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QTFE.FOR
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1985-11-29
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C
C ..................................................................
C
C SUBROUTINE QTFE
C
C PURPOSE
C TO COMPUTE THE VECTOR OF INTEGRAL VALUES FOR A GIVEN
C EQUIDISTANT TABLE OF FUNCTION VALUES.
C
C USAGE
C CALL QTFE (H,Y,Z,NDIM)
C
C DESCRIPTION OF PARAMETERS
C H - THE INCREMENT OF ARGUMENT VALUES.
C Y - THE INPUT VECTOR OF FUNCTION VALUES.
C Z - THE RESULTING VECTOR OF INTEGRAL VALUES. Z MAY BE
C IDENTICAL WITH Y.
C NDIM - THE DIMENSION OF VECTORS Y AND Z.
C
C REMARKS
C NO ACTION IN CASE NDIM LESS THAN 1.
C
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
C NONE
C
C METHOD
C BEGINNING WITH Z(1)=0, EVALUATION OF VECTOR Z IS DONE BY
C MEANS OF TRAPEZOIDAL RULE (SECOND ORDER FORMULA).
C FOR REFERENCE, SEE
C F.B.HILDEBRAND, INTRODUCTION TO NUMERICAL ANALYSIS,
C MCGRAW-HILL, NEW YORK/TORONTO/LONDON, 1956, PP.75.
C
C ..................................................................
C
SUBROUTINE QTFE(H,Y,Z,NDIM)
C
C
DIMENSION Y(1),Z(1)
C
SUM2=0.
IF(NDIM-1)4,3,1
1 HH=.5*H
C
C INTEGRATION LOOP
DO 2 I=2,NDIM
SUM1=SUM2
SUM2=SUM2+HH*(Y(I)+Y(I-1))
2 Z(I-1)=SUM1
3 Z(NDIM)=SUM2
4 RETURN
END