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|
C @(#)necwlcopt.for 19.1 (ES0-DMD) 02/25/03 14:20:26
C===========================================================================
C Copyright (C) 1995 European Southern Observatory (ESO)
C
C This program is free software; you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation; either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public
C License along with this program; if not, write to the Free
C Software Foundation, Inc., 675 Massachusetss Ave, Cambridge,
C MA 02139, USA.
C
C Corresponding concerning ESO-MIDAS should be addressed as follows:
C Internet e-mail: midas@eso.org
C Postal address: European Southern Observatory
C Data Management Division
C Karl-Schwarzschild-Strasse 2
C D 85748 Garching bei Muenchen
C GERMANY
C===========================================================================
C
C+++++++++++++++++++++++++++++++++++++++++++++++++++++++
C.COPYRIGHT (C) 1992 European Southern Observatory
C.IDENT wlcoptim.for
C.AUTHOR Pascal Ballester, ESO - Garching
C.KEYWORDS Spectroscopy, Echelle,
C.PURPOSE Computes optimal parameters for the
C wavelength calibration
C.VERSION 1.0 Creation 1992-MAY-26
C-------------------------------------------------------
C
C
C Program : Wavelength Calibration Least Squares Solutions
C
C This program has been partly generated using Macsyma to
C solve the following least-square problem:
C
C Xr(i) = cos(a) * X(i) + bin * sin(a) * Y(i) (1)
C
C takes into account a binning factor of the ccd and a rotation
C of the detector.
C
C F(Xr(i)) = B * Xr(i) + A = (m+p(i))*lambda(i) (2)
C
C is the echelle relation applied in the rotated space and approximated
C by a linear relation. m is the absolute order number of a line
C and p(i) is relative order number of the other lines.
C
C Macsyma has been used to find different optima, like:
C - The absolute order number of the first identification : m
C - The binning factor : bin
C - In method ANGLE, the angle of rotation : a
C - In method PAIR, the wavelength of the two pairs : lambda(1), lambda(2)
C
C The different least-square solutions are used to compute the optimal
C value of a parameter, assuming that all other parameters are correctly
C provided. This is a cross-check of the entered values. By computing
C the new rms after replacement of a parameter by its optimal value,
C it is possible to provide a diagnosis of what action would benefit
C the most to solve the problem.
C
C INPUT:
C IN_A/C/1/60 Name of line table
C IN_B/C/1/60 Method (PAIR or ANGLE)
C INPUTR/R/1/2 Angle of rotation, Binning ratio.
C
C OUTPUT:
C OUTPUTI/I/1/1 Order number of the first line
C OUTPUTR/R/1/2 Optimal rotation angle, Optimal binning factor
C
IMPLICIT NONE
