1
EXAMPLE 1
TEST SIMPLE ODR PROBLEM
WITH ANALYTIC DERIVATIVES USING DODR.
DATA SET REFERENCE: DRAPER AND SMITH, 1981, EXERCISE I, PAGE 521-522
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** DERIVATIVE CHECKING REPORT FOR FIT BY METHOD OF ODR ***
FOR RESPONSE 1 OF OBSERVATION 1
USER
SUPPLIED RELATIVE DERIVATIVE
DERIVATIVE WRT VALUE DIFFERENCE ASSESSMENT
BETA( 1) -3.18D+01 4.26D-08 VERIFIED
BETA( 2) 1.98D-05 1.30D-08 VERIFIED
DELTA( 1, 1) -3.37D-03 5.33D-08 VERIFIED
DELTA( 1, 2) -5.11D-03 7.38D-08 VERIFIED
NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS 16
(ESTIMATED BY ODRPACK)
NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN
USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVE FOR
USER SUPPLIED DERIVATIVE TO BE CONSIDERED VERIFIED 4
ROW NUMBER AT WHICH DERIVATIVES WERE CHECKED 1
-VALUES OF THE EXPLANATORY VARIABLES AT THIS ROW
X( 1, 1) 1.09000000D+02
X( 1, 2) 6.00000000D+02
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- PROBLEM SIZE:
N = 8 (NUMBER WITH NONZERO WEIGHT = 8)
NQ = 1
M = 2
NP = 2 (NUMBER UNFIXED = 2)
--- CONTROL VALUES:
JOB = 00020
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE INITIALIZED TO ZERO.
C=0 ==> COVARIANCE MATRIX WILL BE COMPUTED USING
DERIVATIVES RE-EVALUATED AT THE SOLUTION.
D=2 ==> DERIVATIVES ARE SUPPLIED BY USER.
DERIVATIVES WERE CHECKED.
RESULTS APPEAR CORRECT.
E=0 ==> METHOD IS EXPLICIT ODR.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE)
MAXIT = 50 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 6.76620105D-01
SUM OF SQUARED WEIGHTED DELTAS = 0.00000000D+00
SUM OF SQUARED WEIGHTED EPSILONS = 6.76620105D-01
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE
(K) (IFIXB) (SCLB)
1 1.15500000D-02 NO 8.65800866D+01
2 5.00000000D+03 NO 2.00000000D-04
--- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:
INDEX X(I,J) DELTA(I,J) FIXED SCALE WEIGHT
(I,J) (IFIXX) (SCLD) (WD)
1,1 1.090D+02 0.000D+00 NO 9.17D-03 1.00D+00
N,1 6.800D+01 0.000D+00 NO 1.47D-02 1.00D+00
1,2 6.000D+02 0.000D+00 NO 1.56D-03 1.00D+00
N,2 6.400D+02 0.000D+00 NO 1.56D-03 1.00D+00
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 9.120D-01 1.000D+00
N,1 3.760D-01 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF ODR ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
1 18 1.96944D-01 7.0893D-01 4.1620D-01 1.510D+00 YES
2 19 1.86553D-03 9.9053D-01 9.9572D-01 6.711D-01 YES
3 20 7.53265D-04 5.9622D-01 5.9632D-01 4.625D-02 YES
4 21 7.53264D-04 7.5670D-07 7.5713D-07 2.259D-05 YES
5 22 7.53264D-04 3.2574D-13 3.3214D-13 1.810D-08 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- STOPPING CONDITIONS:
INFO = 1 ==> SUM OF SQUARES CONVERGENCE.
NITER = 5 (NUMBER OF ITERATIONS)
NFEV = 22 (NUMBER OF FUNCTION EVALUATIONS)
NJEV = 6 (NUMBER OF JACOBIAN EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 8.70D-02 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 7.53263957D-04
SUM OF SQUARED WEIGHTED DELTAS = 5.82361429D-07
SUM OF SQUARED WEIGHTED EPSILONS = 7.52681595D-04
--- RESIDUAL STANDARD DEVIATION = 1.12046416D-02
DEGREES OF FREEDOM = 6
--- ESTIMATED BETA(J), J = 1, ..., NP:
BETA S.D. BETA ---- 95% CONFIDENCE INTERVAL ----
1 3.65797302D-03 4.2218D-05 3.55466818D-03 TO 3.76127786D-03
2 2.76273320D+04 2.2245D+02 2.70830140D+04 TO 2.81716499D+04
--- ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
I EPSILON(I,1) DELTA(I,1) DELTA(I,2)
1 1.67519647D-03 1.26771981D-06 1.06044027D-05
2 2.04207811D-03 1.15465196D-05 5.06224853D-05
3 -2.06741955D-02 -6.44374753D-06 -5.83522780D-04
4 2.42895060D-03 1.35332858D-05 6.02457198D-05
5 7.27227474D-03 2.10381027D-06 2.05043707D-04
6 4.07668337D-03 2.17324633D-05 1.01143283D-04
7 1.30331782D-02 3.89740068D-06 3.67888393D-04
8 -8.54482325D-03 -4.62274242D-05 -2.12025259D-04
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
2.762733195780256937723606824875D+04 7.532639569022918889229512018346D-04 1
NEW TEST RESULT =
2.762733195759230511612258851528D+04 7.532639569023399190791923096810D-04 1
DIFFERENCE = 2.10264D-07 4.80302D-17
RELATIVE ERROR = 7.61073D-12 6.37627D-14
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 2
TEST SIMPLE OLS PROBLEM
WITH FINITE DIFFERENCE DERIVATIVES USING DODR.
DATA SET REFERENCE: DRAPER AND SMITH, 1981, EXERCISE I, PAGE 521-522
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF OLS ***
--- PROBLEM SIZE:
N = 8 (NUMBER WITH NONZERO WEIGHT = 8)
NQ = 1
M = 2
NP = 2 (NUMBER UNFIXED = 2)
--- CONTROL VALUES:
JOB = 00002
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE FIXED AT ZERO SINCE E=2.
C=0 ==> COVARIANCE MATRIX WILL BE COMPUTED USING
DERIVATIVES RE-EVALUATED AT THE SOLUTION.
D=0 ==> DERIVATIVES ARE ESTIMATED BY FORWARD DIFFERENCES.
E=2 ==> METHOD IS EXPLICIT OLS.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE)
MAXIT = 50 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 6.76620105D-01
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE DERIVATIVE
STEP SIZE
(K) (IFIXB) (SCLB) (STPB)
1 1.15500000D-02 NO 8.65800866D+01 1.00000D-10
2 5.00000000D+03 NO 2.00000000D-04 1.00000D-10
--- EXPLANATORY VARIABLE SUMMARY:
INDEX X(I,J)
(I,J)
1,1 1.090D+02
N,1 6.800D+01
1,2 6.000D+02
N,2 6.400D+02
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 9.120D-01 1.000D+00
N,1 3.760D-01 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF OLS ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
1 8 1.96947D-01 7.0893D-01 4.1620D-01 1.510D+00 YES
2 11 1.86608D-03 9.9052D-01 9.9572D-01 6.711D-01 YES
3 14 7.53847D-04 5.9603D-01 5.9612D-01 4.625D-02 YES
4 17 7.53847D-04 3.6519D-07 3.6481D-07 2.231D-05 YES
5 20 7.53847D-04 -6.6525D-13 7.3426D-13 8.211D-09 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF OLS ***
--- STOPPING CONDITIONS:
INFO = 1 ==> SUM OF SQUARES CONVERGENCE.
NITER = 5 (NUMBER OF ITERATIONS)
NFEV = 22 (NUMBER OF FUNCTION EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 8.70D-02 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 7.53846772D-04
--- RESIDUAL STANDARD DEVIATION = 1.12089754D-02
DEGREES OF FREEDOM = 6
--- ESTIMATED BETA(J), J = 1, ..., NP:
BETA S.D. BETA ---- 95% CONFIDENCE INTERVAL ----
1 3.65797271D-03 4.2220D-05 3.55466516D-03 TO 3.76128026D-03
2 2.76273261D+04 2.2246D+02 2.70829945D+04 TO 2.81716577D+04
--- ESTIMATED EPSILON(I, 1), I = 1, ..., N:
INDEX VALUE -------------->
1 TO 4 1.67524573D-03 2.04353733D-03 -2.06907512D-02 2.43065938D-03
5 TO 8 7.27797278D-03 4.07944774D-03 1.30434799D-02 -8.55019524D-03
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
2.762732630143672940903343260288D+04 7.538467722687131359823875520476D-04 1
NEW TEST RESULT =
2.762732613563912309473380446434D+04 7.538467722687815491394713873774D-04 1
DIFFERENCE = 1.65798D-04 6.84132D-17
RELATIVE ERROR = 6.00122D-09 9.07521D-14
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 3
TEST PARAMETER FIXING CAPABILITIES FOR POORLY SCALED OLS PROBLEM
WITH ANALYTIC DERIVATIVES USING DODRC.
