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- C C.L.LAWSON AND R.J.HANSON, JET PROPULSION LABORATORY, 1973 JUN 15 PR600200
- C TO APPEAR IN 'SOLVING LEAST SQUARES PROBLEMS', PRENTICE-HALL, 1974PR600300
- C DEMONSTRATE THE USE OF THE SUBROUTINE LDP FOR LEAST PR600400
- C DISTANCE PROGRAMMING BY SOLVING THE CONSTRAINED LINE DATA FITTING PR600500
- C PROBLEM OF CHAPTER 23. PR600600
- C PR600700
- DIMENSION E(4,2), F(4), G(3,2), H(3), G2(3,2), H2(3), X(2), Z(2), PR600800
- 1W(4) PR600900
- DIMENSION WLDP(21), S(6), T(4) PR601000
- INTEGER INDEX(3) PR601100
- C PR601200
- C Set math to execute single precision in 23-bit mantissa format.
- CALL MPBRQQ
- C
- WRITE (6,110) PR601300
- MDE=4 PR601400
- MDGH=3 PR601500
- C PR601600
- ME=4 PR601700
- MG=3 PR601800
- N=2 PR601900
- C DEFINE THE LEAST SQUARES AND CONSTRAINT MATRICES. PR602000
- T(1)=0.25 PR602100
- T(2)=0.5 PR602200
- T(3)=0.5 PR602300
- T(4)=0.8 PR602400
- C PR602500
- W(1)=0.5 PR602600
- W(2)=0.6 PR602700
- W(3)=0.7 PR602800
- W(4)=1.2 PR602900
- C PR603000
- DO 10 I=1,ME PR603100
- E(I,1)=T(I) PR603200
- E(I,2)=1. PR603300
- 10 F(I)=W(I) PR603400
- C PR603500
- G(1,1)=1. PR603600
- G(1,2)=0. PR603700
- G(2,1)=0. PR603800
- G(2,2)=1. PR603900
- G(3,1)=-1. PR604000
- G(3,2)=-1. PR604100
- C PR604200
- H(1)=0. PR604300
- H(2)=0. PR604400
- H(3)=-1. PR604500
- C PR604600
- C COMPUTE THE SINGULAR VALUE DECOMPOSITION OF THE MATRIX, E. PR604700
- C PR604800
- CALL SVDRS (E,MDE,ME,N,F,1,1,S) PR604900
- C PR605000
- WRITE (6,120) ((E(I,J),J=1,N),I=1,N) PR605100
- WRITE (6,130) F,(S(J),J=1,N) PR605200
- C PR605300
- C GENERALLY RANK DETERMINATION AND LEVENBERG-MARQUARDT PR605400
- C STABILIZATION COULD BE INSERTED HERE. PR605500
- C PR605600
- C DEFINE THE CONSTRAINT MATRIX FOR THE Z COORDINATE SYSTEM. PR605700
- DO 30 I=1,MG PR605800
- DO 30 J=1,N PR605900
- SM=0. PR606000
- DO 20 L=1,N PR606100
- 20 SM=SM+G(I,L)*E(L,J) PR606200
- 30 G2(I,J)=SM/S(J) PR606300
- C DEFINE CONSTRAINT RT SIDE FOR THE Z COORDINATE SYSTEM. PR606400
- DO 50 I=1,MG PR606500
- SM=0. PR606600
- DO 40 J=1,N PR606700
- 40 SM=SM+G2(I,J)*F(J) PR606800
- 50 H2(I)=H(I)-SM PR606900
- C PR607000
- WRITE (6,140) ((G2(I,J),J=1,N),I=1,MG) PR607100
- WRITE (6,150) H2 PR607200
- C PR607300
- C SOLVE THE CONSTRAINED PROBLEM IN Z-COORDINATES.PR607400
- C PR607500
- CALL LDP (G2,MDGH,MG,N,H2,Z,ZNORM,WLDP,INDEX,MODE) PR607600
- C PR607700
- WRITE (6,200) MODE,ZNORM PR607800
- WRITE (6,160) Z PR607900
- C PR608000
- C TRANSFORM BACK FROM Z-COORDINATES TO X-COORDINATES.PR608100
- DO 60 J=1,N PR608200
- 60 Z(J)=(Z(J)+F(J))/S(J) PR608300
- DO 80 I=1,N PR608400
- SM=0. PR608500
- DO 70 J=1,N PR608600
- 70 SM=SM+E(I,J)*Z(J) PR608700
- 80 X(I)=SM PR608800
- RES=ZNORM**2 PR608900
- NP1=N+1 PR609000
- DO 90 I=NP1,ME PR609100
- 90 RES=RES+F(I)**2 PR609200
- RES=SQRT(RES) PR609300
- C COMPUTE THE RESIDUALS. PR609400
- DO 100 I=1,ME PR609500
- 100 F(I)=W(I)-X(1)*T(I)-X(2) PR609600
- WRITE (6,170) (X(J),J=1,N) PR609700
- WRITE (6,180) (I,F(I),I=1,ME) PR609800
- WRITE (6,190) RES PR609900
- STOP PR610000
- C PR610100
- 110 FORMAT (46H0PROG6.. EXAMPLE OF CONSTRAINED CURVE FITTING,26H USINPR610200
- 1G THE SUBROUTINE LDP.,/43H0RELATED INTERMEDIATE QUANTITIES ARE GIVPR610300
- 2EN.) PR610400
- 120 FORMAT (10H0V = ,2F10.5/(10X,2F10.5)) PR610500
- 130 FORMAT (10H0F TILDA =,4F10.5/10H0S = ,2F10.5) PR610600
- 140 FORMAT (10H0G TILDA =,2F10.5/(10X,2F10.5)) PR610700
- 150 FORMAT (10H0H TILDA =,3F10.5) PR610800
- 160 FORMAT (10H0Z = ,2F10.5) PR610900
- 170 FORMAT (52H0THE COEFICIENTS OF THE FITTED LINE F(T)=X(1)*T+X(2),12PR611000
- 1H ARE : /
- 2' X(1) = ',F10.5,14H AND X(2) = ,F10.5) PR611100
- 180 FORMAT (30H0THE CONSECUTIVE RESIDUALS ARE/1X,4(I5,F10.5)) PR611200
- 190 FORMAT (23H0THE RESIDUALS NORM IS ,F10.5) PR611300
- 200 FORMAT (18H0MODE (FROM LDP) =,I3,2X,7HZNORM =,F10.5) PR611400
- C PR611500
- END PR611600
