Fcalva/OpenLibm
1
0
Fork 0
mirror of https://git.planet-casio.com/Lephenixnoir/OpenLibm.git synced 2025-01-01 06:23:39 +01:00
Code Issues Projects Releases Packages Wiki Activity Actions
OpenLibm/slatec/dqk15.f
Viral B. Shah c977aa998f Add Makefile.extras to build libopenlibm-extras. 
Replace amos with slatec
2012-12-31 16:37:05 -05:00

185 lines
6.8 KiB
Fortran
Raw Blame History

*DECK DQK15
SUBROUTINE DQK15 (F, A, B, RESULT, ABSERR, RESABS, RESASC)
C***BEGIN PROLOGUE DQK15
C***PURPOSE To compute I = Integral of F over (A,B), with error
C estimate
C J = integral of ABS(F) over (A,B)
C***LIBRARY SLATEC (QUADPACK)
C***CATEGORY H2A1A2
C***TYPE DOUBLE PRECISION (QK15-S, DQK15-D)
C***KEYWORDS 15-POINT GAUSS-KRONROD RULES, QUADPACK, QUADRATURE
C***AUTHOR Piessens, Robert
C Applied Mathematics and Programming Division
C K. U. Leuven
C de Doncker, Elise
C Applied Mathematics and Programming Division
C K. U. Leuven
C***DESCRIPTION
C
C Integration rules
C Standard fortran subroutine
C Double precision version
C
C PARAMETERS
C ON ENTRY
C F - Double precision
C Function subprogram defining the integrand
C FUNCTION F(X). The actual name for F needs to be
C Declared E X T E R N A L in the calling program.
C
C A - Double precision
C Lower limit of integration
C
C B - Double precision
C Upper limit of integration
C
C ON RETURN
C RESULT - Double precision
C Approximation to the integral I
C Result is computed by applying the 15-POINT
C KRONROD RULE (RESK) obtained by optimal addition
C of abscissae to the 7-POINT GAUSS RULE(RESG).
C
C ABSERR - Double precision
C Estimate of the modulus of the absolute error,
C which should not exceed ABS(I-RESULT)
C
C RESABS - Double precision
C Approximation to the integral J
C
C RESASC - Double precision
C Approximation to the integral of ABS(F-I/(B-A))
C over (A,B)
C
C***REFERENCES (NONE)
C***ROUTINES CALLED D1MACH
C***REVISION HISTORY (YYMMDD)
C 800101 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C***END PROLOGUE DQK15
C
DOUBLE PRECISION A,ABSC,ABSERR,B,CENTR,DHLGTH,
1 D1MACH,EPMACH,F,FC,FSUM,FVAL1,FVAL2,FV1,FV2,HLGTH,RESABS,RESASC,
2 RESG,RESK,RESKH,RESULT,UFLOW,WG,WGK,XGK
INTEGER J,JTW,JTWM1
EXTERNAL F
C
DIMENSION FV1(7),FV2(7),WG(4),WGK(8),XGK(8)
C
C THE ABSCISSAE AND WEIGHTS ARE GIVEN FOR THE INTERVAL (-1,1).
C BECAUSE OF SYMMETRY ONLY THE POSITIVE ABSCISSAE AND THEIR
C CORRESPONDING WEIGHTS ARE GIVEN.
C
C XGK - ABSCISSAE OF THE 15-POINT KRONROD RULE
C XGK(2), XGK(4), ... ABSCISSAE OF THE 7-POINT
C GAUSS RULE
C XGK(1), XGK(3), ... ABSCISSAE WHICH ARE OPTIMALLY
C ADDED TO THE 7-POINT GAUSS RULE
C
C WGK - WEIGHTS OF THE 15-POINT KRONROD RULE
C
C WG - WEIGHTS OF THE 7-POINT GAUSS RULE
C
C
C GAUSS QUADRATURE WEIGHTS AND KRONROD QUADRATURE ABSCISSAE AND WEIGHTS
C AS EVALUATED WITH 80 DECIMAL DIGIT ARITHMETIC BY L. W. FULLERTON,
C BELL LABS, NOV. 1981.
