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SUBROUTINE QSF

PURPOSE
   TO COMPUTE THE VECTOR OF INTEGRAL VALUES FOR A GIVEN
   EQUIDISTANT TABLE OF FUNCTION VALUES.

USAGE
   CALL QSF (H,Y,Z,NDIM)

DESCRIPTION OF PARAMETERS
   H	  - THE INCREMENT OF ARGUMENT VALUES.
   Y	  - THE INPUT VECTOR OF FUNCTION VALUES.
   Z	  - THE RESULTING VECTOR OF INTEGRAL VALUES. Z MAY BE
	    IDENTICAL WITH Y.
   NDIM   - THE DIMENSION OF VECTORS Y AND Z.

REMARKS
   NO ACTION IN CASE NDIM LESS THAN 3.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   BEGINNING WITH Z(1)=0, EVALUATION OF VECTOR Z IS DONE BY
   MEANS OF SIMPSONS RULE TOGETHER WITH NEWTONS 3/8 RULE OR A
   COMBINATION OF THESE TWO RULES. TRUNCATION ERROR IS OF
   ORDER H**5 (I.E. FOURTH ORDER METHOD). ONLY IN CASE NDIM=3
   TRUNCATION ERROR OF Z(2) IS OF ORDER H**4.
   FOR REFERENCE, SEE
   (1) F.B.HILDEBRAND, INTRODUCTION TO NUMERICAL ANALYSIS,
       MCGRAW-HILL, NEW YORK/TORONTO/LONDON, 1956, PP.71-76.
   (2) R.ZURMUEHL, PRAKTISCHE MATHEMATIK FUER INGENIEURE UND
       PHYSIKER, SPRINGER, BERLIN/GOETTINGEN/HEIDELBERG, 1963,
       PP.214-221.