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fit_pda.f
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fit_pda.f
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C Routines from the Starlink PDA library needed by the Fit module in mfit
C Collated by John Young 2009-11-03
SUBROUTINE PDA_BAKSLD(NR,N,A,X,B)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
C PURPOSE
C -------
C SOLVE AX=B WHERE A IS UPPER TRIANGULAR MATRIX.
C NOTE THAT A IS INPUT AS A LOWER TRIANGULAR MATRIX AND
C THAT THIS ROUTINE TAKES ITS TRANSPOSE IMPLICITLY.
C
C PARAMETERS
C ----------
C NR --> ROW DIMENSION OF MATRIX
C N --> DIMENSION OF PROBLEM
C A(N,N) --> LOWER TRIANGULAR MATRIX (PRESERVED)
C X(N) <-- SOLUTION VECTOR
C B(N) --> RIGHT-HAND SIDE VECTOR
C
C NOTE
C ----
C IF B IS NO LONGER REQUIRED BY CALLING ROUTINE,
C THEN VECTORS B AND X MAY SHARE THE SAME STORAGE.
C
DIMENSION A(NR,1),X(N),B(N)
C
C SOLVE (L-TRANSPOSE)X=B. (BACK SOLVE)
C
I=N
X(I)=B(I)/A(I,I)
IF(N.EQ.1) RETURN
30 IP1=I
I=I-1
SUM=0.D0
DO 40 J=IP1,N
SUM=SUM+A(J,I)*X(J)
40 CONTINUE
X(I)=(B(I)-SUM)/A(I,I)
IF(I.GT.1) GO TO 30
RETURN
END
SUBROUTINE PDA_CHLDCD(NR,N,A,DIAGMX,TOL,ADDMAX)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
C PURPOSE
C -------
C FIND THE PERTURBED L(L-TRANSPOSE) [WRITTEN LL+] DECOMPOSITION
C OF A+D, WHERE D IS A NON-NEGATIVE DIAGONAL MATRIX ADDED TO A IF
C NECESSARY TO ALLOW THE CHOLESKY DECOMPOSITION TO CONTINUE.
C
C PARAMETERS
C ----------
C NR --> ROW DIMENSION OF MATRIX
C N --> DIMENSION OF PROBLEM
C A(N,N) <--> ON ENTRY: MATRIX FOR WHICH TO FIND PERTURBED
C CHOLESKY DECOMPOSITION
C ON EXIT: CONTAINS L OF LL+ DECOMPOSITION
C IN LOWER TRIANGULAR PART AND DIAGONAL OF "A"
C DIAGMX --> MAXIMUM DIAGONAL ELEMENT OF "A"
C TOL --> TOLERANCE
C ADDMAX <-- MAXIMUM AMOUNT IMPLICITLY ADDED TO DIAGONAL OF "A"
C IN FORMING THE CHOLESKY DECOMPOSITION OF A+D
C INTERNAL VARIABLES
C ------------------
C AMINL SMALLEST ELEMENT ALLOWED ON DIAGONAL OF L
C AMNLSQ =AMINL**2
C OFFMAX MAXIMUM OFF-DIAGONAL ELEMENT IN COLUMN OF A
C
C
C DESCRIPTION
C -----------
C THE NORMAL CHOLESKY DECOMPOSITION IS PERFORMED. HOWEVER, IF AT ANY
C POINT THE ALGORITHM WOULD ATTEMPT TO SET L(I,I)=SQRT(TEMP)
C WITH TEMP < TOL*DIAGMX, THEN L(I,I) IS SET TO SQRT(TOL*DIAGMX)
C INSTEAD. THIS IS EQUIVALENT TO ADDING TOL*DIAGMX-TEMP TO A(I,I)
C
C
DIMENSION A(NR,1)
C
ADDMAX=0.D0
AMINL=SQRT(DIAGMX*TOL)
AMNLSQ=AMINL*AMINL
C
C FORM COLUMN J OF L
C
DO 100 J=1,N
C FIND DIAGONAL ELEMENTS OF L
SUM=0.D0
IF(J.EQ.1) GO TO 20
JM1=J-1
DO 10 K=1,JM1
SUM=SUM + A(J,K)*A(J,K)
10 CONTINUE
20 TEMP=A(J,J)-SUM
IF(TEMP.LT.AMNLSQ) GO TO 30
C IF(TEMP.GE.AMINL**2)
C THEN
A(J,J)=SQRT(TEMP)
GO TO 40
C ELSE
C
C FIND MAXIMUM OFF-DIAGONAL ELEMENT IN COLUMN
30 OFFMAX=0.D0
IF(J.EQ.N) GO TO 37
JP1=J+1
DO 35 I=JP1,N
IF(ABS(A(I,J)).GT.OFFMAX) OFFMAX=ABS(A(I,J))
35 CONTINUE
37 IF(OFFMAX.LE.AMNLSQ) OFFMAX=AMNLSQ
C
C ADD TO DIAGONAL ELEMENT TO ALLOW CHOLESKY DECOMPOSITION TO CONTINUE
A(J,J)=SQRT(OFFMAX)
ADDMAX=MAX(ADDMAX,OFFMAX-TEMP)
C ENDIF
C
C FIND I,J ELEMENT OF LOWER TRIANGULAR MATRIX
40 IF(J.EQ.N) GO TO 100
JP1=J+1
DO 70 I=JP1,N
SUM=0.0D0
IF(J.EQ.1) GO TO 60
JM1=J-1
DO 50 K=1,JM1
SUM=SUM+A(I,K)*A(J,K)
50 CONTINUE
60 A(I,J)=(A(I,J)-SUM)/A(J,J)
70 CONTINUE
100 CONTINUE
RETURN
END
SUBROUTINE PDA_CHLHSD(NR,N,A,EPSM,SX,UDIAG)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
C PURPOSE
C -------
C FIND THE L(L-TRANSPOSE) [WRITTEN LL+] DECOMPOSITION OF THE PERTURBED
C MODEL HESSIAN MATRIX A+MU*I(WHERE MU\0 AND I IS THE IDENTITY MATRIX)
C WHICH IS SAFELY POSITIVE DEFINITE. IF A IS SAFELY POSITIVE DEFINITE
C UPON ENTRY, THEN MU=0.