INTEGER MAXDIM
PARAMETER (MAXDIM=1500)
DOUBLE PRECISION IX(MAXDIM), IY(MAXDIM)
DOUBLE PRECISION IP(MAXDIM), IL(MAXDIM)
DOUBLE PRECISION SX, SY, SX2, SY2, SXY
C DOUBLE PRECISION SML2K, SXMLK, SYMLK, SMLK
DOUBLE PRECISION SP2L2K, BUFFER
DOUBLE PRECISION SXLK, SXPLK, SYLK, SYPLK, SPLK, SLK
DOUBLE PRECISION SL2K, SPL2K, PK, LK, XK, YK, RMSLK
DOUBLE PRECISION SML2, SP2L2, SXML, SYML, SML
DOUBLE PRECISION SXL, SXPL, SYL, SYPL, SPL, SL
DOUBLE PRECISION SL2, SPL2, SBIN
INTEGER M, N, K, M2OPT, LOOP, ERROR, P
DOUBLE PRECISION BIN, PI, MDP, MINRMS(MAXDIM)
DOUBLE PRECISION A, B1
DOUBLE PRECISION TGA1, TGA2, AOPT
REAL OUTANG, RBIN
DOUBLE PRECISION L1,L2,X1,X2,XP1,XP2,L1OPT,L2OPT
DOUBLE PRECISION SXR, SXR2, SXRML, DET, COEFA, COEFB, RMS
DOUBLE PRECISION L1OLD, L2OLD, RMSL1, RMSL2
CHARACTER MODE*5, METHOD*10, TEXT*80
INTEGER MOLD, ROW
DOUBLE PRECISION RMSM, MRMS, ARMS, BRMS, AOLD, BOLD
DOUBLE PRECISION LKOPT(MAXDIM), LKO
CHARACTER TABLE*60
INTEGER IAV, KUN, KNUL, ISTAT, ICOLX, ICOLW
INTEGER ICOLO, ICOLN, TID, NCOL1, NROW1, NSC1
INTEGER NACOL, NAROW, MADRID
LOGICAL SELECT
INCLUDE 'MID_INCLUDE:ST_DEF.INC'
COMMON/VMR/MADRID(1)
INCLUDE 'MID_INCLUDE:ST_DAT.INC'
C
C Initialisations
C
C ... Init input table
C
CALL STSPRO('WLCLS')
CALL STKRDC('IN_A',1,1,60,IAV,TABLE,KUN,KNUL,ISTAT)
CALL TBTOPN(TABLE,F_U_MODE,TID,ISTAT)
C
CALL TBIGET(TID,NCOL1,NROW1,NSC1,NACOL,NAROW,ISTAT)
CALL TBCSER(TID,':X ' ,ICOLX,ISTAT)
CALL TBCSER(TID,':IDENT' ,ICOLW,ISTAT)
CALL TBCSER(TID,':ORDER' ,ICOLO,ISTAT)
CALL TBCSER(TID,':YNEW' ,ICOLN,ISTAT)
CALL STKRDC('IN_B',1,1,10,IAV,METHOD,KUN,KNUL,ISTAT)
CALL STKRDR('INPUTR',1,1,IAV,OUTANG,KUN,KNUL,ISTAT) ! Rotation angle
CALL STKRDR('INPUTR',2,1,IAV,RBIN,KUN,KNUL,ISTAT) ! Binning factor
PI = 3.14159
A = OUTANG*PI/180.
BIN = RBIN
ERROR = 0
IF (METHOD(1:1) .EQ. 'p') WRITE(METHOD,111) 'PAIR'
IF (METHOD(1:1) .EQ. 'a') WRITE(METHOD,111) 'ANGLE'
111 FORMAT(A5)
N = 0
DO 100 ROW = NROW1, 1, -1
CALL TBSGET(TID, ROW, SELECT, ISTAT)
IF (SELECT) THEN
N = N + 1
CALL TBERDD(TID, ROW, ICOLO, IP(N), KNUL, ISTAT)
CALL TBERDD(TID, ROW, ICOLX, IX(N), KNUL, ISTAT)
CALL TBERDD(TID, ROW, ICOLN, IY(N), KNUL, ISTAT)
CALL TBERDD(TID, ROW, ICOLW, IL(N), KNUL, ISTAT)
ENDIF
100 CONTINUE
M = IP(1)
DO 110 ROW = 1, N
IP(ROW) = IP(ROW) - M
110 CONTINUE
C Check maximum size of arrays
IF (MAXDIM .LE. (N+10)) THEN
CALL STTPUT(
+ 'Buffer size MAXDIM too small in module wlcoptim',ISTAT)
GOTO 1900
ENDIF
C Check organisation of data if method PAIR
IF (METHOD(1:1) .EQ. 'P') THEN
IF (IL(1) .NE. IL(2)) ERROR = 1
IF (IL(3) .NE. IL(4)) ERROR = 1
IF (IP(2) .NE. (IP(1)+1)) ERROR = 1
IF (IP(4) .NE. (IP(3)+1)) ERROR = 1
IF (N .NE. 4) ERROR = 1
IF (ERROR .EQ. 1) THEN
IF (IL(1).EQ.IL(3).AND.IL(2).EQ.IL(4).AND.IP(3).EQ.