DATA SET REFERENCE: BOGGS, BYRD AND SCHNABEL, 1985, EXAMPLE 3
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF OLS ***
--- PROBLEM SIZE:
N = 44 (NUMBER WITH NONZERO WEIGHT = 44)
NQ = 1
M = 1
NP = 9 (NUMBER UNFIXED = 4)
--- CONTROL VALUES:
JOB = 00042
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE FIXED AT ZERO SINCE E=2.
C=0 ==> COVARIANCE MATRIX WILL BE COMPUTED USING
DERIVATIVES RE-EVALUATED AT THE SOLUTION.
D=4 ==> DERIVATIVES ARE SUPPLIED BY USER.
DERIVATIVES WERE NOT CHECKED.
E=2 ==> METHOD IS EXPLICIT OLS.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE)
MAXIT = 50 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 7.28536065D+16
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE
(K) (IFIXB) (SCLB)
1 2.81887509D-06 NO 3.54751440D+05
2 -2.31290549D-03 NO 4.32356620D+02
3 5.83035556D+00 NO 1.71516126D-01
4 0.00000000D+00 YES 3.54751440D+06
5 4.06910776D+07 NO 2.45754121D-08
6 1.38001105D-03 YES 7.24631878D+02
7 5.96038513D-02 YES 1.67774393D+01
8 6.70582099D+00 YES 1.49124172D-01
9 1.06994410D+09 YES 9.34628267D-10
--- EXPLANATORY VARIABLE SUMMARY:
INDEX X(I,J)
(I,J)
1,1 2.500D-09
N,1 1.000D+00
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 9.882D-01 1.000D+00
N,1 9.473D-01 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF OLS ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
1 6 1.21281D-05 1.0000D+00 1.0000D+00 1.492D+00 YES
2 7 1.21281D-05 9.5556D-11 9.5522D-11 5.559D-06 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF OLS ***
--- STOPPING CONDITIONS:
INFO = 1 ==> SUM OF SQUARES CONVERGENCE.
NITER = 2 (NUMBER OF ITERATIONS)
NFEV = 7 (NUMBER OF FUNCTION EVALUATIONS)
NJEV = 3 (NUMBER OF JACOBIAN EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 1.29D-11 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 1.21280859D-05
--- RESIDUAL STANDARD DEVIATION = 5.50637947D-04
DEGREES OF FREEDOM = 40
--- ESTIMATED BETA(J), J = 1, ..., NP:
BETA S.D. BETA ---- 95% CONFIDENCE INTERVAL ----
1 2.38645545D-06 4.4960D-07 1.47777105D-06 TO 3.29513984D-06
2 -2.20450067D-03 4.0156D-05 -2.28565970D-03 TO -2.12334164D-03
3 3.82273198D+00 3.8316D-02 3.74529214D+00 TO 3.90017183D+00
4 0.00000000D+00 FIXED
5 4.53364001D-01 5.2741D-03 4.42704540D-01 TO 4.64023461D-01
6 1.38001105D-03 FIXED
7 5.96038513D-02 FIXED
8 6.70582099D+00 FIXED
9 1.06994410D+09 FIXED
--- ESTIMATED EPSILON(I, 1), I = 1, ..., N:
INDEX VALUE -------------->
1 TO 4 -5.85324109D-05 -9.89224867D-05 -1.71864030D-04 -2.11456078D-04
5 TO 8 -1.06612999D-04 -1.60370107D-04 -1.43278823D-04 -1.34968263D-04
9 TO 12 -1.60812918D-04 -1.51389652D-04 -1.19183078D-04 -2.93209254D-05
13 TO 16 1.08239237D-06 7.94004452D-05 1.18795055D-04 3.21769268D-04
17 TO 20 4.09322682D-04 4.95327906D-04 6.44709193D-04 7.10211016D-04
21 TO 24 6.96631790D-04 6.54863075D-04 4.84585766D-04 2.18339263D-04
25 TO 28 1.85543339D-05 -5.72168484D-06 -6.98195693D-05 -5.27688631D-05
29 TO 32 -3.09355634D-04 -6.82422839D-04 -1.05015195D-03 -1.24256230D-03
33 TO 36 -1.18147768D-03 -9.69898761D-04 -3.02918582D-04 5.21338703D-04
37 TO 40 9.05536868D-04 1.11473330D-03 7.90515099D-04 3.26581432D-04
41 TO 44 -3.27114252D-04 -2.76556749D-04 -5.87219618D-04 9.24026601D-05
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
1.069944100000000000000000000000D+09 1.212808593256056320566077522116D-05 3
NEW TEST RESULT =
1.069944100000000000000000000000D+09 1.212808593255948069755418422533D-05 1
DIFFERENCE = 0.00000D+00 1.08251D-18
RELATIVE ERROR = 0.00000D+00 8.92563D-14
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 4
TEST WEIGHTING CAPABILITIES FOR ODR PROBLEM
WITH ANALYTIC DERIVATIVES USING DODRC.
ALSO SHOWS SOLUTION OF POORLY SCALED ODR PROBLEM.
(DERIVATIVE CHECKING TURNED OFF.)
DATA SET REFERENCE: BOGGS, BYRD AND SCHNABEL, 1985, EXAMPLE 3
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- PROBLEM SIZE:
N = 44 (NUMBER WITH NONZERO WEIGHT = 43)
NQ = 1
M = 1
NP = 9 (NUMBER UNFIXED = 6)
--- CONTROL VALUES:
JOB = 00030
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE INITIALIZED TO ZERO.
C=0 ==> COVARIANCE MATRIX WILL BE COMPUTED USING
DERIVATIVES RE-EVALUATED AT THE SOLUTION.
D=3 ==> DERIVATIVES ARE SUPPLIED BY USER.
DERIVATIVES WERE NOT CHECKED.
E=0 ==> METHOD IS EXPLICIT ODR.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE)
MAXIT = 50 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 1.21253014D-05
SUM OF SQUARED WEIGHTED DELTAS = 0.00000000D+00
SUM OF SQUARED WEIGHTED EPSILONS = 1.21253014D-05
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE
(K) (IFIXB) (SCLB)
1 2.38645545D-06 NO 4.19031498D+05
2 -2.20450067D-03 NO 4.53617462D+02
3 3.82273198D+00 NO 2.61593019D-01
4 0.00000000D+00 YES 4.19031498D+06
5 4.53364001D-01 NO 2.20573314D+00
6 1.38001105D-03 NO 7.24631878D+02
7 5.96038513D-02 NO 1.67774393D+01
8 6.70582099D+00 YES 1.49124172D-01
9 1.06994410D+09 YES 9.34628267D-10
--- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:
INDEX X(I,J) DELTA(I,J) FIXED SCALE WEIGHT
(I,J) (IFIXX) (SCLD) (WD)
1,1 2.500D-09 0.000D+00 NO 4.00D+08 1.60D+13
N,1 1.000D+00 0.000D+00 NO 1.00D+00 1.00D-04
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 9.882D-01 1.000D+00
N,1 9.473D-01 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF ODR ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N BETA -------------->
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP INDEX VALUE
---- ------ ----------- ----------- ----------- --------- ---- ----- -----
1 8 5.61552D-06 5.3688D-01 6.0227D-01 1.254D-01 NO 1 TO 3 2.61670550D-06 -1.84847540D-03 3.81743723D+00
4 TO 6 0.00000000D+00 4.52780748D-01 1.17294940D-03
7 TO 9 5.14825868D-02 6.70582099D+00 1.06994410D+09
4 14 1.20726D-06 3.8806D-01 4.3619D-01 1.718D-01 NO 1 TO 3 4.42164742D-06 -1.27576009D-03 3.52384009D+00
4 TO 6 0.00000000D+00 4.92690445D-01 1.19191347D-03
7 TO 9 3.79861567D-02 6.70582099D+00 1.06994410D+09
7 20 7.87180D-07 9.9505D-02 1.1349D-01 1.097D-01 NO 1 TO 3 7.45301071D-06 -1.19673931D-03 3.48901832D+00
4 TO 6 0.00000000D+00 4.97376025D-01 1.65051648D-03
7 TO 9 3.53474898D-02 6.70582099D+00 1.06994410D+09
10 25 6.28791D-07 8.1375D-02 1.1318D-01 1.295D-01 NO 1 TO 3 1.15483151D-05 -1.13356151D-03 3.45980744D+00
4 TO 6 0.00000000D+00 5.01308411D-01 2.15310228D-03
7 TO 9 3.30381120D-02 6.70582099D+00 1.06994410D+09
13 28 5.58511D-07 2.2830D-02 3.5267D-02 9.439D-02 NO 1 TO 3 1.64242675D-05 -1.08860021D-03 3.43773581D+00
4 TO 6 0.00000000D+00 5.04280654D-01 2.62714475D-03
7 TO 9 3.12106008D-02 6.70582099D+00 1.06994410D+09
16 31 5.45208D-07 4.9324D-03 4.9324D-03 4.697D-03 YES 1 TO 3 1.95894709D-05 -1.06852377D-03 3.42732564D+00
4 TO 6 0.00000000D+00 5.05682583D-01 2.88788569D-03
7 TO 9 3.03155365D-02 6.70582099D+00 1.06994410D+09
*** FINAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- STOPPING CONDITIONS:
INFO = 1 ==> SUM OF SQUARES CONVERGENCE.