C
C PARAMETERS
C ----------
C NR --> ROW DIMENSION OF MATRIX
C N --> DIMENSION OF PROBLEM
C A(N,N) <--> ON ENTRY; "A" IS MODEL HESSIAN (ONLY LOWER
C TRIANGULAR PART AND DIAGONAL STORED)
C ON EXIT: A CONTAINS L OF LL+ DECOMPOSITION OF
C PERTURBED MODEL HESSIAN IN LOWER TRIANGULAR
C PART AND DIAGONAL AND CONTAINS HESSIAN IN UPPER
C TRIANGULAR PART AND UDIAG
C EPSM --> MACHINE EPSILON
C SX(N) --> DIAGONAL SCALING MATRIX FOR X
C UDIAG(N) <-- ON EXIT: CONTAINS DIAGONAL OF HESSIAN
C
C INTERNAL VARIABLES
C ------------------
C TOL TOLERANCE
C DIAGMN MINIMUM ELEMENT ON DIAGONAL OF A
C DIAGMX MAXIMUM ELEMENT ON DIAGONAL OF A
C OFFMAX MAXIMUM OFF-DIAGONAL ELEMENT OF A
C OFFROW SUM OF OFF-DIAGONAL ELEMENTS IN A ROW OF A
C EVMIN MINIMUM EIGENVALUE OF A
C EVMAX MAXIMUM EIGENVALUE OF A
C
C DESCRIPTION
C -----------
C 1. IF "A" HAS ANY NEGATIVE DIAGONAL ELEMENTS, THEN CHOOSE MU>0
C SUCH THAT THE DIAGONAL OF A:=A+MU*I IS ALL POSITIVE
C WITH THE RATIO OF ITS SMALLEST TO LARGEST ELEMENT ON THE
C ORDER OF SQRT(EPSM).
C
C 2. "A" UNDERGOES A PERTURBED CHOLESKY DECOMPOSITION WHICH
C RESULTS IN AN LL+ DECOMPOSITION OF A+D, WHERE D IS A
C NON-NEGATIVE DIAGONAL MATRIX WHICH IS IMPLICITLY ADDED TO
C "A" DURING THE DECOMPOSITION IF "A" IS NOT POSITIVE DEFINITE.
C "A" IS RETAINED AND NOT CHANGED DURING THIS PROCESS BY
C COPYING L INTO THE UPPER TRIANGULAR PART OF "A" AND THE
C DIAGONAL INTO UDIAG. THEN THE CHOLESKY DECOMPOSITION ROUTINE
C IS CALLED. ON RETURN, ADDMAX CONTAINS MAXIMUM ELEMENT OF D.
C
C 3. IF ADDMAX=0, "A" WAS POSITIVE DEFINITE GOING INTO STEP 2
C AND RETURN IS MADE TO CALLING PROGRAM. OTHERWISE,
C THE MINIMUM NUMBER SDD WHICH MUST BE ADDED TO THE
C DIAGONAL OF A TO MAKE IT SAFELY STRICTLY DIAGONALLY DOMINANT
C IS CALCULATED. SINCE A+ADDMAX*I AND A+SDD*I ARE SAFELY
C POSITIVE DEFINITE, CHOOSE MU=MIN(ADDMAX,SDD) AND DECOMPOSE
C A+MU*I TO OBTAIN L.
C
DIMENSION A(NR,1),SX(N),UDIAG(N)
C
C SCALE HESSIAN
C PRE- AND POST- MULTIPLY "A" BY INV(SX)
C
DO 20 J=1,N
DO 10 I=J,N
A(I,J)=A(I,J)/(SX(I)*SX(J))
10 CONTINUE
20 CONTINUE
C
C STEP1
C -----
C NOTE: IF A DIFFERENT TOLERANCE IS DESIRED THROUGHOUT THIS
C ALGORITHM, CHANGE TOLERANCE HERE:
TOL=SQRT(EPSM)
C
DIAGMX=A(1,1)
DIAGMN=A(1,1)
IF(N.EQ.1) GO TO 35
DO 30 I=2,N
IF(A(I,I).LT.DIAGMN) DIAGMN=A(I,I)
IF(A(I,I).GT.DIAGMX) DIAGMX=A(I,I)
30 CONTINUE
35 POSMAX=MAX(DIAGMX,0.D0)
C
C DIAGMN .LE. 0
C
IF(DIAGMN.GT.POSMAX*TOL) GO TO 100
C IF(DIAGMN.LE.POSMAX*TOL)
C THEN
AMU=TOL*(POSMAX-DIAGMN)-DIAGMN
IF(AMU.NE.0.D0) GO TO 60
C IF(AMU.EQ.0.)
C THEN
C
C FIND LARGEST OFF-DIAGONAL ELEMENT OF A
OFFMAX=0.D0
IF(N.EQ.1) GO TO 50
DO 45 I=2,N
IM1=I-1
DO 40 J=1,IM1
IF(ABS(A(I,J)).GT.OFFMAX) OFFMAX=ABS(A(I,J))
40 CONTINUE
45 CONTINUE
50 AMU=OFFMAX
IF(AMU.NE.0.D0) GO TO 55
C IF(AMU.EQ.0.)
C THEN
AMU=1.0D0
GO TO 60
C ELSE
55 AMU=AMU*(1.0D0+TOL)
C ENDIF
C ENDIF
C
C A=A + MU*I
C
60 DO 65 I=1,N
A(I,I)=A(I,I)+AMU
65 CONTINUE
DIAGMX=DIAGMX+AMU
C ENDIF
C
C STEP2
C -----
C COPY LOWER TRIANGULAR PART OF "A" TO UPPER TRIANGULAR PART
C AND DIAGONAL OF "A" TO UDIAG
C
100 CONTINUE
DO 110 J=1,N
UDIAG(J)=A(J,J)
IF(J.EQ.N) GO TO 110
JP1=J+1
DO 105 I=JP1,N
A(J,I)=A(I,J)
105 CONTINUE
110 CONTINUE
C
CALL PDA_CHLDCD(NR,N,A,DIAGMX,TOL,ADDMAX)
C
C
C STEP3
C -----
C IF ADDMAX=0, "A" WAS POSITIVE DEFINITE GOING INTO STEP 2,
C THE LL+ DECOMPOSITION HAS BEEN DONE, AND WE RETURN.
C OTHERWISE, ADDMAX>0. PERTURB "A" SO THAT IT IS SAFELY
C DIAGONALLY DOMINANT AND FIND LL+ DECOMPOSITION
C
IF(ADDMAX.LE.0.D0) GO TO 170
C IF(ADDMAX.GT.0.)