C (IP(1)+1).AND.IP(4).EQ.(IP(2)+1).AND.N.EQ.4) THEN
ERROR = 0
BUFFER = IL(2)
IL(2) = IL(3)
IL(3) = BUFFER
BUFFER = IX(2)
IX(2) = IX(3)
IX(3) = BUFFER
BUFFER = IY(2)
IY(2) = IY(3)
IY(3) = BUFFER
BUFFER = IP(2)
IP(2) = IP(3)
IP(3) = NINT(BUFFER)
ELSE
CALL STTPUT(
+ 'Error: Identifications are wrongly organized',ISTAT)
CALL STTPUT(
+ 'Remember : First line: left-hand side, then right-side',
+ ISTAT)
CALL STTPUT(
+ ' Second line: left-hand side, then right-side',
+ ISTAT)
GOTO 1900
ENDIF
ENDIF
ENDIF
C Check that identifications are in different orders for method ANGLE
IF (METHOD(1:1) .EQ. 'A') THEN
SPL = 0.D0
DO 200 ROW = 1,N
SPL = SPL + IP(ROW)
200 CONTINUE
C234567890123456789012345678901234567890123456789012345678901234567890123456
IF (SPL .LT. 0.5) THEN
CALL STTPUT(
+ 'Error: Identifications cannot be all in the same order',ISTAT)
GOTO 1900
ENDIF
ENDIF
C Computes sums
SX = 0.D0
SY = 0.D0
SX2 = 0.D0
SXY = 0.D0
SY2 = 0.D0
SYL = 0.D0
SYPL = 0.D0
SPL = 0.D0
SL = 0.D0
SL2 = 0.D0
SPL2 = 0.D0
SP2L2 = 0.D0
SXL = 0.D0
SXPL = 0.D0
DO 10 LOOP = 1 , N
SX = SX + IX(LOOP)
SY = SY + IY(LOOP)
SX2 = SX2 + IX(LOOP)*IX(LOOP)
SY2 = SY2 + IY(LOOP)*IY(LOOP)
SXY = SXY + IX(LOOP)*IY(LOOP)
SYL = SYL + IY(LOOP)*IL(LOOP)
SYPL = SYPL + IY(LOOP)*IP(LOOP)*IL(LOOP)
SPL = SPL + IP(LOOP)*IL(LOOP)
SL = SL + IL(LOOP)
SL2 = SL2 + IL(LOOP)*IL(LOOP)
SPL2 = SPL2 + IP(LOOP)*IL(LOOP)**2
SP2L2 = SP2L2 + IP(LOOP)**2*IL(LOOP)**2
SXL = SXL + IX(LOOP)*IL(LOOP)
SXPL = SXPL + IX(LOOP)*IP(LOOP)*IL(LOOP)
10 CONTINUE
SXML = M*SXL + SXPL
SYML = M*SYL + SYPL
SML = M*SL + SPL
SML2 = M*M*SL2 + 2*M*SPL2 + SP2L2
C Computes a linear fit and display results
SXR = COS(A)*SX + BIN*SIN(A)*SY
SXR2 = SX2*COS(A)**2+2*SXY*COS(A)*BIN*SIN(A)+
1 SY2*SIN(A)**2*BIN**2
SXRML = SXML*COS(A)+SYML*SIN(A)*BIN
DET = N*SXR2-SXR*SXR
COEFA = (SML*SXR2-SXR*SXRML)/DET
COEFB = (N*SXRML-SXR*SML)/DET
RMS = SML2-2*COEFA*COEFB*SXR-COEFB*COEFB*SXR2-N*COEFA*COEFA
RMS = SQRT(RMS/N)
C Display header
WRITE(TEXT,510)
CALL STTPUT(TEXT,ISTAT)
WRITE(TEXT,570)
CALL STTPUT(TEXT,ISTAT)
WRITE(TEXT,510)
CALL STTPUT(TEXT,ISTAT)
WRITE(TEXT,520)
CALL STTPUT(TEXT,ISTAT)
WRITE(TEXT,500) COEFA,COEFB,RMS
CALL STTPUT(TEXT,ISTAT)
WRITE(TEXT,510)
CALL STTPUT(TEXT,ISTAT)
WRITE(TEXT,530)
CALL STTPUT(TEXT,ISTAT)
WRITE(TEXT,510)
CALL STTPUT(TEXT,ISTAT)
500 FORMAT (1X,'* A = ',F12.5,' B= ',F12.5,' RMS = ',F12.3,7X,'*')
510 FORMAT (1X,61('*'))
520 FORMAT (1X,'*',10X,'Linear fit of : m * lambda = b * xr + a',
C 10X,'*')
530 FORMAT (1X,'* Parameter * Value * Optimum *',
C ' RMS *')
540 FORMAT (1X,'*',A16,' *',F12.5,' *',F13.5,' *',F11.2,' *')
550 FORMAT (1X,'*',' Ident ',I6,4X,'*',F12.5,' *',F13.5,' *',
C F11.2,' *')