NITER = 17 (NUMBER OF ITERATIONS)
NFEV = 32 (NUMBER OF FUNCTION EVALUATIONS)
NJEV = 18 (NUMBER OF JACOBIAN EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 1.47D-05 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 5.45208463D-07
SUM OF SQUARED WEIGHTED DELTAS = 3.42359109D-07
SUM OF SQUARED WEIGHTED EPSILONS = 2.02849354D-07
--- RESIDUAL STANDARD DEVIATION = 1.21389307D-04
DEGREES OF FREEDOM = 37
--- ESTIMATED BETA(J), J = 1, ..., NP:
BETA S.D. BETA ---- 95% CONFIDENCE INTERVAL ----
1 1.95896506D-05 5.2652D-06 8.92132429D-06 TO 3.02579770D-05
2 -1.06852151D-03 4.0956D-05 -1.15150733D-03 TO -9.85535692D-04
3 3.42732422D+00 3.3460D-02 3.35952743D+00 TO 3.49512102D+00
4 0.00000000D+00 FIXED
5 5.05682776D-01 4.6737D-03 4.96213014D-01 TO 5.15152539D-01
6 2.88789682D-03 4.2486D-04 2.02704328D-03 TO 3.74875036D-03
7 3.03154590D-02 1.5303D-03 2.72147165D-02 TO 3.34162015D-02
8 6.70582099D+00 FIXED
9 1.06994410D+09 FIXED
--- ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
I EPSILON(I,1) DELTA(I,1)
1 8.85704614D-05 6.98843476D-18
2 4.81782606D-05 2.49126529D-17
3 -2.47652440D-05 -3.12643640D-17
4 -6.44008812D-05 -6.58477834D-15
5 3.99462567D-05 5.03680509D-13
6 -1.54472294D-05 -3.10491252D-12
7 -1.08794814D-06 -1.10028017D-12
8 3.38839665D-06 1.07375440D-11
9 -3.34647877D-05 -5.23790915D-10
10 -3.95633534D-05 -1.89047768D-09
11 -2.74448529D-05 -3.06142579D-09
12 3.77539089D-05 8.26372134D-09
13 2.28560536D-05 1.10178971D-08
14 5.82190084D-06 7.03986833D-09
15 -6.81553078D-05 -1.45785334D-07
16 1.37311975D-05 3.83594668D-08
17 -1.58688240D-05 -3.81391617D-08
18 -3.32724245D-05 1.87300323D-10
19 3.37523234D-05 -1.85167391D-07
20 4.22264215D-05 -6.36459049D-07
21 -3.75576871D-06 1.88580887D-07
22 2.00621152D-05 -2.22759156D-06
23 -5.50627156D-06 1.10401389D-06
24 -6.88013739D-05 2.19196573D-05
25 -5.04979294D-05 2.33881198D-05
26 2.10761672D-05 -1.14828512D-05
27 5.74011372D-05 -3.62530551D-05
28 3.02389774D-04 0.00000000D+00
29 1.74166008D-04 -1.77161571D-04
30 1.98064654D-05 -2.39431909D-05
31 -7.90410048D-05 1.24670749D-04
32 -1.47683404D-04 2.76450567D-04
33 -1.12277273D-04 2.31472249D-04
34 -4.79553114D-05 9.93157475D-05
35 1.40511415D-04 -1.42581252D-04
36 1.62614218D-04 7.17271525D-04
37 1.08724514D-04 1.23259791D-03
38 -1.15956129D-05 -4.16815657D-04
39 -6.38721344D-05 -4.42575705D-03
40 -1.03209160D-04 -9.45381806D-03
41 -9.34250030D-05 -1.39895132D-02
42 -1.23336490D-05 -3.09254631D-03
43 1.69666481D-05 6.57971401D-03
44 6.58708761D-05 3.70510371D-02
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
1.069944100000000000000000000000D+09 5.452084633790605642698293836768D-07 1
NEW TEST RESULT =
1.069944100000000000000000000000D+09 5.452084633791027041589552851186D-07 1
DIFFERENCE = 0.00000D+00 4.21399D-20
RELATIVE ERROR = 0.00000D+00 7.72913D-14
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 5
TEST DELTA INITIALIZATION CAPABILITIES
AND USE OF ISTOP TO RESTRICT PARAMETER VALUES FOR ODR PROBLEM
WITH ANALYTIC DERIVATIVES USING DODRC.
DATA SET REFERENCE: BOGGS, BYRD AND SCHNABEL, 1985, EXAMPLE 1
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** DERIVATIVE CHECKING REPORT FOR FIT BY METHOD OF ODR ***
FOR RESPONSE 1 OF OBSERVATION 1
USER
SUPPLIED RELATIVE DERIVATIVE
DERIVATIVE WRT VALUE DIFFERENCE ASSESSMENT
BETA( 1) -9.79D-01 3.27D-08 VERIFIED
BETA( 2) 9.59D-01 3.34D-08 VERIFIED
DELTA( 1, 1) -9.59D-01 4.04D-07 VERIFIED
NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS 16
(ESTIMATED BY ODRPACK)
NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN
USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVE FOR
USER SUPPLIED DERIVATIVE TO BE CONSIDERED VERIFIED 4
ROW NUMBER AT WHICH DERIVATIVES WERE CHECKED 1
-VALUES OF THE EXPLANATORY VARIABLES AT THIS ROW
X( 1, 1) -2.13701920D-02
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- PROBLEM SIZE:
N = 40 (NUMBER WITH NONZERO WEIGHT = 40)
NQ = 1
M = 1
NP = 2 (NUMBER UNFIXED = 2)
--- CONTROL VALUES:
JOB = 01020
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=1 ==> DELTAS ARE INITIALIZED BY USER.
C=0 ==> COVARIANCE MATRIX WILL BE COMPUTED USING
DERIVATIVES RE-EVALUATED AT THE SOLUTION.
D=2 ==> DERIVATIVES ARE SUPPLIED BY USER.
DERIVATIVES WERE CHECKED.
RESULTS APPEAR CORRECT.
