*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 1 Return to user for accumulation of blocks
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 .<LOOP
C . CALL DBOLS()
C . IF(IOPT(LP+1) .EQ. 1) THEN
C . IOPT(LP+3)=# OF ROWS IN THE NEW BLOCK; USER DEFINED
C . PLACE NEW BLOCK OF IOPT(LP+3) ROWS IN
C . W(*,*) STARTING AT ROW IOPT(LP+2).
C .
C . IF( THIS IS THE LAST BLOCK OF EQUATIONS ) THEN
C . IOPT(LP+1)=2
C .<------CYCLE LOOP
C . ELSE IF (IOPT(LP+1) .EQ. 2) THEN
C <-------EXIT LOOP SOLUTION COMPUTED IF MODE .GE. 0
C . ELSE
C . ERROR CONDITION; SHOULD NOT HAPPEN.
C .<END LOOP
C
C Use of this option adds 4 to the required length of IOPT(*).
C
C
C 2
C -
C This option is useful for checking the lengths of all arrays used
C by DBOLS() against their actual requirements for this problem.
C The idea is simple: the user's program unit passes the declared
C dimension information of the arrays. These values are compared
C against the problem-dependent needs within the subprogram. If any
C of the dimensions are too small an error message is printed and a
C negative value of MODE is returned, -11 to -17. The printed error
C message tells how long the dimension should be. If LP is the
C processing pointer for IOPT(*),
C
C IOPT(LP)=2
C IOPT(LP+1)=Row dimension of W(*,*)
C IOPT(LP+2)=Col. dimension of W(*,*)
C IOPT(LP+3)=Dimensions of BL(*),BU(*),IND(*)
C IOPT(LP+4)=Dimension of X(*)
C IOPT(LP+5)=Dimension of RW(*)
C IOPT(LP+6)=Dimension of IW(*)
C IOPT(LP+7)=Dimension of IOPT(*)
C .
C CALL DBOLS()
C
C Use of this option adds 8 to the required length of IOPT(*).
C
C 3
C -
C This option changes the type of scaling for the data matrix E.
C Nominally each nonzero column of E is scaled so that the
C magnitude of its largest entry is equal to the value ONE. If LP
C is the processing pointer for IOPT(*),
C
C IOPT(LP)=3
C IOPT(LP+1)=1,2 or 3
C 1= Nominal scaling as noted;
C 2= Each nonzero column scaled to have length ONE;
C 3= Identity scaling; scaling effectively suppressed.
C .
C CALL DBOLS()
C
C Use of this option adds 2 to the required length of IOPT(*).
C
C 4
C -
C This option allows the user to provide arbitrary (positive)
C column scaling for the matrix E. If LP is the processing pointer
C for IOPT(*),
C
C IOPT(LP)=4
C IOPT(LP+1)=IOFF
C X(NCOLS+IOFF),...,X(NCOLS+IOFF+NCOLS-1)
C = Positive scale factors for cols. of E.
C .
C CALL DBOLS()
C
C Use of this option adds 2 to the required length of IOPT(*) and
C NCOLS to the required length of X(*).
C
C 5
C -
C This option allows the user to provide an option array to the
C low-level subprogram DBOLSM(). If LP is the processing pointer
C for IOPT(*),
C
C IOPT(LP)=5
C IOPT(LP+1)= Position in IOPT(*) where option array
C data for DBOLSM() begins.
C .
C CALL DBOLS()
C
C Use of this option adds 2 to the required length of IOPT(*).
C
C 6
C -
C Move the processing pointer (either forward or backward) to the
C location IOPT(LP+1). The processing point is moved to entry
C LP+2 of IOPT(*) if the option is left with -6 in IOPT(LP). For
C example to skip over locations 3,...,NCOLS+2 of IOPT(*),
C
C IOPT(1)=6
C IOPT(2)=NCOLS+3
C (IOPT(I), I=3,...,NCOLS+2 are not defined here.)
C IOPT(NCOLS+3)=99
C CALL DBOLS()
C
C CAUTION: Misuse of this option can yield some very hard
C -to-find bugs. Use it with care.
C
C 99
C --
C There are no more options to change.
C
C Only option numbers -99, -6,-5,...,-1, 1,2,...,6, and 99 are
C permitted. Other values are errors. Options -99,-1,...,-6 mean
C that the respective options 99,1,...,6 are left at their default
C values. An example is the option to modify the (rank) tolerance:
C
C IOPT(1)=-3 Option is recognized but not changed
C IOPT(2)=2 Scale nonzero cols. to have length ONE
C IOPT(3)=99
C
C ERROR MESSAGES for DBOLS()
C ----- -------- --- -------
C
C WARNING IN...