560 FORMAT (1X,'*',A16,' * ',I6,' * ',I7,' *',F11.2,' *')
570 FORMAT (1X,'*',13X,'Wavelength Calibration Diagnosis',14X,'*')
C Least square solutions for the methods PAIR and ANGLE
C Optimal Rotation Angle
DET = ABS(N*SYML-SML*SY)
IF (DET .GT. 0.01) THEN
TGA1 = (N*(SX2*SYML-SXML*SXY)-SX**2*SYML+SML*(SX*SXY-SX2
1 *SY)+SX*SXML*SY)/(BIN*(N*(SXML*SY2-SXY*SYML)+SX*SY*SYML+SML*(SX
2 Y*SY-SX*SY2)-SXML*SY**2))
TGA2 = -(N*SXML-SML*SX)/(BIN*(N*SYML-SML*SY))
AOPT = ATAN(TGA1)
ELSE
AOPT = -999
ENDIF
C Optimal Binning Factor
IF (ABS(A) .GT. 0.02) THEN
B1 = COS(A)*(N*(SX2*SYML-SXML*SXY)-SX**2*SYML+SML*(SX*SXY-SX2*SY
1 )+SX*SXML*SY)/(SIN(A)*(N*(SXML*SY2-SXY*SYML)+SX*SY*SYML+SML*(SX
2 Y*SY-SX*SY2)-SXML*SY**2))
ELSE
B1 = -999
ENDIF
C Optimal Absolute Order Number for the first identified line
MDP = -((SIN(A)**2*BIN**2*N*SYL-SIN(A)**2*BIN**2*SL*SY+COS(
1 A)*SIN(A)*BIN*N*SXL-COS(A)*SIN(A)*BIN*SL*SX)*SYPL+(-SIN(A)**2*B
2 IN**2*SPL*SY+COS(A)*SIN(A)*BIN*N*SXPL-COS(A)*SIN(A)*BIN*SPL*SX)
3 *SYL+(SIN(A)**2*BIN**2*SL*SPL-SIN(A)**2*BIN**2*N*SPL2)*SY2+SIN(
4 A)**2*BIN**2*SPL2*SY**2+(-COS(A)*SIN(A)*BIN*SL*SXPL-COS(A)*SIN(
5 A)*BIN*SPL*SXL+2*COS(A)*SIN(A)*BIN*SPL2*SX)*SY+(2*COS(A)*SIN(A)
6 *BIN*SL*SPL-2*COS(A)*SIN(A)*BIN*N*SPL2)*SXY+(COS(A)**2*N*SXL-CO
7 S(A)**2*SL*SX)*SXPL-COS(A)**2*SPL*SX*SXL+(COS(A)**2*SL*SPL-COS(
8 A)**2*N*SPL2)*SX2+COS(A)**2*SPL2*SX**2)/(SIN(A)**2*BIN**2*N*SYL
9 **2+(-2*SIN(A)**2*BIN**2*SL*SY+2*COS(A)*SIN(A)*BIN*N*SXL-2*COS(
: A)*SIN(A)*BIN*SL*SX)*SYL+(SIN(A)**2*BIN**2*SL**2-SIN(A)**2*BIN*
; *2*N*SL2)*SY2+SIN(A)**2*BIN**2*SL2*SY**2+(2*COS(A)*SIN(A)*BIN*S
< L2*SX-2*COS(A)*SIN(A)*BIN*SL*SXL)*SY+(2*COS(A)*SIN(A)*BIN*SL**2
= -2*COS(A)*SIN(A)*BIN*N*SL2)*SXY+COS(A)**2*N*SXL**2-2*COS(A)**2*
> SL*SX*SXL+(COS(A)**2*SL**2-COS(A)**2*N*SL2)*SX2+COS(A)**2*SL2*S
? X**2)
M2OPT = NINT(MDP)
C Compute new rms if a value is changed.
MOLD = M ! Keep the old value in memory
M = M2OPT ! Replace current value by optimum
MODE = 'M' ! Set the mode
GOTO 1000 ! Compute rms
1001 CONTINUE ! Return point
M = MOLD ! Restore old value
MRMS = RMSM ! Store rms
MINRMS(1) = RMSM
WRITE(TEXT,560) 'Order number',M,M2OPT,MRMS
CALL STTPUT(TEXT,ISTAT)
CALL STKWRI('OUTPUTI',M2OPT,1,1,KUN,ISTAT)
AOLD = A
A = AOPT
MODE = 'A'
GOTO 1000
1002 CONTINUE ! Return point
A = AOLD
ARMS = RMSM
MINRMS(2) = RMSM
WRITE(TEXT,540) 'Rotation angle',(A*180./PI),(AOPT*180/PI),ARMS
CALL STTPUT(TEXT,ISTAT)
OUTANG = AOPT*180./PI
CALL STKWRR('OUTPUTR',OUTANG,1,1,KUN,ISTAT)
BOLD = BIN
BIN = B1
MODE = 'B'
GOTO 1000
1003 CONTINUE ! Return point
BIN = BOLD
BRMS = RMSM
MINRMS(3) = RMSM
IF (B1 .GT. 0) THEN
WRITE(TEXT,540) 'Binning factor',BIN,SQRT(B1),BRMS
CALL STTPUT(TEXT,ISTAT)
ELSE
WRITE(TEXT,540) 'Binning factor',BIN,BIN,0.