C THEN
C
C RESTORE ORIGINAL "A" (LOWER TRIANGULAR PART AND DIAGONAL)
C
DO 120 J=1,N
A(J,J)=UDIAG(J)
IF(J.EQ.N) GO TO 120
JP1=J+1
DO 115 I=JP1,N
A(I,J)=A(J,I)
115 CONTINUE
120 CONTINUE
C
C FIND SDD SUCH THAT A+SDD*I IS SAFELY POSITIVE DEFINITE
C NOTE: EVMIN<0 SINCE A IS NOT POSITIVE DEFINITE;
C
EVMIN=0.D0
EVMAX=A(1,1)
DO 150 I=1,N
OFFROW=0.D0
IF(I.EQ.1) GO TO 135
IM1=I-1
DO 130 J=1,IM1
OFFROW=OFFROW+ABS(A(I,J))
130 CONTINUE
135 IF(I.EQ.N) GO TO 145
IP1=I+1
DO 140 J=IP1,N
OFFROW=OFFROW+ABS(A(J,I))
140 CONTINUE
145 EVMIN=MIN(EVMIN,A(I,I)-OFFROW)
EVMAX=MAX(EVMAX,A(I,I)+OFFROW)
150 CONTINUE
SDD=TOL*(EVMAX-EVMIN)-EVMIN
C
C PERTURB "A" AND DECOMPOSE AGAIN
C
AMU=MIN(SDD,ADDMAX)
DO 160 I=1,N
A(I,I)=A(I,I)+AMU
UDIAG(I)=A(I,I)
160 CONTINUE
C
C "A" NOW GUARANTEED SAFELY POSITIVE DEFINITE
C
CALL PDA_CHLDCD(NR,N,A,0.0D0,TOL,ADDMAX)
C ENDIF
C
C UNSCALE HESSIAN AND CHOLESKY DECOMPOSITION MATRIX
C
170 DO 190 J=1,N
DO 175 I=J,N
A(I,J)=SX(I)*A(I,J)
175 CONTINUE
IF(J.EQ.1) GO TO 185
JM1=J-1
DO 180 I=1,JM1
A(I,J)=SX(I)*SX(J)*A(I,J)
180 CONTINUE
185 UDIAG(J)=UDIAG(J)*SX(J)*SX(J)
190 CONTINUE
RETURN
END
SUBROUTINE PDA_D1FCND(N,X,G)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
C PURPOSE
C -------
C DUMMY ROUTINE TO PREVENT UNSATISFIED EXTERNAL DIAGNOSTIC
C WHEN SPECIFIC ANALYTIC GRADIENT FUNCTION NOT SUPPLIED.
C
DIMENSION X(N),G(N)
G(N)=G(N)
X(N)=X(N)
STOP
END
SUBROUTINE PDA_D2FCND(NR,N,X,H)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
C PURPOSE
C -------
C DUMMY ROUTINE TO PREVENT UNSATISFIED EXTERNAL DIAGNOSTIC
C WHEN SPECIFIC ANALYTIC HESSIAN FUNCTION NOT SUPPLIED.
C
DIMENSION X(N),H(NR,1)
H(NR,1)=H(NR,1)
X(N)=X(N)
STOP
END
*DECK PDA_D9B1MP
SUBROUTINE PDA_D9B1MP (X, AMPL, THETA, STATUS)
C***BEGIN PROLOGUE PDA_D9B1MP
C***SUBSIDIARY
C***PURPOSE Evaluate the modulus and phase for the J1 and Y1 Bessel
C functions.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY C10A1
C***TYPE DOUBLE PRECISION (PDA_D9B1MP-D)
C***KEYWORDS BESSEL FUNCTION, FNLIB, MODULUS, PHASE, SPECIAL FUNCTIONS
C***AUTHOR Fullerton, W., (LANL)
C***DESCRIPTION
C
C Evaluate the modulus and phase for the Bessel J1 and Y1 functions.
C
C Series for BM1 on the interval 1.56250E-02 to 6.25000E-02
C with weighted error 4.91E-32
C log weighted error 31.31
C significant figures required 30.04
C decimal places required 32.09
C
C Series for BT12 on the interval 1.56250E-02 to 6.25000E-02
C with weighted error 3.33E-32
C log weighted error 31.48
C significant figures required 31.05
C decimal places required 32.27
C
C Series for BM12 on the interval 0. to 1.56250E-02
C with weighted error 5.01E-32
C log weighted error 31.30
C significant figures required 29.99
C decimal places required 32.10
C
C Series for BTH1 on the interval 0. to 1.56250E-02
C with weighted error 2.82E-32
C log weighted error 31.55
C significant figures required 31.12
C decimal places required 32.37
C
C STATUS Returned error status.
C The status must be zero on entry. This
C routine does not check the status on entry.
C
C***SEE ALSO PDA_DBESJ1, DBESY1
C***REFERENCES (NONE)
C***ROUTINES CALLED PDA_D1MACH, PDA_DCSEVL, PDA_INITDS, PDA_XERMSG
C***REVISION HISTORY (YYMMDD)
C 770701 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to PDA_XERMSG. (THJ)
C 900720 Routine changed from user-callable to subsidiary. (WRB)
C 920618 Removed space from variable name and code restructured to
C use IF-THEN-ELSE. (RWC, WRB)
C 950404 Implement status. (HME)
C***END PROLOGUE PDA_D9B1MP
INTEGER STATUS
DOUBLE PRECISION X, AMPL, THETA, BM1CS(37), BT12CS(39),
1 BM12CS(40), BTH1CS(44), XMAX, PI4, Z, PDA_D1MACH, PDA_DCSEVL
LOGICAL FIRST
SAVE BM1CS, BT12CS, BTH1CS, BM12CS, PI4, NBM1, NBT12,
1 NBM12, NBTH1, XMAX, FIRST
DATA BM1CS( 1) / +.1069845452 6180630149 6998530853 8 D+0 /
DATA BM1CS( 2) / +.3274915039 7159649007 2905514344 5 D-2 /
DATA BM1CS( 3) / -.2987783266 8316985920 3044577793 8 D-4 /
DATA BM1CS( 4) / +.8331237177 9919745313 9322266902 3 D-6 /
DATA BM1CS( 5) / -.4112665690 3020073048 9638172549 8 D-7 /
DATA BM1CS( 6) / +.2855344228 7892152207 1975766316 1 D-8 /
DATA BM1CS( 7) / -.2485408305 4156238780 6002659605 5 D-9 /
DATA BM1CS( 8) / +.2543393338 0725824427 4248439717 4 D-10 /
DATA BM1CS( 9) / -.2941045772 8229675234 8975082790 9 D-11 /
DATA BM1CS( 10) / +.3743392025 4939033092 6505615362 6 D-12 /
DATA BM1CS( 11) / -.5149118293 8211672187 2054824352 7 D-13 /
DATA BM1CS( 12) / +.7552535949 8651439080 3404076419 9 D-14 /
DATA BM1CS( 13) / -.1169409706 8288464441 6629062246 4 D-14 /
DATA BM1CS( 14) / +.1896562449 4347915717 2182460506 0 D-15 /
DATA BM1CS( 15) / -.3201955368 6932864206 6477531639 4 D-16 /
DATA BM1CS( 16) / +.5599548399 3162041144 8416990549 3 D-17 /
DATA BM1CS( 17) / -.1010215894 7304324431 1939044454 4 D-17 /