C DBOLS(). MDW=(I1) MUST BE POSITIVE.
C IN ABOVE MESSAGE, I1= 0
C ERROR NUMBER = 2
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). NCOLS=(I1) THE NO. OF VARIABLES MUST BE POSITIVE.
C IN ABOVE MESSAGE, I1= 0
C ERROR NUMBER = 3
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). FOR J=(I1), IND(J)=(I2) MUST BE 1-4.
C IN ABOVE MESSAGE, I1= 1
C IN ABOVE MESSAGE, I2= 0
C ERROR NUMBER = 4
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). FOR J=(I1), BOUND BL(J)=(R1) IS .GT. BU(J)=(R2).
C IN ABOVE MESSAGE, I1= 1
C IN ABOVE MESSAGE, R1= 0.
C IN ABOVE MESSAGE, R2= ABOVE MESSAGE, I1= 0
C ERROR NUMBER = 6
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). ISCALE OPTION=(I1) MUST BE 1-3.
C IN ABOVE MESSAGE, I1= 0
C ERROR NUMBER = 7
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). OFFSET PAST X(NCOLS) (I1) FOR USER-PROVIDED COLUMN SCALING
C MUST BE POSITIVE.
C IN ABOVE MESSAGE, I1= 0
C ERROR NUMBER = 8
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). EACH PROVIDED COL. SCALE FACTOR MUST BE POSITIVE.
C COMPONENT (I1) NOW = (R1).
C IN ABOVE MESSAGE, I1= ND. .LE. MDW=(I2).
C IN ABOVE MESSAGE, I1= 1
C IN ABOVE MESSAGE, I2= 0
C ERROR NUMBER = 10
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS().THE ROW DIMENSION OF W(,)=(I1) MUST BE .GE.THE NUMBER OF ROWS=
C (I2).
C IN ABOVE MESSAGE, I1= 0
C IN ABOVE MESSAGE, I2= 1
C ERROR NUMBER = 11
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). THE COLUMN DIMENSION OF W(,)=(I1) MUST BE .GE. NCOLS+1=(I2).
C IN ABOVE MESSAGE, I1= 0
C IN ABOVE MESSAGE, I2= 2
C ERROR NUMBER = 12
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS().THE DIMENSIONS OF THE ARRAYS BL(),BU(), AND IND()=(I1) MUST BE
C .GE. NCOLS=(I2).
C IN ABOVE MESSAGE, I1= 0
C IN ABOVE MESSAGE, I2= 1
C ERROR NUMBER = 13
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). THE DIMENSION OF X()=(I1) MUST BE .GE. THE REQD. LENGTH=(I2).
C IN ABOVE MESSAGE, I1= 0
C IN ABOVE MESSAGE, I2= 2
C ERROR NUMBER = 14
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS(). THE DIMENSION OF RW()=(I1) MUST BE .GE. 5*NCOLS=(I2).
C IN ABOVE MESSAGE, I1= 0
C IN ABOVE MESSAGE, I2= 3
C ERROR NUMBER = 15
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS() THE DIMENSION OF IW()=(I1) MUST BE .GE. 2*NCOLS=(I2).
C IN ABOVE MESSAGE, I1= 0
C IN ABOVE MESSAGE, I2= 2
C ERROR NUMBER = 16
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C WARNING IN...
C DBOLS() THE DIMENSION OF IOPT()=(I1) MUST BE .GE. THE REQD. LEN.=(I2).
C IN ABOVE MESSAGE, I1= 0
C IN ABOVE MESSAGE, I2= 1
C ERROR NUMBER = 17
C (NORMALLY A RETURN TO THE USER TAKES PLACE FOLLOWING THIS MESSAGE.)
C
C***REFERENCES R. J. Hanson, Linear least squares with bounds and
C linear constraints, Report SAND82-1517, Sandia
C Laboratories, August 1982.
C***ROUTINES CALLED 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
C
C SOLVE LINEAR LEAST SQUARES SYSTEM WITH BOUNDS ON
C SELECTED VARIABLES.
C REVISED 850329-1400
C REVISED YYMMDD-HHMM
C TO CHANGE THIS SUBPROGRAM FROM SINGLE TO DOUBLE PRECISION BEGIN
C EDITING AT THE CARD 'C++'.
