C TLEP 10
C ..................................................................TLEP 20
C TLEP 30
C SUBROUTINE TLEP TLEP 40
C TLEP 50
C PURPOSE TLEP 60
C A SERIES EXPANSION IN LEGENDRE POLYNOMIALS WITH INDEPENDENT TLEP 70
C VARIABLE X IS TRANSFORMED TO A POLYNOMIAL WITH INDEPENDENT TLEP 80
C VARIABLE Z, WHERE X=A*Z+B TLEP 90
C TLEP 100
C USAGE TLEP 110
C CALL TLEP(A,B,POL,N,C,WORK) TLEP 120
C TLEP 130
C DESCRIPTION OF PARAMETERS TLEP 140
C A - FACTOR OF LINEAR TERM IN GIVEN LINEAR TRANSFORMATIONTLEP 150
C B - CONSTANT TERM IN GIVEN LINEAR TRANSFORMATION TLEP 160
C POL - COEFFICIENT VECTOR OF POLYNOMIAL (RESULTANT VALUE) TLEP 170
C COEFFICIENTS ARE ORDERED FROM LOW TO HIGH TLEP 180
C N - DIMENSION OF COEFFICIENT VECTORS POL AND C TLEP 190
C C - GIVEN COEFFICIENT VECTOR OF EXPANSION TLEP 200
C COEFFICIENTS ARE ORDERED FROM LOW TO HIGH TLEP 210
C POL AND C MAY BE IDENTICALLY LOCATED TLEP 220
C WORK - WORKING STORAGE OF DIMENSION 2*N TLEP 230
C TLEP 240
C REMARKS TLEP 250
C COEFFICIENT VECTOR C REMAINS UNCHANGED IF NOT COINCIDING TLEP 260
C WITH COEFFICIENT VECTOR POL. TLEP 270
C OPERATION IS BYPASSED IN CASE N LESS THAN 1. TLEP 280
C THE LINEAR TRANSFORMATION X=A*Z+B OR Z=(1/A)(X-B) TRANSFORMSTLEP 290
C THE RANGE (-1,+1) IN X TO THE RANGE (ZL,ZR) IN Z, WHERE TLEP 300
C ZL=-(1+B)/A AND ZR=(1-B)/A. TLEP 310
C FOR GIVEN ZL, ZR WE HAVE A=2/(ZR-ZL) AND B=-(ZR+ZL)/(ZR-ZL) TLEP 320
C TLEP 330
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED TLEP 340
C NONE TLEP 350
C TLEP 360
C METHOD TLEP 370
C THE TRANSFORMATION IS BASED ON THE RECURRENCE EQUATION TLEP 380
C FOR LEGENDRE POLYNOMIALS P(N,X) TLEP 390
C P(N+1,X)=2*X*P(N,X)-P(N-1,X)-(X*P(N,X)-P(N-1,X))/(N+1), TLEP 400
C WHERE THE FIRST TERM IN BRACKETS IS THE INDEX, TLEP 410
C THE SECOND IS THE ARGUMENT. TLEP 420
C STARTING VALUES ARE P(0,X)=1, P(1,X)=X. TLEP 430
C THE TRANSFORMATION IS IMPLICITLY DEFINED BY MEANS OF TLEP 440
C X=A*Z+B TOGETHER WITH TLEP 450
C SUM(POL(I)*Z**(I-1), SUMMED OVER I FROM 1 TO N) TLEP 460
C =SUM(C(I)*P(I-1,X), SUMMED OVER I FROM 1 TO N). TLEP 470
C TLEP 480
C ..................................................................TLEP 490
C TLEP 500
SUBROUTINE TLEP(A,B,POL,N,C,WORK) TLEP 510
C TLEP 520
DIMENSION POL(1),C(1),WORK(1) TLEP 530
C TLEP 540
C TEST OF DIMENSION TLEP 550
IF(N-1)2,1,3 TLEP 560
C TLEP 570
C DIMENSION LESS THAN 2 TLEP 580
1 POL(1)=C(1) TLEP 590
2 RETURN TLEP 600
C TLEP 610
3 POL(1)=C(1)+B*C(2) TLEP 620
POL(2)=A*C(2) TLEP 630
IF(N-2)2,2,4 TLEP 640
C TLEP 650
C INITIALIZATION TLEP 660
4 WORK(1)=1. TLEP 670
WORK(2)=B TLEP 680
WORK(3)=0. TLEP 690
WORK(4)=A TLEP 700
FI=1. TLEP 710
C TLEP 720
C CALCULATE COEFFICIENT VECTOR OF NEXT LEGENDRE POLYNOMIAL TLEP 730
C AND ADD MULTIPLE OF THIS VECTOR TO POLYNOMIAL POL TLEP 740
DO 6 J=3,N TLEP 750
FI=FI+1. TLEP 760
Q=1./FI-1. TLEP 770
Q1=1.-Q TLEP 780
P=0. TLEP 790
C TLEP 800
DO 5 K=2,J TLEP 810
H=(A*P+B*WORK(2*K-2))*Q1+Q*WORK(2*K-3) TLEP 820
P=WORK(2*K-2) TLEP 830
WORK(2*K-2)=H TLEP 840
WORK(2*K-3)=P TLEP 850
5 POL(K-1)=POL(K-1)+H*C(J) TLEP 860
WORK(2*J-1)=0. TLEP 870
WORK(2*J)=A*P*Q1 TLEP 880
6 POL(J)=C(J)*WORK(2*J) TLEP 890
RETURN TLEP 900
END TLEP 910