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QH8.FOR
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1985-11-29
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52 lines
C
C ..................................................................
C
C SUBROUTINE QH8
C
C PURPOSE
C TO COMPUTE INTEGRAL(EXP(-X*X)*FCT(X), SUMMED OVER X FROM
C -INFINITY TO +INFINITY).
C
C USAGE
C CALL QH8 (FCT,Y)
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT
C
C DESCRIPTION OF PARAMETERS
C FCT - THE NAME OF AN EXTERNAL FUNCTION SUBPROGRAM USED.
C Y - THE RESULTING INTEGRAL VALUE.
C
C REMARKS
C NONE
C
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
C THE EXTERNAL FUNCTION SUBPROGRAM FCT(X) MUST BE FURNISHED
C BY THE USER.
C
C METHOD
C EVALUATION IS DONE BY MEANS OF 8-POINT GAUSSIAN-HERMITE
C QUADRATURE FORMULA, WHICH INTEGRATES EXACTLY WHENEVER
C FCT(X) IS A POLYNOMIAL UP TO DEGREE 15.
C FOR REFERENCE, SEE
C V.I.KRYLOV, APPROXIMATE CALCULATION OF INTEGRALS,
C MACMILLAN, NEW YORK/LONDON, 1962, PP.129-130 AND 343-346.
C
C ..................................................................
C
SUBROUTINE QH8(FCT,Y)
C
C
X=2.930637
Z=-X
Y=.0001996041*(FCT(X)+FCT(Z))
X=1.981657
Z=-X
Y=Y+.01707798*(FCT(X)+FCT(Z))
X=1.157194
Z=-X
Y=Y+.2078023*(FCT(X)+FCT(Z))
X=.3811870
Z=-X
Y=Y+.6611470*(FCT(X)+FCT(Z))
RETURN
END