DATA BM1CS( 18) / +.1873844985 7275629833 0204271957 3 D-18 /
DATA BM1CS( 19) / -.3563537470 3285802192 7430143999 9 D-19 /
DATA BM1CS( 20) / +.6931283819 9712383304 2276351999 9 D-20 /
DATA BM1CS( 21) / -.1376059453 4065001522 5140893013 3 D-20 /
DATA BM1CS( 22) / +.2783430784 1070802205 9977932799 9 D-21 /
DATA BM1CS( 23) / -.5727595364 3205616893 4866943999 9 D-22 /
DATA BM1CS( 24) / +.1197361445 9188926725 3575679999 9 D-22 /
DATA BM1CS( 25) / -.2539928509 8918719766 4144042666 6 D-23 /
DATA BM1CS( 26) / +.5461378289 6572959730 6961919999 9 D-24 /
DATA BM1CS( 27) / -.1189211341 7733202889 8628949333 3 D-24 /
DATA BM1CS( 28) / +.2620150977 3400815949 5782400000 0 D-25 /
DATA BM1CS( 29) / -.5836810774 2556859019 2093866666 6 D-26 /
DATA BM1CS( 30) / +.1313743500 0805957734 2361599999 9 D-26 /
DATA BM1CS( 31) / -.2985814622 5103803553 3277866666 6 D-27 /
DATA BM1CS( 32) / +.6848390471 3346049376 2559999999 9 D-28 /
DATA BM1CS( 33) / -.1584401568 2224767211 9296000000 0 D-28 /
DATA BM1CS( 34) / +.3695641006 5709380543 0101333333 3 D-29 /
DATA BM1CS( 35) / -.8687115921 1446682430 1226666666 6 D-30 /
DATA BM1CS( 36) / +.2057080846 1587634629 2906666666 6 D-30 /
DATA BM1CS( 37) / -.4905225761 1162255185 2373333333 3 D-31 /
DATA BT12CS( 1) / +.7382386012 8742974662 6208397927 64 D+0 /
DATA BT12CS( 2) / -.3336111317 4483906384 4701476811 89 D-2 /
DATA BT12CS( 3) / +.6146345488 8046964698 5148994201 86 D-4 /
DATA BT12CS( 4) / -.2402458516 1602374264 9776354695 68 D-5 /
DATA BT12CS( 5) / +.1466355557 7509746153 2105919972 04 D-6 /
DATA BT12CS( 6) / -.1184191730 5589180567 0051475049 83 D-7 /
DATA BT12CS( 7) / +.1157419896 3919197052 1254663030 55 D-8 /
DATA BT12CS( 8) / -.1300116112 9439187449 3660077945 71 D-9 /
DATA BT12CS( 9) / +.1624539114 1361731937 7421662736 67 D-10 /
DATA BT12CS( 10) / -.2208963682 1403188752 1554417701 28 D-11 /
DATA BT12CS( 11) / +.3218030425 8553177090 4743586537 78 D-12 /
DATA BT12CS( 12) / -.4965314793 2768480785 5520211353 81 D-13 /
DATA BT12CS( 13) / +.8043890043 2847825985 5588826393 17 D-14 /
DATA BT12CS( 14) / -.1358912131 0161291384 6947126822 82 D-14 /
DATA BT12CS( 15) / +.2381050439 7147214869 6765296059 73 D-15 /
DATA BT12CS( 16) / -.4308146636 3849106724 4712414207 99 D-16 /
DATA BT12CS( 17) / +.8020254403 2771002434 9935125504 00 D-17 /
DATA BT12CS( 18) / -.1531631064 2462311864 2300274687 99 D-17 /
DATA BT12CS( 19) / +.2992860635 2715568924 0730405546 66 D-18 /
DATA BT12CS( 20) / -.5970996465 8085443393 8156366506 66 D-19 /
DATA BT12CS( 21) / +.1214028966 9415185024 1608526506 66 D-19 /
DATA BT12CS( 22) / -.2511511469 6612948901 0069777066 66 D-20 /
DATA BT12CS( 23) / +.5279056717 0328744850 7383807999 99 D-21 /
DATA BT12CS( 24) / -.1126050922 7550498324 3611613866 66 D-21 /
DATA BT12CS( 25) / +.2434827735 9576326659 6634624000 00 D-22 /
DATA BT12CS( 26) / -.5331726123 6931800130 0384426666 66 D-23 /
DATA BT12CS( 27) / +.1181361505 9707121039 2059903999 99 D-23 /
DATA BT12CS( 28) / -.2646536828 3353523514 8567893333 33 D-24 /
DATA BT12CS( 29) / +.5990339404 1361503945 5778133333 33 D-25 /
DATA BT12CS( 30) / -.1369085463 0829503109 1363839999 99 D-25 /
DATA BT12CS( 31) / +.3157679015 4380228326 4136533333 33 D-26 /
DATA BT12CS( 32) / -.7345791508 2084356491 4005333333 33 D-27 /
DATA BT12CS( 33) / +.1722808148 0722747930 7059200000 00 D-27 /
DATA BT12CS( 34) / -.4071690796 1286507941 0688000000 00 D-28 /
DATA BT12CS( 35) / +.9693474513 6779622700 3733333333 33 D-29 /
DATA BT12CS( 36) / -.2323763633 7765716765 3546666666 66 D-29 /
DATA BT12CS( 37) / +.5607451067 3522029406 8906666666 66 D-30 /
DATA BT12CS( 38) / -.1361646539 1539005860 5226666666 66 D-30 /
DATA BT12CS( 39) / +.3326310923 3894654388 9066666666 66 D-31 /
DATA BM12CS( 1) / +.9807979156 2330500272 7209354693 7 D-1 /
DATA BM12CS( 2) / +.1150961189 5046853061 7548348460 2 D-2 /
DATA BM12CS( 3) / -.4312482164 3382054098 8935809773 2 D-5 /
DATA BM12CS( 4) / +.5951839610 0888163078 1302980183 2 D-7 /
DATA BM12CS( 5) / -.1704844019 8269098574 0070158647 8 D-8 /
DATA BM12CS( 6) / +.7798265413 6111095086 5817382740 1 D-10 /
DATA BM12CS( 7) / -.4958986126 7664158094 9175495186 5 D-11 /
DATA BM12CS( 8) / +.4038432416 4211415168 3820226514 4 D-12 /
DATA BM12CS( 9) / -.3993046163 7251754457 6548384664 5 D-13 /
DATA BM12CS( 10) / +.4619886183 1189664943 1334243277 5 D-14 /
DATA BM12CS( 11) / -.6089208019 0953833013 4547261933 3 D-15 /
DATA BM12CS( 12) / +.8960930916 4338764821 5704804124 9 D-16 /
DATA BM12CS( 13) / -.1449629423 9420231229 1651891892 5 D-16 /
DATA BM12CS( 14) / +.2546463158 5377760561 6514964806 8 D-17 /
DATA BM12CS( 15) / -.4809472874 6478364442 5926371862 0 D-18 /
DATA BM12CS( 16) / +.9687684668 2925990490 8727583912 4 D-19 /
