+00 .117E-10 .727E+00 .851E-11 .117E-10 327 0 ERROR DETECTED , I = 11 IFAIL= -1 6.5 0.10000005E+01 0.10000000E+01 .220E-06 .517E-06 .120E-06 .220E-06 .517E-06 241 0 ERROR DETECTED , I = 13 IFAIL= -1 7.5 -.41956578E-10 0.00000000E+00 .930E-01 .420E-10 .930E-01 .390E-11 .420E-10 457 0 ERROR DETECTED , I = 15 IFAIL= -1 8.5 0.10000036E+01 0.10000000E+01 .231E-06 .355E-05 .131E-06 .231E-06 .355E-05 259 0 ERROR DETECTED , I = 17 IFAIL= -1 ERROR DETECTED , I = 18 IFAIL= -1 ERROR DETECTED , I = 19 IFAIL= -1 10.5 0.10001199E+01 0.10000000E+01 .200E-06 .120E-03 .100E-06 .200E-06 .120E-03 241 0 ERROR DETECTED , I = 21 IFAIL= -1 ERROR DETECTED , I = 22 IFAIL= -1 ERROR DETECTED , I = 23 IFAIL= -1 12.5 0.10132066E+01 0.10000000E+01 .151E-06 .132E-01 .511E-07 .153E-06 .132E-01 331 0 ERROR DETECTED , I = 25 IFAIL= -1 ERROR DETECTED , I = 26 IFAIL= -1 ERROR DETECTED , I = 27 IFAIL= -1 14.5 0.11366198E+01 0.10000000E+01 .189E-06 .137E+00 .893E-07 .215E-06 .137E+00 81 0 15.0 0.50000000E+00 0.50000000E+00 .201E-06 .849E-08 .101E-06 .101E-06 .424E-08 87 0 15.5 -.13661988E+00 0.00000000E+00 .258E-06 .137E+00 .158E-06 .352E-07 .137E+00 95 0 16.0 0.50000002E+00 0.50000000E+00 .163E-06 .314E-07 .632E-07 .816E-07 .157E-07 85 0 16.5 0.11366198E+01 0.10000000E+01 .207E-06 .137E+00 .107E-06 .235E-06 .137E+00 89 0 17.0 0.49999993E+00 0.50000000E+00 .124E-06 .131E-06 .238E-07 .619E-07 .654E-07 29 0 17.5 0.49999995E+00 0.00000000E+00 .102E-06 .500E+00 .215E-08 .511E-07 .500E+00 39 0 18.0 0.49999998E+00 0.50000000E+00 .211E-06 .412E-07 .111E-06 .105E-06 .206E-07 33 0 18.5 0.49999999E+00 0.10000000E+01 .157E-06 .500E+00 .573E-07 .787E-07 .500E+00 29 0 19.0 0.49999999E+00 0.50000000E+00 .145E-06 .112E-07 .446E-07 .723E-07 .562E-08 29 0 19.5 0.50000001E+00 0.00000000E+00 .222E-06 .500E+00 .122E-06 .111E-06 .500E+00 27 0 20.0 0.50000000E+00 0.50000000E+00 .198E-06 .383E-08 .977E-07 .989E-07 .191E-08 27 0 30.0 0.50000000E+00 0.50000000E+00 .137E-06 .785E-09 .370E-07 .685E-07 .393E-09 25 0 35.0 0.50000000E+00 0.50000000E+00 .133E-06 .219E-08 .334E-07 .667E-07 .109E-08 25 0 40.0 0.50000000E+00 0.50000000E+00 .128E-06 .315E-08 .284E-07 .642E-07 .157E-08 25 0 45.0 0.50000000E+00 0.50000000E+00 .127E-06 .140E-08 .267E-07 .634E-07 .699E-09 25 0 50.0 0.50000000E+00 0.50000000E+00 .119E-06 .146E-08 .191E-07 .596E-07 .732E-09 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 16 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.53350719E+00 0.53350720E+00 .125E-06 .668E-09 .246E-07 .665E-07 .357E-09 25 0 1.5 0.52542443E+00 0.52542443E+00 .136E-06 .329E-09 .358E-07 .714E-07 .173E-09 25 0 2.0 0.41927963E+00 0.41927963E+00 .151E-06 .314E-09 .515E-07 .635E-07 .132E-09 25 0 2.5 0.27410990E+00 0.27410990E+00 .162E-06 .479E-09 .620E-07 .444E-07 .131E-09 25 0 3.0 0.13324264E+00 0.13324264E+00 .164E-06 .215E-08 .643E-07 .219E-07 .286E-09 25 0 3.5 0.22128235E-01 0.22128235E-01 .126E-06 .148E-08 .257E-07 .278E-08 .326E-10 29 0 4.0 -.49529880E-01 -.49529880E-01 .177E-06 .294E-09 .768E-07 .876E-08 .145E-10 29 0 4.5 -.83448969E-01 -.83448969E-01 .111E-06 .473E-09 .114E-07 .929E-08 .394E-10 29 0 5.0 -.87942421E-01 -.87942421E-01 .110E-06 .130E-08 .101E-07 .968E-08 .115E-09 29 0 5.5 -.73722493E-01 -.73722493E-01 .234E-06 .519E-09 .134E-06 .172E-07 .383E-10 27 0 6.0 -.50892320E-01 -.50892318E-01 .256E-06 .264E-07 .156E-06 .130E-07 .135E-08 27 0 6.5 -.27238839E-01 -.27238839E-01 .195E-06 .107E-07 .951E-07 .531E-08 .292E-09 29 0 7.0 -.76437138E-02 -.76437137E-02 .126E-06 .523E-08 .262E-07 .965E-09 .400E-10 33 0 7.5 0.57141734E-02 0.57141734E-02 .118E-06 .505E-09 .181E-07 .675E-09 .289E-11 33 0 8.0 0.12715096E-01 0.12715096E-01 .191E-06 .698E-08 .909E-07 .243E-08 .888E-10 33 0 8.5 0.14511338E-01 0.14511338E-01 .175E-06 .147E-07 .746E-07 .253E-08 .213E-09 31 0 9.0 0.12804671E-01 0.12804671E-01 .150E-06 .658E-08 .496E-07 .192E-08 .843E-10 35 0 9.5 0.93022340E-02 0.93022340E-02 .198E-06 .342E-09 .982E-07 .184E-08 .318E-11 35 0 10.0 0.53854806E-02 0.53854806E-02 .116E-06 .621E-09 .158E-07 .623E-09 .334E-11 37 0 10.5 0.19721385E-02 0.19721385E-02 .134E-06 .490E-09 .335E-07 .263E-09 .966E-12 37 0 11.0 -.47816316E-03 -.47816316E-03 .133E-06 .636E-09 .333E-07 .637E-10 .304E-12 41 0 11.5 -.18722106E-02 -.18722105E-02 .103E-06 .841E-08 .334E-08 .193E-09 .157E-10 39 0 12.0 -.23569928E-02 -.23569927E-02 .160E-06 .133E-07 .598E-07 .377E-09 .313E-10 39 0 12.5 -.21968666E-02 -.21968666E-02 .178E-06 .925E-08 .777E-07 .390E-09 .203E-10 39 0 13.0 -.16764380E-02 -.16764380E-02 .205E-06 .254E-08 .105E-06 .344E-09 .426E-11 41 0 13.5 -.10377546E-02 -.10377546E-02 .135E-06 .211E-08 .350E-07 .140E-09 .219E-11 43 0 14.0 -.45041187E-03 -.45041187E-03 .121E-06 .457E-09 .213E-07 .546E-10 .206E-12 47 0 14.5 -.73821023E-05 -.73821019E-05 .368E-06 .573E-07 .268E-06 .272E-11 .423E-12 49 0 15.0 0.26275145E-03 0.26275147E-03 .227E-06 .628E-07 .127E-06 .598E-10 .165E-10 43 0 15.5 0.37596702E-03 0.37596702E-03 .108E-06 .194E-08 .773E-08 .405E-10 .728E-12 45 0 16.0 0.37219184E-03 0.37219184E-03 .188E-06 .108E-07 .876E-07 .698E-10 .403E-11 45 0 16.5 0.29818561E-03 0.29818562E-03 .161E-06 .230E-07 .610E-07 .480E-10 .686E-11 43 0 17.0 0.19584215E-03 0.19584214E-03 .137E-06 .849E-07 .373E-07 .269E-10 .166E-10 43 0 17.5 0.96031484E-04 0.96031484E-04 .227E-06 .219E-08 .127E-06 .218E-10 .211E-12 45 0 18.0 0.16989259E-04 0.16989262E-04 .143E-06 .160E-06 .431E-07 .243E-11 .271E-11 51 0 18.5 -.34225876E-04 -.34225876E-04 .153E-06 .414E-08 .529E-07 .523E-11 .142E-12 57 0 19.0 -.58694553E-04 -.58694553E-04 .173E-06 .914E-08 .732E-07 .102E-10 .537E-12 53 0 19.5 -.62225885E-04 -.62225889E-04 .236E-06 .652E-07 .136E-06 .147E-10 .406E-11 49 0 20.0 -.52377644E-04 -.52377645E-04 .227E-06 .165E-07 .127E-06 .119E-10 .866E-12 53 0 30.0 0.26490904E-06 0.26490956E-06 .100E-06 .195E-05 .000E+00 .265E-13 .515E-12 67 0 35.0 -.25905040E-07 -.25906053E-07 .291E-04 .391E-04 .290E-04 .754E-12 .101E-11 69 0 40.0 -.19776904E-09 -.19849321E-09 .115E-02 .365E-02 .115E-02 .228E-12 .724E-12 69 0 45.0 0.18665320E-09 0.18670908E-09 .100E-06 .299E-03 .877E-15 .187E-16 .559E-13 79 0 50.0 -.74768699E-11 -.10096387E-10 .538E+00 .259E+00 .538E+00 .403E-11 .262E-11 65 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 17 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.10017875E+02 0.10017875E+02 .136E-06 .532E-10 .361E-07 .136E-05 .533E-09 23 0 1.5 0.45003011E+02 0.45003011E+02 .157E-06 .583E-09 .575E-07 .709E-05 .263E-07 21 0 2.0 0.20171316E+03 0.20171316E+03 .152E-06 .609E-12 .518E-07 .306E-04 .123E-09 21 0 2.5 0.90402093E+03 0.90402093E+03 .102E-06 .426E-08 .239E-08 .926E-04 .385E-05 21 0 3.0 0.40515499E+04 0.40515419E+04 .149E-06 .198E-05 .489E-07 .603E-03 .804E-02 19 0 3.5 0.18174649E+05 0.18157751E+05 .102E-06 .931E-03 .237E-08 .186E-02 .169E+02 19 0 4.0 0.14422952E+06 0.81377396E+05 .163E-06 .772E+00 .635E-07 .236E-01 .629E+05 15 0 4.5 -.17943207E+04 0.36470818E+06 .111E-06 .100E+01 .115E-07 .200E-03 .367E+06 19 0 5.0 -.17072764E+02 0.16345087E+07 .128E-06 .100E+01 .278E-07 .218E-05 .163E+07 21 0 5.5 -.16324131E+00 0.73253597E+07 .128E-06 .100E+01 .280E-07 .209E-07 .733E+07 25 0 6.0 -.15608556E-02 0.32829985E+08 .140E-06 .100E+01 .402E-07 .219E-09 .328E+08 27 0 6.5 -.14925908E-04 0.14713378E+09 .174E-06 .100E+01 .739E-07 .260E-11 .147E+09 33 0 7.0 -.14307722E-06 0.65940787E+09 .475E-05 .100E+01 .465E-05 .680E-12 .659E+09 35 0 7.5 -.14489745E-08 0.29552610E+10 .419E-03 .100E+01 .419E-03 .607E-12 .296E+10 41 0 8.0 -.34342138E-10 0.13244561E+11 .244E-01 .100E+01 .244E-01 .838E-12 .132E+11 35 0 8.5 -.33622034E-11 0.59358005E+11 .100E-06 .100E+01 .000E+00 .336E-18 .594E+11 39 0 9.0 -.24100439E-12 0.26602412E+12 .200E+01 .100E+01 .200E+01 .482E-12 .266E+12 37 0 9.5 -.11286592E-11 0.11922374E+13 .200E+00 .100E+01 .200E+00 .226E-12 .119E+13 33 0 10.0 0.42473162E-12 0.53432373E+13 .100E+01 .100E+01 .100E+01 .425E-12 .534E+13 39 0 10.5 -.80225696E-12 0.23946728E+14 .100E-06 .100E+01 .000E+00 .802E-19 .239E+14 37 0 11.0 0.76024839E-12 0.10732179E+15 .500E+00 .100E+01 .500E+00 .380E-12 .107E+15 31 0 11.5 -.18065120E-12 0.48098289E+15 .100E+01 .100E+01 .100E+01 .181E-12 .481E+15 37 0 12.0 -.12051613E-11 0.21556158E+16 .571E+00 .100E+01 .571E+00 .689E-12 .216E+16 29 0 12.5 0.98683667E-12 0.96607997E+16 .100E-06 .100E+01 .000E+00 .987E-19 .966E+16 35 0 13.0 -.12597054E-11 0.43296700E+17 .250E+00 .100E+01 .250E+00 .315E-12 .433E+17 31 0 13.5 -.75523841E-12 0.19404235E+18 .800E+00 .100E+01 .800E+00 .604E-12 .194E+18 29 0 14.0 -.13063685E-11 0.86963747E+18 .222E+00 .100E+01 .222E+00 .290E-12 .870E+18 31 0 14.5 0.27942817E-12 0.38974447E+19 .100E-06 .100E+01 .000E+00 .279E-19 .390E+19 33 0 15.0 0.80808766E-12 0.17467136E+20 .333E+00 .100E+01 .333E+00 .269E-12 .175E+20 33 0 15.5 0.18201255E-11 0.78282270E+20 .429E+00 .100E+01 .429E+00 .780E-12 .783E+20 27 0 16.0 -.25131785E-12 0.35083680E+21 .250E+01 .100E+01 .250E+01 .628E-12 .351E+21 31 0 16.5 0.24319645E-12 0.15723414E+22 .100E-06 .100E+01 .000E+00 .243E-19 .157E+22 37 0 17.0 0.70679011E-12 0.70467454E+22 .100E-06 .100E+01 .798E-15 .707E-19 .705E+22 33 0 17.5 -.10281101E-11 0.31581322E+23 .444E+00 .100E+01 .444E+00 .457E-12 .316E+23 33 0 18.0 -.11088481E-12 0.14153767E+24 .100E-06 .100E+01 .000E+00 .111E-19 .142E+24 31 0 18.5 -.43092121E-12 0.63432781E+24 .100E-06 .100E+01 .000E+00 .431E-19 .634E+24 39 0 19.0 -.10475406E-12 0.28428600E+25 .200E+01 .100E+01 .200E+01 .210E-12 .284E+25 35 0 19.5 0.61164680E-12 0.12740815E+26 .333E+00 .100E+01 .333E+00 .204E-12 .127E+26 29 0 20.0 -.99278216E-12 0.57100369E+26 .100E-06 .100E+01 .169E-14 .993E-19 .571E+26 27 0 30.0 0.13075553E-12 0.61020165E+39 .400E+01 .100E+01 .400E+01 .523E-12 .610E+39 25 0 35.0 -.55892758E-12 0.19947598E+46 .600E+00 .100E+01 .600E+00 .335E-12 .199E+46 17 0 40.0 -.14647169E-11 0.65209044E+52 .133E+00 .100E+01 .133E+00 .195E-12 .652E+52 43 0 45.0 0.17339597E-12 0.21316950E+59 .100E-06 .100E+01 .000E+00 .173E-19 .213E+59 25 0 50.0 -.77963874E-13 0.69685479E+65 .150E+01 .100E+01 .150E+01 .117E-12 .697E+65 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 18 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.10000000E+01 0.10000000E+01 .154E-06 .405E-09 .543E-07 .768E-08 .405E-09 23 0 1.5 0.75937500E+01 0.75937500E+01 .121E-06 .306E-10 .215E-07 .102E-07 .232E-09 25 0 2.0 0.32000000E+02 0.32000000E+02 .103E-06 .249E-09 .349E-08 .821E-08 .796E-08 25 0 2.5 0.97656250E+02 0.97656250E+02 .109E-06 .192E-09 .917E-08 .590E-08 .187E-07 27 0 3.0 0.24300000E+03 0.24300000E+03 .117E-06 .117E-09 .165E-07 .349E-08 .285E-07 27 0 3.5 0.52521875E+03 0.52521875E+03 .169E-06 .158E-08 .689E-07 .244E-08 .832E-06 27 0 4.0 0.10240000E+04 0.10240000E+04 .155E-06 .116E-07 .547E-07 .973E-09 .119E-04 27 0 4.5 0.18452813E+04 0.18452812E+04 .172E-06 .815E-08 .722E-07 .436E-09 .150E-04 29 0 5.0 0.31250000E+04 0.31250000E+04 .220E-06 .643E-08 .120E-06 .211E-09 .201E-04 31 0 5.5 0.50328440E+04 0.50328437E+04 .133E-06 .524E-07 .328E-07 .456E-10 .264E-03 29 0 6.0 0.77760000E+04 0.77760000E+04 .135E-06 .217E-08 .347E-07 .160E-10 .168E-04 37 0 6.5 0.11602906E+05 0.11602906E+05 .148E-06 .278E-07 .480E-07 .584E-11 .322E-03 35 0 7.0 0.16807000E+05 0.16807000E+05 .258E-06 .119E-07 .158E-06 .329E-11 .200E-03 37 0 7.5 0.23730470E+05 0.23730469E+05 .183E-06 .336E-07 .827E-07 .733E-12 .798E-03 41 0 8.0 0.32768001E+05 0.32768000E+05 .100E-06 .281E-07 .000E+00 .124E-12 .922E-03 45 0 8.5 0.44370540E+05 0.44370531E+05 .100E-06 .193E-06 .158E-14 .374E-13 .857E-02 43 0 9.0 0.59048814E+05 0.59049000E+05 .769E-06 .315E-05 .669E-06 .853E-13 .186E+00 39 0 9.5 0.77378052E+05 0.77378094E+05 .245E-05 .541E-06 .235E-05 .794E-13 .418E-01 41 0 10.0 0.10000181E+06 0.10000000E+06 .842E-05 .181E-04 .832E-05 .788E-13 .181E+01 47 0 10.5 0.12766814E+06 0.12762816E+06 .238E-02 .313E-03 .238E-02 .634E-11 .400E+02 31 0 11.0 0.16104437E+06 0.16105100E+06 .537E-04 .412E-04 .536E-04 .403E-13 .663E+01 45 0 11.5 0.20077255E+06 0.20113572E+06 .195E-03 .181E-02 .195E-03 .407E-13 .363E+03 45 0 12.0 0.24817770E+06 0.24883200E+06 .143E-02 .263E-02 .143E-02 .823E-13 .654E+03 35 0 12.5 0.30438814E+06 0.30517578E+06 .842E-01 .258E-02 .842E-01 .133E-11 .788E+03 33 0 13.0 0.36840667E+06 0.37129300E+06 .100E-06 .777E-02 .000E+00 .425E-18 .289E+04 49 0 13.5 0.26016849E+06 0.44840334E+06 .563E+00 .420E+00 .563E+00 .377E-12 .188E+06 35 0 14.0 0.29242068E+06 0.53782400E+06 .250E+00 .456E+00 .250E+00 .420E-13 .245E+06 39 0 14.5 -.13131003E+07 0.64097341E+06 .100E-06 .305E+01 .491E-15 .168E-19 .195E+07 45 0 15.0 0.14725337E+07 0.75937500E+06 .220E+02 .939E+00 .220E+02 .927E-12 .713E+06 33 0 15.5 0.19797223E+08 0.89466097E+06 .267E+01 .211E+02 .267E+01 .337E-12 .189E+08 37 0 16.0 0.29548642E+08 0.10485760E+07 .100E+01 .272E+02 .100E+01 .421E-13 .285E+08 41 0 16.5 -.52884598E+09 0.12229810E+07 .750E+00 .433E+03 .750E+00 .126E-12 .530E+09 41 0 17.0 -.11823433E+10 0.14198570E+07 .500E+00 .834E+03 .500E+00 .419E-13 .118E+10 41 0 17.5 -.79254373E+10 0.16413086E+07 .333E+00 .483E+04 .333E+00 .418E-13 .793E+10 35 0 18.0 -.11799456E+11 0.18895680E+07 .100E+01 .625E+04 .100E+01 .417E-13 .118E+11 43 0 18.5 0.21070655E+12 0.21669987E+07 .250E+00 .972E+05 .250E+00 .415E-13 .211E+12 29 0 19.0 -.70520139E+12 0.24760990E+07 .333E+00 .285E+06 .333E+00 .413E-13 .705E+12 35 0 19.5 0.31457495E+13 0.28195062E+07 .100E+01 .112E+07 .100E+01 .123E-12 .315E+13 39 0 20.0 0.00000000E+00 0.32000000E+07 .100E-06 .100E+01 .000E+00 .000E+00 .320E+07 43 0 30.0 -.30563882E+27 0.24300000E+08 .286E+00 .126E+20 .286E+00 .716E-13 .306E+27 27 0 35.0 -.26496569E+33 0.52521875E+08 .100E+01 .504E+25 .100E+01 .664E-13 .265E+33 43 0 40.0 -.40255400E+39 0.10240000E+09 .100E+01 .393E+31 .100E+01 .309E-13 .403E+39 25 0 45.0 0.36796141E+46 0.18452812E+09 .100E-06 .199E+38 .000E+00 .863E-20 .368E+46 25 0 50.0 -.37491413E+52 0.31250000E+09 .500E+01 .120E+44 .500E+01 .135E-12 .375E+52 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 19 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.42073549E+00 0.42073549E+00 .104E-06 .302E-10 .408E-08 .438E-07 .127E-10 25 0 1.5 0.74812124E+00 0.74812124E+00 .105E-06 .427E-10 .470E-08 .783E-07 .320E-10 25 0 2.0 0.90929743E+00 0.90929743E+00 .106E-06 .127E-09 .562E-08 .960E-07 .116E-09 25 0 2.5 0.74809018E+00 0.74809018E+00 .105E-06 .330E-09 .480E-08 .784E-07 .247E-09 25 0 3.0 0.21168001E+00 0.21168001E+00 .200E-06 .176E-08 .100E-06 .424E-07 .373E-09 25 0 3.5 -.61387065E+00 -.61387065E+00 .122E-06 .202E-09 .224E-07 .751E-07 .124E-09 27 0 4.0 -.15136050E+01 -.15136050E+01 .119E-06 .393E-10 .194E-07 .181E-06 .594E-10 27 0 4.5 -.21994428E+01 -.21994428E+01 .127E-06 .407E-12 .273E-07 .280E-06 .896E-12 27 0 5.0 -.23973107E+01 -.23973107E+01 .151E-06 .121E-09 .506E-07 .361E-06 .291E-09 27 0 5.5 -.19402359E+01 -.19402359E+01 .106E-06 .327E-10 .580E-08 .205E-06 .635E-10 29 0 6.0 -.83824649E+00 -.83824649E+00 .122E-06 .164E-09 .221E-07 .102E-06 .138E-09 29 0 6.5 0.69913996E+00 0.69913996E+00 .148E-06 .102E-08 .485E-07 .104E-06 .713E-09 29 0 7.0 0.22994531E+01 0.22994531E+01 .122E-06 .572E-09 .216E-07 .280E-06 .132E-08 29 0 7.5 0.35174999E+01 0.35174999E+01 .119E-06 .439E-10 .190E-07 .418E-06 .154E-09 29 0 8.0 0.39574330E+01 0.39574330E+01 .118E-06 .699E-09 .176E-07 .465E-06 .277E-08 29 0 8.5 0.33935702E+01 0.33935702E+01 .121E-06 .720E-09 .207E-07 .410E-06 .244E-08 29 0 9.0 0.18545332E+01 0.18545332E+01 .142E-06 .461E-09 .419E-07 .263E-06 .856E-09 31 0 9.5 -.35696782E+00 -.35696782E+00 .142E-06 .140E-09 .423E-07 .508E-07 .500E-10 33 0 10.0 -.27201056E+01 -.27201056E+01 .113E-06 .627E-10 .129E-07 .307E-06 .171E-09 33 0 10.5 -.46184027E+01 -.46184027E+01 .114E-06 .143E-09 .144E-07 .528E-06 .660E-09 33 0 11.0 -.54999461E+01 -.54999461E+01 .122E-06 .952E-09 .216E-07 .669E-06 .524E-08 33 0 11.5 -.50338500E+01 -.50338500E+01 .144E-06 .462E-09 .436E-07 .723E-06 .233E-08 33 0 12.0 -.32194375E+01 -.32194375E+01 .113E-06 .747E-10 .128E-07 .363E-06 .240E-09 35 0 12.5 -.41451186E+00 -.41451186E+00 .192E-06 .639E-10 .916E-07 .794E-07 .265E-10 35 0 13.0 0.27310857E+01 0.27310857E+01 .105E-06 .137E-10 .501E-08 .287E-06 .373E-10 35 0 13.5 0.54255449E+01 0.54255449E+01 .114E-06 .132E-10 .141E-07 .619E-06 .716E-10 35 0 14.0 0.69342515E+01 0.69342515E+01 .109E-06 .519E-09 .850E-08 .752E-06 .360E-08 35 0 14.5 0.67779892E+01 0.67779892E+01 .136E-06 .342E-08 .361E-07 .923E-06 .232E-07 35 0 15.0 0.48771588E+01 0.48771588E+01 .125E-06 .460E-09 .253E-07 .611E-06 .224E-08 37 0 15.5 0.16001230E+01 0.16001230E+01 .101E-06 .217E-10 .103E-08 .162E-06 .348E-10 41 0 16.0 -.23032265E+01 -.23032265E+01 .127E-06 .426E-10 .269E-07 .292E-06 .980E-10 39 0 16.5 -.58722291E+01 -.58722291E+01 .125E-06 .632E-10 .248E-07 .733E-06 .371E-09 39 0 17.0 -.81718787E+01 -.81718787E+01 .143E-06 .191E-09 .433E-07 .117E-05 .156E-08 39 0 17.5 -.85367275E+01 -.85367275E+01 .143E-06 .229E-09 .431E-07 .122E-05 .196E-08 39 0 18.0 -.67588852E+01 -.67588852E+01 .115E-06 .143E-08 .151E-07 .778E-06 .964E-08 41 0 18.5 -.31679457E+01 -.31679457E+01 .170E-06 .244E-08 .696E-07 .537E-06 .774E-08 41 0 19.0 0.14238335E+01 0.14238335E+01 .118E-06 .340E-09 .185E-07 .169E-06 .484E-09 43 0 19.5 0.59040137E+01 0.59040137E+01 .122E-06 .482E-09 .219E-07 .719E-06 .284E-08 43 0 20.0 0.91294525E+01 0.91294525E+01 .216E-06 .283E-08 .116E-06 .198E-05 .258E-07 41 0 30.0 -.14820474E+02 -.14820474E+02 .195E-06 .137E-09 .947E-07 .289E-05 .203E-08 53 0 35.0 -.74931974E+01 -.74931967E+01 .105E-06 .949E-07 .470E-08 .785E-06 .711E-06 61 0 40.0 0.14902230E+02 0.14902263E+02 .100E-06 .220E-05 .000E+00 .149E-05 .328E-04 67 0 45.0 0.19145821E+02 0.19145329E+02 .100E-06 .257E-04 .000E+00 .191E-05 .491E-03 71 0 50.0 -.65732651E+01 -.65593713E+01 .100E-06 .212E-02 .000E+00 .657E-06 .139E-01 75 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 20 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.36787944E+00 0.36787944E+00 .134E-06 .187E-09 .335E-07 .491E-07 .687E-10 25 0 1.5 0.22313016E+00 0.22313016E+00 .198E-06 .449E-08 .980E-07 .442E-07 .100E-08 23 0 2.0 0.13533528E+00 0.13533528E+00 .129E-06 .941E-11 .295E-07 .175E-07 .127E-11 27 0 2.5 0.82084998E-01 0.82084999E-01 .116E-06 .216E-08 .162E-07 .953E-08 .177E-09 27 0 3.0 0.49787068E-01 0.49787068E-01 .138E-06 .807E-09 .380E-07 .687E-08 .402E-10 27 0 3.5 0.30197383E-01 0.30197383E-01 .187E-06 .786E-09 .867E-07 .564E-08 .237E-10 27 0 4.0 0.18315639E-01 0.18315639E-01 .165E-06 .425E-08 .650E-07 .302E-08 .778E-10 25 0 4.5 0.11108997E-01 0.11108997E-01 .131E-06 .112E-08 .309E-07 .145E-08 .124E-10 29 0 5.0 0.67379470E-02 0.67379470E-02 .138E-06 .126E-08 .381E-07 .930E-09 .850E-11 29 0 5.5 0.40867715E-02 0.40867714E-02 .126E-06 .569E-08 .261E-07 .515E-09 .232E-10 29 0 6.0 0.24787522E-02 0.24787522E-02 .164E-06 .254E-07 .637E-07 .406E-09 .629E-10 29 0 6.5 0.15034392E-02 0.15034392E-02 .251E-06 .465E-08 .151E-06 .377E-09 .698E-11 31 0 7.0 0.91188196E-03 0.91188197E-03 .170E-06 .164E-08 .699E-07 .155E-09 .149E-11 31 0 7.5 0.55308440E-03 