C CHANGE THIS SUBPROGRAM NAME TO DBOLS AND THE STRINGS
C /SCOPY/ TO /DCOPY/, /SBOL/ TO /DBOL/,
C /SNRM2/ TO /DNRM2/, /ISAMAX/ TO /IDAMAX/,
C /SROTG/ TO /DROTG/, /SROT/ TO /DROT/, /E0/ TO /D0/,
C /REAL / TO /DOUBLE PRECISION/.
C ++
DOUBLE PRECISION W(MDW,*),BL(*),BU(*),X(*),RW(*)
DOUBLE PRECISION SC, SS, ONE, DNRM2, RNORM, ZERO
C
C THIS VARIABLE SHOULD REMAIN TYPE REAL.
INTEGER IND(*),IOPT(*),IW(*)
LOGICAL CHECKL
CHARACTER*8 XERN1, XERN2
CHARACTER*16 XERN3, XERN4
SAVE IGO,LOCACC,LOPT,ISCALE
DATA IGO/0/
C***FIRST EXECUTABLE STATEMENT DBOLS
NERR = 0
MODE = 0
IF (IGO.EQ.0) THEN
C DO(CHECK VALIDITY OF INPUT DATA)
C PROCEDURE(CHECK VALIDITY OF INPUT DATA)
C
C SEE THAT MDW IS .GT.0. GROSS CHECK ONLY.
IF (MDW.LE.0) THEN
WRITE (XERN1, '(I8)') MDW
CALL XERMSG ('SLATEC', 'DBOLS', 'MDW = ' // XERN1 //
* ' MUST BE POSITIVE.', 2, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
C
C SEE THAT NUMBER OF UNKNOWNS IS POSITIVE.
IF (NCOLS.LE.0) THEN
WRITE (XERN1, '(I8)') NCOLS
CALL XERMSG ('SLATEC', 'DBOLS', 'NCOLS = ' // XERN1 //
* ' THE NO. OF VARIABLES MUST BE POSITIVE.', 3, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
C
C SEE THAT CONSTRAINT INDICATORS ARE ALL WELL-DEFINED.
DO 10 J = 1,NCOLS
IF (IND(J).LT.1 .OR. IND(J).GT.4) THEN
WRITE (XERN1, '(I8)') J
WRITE (XERN2, '(I8)') IND(J)
CALL XERMSG ('SLATEC', 'DBOLS', 'IND(' // XERN1 //
* ') = ' // XERN2 // ' MUST BE 1-4.', 4, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
10 CONTINUE
C
C SEE THAT BOUNDS ARE CONSISTENT.
DO 20 J = 1,NCOLS
IF (IND(J).EQ.3) THEN
IF (BL(J).GT.BU(J)) THEN
WRITE (XERN1, '(I8)') J
WRITE (XERN3, '(1PE15.6)') BL(J)
WRITE (XERN4, '(1PE15.6)') BU(J)
CALL XERMSG ('SLATEC', 'DBOLS', 'BOUND BL(' //
* XERN1 // ') = ' // XERN3 // ' IS .GT. BU(' //
* XERN1 // ') = ' // XERN4, 5, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
ENDIF
20 CONTINUE
C END PROCEDURE
C DO(PROCESS OPTION ARRAY)
C PROCEDURE(PROCESS OPTION ARRAY)
ZERO = 0.D0
ONE = 1.D0
CHECKL = .FALSE.
LENX = NCOLS
ISCALE = 1
IGO = 2
LOPT = 0
LP = 0
LDS = 0
30 CONTINUE
LP = LP + LDS
IP = IOPT(LP+1)
JP = ABS(IP)
C
C TEST FOR NO MORE OPTIONS.
IF (IP.EQ.99) THEN
IF (LOPT.EQ.0) LOPT = LP + 1
GO TO 50
ELSE IF (JP.EQ.99) THEN
LDS = 1
GO TO 30
ELSE IF (JP.EQ.1) THEN
IF (IP.GT.0) THEN
C
C SET UP DIRECTION FLAG, ROW STACKING POINTER
C LOCATION, AND LOCATION FOR NUMBER OF NEW ROWS.
LOCACC = LP + 2
C
C IOPT(LOCACC-1)=OPTION NUMBER FOR SEQ. ACCUMULATION.
C CONTENTS.. IOPT(LOCACC )=USER DIRECTION FLAG, 1 OR 2.
C IOPT(LOCACC+1)=ROW STACKING POINTER.
C IOPT(LOCACC+2)=NUMBER OF NEW ROWS TO PROCESS.