CALL STTPUT(TEXT,ISTAT)
ENDIF
C
C Least square solutions for the method PAIR
IF (METHOD(1:1) .EQ. 'P') THEN
X1 = IX(1)
XP1 = IX(2)
X2 = IX(3)
XP2 = IX(4)
P = IP(3) - IP(1)
L1 = IL(1)
L2 = IL(3)
L1OPT = (((2*L2*M+L2)*P+2*L2*M**2+L2*M)*XP2**2+((L2*P+2*L2*M+2*L2)
1 *XP1+((-4*L2*M-2*L2)*P-4*L2*M**2-4*L2*M-L2)*X2+(-L2*P-L2)*X1)
2 *XP2+(2*L2*M*P+2*L2*M**2+L2*M)*XP1**2+((L2*P-L2)*X2+
3 ((-4*L2*M-2*L2)*P-4*L2*M**2-4*L2*M-L2)*X1)*XP1+((2*L2*M+L2)*P+
4 2*L2*M**2+3*L2*M+L2)*X2**2+(-L2*P-2*L2*M)*X1*X2+((2*L2*M+2*L2)
5 *P+2*L2*M**2+3*L2*M+L2)*X1**2)/((2*M**2+2*M+2)*XP2**2+(2*M*XP1
6 +(-4*M**2-4*M-2)*X2+(-2*M-2)*X1)*XP2+2*M**2*XP1**2+(2*M*X2+(-4
7 *M**2-4*M)*X1)*XP1+(2*M**2+2*M+2)*X2**2+(-2*M-2)*X1*X2+(2*M**2
8 +4*M+2)*X1**2)
L1OLD = L1
L1 = L1OPT
RMSL1 = -4*((2*L2*P+2*(L2+L1)*M+L2+L1)*(XP2**2+XP1**2+X2**2+X1**2)
1 -(XP2+XP1+X2+X1)*(L2*(P+M+1)*XP2+L1*(M+1)*XP1+L2*(P+M)*X2+L1*M*X1
2 ))**2/(4*(XP2**2+XP1**2+X2**2+X1**2)-(XP2+XP1+X2+X1)**2)**2-2*(
3 XP2+XP1+X2+X1)*(4*(L2*(P+M+1)*XP2+L1*(M+1)*XP1+L2*(P+M)*X2+L1*M
4 *X1)-(2*L2*P+2*(L2+L1)*M+L2+L1)*(XP2+XP1+X2+X1))*((2*L2*P+2*(L2
5 +L1)*M+L2+L1)*(XP2**2+XP1**2+X2**2+X1**2)-(XP2+XP1+X2+X1)*(L2*(
6 P+M+1)*XP2+L1*(M+1)*XP1+L2*(P+M)*X2+L1*M*X1))/(4*(XP2**2+XP1**2
7 +X2**2+X1**2)-(XP2+XP1+X2+X1)**2)**2-(4*(L2*(P+M+1)*XP2+L1*(M+1
8 )*XP1+L2*(P+M)*X2+L1*M*X1)-(2*L2*P+2*(L2+L1)*M+L2+L1)*(XP2+XP1+
9 X2+X1))**2*(XP2**2+XP1**2+X2**2+X1**2)/(4*(XP2**2+XP1**2+X2**2+
: X1**2)-(XP2+XP1+X2+X1)**2)**2+L2**2*(P+M+1)**2+L2**2*(P+M)**2+L
; 1**2*(M+1)**2+L1**2*M**2
L1 = L1OLD
L2OPT = (((2*L1*M+L1)*P+2*L1*M**2+L1*M)*XP2**2+((L1*P+2*L1*M+2
1 *L1)*XP1+((-4*L1*M-2*L1)*P-4*L1*M**2-4*L1*M-L1)*X2+(-L1*P-L1)*X
2 1)*XP2+(2*L1*M*P+2*L1*M**2+L1*M)*XP1**2+((L1*P-L1)*X2+((-4*L1*M
3 -2*L1)*P-4*L1*M**2-4*L1*M-L1)*X1)*XP1+((2*L1*M+L1)*P+2*L1*M**2+
4 3*L1*M+L1)*X2**2+(-L1*P-2*L1*M)*X1*X2+((2*L1*M+2*L1)*P+2*L1*M**
5 2+3*L1*M+L1)*X1**2)/((2*P**2+4*M*P+2*M**2)*XP2**2+((2*P+2*M)*XP
6 1+(-4*P**2+(-8*M-4)*P-4*M**2-4*M)*X2+(2*P+2*M)*X1)*XP2+(2*P**2+
7 (4*M+2)*P+2*M**2+2*M+2)*XP1**2+((-2*P-2*M-2)*X2+(-4*P**2+(-8*M-
