C QHFG 10
C ..................................................................QHFG 20
C QHFG 30
C SUBROUTINE QHFG QHFG 40
C QHFG 50
C PURPOSE QHFG 60
C TO COMPUTE THE VECTOR OF INTEGRAL VALUES FOR A GIVEN QHFG 70
C GENERAL TABLE OF ARGUMENT, FUNCTION, AND DERIVATIVE VALUES. QHFG 80
C QHFG 90
C USAGE QHFG 100
C CALL QHFG (X,Y,DERY,Z,NDIM) QHFG 110
C QHFG 120
C DESCRIPTION OF PARAMETERS QHFG 130
C X - THE INPUT VECTOR OF ARGUMENT VALUES. QHFG 140
C Y - THE INPUT VECTOR OF FUNCTION VALUES. QHFG 150
C DERY - THE INPUT VECTOR OF DERIVATIVE VALUES. QHFG 160
C Z - THE RESULTING VECTOR OF INTEGRAL VALUES. Z MAY BE QHFG 170
C IDENTICAL WITH X,Y OR DERY. QHFG 180
C NDIM - THE DIMENSION OF VECTORS X,Y,DERY,Z. QHFG 190
C QHFG 200
C REMARKS QHFG 210
C NO ACTION IN CASE NDIM LESS THAN 1. QHFG 220
C QHFG 230
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED QHFG 240
C NONE QHFG 250
C QHFG 260
C METHOD QHFG 270
C BEGINNING WITH Z(1)=0, EVALUATION OF VECTOR Z IS DONE BY QHFG 280
C MEANS OF HERMITEAN FOURTH ORDER INTEGRATION FORMULA. QHFG 290
C FOR REFERENCE, SEE QHFG 300
C (1) F.B.HILDEBRAND, INTRODUCTION TO NUMERICAL ANALYSIS, QHFG 310
C MCGRAW-HILL, NEW YORK/TORONTO/LONDON, 1956, PP.314-319. QHFG 320
C (2) R.ZURMUEHL, PRAKTISCHE MATHEMATIK FUER INGENIEURE UND QHFG 330
C PHYSIKER, SPRINGER, BERLIN/GOETTINGEN/HEIDELBERG, 1963, QHFG 340
C PP.227-230. QHFG 350
C QHFG 360
C ..................................................................QHFG 370
C QHFG 380
SUBROUTINE QHFG(X,Y,DERY,Z,NDIM) QHFG 390
C QHFG 400
C QHFG 410
DIMENSION X(1),Y(1),DERY(1),Z(1) QHFG 420
C QHFG 430
SUM2=0. QHFG 440
IF(NDIM-1)4,3,1 QHFG 450
C QHFG 460
C INTEGRATION LOOP QHFG 470
1 DO 2 I=2,NDIM QHFG 480
SUM1=SUM2 QHFG 490
SUM2=.5*(X(I)-X(I-1)) QHFG 500
SUM2=SUM1+SUM2*((Y(I)+Y(I-1))+.3333333*SUM2*(DERY(I-1)-DERY(I))) QHFG 510
2 Z(I-1)=SUM1 QHFG 520
3 Z(NDIM)=SUM2 QHFG 530
4 RETURN QHFG 540
END QHFG 550