SUBROUTINE BNDSOL (MODE,G,MDG,NB,IP,IR,X,N,RNORM) BSL00100 C C.L.LAWSON AND R.J.HANSON, JET PROPULSION LABORATORY, 1973 JUN 12 BSL00200 C TO APPEAR IN 'SOLVING LEAST SQUARES PROBLEMS', PRENTICE-HALL, 1974BSL00300 C SEQUENTIAL SOLUTION OF A BANDED LEAST SQUARES PROBLEM.. BSL00400 C SOLUTION PHASE. FOR THE ACCUMULATION PHASE USE BNDACC. BSL00500 C BSL00600 C MODE = 1 SOLVE R*X=Y WHERE R AND Y ARE IN THE G( ) ARRAY BSL00700 C AND X WILL BE STORED IN THE X( ) ARRAY. BSL00800 C 2 SOLVE (R**T)*X=Y WHERE R IS IN G( ), BSL00900 C Y IS INITIALLY IN X( ), AND X REPLACES Y IN X( ), BSL01000 C 3 SOLVE R*X=Y WHERE R IS IN G( ). BSL01100 C Y IS INITIALLY IN X( ), AND X REPLACES Y IN X( ). BSL01200 C BSL01300 C THE SECOND SUBSCRIPT OF G( ) MUST BE DIMENSIONED AT LEAST BSL01400 C NB+1 IN THE CALLING PROGRAM. BSL01500 DIMENSION G(MDG,1),X(N) BSL01600 ZERO=0. BSL01700 C BSL01800 RNORM=ZERO BSL01900 GO TO (10,90,50), MODE BSL02000 C ********************* MODE = 1 BSL02100 C ALGC STEP 26 BSL02200 10 DO 20 J=1,N BSL02300 20 X(J)=G(J,NB+1) BSL02400 RSQ=ZERO BSL02500 NP1=N+1 BSL02600 IRM1=IR-1 BSL02700 IF (NP1.GT.IRM1) GO TO 40 BSL02800 DO 30 J=NP1,IRM1 BSL02900 30 RSQ=RSQ+G(J,NB+1)**2 BSL03000 RNORM=SQRT(RSQ) BSL03100 40 CONTINUE BSL03200 C ********************* MODE = 3 BSL03300 C ALG. STEP 27 BSL03400 50 DO 80 II=1,N BSL03500 I=N+1-II BSL03600 C ALG. STEP 28 BSL03700 S=ZERO BSL03800 L=MAX0(0,I-IP) BSL03900 C ALG. STEP 29 BSL04000 IF (I.EQ.N) GO TO 70 BSL04100 C ALG. STEP 30 BSL04200 IE=MIN0(N+1-I,NB) BSL04300 DO 60 J=2,IE BSL04400 JG=J+L BSL04500 IX=I-1+J BSL04600 60 S=S+G(I,JG)*X(IX) BSL04700 C ALG. STEP 31 BSL04800 70 IF (G(I,L+1)) 80,130,80 BSL04900 80 X(I)=(X(I)-S)/G(I,L+1) BSL05000 C ALG. STEP 32 BSL05100 RETURN BSL05200 C ********************* MODE = 2 BSL05300 90 DO 120 J=1,N BSL05400 S=ZERO BSL05500 IF (J.EQ.1) GO TO 110 BSL05600 I1=MAX0(1,J-NB+1) BSL05700 I2=J-1 BSL05800 DO 100 I=I1,I2 BSL05900 L=J-I+1+MAX0(0,I-IP) BSL06000 100 S=S+X(I)*G(I,L) BSL06100 110 L=MAX0(0,J-IP) BSL06200 IF (G(J,L+1)) 120,130,120 BSL06300 120 X(J)=(X(J)-S)/G(J,L+1) BSL06400 RETURN BSL06500 C BSL06600 130 WRITE (6,140) MODE,I,J,L BSL06700 STOP BSL06800 140 FORMAT (30H0ZERO DIAGONAL TERM IN BNDSOL.,12H MODE,I,J,L=,4I6) BSL06900 END BSL07000