C USER ACTION WITH THIS OPTION..
C (SET UP OPTION DATA FOR SEQ. ACCUMULATION IN IOPT(*).
C MUST ALSO START PROCESS WITH IOPT(LOCACC)=1.)
C (MOVE BLOCK OF EQUATIONS INTO W(*,*) STARTING AT FIRST
C ROW OF W(*,*). SET IOPT(LOCACC+2)=NO. OF ROWS IN BLOCK.)
C LOOP
C CALL DBOLS()
C
C IF(IOPT(LOCACC) .EQ. 1) THEN
C STACK EQUAS., STARTING AT ROW IOPT(LOCACC+1),
C INTO W(*,*).
C SET IOPT(LOCACC+2)=NO. OF EQUAS.
C IF LAST BLOCK OF EQUAS., SET IOPT(LOCACC)=2.
C ELSE IF IOPT(LOCACC) .EQ. 2) THEN
C (PROCESS IS OVER. EXIT LOOP.)
C ELSE
C (ERROR CONDITION. SHOULD NOT HAPPEN.)
C END IF
C END LOOP
C SET IOPT(LOCACC-1)=-OPTION NUMBER FOR SEQ. ACCUMULATION.
C CALL DBOLS( )
IOPT(LOCACC+1) = 1
IGO = 1
ENDIF
LDS = 4
GO TO 30
ELSE IF (JP.EQ.2) THEN
IF (IP.GT.0) THEN
C
C GET ACTUAL LENGTHS OF ARRAYS FOR CHECKING AGAINST NEEDS.
LOCDIM = LP + 2
C
C LMDW.GE.MROWS
C LNDW.GE.NCOLS+1
C LLB .GE.NCOLS
C LLX .GE.NCOLS+EXTRA REQD. IN OPTIONS.
C LLRW.GE.5*NCOLS
C LLIW.GE.2*NCOLS
C LIOP.GE. AMOUNT REQD. FOR IOPTION ARRAY.
LMDW = IOPT(LOCDIM)
LNDW = IOPT(LOCDIM+1)
LLB = IOPT(LOCDIM+2)
LLX = IOPT(LOCDIM+3)
LLRW = IOPT(LOCDIM+4)
LLIW = IOPT(LOCDIM+5)
LIOPT = IOPT(LOCDIM+6)
CHECKL = .TRUE.
ENDIF
LDS = 8
GO TO 30
C
C OPTION TO MODIFY THE COLUMN SCALING.
ELSE IF (JP.EQ.3) THEN
IF (IP.GT.0) THEN
ISCALE = IOPT(LP+2)
C
C SEE THAT ISCALE IS 1 THRU 3.
IF (ISCALE.LT.1 .OR. ISCALE.GT.3) THEN
WRITE (XERN1, '(I8)') ISCALE
CALL XERMSG ('SLATEC', 'DBOLS', 'ISCALE OPTION = '
* // XERN1 // ' MUST BE 1-3', 7, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
ENDIF
LDS = 2
C CYCLE FOREVER
GO TO 30
C
C IN THIS OPTION THE USER HAS PROVIDED SCALING. THE
C SCALE FACTORS FOR THE COLUMNS BEGIN IN X(NCOLS+IOPT(LP+2)).
ELSE IF (JP.EQ.4) THEN
IF (IP.GT.0) THEN
ISCALE = 4
IF (IOPT(LP+2).LE.0) THEN
WRITE (XERN1, '(I8)') IOPT(LP+2)
CALL XERMSG ('SLATEC', 'DBOLS',
* 'OFFSET PAST X(NCOLS) (' // XERN1 //
* ') FOR USER-PROVIDED COLUMN SCALING MUST ' //
* 'BE POSITIVE.', 8, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
CALL DCOPY(NCOLS,X(NCOLS+IOPT(LP+2)),1,RW,1)
LENX = LENX + NCOLS
DO 40 J = 1,NCOLS
IF (RW(J).LE.ZERO) THEN
WRITE (XERN1, '(I8)') J
WRITE (XERN3, '(1PE15.6)') RW(J)
CALL XERMSG ('SLATEC', 'DBOLS',
* 'EACH PROVIDED COLUMN SCALE FACTOR ' //
* 'MUST BE POSITIVE.$$COMPONENT ' // XERN1 //
* ' NOW = ' // XERN3, 9, 1)
GO TO 190
ENDIF
40 CONTINUE
ENDIF
LDS = 2
C CYCLE FOREVER
GO TO 30
C
C IN THIS OPTION AN OPTION ARRAY IS PROVIDED TO DBOLSM().
