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OpenLibm/slatec/qk61.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 QK61
SUBROUTINE QK61 (F, A, B, RESULT, ABSERR, RESABS, RESASC)
C***BEGIN PROLOGUE QK61
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 SINGLE PRECISION (QK61-S, DQK61-D)
C***KEYWORDS 61-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 rule
C Standard fortran subroutine
C Real version
C
C
C PARAMETERS
C ON ENTRY
C F - Real
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 - Real
C Lower limit of integration
C
C B - Real
C Upper limit of integration
C
C ON RETURN
C RESULT - Real
C Approximation to the integral I
C RESULT is computed by applying the 61-point
C Kronrod rule (RESK) obtained by optimal addition of
C abscissae to the 30-point Gauss rule (RESG).
C
C ABSERR - Real
C Estimate of the modulus of the absolute error,
C which should equal or exceed ABS(I-RESULT)
C
C RESABS - Real
C Approximation to the integral J
C
C RESASC - Real
C Approximation to the integral of ABS(F-I/(B-A))
C
C***REFERENCES (NONE)
C***ROUTINES CALLED R1MACH
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 QK61
C
REAL A,ABSC,ABSERR,B,CENTR,DHLGTH,EPMACH,F,FC,FSUM,FVAL1,FVAL2,
1 FV1,FV2,HLGTH,RESABS,RESASC,RESG,RESK,RESKH,RESULT,R1MACH,UFLOW,
2 WG,WGK,XGK
INTEGER J,JTW,JTWM1
EXTERNAL F
C
DIMENSION FV1(30),FV2(30),XGK(31),WGK(31),WG(15)
C
C THE ABSCISSAE AND WEIGHTS ARE GIVEN FOR THE
C INTERVAL (-1,1). BECAUSE OF SYMMETRY ONLY THE POSITIVE
C ABSCISSAE AND THEIR CORRESPONDING WEIGHTS ARE GIVEN.
C
C XGK - ABSCISSAE OF THE 61-POINT KRONROD RULE
C XGK(2), XGK(4) ... ABSCISSAE OF THE 30-POINT
C GAUSS RULE
C XGK(1), XGK(3) ... OPTIMALLY ADDED ABSCISSAE
C TO THE 30-POINT GAUSS RULE
C
C WGK - WEIGHTS OF THE 61-POINT KRONROD RULE
C
C WG - WEIGHTS OF THE 30-POINT GAUSS RULE
C
SAVE XGK, WGK, WG
DATA XGK(1),XGK(2),XGK(3),XGK(4),XGK(5),XGK(6),XGK(7),XGK(8),
1 XGK(9),XGK(10)/
2 0.9994844100504906E+00, 0.9968934840746495E+00,
3 0.9916309968704046E+00, 0.9836681232797472E+00,
4 0.9731163225011263E+00, 0.9600218649683075E+00,
5 0.9443744447485600E+00, 0.9262000474292743E+00,
6 0.9055733076999078E+00, 0.8825605357920527E+00/
DATA XGK(11),XGK(12),XGK(13),XGK(14),XGK(15),XGK(16),
1 XGK(17),XGK(18),XGK(19),XGK(20)/
2 0.8572052335460611E+00, 0.8295657623827684E+00,
3 0.7997278358218391E+00, 0.7677774321048262E+00,
4 0.7337900624532268E+00, 0.6978504947933158E+00,
5 0.6600610641266270E+00, 0.6205261829892429E+00,
6 0.5793452358263617E+00, 0.5366241481420199E+00/
DATA XGK(21),XGK(22),XGK(23),XGK(24),
1 XGK(25),XGK(26),XGK(27),XGK(28),XGK(29),XGK(30),XGK(31)/
2 0.4924804678617786E+00, 0.4470337695380892E+00,
3 0.4004012548303944E+00, 0.3527047255308781E+00,
