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