E=0 ==> METHOD IS EXPLICIT ODR.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE)
MAXIT = 50 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 2.13003002D+02
SUM OF SQUARED WEIGHTED DELTAS = 2.22998645D-03
SUM OF SQUARED WEIGHTED EPSILONS = 2.13000772D+02
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE
(K) (IFIXB) (SCLB)
1 1.00000000D+00 NO 2.00000000D-01
2 1.00000000D+00 NO 1.00000000D+00
--- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:
INDEX X(I,J) DELTA(I,J) FIXED SCALE WEIGHT
(I,J) (IFIXX) (SCLD) (WD)
1,1 -2.137D-02 0.000D+00 NO 2.00D+00 1.00D+00
N,1 1.993D+00 0.000D+00 NO 2.00D+00 1.00D+00
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 -1.196D+00 1.000D+00
N,1 1.262D+00 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF ODR ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
1 15 2.61860D+01 8.7706D-01 9.9181D-01 7.180D-02 NO
2 19 2.69487D+00 8.9709D-01 9.5185D-01 5.373D-02 NO
3 22 1.14955D+00 5.7343D-01 5.8129D-01 2.076D-02 NO
4 24 1.09672D+00 4.5960D-02 4.6016D-02 4.042D-03 NO
5 26 1.08906D+00 6.9802D-03 6.9780D-03 8.578D-04 NO
6 29 1.08621D+00 2.6219D-03 2.6215D-03 3.355D-04 NO
7 32 1.08509D+00 1.0280D-03 1.0280D-03 1.332D-04 NO
8 34 1.08487D+00 2.0456D-04 2.0456D-04 2.659D-05 NO
9 37 1.08478D+00 8.1706D-05 8.1705D-05 1.063D-05 NO
10 40 1.08475D+00 3.2663D-05 3.2663D-05 4.252D-06 NO
11 43 1.08473D+00 1.3062D-05 1.3062D-05 1.700D-06 NO
12 44 1.08473D+00 1.3062D-06 1.3062D-06 1.700D-07 NO
13 48 1.08473D+00 1.0449D-06 1.0449D-06 1.360D-07 NO
14 49 1.08473D+00 1.0449D-07 1.0449D-07 1.360D-08 NO
15 52 1.08473D+00 4.1797D-08 4.1797D-08 5.441D-09 NO
16 55 1.08473D+00 1.6719D-09 1.6719D-09 2.177D-10 NO
*** FINAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- STOPPING CONDITIONS:
INFO = 1 ==> SUM OF SQUARES CONVERGENCE.
NITER = 16 (NUMBER OF ITERATIONS)
NFEV = 55 (NUMBER OF FUNCTION EVALUATIONS)
NJEV = 17 (NUMBER OF JACOBIAN EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 4.55D-01 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 1.08472869D+00
SUM OF SQUARED WEIGHTED DELTAS = 8.40017240D-03
SUM OF SQUARED WEIGHTED EPSILONS = 1.07632852D+00
--- RESIDUAL STANDARD DEVIATION = 1.68954111D-01
DEGREES OF FREEDOM = 38
--- ESTIMATED BETA(J), J = 1, ..., NP:
BETA S.D. BETA ---- 95% CONFIDENCE INTERVAL ----
1 1.01000000D+00 5.4611D-02 8.99445893D-01 TO 1.12055411D+00
2 1.00806508D+00 2.8682D-02 9.50000743D-01 TO 1.06612941D+00
--- ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
I EPSILON(I,1) DELTA(I,1)
1 2.13840659D-01 7.72546758D-04
2 2.25560304D-01 9.41129554D-04
3 1.04497486D-01 5.45425660D-04
4 -1.50874326D-01 -6.68930741D-04
5 -2.53059717D-01 -1.47995790D-03
6 1.00819860D-01 7.61395327D-04
7 -2.08153575D-01 -1.47827218D-03
8 -2.07020851D-02 -6.56435112D-05
9 8.29941689D-02 9.01373708D-04
10 8.32053215D-02 1.31278062D-03
11 -2.74508126D-02 -1.60088981D-04
12 -2.31693881D-02 -9.77002251D-05
13 2.80662023D-01 6.40983340D-03
14 -2.33380568D-01 -8.18107398D-03
15 2.90886301D-01 1.07469430D-02
16 5.51250039D-04 2.30850838D-03
17 -8.54153789D-03 2.87442762D-03
18 -3.14043264D-02 -2.69146898D-02
19 -2.33002803D-02 -4.35952599D-02
20 -1.25678379D-03 5.32820350D-02
21 -1.97974590D-05 2.03929764D-02
22 1.61303539D-03 -3.27077555D-03
23 2.03791618D-02 4.03459318D-02
24 3.79059604D-02 2.89275631D-03
25 1.15361308D-01 1.53906991D-02
26 -1.59261060D-01 -1.09534748D-02
27 -4.08298033D-01 -1.48581627D-02
28 1.32135752D-01 3.24792549D-03
29 1.05612345D-01 2.07767148D-03
30 9.18128552D-02 1.14522968D-03
31 -5.70692650D-02 -1.03708418D-03
32 3.58111933D-01 4.54918829D-03
33 1.95909122D-01 2.02871320D-03
34 -1.92950972D-01 -1.76449168D-03
35 -1.71485464D-02 -2.84782108D-04
36 -1.37149959D-01 -9.97503592D-04
37 -2.06598358D-01 -1.25925941D-03
38 3.24011770D-02 1.01793800D-04
39 1.54243454D-01 5.78989068D-04
40 -2.35594637D-01 -9.23080829D-04
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
1.426988156377258620821635304310D+00 1.084728687127432200654197913536D+00 1
NEW TEST RESULT =
1.426988156353226067096784390742D+00 1.084728687476404607181734718324D+00 1
DIFFERENCE = 2.40326D-11 3.48972D-10
RELATIVE ERROR = 1.68415D-11 3.21714D-10
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 6
TEST STIFF STOPPING CONDITIONS FOR UNSCALED ODR PROBLEM
WITH ANALYTIC DERIVATIVES USING DODRC.
DATA SET REFERENCE: HIMMELBLAU, 1970, EXAMPLE 6.2-4, PAGE 188
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** DERIVATIVE CHECKING REPORT FOR FIT BY METHOD OF ODR ***
FOR RESPONSE 1 OF OBSERVATION 6
USER
SUPPLIED RELATIVE DERIVATIVE
DERIVATIVE WRT VALUE DIFFERENCE ASSESSMENT
BETA( 1) 1.00D+00 0.00D+00 VERIFIED
BETA( 2) 6.07D-01 3.67D-08 VERIFIED
BETA( 3) 1.82D+00 1.92D-07 VERIFIED
DELTA( 6, 1) 3.00D+00 9.93D-08 VERIFIED
DELTA( 6, 2) -9.10D-01 1.92D-07 VERIFIED
NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS 16
(ESTIMATED BY ODRPACK)
NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN
USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVE FOR
USER SUPPLIED DERIVATIVE TO BE CONSIDERED VERIFIED 4
ROW NUMBER AT WHICH DERIVATIVES WERE CHECKED 6
-VALUES OF THE EXPLANATORY VARIABLES AT THIS ROW
X( 6, 1) 1.00000000D+00
X( 6, 2) 1.00000000D+00
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- PROBLEM SIZE:
N = 13 (NUMBER WITH NONZERO WEIGHT = 13)
NQ = 1
M = 2
NP = 3 (NUMBER UNFIXED = 3)
--- CONTROL VALUES:
JOB = 00020
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE INITIALIZED TO ZERO.
C=0 ==> COVARIANCE MATRIX WILL BE COMPUTED USING
DERIVATIVES RE-EVALUATED AT THE SOLUTION.
D=2 ==> DERIVATIVES ARE SUPPLIED BY USER.
DERIVATIVES WERE CHECKED.
RESULTS APPEAR CORRECT.
E=0 ==> METHOD IS EXPLICIT ODR.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 2.22D-14 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 2.22D-16 (PARAMETER STOPPING TOLERANCE)
MAXIT = 2 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 1.79305083D-01
SUM OF SQUARED WEIGHTED DELTAS = 0.00000000D+00
SUM OF SQUARED WEIGHTED EPSILONS = 1.79305083D-01
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE
(K) (IFIXB) (SCLB)
1 3.00000000D+00 NO 3.33333333D-01
2 3.00000000D+00 NO 3.33333333D-01
3 -5.00000000D-01 NO 3.33333333D-01
--- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:
INDEX X(I,J) DELTA(I,J) FIXED SCALE WEIGHT
(I,J) (IFIXX) (SCLD) (WD)
1,1 0.000D+00 0.000D+00 NO 1.00D+01 1.00D+00
N,1 2.900D+00 0.000D+00 NO 3.45D-01 1.00D+00
1,2 0.000D+00 0.000D+00 NO 1.00D+01 1.00D+00
N,2 1.800D+00 0.000D+00 NO 3.33D-01 1.00D+00
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 2.930D+00 1.000D+00
N,1 9.810D+00 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF ODR ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
1 21 1.48223D-02 9.1733D-01 9.1674D-01 1.050D+00 YES
2 22 1.47797D-02 2.8741D-03 2.8968D-03 2.693D-02 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- STOPPING CONDITIONS:
INFO = 4 ==> ITERATION LIMIT REACHED.