0.55308437E-03 .243E-06 .468E-07 .143E-06 .135E-09 .259E-10 31 0 8.0 0.33546263E-03 0.33546263E-03 .124E-06 .178E-07 .242E-07 .416E-10 .597E-11 33 0 8.5 0.20346837E-03 0.20346837E-03 .174E-06 .256E-07 .742E-07 .354E-10 .521E-11 35 0 9.0 0.12340980E-03 0.12340980E-03 .116E-06 .686E-08 .155E-07 .143E-10 .846E-12 33 0 9.5 0.74851829E-04 0.74851830E-04 .208E-06 .634E-08 .108E-06 .156E-10 .474E-12 35 0 10.0 0.45399936E-04 0.45399930E-04 .193E-06 .145E-06 .933E-07 .878E-11 .659E-11 37 0 10.5 0.27536451E-04 0.27536449E-04 .229E-06 .583E-07 .129E-06 .629E-11 .160E-11 39 0 11.0 0.16701701E-04 0.16701701E-04 .203E-06 .401E-07 .103E-06 .340E-11 .669E-12 39 0 11.5 0.10130091E-04 0.10130094E-04 .211E-06 .211E-06 .111E-06 .214E-11 .213E-11 41 0 12.0 0.61442095E-05 0.61442124E-05 .144E-05 .463E-06 .134E-05 .884E-11 .285E-11 37 0 12.5 0.37266517E-05 0.37266532E-05 .139E-05 .401E-06 .129E-05 .520E-11 .150E-11 37 0 13.0 0.22603296E-05 0.22603294E-05 .332E-06 .806E-07 .232E-06 .750E-12 .182E-12 39 0 13.5 0.13709603E-05 0.13709591E-05 .474E-06 .871E-06 .374E-06 .649E-12 .119E-11 35 0 14.0 0.83152973E-06 0.83152872E-06 .372E-05 .122E-05 .362E-05 .309E-11 .101E-11 37 0 14.5 0.50434553E-06 0.50434766E-06 .107E-05 .422E-05 .973E-06 .541E-12 .213E-11 43 0 15.0 0.30590459E-06 0.30590232E-06 .100E-06 .741E-05 .246E-14 .306E-13 .227E-11 37 0 15.5 0.18553996E-06 0.18553914E-06 .100E-06 .441E-05 .000E+00 .186E-13 .819E-12 41 0 16.0 0.11253563E-06 0.11253517E-06 .420E-05 .402E-05 .410E-05 .473E-12 .452E-12 41 0 16.5 0.68255948E-07 0.68256034E-07 .100E-06 .126E-05 .000E+00 .683E-14 .862E-13 41 0 17.0 0.41400689E-07 0.41399377E-07 .108E-04 .317E-04 .107E-04 .448E-12 .131E-11 41 0 17.5 0.25110758E-07 0.25109992E-07 .100E-06 .305E-04 .000E+00 .251E-14 .766E-12 49 0 18.0 0.15230036E-07 0.15229980E-07 .100E-06 .372E-05 .000E+00 .152E-14 .566E-13 39 0 18.5 0.92386925E-08 0.92374497E-08 .456E-04 .135E-03 .455E-04 .421E-12 .124E-11 39 0 19.0 0.56021438E-08 0.56027964E-08 .221E-03 .116E-03 .221E-03 .124E-11 .653E-12 43 0 19.5 0.33985575E-08 0.33982678E-08 .597E-03 .852E-04 .597E-03 .203E-11 .290E-12 31 0 20.0 0.20616479E-08 0.20611536E-08 .387E-03 .240E-03 .387E-03 .797E-12 .494E-12 35 0 30.0 -.11881200E-11 0.93576230E-13 .500E+00 .137E+02 .500E+00 .594E-12 .128E-11 45 0 35.0 -.34249118E-11 0.63051168E-15 .846E+00 .543E+04 .846E+00 .290E-11 .343E-11 25 0 40.0 -.47338956E-12 0.42483543E-17 .100E-06 .111E+06 .759E-15 .473E-19 .473E-12 31 0 45.0 -.64460122E-12 0.28625186E-19 .100E-06 .225E+08 .000E+00 .645E-19 .645E-12 35 0 50.0 0.98361788E-12 0.19287498E-21 .100E-06 .510E+10 .000E+00 .984E-19 .984E-12 27 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 21 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.54030231E+00 0.54030231E+00 .107E-06 .228E-08 .738E-08 .580E-07 .123E-08 25 0 1.5 0.70737202E-01 0.70737202E-01 .192E-06 .347E-09 .921E-07 .136E-07 .245E-10 27 0 2.0 -.41614683E+00 -.41614684E+00 .202E-06 .598E-08 .102E-06 .839E-07 .249E-08 25 0 2.5 -.80114362E+00 -.80114362E+00 .214E-06 .224E-08 .114E-06 .172E-06 .180E-08 25 0 3.0 -.98999250E+00 -.98999250E+00 .122E-06 .437E-09 .218E-07 .121E-06 .433E-09 27 0 3.5 -.93645669E+00 -.93645669E+00 .134E-06 .702E-09 .338E-07 .125E-06 .658E-09 27 0 4.0 -.65364362E+00 -.65364362E+00 .183E-06 .816E-08 .826E-07 .119E-06 .533E-08 27 0 4.5 -.21079580E+00 -.21079580E+00 .125E-06 .134E-08 .245E-07 .262E-07 .282E-09 29 0 5.0 0.28366219E+00 0.28366219E+00 .122E-06 .107E-08 .217E-07 .345E-07 .303E-09 29 0 5.5 0.70866977E+00 0.70866977E+00 .115E-06 .503E-09 .149E-07 .814E-07 .357E-09 29 0 6.0 0.96017029E+00 0.96017029E+00 .102E-06 .141E-08 .226E-08 .982E-07 .136E-08 29 0 6.5 0.97658762E+00 0.97658763E+00 .109E-06 .786E-09 .897E-08 .106E-06 .768E-09 29 0 7.0 0.75390225E+00 0.75390225E+00 .117E-06 .213E-08 .167E-07 .880E-07 .161E-08 29 0 7.5 0.34663532E+00 0.34663532E+00 .160E-06 .101E-09 .595E-07 .553E-07 .350E-10 31 0 8.0 -.14550004E+00 -.14550003E+00 .215E-06 .115E-07 .115E-06 .314E-07 .168E-08 31 0 8.5 -.60201190E+00 -.60201190E+00 .145E-06 .108E-08 .448E-07 .872E-07 .650E-09 31 0 9.0 -.91113026E+00 -.91113026E+00 .165E-06 .166E-08 .649E-07 .150E-06 .151E-08 31 0 9.5 -.99717216E+00 -.99717216E+00 .197E-06 .437E-09 .967E-07 .196E-06 .435E-09 31 0 10.0 -.83907153E+00 -.83907153E+00 .136E-06 .161E-08 .357E-07 .114E-06 .135E-08 33 0 10.5 -.47553693E+00 -.47553693E+00 .169E-06 .268E-08 .694E-07 .806E-07 .128E-08 33 0 11.0 0.44256980E-02 0.44256980E-02 .186E-06 .224E-08 .859E-07 .823E-09 .993E-11 39 0 11.5 0.48330476E+00 0.48330476E+00 .177E-06 .105E-09 .768E-07 .854E-07 .509E-10 35 0 12.0 0.84385396E+00 0.84385396E+00 .110E-06 .165E-09 .988E-08 .927E-07 .139E-09 37 0 12.5 0.99779829E+00 0.99779828E+00 .217E-06 .866E-08 .117E-06 .217E-06 .864E-08 33 0 13.0 0.90744679E+00 0.90744678E+00 .219E-06 .102E-07 .119E-06 .198E-06 .921E-08 33 0 13.5 0.59492066E+00 0.59492066E+00 .137E-06 .266E-08 .370E-07 .815E-07 .158E-08 37 0 14.0 0.13673722E+00 0.13673722E+00 .165E-06 .655E-08 .649E-07 .225E-07 .895E-09 39 0 14.5 -.35492427E+00 -.35492427E+00 .147E-06 .688E-10 .471E-07 .522E-07 .244E-10 39 0 15.0 -.75968791E+00 -.75968791E+00 .186E-06 .559E-08 .858E-07 .141E-06 .424E-08 37 0 15.5 -.97845347E+00 -.97845346E+00 .105E-06 .271E-08 .482E-08 .103E-06 .265E-08 39 0 16.0 -.95765948E+00 -.95765948E+00 .121E-06 .162E-08 .209E-07 .116E-06 .155E-08 39 0 16.5 -.70239706E+00 -.70239706E+00 .115E-06 .355E-09 .148E-07 .806E-07 .250E-09 41 0 17.0 -.27516334E+00 -.27516334E+00 .163E-06 .111E-09 .628E-07 .448E-07 .306E-10 41 0 17.5 0.21943996E+00 0.21943996E+00 .124E-06 .298E-08 .238E-07 .272E-07 .654E-09 43 0 18.0 0.66031671E+00 0.66031671E+00 .120E-06 .418E-09 .205E-07 .796E-07 .276E-09 43 0 18.5 0.93952489E+00 0.93952489E+00 .153E-06 .763E-09 .526E-07 .143E-06 .717E-09 41 0 19.0 0.98870462E+00 0.98870462E+00 .131E-06 .598E-09 .307E-07 .129E-06 .592E-09 43 0 19.5 0.79581497E+00 0.79581497E+00 .152E-06 .130E-08 .523E-07 .121E-06 .104E-08 43 0 20.0 0.40808206E+00 0.40808206E+00 .158E-06 .124E-08 .577E-07 .644E-07 .505E-09 45 0 30.0 0.15425145E+00 0.15425145E+00 .105E-06 .255E-08 .460E-08 .161E-07 .393E-09 59 0 35.0 -.90369231E+00 -.90369221E+00 .147E-06 .117E-06 .474E-07 .133E-06 .106E-06 63 0 40.0 -.66693931E+00 -.66693806E+00 .100E-06 .188E-05 .000E+00 .667E-07 .125E-05 73 0 45.0 0.52532663E+00 0.52532199E+00 .100E-06 .883E-05 .000E+00 .525E-07 .464E-05 73 0 50.0 0.96505725E+00 0.96496603E+00 .100E-06 .945E-04 .000E+00 .965E-07 .912E-04 79 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 22 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.12840254E+01 0.12840254E+01 .113E-06 .679E-09 .131E-07 .145E-06 .872E-09 23 0 1.5 0.21824871E+01 0.21824871E+01 .128E-06 .598E-09 .279E-07 .279E-06 .131E-08 23 0 2.0 0.32974425E+01 0.32974425E+01 .140E-06 .516E-09 .396E-07 .460E-06 .170E-08 23 0 2.5 0.46706149E+01 0.46706149E+01 .149E-06 .422E-09 .486E-07 .694E-06 .197E-08 23 0 3.0 0.63510000E+01 0.63510000E+01 .155E-06 .423E-09 .552E-07 .986E-06 .268E-08 23 0 3.5 0.83960635E+01 0.83960635E+01 .159E-06 .333E-09 .594E-07 .134E-05 .280E-08 23 0 4.0 0.10873127E+02 0.10873127E+02 .162E-06 .289E-09 .618E-07 .176E-05 .315E-08 23 0 4.5 0.13860976E+02 0.13860976E+02 .163E-06 .279E-09 .626E-07 .225E-05 .387E-08 23 0 5.0 0.17451715E+02 0.17451715E+02 .162E-06 .189E-09 .618E-07 .282E-05 .331E-08 23 0 5.5 0.21752922E+02 0.21752922E+02 .161E-06 .161E-09 .609E-07 .350E-05 .350E-08 23 0 6.0 0.26890134E+02 0.26890134E+02 .159E-06 .130E-09 .590E-07 .428E-05 .350E-08 23 0 6.5 0.33009724E+02 0.33009724E+02 .156E-06 .951E-10 .561E-07 .515E-05 .314E-08 23 0 7.0 0.40282219E+02 0.40282219E+02 .153E-06 .611E-10 .526E-07 .615E-05 .246E-08 23 0 7.5 0.48906143E+02 0.48906143E+02 .149E-06 .431E-10 .486E-07 .727E-05 .211E-08 23 0 8.0 0.59112449E+02 0.59112449E+02 .144E-06 .100E-10 .442E-07 .853E-05 .593E-09 23 0 8.5 0.71169629E+02 0.71169629E+02 .140E-06 .258E-11 .397E-07 .994E-05 .184E-09 23 0 9.0 0.85389623E+02 0.85389623E+02 .135E-06 .129E-10 .351E-07 .115E-04 .110E-08 23 0 9.5 0.10213463E+03 0.10213463E+03 .131E-06 .259E-10 .306E-07 .133E-04 .265E-08 23 0 10.0 0.12182494E+03 0.12182494E+03 .206E-06 .157E-08 .106E-06 .251E-04 .191E-06 21 0 10.5 0.14494803E+03 0.14494803E+03 .147E-06 .146E-08 .473E-07 .214E-04 .211E-06 21 0 11.0 0.17206895E+03 0.17206895E+03 .139E-06 .133E-08 .386E-07 .239E-04 .229E-06 21 0 11.5 0.20384238E+03 0.20384238E+03 .172E-06 .120E-08 .721E-07 .351E-04 .245E-06 21 0 12.0 0.24102644E+03 0.24102644E+03 .198E-06 .107E-08 .981E-07 .477E-04 .258E-06 21 0 12.5 0.28449869E+03 0.28449869E+03 .109E-06 .453E-10 .856E-08 .309E-04 .129E-07 23 0 13.0 0.33527442E+03 0.33527442E+03 .106E-06 .430E-10 .603E-08 .355E-04 .144E-07 23 0 13.5 0.39452783E+03 0.39452783E+03 .104E-06 .408E-10 .384E-08 .410E-04 .161E-07 23 0 14.0 0.46361633E+03 0.46361633E+03 .102E-06 .373E-10 .198E-08 .473E-04 .173E-07 23 0 14.5 0.54410849E+03 0.54410849E+03 .101E-06 .345E-10 .550E-09 .547E-04 .187E-07 23 0 15.0 0.63781623E+03 0.63781623E+03 .102E-06 .296E-10 .160E-08 .648E-04 .189E-07 23 0 15.5 0.74683182E+03 0.74683182E+03 .102E-06 .263E-10 .242E-08 .765E-04 .196E-07 23 0 16.0 0.87357040E+03 0.87357040E+03 .103E-06 .233E-10 .301E-08 .900E-04 .203E-07 23 0 16.5 0.10208189E+04 0.10208189E+04 .103E-06 .195E-10 .342E-08 .106E-03 .199E-07 23 0 17.0 0.11917920E+04 0.11917920E+04 .104E-06 .168E-10 .366E-08 .124E-03 .200E-07 23 0 17.5 0.13901972E+04 0.13901972E+04 .202E-06 .335E-10 .102E-06 .281E-03 .466E-07 21 0 18.0 