Enter your search terms Submit search form
	Web pdp-10.trailing-edge.com

SUBROUTINE DAPCH

PURPOSE
   SET UP NORMAL EQUATIONS OF LEAST SQUARES FIT IN TERMS OF
   CHEBYSHEV POLYNOMIALS FOR A GIVEN DISCRETE FUNCTION

USAGE
   CALL DAPCH(DATI,N,IP,XD,X0,WORK,IER)

DESCRIPTION OF PARAMETERS
   DATI  - VECTOR OF DIMENSION 3*N (OR DIMENSION 2*N+1)
	   CONTAINING THE GIVEN ARGUMENTS, FOLLOWED BY THE
	   FUNCTION VALUES AND N (RESPECTIVELY 1) WEIGHT
	   VALUES. THE CONTENT OF VECTOR DATI REMAINS
	   UNCHANGED.
	   DATI MUST BE OF DOUBLE PRECISION
   N	 - NUMBER OF GIVEN POINTS
   IP	 - DIMENSION OF LEAST SQUARES FIT, I.E. NUMBER OF
	   CHEBYSHEV POLYNOMIALS USED AS FUNDAMENTAL FUNCTIONS
	   IP SHOULD NOT EXCEED N
   XD	 - RESULTANT MULTIPLICATIVE CONSTANT FOR LINEAR
	   TRANSFORMATION OF ARGUMENT RANGE
	   XD MUST BE DOUBLE PRECISION
   X0	 - RESULTANT ADDITIVE CONSTANT FOR LINEAR
	   TRANSFORMATION OF ARGUMENT RANGE
	   X0 MUST BE DOUBLE PRECISION
   WORK  - WORKING STORAGE OF DIMENSION (IP+1)*(IP+2)/2
	   ON RETURN WORK CONTAINS THE SYMMETRIC COEFFICIENT
	   MATRIX OF THE NORMAL EQUATIONS IN COMPRESSED FORM
	   FOLLOWED IMMEDIATELY BY RIGHT HAND SIDE
	   AND SQUARE SUM OF FUNCTION VALUES
	   WORK MUST BE OF DOUBLE PRECISION
   IER	 - RESULTING ERROR PARAMETER
	   IER =-1 MEANS FORMAL ERRORS IN DIMENSION
	   IER = 0 MEANS NO ERRORS
	   IER = 1 MEANS COINCIDING ARGUMENTS

REMARKS
   NO WEIGHTS ARE USED IF THE VALUE OF DATI(2*N+1) IS
   NOT POSITIVE.
   EXECUTION OF SUBROUTINE DAPCH IS A PREPARATORY STEP FOR
   CALCULATION OF LEAST SQUARES FITS IN CHEBYSHEV POLYNOMIALS
   IT SHOULD BE FOLLOWED BY EXECUTION OF SUBROUTINE DAPFS

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   THE LEAST SQUARE FIT IS DETERMINED USING CHEBYSHEV
   POLYNOMIALS AS FUNDAMENTAL FUNCTION SYSTEM.
   THE METHOD IS DISCUSSED IN THE ARTICLE
   A.T.BERZTISS, LEAST SQUARES FITTING TO IRREGULARLY SPACED
   DATA, SIAM REVIEW, VOL.6, ISS.3, 1964, PP. 203-227.