NITER = 2 (NUMBER OF ITERATIONS)
NFEV = 22 (NUMBER OF FUNCTION EVALUATIONS)
NJEV = 3 (NUMBER OF JACOBIAN EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 2.28D-01 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 1.47796721D-02
SUM OF SQUARED WEIGHTED DELTAS = 1.33891597D-02
SUM OF SQUARED WEIGHTED EPSILONS = 1.39051238D-03
--- RESIDUAL STANDARD DEVIATION = 3.84443391D-02
DEGREES OF FREEDOM = 10
--- ESTIMATED BETA(J), J = 1, ..., NP:
BETA S.D. BETA ---- 95% CONFIDENCE INTERVAL ----
1 3.02127269D+00 3.6888D-02 2.93902959D+00 TO 3.10351579D+00
2 2.95883347D+00 8.3319D-02 2.77306895D+00 TO 3.14459799D+00
3 -5.25432714D-01 3.0453D-02 -5.93328437D-01 TO -4.57536992D-01
--- ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
I EPSILON(I,1) DELTA(I,1) DELTA(I,2)
1 2.30719900D-03 -6.95012295D-03 3.55910649D-03
2 -1.82563237D-02 5.51320253D-02 -1.69143244D-02
3 2.15864761D-02 -6.50743998D-02 1.16586122D-02
4 3.12413384D-03 -9.35402855D-03 9.99213291D-04
5 6.40415322D-03 -1.93295345D-02 9.86829589D-03
6 2.82279358D-03 -8.48602806D-03 2.57756334D-03
7 -1.19110059D-02 3.59974322D-02 -6.51316549D-03
8 5.71926168D-04 -1.67110502D-03 3.01261303D-04
9 -2.29090591D-03 6.89012388D-03 -3.54298530D-03
10 -5.27479950D-03 1.59368352D-02 -4.86034770D-03
11 -1.37120696D-02 4.14217198D-02 -7.49927629D-03
12 8.43418310D-03 -2.54123018D-02 4.57142724D-03
13 9.63073868D-03 -2.90305923D-02 5.79461938D-03
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
4.261321829513978975967347651022D+00 1.477967210398420730421698010559D-02 4
NEW TEST RESULT =
4.261321829513978975967347651022D+00 1.477967210398419516115264826794D-02 4
DIFFERENCE = 0.00000D+00 1.21431D-17
RELATIVE ERROR = 0.00000D+00 8.21606D-16
*** STOPPING CONDITIONS SHOW CONVERGENCE NOT ATTAINED. ***
NO FURTHER COMPARISONS MADE BETWEEN RESULTS.
1
EXAMPLE 7
TEST RESTART FOR UNSCALED ODR PROBLEM
WITH ANALYTIC DERIVATIVES USING DODRC.
DATA SET REFERENCE: HIMMELBLAU, 1970, EXAMPLE 6.2-4, PAGE 188
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- PROBLEM SIZE:
N = 13 (NUMBER WITH NONZERO WEIGHT = 13)
NQ = 1
M = 2
NP = 3 (NUMBER UNFIXED = 3)
--- CONTROL VALUES:
JOB = 20220
= ABCDE, WHERE
A=2 ==> FIT IS A RESTART.
B=0 ==> DELTAS ARE INITIALIZED TO ZERO.
C=2 ==> COVARIANCE MATRIX WILL NOT BE COMPUTED.
D=2 ==> DERIVATIVES ARE SUPPLIED BY USER.
DERIVATIVES WERE CHECKED.
RESULTS APPEAR CORRECT.
E=0 ==> METHOD IS EXPLICIT ODR.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 2.22D-14 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 2.22D-16 (PARAMETER STOPPING TOLERANCE)
MAXIT = 52 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 1.47796721D-02
SUM OF SQUARED WEIGHTED DELTAS = 1.33891597D-02
SUM OF SQUARED WEIGHTED EPSILONS = 1.39051238D-03
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE
(K) (IFIXB) (SCLB)
1 3.02127269D+00 NO 3.33333333D-01
2 2.95883347D+00 NO 3.33333333D-01
3 -5.25432714D-01 NO 3.33333333D-01
--- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:
INDEX X(I,J) DELTA(I,J) FIXED SCALE WEIGHT
(I,J) (IFIXX) (SCLD) (WD)
1,1 0.000D+00 -6.950D-03 NO 1.00D+01 1.00D+00
N,1 2.900D+00 -2.903D-02 NO 3.45D-01 1.00D+00
1,2 0.000D+00 3.559D-03 NO 1.00D+01 1.00D+00
N,2 1.800D+00 5.795D-03 NO 3.33D-01 1.00D+00
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 2.930D+00 1.000D+00
N,1 9.810D+00 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF ODR ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
3 23 1.47797D-02 7.3362D-07 7.4861D-07 8.411D-04 YES
4 24 1.47797D-02 4.5525D-10 4.6927D-10 2.427D-05 YES
5 25 1.47797D-02 4.3698D-13 4.5367D-13 7.007D-07 YES
6 26 1.47797D-02 1.7764D-15 4.7183D-16 2.313D-08 YES
7 27 1.47797D-02 1.5543D-15 5.0722D-19 7.195D-10 YES
8 28 1.47797D-02 -1.7764D-15 5.5343D-22 1.204D-11 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- STOPPING CONDITIONS:
INFO = 1 ==> SUM OF SQUARES CONVERGENCE.
NITER = 8 (NUMBER OF ITERATIONS)
NFEV = 28 (NUMBER OF FUNCTION EVALUATIONS)
NJEV = 9 (NUMBER OF JACOBIAN EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 2.28D-01 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 1.47796613D-02
SUM OF SQUARED WEIGHTED DELTAS = 1.33923007D-02
SUM OF SQUARED WEIGHTED EPSILONS = 1.38736056D-03
--- ESTIMATED BETA(J), J = 1, ..., NP:
INDEX VALUE -------------->
1 TO 3 3.02122470D+00 2.95882000D+00 -5.25382883D-01
N.B. NO PARAMETERS WERE FIXED BY THE USER OR DROPPED AT THE LAST
ITERATION BECAUSE THEY CAUSED THE MODEL TO BE RANK DEFICIENT.
--- ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
I EPSILON(I,1) DELTA(I,1) DELTA(I,2)
1 2.29869910D-03 -6.94488650D-03 3.56666879D-03
2 -1.82412535D-02 5.51109257D-02 -1.69175847D-02
3 2.15545172D-02 -6.51210396D-02 1.16448520D-02
4 3.10769668D-03 -9.38904997D-03 9.98372544D-04
5 6.39050599D-03 -1.93071545D-02 9.88268089D-03
6 2.81290078D-03 -8.49840531D-03 2.58219366D-03
7 -1.19105692D-02 3.59845058D-02 -6.49632104D-03
8 5.59803317D-04 -1.69129161D-03 3.04241701D-04
9 -2.28908821D-03 6.91584984D-03 -3.56508956D-03
10 -5.27648150D-03 1.59414362D-02 -4.86270054D-03
11 -1.37112916D-02 4.14248928D-02 -7.48235509D-03
12 8.41203973D-03 -2.54146622D-02 4.56155790D-03
13 9.60776220D-03 -2.90272085D-02 5.78348338D-03
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
4.261272307142888848829898051918D+00 1.477966125465374376546368040408D-02 1
NEW TEST RESULT =
4.261272307140899329169769771397D+00 1.477966125465366917235421340138D-02 1
DIFFERENCE = 1.98952D-12 7.45931D-17
RELATIVE ERROR = 4.66884D-13 5.04701D-15
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 8
TEST USE OF TAUFAC TO RESTRICT FIRST STEP FOR ODR PROBLEM
WITH FINITE DIFFERENCE DERIVATIVES USING DODRC.
DATA SET REFERENCE: POWELL AND MACDONALD, 1972, TABLES 7 AND 8, PAGES 153-154
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- PROBLEM SIZE:
N = 14 (NUMBER WITH NONZERO WEIGHT = 14)
NQ = 1
M = 1
NP = 3 (NUMBER UNFIXED = 3)
--- CONTROL VALUES:
JOB = 00210
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE INITIALIZED TO ZERO.
C=2 ==> COVARIANCE MATRIX WILL NOT BE COMPUTED.
D=1 ==> DERIVATIVES ARE ESTIMATED BY CENTRAL DIFFERENCES.