C
SAVE WG, XGK, WGK
DATA WG ( 1) / 0.1294849661 6886969327 0611432679 082 D0 /
DATA WG ( 2) / 0.2797053914 8927666790 1467771423 780 D0 /
DATA WG ( 3) / 0.3818300505 0511894495 0369775488 975 D0 /
DATA WG ( 4) / 0.4179591836 7346938775 5102040816 327 D0 /
C
DATA XGK ( 1) / 0.9914553711 2081263920 6854697526 329 D0 /
DATA XGK ( 2) / 0.9491079123 4275852452 6189684047 851 D0 /
DATA XGK ( 3) / 0.8648644233 5976907278 9712788640 926 D0 /
DATA XGK ( 4) / 0.7415311855 9939443986 3864773280 788 D0 /
DATA XGK ( 5) / 0.5860872354 6769113029 4144838258 730 D0 /
DATA XGK ( 6) / 0.4058451513 7739716690 6606412076 961 D0 /
DATA XGK ( 7) / 0.2077849550 0789846760 0689403773 245 D0 /
DATA XGK ( 8) / 0.0000000000 0000000000 0000000000 000 D0 /
C
DATA WGK ( 1) / 0.0229353220 1052922496 3732008058 970 D0 /
DATA WGK ( 2) / 0.0630920926 2997855329 0700663189 204 D0 /
DATA WGK ( 3) / 0.1047900103 2225018383 9876322541 518 D0 /
DATA WGK ( 4) / 0.1406532597 1552591874 5189590510 238 D0 /
DATA WGK ( 5) / 0.1690047266 3926790282 6583426598 550 D0 /
DATA WGK ( 6) / 0.1903505780 6478540991 3256402421 014 D0 /
DATA WGK ( 7) / 0.2044329400 7529889241 4161999234 649 D0 /
DATA WGK ( 8) / 0.2094821410 8472782801 2999174891 714 D0 /
C
C
C LIST OF MAJOR VARIABLES
C -----------------------
C
C CENTR - MID POINT OF THE INTERVAL
C HLGTH - HALF-LENGTH OF THE INTERVAL
C ABSC - ABSCISSA
C FVAL* - FUNCTION VALUE
C RESG - RESULT OF THE 7-POINT GAUSS FORMULA
C RESK - RESULT OF THE 15-POINT KRONROD FORMULA
C RESKH - APPROXIMATION TO THE MEAN VALUE OF F OVER (A,B),
C I.E. TO I/(B-A)
C
C MACHINE DEPENDENT CONSTANTS
C ---------------------------
C
C EPMACH IS THE LARGEST RELATIVE SPACING.
C UFLOW IS THE SMALLEST POSITIVE MAGNITUDE.
C
C***FIRST EXECUTABLE STATEMENT DQK15
EPMACH = D1MACH(4)
UFLOW = D1MACH(1)
C
CENTR = 0.5D+00*(A+B)
HLGTH = 0.5D+00*(B-A)
DHLGTH = ABS(HLGTH)
C
C COMPUTE THE 15-POINT KRONROD APPROXIMATION TO
C THE INTEGRAL, AND ESTIMATE THE ABSOLUTE ERROR.
C
FC = F(CENTR)
RESG = FC*WG(4)
RESK = FC*WGK(8)
RESABS = ABS(RESK)
DO 10 J=1,3
JTW = J*2
ABSC = HLGTH*XGK(JTW)
FVAL1 = F(CENTR-ABSC)
FVAL2 = F(CENTR+ABSC)
FV1(JTW) = FVAL1
FV2(JTW) = FVAL2
FSUM = FVAL1+FVAL2
RESG = RESG+WG(J)*FSUM
RESK = RESK+WGK(JTW)*FSUM
RESABS = RESABS+WGK(JTW)*(ABS(FVAL1)+ABS(FVAL2))
10 CONTINUE
DO 15 J = 1,4
JTWM1 = J*2-1
ABSC = HLGTH*XGK(JTWM1)
FVAL1 = F(CENTR-ABSC)
FVAL2 = F(CENTR+ABSC)
FV1(JTWM1) = FVAL1
FV2(JTWM1) = FVAL2
FSUM = FVAL1+FVAL2
RESK = RESK+WGK(JTWM1)*FSUM
RESABS = RESABS+WGK(JTWM1)*(ABS(FVAL1)+ABS(FVAL2))
15 CONTINUE
RESKH = RESK*0.5D+00
RESASC = WGK(8)*ABS(FC-RESKH)
DO 20 J=1,7
RESASC = RESASC+WGK(J)*(ABS(FV1(J)-RESKH)+ABS(FV2(J)-RESKH))
20 CONTINUE
RESULT = RESK*HLGTH
RESABS = RESABS*DHLGTH
RESASC = RESASC*DHLGTH
ABSERR = ABS((RESK-RESG)*HLGTH)
IF(RESASC.NE.0.0D+00.AND.ABSERR.NE.0.0D+00)
1 ABSERR = RESASC*MIN(0.1D+01,(0.2D+03*ABSERR/RESASC)**1.5D+00)
IF(RESABS.GT.UFLOW/(0.5D+02*EPMACH)) ABSERR = MAX
1 ((EPMACH*0.5D+02)*RESABS,ABSERR)
RETURN
END
Reference in a new issue View git blame Copy permalink