C QHSG 10
C ..................................................................QHSG 20
C QHSG 30
C SUBROUTINE QHSG QHSG 40
C QHSG 50
C PURPOSE QHSG 60
C TO COMPUTE THE VECTOR OF INTEGRAL VALUES FOR A GIVEN QHSG 70
C GENERAL TABLE OF ARGUMENT, FUNCTION, FIRST DERIVATIVE, QHSG 80
C AND SECOND DERIVATIVE VALUES. QHSG 90
C QHSG 100
C USAGE QHSG 110
C CALL QHSG (X,Y,FDY,SDY,Z,NDIM) QHSG 120
C QHSG 130
C DESCRIPTION OF PARAMETERS QHSG 140
C X - THE INPUT VECTOR OF ARGUMENT VALUES. QHSG 150
C Y - THE INPUT VECTOR OF FUNCTION VALUES. QHSG 160
C FDY - THE INPUT VECTOR OF FIRST DERIVATIVE. QHSG 170
C SDY - THE INPUT VECTOR OF SECOND DERIVATIVE. QHSG 180
C Z - THE RESULTING VECTOR OF INTEGRAL VALUES. Z MAY BE QHSG 190
C IDENTICAL WITH X,Y,FDY OR SDY. QHSG 200
C NDIM - THE DIMENSION OF VECTORS X,Y,FDY,SDY,Z. QHSG 210
C QHSG 220
C REMARKS QHSG 230
C NO ACTION IN CASE NDIM LESS THAN 1. QHSG 240
C QHSG 250
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED QHSG 260
C NONE QHSG 270
C QHSG 280
C METHOD QHSG 290
C BEGINNING WITH Z(1)=0, EVALUATION OF VECTOR Z IS DONE BY QHSG 300
C MEANS OF HERMITEAN SIXTH ORDER INTEGRATION FORMULA. QHSG 310
C FOR REFERENCE, SEE QHSG 320
C R.ZURMUEHL, PRAKTISCHE MATHEMATIK FUER INGENIEURE UND QHSG 330
C PHYSIKER, SPRINGER, BERLIN/GOETTINGEN/HEIDELBERG, 1963, QHSG 340
C PP.227-230. QHSG 350
C QHSG 360
C ..................................................................QHSG 370
C QHSG 380
SUBROUTINE QHSG(X,Y,FDY,SDY,Z,NDIM) QHSG 390
C QHSG 400
C QHSG 410
DIMENSION X(1),Y(1),FDY(1),SDY(1),Z(1) QHSG 420
C QHSG 430
SUM2=0. QHSG 440
IF(NDIM-1)4,3,1 QHSG 450
C QHSG 460
C INTEGRATION LOOP QHSG 470
1 DO 2 I=2,NDIM QHSG 480
SUM1=SUM2 QHSG 490
SUM2=.5*(X(I)-X(I-1)) QHSG 500
0SUM2=SUM1+SUM2*((Y(I-1)+Y(I))+.4*SUM2*((FDY(I-1)-FDY(I))+ QHSG 510
1 .1666667*SUM2*(SDY(I-1)+SDY(I)))) QHSG 520
2 Z(I-1)=SUM1 QHSG 530
3 Z(NDIM)=SUM2 QHSG 540
4 RETURN QHSG 550
END QHSG 560