DATA BM12CS( 17) / -.2067213372 2779660232 4503811755 1 D-19 /
DATA BM12CS( 18) / +.4646651559 1503847318 0276780959 0 D-20 /
DATA BM12CS( 19) / -.1094966128 8483341382 4135132833 9 D-20 /
DATA BM12CS( 20) / +.2693892797 2886828609 0570761278 5 D-21 /
DATA BM12CS( 21) / -.6894992910 9303744778 1897002685 7 D-22 /
DATA BM12CS( 22) / +.1830268262 7520629098 9066855474 0 D-22 /
DATA BM12CS( 23) / -.5025064246 3519164281 5611355322 4 D-23 /
DATA BM12CS( 24) / +.1423545194 4548060396 3169363419 4 D-23 /
DATA BM12CS( 25) / -.4152191203 6164503880 6888676980 1 D-24 /
DATA BM12CS( 26) / +.1244609201 5039793258 8233007654 7 D-24 /
DATA BM12CS( 27) / -.3827336370 5693042994 3191866128 6 D-25 /
DATA BM12CS( 28) / +.1205591357 8156175353 7472398183 5 D-25 /
DATA BM12CS( 29) / -.3884536246 3764880764 3185936112 4 D-26 /
DATA BM12CS( 30) / +.1278689528 7204097219 0489528346 1 D-26 /
DATA BM12CS( 31) / -.4295146689 4479462720 6193691591 2 D-27 /
DATA BM12CS( 32) / +.1470689117 8290708864 5680270798 3 D-27 /
DATA BM12CS( 33) / -.5128315665 1060731281 8037401779 6 D-28 /
DATA BM12CS( 34) / +.1819509585 4711693854 8143737328 6 D-28 /
DATA BM12CS( 35) / -.6563031314 8419808676 1863505037 3 D-29 /
DATA BM12CS( 36) / +.2404898976 9199606531 9891487583 4 D-29 /
DATA BM12CS( 37) / -.8945966744 6906124732 3495824297 9 D-30 /
DATA BM12CS( 38) / +.3376085160 6572310266 3714897824 0 D-30 /
DATA BM12CS( 39) / -.1291791454 6206563609 1309991696 6 D-30 /
DATA BM12CS( 40) / +.5008634462 9588105206 8495150125 4 D-31 /
DATA BTH1CS( 1) / +.7474995720 3587276055 4434839696 95 D+0 /
DATA BTH1CS( 2) / -.1240077714 4651711252 5457775413 84 D-2 /
DATA BTH1CS( 3) / +.9925244240 4424527376 6414976895 92 D-5 /
DATA BTH1CS( 4) / -.2030369073 7159711052 4193753756 08 D-6 /
DATA BTH1CS( 5) / +.7535961770 5690885712 1840175836 29 D-8 /
DATA BTH1CS( 6) / -.4166161271 5343550107 6300238562 28 D-9 /
DATA BTH1CS( 7) / +.3070161807 0834890481 2451020912 16 D-10 /
DATA BTH1CS( 8) / -.2817849963 7605213992 3240088839 24 D-11 /
DATA BTH1CS( 9) / +.3079069673 9040295476 0281468216 47 D-12 /
DATA BTH1CS( 10) / -.3880330026 2803434112 7873475547 81 D-13 /
DATA BTH1CS( 11) / +.5509603960 8630904934 5617262085 62 D-14 /
DATA BTH1CS( 12) / -.8659006076 8383779940 1033989539 94 D-15 /
DATA BTH1CS( 13) / +.1485604914 1536749003 4236890606 83 D-15 /
DATA BTH1CS( 14) / -.2751952981 5904085805 3712121250 09 D-16 /
DATA BTH1CS( 15) / +.5455079609 0481089625 0362236409 23 D-17 /
DATA BTH1CS( 16) / -.1148653450 1983642749 5436310271 77 D-17 /
DATA BTH1CS( 17) / +.2553521337 7973900223 1990525335 22 D-18 /
DATA BTH1CS( 18) / -.5962149019 7413450395 7682879078 49 D-19 /
DATA BTH1CS( 19) / +.1455662290 2372718620 2883020058 33 D-19 /
DATA BTH1CS( 20) / -.3702218542 2450538201 5797760195 93 D-20 /
DATA BTH1CS( 21) / +.9776307412 5345357664 1684345179 24 D-21 /
DATA BTH1CS( 22) / -.2672682163 9668488468 7237753930 52 D-21 /
DATA BTH1CS( 23) / +.7545330038 4983271794 0381906557 64 D-22 /
DATA BTH1CS( 24) / -.2194789991 9802744897 8923833716 47 D-22 /
DATA BTH1CS( 25) / +.6564839462 3955262178 9069998174 93 D-23 /
DATA BTH1CS( 26) / -.2015560429 8370207570 7840768695 19 D-23 /
DATA BTH1CS( 27) / +.6341776855 6776143492 1446671856 70 D-24 /
DATA BTH1CS( 28) / -.2041927788 5337895634 8137699555 91 D-24 /
DATA BTH1CS( 29) / +.6719146422 0720567486 6589800185 51 D-25 /
DATA BTH1CS( 30) / -.2256907911 0207573595 7090036873 36 D-25 /
DATA BTH1CS( 31) / +.7729771989 2989706370 9269598719 29 D-26 /
DATA BTH1CS( 32) / -.2696744451 2294640913 2114240809 20 D-26 /
DATA BTH1CS( 33) / +.9574934451 8502698072 2955219336 27 D-27 /
DATA BTH1CS( 34) / -.3456916844 8890113000 1756808276 27 D-27 /
DATA BTH1CS( 35) / +.1268123481 7398436504 2119862383 74 D-27 /
DATA BTH1CS( 36) / -.4723253663 0722639860 4649937134 45 D-28 /
DATA BTH1CS( 37) / +.1785000847 8186376177 8586197964 17 D-28 /
DATA BTH1CS( 38) / -.6840436100 4510395406 2152235667 46 D-29 /
DATA BTH1CS( 39) / +.2656602867 1720419358 2934226722 12 D-29 /
DATA BTH1CS( 40) / -.1045040252 7914452917 7141614846 70 D-29 /
DATA BTH1CS( 41) / +.4161829082 5377144306 8619171970 64 D-30 /
DATA BTH1CS( 42) / -.1677163920 3643714856 5013478828 87 D-30 /
DATA BTH1CS( 43) / +.6836199777 6664389173 5359280285 28 D-31 /
DATA BTH1CS( 44) / -.2817224786 1233641166 7395746228 10 D-31 /
DATA PI4 / 0.7853981633 9744830961 5660845819 876 D0 /
DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT PDA_D9B1MP
IF (FIRST) THEN
ETA = 0.1*REAL(PDA_D1MACH(3))
NBM1 = PDA_INITDS (BM1CS, 37, ETA, STATUS)
NBT12 = PDA_INITDS (BT12CS, 39, ETA, STATUS)
NBM12 = PDA_INITDS (BM12CS, 40, ETA, STATUS)
NBTH1 = PDA_INITDS (BTH1CS, 44, ETA, STATUS)
C
XMAX = 1.0D0/PDA_D1MACH(4)
ENDIF
FIRST = .FALSE.