ELSE IF (JP.EQ.5) THEN
IF (IP.GT.0) THEN
LOPT = IOPT(LP+2)
ENDIF
LDS = 2
C CYCLE FOREVER
GO TO 30
C
C THIS OPTION USES THE NEXT LOC OF IOPT(*) AS AN
C INCREMENT TO SKIP.
ELSE IF (JP.EQ.6) THEN
IF (IP.GT.0) THEN
LP = IOPT(LP+2) - 1
LDS = 0
ELSE
LDS = 2
ENDIF
C CYCLE FOREVER
GO TO 30
C
C NO VALID OPTION NUMBER WAS NOTED. THIS IS AN ERROR CONDITION.
ELSE
WRITE (XERN1, '(I8)') JP
CALL XERMSG ('SLATEC', 'DBOLS', 'THE OPTION NUMBER = ' //
* XERN1 // ' IS NOT DEFINED.', 6, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
50 CONTINUE
C END PROCEDURE
IF (CHECKL) THEN
C DO(CHECK LENGTHS OF ARRAYS)
C PROCEDURE(CHECK LENGTHS OF ARRAYS)
C
C THIS FEATURE ALLOWS THE USER TO MAKE SURE THAT THE
C ARRAYS ARE LONG ENOUGH FOR THE INTENDED PROBLEM SIZE AND USE.
IF (LMDW.LT.MROWS) THEN
WRITE (XERN1, '(I8)') LMDW
WRITE (XERN2, '(I8)') MROWS
CALL XERMSG ('SLATEC', 'DBOLS',
* 'THE ROW DIMENSION OF W(,) = ' // XERN1 //
* ' MUST BE .GE. THE NUMBER OF ROWS = ' // XERN2,
* 11, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
IF (LNDW.LT.NCOLS+1) THEN
WRITE (XERN1, '(I8)') LNDW
WRITE (XERN2, '(I8)') NCOLS+1
CALL XERMSG ('SLATEC', 'DBOLS',
* 'THE COLUMN DIMENSION OF W(,) = ' // XERN1 //
* ' MUST BE .GE. NCOLS+1 = ' // XERN2, 12, 1)
GO TO 190
ENDIF
IF (LLB.LT.NCOLS) THEN
WRITE (XERN1, '(I8)') LLB
WRITE (XERN2, '(I8)') NCOLS
CALL XERMSG ('SLATEC', 'DBOLS',
* 'THE DIMENSIONS OF THE ARRAYS BL(), BU(), AND IND() = '
* // XERN1 // ' MUST BE .GE. NCOLS = ' // XERN2,
* 13, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
IF (LLX.LT.LENX) THEN
WRITE (XERN1, '(I8)') LLX
WRITE (XERN2, '(I8)') LENX
CALL XERMSG ('SLATEC', 'DBOLS',
* 'THE DIMENSION OF X() = ' // XERN1 //
* ' MUST BE .GE. THE REQUIRED LENGTH = ' // XERN2,
* 14, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
IF (LLRW.LT.5*NCOLS) THEN
WRITE (XERN1, '(I8)') LLRW
WRITE (XERN2, '(I8)') 5*NCOLS
CALL XERMSG ('SLATEC', 'DBOLS',
* 'THE DIMENSION OF RW() = ' // XERN1 //
* ' MUST BE .GE. 5*NCOLS = ' // XERN2, 15, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
IF (LLIW.LT.2*NCOLS) THEN
WRITE (XERN1, '(I8)') LLIW
WRITE (XERN2, '(I8)') 2*NCOLS
CALL XERMSG ('SLATEC', 'DBOLS',
* 'THE DIMENSION OF IW() = ' // XERN1 //
* ' MUST BE .GE. 2*NCOLS = ' // XERN2, 16, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
IF (LIOPT.LT.LP+1) THEN
WRITE (XERN1, '(I8)') LIOPT
WRITE (XERN2, '(I8)') LP+1
CALL XERMSG ('SLATEC', 'DBOLS',
* 'THE DIMENSION OF IOPT() = ' // XERN1 //
* ' MUST BE .GE. THE REQUIRED LEN = ' // XERN2, 17,1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
C END PROCEDURE
ENDIF
ENDIF
GO TO (60,90),IGO
GO TO 180
C
C GO BACK TO THE USER FOR ACCUMULATION OF LEAST SQUARES
C EQUATIONS AND DIRECTIONS TO QUIT PROCESSING.