0.16203084E+04 0.16203084E+04 .191E-06 .420E-11 .914E-07 .310E-03 .681E-08 21 0 18.5 0.18870513E+04 0.18870513E+04 .181E-06 .336E-10 .806E-07 .341E-03 .635E-07 21 0 19.0 0.21961014E+04 0.21961014E+04 .170E-06 .560E-10 .700E-07 .373E-03 .123E-06 21 0 19.5 0.25539960E+04 0.25539960E+04 .160E-06 .725E-10 .598E-07 .408E-03 .185E-06 21 0 20.0 0.29682632E+04 0.29682632E+04 .150E-06 .838E-10 .501E-07 .446E-03 .249E-06 21 0 30.0 0.54241274E+05 0.54241272E+05 .185E-06 .217E-07 .852E-07 .100E-01 .118E-02 19 0 35.0 0.22087489E+06 0.22087408E+06 .113E-06 .363E-05 .132E-07 .250E-01 .802E+00 19 0 40.0 0.88159655E+06 0.88105863E+06 .106E-06 .611E-03 .599E-08 .934E-01 .538E+03 19 0 45.0 0.38280223E+07 0.34595964E+07 .113E-06 .106E+00 .129E-07 .432E+00 .368E+06 17 0 50.0 0.27108515E+08 0.13416864E+08 .154E-06 .102E+01 .545E-07 .419E+01 .137E+08 15 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 23 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.11283792E+01 0.11283792E+01 .120E-06 .334E-09 .196E-07 .105E-06 .376E-09 25 0 1.5 0.13819766E+01 0.13819766E+01 .119E-06 .549E-09 .188E-07 .113E-06 .759E-09 25 0 2.0 0.15957691E+01 0.15957691E+01 .119E-06 .524E-09 .188E-07 .115E-06 .836E-09 25 0 2.5 0.17841241E+01 0.17841241E+01 .119E-06 .347E-09 .189E-07 .114E-06 .619E-09 25 0 3.0 0.19544100E+01 0.19544100E+01 .115E-06 .817E-09 .154E-07 .107E-06 .160E-08 25 0 3.5 0.21110041E+01 0.21110041E+01 .113E-06 .105E-08 .126E-07 .990E-07 .221E-08 25 0 4.0 0.22567583E+01 0.22567583E+01 .112E-06 .137E-09 .117E-07 .927E-07 .310E-09 25 0 4.5 0.23936537E+01 0.23936537E+01 .108E-06 .209E-09 .810E-08 .840E-07 .501E-09 25 0 5.0 0.25231325E+01 0.25231325E+01 .101E-06 .303E-08 .145E-08 .733E-07 .765E-08 25 0 5.5 0.26462837E+01 0.26462837E+01 .106E-06 .132E-08 .588E-08 .708E-07 .348E-08 25 0 6.0 0.27639532E+01 0.27639532E+01 .115E-06 .686E-09 .148E-07 .708E-07 .190E-08 25 0 6.5 0.28768137E+01 0.28768137E+01 .122E-06 .130E-08 .218E-07 .690E-07 .373E-08 25 0 7.0 0.29854107E+01 0.29854107E+01 .132E-06 .213E-08 .322E-07 .686E-07 .635E-08 25 0 7.5 0.30901936E+01 0.30901936E+01 .141E-06 .150E-08 .413E-07 .670E-07 .462E-08 25 0 8.0 0.31915382E+01 0.31915382E+01 .155E-06 .380E-09 .553E-07 .671E-07 .121E-08 25 0 8.5 0.32897623E+01 0.32897623E+01 .165E-06 .240E-08 .649E-07 .648E-07 .791E-08 25 0 9.0 0.33851375E+01 0.33851375E+01 .177E-06 .104E-08 .773E-07 .633E-07 .351E-08 25 0 9.5 0.34778982E+01 0.34778982E+01 .130E-06 .283E-08 .297E-07 .420E-07 .984E-08 27 0 10.0 0.35682482E+01 0.35682482E+01 .119E-06 .677E-09 .195E-07 .350E-07 .242E-08 27 0 10.5 0.36563664E+01 0.36563664E+01 .122E-06 .344E-09 .220E-07 .323E-07 .126E-08 27 0 11.0 0.37424103E+01 0.37424103E+01 .115E-06 .337E-09 .151E-07 .275E-07 .126E-08 27 0 11.5 0.38265199E+01 0.38265199E+01 .106E-06 .712E-09 .625E-08 .229E-07 .273E-08 27 0 12.0 0.39088201E+01 0.39088201E+01 .119E-06 .103E-08 .189E-07 .231E-07 .402E-08 27 0 12.5 0.39894228E+01 0.39894228E+01 .114E-06 .621E-09 .142E-07 .200E-07 .248E-08 27 0 13.0 0.40684289E+01 0.40684289E+01 .132E-06 .170E-08 .320E-07 .208E-07 .693E-08 27 0 13.5 0.41459298E+01 0.41459298E+01 .116E-06 .641E-09 .159E-07 .164E-07 .266E-08 27 0 14.0 0.42220083E+01 0.42220082E+01 .123E-06 .114E-08 .231E-07 .157E-07 .481E-08 27 0 14.5 0.42967399E+01 0.42967399E+01 .106E-06 .186E-09 .593E-08 .121E-07 .798E-09 27 0 15.0 0.43701937E+01 0.43701937E+01 .125E-06 .121E-08 .251E-07 .129E-07 .527E-08 27 0 15.5 0.44424332E+01 0.44424332E+01 .117E-06 .451E-09 .166E-07 .107E-07 .200E-08 27 0 16.0 0.45135167E+01 0.45135167E+01 .146E-06 .245E-08 .465E-07 .121E-07 .110E-07 27 0 16.5 0.45834979E+01 0.45834978E+01 .151E-06 .733E-08 .509E-07 .112E-07 .336E-07 27 0 17.0 0.46524265E+01 0.46524265E+01 .110E-06 .336E-08 .964E-08 .728E-08 .156E-07 27 0 17.5 0.47203487E+01 0.47203487E+01 .182E-06 .456E-08 .816E-07 .108E-07 .215E-07 27 0 18.0 0.47873074E+01 0.47873074E+01 .112E-06 .123E-09 .120E-07 .596E-08 .591E-09 27 0 18.5 0.48533423E+01 0.48533423E+01 .200E-06 .411E-08 .997E-07 .950E-08 .199E-07 27 0 19.0 0.49184908E+01 0.49184908E+01 .135E-06 .978E-09 .347E-07 .573E-08 .481E-08 29 0 19.5 0.49827875E+01 0.49827875E+01 .136E-06 .361E-08 .356E-07 .516E-08 .180E-07 29 0 20.0 0.50462651E+01 0.50462650E+01 .186E-06 .877E-08 .855E-07 .631E-08 .443E-07 25 0 30.0 0.61803873E+01 0.61803872E+01 .166E-06 .180E-07 .659E-07 .567E-09 .111E-06 31 0 35.0 0.66755812E+01 0.66755812E+01 .157E-06 .849E-08 .574E-07 .166E-09 .567E-07 33 0 40.0 0.71364965E+01 0.71364965E+01 .122E-06 .115E-07 .216E-07 .394E-10 .824E-07 37 0 45.0 0.75693982E+01 0.75693976E+01 .169E-06 .846E-07 .687E-07 .166E-10 .641E-06 33 0 50.0 0.79788459E+01 0.79788456E+01 .182E-06 .377E-07 .822E-07 .542E-11 .300E-06 39 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 24 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.20755375E+00 0.20755375E+00 .109E-06 .880E-09 .896E-08 .226E-07 .183E-09 27 0 1.5 0.10278689E+00 0.10278689E+00 .280E-06 .364E-08 .180E-06 .287E-07 .375E-09 25 0 2.0 0.53990967E-01 0.53990967E-01 .191E-06 .361E-08 .912E-07 .103E-07 .195E-09 27 0 2.5 0.29289965E-01 0.29289965E-01 .161E-06 .156E-07 .610E-07 .472E-08 .458E-09 25 0 3.0 0.16217391E-01 0.16217391E-01 .279E-06 .565E-08 .179E-06 .453E-08 .917E-10 25 0 3.5 0.91066859E-02 0.91066858E-02 .194E-06 .531E-08 .941E-07 .177E-08 .483E-10 29 0 4.0 0.51667464E-02 0.51667463E-02 .128E-06 .290E-08 .279E-07 .661E-09 .150E-10 31 0 4.5 0.29545656E-02 0.29545656E-02 .210E-06 .929E-08 .110E-06 .621E-09 .274E-10 31 0 5.0 0.17000732E-02 0.17000733E-02 .208E-06 .659E-07 .108E-06 .354E-09 .112E-09 27 0 5.5 0.98315969E-03 0.98315970E-03 .174E-06 .812E-08 .737E-07 .171E-09 .798E-11 33 0 6.0 0.57092955E-03 0.57092958E-03 .104E-06 .538E-07 .427E-08 .595E-10 .307E-10 31 0 6.5 0.33270110E-03 0.33270111E-03 .204E-06 .477E-07 .104E-06 .678E-10 .159E-10 31 0 7.0 0.19445302E-03 0.19445301E-03 .359E-06 .326E-07 .259E-06 .697E-10 .634E-11 29 0 7.5 0.11394252E-03 0.11394252E-03 .155E-06 .212E-07 .548E-07 .176E-10 .241E-11 35 0 8.0 0.66915117E-04 0.66915113E-04 .115E-06 .563E-07 .148E-07 .768E-11 .377E-11 37 0 8.5 0.39374270E-04 0.39374269E-04 .124E-06 .116E-07 .241E-07 .489E-11 .458E-12 39 0 9.0 0.23208843E-04 0.23208842E-04 .218E-06 .343E-07 .118E-06 .505E-11 .796E-12 35 0 9.5 0.13701422E-04 0.13701423E-04 .228E-06 .639E-07 .128E-06 .312E-11 .875E-12 41 0 10.0 0.80999168E-05 0.80999110E-05 .228E-05 .727E-06 .218E-05 .185E-10 .589E-11 33 0 10.5 0.47944430E-05 0.47944451E-05 .269E-06 .456E-06 .169E-06 .129E-11 .219E-11 41 0 11.0 0.28411174E-05 0.28411190E-05 .925E-06 .569E-06 .825E-06 .263E-11 .162E-11 33 0 11.5 0.16853422E-05 0.16853480E-05 .189E-05 .348E-05 .179E-05 .319E-11 .586E-11 33 0 12.0 0.10006929E-05 0.10006925E-05 .229E-05 .371E-06 .219E-05 .229E-11 .371E-12 39 0 12.5 0.59469358E-06 0.59468781E-06 .248E-05 .971E-05 .238E-05 .147E-11 .577E-11 41 0 13.0 0.35369329E-06 0.35369191E-06 .204E-05 .392E-05 .194E-05 .721E-12 .139E-11 37 0 13.5 0.21051604E-06 0.21051482E-06 .100E-06 .578E-05 .000E+00 .211E-13 .122E-11 39 0 14.0 0.12538398E-06 0.12538290E-06 .310E-04 .862E-05 .309E-04 .389E-11 .108E-11 37 0 14.5 0.74723663E-07 0.74725886E-07 .758E-04 .297E-04 .757E-04 .566E-11 .222E-11 31 0 15.0 0.44552401E-07 0.44561747E-07 .549E-03 .210E-03 .549E-03 .245E-10 .935E-11 29 0 15.5 0.26590808E-07 0.26588556E-07 .100E-06 .847E-04 .000E+00 .266E-14 .225E-11 49 0 16.0 0.15870167E-07 0.15872793E-07 .110E-03 .165E-03 .110E-03 .174E-11 .263E-11 45 0 16.5 0.94668119E-08 0.94803450E-08 .167E-02 .143E-02 .167E-02 .158E-10 .135E-10 27 0 17.0 0.56637129E-08 0.56649282E-08 .976E-04 .215E-03 .975E-04 .553E-12 .122E-11 41 0 17.5 0.33861951E-08 0.33865119E-08 .318E-03 .935E-04 .318E-03 .108E-11 .317E-12 35 0 18.0 0.20236037E-08 0.20252943E-08 .260E-03 .835E-03 .260E-03 .527E-12 .169E-11 39 0 18.5 0.12097144E-08 0.12116893E-08 .128E-02 .163E-02 .128E-02 .154E-11 .197E-11 37 0 19.0 0.72646324E-09 0.72519217E-09 .100E-06 .175E-02 .711E-15 .726E-16 .127E-11 37 0 19.5 0.43250623E-09 0.43417555E-09 .228E-02 .384E-02 .228E-02 .985E-12 .167E-11 33 0 20.0 0.26329906E-09 0.26002819E-09 .916E-02 .126E-01 .916E-02 .241E-11 .327E-11 31 0 30.0 0.30590063E-11 0.96389556E-14 .222E+00 .316E+03 .222E+00 .680E-12 .305E-11 59 0 35.0 -.29635466E-12 0.60129027E-16 .600E+01 .493E+04 .600E+01 .178E-11 .296E-12 25 0 40.0 -.52551197E-12 0.37897956E-18 .150E+01 .139E+07 .150E+01 .788E-12 .526E-12 31 0 45.0 0.70808353E-12 0.24075046E-20 .333E+00 .294E+09 .333E+00 .236E-12 .708E-12 27 0 50.0 -.42850376E-12 0.15389197E-22 .100E-06 .278E+11 .000E+00 .429E-19 .429E-12 33 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 25 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.28209479E+01 0.28209479E+01 .109E-06 .882E-09 .899E-08 .307E-06 .249E-08 25 0 1.5 0.32246121E+01 0.32246121E+01 .119E-06 .559E-09 .189E-07 .383E-06 .180E-08 25 0 2.0 0.35904805E+01 0.35904805E+01 .115E-06 .613E-09 .153E-07 .414E-06 .220E-08 25 0 2.5 0.39250731E+01 0.39250731E+01 .113E-06 .801E-09 .130E-07 .444E-06 .315E-08 25 0 3.0 0.42345551E+01 0.42345551E+01 .115E-06 .165E-09 .150E-07 .487E-06 .699E-09 25 0 3.5 0.45235803E+01 0.45235803E+01 .116E-06 .786E-09 .155E-07 .523E-06 .356E-08 25 0 4.0 0.47956115E+01 0.47956115E+01 .115E-06 .675E-09 .147E-07 .550E-06 .324E-08 25 0 4.5 0.50532689E+01 0.50532689E+01 .115E-06 .197E-09 .151E-07 .582E-06 .997E-09 25 0 5.0 0.52985783E+01 0.52985783E+01 .116E-06 .669E-09 .162E-07 .616E-06 .355E-08 25 0 5.5 0.55331387E+01 0.55331387E+01 .116E-06 .714E-09 .156E-07 .639E-06 .395E-08 25 0 6.0 0.57582358E+01 0.57582358E+01 .117E-06 .721E-09 .167E-07 .672E-06 .415E-08 25 0 6.5 0.59749208E+01 0.59749208E+01 .118E-06 .375E-09 .175E-07 .702E-06 .224E-08 25 0 7.0 0.61840649E+01 0.61840649E+01 .117E-06 .237E-09 .171E-07 .724E-06 .147E-08 25 0 7.5 0.63864001E+01 0.63864001E+01 .117E-06 .508E-09 .167E-07 .745E-06 .325E-08 25 0 8.0 0.65825476E+01 0.65825476E+01 .117E-06 .727E-09 .166E-07 .768E-06 .479E-08 25 0 8.5 0.67730401E+01 0.67730401E+01 .116E-06 .222E-09 .162E-07 .787E-06 .151E-08 25 0 9.0 0.69583382E+01 0.69583382E+01 .116E-06 .156E-09 .162E-07 .809E-06 .109E-08 25 0 9.5 0.71388436E+01 0.71388436E+01 .116E-06 .171E-09 .163E-07 .830E-06 .122E-08 25 0 10.0 0.73149089E+01 0.73149089E+01 .116E-06 .265E-09 .163E-07 .850E-06 .194E-08 25 0 10.5 0.74868455E+01 0.74868455E+01 .118E-06 .479E-09 .179E-07 .883E-06 .359E-08 25 0 11.0 0.76549302E+01 0.76549302E+01 .117E-06 .425E-09 .172E-07 .897E-06 .325E-08 25 0 11.5 0.78194103E+01 0.78194103E+01 .117E-06 .322E-09 .171E-07 .915E-06 .252E-08 25 0 12.0 0.79805077E+01 0.79805077E+01 .116E-06 .930E-10 .165E-07 .930E-06 .742E-09 25 0 12.5 0.81384225E+01 0.81384225E+01 .117E-06 .882E-10 .171E-07 .953E-06 .718E-09 25 0 13.0 0.82933359E+01 0.82933359E+01 .119E-06 .101E-08 .192E-07 .989E-06 .837E-08 25 0 13.5 0.84454125E+01 0.84454125E+01 .117E-06 .797E-11 .169E-07 .987E-06 .673E-10 25 0 14.0 0.85948025E+01 0.85948025E+01 .118E-06 .520E-09 .177E-07 .101E-05 .447E-08 25 0 14.5 0.87416432E+01 0.87416432E+01 .119E-06 .790E-09 .187E-07 .104E-05 .690E-08 25 0 15.0 0.88860606E+01 0.88860606E+01 .118E-06 .495E-09 .181E-07 .105E-05 .440E-08 25 0 15.5 0.90281707E+01 0.90281707E+01 .118E-06 .489E-09 .179E-07 .106E-05 .442E-08 25 0 16.0 0.91680807E+01 0.91680807E+01 .117E-06 .148E-09 .168E-07 .107E-05 .136E-08 25 0 16.5 0.93058896E+01 0.93058896E+01 .117E-06 .202E-09 .174E-07 .109E-05 .188E-08 25 0 17.0 0.94416891E+01 0.94416891E+01 .117E-06 .687E-10 .170E-07 .110E-05 .649E-09 25 0 17.5 0.95755645E+01 0.95755645E+01 .117E-06 .382E-09 .169E-07 .112E-05 .366E-08 25 0 18.0 0.97075955E+01 0.97075955E+01 .117E-06 .459E-09 .169E-07 .113E-05 .445E-08 25 0 18.5 0.98378560E+01 0.98378560E+01 .118E-06 .407E-09 .182E-07 .116E-05 .400E-08 25 0 19.0 0.99664155E+01 0.99664155E+01 .117E-06 .202E-09 .169E-07 .116E-05 .201E-08 25 0 19.5 0.10093339E+02 0.10093339E+02 .118E-06 .310E-09 .182E-07 .119E-05 .312E-08 25 0 20.0 0.10218687E+02 0.10218687E+02 .118E-06 .202E-09 .175E-07 .120E-05 .206E-08 25 0 30.0 0.12463781E+02 0.12463781E+02 .117E-06 .626E-09 .174E-07 .146E-05 .780E-08 25 0 35.0 0.13446528E+02 0.13446528E+02 .117E-06 .182E-09 .172E-07 .158E-05 .245E-08 25 0 40.0 0.14362199E+02 0.14362199E+02 .117E-06 .365E-09 .173E-07 .168E-05 .524E-08 25 0 45.0 0.15222900E+02 0.15222900E+02 .117E-06 .392E-09 .174E-07 .179E-05 .597E-08 25 0 50.0 0.16037480E+02 0.16037480E+02 .118E-06 .384E-09 .179E-07 .189E-05 .615E-08 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 26 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.15058434E+00 0.15058434E+00 .105E-06 .207E-09 .472E-08 .158E-07 .312E-10 23 0 1.5 0.44569459E+00 0.44569459E+00 .116E-06 .274E-09 .158E-07 .516E-07 .122E-09 23 0 2.0 0.87079555E+00 0.87079555E+00 .140E-06 .400E-09 .401E-07 .122E-06 .348E-09 23 0 2.5 0.13006656E+01 0.13006656E+01 .196E-06 .649E-09 .960E-07 .255E-06 .844E-09 23 0 3.0 0.15555487E+01 0.15555487E+01 .124E-06 .207E-10 .236E-07 .192E-06 .322E-10 25 0 3.5 0.14634076E+01 0.14634076E+01 .156E-06 .169E-10 .557E-07 .228E-06 .248E-10 25 0 4.0 0.92888599E+00 0.92888599E+00 .107E-06 .347E-10 .732E-08 .997E-07 .322E-10 27 0 4.5 -.14474510E-01 -.14474510E-01 .117E-06 .156E-08 .172E-07 .170E-08 .226E-10 29 0 5.0 -.11886176E+01 -.11886176E+01 .115E-06 .978E-10 .151E-07 .137E-06 .116E-09 27 0 5.5 -.23016120E+01 -.23016120E+01 .110E-06 .145E-09 .997E-08 .253E-06 .335E-09 27 0 6.0 -.30202186E+01 -.30202186E+01 .105E-06 .309E-09 .535E-08 .318E-06 .933E-09 27 0 6.5 -.30663498E+01 -.30663498E+01 .123E-06 .417E-09 .233E-07 .378E-06 .128E-08 27 0 7.0 -.23101646E+01 -.23101646E+01 .118E-06 .452E-10 .184E-07 .274E-06 .104E-09 29 0 7.5 -.83088245E+00 -.83088245E+00 .108E-06 .535E-11 .833E-08 .900E-07 .444E-11 31 0 8.0 0.10766793E+01 0.10766793E+01 .113E-06 .559E-09 .127E-07 .121E-06 .602E-09 31 0 8.5 0.29577941E+01 0.29577941E+01 .109E-06 .107E-09 .920E-08 .323E-06 .315E-09 31 0 9.0 0.43061454E+01 0.43061454E+01 .112E-06 .106E-09 .125E-07 .484E-06 .455E-09 31 0 9.5 0.46989922E+01 0.46989922E+01 .121E-06 .178E-09 .211E-07 .569E-06 .837E-09 31 0 10.0 0.39233471E+01 0.39233471E+01 .146E-06 .674E-10 .456E-07 .571E-06 .265E-09 31 0 10.5 0.20567210E+01 0.20567210E+01 .103E-06 .256E-10 .299E-08 .212E-06 .526E-10 33 0 11.0 -.52433644E+00 -.52433644E+00 .104E-06 .221E-08 .420E-08 .546E-07 .116E-08 33 0 11.5 -.32167285E+01 -.32167285E+01 .108E-06 .273E-09 .773E-08 .347E-06 .877E-09 33 0 12.0 -.53314102E+01 -.53314102E+01 .149E-06 .327E-08 .485E-07 .792E-06 .174E-07 31 0 12.5 -.62694002E+01 -.62694002E+01 .149E-06 .112E-09 .485E-07 .931E-06 .700E-09 33 0 13.0 -.56883206E+01 -.56883206E+01 .112E-06 .304E-10 .123E-07 .639E-06 .173E-09 35 0 13.5 -.36138223E+01 -.36138223E+01 .143E-06 .213E-09 .433E-07 .518E-06 .771E-09 35 0 14.0 -.46185685E+00 -.46185685E+00 .164E-06 .259E-10 .636E-07 .756E-07 .120E-10 37 0 14.5 0.30406485E+01 0.30406485E+01 .113E-06 .699E-09 .130E-07 .344E-06 .212E-08 37 0 15.0 0.60228033E+01 0.60228033E+01 .116E-06 .106E-10 .163E-07 .700E-06 .639E-10 37 0 15.5 0.76862481E+01 0.76862481E+01 .119E-06 .654E-10 .190E-07 .914E-06 .503E-09 37 0 16.0 0.75173242E+01 0.75173242E+01 .160E-06 .775E-09 .596E-07 .120E-05 .583E-08 37 0 16.5 0.54388831E+01 0.54388831E+01 .108E-06 .247E-10 .762E-08 .585E-06 .135E-09 39 0 17.0 0.18581896E+01 0.18581896E+01 .124E-06 .678E-10 .236E-07 .230E-06 .126E-09 39 0 17.5 -.24079127E+01 -.24079127E+01 .153E-06 .703E-09 .526E-07 .367E-06 .169E-08 39 0 18.0 -.63183440E+01 -.63183440E+01 .183E-06 .539E-08 .826E-07 .115E-05 .340E-07 37 0 18.5 -.88618456E+01 -.88618456E+01 .148E-06 .152E-08 .478E-07 .131E-05 .135E-07 39 0 19.0 -.93177553E+01 -.93177553E+01 .127E-06 .994E-10 .266E-07 .118E-05 .927E-09 41 0 19.5 -.74564260E+01 -.74564260E+01 .145E-06 .279E-09 .454E-07 .108E-05 .208E-08 41 0 20.0 -.36243480E+01 -.36243480E+01 .117E-06 .535E-09 .174E-07 .425E-06 .194E-08 43 0 30.0 -.28077876E+01 -.28077876E+01 .193E-06 .279E-08 .931E-07 .542E-06 .784E-08 53 0 35.0 0.15600522E+02 0.15600522E+02 .100E-06 .138E-07 .000E+00 .156E-05 .215E-06 63 0 40.0 0.13711371E+02 0.13711318E+02 .100E-06 .386E-05 .000E+00 .137E-05 .529E-04 65 0 45.0 -.11394404E+02 -.11394293E+02 .100E-06 .977E-05 .000E+00 .114E-05 .111E-03 71 0 50.0 -.24262485E+02 -.24255338E+02 .100E-06 .295E-03 .000E+00 .243E-05 .715E-02 79 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 27 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.26424112E+00 0.26424112E+00 .101E-06 .195E-10 .895E-09 .267E-07 .514E-11 25 0 1.5 0.44217460E+00 0.44217460E+00 .103E-06 .737E-11 .307E-08 .456E-07 .326E-11 25 0 2.0 0.59399415E+00 0.59399415E+00 .189E-06 .791E-09 .894E-07 .113E-06 .470E-09 23 0 2.5 0.71270250E+00 0.71270250E+00 .157E-06 .900E-09 .575E-07 .112E-06 .641E-09 23 0 3.0 0.80085173E+00 0.80085173E+00 .119E-06 .972E-09 .185E-07 .949E-07 .778E-09 23 0 3.5 0.86411177E+00 0.86411177E+00 .154E-06 .910E-09 .538E-07 .133E-06 .786E-09 23 0 4.0 0.90842180E+00 0.90842181E+00 .196E-06 .102E-08 .957E-07 .178E-06 .927E-09 23 0 4.5 0.93890052E+00 0.93890052E+00 .119E-06 .213E-10 .189E-07 .112E-06 .200E-10 25 0 5.0 0.95957232E+00 0.95957232E+00 .119E-06 .392E-09 .194E-07 .115E-06 .376E-09 25 0 5.5 0.97343599E+00 0.97343599E+00 .120E-06 .501E-10 .203E-07 .117E-06 .488E-10 25 0 6.0 0.98264873E+00 0.98264873E+00 .121E-06 .177E-09 .210E-07 .119E-06 .174E-09 25 0 6.5 0.98872421E+00 0.98872421E+00 .121E-06 .957E-10 .208E-07 .119E-06 .946E-10 25 0 7.0 0.99270494E+00 0.99270494E+00 .121E-06 .198E-09 .207E-07 .120E-06 .196E-09 25 0 7.5 0.99529878E+00 0.99529878E+00 .121E-06 .675E-11 .208E-07 .120E-06 .672E-11 25 0 8.0 0.99698084E+00 0.99698084E+00 .121E-06 .518E-10 .214E-07 .121E-06 .517E-10 25 0 8.5 0.99806705E+00 0.99806705E+00 .121E-06 .622E-10 .213E-07 .121E-06 .621E-10 25 0 9.0 0.99876590E+00 0.99876590E+00 .121E-06 .289E-09 .213E-07 .121E-06 .288E-09 25 0 9.5 0.99921406E+00 0.99921406E+00 .121E-06 .257E-09 .211E-07 .121E-06 .257E-09 25 0 10.0 0.99950060E+00 0.99950060E+00 .120E-06 .143E-09 .204E-07 .120E-06 .143E-09 25 0 10.5 0.99968333E+00 0.99968333E+00 .121E-06 .218E-09 .213E-07 .121E-06 .218E-09 25 0 11.0 0.99979958E+00 0.99979958E+00 .121E-06 .375E-10 .205E-07 .121E-06 .374E-10 25 0 11.5 0.99987337E+00 0.99987337E+00 .121E-06 .393E-09 .211E-07 .121E-06 .393E-09 25 0 12.0 0.99992013E+00 0.99992013E+00 .121E-06 .502E-09 .209E-07 .121E-06 .502E-09 25 0 12.5 0.99994969E+00 0.99994969E+00 .120E-06 .183E-09 .204E-07 .120E-06 .183E-09 25 0 13.0 0.99996836E+00 0.99996836E+00 .121E-06 .345E-10 .209E-07 .121E-06 .345E-10 25 0 13.5 0.99998012E+00 0.99998012E+00 .121E-06 .380E-09 .208E-07 .121E-06 .380E-09 25 0 14.0 0.99998753E+00 0.99998753E+00 .121E-06 .121E-09 .211E-07 .121E-06 .121E-09 25 0 14.5 0.99999218E+00 0.99999218E+00 .120E-06 .484E-09 .199E-07 .120E-06 .484E-09 25 0 15.0 0.99999511E+00 0.99999511E+00 .120E-06 .113E-10 .196E-07 .120E-06 .113E-10 25 0 15.5 0.99999694E+00 0.99999694E+00 .120E-06 .624E-09 .197E-07 .120E-06 .624E-09 25 0 16.0 0.99999809E+00 0.99999809E+00 .121E-06 .490E-09 .206E-07 .121E-06 .490E-09 25 0 16.5 0.99999881E+00 0.99999881E+00 .120E-06 .145E-09 .199E-07 .120E-06 .145E-09 25 0 17.0 0.99999926E+00 0.99999925E+00 .119E-06 .685E-09 .193E-07 .119E-06 .685E-09 25 0 17.5 0.99999954E+00 0.99999954E+00 .120E-06 .284E-09 .196E-07 .120E-06 .284E-09 25 0 18.0 0.99999971E+00 0.99999971E+00 .119E-06 .211E-09 .189E-07 .119E-06 .211E-09 25 0 18.5 0.99999982E+00 0.99999982E+00 .119E-06 .380E-09 .189E-07 .119E-06 .380E-09 25 0 19.0 0.99999989E+00 0.99999989E+00 .120E-06 .598E-09 .205E-07 .120E-06 .598E-09 25 0 19.5 0.99999993E+00 0.99999993E+00 .119E-06 .114E-09 .188E-07 .119E-06 .114E-09 25 0 20.0 0.99999996E+00 0.99999996E+00 .118E-06 .239E-09 .185E-07 .118E-06 .239E-09 25 0 30.0 0.10000000E+01 0.10000000E+01 .118E-06 .691E-09 .176E-07 .118E-06 .691E-09 25 0 35.0 0.10000000E+01 0.10000000E+01 .118E-06 .637E-09 .180E-07 .118E-06 .637E-09 25 0 40.0 0.10000000E+01 0.10000000E+01 .116E-06 .798E-09 .160E-07 .116E-06 .798E-09 25 0 45.0 0.10000000E+01 0.10000000E+01 .115E-06 .870E-09 .153E-07 .115E-06 .870E-09 25 0 50.0 0.10000000E+01 0.10000000E+01 .116E-06 .433E-09 .158E-07 .116E-06 .433E-09 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 28 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.56826684E+00 0.56826684E+00 .161E-06 .272E-10 .612E-07 .916E-07 .155E-10 23 0 1.5 0.16730541E+01 0.16730541E+01 .201E-06 .159E-08 .101E-06 .337E-06 .267E-08 21 0 2.0 0.45667336E+01 0.45667336E+01 .105E-06 .344E-10 .539E-08 .481E-06 .157E-09 23 0 2.5 0.12381308E+02 0.12381308E+02 .200E-06 .151E-09 .998E-07 .247E-05 .187E-08 21 0 3.0 0.33623498E+02 0.33623498E+02 .138E-06 .954E-10 .382E-07 .465E-05 .321E-08 21 0 3.5 0.91384597E+02 0.91384597E+02 .105E-06 .588E-09 .481E-08 .958E-05 .537E-07 21 0 4.0 0.24841036E+03 0.24841036E+03 .103E-06 .328E-07 .282E-08 .255E-04 .815E-05 21 0 4.5 0.67525668E+03 0.67525534E+03 .147E-06 .198E-05 .468E-07 .992E-04 .134E-02 19 0 5.0 0.18357583E+04 0.18355385E+04 .118E-06 .120E-03 .180E-07 .217E-03 .220E+00 19 0 5.5 0.50258087E+04 0.49895122E+04 .204E-06 .727E-02 .104E-06 .102E-02 .363E+02 17 0 6.0 0.24038254E+05 0.13562900E+05 .123E-06 .772E+00 .225E-07 .295E-02 .105E+05 17 0 6.5 -.14575125E+04 0.36867783E+05 .194E-06 .104E+01 .938E-07 .282E-03 .383E+05 19 0 7.0 -.63202584E+02 0.10021702E+06 .113E-06 .100E+01 .131E-07 .715E-05 .100E+06 23 0 7.5 -.28455355E+01 0.27241811E+06 .109E-06 .100E+01 .876E-08 .309E-06 .272E+06 25 0 8.0 -.12823869E+00 0.74050921E+06 .130E-06 .100E+01 .302E-07 .167E-07 .741E+06 27 0 8.5 -.57897183E-02 0.20129127E+07 .118E-06 .100E+01 .175E-07 .680E-09 .201E+07 31 0 9.0 -.25205416E-03 0.54716641E+07 .115E-06 .100E+01 .153E-07 .291E-10 .547E+07 33 0 9.5 0.19645184E-06 0.14873525E+08 .941E-06 .100E+01 .841E-06 .185E-12 .149E+08 41 0 10.0 0.58613634E-05 0.40430433E+08 .180E-06 .100E+01 .797E-07 .105E-11 .404E+08 43 0 10.5 0.61401770E-06 0.10990131E+09 .130E-05 .100E+01 .120E-05 .798E-12 .110E+09 43 0 11.0 -.18503217E-05 0.29874274E+09 .175E-06 .100E+01 .755E-07 .325E-12 .299E+09 45 0 11.5 -.16879950E-05 0.81206695E+09 .100E-06 .100E+01 .000E+00 .169E-12 .812E+09 49 0 12.0 -.64624670E-06 0.22074268E+10 .296E-06 .100E+01 .196E-06 .191E-12 .221E+10 55 0 12.5 0.11308133E-06 0.60004083E+10 .100E-06 .100E+01 .000E+00 .113E-13 .600E+10 55 0 13.0 0.32660976E-06 0.16310801E+11 .455E-06 .100E+01 .355E-06 .149E-12 .163E+11 55 0 13.5 0.21508086E-06 0.44337353E+11 .113E-05 .100E+01 .103E-05 .244E-12 .443E+11 51 0 14.0 0.48877041E-07 0.12052142E+12 .766E-04 .100E+01 .765E-04 .375E-11 .121E+12 47 0 14.5 -.40711777E-07 0.32761119E+12 .100E-06 .100E+01 .000E+00 .407E-14 .328E+12 57 0 15.0 -.49975673E-07 0.89053955E+12 .209E-05 .100E+01 .199E-05 .104E-12 .891E+12 51 0 15.5 -.24297926E-07 0.24207375E+13 .809E-03 .100E+01 .809E-03 .197E-10 .242E+13 51 0 16.0 -.71091326E-09 0.65802467E+13 .189E-02 .100E+01 .189E-02 .134E-11 .658E+13 55 0 16.5 0.83810149E-08 0.17886965E+14 .193E-03 .100E+01 .193E-03 .162E-11 .179E+14 49 0 17.0 0.68478772E-08 0.48621812E+14 .128E-04 .100E+01 .127E-04 .877E-13 .486E+14 59 0 17.5 0.22979195E-08 0.13216779E+15 .736E-04 .100E+01 .735E-04 .169E-12 .132E+15 59 0 18.0 -.71244878E-09 0.35926930E+15 .173E-03 .100E+01 .173E-03 .123E-12 .359E+15 57 0 18.5 -.14058690E-08 0.97659520E+15 .100E-06 .100E+01 .000E+00 .141E-15 .977E+15 63 0 19.0 -.84195145E-09 0.26546610E+16 .111E-01 .100E+01 .111E-01 .934E-11 .265E+16 51 0 19.5 -.14535093E-09 0.72161167E+16 .100E-06 .100E+01 .000E+00 .145E-16 .722E+16 69 0 20.0 0.19661058E-09 0.19615439E+17 .636E-02 .100E+01 .636E-02 .125E-11 .196E+17 61 0 30.0 0.48693692E-13 0.95167282E+25 .100E+01 .100E+01 .100E+01 .487E-13 .952E+25 41 0 35.0 0.12508194E-12 0.20961989E+30 .333E+00 .100E+01 .333E+00 .417E-13 .210E+30 27 0 40.0 0.72921727E-13 0.46171853E+34 .500E+00 .100E+01 .500E+00 .365E-13 .462E+34 27 0 45.0 -.48597266E-13 0.10170027E+39 .100E-06 .100E+01 .000E+00 .486E-20 .102E+39 27 0 50.0 0.11660701E-12 0.22400976E+43 .250E+00 .100E+01 .250E+00 .292E-13 .224E+43 23 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 29 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 -.19128983E+01 -.19128983E+01 .174E-06 .394E-08 .738E-07 .450E-07 .753E-08 27 0 1.5 -.14143063E+01 -.14143063E+01 .286E-06 .127E-08 .186E-06 .202E-07 .180E-08 27 0 2.0 -.23749679E+00 -.23749678E+00 .215E-06 .193E-07 .115E-06 .934E-09 .457E-08 33 0 2.5 0.86784465E+00 0.86784464E+00 .170E-06 .931E-08 .705E-07 .997E-09 .808E-08 35 0 3.0 0.13001085E+01 0.13001085E+01 .198E-06 .701E-08 .979E-07 .638E-09 .912E-08 37 0 3.5 0.96591938E+00 0.96591940E+00 .163E-06 .110E-07 .632E-07 .144E-09 .107E-07 39 0 4.0 0.25407169E+00 0.25407179E+00 .144E-06 .391E-06 .441E-07 .123E-10 .994E-07 41 0 4.5 -.31125959E+00 -.31125976E+00 .143E-06 .540E-06 .430E-07 .549E-11 .168E-06 53 0 5.0 -.44909358E+00 -.44909349E+00 .220E-06 .201E-06 .120E-06 .448E-11 .902E-07 55 0 5.5 -.25608897E+00 -.25608876E+00 .287E-06 .847E-06 .187E-06 .123E-11 .217E-06 59 0 6.0 -.38772263E-01 -.38772109E-01 .502E-05 .397E-05 .492E-05 .120E-11 .154E-06 53 0 6.5 -.21270705E-01 -.21274106E-01 .160E-04 .160E-03 .159E-04 .768E-12 .340E-05 61 0 7.0 -.17634886E+00 -.17633287E+00 .518E-05 .907E-04 .508E-05 .760E-12 .160E-04 63 0 7.5 -.29499616E+00 -.29501953E+00 .363E-04 .792E-04 .362E-04 .328E-11 .234E-04 105 0 8.0 -.20302636E+00 -.20303986E+00 .311E-04 .665E-04 .310E-04 .711E-12 .135E-04 47 0 8.5 0.76963486E-01 0.76905545E-01 .108E-03 .753E-03 .108E-03 .345E-12 .579E-04 53 0 9.0 0.34757739E+00 0.34921044E+00 .381E-03 .468E-02 .381E-03 .202E-11 .163E-02 119 0 9.5 0.41954494E+00 0.41807932E+00 .419E-03 .351E-02 .418E-03 .984E-12 .147E-02 51 0 10.0 0.24995647E+00 0.24943072E+00 .620E-03 .211E-02 .620E-03 .320E-12 .526E-03 71 0 10.5 -.15207291E-01 -.13750920E-01 .270E-01 .106E+00 .270E-01 .312E-12 .146E-02 51 0 11.0 -.19070855E+00 -.18261573E+00 .571E-02 .443E-01 .571E-02 .304E-12 .809E-02 61 0 11.5 -.15608229E+00 -.17671961E+00 .926E-01 .117E+00 .926E-01 .148E-11 .206E-01 49 0 12.0 -.24541070E+00 -.69945825E-01 .938E-01 .251E+01 .938E-01 .869E-12 .175E+00 53 0 12.5 0.81423502E-01 -.10552748E-02 .250E+00 .782E+02 .250E+00 .283E-12 .825E-01 53 0 13.0 -.21620355E+00 -.40081148E-01 .750E+00 .439E+01 .750E+00 .828E-12 .176E+00 53 0 13.5 -.27279624E+01 -.13141622E+00 .526E-01 .198E+02 .526E-01 .270E-12 .260E+01 53 0 14.0 -.76307324E+00 -.15704901E+00 .100E-06 .386E+01 .000E+00 .528E-19 .606E+00 49 0 14.5 0.38542530E+02 -.54225278E-01 .316E+00 .712E+03 .316E+00 .310E-11 .386E+02 35 0 15.0 0.53947895E+01 0.12185858E+00 .400E+01 .433E+02 .400E+01 .202E-11 .527E+01 43 0 15.5 -.14352506E+03 0.24428333E+00 .500E-01 .589E+03 .500E-01 .247E-12 .144E+03 29 0 16.0 0.19099137E+02 0.22398536E+00 .100E+01 .843E+02 .100E+01 .242E-12 .189E+02 51 0 16.5 0.50849826E+02 0.83529735E-01 .430E+02 .608E+03 .430E+02 .102E-10 .508E+02 27 0 17.0 -.37920994E+04 -.67459640E-01 .243E+01 .562E+05 .243E+01 .158E-10 .379E+04 25 0 17.5 0.79383388E+04 -.12835796E+00 .136E+00 .618E+05 .136E+00 .683E-12 .794E+04 43 0 18.0 -.57702276E+04 -.87586711E-01 .167E+00 .659E+05 .167E+00 .223E-12 .577E+04 33 0 18.5 -.51280507E+04 -.18822794E-01 .300E+01 .272E+06 .300E+01 .131E-11 .513E+04 39 0 19.0 0.13676506E+05 -.35401025E-02 .500E+00 .386E+07 .500E+00 .215E-12 .137E+05 41 0 19.5 0.12770403E+06 -.54274055E-01 .200E+01 .235E+07 .200E+01 .295E-11 .128E+06 41 0 20.0 0.77897395E+06 -.10750201E+00 .125E+00 .725E+07 .125E+00 .414E-12 .779E+06 41 0 30.0 0.48296839E+15 -.73777629E-01 .213E+01 .655E+16 .213E+01 .899E-11 .483E+15 17 0 35.0 0.33439723E+18 0.87829223E-01 .100E+01 .381E+19 .100E+01 .133E-12 .334E+18 25 0 40.0 0.65750875E+23 0.27827541E-01 .100E+00 .236E+25 .100E+00 .119E-12 .658E+23 21 0 45.0 0.15691519E+28 -.43262027E-01 .333E+00 .363E+29 .333E+00 .429E-12 .157E+28 19 0 50.0 -.23624731E+32 -.41058862E-02 .100E-06 .575E+34 .000E+00 .879E-19 .236E+32 27 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 30 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.63212056E+00 0.63212056E+00 .184E-06 .535E-08 .836E-07 .116E-06 .338E-08 25 0 1.5 0.51791323E+00 0.51791323E+00 .139E-06 .192E-08 .385E-07 .717E-07 .994E-09 25 0 2.0 0.43233236E+00 0.43233236E+00 .121E-06 .451E-09 .213E-07 .524E-07 .195E-09 25 0 2.5 0.36716600E+00 0.36716600E+00 .116E-06 .264E-08 .155E-07 .424E-07 .970E-09 25 0 3.0 0.31673764E+00 0.31673764E+00 .168E-06 .308E-08 .678E-07 .532E-07 .975E-09 25 0 3.5 0.27708646E+00 0.27708646E+00 .126E-06 .161E-08 .255E-07 .348E-07 .447E-09 25 0 4.0 0.24542109E+00 