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