C CASE 1
60 CONTINUE
C DO(ACCUMULATE LEAST SQUARES EQUATIONS)
C PROCEDURE(ACCUMULATE LEAST SQUARES EQUATIONS)
MROWS = IOPT(LOCACC+1) - 1
INROWS = IOPT(LOCACC+2)
MNEW = MROWS + INROWS
IF (MNEW.LT.0 .OR. MNEW.GT.MDW) THEN
WRITE (XERN1, '(I8)') MNEW
WRITE (XERN2, '(I8)') MDW
CALL XERMSG ('SLATEC', 'DBOLS', 'NO. OF ROWS = ' // XERN1 //
* ' MUST BE .GE. 0 .AND. .LE. MDW = ' // XERN2, 10, 1)
C DO(RETURN TO USER PROGRAM UNIT)
GO TO 190
ENDIF
DO 80 J = 1,MIN(NCOLS+1,MNEW)
DO 70 I = MNEW,MAX(MROWS,J) + 1,-1
IBIG = IDAMAX(I-J,W(J,J),1) + J - 1
C
C PIVOT FOR INCREASED STABILITY.
CALL DROTG(W(IBIG,J),W(I,J),SC,SS)
CALL DROT(NCOLS+1-J,W(IBIG,J+1),MDW,W(I,J+1),MDW,SC,SS)
W(I,J) = ZERO
70 CONTINUE
80 CONTINUE
MROWS = MIN(NCOLS+1,MNEW)
IOPT(LOCACC+1) = MROWS + 1
IGO = IOPT(LOCACC)
C END PROCEDURE
IF (IGO.EQ.2) THEN
IGO = 0
ENDIF
GO TO 180
C CASE 2
90 CONTINUE
C DO(INITIALIZE VARIABLES AND DATA VALUES)
C PROCEDURE(INITIALIZE VARIABLES AND DATA VALUES)
DO 150 J = 1,NCOLS
GO TO (100,110,120,130),ISCALE
GO TO 140
100 CONTINUE
C CASE 1
C
C THIS IS THE NOMINAL SCALING. EACH NONZERO
C COL. HAS MAX. NORM EQUAL TO ONE.
IBIG = IDAMAX(MROWS,W(1,J),1)
RW(J) = ABS(W(IBIG,J))
IF (RW(J).EQ.ZERO) THEN
RW(J) = ONE
ELSE
RW(J) = ONE/RW(J)
ENDIF
GO TO 140
110 CONTINUE
C CASE 2
C
C THIS CHOICE OF SCALING MAKES EACH NONZERO COLUMN
C HAVE EUCLIDEAN LENGTH EQUAL TO ONE.
RW(J) = DNRM2(MROWS,W(1,J),1)
IF (RW(J).EQ.ZERO) THEN
RW(J) = ONE
ELSE
RW(J) = ONE/RW(J)
ENDIF
GO TO 140
120 CONTINUE
C CASE 3
C
C THIS CASE EFFECTIVELY SUPPRESSES SCALING BY SETTING
C THE SCALING MATRIX TO THE IDENTITY MATRIX.
RW(1) = ONE
CALL DCOPY(NCOLS,RW,0,RW,1)
GO TO 160
130 CONTINUE
C CASE 4
GO TO 160
140 CONTINUE
150 CONTINUE
160 CONTINUE
C END PROCEDURE
C DO(SOLVE BOUNDED LEAST SQUARES PROBLEM)
C PROCEDURE(SOLVE BOUNDED LEAST SQUARES PROBLEM)
C
C INITIALIZE IBASIS(*), J=1,NCOLS, AND IBB(*), J=1,NCOLS,
C TO =J,AND =1, FOR USE IN DBOLSM( ).
DO 170 J = 1,NCOLS
IW(J) = J
IW(J+NCOLS) = 1
RW(3*NCOLS+J) = BL(J)
RW(4*NCOLS+J) = BU(J)
170 CONTINUE
CALL DBOLSM(W,MDW,MROWS,NCOLS,RW(3*NCOLS+1),RW(4*NCOLS+1),IND,
. IOPT(LOPT),X,RNORM,MODE,RW(NCOLS+1),RW(2*NCOLS+1),RW,
. IW,IW(NCOLS+1))
C END PROCEDURE
IGO = 0
180 CONTINUE
RETURN
C PROCEDURE(RETURN TO USER PROGRAM UNIT)
190 IF(MODE.GE.0)MODE = -NERR
IGO = 0
RETURN
C END PROCEDURE
END
