C DTCS 10
C ..................................................................DTCS 20
C DTCS 30
C SUBROUTINE DTCSP DTCS 40
C DTCS 50
C PURPOSE DTCS 60
C A SERIES EXPANSION IN SHIFTED CHEBYSHEV POLYNOMIALS WITH DTCS 70
C INDEPENDENT VARIABLE X IS TRANSFORMED TO A POLYNOMIAL WITH DTCS 80
C INDEPENDENT VARIABLE Z, WHERE X=A*Z+B. DTCS 90
C DTCS 100
C USAGE DTCS 110
C CALL DTCSP(A,B,POL,N,C,WORK) DTCS 120
C DTCS 130
C DESCRIPTION OF PARAMETERS DTCS 140
C A - FACTOR OF LINEAR TERM IN GIVEN LINEAR TRANSFORMATIONDTCS 150
C DOUBLE PRECISION VARIABLE DTCS 160
C B - CONSTANT TERM IN GIVEN LINEAR TRANSFORMATION DTCS 170
C DOUBLE PRECISION VARIABLE DTCS 180
C POL - COEFFICIENT VECTOR OF POLYNOMIAL (RESULTANT VALUE) DTCS 190
C COEFFICIENTS ARE ORDERED FROM LOW TO HIGH DTCS 200
C DOUBLE PRECISION VECTOR DTCS 210
C N - DIMENSION OF COEFFICIENT VECTORS POL AND C DTCS 220
C C - GIVEN COEFFICIENT VECTOR OF EXPANSION DTCS 230
C POL AND C MAY BE IDENTICALLY LOCATED DTCS 240
C COEFFICIENTS ARE ORDERED FROM LOW TO HIGH DTCS 250
C DOUBLE PRECISION VECTOR DTCS 260
C WORK - WORKING STORAGE OF DIMENSION 2*N DTCS 270
C DOUBLE PRECISION ARRAY DTCS 280
C DTCS 290
C REMARKS DTCS 300
C COEFFICIENT VECTOR C REMAINS UNCHANGED IF NOT COINCIDING DTCS 310
C WITH COEFFICIENT VECTOR POL. DTCS 320
C OPERATION IS BYPASSED IN CASE N LESS THAN 1. DTCS 330
C THE LINEAR TRANSFORMATION X=A*Z+B OR Z=(1/A)(X-B) TRANSFORMSDTCS 340
C THE RANGE (0,1) IN X TO THE RANGE (ZL,ZR) IN Z, WHERE DTCS 350
C ZL=-B/A AND ZR=(1-B)/A. DTCS 360
C FOR GIVEN ZL, ZR WE HAVE A=1/(ZR-ZL) AND B=-ZL/(ZR-ZL). DTCS 370
C DTCS 380
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DTCS 390
C NONE DTCS 400
C DTCS 410
C METHOD DTCS 420
C THE TRANSFORMATION IS BASED ON THE RECURRENCE EQUATION FOR DTCS 430
C SHIFTED CHEBYSHEV POLYNOMIALS TS(N,X) DTCS 440
C TS(N+1,X)=(4*X-2)*TS(N,X)-TS(N-1,X), DTCS 450
C WHERE THE FIRST TERM IN BRACKETS IS THE INDEX, DTCS 460
C THE SECOND IS THE ARGUMENT. DTCS 470
C STARTING VALUES ARE TS(0,X)=1, TS(1,X)=2*X-1. DTCS 480
C THE TRANSFORMATION IS IMPLICITLY DEFINED BY MEANS OF DTCS 490
C X=A*Z+B TOGETHER WITH DTCS 500
C SUM(POL(I)*Z**(I-1), SUMMED OVER I FROM 1 TO N) DTCS 510
C =SUM(C(I)*TS(I-1,X), SUMMED OVER I FROM 1 TO N). DTCS 520
C DTCS 530
C ..................................................................DTCS 540
C DTCS 550
SUBROUTINE DTCSP(A,B,POL,N,C,WORK) DTCS 560
C DTCS 570
DIMENSION POL(1),C(1),WORK(1) DTCS 580
DOUBLE PRECISION A,B,POL,C,WORK,H,P,XD,X0 DTCS 590
C DTCS 600
C TEST OF DIMENSION DTCS 610
IF(N-1)2,1,3 DTCS 620
C DTCS 630
C DIMENSION LESS THAN 2 DTCS 640
1 POL(1)=C(1) DTCS 650
2 RETURN DTCS 660
C DTCS 670
3 XD=A+A DTCS 680
X0=B+B-1.D0 DTCS 690
POL(1)=C(1)+C(2)*X0 DTCS 700
POL(2)=C(2)*XD DTCS 710
IF(N-2)2,2,4 DTCS 720
C DTCS 730
C INITIALIZATION DTCS 740
4 WORK(1)=1.D0 DTCS 750
WORK(2)=X0 DTCS 760
WORK(3)=0.D0 DTCS 770
WORK(4)=XD DTCS 780
XD=XD+XD DTCS 790
X0=X0+X0 DTCS 800
C DTCS 810
C CALCULATE COEFFICIENT VECTOR OF NEXT SHIFTED CHEBYSHEV DTCS 820
C POLYNOMIAL AND ADD MULTIPLE OF THIS VECTOR TO POLYNOMIAL POL DTCS 830
DO 6 J=3,N DTCS 840
P=0.D0 DTCS 850
C DTCS 860
DO 5 K=2,J DTCS 870
H=P-WORK(2*K-3)+X0*WORK(2*K-2) DTCS 880
P=WORK(2*K-2) DTCS 890
WORK(2*K-2)=H DTCS 900
WORK(2*K-3)=P DTCS 910
POL(K-1)=POL(K-1)+H*C(J) DTCS 920
5 P=XD*P DTCS 930
WORK(2*J-1)=0.D0 DTCS 940
WORK(2*J)=P DTCS 950
6 POL(J)=C(J)*P DTCS 960
RETURN DTCS 970
END DTCS 980