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

SUBROUTINE DTLAP

PURPOSE
   A SERIES EXPANSION IN LAGUERRE POLYNOMIALS WITH INDEPENDENT
   VARIABLE X IS TRANSFORMED TO A POLYNOMIAL WITH INDEPENDENT
   VARIABLE Z, WHERE X=A*Z+B

USAGE
   CALL DTLAP(A,B,POL,N,C,WORK)

DESCRIPTION OF PARAMETERS
   A	 - FACTOR OF LINEAR TERM IN GIVEN LINEAR TRANSFORMATION
	   DOUBLE PRECISION VARIABLE
   B	 - CONSTANT TERM IN GIVEN LINEAR TRANSFORMATION
	   DOUBLE PRECISION VARIABLE
   POL	 - COEFFICIENT VECTOR OF POLYNOMIAL (RESULTANT VALUE)
	   COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
	   DOUBLE PRECISION VECTOR
   N	 - DIMENSION OF COEFFICIENT VECTORS POL AND C
   C	 - GIVEN COEFFICIENT VECTOR OF EXPANSION
	   COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
	   POL AND C MAY BE IDENTICALLY LOCATED
	   DOUBLE PRECISION VECTOR
   WORK  - WORKING STORAGE OF DIMENSION 2*N
	   DOUBLE PRECISION ARRAY

REMARKS
   COEFFICIENT VECTOR C REMAINS UNCHANGED IF NOT COINCIDING
   WITH COEFFICIENT VECTOR POL.
   OPERATION IS BYPASSED IN CASE N LESS THAN 1.
   THE LINEAR TRANSFORMATION X=A*Z+B OR Z=(1/A)(X-B) TRANSFORMS
   THE RANGE (0,C) IN X TO THE RANGE (ZL,ZR) IN Z, WHERE
   ZL=-B/A AND ZR=(C-B)/A.
   FOR GIVEN ZL, ZR AND C WE HAVE A=C/(ZR-ZL) AND
   B=-C*ZL/(ZR-ZL)

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   THE TRANSFORMATION IS BASED ON THE RECURRENCE EQUATION
   FOR LAGUERRE POLYNOMIALS L(N,X)
   L(N+1,X)=2*L(N,X)-L(N-1,X)-((1+X)*L(N,X)-L(N-1,X))/(N+1),
   WHERE THE FIRST TERM IN BRACKETS IS THE INDEX,
   THE SECOND IS THE ARGUMENT.
   STARTING VALUES ARE L(0,X)=1, L(1,X)=1-X.
   THE TRANSFORMATION IS IMPLICITLY DEFINED BY MEANS OF
   X=A*Z+B TOGETHER WITH
   SUM(POL(I)*Z**(I-1), SUMMED OVER I FROM 1 TO N)
   =SUM(C(I)*L(I-1,X), SUMMED OVER I FROM 1 TO N).