SLATEC Routines --- DBOLS ---

```*DECK DBOLS
SUBROUTINE DBOLS (W, MDW, MROWS, NCOLS, BL, BU, IND, IOPT, X,
+   RNORM, MODE, RW, IW)
C***BEGIN PROLOGUE  DBOLS
C***PURPOSE  Solve the problem
C                 E*X = F (in the least  squares  sense)
C            with bounds on selected X values.
C***LIBRARY   SLATEC
C***CATEGORY  K1A2A, G2E, G2H1, G2H2
C***TYPE      DOUBLE PRECISION (SBOLS-S, DBOLS-D)
C***KEYWORDS  BOUNDS, CONSTRAINTS, INEQUALITY, LEAST SQUARES, LINEAR
C***AUTHOR  Hanson, R. J., (SNLA)
C***DESCRIPTION
C
C   **** All INPUT and OUTPUT real variables are DOUBLE PRECISION ****
C
C     The user must have dimension statements of the form:
C
C       DIMENSION W(MDW,NCOLS+1), BL(NCOLS), BU(NCOLS),
C      * X(NCOLS+NX), RW(5*NCOLS)
C       INTEGER IND(NCOLS), IOPT(1+NI), IW(2*NCOLS)
C
C     (Here NX=number of extra locations required for option 4; NX=0
C     for no options; NX=NCOLS if this option is in use. Here NI=number
C     of extra locations required for options 1-6; NI=0 for no
C     options.)
C
C   INPUT
C   -----
C
C    --------------------
C    W(MDW,*),MROWS,NCOLS
C    --------------------
C     The array W(*,*) contains the matrix [E:F] on entry. The matrix
C     [E:F] has MROWS rows and NCOLS+1 columns. This data is placed in
C     the array W(*,*) with E occupying the first NCOLS columns and the
C     right side vector F in column NCOLS+1. The row dimension, MDW, of
C     the array W(*,*) must satisfy the inequality MDW .ge. MROWS.
C     Other values of MDW are errors. The values of MROWS and NCOLS
C     must be positive. Other values are errors. There is an exception
C     to this when using option 1 for accumulation of blocks of
C     equations. In that case MROWS is an OUTPUT variable ONLY, and the
C     matrix data for [E:F] is placed in W(*,*), one block of rows at a
C     time.  MROWS contains the number of rows in the matrix after
C     triangularizing several blocks of equations. This is an OUTPUT
C     parameter ONLY when option 1 is used. See IOPT(*) CONTENTS
C     for details about option 1.
C
C    ------------------
C    BL(*),BU(*),IND(*)
C    ------------------
C     These arrays contain the information about the bounds that the
C     solution values are to satisfy. The value of IND(J) tells the
C     type of bound and BL(J) and BU(J) give the explicit values for
C     the respective upper and lower bounds.
C
C    1.    For IND(J)=1, require X(J) .ge. BL(J).
C          (the value of BU(J) is not used.)
C    2.    For IND(J)=2, require X(J) .le. BU(J).
C          (the value of BL(J) is not used.)
C    3.    For IND(J)=3, require X(J) .ge. BL(J) and
C                                X(J) .le. BU(J).
C    4.    For IND(J)=4, no bounds on X(J) are required.
C          (the values of BL(J) and BU(J) are not used.)
C
C     Values other than 1,2,3 or 4 for IND(J) are errors. In the case
C     IND(J)=3 (upper and lower bounds) the condition BL(J) .gt. BU(J)
C     is an error.
C
C    -------
C    IOPT(*)
C    -------
C     This is the array where the user can specify nonstandard options
C     for DBOLSM( ). Most of the time this feature can be ignored by
C     setting the input value IOPT(1)=99. Occasionally users may have
C     needs that require use of the following subprogram options. For
C     details about how to use the options see below: IOPT(*) CONTENTS.
C
C     Option Number   Brief Statement of Purpose
C     ------ ------   ----- --------- -- -------
C                     of least squares equations.
C           2         Check lengths of all arrays used in the
C                     subprogram.
C           3         Standard scaling of the data matrix, E.
C           4         User provides column scaling for matrix E.
