C DTCN 10
C ..................................................................DTCN 20
C DTCN 30
C SUBROUTINE DTCNP DTCN 40
C DTCN 50
C PURPOSE DTCN 60
C A SERIES EXPANSION IN CHEBYSHEV POLYNOMIALS WITH INDEPENDENTDTCN 70
C VARIABLE X IS TRANSFORMED TO A POLYNOMIAL WITH INDEPENDENT DTCN 80
C VARIABLE Z, WHERE X=A*Z+B. DTCN 90
C DTCN 100
C USAGE DTCN 110
C CALL DTCNP(A,B,POL,N,C,WORK) DTCN 120
C DTCN 130
C DESCRIPTION OF PARAMETERS DTCN 140
C A - FACTOR OF LINEAR TERM IN GIVEN LINEAR TRANSFORMATIONDTCN 150
C DOUBLE PRECISION VARIABLE DTCN 160
C B - CONSTANT TERM IN GIVEN LINEAR TRANSFORMATION DTCN 170
C DOUBLE PRECISION VARIABLE DTCN 180
C POL - COEFFICIENT VECTOR OF POLYNOMIAL (RESULTANT VALUE) DTCN 190
C COEFFICIENTS ARE ORDERED FROM LOW TO HIGH DTCN 200
C DOUBLE PRECISION VECTOR DTCN 210
C N - DIMENSION OF COEFFICIENT VECTORS POL AND C DTCN 220
C C - GIVEN COEFFICIENT VECTOR OF EXPANSION DTCN 230
C COEFFICIENTS ARE ORDERED FROM LOW TO HIGH DTCN 240
C POL AND C MAY BE IDENTICALLY LOCATED DTCN 250
C DOUBLE PRECISION VECTOR DTCN 260
C WORK - WORKING STORAGE OF DIMENSION 2*N DTCN 270
C DOUBLE PRECISION ARRAY DTCN 280
C DTCN 290
C REMARKS DTCN 300
C COEFFICIENT VECTOR C REMAINS UNCHANGED IF NOT COINCIDING DTCN 310
C WITH COEFFICIENT VECTOR POL. DTCN 320
C OPERATION IS BYPASSED IN CASE N LESS THAN 1. DTCN 330
C THE LINEAR TRANSFORMATION X=A*Z+B OR Z=(1/A)(X-B) TRANSFORMSDTCN 340
C THE RANGE (-1,+1) IN X TO THE RANGE (ZL,ZR) IN Z, WHERE DTCN 350
C ZL=-(1+B)/A AND ZR=(1-B)/A. DTCN 360
C FOR GIVEN ZL, ZR WE HAVE A=2/(ZR-ZL) AND B=-(ZR+ZL)/(ZR-ZL) DTCN 370
C DTCN 380
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DTCN 390
C NONE DTCN 400
C DTCN 410
C METHOD DTCN 420
C THE TRANSFORMATION IS BASED ON THE RECURRENCE EQUATION DTCN 430
C FOR CHEBYSHEV POLYNOMIALS T(N,X) DTCN 440
C T(N+1,X)=2*X*T(N,X)-T(N-1,X), DTCN 450
C WHERE THE FIRST TERM IN BRACKETS IS THE INDEX, DTCN 460
C THE SECOND IS THE ARGUMENT. DTCN 470
C STARTING VALUES ARE T(0,X)=1, T(1,X)=X. DTCN 480
C THE TRANSFORMATION IS IMPLICITLY DEFINED BY MEANS OF DTCN 490
C X = A*Z+B TOGETHER WITH DTCN 500
C SUM(POL(I)*Z**(I-1), SUMMED OVER I FROM 1 TO N) DTCN 510
C =SUM(C(I)*T(I-1,X), SUMMED OVER I FROM 1 TO N). DTCN 520
C DTCN 530
C ..................................................................DTCN 540
C DTCN 550
SUBROUTINE DTCNP(A,B,POL,N,C,WORK) DTCN 560
C DTCN 570
DIMENSION POL(1),C(1),WORK(1) DTCN 580
DOUBLE PRECISION A,B,POL,C,WORK,H,P,XD,X0 DTCN 590
C DTCN 600
C TEST OF DIMENSION DTCN 610
IF(N-1)2,1,3 DTCN 620
C DTCN 630
C DIMENSION LESS THAN 2 DTCN 640
1 POL(1)=C(1) DTCN 650
2 RETURN DTCN 660
C DTCN 670
3 POL(1)=C(1)+C(2)*B DTCN 680
POL(2)=C(2)*A DTCN 690
IF(N-2)2,2,4 DTCN 700
C DTCN 710
C INITIALIZATION DTCN 720
4 WORK(1)=1.D0 DTCN 730
WORK(2)=B DTCN 740
WORK(3)=0.D0 DTCN 750
WORK(4)=A DTCN 760
XD=A+A DTCN 770
X0=B+B DTCN 780
C DTCN 790
C CALCULATE COEFFICIENT VECTOR OF NEXT CHEBYSHEV POLYNOMIAL DTCN 800
C AND ADD MULTIPLE OF THIS VECTOR TO POLYNOMIAL POL DTCN 810
DO 6 J=3,N DTCN 820
P=0.D0 DTCN 830
C DTCN 840
DO 5 K=2,J DTCN 850
H=P-WORK(2*K-3)+X0*WORK(2*K-2) DTCN 860
P=WORK(2*K-2) DTCN 870
WORK(2*K-2)=H DTCN 880
WORK(2*K-3)=P DTCN 890
POL(K-1)=POL(K-1)+H*C(J) DTCN 900
5 P=XD*P DTCN 910
WORK(2*J-1)=0.D0 DTCN 920
WORK(2*J)=P DTCN 930
6 POL(J)=C(J)*P DTCN 940
RETURN DTCN 950
END DTCN 960