E=0 ==> METHOD IS EXPLICIT ODR.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D-02
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE)
MAXIT = 50 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 6.65183875D+01
SUM OF SQUARED WEIGHTED DELTAS = 0.00000000D+00
SUM OF SQUARED WEIGHTED EPSILONS = 6.65183875D+01
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE DERIVATIVE
STEP SIZE
(K) (IFIXB) (SCLB) (STPB)
1 2.50000000D+01 NO 3.33333333D-02 4.64159D-06
2 3.00000000D+01 NO 3.33333333D-02 4.64159D-06
3 6.00000000D+00 NO 3.33333333D-02 4.64159D-06
--- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:
INDEX X(I,J) DELTA(I,J) FIXED SCALE WEIGHT DERIVATIVE
STEP SIZE
(I,J) (IFIXX) (SCLD) (WD) (STPD)
1,1 1.000D+00 0.000D+00 NO 1.00D+00 1.00D+00 4.64159D-06
N,1 1.400D+01 0.000D+00 NO 7.14D-02 1.00D+00 4.64159D-06
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 2.638D+01 1.000D+00
N,1 2.222D+01 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF ODR ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
1 21 1.65304D-03 9.9998D-01 9.9998D-01 1.906D-01 YES
2 30 1.14442D-03 3.0769D-01 3.0772D-01 5.736D-03 YES
3 39 1.14442D-03 2.8528D-06 2.8589D-06 4.489D-05 YES
4 48 1.14442D-03 9.2508D-11 9.3866D-11 7.581D-07 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- STOPPING CONDITIONS:
INFO = 1 ==> SUM OF SQUARES CONVERGENCE.
NITER = 4 (NUMBER OF ITERATIONS)
NFEV = 48 (NUMBER OF FUNCTION EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 5.38D-03 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 1.14441947D-03
SUM OF SQUARED WEIGHTED DELTAS = 1.25033077D-04
SUM OF SQUARED WEIGHTED EPSILONS = 1.01938640D-03
--- ESTIMATED BETA(J), J = 1, ..., NP:
INDEX VALUE -------------->
1 TO 3 2.71167487D+01 3.36427043D+01 6.62121910D+00
N.B. NO PARAMETERS WERE FIXED BY THE USER OR DROPPED AT THE LAST
ITERATION BECAUSE THEY CAUSED THE MODEL TO BE RANK DEFICIENT.
--- ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
I EPSILON(I,1) DELTA(I,1)
1 7.59801116D-03 4.97540746D-03
2 7.39164816D-04 4.06579050D-04
3 -6.94196648D-03 -3.28158116D-03
4 -1.71319408D-02 -7.08391784D-03
5 -7.84792233D-03 -2.87575737D-03
6 3.89544361D-03 1.27960336D-03
7 1.08567684D-02 3.22813867D-03
8 7.23311504D-03 1.96282386D-03
9 7.22701041D-03 1.80177855D-03
10 7.62288350D-03 1.75618816D-03
11 5.74541441D-03 1.22941679D-03
12 -6.34168099D-04 -1.26609681D-04
13 -3.71790892D-03 -6.95241813D-04
14 -1.46591743D-02 -2.57682804D-03
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
4.371487317909745229371765162796D+01 1.144419474408286127933842557525D-03 1
NEW TEST RESULT =
4.371487334212800135446741478518D+01 1.144419474408238639878687692431D-03 1
DIFFERENCE = 1.63031D-07 4.74881D-17
RELATIVE ERROR = 3.72941D-09 4.14953D-14
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 9
TEST IMPLICIT MODEL FOR OLS PROBLEM
USING DODRC.
DATA SET REFERENCE: FULLER, 1987, TABLE 3.2.10, PAGES 244-245
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- PROBLEM SIZE:
N = 20 (NUMBER WITH NONZERO WEIGHT = 20)
NQ = 1
M = 2
NP = 5 (NUMBER UNFIXED = 5)
--- CONTROL VALUES:
JOB = 00001
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE INITIALIZED TO ZERO.
C=0 ==> COVARIANCE MATRIX WILL BE COMPUTED USING
DERIVATIVES RE-EVALUATED AT THE SOLUTION.
D=0 ==> DERIVATIVES ARE ESTIMATED BY FORWARD DIFFERENCES.
E=1 ==> METHOD IS IMPLICIT ODR.
NDIGIT = 15 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 6.06D-06 (PARAMETER STOPPING TOLERANCE)
MAXIT = 100 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL SUM OF SQUARED WEIGHTED DELTAS = 0.00000000D+00
INITIAL PENALTY FUNCTION VALUE = 8.39823392D-01
PENALTY TERM = 8.39823392D-01
PENALTY PARAMETER = 1.0D+01
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE DERIVATIVE
STEP SIZE
(K) (IFIXB) (SCLB) (STPB)
1 -1.00000000D+00 NO 1.00000000D+00 3.16228D-10
2 -3.00000000D+00 NO 3.33333333D-01 3.16228D-10
3 9.00000000D-02 NO 1.11111111D+01 3.16228D-10
4 2.00000000D-02 NO 5.00000000D+01 3.16228D-10
5 8.00000000D-02 NO 1.25000000D+01 3.16228D-10
--- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:
INDEX X(I,J) DELTA(I,J) FIXED SCALE WEIGHT DERIVATIVE
STEP SIZE
(I,J) (IFIXX) (SCLD) (WD) (STPD)
1,1 5.000D-01 0.000D+00 NO 2.00D+00 1.00D+00 3.16228D-10
N,1 -3.440D+00 0.000D+00 NO 2.91D-01 1.00D+00 3.16228D-10
1,2 -1.200D-01 0.000D+00 NO 8.33D+00 1.00D+00 3.16228D-10
N,2 -4.860D+00 0.000D+00 NO 2.06D-01 1.00D+00 3.16228D-10
*** ITERATION REPORTS FOR FIT BY METHOD OF ODR ***
CUM. PENALTY ACT. REL. PRED. REL.
IT. NO. FN FUNCTION SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS VALUE REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
PENALTY PARAMETER VALUE = 1.0E+01
1 13 6.95806D-02 9.1715D-01 9.2121D-01 3.787D-01 YES
2 21 6.86021D-02 1.4063D-02 1.3989D-02 4.791D-02 YES
3 29 6.85929D-02 1.3366D-04 1.3152D-04 2.458D-03 YES
4 37 6.85929D-02 2.8035D-07 2.5896D-07 3.301D-04 YES
5 45 6.85929D-02 2.2442D-09 2.0585D-09 2.466D-05 YES
PENALTY PARAMETER VALUE = 1.0E+02
6 71 8.58086D-02 5.8379D-01 5.8368D-01 7.423D-02 YES
7 79 8.57904D-02 2.1187D-04 2.1044D-04 1.733D-02 YES
8 87 8.57902D-02 2.9685D-06 2.9272D-06 6.287D-04 YES
9 95 8.57902D-02 6.9621D-09 6.7263D-09 7.071D-05 YES
PENALTY PARAMETER VALUE = 1.0E+03
10 116 8.79954D-02 1.7982D-01 1.7982D-01 8.918D-03 YES
11 124 8.79951D-02 3.5396D-06 3.4883D-06 2.281D-03 YES
12 132 8.79951D-02 2.0851D-08 1.9954D-08 8.141D-05 YES
13 140 8.79951D-02 1.1440D-10 1.1132D-10 7.103D-06 YES
PENALTY PARAMETER VALUE = 1.0E+04
14 161 8.82218D-02 2.2544D-02 2.2544D-02 9.096D-04 YES
15 169 8.82218D-02 3.7995D-08 3.6729D-08 2.331D-04 YES
16 177 8.82218D-02 1.6593D-10 1.5080D-10 8.213D-06 YES
PENALTY PARAMETER VALUE = 1.0E+05
17 195 8.82446D-02 2.3129D-03 2.3129D-03 8.969D-05 YES
18 203 8.82446D-02 2.6031D-10 2.3349D-10 1.092D-05 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- STOPPING CONDITIONS:
INFO = 2 ==> PARAMETER CONVERGENCE.