C           5         Provide option array to the low-level
C                     subprogram DBOLSM( ).
C           6         Move the IOPT(*) processing pointer.
C          99         No more options to change.
C
C    ----
C    X(*)
C    ----
C     This array is used to pass data associated with option 4. Ignore
C     this parameter if this option is not used. Otherwise see below:
C     IOPT(*) CONTENTS.
C
C    OUTPUT
C    ------
C
C    ----------
C    X(*),RNORM
C    ----------
C     The array X(*) contains a solution (if MODE .ge.0 or .eq.-22) for
C     the constrained least squares problem. The value RNORM is the
C     minimum residual vector length.
C
C    ----
C    MODE
C    ----
C     The sign of MODE determines whether the subprogram has completed
C     normally, or encountered an error condition or abnormal status. A
C     value of MODE .ge. 0 signifies that the subprogram has completed
C     normally. The value of MODE (.GE. 0) is the number of variables
C     in an active status: not at a bound nor at the value ZERO, for
C     the case of free variables. A negative value of MODE will be one
C     of the cases -37,-36,...,-22, or -17,...,-2. Values .lt. -1
C     correspond to an abnormal completion of the subprogram. To
C     understand the abnormal completion codes see below: ERROR
C     MESSAGES for DBOLS( ). AN approximate solution will be returned
C     to the user only when max. iterations is reached, MODE=-22.
C     Values for MODE=-37,...,-22 come from the low-level subprogram
C     DBOLSM(). See the section ERROR MESSAGES for DBOLSM() in the
C     documentation for DBOLSM().
C
C    -----------
C    RW(*),IW(*)
C    -----------
C     These are working arrays with 5*NCOLS and 2*NCOLS entries.
C     (normally the user can ignore the contents of these arrays,
C     but they must be dimensioned properly.)
C
C    IOPT(*) CONTENTS
C    ------- --------
C     The option array allows a user to modify internal variables in
C     the subprogram without recompiling the source code. A central
C     goal of the initial software design was to do a good job for most
C     people. Thus the use of options will be restricted to a select
C     group of users. The processing of the option array proceeds as
C     follows: a pointer, here called LP, is initially set to the value
C     1. This value is updated as each option is processed. At the
C     pointer position the option number is extracted and used for
C     locating other information that allows for options to be changed.
C     The portion of the array IOPT(*) that is used for each option is
C     fixed; the user and the subprogram both know how many locations
C     are needed for each option. A great deal of error checking is
C     done by the subprogram on the contents of the option array.
C     Nevertheless it is still possible to give the subprogram optional
C     input that is meaningless. For example option 4 uses the
C     locations X(NCOLS+IOFF),...,X(NCOLS+IOFF+NCOLS-1) for passing
C     scaling data. The user must manage the allocation of these
C     locations.
C
C   1
C   -
C     This option allows the user to solve problems with a large number
C     of rows compared to the number of variables. The idea is that the
C     subprogram returns to the user (perhaps many times) and receives
C     new least squares equations from the calling program unit.
C     Eventually the user signals "that's all" and then computes the
C     solution with one final call to subprogram DBOLS( ). The value of
C     MROWS is an OUTPUT variable when this option is used. Its value
C     is always in the range 0 .le. MROWS .le. NCOLS+1. It is equal to
C     the number of rows after the triangularization of the entire set
C     of equations. If LP is the processing pointer for IOPT(*), the
C     usage for the sequential processing of blocks of equations is
C
C        IOPT(LP)=1
C        Move block of equations to W(*,*) starting at
C        the first row of W(*,*).
C        IOPT(LP+3)=# of rows in the block; user defined
C
C     The user now calls DBOLS( ) in a loop. The value of IOPT(LP+1)
C     directs the user's action. The value of IOPT(LP+2) points to
C     where the subsequent rows are to be placed in W(*,*).
C
C      .DBOLSM, DCOPY, DNRM2, DROT, DROTG, IDAMAX, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   821220  DATE WRITTEN
C   891006  Cosmetic changes to prologue.  (WRB)
C   891006  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900510  Convert XERRWV calls to XERMSG calls.  (RWC)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DBOLS
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