C
IF (X .LT. 4.0D0) THEN
CALL PDA_XERMSG ('SLATEC', 'PDA_D9B1MP', 'X must be .GE. 4',
+ 1, 2, STATUS)
AMPL = 0.0D0
THETA = 0.0D0
ELSE IF (X .LE. 8.0D0) THEN
Z = (128.0D0/(X*X) - 5.0D0)/3.0D0
AMPL = (0.75D0 + PDA_DCSEVL (Z, BM1CS, NBM1, STATUS))/SQRT(X)
THETA = X - 3.0D0*PI4 + PDA_DCSEVL (Z, BT12CS, NBT12, STATUS)/X
ELSE
IF (X .GT. XMAX) CALL PDA_XERMSG ('SLATEC', 'PDA_D9B1MP',
+ 'No precision because X is too big', 2, 2, STATUS)
C
Z = 128.0D0/(X*X) - 1.0D0
AMPL = (0.75D0 + PDA_DCSEVL (Z, BM12CS, NBM12, STATUS))/SQRT(X)
THETA = X - 3.0D0*PI4 + PDA_DCSEVL (Z, BTH1CS, NBTH1, STATUS)/X
ENDIF
RETURN
END
*DECK PDA_DBESJ1
DOUBLE PRECISION FUNCTION PDA_DBESJ1 (X, STATUS)
C***BEGIN PROLOGUE PDA_DBESJ1
C***PURPOSE Compute the Bessel function of the first kind of order one.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY C10A1
C***TYPE DOUBLE PRECISION (BESJ1-S, PDA_DBESJ1-D)
C***KEYWORDS BESSEL FUNCTION, FIRST KIND, FNLIB, PDA_ORDER ONE,
C SPECIAL FUNCTIONS
C***AUTHOR Fullerton, W., (LANL)
C***DESCRIPTION
C
C PDA_DBESJ1(X) calculates the double precision Bessel function of the
C first kind of order one for double precision argument X.
C
C Series for BJ1 on the interval 0. to 1.60000E+01
C with weighted error 1.16E-33
C log weighted error 32.93
C significant figures required 32.36
C decimal places required 33.57
C
C STATUS Returned error status.
C The status must be zero on entry. This
C routine does not check the status on entry.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED PDA_D1MACH, PDA_D9B1MP, PDA_DCSEVL, PDA_INITDS, PDA_XERMSG
C***REVISION HISTORY (YYMMDD)
C 780601 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to PDA_XERMSG. (THJ)
C 910401 Corrected error in code which caused values to have the
C wrong sign for arguments less than 4.0. (WRB)
C 950404 Implement status. (HME)
C***END PROLOGUE PDA_DBESJ1
INTEGER STATUS
DOUBLE PRECISION X, BJ1CS(19), AMPL, THETA, XSML, XMIN, Y,
1 PDA_D1MACH, PDA_DCSEVL
LOGICAL FIRST
SAVE BJ1CS, NTJ1, XSML, XMIN, FIRST
DATA BJ1CS( 1) / -.1172614151 3332786560 6240574524 003 D+0 /
DATA BJ1CS( 2) / -.2536152183 0790639562 3030884554 698 D+0 /
DATA BJ1CS( 3) / +.5012708098 4469568505 3656363203 743 D-1 /
DATA BJ1CS( 4) / -.4631514809 6250819184 2619728789 772 D-2 /
DATA BJ1CS( 5) / +.2479962294 1591402453 9124064592 364 D-3 /
DATA BJ1CS( 6) / -.8678948686 2788258452 1246435176 416 D-5 /
DATA BJ1CS( 7) / +.2142939171 4379369150 2766250991 292 D-6 /
DATA BJ1CS( 8) / -.3936093079 1831797922 9322764073 061 D-8 /
DATA BJ1CS( 9) / +.5591182317 9468800401 8248059864 032 D-10 /
DATA BJ1CS( 10) / -.6327616404 6613930247 7695274014 880 D-12 /
DATA BJ1CS( 11) / +.5840991610 8572470032 6945563268 266 D-14 /
DATA BJ1CS( 12) / -.4482533818 7012581903 9135059199 999 D-16 /
DATA BJ1CS( 13) / +.2905384492 6250246630 6018688000 000 D-18 /
DATA BJ1CS( 14) / -.1611732197 8414416541 2118186666 666 D-20 /
DATA BJ1CS( 15) / +.7739478819 3927463729 8346666666 666 D-23 /
DATA BJ1CS( 16) / -.3248693782 1119984114 3466666666 666 D-25 /
DATA BJ1CS( 17) / +.1202237677 2274102272 0000000000 000 D-27 /
DATA BJ1CS( 18) / -.3952012212 6513493333 3333333333 333 D-30 /
DATA BJ1CS( 19) / +.1161678082 2664533333 3333333333 333 D-32 /
DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT PDA_DBESJ1
IF (FIRST) THEN
NTJ1 = PDA_INITDS (BJ1CS, 19, 0.1*REAL(PDA_D1MACH(3)), STATUS)
C
XSML = SQRT(8.0D0*PDA_D1MACH(3))
XMIN = 2.0D0*PDA_D1MACH(1)
ENDIF
FIRST = .FALSE.