8 4)*P-4*M**2-4*M-2)*X1)*XP1+(2*P**2+(4*M+4)*P+2*M**2+4*M+2)*X2**
9 2+(-2*P-2*M-2)*X1*X2+(2*P**2+(4*M+2)*P+2*M**2+2*M+2)*X1**2)
L2OLD = L2
L2 = L2OPT
RMSL2 = -4*((2*L2*P+2*(L2+L1)*M+L2+L1)*(XP2**2+XP1**2+X2**2+X1**2)
1 -(XP2+XP1+X2+X1)*(L2*(P+M+1)*XP2+L1*(M+1)*XP1+L2*(P+M)*X2+L1*M*X1
2 ))**2/(4*(XP2**2+XP1**2+X2**2+X1**2)-(XP2+XP1+X2+X1)**2)**2-2*(
3 XP2+XP1+X2+X1)*(4*(L2*(P+M+1)*XP2+L1*(M+1)*XP1+L2*(P+M)*X2+L1*M
4 *X1)-(2*L2*P+2*(L2+L1)*M+L2+L1)*(XP2+XP1+X2+X1))*((2*L2*P+2*(L2
5 +L1)*M+L2+L1)*(XP2**2+XP1**2+X2**2+X1**2)-(XP2+XP1+X2+X1)*(L2*(
6 P+M+1)*XP2+L1*(M+1)*XP1+L2*(P+M)*X2+L1*M*X1))/(4*(XP2**2+XP1**2
7 +X2**2+X1**2)-(XP2+XP1+X2+X1)**2)**2-(4*(L2*(P+M+1)*XP2+L1*(M+1
8 )*XP1+L2*(P+M)*X2+L1*M*X1)-(2*L2*P+2*(L2+L1)*M+L2+L1)*(XP2+XP1+
9 X2+X1))**2*(XP2**2+XP1**2+X2**2+X1**2)/(4*(XP2**2+XP1**2+X2**2+
: X1**2)-(XP2+XP1+X2+X1)**2)**2+L2**2*(P+M+1)**2+L2**2*(P+M)**2+L
; 1**2*(M+1)**2+L1**2*M**2
RMSL1 = SQRT(RMSL1/4.)
RMSL2 = SQRT(RMSL2/4.)
WRITE(TEXT,540) 'Ident. 1 and 2',L1OLD,L1OPT,RMSL1
CALL STTPUT(TEXT,ISTAT)
WRITE(TEXT,540) 'Ident. 3 and 4',L2OLD,L2OPT,RMSL2
CALL STTPUT(TEXT,ISTAT)
MINRMS(4) = RMSL1
MINRMS(5) = RMSL1
MINRMS(6) = RMSL2
MINRMS(7) = RMSL2
LKOPT(1) = L1OPT
LKOPT(2) = L1OPT
LKOPT(3) = L2OPT
LKOPT(4) = L2OPT
ENDIF
C Optimal Wavelength for each of the computed wavelength IL(LOOP)
IF (METHOD(1:1) .EQ. 'A') THEN
DO 50 K = 1,N
PK = IP(K)
LK = IL(K)
XK = IX(K)
YK = IY(K)
SYLK = 0.D0
SYPLK = 0.D0
SPLK = 0.D0
SLK = 0.D0
SL2K = 0.D0
SPL2K = 0.D0
SP2L2K = 0.D0
SXLK = 0.D0
SXPLK = 0.D0
DO 30 LOOP = 1 , N
IF (LOOP.NE.K) THEN
SYLK = SYLK + IY(LOOP)*IL(LOOP)
SYPLK = SYPLK + IY(LOOP)*IP(LOOP)*IL(LOOP)
SPLK = SPLK + IP(LOOP)*IL(LOOP)
SLK = SLK + IL(LOOP)
SL2K = SL2K + IL(LOOP)*IL(LOOP)
SPL2K = SPL2K + IP(LOOP)*IL(LOOP)**2
SP2L2K = SP2L2K + IP(LOOP)**2*IL(LOOP)**2
SXLK = SXLK + IX(LOOP)*IL(LOOP)
SXPLK = SXPLK + IX(LOOP)*IP(LOOP)*IL(LOOP)
ENDIF
30 CONTINUE
C The formula for LKOPT is splitted in two parts (too big for the poor
C compiler !!)