0.24542109E+00 .157E-06 .122E-08 .570E-07 .385E-07 .300E-09 25 0 4.5 0.21975356E+00 0.21975356E+00 .158E-06 .296E-08 .583E-07 .348E-07 .650E-09 25 0 5.0 0.19865240E+00 0.19865241E+00 .192E-06 .299E-07 .917E-07 .381E-07 .593E-08 23 0 5.5 0.18107513E+00 0.18107513E+00 .198E-06 .187E-07 .978E-07 .358E-07 .338E-08 23 0 6.0 0.16625354E+00 0.16625354E+00 .177E-06 .768E-08 .767E-07 .294E-07 .128E-08 23 0 6.5 0.15361485E+00 0.15361486E+00 .148E-06 .274E-07 .477E-07 .227E-07 .421E-08 23 0 7.0 0.14272687E+00 0.14272687E+00 .148E-06 .341E-07 .480E-07 .211E-07 .487E-08 23 0 7.5 0.13325959E+00 0.13325959E+00 .161E-06 .144E-07 .606E-07 .214E-07 .191E-08 23 0 8.0 0.12495807E+00 0.12495807E+00 .240E-06 .265E-08 .140E-06 .300E-07 .331E-09 23 0 8.5 0.11762312E+00 0.11762312E+00 .162E-06 .138E-07 .624E-07 .191E-07 .162E-08 23 0 9.0 0.11109740E+00 0.11109740E+00 .170E-06 .772E-08 .705E-07 .189E-07 .858E-09 23 0 9.5 0.10525528E+00 0.10525528E+00 .216E-06 .132E-07 .116E-06 .228E-07 .139E-08 23 0 10.0 0.99995460E-01 0.99995460E-01 .104E-06 .410E-11 .385E-08 .104E-07 .410E-12 29 0 10.5 0.95235473E-01 0.95235473E-01 .236E-06 .123E-08 .136E-06 .224E-07 .117E-09 25 0 11.0 0.90907570E-01 0.90907573E-01 .216E-06 .259E-07 .116E-06 .197E-07 .235E-08 23 0 11.5 0.86955644E-01 0.86955641E-01 .245E-06 .312E-07 .145E-06 .213E-07 .271E-08 23 0 12.0 0.83332821E-01 0.83332821E-01 .232E-06 .167E-08 .132E-06 .193E-07 .139E-09 23 0 12.5 0.79999702E-01 0.79999702E-01 .211E-06 .237E-08 .111E-06 .169E-07 .189E-09 25 0 13.0 0.76922903E-01 0.76922903E-01 .193E-06 .900E-09 .934E-07 .149E-07 .692E-10 25 0 13.5 0.74073972E-01 0.74073973E-01 .107E-06 .301E-08 .674E-08 .791E-08 .223E-09 25 0 14.0 0.71428512E-01 0.71428512E-01 .131E-06 .328E-08 .306E-07 .933E-08 .234E-09 25 0 14.5 0.68965482E-01 0.68965482E-01 .133E-06 .142E-08 .332E-07 .919E-08 .976E-10 25 0 15.0 0.66666646E-01 0.66666646E-01 .138E-06 .862E-08 .380E-07 .920E-08 .575E-09 25 0 15.5 0.64516117E-01 0.64516117E-01 .177E-06 .459E-08 .770E-07 .114E-07 .296E-09 25 0 16.0 0.62499993E-01 0.62499993E-01 .137E-06 .570E-08 .373E-07 .858E-08 .356E-09 25 0 16.5 0.60606057E-01 0.60606056E-01 .194E-06 .790E-08 .938E-07 .117E-07 .479E-09 25 0 17.0 0.58823527E-01 0.58823527E-01 .139E-06 .184E-08 .387E-07 .816E-08 .109E-09 25 0 17.5 0.57142856E-01 0.57142856E-01 .208E-06 .129E-08 .108E-06 .119E-07 .736E-10 25 0 18.0 0.55555555E-01 0.55555555E-01 .107E-06 .132E-08 .661E-08 .592E-08 .732E-10 25 0 18.5 0.54054054E-01 0.54054054E-01 .195E-06 .313E-08 .949E-07 .105E-07 .169E-09 25 0 19.0 0.52631579E-01 0.52631579E-01 .133E-06 .210E-08 .326E-07 .698E-08 .111E-09 25 0 19.5 0.51282051E-01 0.51282051E-01 .139E-06 .630E-08 .390E-07 .713E-08 .323E-09 25 0 20.0 0.50000000E-01 0.50000000E-01 .166E-06 .140E-09 .661E-07 .830E-08 .701E-11 25 0 30.0 0.33333333E-01 0.33333333E-01 .154E-06 .363E-08 .539E-07 .513E-08 .121E-09 25 0 35.0 0.28571429E-01 0.28571429E-01 .144E-06 .120E-09 .444E-07 .413E-08 .344E-11 25 0 40.0 0.25000000E-01 0.25000000E-01 .183E-06 .418E-08 .834E-07 .458E-08 .104E-09 25 0 45.0 0.22222222E-01 0.22222222E-01 .103E-06 .197E-09 .258E-08 .228E-08 .439E-11 29 0 50.0 0.20000000E-01 0.20000000E-01 .145E-06 .257E-08 .447E-07 .289E-08 .514E-10 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 31 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 -.57721566E+00 -.57721560E+00 .106E-06 .112E-06 .647E-08 .615E-07 .648E-07 27 0 1.5 -.98268077E+00 -.98268071E+00 .191E-06 .680E-07 .906E-07 .187E-06 .668E-07 25 0 2.0 -.12703628E+01 -.12703628E+01 .171E-06 .519E-07 .713E-07 .218E-06 .660E-07 25 0 2.5 -.14935064E+01 -.14935063E+01 .155E-06 .445E-07 .552E-07 .232E-06 .664E-07 25 0 3.0 -.16758280E+01 -.16758279E+01 .149E-06 .403E-07 .491E-07 .250E-06 .676E-07 25 0 3.5 -.18299786E+01 -.18299786E+01 .142E-06 .370E-07 .424E-07 .261E-06 .676E-07 25 0 4.0 -.19635100E+01 -.19635100E+01 .144E-06 .314E-07 .442E-07 .283E-06 .617E-07 25 0 4.5 -.20812931E+01 -.20812930E+01 .138E-06 .336E-07 .384E-07 .288E-06 .698E-07 25 0 5.0 -.21866536E+01 -.21866535E+01 .138E-06 .294E-07 .383E-07 .302E-06 .643E-07 25 0 5.5 -.22819638E+01 -.22819637E+01 .138E-06 .278E-07 .375E-07 .314E-06 .635E-07 25 0 6.0 -.23689751E+01 -.23689751E+01 .136E-06 .276E-07 .357E-07 .322E-06 .653E-07 25 0 6.5 -.24490178E+01 -.24490178E+01 .133E-06 .283E-07 .327E-07 .325E-06 .694E-07 25 0 7.0 -.25231258E+01 -.25231257E+01 .133E-06 .265E-07 .333E-07 .336E-06 .670E-07 25 0 7.5 -.25921187E+01 -.25921186E+01 .133E-06 .252E-07 .330E-07 .345E-06 .654E-07 25 0 8.0 -.26566572E+01 -.26566571E+01 .135E-06 .249E-07 .350E-07 .359E-06 .661E-07 25 0 8.5 -.27172818E+01 -.27172818E+01 .130E-06 .253E-07 .300E-07 .353E-06 .686E-07 25 0 9.0 -.27744402E+01 -.27744402E+01 .131E-06 .238E-07 .308E-07 .363E-06 .660E-07 25 0 9.5 -.28285075E+01 -.28285074E+01 .131E-06 .234E-07 .306E-07 .370E-06 .662E-07 25 0 10.0 -.28798008E+01 -.28798007E+01 .131E-06 .223E-07 .307E-07 .376E-06 .643E-07 25 0 10.5 -.29285909E+01 -.29285909E+01 .131E-06 .230E-07 .309E-07 .383E-06 .674E-07 25 0 11.0 -.29751109E+01 -.29751109E+01 .129E-06 .225E-07 .289E-07 .384E-06 .671E-07 25 0 11.5 -.30195627E+01 -.30195626E+01 .131E-06 .222E-07 .308E-07 .395E-06 .670E-07 25 0 12.0 -.30621223E+01 -.30621222E+01 .129E-06 .222E-07 .293E-07 .396E-06 .680E-07 25 0 12.5 -.31029443E+01 -.31029442E+01 .130E-06 .204E-07 .302E-07 .404E-06 .632E-07 25 0 13.0 -.31421650E+01 -.31421650E+01 .129E-06 .215E-07 .289E-07 .405E-06 .677E-07 25 0 13.5 -.31799054E+01 -.31799053E+01 .128E-06 .205E-07 .283E-07 .408E-06 .651E-07 25 0 14.0 -.32162730E+01 -.32162729E+01 .128E-06 .208E-07 .280E-07 .412E-06 .670E-07 25 0 14.5 -.32513643E+01 -.32513642E+01 .129E-06 .202E-07 .288E-07 .419E-06 .656E-07 25 0 15.0 -.32852659E+01 -.32852658E+01 .128E-06 .209E-07 .282E-07 .421E-06 .686E-07 25 0 15.5 -.33180557E+01 -.33180556E+01 .128E-06 .205E-07 .285E-07 .426E-06 .680E-07 25 0 16.0 -.33498044E+01 -.33498043E+01 .129E-06 .187E-07 .287E-07 .431E-06 .626E-07 25 0 16.5 -.33805760E+01 -.33805760E+01 .128E-06 .195E-07 .276E-07 .431E-06 .660E-07 25 0 17.0 -.34104290E+01 -.34104289E+01 .126E-06 .195E-07 .261E-07 .430E-06 .666E-07 25 0 17.5 -.34394165E+01 -.34394165E+01 .127E-06 .197E-07 .272E-07 .437E-06 .678E-07 25 0 18.0 -.34675874E+01 -.34675874E+01 .126E-06 .193E-07 .256E-07 .436E-06 .671E-07 25 0 18.5 -.34949864E+01 -.34949863E+01 .127E-06 .191E-07 .269E-07 .444E-06 .667E-07 25 0 19.0 -.35216546E+01 -.35216546E+01 .125E-06 .189E-07 .255E-07 .442E-06 .664E-07 25 0 19.5 -.35476301E+01 -.35476301E+01 .125E-06 .190E-07 .253E-07 .444E-06 .673E-07 25 0 20.0 -.35729479E+01 -.35729479E+01 .127E-06 .189E-07 .266E-07 .453E-06 .674E-07 25 0 30.0 -.39784130E+01 -.39784130E+01 .124E-06 .164E-07 .236E-07 .492E-06 .652E-07 25 0 35.0 -.41325637E+01 -.41325637E+01 .123E-06 .163E-07 .230E-07 .508E-06 .672E-07 25 0 40.0 -.42660951E+01 -.42660951E+01 .122E-06 .159E-07 .223E-07 .522E-06 .679E-07 25 0 45.0 -.43838782E+01 -.43838781E+01 .122E-06 .147E-07 .218E-07 .534E-06 .643E-07 25 0 50.0 -.44892387E+01 -.44892386E+01 .122E-06 .139E-07 .223E-07 .549E-06 .626E-07 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 32 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.99991504E+00 0.10000000E+01 .144E-06 .850E-04 .437E-07 .144E-06 .850E-04 467 0 1.5 0.10000000E+01 0.10000000E+01 .208E-06 .164E-09 .108E-06 .208E-06 .164E-09 31 0 2.0 0.10000000E+01 0.10000000E+01 .126E-06 .261E-09 .257E-07 .126E-06 .261E-09 29 0 2.5 0.10000000E+01 0.10000000E+01 .152E-06 .221E-08 .525E-07 .152E-06 .221E-08 27 0 3.0 0.10000000E+01 0.10000000E+01 .110E-06 .490E-09 .104E-07 .110E-06 .490E-09 27 0 3.5 0.10000000E+01 0.10000000E+01 .106E-06 .123E-08 .607E-08 .106E-06 .123E-08 27 0 4.0 0.10000000E+01 0.10000000E+01 .108E-06 .402E-10 .821E-08 .108E-06 .402E-10 27 0 4.5 0.10000000E+01 0.10000000E+01 .106E-06 .331E-09 .574E-08 .106E-06 .331E-09 27 0 5.0 0.10000000E+01 0.10000000E+01 .106E-06 .563E-09 .590E-08 .106E-06 .563E-09 27 0 5.5 0.10000000E+01 0.10000000E+01 .103E-06 .208E-09 .324E-08 .103E-06 .208E-09 27 0 6.0 0.10000000E+01 0.10000000E+01 .103E-06 .222E-09 .273E-08 .103E-06 .222E-09 27 0 6.5 0.10000000E+01 0.10000000E+01 .104E-06 .210E-09 .421E-08 .104E-06 .210E-09 27 0 7.0 0.10000000E+01 0.10000000E+01 .172E-06 .953E-09 .721E-07 .172E-06 .953E-09 25 0 7.5 0.10000000E+01 0.10000000E+01 .157E-06 .262E-09 .572E-07 .157E-06 .262E-09 25 0 8.0 0.10000000E+01 0.10000000E+01 .151E-06 .176E-08 .512E-07 .151E-06 .176E-08 25 0 8.5 0.10000000E+01 0.10000000E+01 .146E-06 .118E-08 .455E-07 .146E-06 .118E-08 25 0 9.0 0.10000000E+01 0.10000000E+01 .139E-06 .192E-09 .393E-07 .139E-06 .192E-09 25 0 9.5 0.10000000E+01 0.10000000E+01 .133E-06 .878E-09 .334E-07 .133E-06 .878E-09 25 0 10.0 0.10000000E+01 0.10000000E+01 .127E-06 .103E-08 .269E-07 .127E-06 .103E-08 25 0 10.5 0.10000000E+01 0.10000000E+01 .119E-06 .581E-09 .192E-07 .119E-06 .581E-09 25 0 11.0 0.10000000E+01 0.10000000E+01 .107E-06 .272E-08 .734E-08 .107E-06 .272E-08 25 0 11.5 0.10000000E+01 0.10000000E+01 .104E-06 .148E-08 .450E-08 .104E-06 .148E-08 25 0 12.0 0.10000000E+01 0.10000000E+01 .107E-06 .719E-09 .692E-08 .107E-06 .719E-09 25 0 12.5 0.10000000E+01 0.10000000E+01 .105E-06 .132E-08 .466E-08 .105E-06 .132E-08 25 0 13.0 0.10000000E+01 0.10000000E+01 .102E-06 .146E-08 .239E-08 .102E-06 .146E-08 25 0 13.5 0.10000000E+01 0.10000000E+01 .108E-06 .606E-09 .781E-08 .108E-06 .606E-09 25 0 14.0 0.10000000E+01 0.10000000E+01 .110E-06 .552E-09 .998E-08 .110E-06 .552E-09 25 0 14.5 0.10000000E+01 