C
Y = ABS(X)
IF (Y.GT.4.0D0) GO TO 20
C
PDA_DBESJ1 = 0.0D0
IF (Y.EQ.0.0D0) RETURN
IF (Y .LE. XMIN) CALL PDA_XERMSG ('SLATEC', 'PDA_DBESJ1',
+ 'ABS(X) SO SMALL J1 UNDERFLOWS', 1, 1, STATUS)
IF (Y.GT.XMIN) PDA_DBESJ1 = 0.5D0*X
IF (Y.GT.XSML) PDA_DBESJ1 = X*(.25D0
1 + PDA_DCSEVL (.125D0*Y*Y-1.D0, BJ1CS, NTJ1, STATUS) )
RETURN
C
20 CALL PDA_D9B1MP (Y, AMPL, THETA, STATUS)
PDA_DBESJ1 = SIGN (AMPL, X) * COS(THETA)
C
RETURN
END
*DECK PDA_DCSEVL
DOUBLE PRECISION FUNCTION PDA_DCSEVL (X, CS, N, STATUS)
C***BEGIN PROLOGUE PDA_DCSEVL
C***PURPOSE Evaluate a Chebyshev series.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY C3A2
C***TYPE DOUBLE PRECISION (CSEVL-S, PDA_DCSEVL-D)
C***KEYWORDS CHEBYSHEV SERIES, FNLIB, SPECIAL FUNCTIONS
C***AUTHOR Fullerton, W., (LANL)
C***DESCRIPTION
C
C Evaluate the N-term Chebyshev series CS at X. Adapted from
C a method presented in the paper by Broucke referenced below.
C
C Input Arguments --
C X value at which the series is to be evaluated.
C CS array of N terms of a Chebyshev series. In evaluating
C CS, only half the first coefficient is summed.
C N number of terms in array CS.
C STATUS Returned error status.
C The status must be zero on entry. This
C routine does not check the status on entry.
C
C***REFERENCES R. Broucke, Ten subroutines for the manipulation of
C Chebyshev series, Algorithm 446, Communications of
C the A.C.M. 16, (1973) pp. 254-256.
C L. Fox and I. B. Parker, Chebyshev Polynomials in
C Numerical Analysis, Oxford University Press, 1968,
C page 56.
C***ROUTINES CALLED PDA_D1MACH, PDA_XERMSG
C***REVISION HISTORY (YYMMDD)
C 770401 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to PDA_XERMSG. (THJ)
C 900329 Prologued revised extensively and code rewritten to allow
C X to be slightly outside interval (-1,+1). (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C 950404 Implement status. (HME)
C***END PROLOGUE PDA_DCSEVL
INTEGER STATUS
DOUBLE PRECISION B0, B1, B2, CS(*), ONEPL, TWOX, X, PDA_D1MACH
LOGICAL FIRST
SAVE FIRST, ONEPL
DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT PDA_DCSEVL
IF (FIRST) ONEPL = 1.0D0 + PDA_D1MACH(4)
FIRST = .FALSE.
IF (N .LT. 1) CALL PDA_XERMSG ('SLATEC', 'PDA_DCSEVL',
+ 'NUMBER OF TERMS .LE. 0', 2, 2, STATUS)
IF (N .GT. 1000) CALL PDA_XERMSG ('SLATEC', 'PDA_DCSEVL',
+ 'NUMBER OF TERMS .GT. 1000', 3, 2, STATUS)
IF (ABS(X) .GT. ONEPL) CALL PDA_XERMSG ('SLATEC', 'PDA_DCSEVL',
+ 'X OUTSIDE THE INTERVAL (-1,+1)', 1, 1, STATUS)
C
B1 = 0.0D0
B0 = 0.0D0
TWOX = 2.0D0*X
DO 10 I = 1,N
B2 = B1
B1 = B0
NI = N + 1 - I
B0 = TWOX*B1 - B2 + CS(NI)
10 CONTINUE
C
PDA_DCSEVL = 0.5D0*(B0-B2)
C
RETURN
END
*DECK PDA_DDOT
DOUBLE PRECISION FUNCTION PDA_DDOT (N, DX, INCX, DY, INCY)
C***BEGIN PROLOGUE PDA_DDOT
C***PURPOSE Compute the inner product of two vectors.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1A4
C***TYPE DOUBLE PRECISION (SDOT-S, PDA_DDOT-D, CDOTU-C)
C***KEYWORDS BLAS, INNER PRODUCT, LINEAR ALGEBRA, VECTOR
C***AUTHOR Lawson, C. L., (JPL)
C Hanson, R. J., (SNLA)
C Kincaid, D. R., (U. of Texas)
C Krogh, F. T., (JPL)
C***DESCRIPTION
C
C B L A S Subprogram
C Description of Parameters
C
C --Input--
C N number of elements in input vector(s)
C DX double precision vector with N elements
C INCX storage spacing between elements of DX
C DY double precision vector with N elements
C INCY storage spacing between elements of DY
C
C --Output--
C PDA_DDOT double precision dot product (zero if N .LE. 0)
C
C Returns the dot product of double precision DX and DY.
C PDA_DDOT = sum for I = 0 to N-1 of DX(LX+I*INCX) * DY(LY+I*INCY),
C where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
C defined in a similar way using INCY.
C
C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
C Krogh, Basic linear algebra subprograms for Fortran
C usage, Algorithm No. 539, Transactions on Mathematical
C Software 5, 3 (September 1979), pp. 308-323.
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 791001 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920310 Corrected definition of LX in DESCRIPTION. (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE PDA_DDOT
DOUBLE PRECISION DX(*), DY(*)
C***FIRST EXECUTABLE STATEMENT PDA_DDOT
PDA_DDOT = 0.0D0
IF (N .LE. 0) RETURN
IF (INCX .EQ. INCY) IF (INCX-1) 5,20,60
C
C Code for unequal or nonpositive increments.
C
5 IX = 1
IY = 1
IF (INCX .LT. 0) IX = (-N+1)*INCX + 1
IF (INCY .LT. 0) IY = (-N+1)*INCY + 1
DO 10 I = 1,N
PDA_DDOT = PDA_DDOT + DX(IX)*DY(IY)
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
RETURN
C
C Code for both increments equal to 1.
C
C Clean-up loop so remaining vector length is a multiple of 5.
C
20 M = MOD(N,5)
IF (M .EQ. 0) GO TO 40
DO 30 I = 1,M
PDA_DDOT = PDA_DDOT + DX(I)*DY(I)
30 CONTINUE
IF (N .LT. 5) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,5
PDA_DDOT = PDA_DDOT + DX(I)*DY(I) + DX(I+1)*DY(I+1)
1 + DX(I+2)*DY(I+2) + DX(I+3)*DY(I+3) + DX(I+4)*DY(I+4)
50 CONTINUE
RETURN
C
C Code for equal, positive, non-unit increments.
