*DECK SBOLS SUBROUTINE SBOLS (W, MDW, MROWS, NCOLS, BL, BU, IND, IOPT, X, + RNORM, MODE, RW, IW) C***BEGIN PROLOGUE SBOLS 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 SINGLE PRECISION (SBOLS-S, DBOLS-D) C***KEYWORDS BOUNDS, CONSTRAINTS, INEQUALITY, LEAST SQUARES, LINEAR C***AUTHOR Hanson, R. J., (SNLA) C***DESCRIPTION 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 SBOLSM( ). 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 SBOLSM( ). 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 SBOLS( ). 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 SBOLSM(). See the section ERROR MESSAGES for SBOLSM() in the C documentation for SBOLSM(). 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 SBOLS( ). 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 SBOLS( ) 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 .