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OpenLibm/slatec/dqk21.f
Viral B. Shah c977aa998f Add Makefile.extras to build libopenlibm-extras. 
Replace amos with slatec
2012-12-31 16:37:05 -05:00

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*DECK DQK21
SUBROUTINE DQK21 (F, A, B, RESULT, ABSERR, RESABS, RESASC)
C***BEGIN PROLOGUE DQK21
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 (QK21-S, DQK21-D)
C***KEYWORDS 21-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 driver 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 21-POINT
C KRONROD RULE (RESK) obtained by optimal addition
C of abscissae to the 10-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 DQK21
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(10),FV2(10),WG(5),WGK(11),XGK(11)
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 21-POINT KRONROD RULE
C XGK(2), XGK(4), ... ABSCISSAE OF THE 10-POINT
C GAUSS RULE
C XGK(1), XGK(3), ... ABSCISSAE WHICH ARE OPTIMALLY
C ADDED TO THE 10-POINT GAUSS RULE
C
C WGK - WEIGHTS OF THE 21-POINT KRONROD RULE
C
C WG - WEIGHTS OF THE 10-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) / 0.0666713443 0868813759 3568809893 332 D0 /
DATA WG ( 2) / 0.1494513491 5058059314 5776339657 697 D0 /
DATA WG ( 3) / 0.2190863625 1598204399 5534934228 163 D0 /
DATA WG ( 4) / 0.2692667193 0999635509 1226921569 469 D0 /
DATA WG ( 5) / 0.2955242247 1475287017 3892994651 338 D0 /
C
DATA XGK ( 1) / 0.9956571630 2580808073 5527280689 003 D0 /
DATA XGK ( 2) / 0.9739065285 1717172007 7964012084 452 D0 /
DATA XGK ( 3) / 0.9301574913 5570822600 1207180059 508 D0 /
DATA XGK ( 4) / 0.8650633666 8898451073 2096688423 493 D0 /
DATA XGK ( 5) / 0.7808177265 8641689706 3717578345 042 D0 /
DATA XGK ( 6) / 0.6794095682 9902440623 4327365114 874 D0 /
DATA XGK ( 7) / 0.5627571346 6860468333 9000099272 694 D0 /
DATA XGK ( 8) / 0.4333953941 2924719079 9265943165 784 D0 /
DATA XGK ( 9) / 0.2943928627 0146019813 1126603103 866 D0 /
DATA XGK ( 10) / 0.1488743389 8163121088 4826001129 720 D0 /
DATA XGK ( 11) / 0.0000000000 0000000000 0000000000 000 D0 /
C
DATA WGK ( 1) / 0.0116946388 6737187427 8064396062 192 D0 /
DATA WGK ( 2) / 0.0325581623 0796472747 8818972459 390 D0 /
DATA WGK ( 3) / 0.0547558965 7435199603 1381300244 580 D0 /
DATA WGK ( 4) / 0.0750396748 1091995276 7043140916 190 D0 /
DATA WGK ( 5) / 0.0931254545 8369760553 5065465083 366 D0 /
DATA WGK ( 6) / 0.1093871588 0229764189 9210590325 805 D0 /
DATA WGK ( 7) / 0.1234919762 6206585107 7958109831 074 D0 /
DATA WGK ( 8) / 0.1347092173 1147332592 8054001771 707 D0 /
DATA WGK ( 9) / 0.1427759385 7706008079 7094273138 717 D0 /
DATA WGK ( 10) / 0.1477391049 0133849137 4841515972 068 D0 /
DATA WGK ( 11) / 0.1494455540 0291690566 4936468389 821 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 10-POINT GAUSS FORMULA
C RESK - RESULT OF THE 21-POINT KRONROD FORMULA
C RESKH - APPROXIMATION TO THE MEAN VALUE OF F OVER (A,B),
C I.E. TO I/(B-A)
C
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 DQK21
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 21-POINT KRONROD APPROXIMATION TO
C THE INTEGRAL, AND ESTIMATE THE ABSOLUTE ERROR.
C
RESG = 0.0D+00
FC = F(CENTR)
RESK = WGK(11)*FC
RESABS = ABS(RESK)
DO 10 J=1,5
JTW = 2*J
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 = 1,5
JTWM1 = 2*J-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(11)*ABS(FC-RESKH)
DO 20 J=1,10
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
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