QUANC8

!DECLARE MODULE TO PASS THE PARAMETER TO THE EXTERNAL FUNCTION
        MODULE FUN_PARAMETER
        REAL T
        END MODULE

!THE EXTERNAL FUNCTION (THE INTEGRAND)
        REAL FUNCTION FUN(Z)
        USE FUN_PARAMETER
        FUN=1/(EXP(1.0)**(1.9 * Z**2) + T)
        RETURN
        END

        USE FUN_PARAMETER
        EXTERNAL FUN
        INTEGER NOFUN, ER, L
        REAL FUN,A,B,RELERR,ABSERR,RESULT,ERREST,FLAG, F_K, EPS
        REAL POINTS(7), FS(7), C(7), D(7), E(7), SEVALS(6), F_KS(6)
        REAL LPOLYNOMIAL_VALUES(6)

!CALCULATE THE INTEGRAL
        PI=4.D0*DATAN (1.D0)
        A=0.0
        B=1
        RELERR=1.E-06
        ABSERR=0.0

        T=-0.5
        DO I=1, 7
            T=T+0.5
            FS(I)=T
            CALL QUANC8(FUN,A,B,ABSERR,RELERR,RESULT, ERREST,NOFUN,FLAG)
            POINTS(I)=RESULT
        END DO

!OBTAIN COEFFICIENTS OF THE SPLINE FUNCTION FOR 0.5<=F<=1.5
        CALL SPLINE(7, FS, POINTS, C, D, E)

!OBTAIN APPROXIMATE VALUES FOR F=0.55+0.1*K (K=0...9) USING THE SPLINE FUNCTION
        K=0
        DO I=1,6
            F_K=0.25+0.5*K
            F_KS(I)=F_K
            SEVALS(I)=SEVAL(7, F_K, FS, POINTS, C, D, E)
            K=K+1
        END DO

!OBTAIN APPROXIMATE VALUES FOR F=0.55+0.1*K (K=0...9) USING THE LAGRANGE POLYNOMIAL
        K=0
        DO L=1,6
            F_K=0.25+0.5*K
            F_KS(L)=F_K
            CALL LAGRANGE_POLINOMIAL(F_KS(L), FS, POINTS, Q)
            LPOLYNOMIAL_VALUES(L)=Q
            K=K+1
        END DO

        PRINT *, "F_KS AND CORRESPONDING VALUES OF THE LAGRANGE POLYNOMIAL"
        PRINT 102, (F_KS(I), LPOLYNOMIAL_VALUES(I), I=1,6)
        PRINT *, "F_KS AND CORRESPONDING VALUES OF THE SPLINE FUNCTION"
        PRINT 102, (F_KS(I), SEVALS(I), I=1,6)
        PRINT *, "COEFFICIENTS OF THE SPLINE FUNCTION"
        PRINT 101,(C(I),D(I),E(I),I=1,7)
        PRINT *, "INTEGRAL VALUES:"
        PRINT 101, POINTS
        PRINT *, "F VALUES:"
        PRINT 101, FS
        PRINT 1,RESULT,ERREST,NOFUN,FLAG
        STOP
    1 FORMAT(10X,'RESULT=',E14.7,3X,'ERREST=',E12.5/11X,'NOFUN=',I8,11X,'FLAG=',F10.3)
    101 FORMAT(5X,3E16.7)
    102 FORMAT(5X,2E16.7)

        CONTAINS
        SUBROUTINE LAGRANGE_POLINOMIAL(F_KS, FS, POINTS, Q)
        REAL Q
        REAL WKX(7), WKXK(7), FS(7), POINTS(7), F_KS(7)
        Q=0
        WKX(:)=1
        WKXK(:)=1

        DO I=1, 7
            DO J=1, 7
                IF (I/=J) THEN
                    WKX(I)=WKX(I)*(F_K-FS(J))
                    WKXK(I)=WKXK(I)*(FS(I)-FS(J))
                END IF
            END DO

            IF (WKXK(I)/=0) THEN
                Q=Q+((WKX(I)/WKXK(I))*POINTS(I))
            END IF
        END DO
        END SUBROUTINE
        END