SBIN = (
< (SIN(A)**2*BIN**2*N*PK+SIN(A)**2*BIN**2*M*N)*YK**2+((2*COS(A)*S
= IN(A)*BIN*N*PK+2*COS(A)*SIN(A)*BIN*M*N)*XK+(-2*SIN(A)**2*BIN**2
> *PK-2*SIN(A)**2*BIN**2*M)*SY+(-2*COS(A)*SIN(A)*BIN*PK-2*COS(A)*
? SIN(A)*BIN*M)*SX)*YK+(COS(A)**2*N*PK+COS(A)**2*M*N)*XK**2+((-2*
@ COS(A)*SIN(A)*BIN*PK-2*COS(A)*SIN(A)*BIN*M)*SY+(-2*COS(A)**2*PK
1 -2*COS(A)**2*M)*SX)*XK+((SIN(A)**2*BIN**2-SIN(A)**2*BIN**2*N)*P
2 K-SIN(A)**2*BIN**2*M*N+SIN(A)**2*BIN**2*M)*SY2+(SIN(A)**2*BIN**
3 2*PK+SIN(A)**2*BIN**2*M)*SY**2+(2*COS(A)*SIN(A)*BIN*PK+2*COS(A)
4 *SIN(A)*BIN*M)*SX*SY+((2*COS(A)*SIN(A)*BIN-2*COS(A)*SIN(A)*BIN*
5 N)*PK-2*COS(A)*SIN(A)*BIN*M*N+2*COS(A)*SIN(A)*BIN*M)*SXY+((COS(
6 A)**2-COS(A)**2*N)*PK-COS(A)**2*M*N+COS(A)**2*M)*SX2+(COS(A)**2
7 *PK+COS(A)**2*M)*SX**2)
LKOPT(K) = -((SIN(A)**2*BIN**2*N*SYPLK+SIN(A)**2*BIN**2*M*N*SY
1 LK+(-SIN(A)**2*BIN**2*SPLK-SIN(A)**2*BIN**2*M*SLK)*SY+COS(A)*SI
2 N(A)*BIN*N*SXPLK+COS(A)*SIN(A)*BIN*M*N*SXLK+(-COS(A)*SIN(A)*BIN
3 *SPLK-COS(A)*SIN(A)*BIN*M*SLK)*SX)*YK+(COS(A)*SIN(A)*BIN*N*SYPL
4 K+COS(A)*SIN(A)*BIN*M*N*SYLK+(-COS(A)*SIN(A)*BIN*SPLK-COS(A)*SI
5 N(A)*BIN*M*SLK)*SY+COS(A)**2*N*SXPLK+COS(A)**2*M*N*SXLK+(-COS(A
6 )**2*SPLK-COS(A)**2*M*SLK)*SX)*XK+(-SIN(A)**2*BIN**2*SY-COS(A)*
7 SIN(A)*BIN*SX)*SYPLK+(-SIN(A)**2*BIN**2*M*SY-COS(A)*SIN(A)*BIN*
8 M*SX)*SYLK+(SIN(A)**2*BIN**2*SPLK+SIN(A)**2*BIN**2*M*SLK)*SY2+(
9 -COS(A)*SIN(A)*BIN*SXPLK-COS(A)*SIN(A)*BIN*M*SXLK)*SY+(2*COS(A)
: *SIN(A)*BIN*SPLK+2*COS(A)*SIN(A)*BIN*M*SLK)*SXY-COS(A)**2*SX*SX
; PLK-COS(A)**2*M*SX*SXLK+(COS(A)**2*SPLK+COS(A)**2*M*SLK)*SX2)/
+ SBIN
LKO = LKOPT(K)
RMSLK = -N*((SPLK+M*SLK+LKO*(PK+M))*(SIN(A)**2*BIN**2*SY2+2*COS(A)
1 *SIN(A)*BIN*SXY+COS(A)**2*SX2)-(SIN(A)*BIN*SY+COS(A)*SX)*(SIN(A
2 )*BIN*(M*(LKO*YK+SYLK)+LKO*PK*YK+SYPLK)+COS(A)*(M*(LKO*XK+SXLK)
C +LKO
3 *PK*XK+SXPLK)))**2/(N*(SIN(A)**2*BIN**2*SY2+2*COS(A)*SIN(A)*BIN
4 *SXY+COS(A)**2*SX2)-(SIN(A)*BIN*SY+COS(A)*SX)**2)**2-2*(SIN(A)*
5 BIN*SY+COS(A)*SX)*(N*(SIN(A)*BIN*(M*(LKO*YK+SYLK)+LKO*PK*YK+SYPLK
6)+COS(A)*(M*(LKO*XK+SXLK)+LKO*PK*XK+SXPLK))-(SPLK+M*SLK+LKO*(PK+M)
7 )*(SIN(A)*BIN*SY+COS(A)*SX))*((SPLK+M*SLK+LKO*(PK+M))*(SIN(A)**2
8 *BIN**2*SY2+2*COS(A)*SIN(A)*BIN*SXY+COS(A)**2*SX2)-(SIN(A)*BIN*
9 SY+COS(A)*SX)*(SIN(A)*BIN*(M*(LKO*YK+SYLK)+LKO*PK*YK+SYPLK)+COS(A