C
60 NS = N*INCX
DO 70 I = 1,NS,INCX
PDA_DDOT = PDA_DDOT + DX(I)*DY(I)
70 CONTINUE
RETURN
END
SUBROUTINE PDA_DGDRVD(NR,N,X,F,G,A,P,XPLS,FPLS,FCN,SX,STEPMX,
+ STEPTL,DLT,IRETCD,MXTAKE,SC,WRK1,WRK2,WRK3,IPR)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
C PURPOSE
C -------
C FIND A NEXT NEWTON ITERATE (XPLS) BY THE DOUBLE DOGLEG METHOD
C
C PARAMETERS
C ----------
C NR --> ROW DIMENSION OF MATRIX
C N --> DIMENSION OF PROBLEM
C X(N) --> OLD ITERATE X[K-1]
C F --> FUNCTION VALUE AT OLD ITERATE, F(X)
C G(N) --> GRADIENT AT OLD ITERATE, G(X), OR APPROXIMATE
C A(N,N) --> CHOLESKY DECOMPOSITION OF HESSIAN
C IN LOWER TRIANGULAR PART AND DIAGONAL
C P(N) --> NEWTON STEP
C XPLS(N) <-- NEW ITERATE X[K]
C FPLS <-- FUNCTION VALUE AT NEW ITERATE, F(XPLS)
C FCN --> NAME OF SUBROUTINE TO EVALUATE FUNCTION
C SX(N) --> DIAGONAL SCALING MATRIX FOR X
C STEPMX --> MAXIMUM ALLOWABLE STEP SIZE
C STEPTL --> RELATIVE STEP SIZE AT WHICH SUCCESSIVE ITERATES
C CONSIDERED CLOSE ENOUGH TO TERMINATE ALGORITHM
C DLT <--> TRUST REGION RADIUS
C [RETAIN VALUE BETWEEN SUCCESSIVE CALLS]
C IRETCD <-- RETURN CODE
C =0 SATISFACTORY XPLS FOUND
C =1 FAILED TO FIND SATISFACTORY XPLS SUFFICIENTLY
C DISTINCT FROM X
C MXTAKE <-- BOOLEAN FLAG INDICATING STEP OF MAXIMUM LENGTH USED
C SC(N) --> WORKSPACE [CURRENT STEP]
C WRK1(N) --> WORKSPACE (AND PLACE HOLDING ARGUMENT TO PDA_TRGUPD)
C WRK2(N) --> WORKSPACE
C WRK3(N) --> WORKSPACE
C IPR --> DEVICE TO WHICH TO SEND OUTPUT
C
DIMENSION X(N),XPLS(N),G(N),P(N)
DIMENSION SX(N)
DIMENSION SC(N),WRK1(N),WRK2(N),WRK3(N)
DIMENSION A(NR,1)
LOGICAL FSTDOG,NWTAKE,MXTAKE
EXTERNAL FCN
C
IRETCD=4
FSTDOG=.TRUE.
TMP=0.D0
DO 5 I=1,N
TMP=TMP+SX(I)*SX(I)*P(I)*P(I)
5 CONTINUE
RNWTLN=SQRT(TMP)
C$ WRITE(IPR,954) RNWTLN
C
100 CONTINUE
C
C FIND NEW STEP BY DOUBLE DOGLEG ALGORITHM
CALL PDA_DGSTPD(NR,N,G,A,P,SX,RNWTLN,DLT,NWTAKE,FSTDOG,
+ WRK1,WRK2,CLN,ETA,SC,IPR,STEPMX)
C
C CHECK NEW POINT AND UPDATE TRUST REGION
CALL PDA_TRGUPD(NR,N,X,F,G,A,FCN,SC,SX,NWTAKE,STEPMX,STEPTL,DLT,
+ IRETCD,WRK3,FPLSP,XPLS,FPLS,MXTAKE,IPR,2,WRK1)
IF(IRETCD.LE.1) RETURN
GO TO 100
950 FORMAT(46H PDA_DGDRVD INITIAL TRUST REGION NOT GIVEN.,
+ 22H COMPUTE CAUCHY STEP.)
951 FORMAT(22H PDA_DGDRVD ALPHA =,E20.13/
+ 22H PDA_DGDRVD BETA =,E20.13/
+ 22H PDA_DGDRVD DLT =,E20.13/
+ 22H PDA_DGDRVD NWTAKE=,L1 )
952 FORMAT(32H PDA_DGDRVD CURRENT STEP (SC))
954 FORMAT(22H0PDA_DGDRVD RNWTLN=,E20.13)
955 FORMAT(18H PDA_DGDRVD ,5(E20.13,3X))
END
SUBROUTINE PDA_DGSTPD(NR,N,G,A,P,SX,RNWTLN,DLT,NWTAKE,FSTDOG,
+ SSD,V,CLN,ETA,SC,IPR,STEPMX)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
C PURPOSE
C -------
C FIND NEW STEP BY DOUBLE DOGLEG ALGORITHM
C
C PARAMETERS
C ----------
C NR --> ROW DIMENSION OF MATRIX
C N --> DIMENSION OF PROBLEM
C G(N) --> GRADIENT AT CURRENT ITERATE, G(X)
C A(N,N) --> CHOLESKY DECOMPOSITION OF HESSIAN IN
C LOWER PART AND DIAGONAL
C P(N) --> NEWTON STEP
C SX(N) --> DIAGONAL SCALING MATRIX FOR X
C RNWTLN --> NEWTON STEP LENGTH
C DLT <--> TRUST REGION RADIUS
C NWTAKE <--> BOOLEAN, =.TRUE. IF NEWTON STEP TAKEN
C FSTDOG <--> BOOLEAN, =.TRUE. IF ON FIRST LEG OF DOGLEG
C SSD(N) <--> WORKSPACE [CAUCHY STEP TO THE MINIMUM OF THE
C QUADRATIC MODEL IN THE SCALED STEEPEST DESCENT
C DIRECTION] [RETAIN VALUE BETWEEN SUCCESSIVE CALLS]
C V(N) <--> WORKSPACE [RETAIN VALUE BETWEEN SUCCESSIVE CALLS]
C CLN <--> CAUCHY LENGTH
C [RETAIN VALUE BETWEEN SUCCESSIVE CALLS]
C ETA [RETAIN VALUE BETWEEN SUCCESSIVE CALLS]
C SC(N) <-- CURRENT STEP
C IPR --> DEVICE TO WHICH TO SEND OUTPUT
C STEPMX --> MAXIMUM ALLOWABLE STEP SIZE
C
C INTERNAL VARIABLES
C ------------------
C CLN LENGTH OF CAUCHY STEP
C
DIMENSION G(N),P(N)
DIMENSION SX(N)
DIMENSION SC(N),SSD(N),V(N)
DIMENSION A(NR,1)
LOGICAL NWTAKE,FSTDOG
IPR=IPR
C
C CAN WE TAKE NEWTON STEP
C
IF(RNWTLN.GT.DLT) GO TO 100
C IF(RNWTLN.LE.DLT)
C THEN
NWTAKE=.TRUE.
DO 10 I=1,N
SC(I)=P(I)
10 CONTINUE
DLT=RNWTLN