NITER = 18 (NUMBER OF ITERATIONS)
NFEV = 217 (NUMBER OF FUNCTION EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 3.18D-02 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL SUM OF SQUARED WEIGHTED DELTAS = 8.82420346D-02
FINAL PENALTY FUNCTION VALUE = 8.82445616D-02
PENALTY TERM = 2.52700897D-06
PENALTY PARAMETER = 1.0D+05
--- RESIDUAL STANDARD DEVIATION = 7.66994283D-02
DEGREES OF FREEDOM = 15
--- ESTIMATED BETA(J), J = 1, ..., NP:
BETA S.D. BETA ---- 95% CONFIDENCE INTERVAL ----
1 -9.99380972D-01 1.1138D-01 -1.23682206D+00 TO -7.61939883D-01
2 -2.93104848D+00 1.0977D-01 -3.16504351D+00 TO -2.69705344D+00
3 8.75730479D-02 4.1061D-03 7.88199915D-02 TO 9.63261044D-02
4 1.62299739D-02 2.7500D-03 1.03676338D-02 TO 2.20923140D-02
5 7.97538008D-02 3.4963D-03 7.23007073D-02 TO 8.72068944D-02
--- ESTIMATED DELTA(I,*), I = 1, ..., N:
I DELTA(I,1) DELTA(I,2)
1 3.40723874D-02 4.76860368D-02
2 -2.65182325D-02 -2.55209375D-02
3 -6.46554198D-02 -4.89656210D-02
4 -6.02229818D-02 -3.67984225D-02
5 1.53930306D-01 4.61089357D-02
6 7.49624603D-02 5.60550739D-03
7 -1.34843681D-02 1.40897870D-03
8 -9.20913712D-02 3.20494708D-02
9 -2.95789191D-02 1.74354120D-02
10 -2.24316152D-03 1.96476563D-03
11 1.75676764D-02 -2.30886080D-02
12 -1.84834167D-02 3.96269350D-02
13 1.65840790D-03 -1.00326725D-01
14 -9.59481801D-03 -6.81523716D-02
15 8.68789767D-03 2.81098730D-02
16 3.24759423D-02 6.89227234D-02
17 3.11881390D-02 4.53121160D-02
18 -7.48532795D-03 -8.53414499D-03
19 5.74203368D-03 5.51928209D-03
20 -3.59272946D-02 -2.83635072D-02
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
3.099048849376848657755090243882D+00 8.824708863783850554263210597128D-02 2
NEW TEST RESULT =
3.099048341282356844317291688640D+00 8.824203462684793164427787814930D-02 2
DIFFERENCE = 5.08094D-07 5.05401D-06
RELATIVE ERROR = 1.63952D-07 5.72711D-05
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 10
TEST MULTIRESPONSE MODEL FOR ODR PROBLEM
WITH FINITE DIFFERENCE DERIVATIVES USING DODRC.
DATA SET REFERENCE: BATES AND WATTS, 1988, TABLE A1.13, PAGES 280-281
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- PROBLEM SIZE:
N = 23 (NUMBER WITH NONZERO WEIGHT = 21)
NQ = 2
M = 1
NP = 5 (NUMBER UNFIXED = 5)
--- CONTROL VALUES:
JOB = 00210
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE INITIALIZED TO ZERO.
C=2 ==> COVARIANCE MATRIX WILL NOT BE COMPUTED.
D=1 ==> DERIVATIVES ARE ESTIMATED BY CENTRAL DIFFERENCES.
E=0 ==> METHOD IS EXPLICIT ODR.
NDIGIT = 15 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE)
MAXIT = 50 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 1.61756061D+03
SUM OF SQUARED WEIGHTED DELTAS = 0.00000000D+00
SUM OF SQUARED WEIGHTED EPSILONS = 1.61756061D+03
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE DERIVATIVE
STEP SIZE
(K) (IFIXB) (SCLB) (STPB)
1 4.00000000D+00 NO 2.50000000D-01 1.00000D-05
2 2.00000000D+00 NO 5.00000000D-01 1.00000D-05
3 7.00000000D+00 NO 1.42857143D-01 1.00000D-05
4 4.00000000D-01 NO 2.50000000D+00 1.00000D-05
5 5.00000000D-01 NO 2.00000000D+00 1.00000D-05
--- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:
INDEX X(I,J) DELTA(I,J) FIXED SCALE WEIGHT DERIVATIVE
STEP SIZE
(I,J) (IFIXX) (SCLD) (WD) (STPD)
1,1 3.000D+01 0.000D+00 YES 3.33D-02 1.11D-07 1.00000D-05
N,1 1.500D+05 0.000D+00 NO 6.67D-06 4.44D-15 1.00000D-05
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 4.220D+00 5.596D+02
N,1 2.759D+00 5.596D+02
1,2 1.360D-01 8.397D+03
N,2 1.390D-01 8.397D+03
*** ITERATION REPORTS FOR FIT BY METHOD OF ODR ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
1 18 2.81264D+02 8.2612D-01 9.9950D-01 1.204D+00 YES
2 31 8.75783D+00 9.6886D-01 9.9813D-01 2.200D-01 YES
3 44 2.48574D+00 7.1617D-01 9.5244D-01 1.597D-01 YES
4 57 4.24412D-01 8.2926D-01 8.3031D-01 2.241D-02 YES
5 70 4.20540D-01 9.1238D-03 9.0876D-03 4.429D-03 YES
6 83 4.20539D-01 2.8954D-06 2.7128D-06 3.930D-04 YES
7 96 4.20539D-01 1.4230D-08 1.3313D-08 2.690D-05 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF ODR ***
--- STOPPING CONDITIONS:
INFO = 1 ==> SUM OF SQUARES CONVERGENCE.
NITER = 7 (NUMBER OF ITERATIONS)
NFEV = 96 (NUMBER OF FUNCTION EVALUATIONS)
IRANK = 0 (RANK DEFICIENCY)
RCOND = 8.15D-03 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 4.20538922D-01
SUM OF SQUARED WEIGHTED DELTAS = 5.54022895D-04
SUM OF SQUARED WEIGHTED EPSILONS = 4.19984899D-01
--- ESTIMATED BETA(J), J = 1, ..., NP:
INDEX VALUE -------------->
1 TO 4 4.37998809D+00 2.43330566D+00 8.00288453D+00 5.10114676D-01
5 5.17390199D-01
N.B. NO PARAMETERS WERE FIXED BY THE USER OR DROPPED AT THE LAST
ITERATION BECAUSE THEY CAUSED THE MODEL TO BE RANK DEFICIENT.
--- ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:
I EPSILON(I,1) EPSILON(I,2) DELTA(I,1)
1 -7.38556281D-03 1.25939922D-03 0.00000000D+00
2 -1.05612518D-03 -1.22845804D-03 0.00000000D+00
3 -2.70861844D-03 -2.14347061D-03 0.00000000D+00
4 4.68593718D-02 -4.25940146D-03 0.00000000D+00
5 8.08104420D-03 -3.47539550D-03 0.00000000D+00
6 1.53882474D-03 3.85293691D-04 3.03694703D+01
7 4.60534881D-03 1.19118721D-03 3.78987347D+01
8 4.50904278D-03 1.23570429D-03 6.22631839D+01
9 -1.00624342D-03 -2.91872299D-04 1.11187207D+02
10 1.05810430D-02 3.27283292D-03 1.15710270D+02
11 6.93618486D-03 2.43480864D-03 2.41437285D+02
12 3.95512337D-05 1.75761986D-05 9.61345659D+02
13 -3.77619651D-03 -2.42909122D-03 1.33029993D+03
14 -5.56743469D-04 -1.70124794D-03 2.07511789D+03
15 2.08264689D-03 -2.23723708D-03 2.90289763D+03
16 -7.50661987D-03 2.16469603D-03 5.21813714D+03
17 -1.56730631D-03 2.03369394D-04 7.54565125D+03
18 -5.93228163D-04 2.72079634D-05 1.74201144D+04
19 1.15244167D-04 -2.42068517D-07 2.42745693D+04
20 2.63614224D-04 5.18444905D-06 3.78492489D+04
21 -3.81043947D-04 -1.03970544D-05 5.53493969D+04
22 -3.36863330D-04 -1.26155472D-05 8.75792611D+04
23 2.87168504D-03 1.41195403D-04 1.29496518D+05
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
9.469917836739933036938055010978D+00 4.205389215588104523391166367219D-01 1
NEW TEST RESULT =
9.469917762502790381518025242258D+00 4.205389215886734533000890223775D-01 1
DIFFERENCE = 7.42371D-08 2.98630D-11
RELATIVE ERROR = 7.83926D-09 7.10113D-11
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 11
TEST DETECTION OF QUESTIONABLE ANALYTIC DERIVATIVES FOR OLS PROBLEM
USING DODRC.