4 0.3040732022736251E+00, 0.2546369261678898E+00,
5 0.2045251166823099E+00, 0.1538699136085835E+00,
6 0.1028069379667370E+00, 0.5147184255531770E-01,
7 0.0E+00 /
DATA WGK(1),WGK(2),WGK(3),WGK(4),WGK(5),WGK(6),WGK(7),WGK(8),
1 WGK(9),WGK(10)/
2 0.1389013698677008E-02, 0.3890461127099884E-02,
3 0.6630703915931292E-02, 0.9273279659517763E-02,
4 0.1182301525349634E-01, 0.1436972950704580E-01,
5 0.1692088918905327E-01, 0.1941414119394238E-01,
6 0.2182803582160919E-01, 0.2419116207808060E-01/
DATA WGK(11),WGK(12),WGK(13),WGK(14),WGK(15),WGK(16),
1 WGK(17),WGK(18),WGK(19),WGK(20)/
2 0.2650995488233310E-01, 0.2875404876504129E-01,
3 0.3090725756238776E-01, 0.3298144705748373E-01,
4 0.3497933802806002E-01, 0.3688236465182123E-01,
5 0.3867894562472759E-01, 0.4037453895153596E-01,
6 0.4196981021516425E-01, 0.4345253970135607E-01/
DATA WGK(21),WGK(22),WGK(23),WGK(24),
1 WGK(25),WGK(26),WGK(27),WGK(28),WGK(29),WGK(30),WGK(31)/
2 0.4481480013316266E-01, 0.4605923827100699E-01,
3 0.4718554656929915E-01, 0.4818586175708713E-01,
4 0.4905543455502978E-01, 0.4979568342707421E-01,
5 0.5040592140278235E-01, 0.5088179589874961E-01,
6 0.5122154784925877E-01, 0.5142612853745903E-01,
7 0.5149472942945157E-01/
DATA WG(1),WG(2),WG(3),WG(4),WG(5),WG(6),WG(7),WG(8)/
1 0.7968192496166606E-02, 0.1846646831109096E-01,
2 0.2878470788332337E-01, 0.3879919256962705E-01,
3 0.4840267283059405E-01, 0.5749315621761907E-01,
4 0.6597422988218050E-01, 0.7375597473770521E-01/
DATA WG(9),WG(10),WG(11),WG(12),WG(13),WG(14),WG(15)/
1 0.8075589522942022E-01, 0.8689978720108298E-01,
2 0.9212252223778613E-01, 0.9636873717464426E-01,
3 0.9959342058679527E-01, 0.1017623897484055E+00,
4 0.1028526528935588E+00/
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 30-POINT GAUSS RULE
C RESK - RESULT OF THE 61-POINT KRONROD RULE
C RESKH - APPROXIMATION TO THE MEAN VALUE OF F
C OVER (A,B), 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 QK61
EPMACH = R1MACH(4)
UFLOW = R1MACH(1)
C
CENTR = 0.5E+00*(B+A)
HLGTH = 0.5E+00*(B-A)
DHLGTH = ABS(HLGTH)
C
C COMPUTE THE 61-POINT KRONROD APPROXIMATION TO THE
C INTEGRAL, AND ESTIMATE THE ABSOLUTE ERROR.
C
RESG = 0.0E+00
FC = F(CENTR)
RESK = WGK(31)*FC
RESABS = ABS(RESK)
DO 10 J=1,15
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=1,15
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*0.5E+00
RESASC = WGK(31)*ABS(FC-RESKH)
DO 20 J=1,30
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.0.0E+00.AND.ABSERR.NE.0.0E+00)
1 ABSERR = RESASC*MIN(0.1E+01,
2 (0.2E+03*ABSERR/RESASC)**1.5E+00)
IF(RESABS.GT.UFLOW/(0.5E+02*EPMACH)) ABSERR = MAX
1 ((EPMACH*0.5E+02)*RESABS,ABSERR)
RETURN
END
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