: )*(M*(LKO*XK+SXLK)+LKO*PK*XK+SXPLK)))/(N*(SIN(A)**2*BIN**2*SY2+2*
; COS(A)*SIN(A)*BIN*SXY+COS(A)**2*SX2)-(SIN(A)*BIN*SY+COS(A)*SX)*
< *2)**2-(SIN(A)**2*BIN**2*SY2+2*COS(A)*SIN(A)*BIN*SXY+COS(A)**2*
+ SX2)*(N*(SIN(A)*BIN*(M*(LKO*YK+SYLK)+LKO*PK*YK+SYPLK)+COS(A)*(M*(
>LKO*XK+SXLK)+LKO*PK*XK+SXPLK))-(SPLK+M*SLK+LKO*(PK+M))*(SIN(A)*BIN
? *SY+COS(A)*SX))**2/(N*(SIN(A)**2*BIN**2*SY2+2*COS(A)*SIN(A)*BIN
@ *SXY+COS(A)**2*SX2)-(SIN(A)*BIN*SY+COS(A)*SX)**2)**2+2*M*SPL2K+
1 SP2L2K+M**2*SL2K+LKO**2*(PK+M)**2
RMSLK = SQRT(RMSLK/N)
MINRMS(3+K) = RMSLK
WRITE(TEXT,550) K,LK,LKOPT(K),RMSLK
CALL STTPUT(TEXT,ISTAT)
50 CONTINUE
ENDIF
WRITE(TEXT,510)
CALL STTPUT(TEXT,ISTAT)
GOTO 2000
C **********************************************************************
1000 CONTINUE
C Computes RMS(A,M,BIN). There are too many parameters to create
C a subroutine. Let's use the good old GOTO.
RMSM = -N*((SPL+M*SL)*(SIN(A)**2*BIN**2*SY2+2*COS(A)*SIN(A)*BIN*S
1 XY+COS(A)**2*SX2)-(SIN(A)*BIN*SY+COS(A)*SX)*(SIN(A)*BIN*(SYPL+M
2 *SYL)+COS(A)*(SXPL+M*SXL)))**2/(N*(SIN(A)**2*BIN**2*SY2+2*COS(A
3 )*SIN(A)*BIN*SXY+COS(A)**2*SX2)-(SIN(A)*BIN*SY+COS(A)*SX)**2)**
4 2-2*(SIN(A)*BIN*SY+COS(A)*SX)*(N*(SIN(A)*BIN*(SYPL+M*SYL)+COS(A
5 )*(SXPL+M*SXL))-(SPL+M*SL)*(SIN(A)*BIN*SY+COS(A)*SX))*((SPL+M*S
6 L)*(SIN(A)**2*BIN**2*SY2+2*COS(A)*SIN(A)*BIN*SXY+COS(A)**2*SX2)
7 -(SIN(A)*BIN*SY+COS(A)*SX)*(SIN(A)*BIN*(SYPL+M*SYL)+COS(A)*(SXP
8 L+M*SXL)))/(N*(SIN(A)**2*BIN**2*SY2+2*COS(A)*SIN(A)*BIN*SXY+COS
9 (A)**2*SX2)-(SIN(A)*BIN*SY+COS(A)*SX)**2)**2-(SIN(A)**2*BIN**2*
: SY2+2*COS(A)*SIN(A)*BIN*SXY+COS(A)**2*SX2)*(N*(SIN(A)*BIN*(SYPL
; +M*SYL)+COS(A)*(SXPL+M*SXL))-(SPL+M*SL)*(SIN(A)*BIN*SY+COS(A)*S
< X))**2/(N*(SIN(A)**2*BIN**2*SY2+2*COS(A)*SIN(A)*BIN*SXY+COS(A)*
= *2*SX2)-(SIN(A)*BIN*SY+COS(A)*SX)**2)**2+2*M*SPL2+SP2L2+M**2*SL
> 2
RMSM = SQRT(RMSM/N)
IF (MODE(1:1) .EQ. 'M') GOTO 1001 ! Absolute order number
IF (MODE(1:1) .EQ. 'A') GOTO 1002 ! Angle
IF (MODE(1:1) .EQ. 'B') GOTO 1003 ! Bin
C **********************************************************************
1900 CONTINUE
ERROR = 1
2000 CONTINUE
CALL STKWRI('OUTPUTI',ERROR,1,1,KUN,ISTAT)
CALL STSEPI
STOP
END
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