DATA SET REFERENCE: POWELL AND MACDONALD, 1972, TABLES 7 AND 8, PAGES 153-154
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** DERIVATIVE CHECKING REPORT FOR FIT BY METHOD OF OLS ***
FOR RESPONSE 1 OF OBSERVATION 1
USER
SUPPLIED RELATIVE DERIVATIVE
DERIVATIVE WRT VALUE DIFFERENCE ASSESSMENT
BETA( 1) 0.00D+00 9.70D-01 QUESTIONABLE (SEE NOTE 3)
BETA( 2) 0.00D+00 2.25D-02 QUESTIONABLE (SEE NOTE 3)
BETA( 3) 0.00D+00 1.05D-02 QUESTIONABLE (SEE NOTE 3)
NOTES:
(3) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES DISAGREE, BUT
RESULTS ARE QUESTIONABLE BECAUSE ONE IS IDENTICALLY ZERO
AND THE OTHER IS NOT.
NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS 16
(ESTIMATED BY ODRPACK)
NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN
USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVE FOR
USER SUPPLIED DERIVATIVE TO BE CONSIDERED VERIFIED 4
ROW NUMBER AT WHICH DERIVATIVES WERE CHECKED 1
-VALUES OF THE EXPLANATORY VARIABLES AT THIS ROW
X( 1, 1) 1.00000000D+00
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** INITIAL SUMMARY FOR FIT BY METHOD OF OLS ***
--- PROBLEM SIZE:
N = 14 (NUMBER WITH NONZERO WEIGHT = 14)
NQ = 1
M = 1
NP = 3 (NUMBER UNFIXED = 3)
--- CONTROL VALUES:
JOB = 00022
= ABCDE, WHERE
A=0 ==> FIT IS NOT A RESTART.
B=0 ==> DELTAS ARE FIXED AT ZERO SINCE E=2.
C=0 ==> COVARIANCE MATRIX WILL BE COMPUTED USING
DERIVATIVES RE-EVALUATED AT THE SOLUTION.
D=2 ==> DERIVATIVES ARE SUPPLIED BY USER.
DERIVATIVES WERE CHECKED.
RESULTS APPEAR QUESTIONABLE.
E=2 ==> METHOD IS EXPLICIT OLS.
NDIGIT = 16 (ESTIMATED BY ODRPACK)
TAUFAC = 1.00D+00
--- STOPPING CRITERIA:
SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE)
PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE)
MAXIT = 50 (MAXIMUM NUMBER OF ITERATIONS)
--- INITIAL WEIGHTED SUM OF SQUARES = 6.65183875D+01
--- FUNCTION PARAMETER SUMMARY:
INDEX BETA(K) FIXED SCALE DERIVATIVE
ASSESSMENT
(K) (IFIXB) (SCLB)
1 2.50000000D+01 NO 3.33333333D-02 QUESTIONABLE
2 3.00000000D+01 NO 3.33333333D-02 QUESTIONABLE
3 6.00000000D+00 NO 3.33333333D-02 QUESTIONABLE
--- EXPLANATORY VARIABLE SUMMARY:
INDEX X(I,J)
(I,J)
1,1 1.000D+00
N,1 1.400D+01
--- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT SUMMARY:
INDEX Y(I,L) WEIGHT
(I,L) (WE)
1,1 2.638D+01 1.000D+00
N,1 2.222D+01 1.000D+00
*** ITERATION REPORTS FOR FIT BY METHOD OF OLS ***
CUM. ACT. REL. PRED. REL.
IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS G-N
NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION TAU/PNORM STEP
---- ------ ----------- ----------- ----------- --------- ----
1 24 6.65184D+01 0.0000D+00 0.0000D+00 0.000D+00 YES
*** FINAL SUMMARY FOR FIT BY METHOD OF OLS ***
--- STOPPING CONDITIONS:
INFO = 1023
= ABCD, WHERE A NONZERO VALUE FOR DIGIT A, B, OR C INDICATES WHY
THE RESULTS MIGHT BE QUESTIONABLE, AND DIGIT D INDICATES
THE ACTUAL STOPPING CONDITION.
A=1 ==> DERIVATIVES ARE QUESTIONABLE.
C=2 ==> DERIVATIVES ARE ZERO RANK AT THE SOLUTION.
D=3 ==> SUM OF SQUARES CONVERGENCE AND PARAMETER CONVERGENCE.
NITER = 1 (NUMBER OF ITERATIONS)
NFEV = 24 (NUMBER OF FUNCTION EVALUATIONS)
NJEV = 2 (NUMBER OF JACOBIAN EVALUATIONS)
IRANK = 3 (RANK DEFICIENCY)
RCOND = 0.00D+00 (INVERSE CONDITION NUMBER)
ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN)
--- FINAL WEIGHTED SUMS OF SQUARES = 6.65183875D+01
--- RESIDUAL STANDARD DEVIATION = 8.15588055D+00
DEGREES OF FREEDOM = 0
--- ESTIMATED BETA(J), J = 1, ..., NP:
BETA S.D. BETA ---- 95% CONFIDENCE INTERVAL ----
1 2.50000000D+01 DROPPED
2 3.00000000D+01 DROPPED
3 6.00000000D+00 DROPPED
--- ESTIMATED EPSILON(I, 1), I = 1, ..., N:
INDEX VALUE -------------->
1 TO 4 -2.12824711D+00 -2.15338202D+00 -2.17361007D+00 -2.19297148D+00
5 TO 8 -2.18753205D+00 -2.17853564D+00 -2.17414444D+00 -2.18046225D+00
9 TO 12 -2.18216734D+00 -2.18292056D+00 -2.18563784D+00 -2.19267768D+00
13 TO 14 -2.19597334D+00 -2.20712839D+00
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
3.950949253027682317451763083227D+01 6.651838750834910740650229854509D+01 1023
NEW TEST RESULT =
3.950949253027682317451763083227D+01 6.651838750834907898479286814108D+01 1023
DIFFERENCE = 0.00000D+00 2.84217D-14
RELATIVE ERROR = 0.00000D+00 4.27276D-16
*** RESULTS AGREE TO WITHIN STOPPING TOLERANCE. ***
1
EXAMPLE 12
TEST DETECTION OF INCORRECT ANALYTIC DERIVATIVES FOR ODR PROBLEM
WITH ANALYTIC DERIVATIVES USING DODRC.
DATA SET REFERENCE: POWELL AND MACDONALD, 1972, TABLES 7 AND 8, PAGES 153-154
*******************************************************
* ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) *
*******************************************************
*** DERIVATIVE CHECKING REPORT FOR FIT BY METHOD OF ODR ***
FOR RESPONSE 1 OF OBSERVATION 1
USER
SUPPLIED RELATIVE DERIVATIVE
DERIVATIVE WRT VALUE DIFFERENCE ASSESSMENT
BETA( 1) 0.00D+00 9.70D-01 QUESTIONABLE (SEE NOTE 3)
BETA( 2) 0.00D+00 2.25D-02 QUESTIONABLE (SEE NOTE 3)
BETA( 3) 0.00D+00 1.05D-02 QUESTIONABLE (SEE NOTE 3)
DELTA( 1, 1) 1.00D+00 1.67D+00 *QUESTIONABLE (SEE NOTE 7)
NOTES:
(3) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES DISAGREE, BUT
RESULTS ARE QUESTIONABLE BECAUSE ONE IS IDENTICALLY ZERO
AND THE OTHER IS NOT.
(7) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES DISAGREE, AND
HAVE FEWER THAN 2 DIGITS IN COMMON. DERIVATIVE CHECKING MUST
BE TURNED OFF IN ORDER TO PROCEED.
NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS 16
(ESTIMATED BY ODRPACK)
NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN
USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVE FOR
USER SUPPLIED DERIVATIVE TO BE CONSIDERED VERIFIED 4
ROW NUMBER AT WHICH DERIVATIVES WERE CHECKED 1
-VALUES OF THE EXPLANATORY VARIABLES AT THIS ROW
X( 1, 1) 1.00000000D+00
COMPARISON OF NEW RESULTS WITH DOUBLE PRECISION CRAY YMP RESULT:
NORM OF BETA SUM OF SQUARED WTD OBS ERRORS INFO
CRAY YMP RESULT =
3.950949253027682317451763083227D+01 6.651838750834910740650229854509D+01 40100
NEW TEST RESULT =
3.950949253027682317451763083227D+01 6.651838750834907898479286814108D+01 40100
DIFFERENCE = 0.00000D+00 2.84217D-14
RELATIVE ERROR = 0.00000D+00 4.27276D-16
*** STOPPING CONDITIONS SHOW CONVERGENCE NOT ATTAINED. ***
NO FURTHER COMPARISONS MADE BETWEEN RESULTS.
1
*** SUMMARY: ALL TESTS AGREE WITH EXPECTED RESULTS. ***