0.10000000E+01 .114E-06 .910E-09 .136E-07 .114E-06 .910E-09 25 0 15.0 0.10000000E+01 0.10000000E+01 .113E-06 .327E-09 .135E-07 .113E-06 .327E-09 25 0 15.5 0.10000000E+01 0.10000000E+01 .114E-06 .974E-10 .136E-07 .114E-06 .974E-10 25 0 16.0 0.10000000E+01 0.10000000E+01 .115E-06 .598E-09 .145E-07 .115E-06 .598E-09 25 0 16.5 0.10000000E+01 0.10000000E+01 .116E-06 .242E-09 .160E-07 .116E-06 .242E-09 25 0 17.0 0.10000000E+01 0.10000000E+01 .118E-06 .155E-09 .177E-07 .118E-06 .155E-09 25 0 17.5 0.10000000E+01 0.10000000E+01 .120E-06 .336E-09 .196E-07 .120E-06 .336E-09 25 0 18.0 0.10000000E+01 0.10000000E+01 .117E-06 .416E-09 .166E-07 .117E-06 .416E-09 25 0 18.5 0.10000000E+01 0.10000000E+01 .117E-06 .542E-09 .170E-07 .117E-06 .542E-09 25 0 19.0 0.10000000E+01 0.10000000E+01 .118E-06 .456E-10 .178E-07 .118E-06 .456E-10 25 0 19.5 0.10000000E+01 0.10000000E+01 .116E-06 .669E-09 .158E-07 .116E-06 .669E-09 25 0 20.0 0.10000000E+01 0.10000000E+01 .117E-06 .141E-09 .174E-07 .117E-06 .141E-09 25 0 30.0 0.10000000E+01 0.10000000E+01 .112E-06 .437E-09 .120E-07 .112E-06 .437E-09 25 0 35.0 0.10000000E+01 0.10000000E+01 .111E-06 .409E-09 .110E-07 .111E-06 .409E-09 25 0 40.0 0.10000000E+01 0.10000000E+01 .111E-06 .353E-09 .111E-07 .111E-06 .353E-09 25 0 45.0 0.10000000E+01 0.10000000E+01 .108E-06 .264E-08 .759E-08 .108E-06 .264E-08 25 0 50.0 0.10000000E+01 0.10000000E+01 .112E-06 .796E-09 .119E-07 .112E-06 .796E-09 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 33 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** ERROR DETECTED , I = 1 IFAIL= -1 1.5 0.10000000E+01 0.10000000E+01 .233E-06 .429E-07 .133E-06 .233E-06 .429E-07 69 0 ERROR DETECTED , I = 3 IFAIL= -1 2.5 0.23803729E-12 0.00000000E+00 .167E+00 .238E-12 .167E+00 .397E-13 .238E-12 157 0 ERROR DETECTED , I = 5 IFAIL= -1 3.5 0.99999990E+00 0.10000000E+01 .102E-06 .954E-07 .228E-08 .102E-06 .954E-07 139 0 ERROR DETECTED , I = 7 IFAIL= -1 4.5 0.30913081E-12 0.00000000E+00 .500E+00 .309E-12 .500E+00 .155E-12 .309E-12 279 0 ERROR DETECTED , I = 9 IFAIL= -1 5.5 0.10000004E+01 0.10000000E+01 .208E-06 .352E-06 .108E-06 .208E-06 .352E-06 203 0 ERROR DETECTED , I = 11 IFAIL= -1 6.5 0.40824785E-11 0.00000000E+00 .375E+00 .408E-11 .375E+00 .153E-11 .408E-11 395 0 ERROR DETECTED , I = 13 IFAIL= -1 7.5 0.10000001E+01 0.10000000E+01 .166E-06 .116E-06 .658E-07 .166E-06 .116E-06 289 0 ERROR DETECTED , I = 15 IFAIL= -1 ERROR DETECTED , I = 16 IFAIL= -1 ERROR DETECTED , I = 17 IFAIL= -1 9.5 0.10000035E+01 0.10000000E+01 .145E-06 .354E-05 .452E-07 .145E-06 .354E-05 289 0 ERROR DETECTED , I = 19 IFAIL= -1 ERROR DETECTED , I = 20 IFAIL= -1 ERROR DETECTED , I = 21 IFAIL= -1 11.5 0.10001191E+01 0.10000000E+01 .205E-06 .119E-03 .105E-06 .205E-06 .119E-03 259 0 ERROR DETECTED , I = 23 IFAIL= -1 ERROR DETECTED , I = 24 IFAIL= -1 ERROR DETECTED , I = 25 IFAIL= -1 13.5 0.99973027E+00 0.10000000E+01 .223E-06 .270E-03 .123E-06 .223E-06 .270E-03 343 0 ERROR DETECTED , I = 27 IFAIL= -1 ERROR DETECTED , I = 28 IFAIL= -1 ERROR DETECTED , I = 29 IFAIL= -1 15.5 0.11366197E+01 0.10000000E+01 .192E-06 .137E+00 .919E-07 .218E-06 .137E+00 89 0 ERROR DETECTED , I = 31 IFAIL= -1 ERROR DETECTED , I = 32 IFAIL= -1 17.0 0.49999998E+00 0.50000000E+00 .225E-06 .307E-07 .125E-06 .113E-06 .154E-07 95 0 17.5 0.50000000E+00 0.10000000E+01 .171E-06 .500E+00 .713E-07 .857E-07 .500E+00 31 0 18.0 0.50000000E+00 0.50000000E+00 .197E-06 .515E-08 .968E-07 .984E-07 .257E-08 27 0 18.5 0.49999999E+00 0.00000000E+00 .144E-06 .500E+00 .445E-07 .722E-07 .500E+00 33 0 19.0 0.49999999E+00 0.50000000E+00 .150E-06 .117E-07 .495E-07 .748E-07 .583E-08 27 0 19.5 0.50000000E+00 0.10000000E+01 .145E-06 .500E+00 .446E-07 .723E-07 .500E+00 27 0 20.0 0.50000000E+00 0.50000000E+00 .125E-06 .835E-08 .249E-07 .624E-07 .417E-08 27 0 30.0 0.50000000E+00 0.50000000E+00 .191E-06 .567E-08 .912E-07 .956E-07 .284E-08 25 0 35.0 0.50000000E+00 0.50000000E+00 .188E-06 .589E-09 .877E-07 .939E-07 .295E-09 25 0 40.0 0.50000000E+00 0.50000000E+00 .175E-06 .199E-08 .751E-07 .875E-07 .993E-09 25 0 45.0 0.50000000E+00 0.50000000E+00 .157E-06 .157E-08 .570E-07 .785E-07 .786E-09 25 0 50.0 0.50000000E+00 0.50000000E+00 .141E-06 .774E-09 .414E-07 .707E-07 .387E-09 25 0 ****************************************************************************************** SUBROUTINE INVLTF NUMERICAL INVERSION OF A LAPLACE TRANSFORM: THIS VERSION USES BOTH REAL AND COMPLEX DOUBLE PRECISION OPERATIONS ****************************************************************************************** TEST FUNCTION : TEST FUNCTION -----> 34 ABSCISSA OF CONVERGENCE ---> ABSCISSA OF CONVERGENCE ---> 0.0 <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< THE T-VALUES AT WHICH THE INVERSE IS REQUIRED ARE T=1,20 STEP=0.5 AND T=20,100 STEP=10. <><><><><><><><><><><><><><><><><><><><><><><<><><><><><><><><><><><><><><><><><><><><><>< ****************************************************************************************** OUTPUT T : POINT AT WHICH THE INVERSE TRANSFORM IS COMPUTED; FEX : EXACT VALUE OF THE INVERSE TRANSFORM; FCAL : COMPUTED VALUE OF THE INVERSE TRANSFORM; ESTREL : ESTIMATED RELATIVE ERROR; RELERR : ACTUAL RELATIVE ERROR; ESTABS : ESTIMATED ABSOLUTE ERROR ; ABSERR : ACTUAL ABSOLUTE ERROR; N : # OF FUNCTION EVALUATIONS; IFAIL : = 0 NO INPUT ERRORS; SUCCESSFUL RUN (ACCURACY REACHED AND IFZEVAL= 1, = 2 VALT LESS THAN ZERO, = -1 ACCURACY NOT REACHED AND IFZEVAL > NMAX;, = -2 THE CHOICE FOR SSBAR MAY BE NOT OPTIMAL; IN SUCH A CASE THE USER MAY SLIGHTLY CHANGE THE DEFAULT VALUE; ****************************************************************************************** TOLL --> 0.1000000E-05 ************************************************************************************** T FCAL FEX ESTREL RELERR TRUNERR ESTABS ABSERR N IFAIL **************************************************************************************** 1.0 0.18393972E+00 0.54711886E+00 .265E-06 .664E+00 .165E-06 .487E-07 .363E+00 25 0 1.5 0.36156510E+00 0.74374312E+00 .205E-06 .514E+00 .105E-06 .741E-07 .382E+00 35 0 2.0 0.56752447E+00 0.86466403E+00 .139E-06 .344E+00 .394E-07 .791E-07 .297E+00 469 0 2.5 0.39757314E+00 0.90108312E+00 .147E-06 .559E+00 .469E-07 .584E-07 .504E+00 51 0 3.0 0.39277297E+00 0.93870920E+00 .110E-06 .582E+00 .954E-08 .430E-07 .546E+00 59 0 3.5 0.48822875E+00 0.96531940E+00 .179E-06 .494E+00 .792E-07 .875E-07 .477E+00 69 0 ERROR DETECTED , I = 7 IFAIL= -1 4.5 0.44416997E+00 0.98661306E+00 .192E-06 .550E+00 .916E-07 .851E-07 .542E+00 83 0 5.0 0.42103541E+00 0.99170519E+00 .256E-06 .575E+00 .156E-06 .108E-06 .571E+00 95 0 5.5 0.50537093E+00 0.99530649E+00 .160E-06 .492E+00 .595E-07 .806E-07 .490E+00 117 0 ERROR DETECTED , I = 11 IFAIL= -1 6.5 0.45047633E+00 0.99818827E+00 .210E-06 .549E+00 .110E-06 .946E-07 .548E+00 133 0 7.0 0.42486046E+00 0.99887742E+00 .168E-06 .575E+00 .679E-07 .713E-07 .574E+00 127 0 7.5 0.50769082E+00 0.99936480E+00 .187E-06 .492E+00 .866E-07 .948E-07 .492E+00 139 0 ERROR DETECTED , I = 15 IFAIL= -1 8.5 0.45132976E+00 0.99975481E+00 .178E-06 .549E+00 .782E-07 .804E-07 .548E+00 173 0 9.0 0.42537979E+00 0.99984808E+00 .195E-06 .575E+00 .947E-07 .828E-07 .574E+00 127 0 9.5 0.50799931E+00 0.99991404E+00 .246E-06 .492E+00 .146E-06 .125E-06 .492E+00 137 0 ERROR DETECTED , I = 19 IFAIL= -1 10.5 0.45161686E+00 0.99996682E+00 .197E-06 .548E+00 .967E-07 .888E-07 .548E+00 103 0 11.0 0.42544986E+00 0.99997944E+00 .171E-06 .575E+00 .709E-07 .727E-07 .575E+00 149 0 11.5 0.50804175E+00 0.99998837E+00 .127E-06 .492E+00 .268E-07 .644E-07 .492E+00 159 0 ERROR DETECTED , I = 23 IFAIL= -1 12.5 0.45145802E+00 0.99999551E+00 .124E-06 .549E+00 .240E-07 .560E-07 .549E+00 171 0 13.0 0.42551762E+00 0.99999722E+00 .222E-06 .574E+00 .122E-06 .945E-07 .574E+00 125 0 13.5 0.50821271E+00 0.99999843E+00 .193E-06 .492E+00 .926E-07 .979E-07 .492E+00 129 0 14.0 0.64951694E+00 0.99999917E+00 .138E-06 .350E+00 .375E-07 .893E-07 .350E+00 193 0 14.5 0.45163429E+00 0.99999939E+00 .156E-06 .548E+00 .561E-07 .705E-07 .548E+00 141 0 15.0 0.42755124E+00 0.99999962E+00 .250E-06 .572E+00 .150E-06 .107E-06 .572E+00 87 0 15.5 0.50598608E+00 0.99999979E+00 .172E-06 .494E+00 .718E-07 .869E-07 .494E+00 87 0 16.0 0.49999991E+00 0.99999989E+00 .194E-06 .500E+00 .943E-07 .971E-07 .500E+00 27 0 16.5 0.49999993E+00 0.99999992E+00 .134E-06 .500E+00 .339E-07 .669E-07 .500E+00 29 0 17.0 0.49999997E+00 0.99999995E+00 .163E-06 .500E+00 .634E-07 .817E-07 .500E+00 27 0 17.5 0.49999998E+00 0.99999997E+00 .216E-06 .500E+00 .116E-06 .108E-06 .500E+00 25 0 18.0 0.49999999E+00 0.99999998E+00 .143E-06 .500E+00 .434E-07 .717E-07 .500E+00 27 0 18.5 0.49999999E+00 0.99999999E+00 .188E-06 .500E+00 .878E-07 .939E-07 .500E+00 27 0 19.0 0.50000000E+00 0.99999999E+00 .130E-06 .500E+00 .300E-07 .650E-07 .500E+00 27 0 19.5 0.49999999E+00 0.10000000E+01 .121E-06 .500E+00 .208E-07 .604E-07 .500E+00 27 0 20.0 0.50000000E+00 0.10000000E+01 .131E-06 .500E+00 .307E-07 .653E-07 .500E+00 27 0 30.0 0.50000000E+00 0.10000000E+01 .147E-06 .500E+00 .472E-07 .736E-07 .500E+00 25 0 35.0 0.50000000E+00 0.10000000E+01 .123E-06 .500E+00 .229E-07 .614E-07 .500E+00 25 0 40.0 0.50000000E+00 0.10000000E+01 .108E-06 .500E+00 .751E-08 .538E-07 .500E+00 25 0 45.0 0.50000000E+00 0.10000000E+01 .115E-06 .500E+00 .152E-07 .576E-07 .500E+00 25 0 50.0 0.50000000E+00 0.10000000E+01 .105E-06 .500E+00 .544E-08 .527E-07 .500E+00 25 0 SHAR_EOF fi # end of overwriting check # End of shell archive exit 0