*DECK SODS
SUBROUTINE SODS (A, X, B, NEQ, NUK, NRDA, IFLAG, WORK, IWORK)
C***BEGIN PROLOGUE SODS
C***SUBSIDIARY
C***PURPOSE Subsidiary to BVSUP
C***LIBRARY SLATEC
C***TYPE SINGLE PRECISION (SODS-S)
C***AUTHOR Watts, H. A., (SNLA)
C***DESCRIPTION
C
C SODS solves the overdetermined system of linear equations A X = B,
C where A is NEQ by NUK and NEQ .GE. NUK. If rank A = NUK,
C X is the UNIQUE least squares solution vector. That is,
C R(1)**2 + ..... + R(NEQ)**2 = minimum
C where R is the residual vector R = B - A X.
C If rank A .LT. NUK , the least squares solution of minimal
C length can be provided.
C SODS is an interfacing routine which calls subroutine LSSODS
C for the solution. LSSODS in turn calls subroutine ORTHOL and
C possibly subroutine OHTROR for the decomposition of A by
C orthogonal transformations. In the process, ORTHOL calls upon
C subroutine CSCALE for scaling.
C
C **********************************************************************
C Input
C **********************************************************************
C
C A -- Contains the matrix of NEQ equations in NUK unknowns and must
C be dimensioned NRDA by NUK. The original A is destroyed
C X -- Solution array of length at least NUK
C B -- Given constant vector of length NEQ, B is destroyed
C NEQ -- Number of equations, NEQ greater or equal to 1
C NUK -- Number of columns in the matrix (which is also the number
C of unknowns), NUK not larger than NEQ
C NRDA -- Row dimension of A, NRDA greater or equal to NEQ
C IFLAG -- Status indicator
C =0 For the first call (and for each new problem defined by
C a new matrix A) when the matrix data is treated as exact
C =-K For the first call (and for each new problem defined by
C a new matrix A) when the matrix data is assumed to be
C accurate to about K digits
C =1 For subsequent calls whenever the matrix A has already
C been decomposed (problems with new vectors B but
C same matrix a can be handled efficiently)
C WORK(*),IWORK(*) -- Arrays for storage of internal information,
C WORK must be dimensioned at least 2 + 5*NUK
C IWORK must be dimensioned at least NUK+2
C IWORK(2) -- Scaling indicator
C =-1 If the matrix A is to be pre-scaled by
C columns when appropriate
C If the scaling indicator is not equal to -1
C no scaling will be attempted
C For most problems scaling will probably not be necessary
C
C **********************************************************************
C OUTPUT
C **********************************************************************
C
C IFLAG -- Status indicator
C =1 If solution was obtained
C =2 If improper input is detected
C =3 If rank of matrix is less than NUK
C If the minimal length least squares solution is
C desired, simply reset IFLAG=1 and call the code again
C X -- Least squares solution of A X = B
C A -- Contains the strictly upper triangular part of the reduced
C matrix and the transformation information
C WORK(*),IWORK(*) -- Contains information needed on subsequent
C Calls (IFLAG=1 case on input) which must not
C be altered
C WORK(1) contains the Euclidean norm of
C the residual vector
C WORK(2) contains the Euclidean norm of
C the solution vector
C IWORK(1) contains the numerically determined
C rank of the matrix A
C
C **********************************************************************
C
C***SEE ALSO BVSUP
C***REFERENCES G. Golub, Numerical methods for solving linear least
C squares problems, Numerische Mathematik 7, (1965),
C pp. 206-216.
C P. Businger and G. Golub, Linear least squares
C solutions by Householder transformations, Numerische
C Mathematik 7, (1965), pp. 269-276.
C H. A. Watts, Solving linear least squares problems
C using SODS/SUDS/CODS, Sandia Report SAND77-0683,
C Sandia Laboratories, 1977.
C***ROUTINES CALLED LSSODS
C***REVISION HISTORY (YYMMDD)
C 750601 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900402 Added TYPE section. (WRB)
C 910408 Updated the AUTHOR and REFERENCES sections. (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE SODS
DIMENSION A(NRDA,*),X(*),B(*),WORK(*),IWORK(*)
C
C***FIRST EXECUTABLE STATEMENT SODS
ITER=0
IS=2
IP=3
KS=2
KD=3
KZ=KD+NUK
KV=KZ+NUK
KT=KV+NUK
KC=KT+NUK
C
CALL LSSODS(A,X,B,NEQ,NUK,NRDA,IFLAG,IWORK(1),IWORK(IS),A,
1 WORK(KD),IWORK(IP),ITER,WORK(1),WORK(KS),
2 WORK(KZ),B,WORK(KV),WORK(KT),WORK(KC))
C
RETURN
END