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# /home/coin/SVN-release/Cgl-0.53.1/DyLP/src/Dylp/dylp.h

Go to the documentation of this file.

    00001 /*
    00002   This file is a part of the Dylp LP distribution.
    00003
    00004         Copyright (C) 2005 -- 2007 Lou Hafer
    00005
    00006         School of Computing Science
    00007         Simon Fraser University
    00008         Burnaby, B.C., V5A 1S6, Canada
    00009         lou@cs.sfu.ca
    00010
    00011   This code is licensed under the terms of the Common Public License (CPL).
    00012 */
    00013
    00014 #ifndef _DYLP_H
    00015 #define _DYLP_H
    00016
    00017 /*
    00018   @(#)dylp.h    4.6     10/15/05
    00019   svn/cvs: $Id: dylp.h 218 2008-03-28 15:57:22Z lou $
    00020
    00021   This file contains definitions related to dylp, a subroutine library which
    00022   implements a dynamic (primal-dual) linear programming algorithm based on
    00023   the algorithm described by Padberg in Linear Optimisation & Extensions,
    00024   Springer-Verlag, 1995.  dylp also owes a debt to previous and contemporary
    00025   codes the author has worked with --- la05, bandbx, zoom/xmp, ylp, and glpk.
    00026
    00027   At minimum, dylp requires only a constraint system. Since it manages a
    00028   dynamically sized private copy of the constraint system while solving the
    00029   LP, there's no point in having the client attach logical variables (they'd
    00030   just get in the way, really).
    00031
    00032   dylp will accept a basis specification. This takes the form of a status
    00033   vector giving the status of all variables, and a basis vector specifying
    00034   the active constraints and their associated basic variables. From this
    00035   dylp will construct an initial active problem which consists of exactly
    00036   the given constraints and basic variables, with the logicals for the
    00037   constraints making up the nonbasic partition.
    00038
    00039   dylp returns as a solution the simplex termination code, the objective
    00040   value (or related value, appropriate for the termination code), status for
    00041   all variables, the active constraints, and the associated primal and dual
    00042   variables (put a little differently, a basis, the values of the basic
    00043   variables, and the dual variables associated with the active constraints).
    00044
    00045   The conditional compilation symbol DYLP_INTERNAL is used to delimit
    00046   definitions that should be considered internal to dylp. Don't define this
    00047   symbol in a client.
    00048 */
    00049
    00050 #include "dylib_errs.h"
    00051 #include "dylib_io.h"
    00052 #include "dy_consys.h"
    00053
    00054 /*
    00055   A few words on notation. Traditional matrix and vector notation for LP
    00056   suffers a bit when limited to ascii text, but it's readable if you're
    00057   familiar with the original. The notation in the comments and code is
    00058   loosely based on Chvatal, "Linear Programming", W.H. Freeman, 1983, which
    00059   the author happens to like.
    00060
    00061   A matrix is represented with a capital letter, e.g., B. A vector is
    00062   represented with a small letter, e.g., x. A subscript is given in angle
    00063   brackets, e.g., x<j> for the jth coefficient of x. An individual element of
    00064   a matrix has two subscripts, e.g., a<i,j> for the element in row i, column
    00065   j. Column and row vectors are shown with one subscript, e.g., a<j> for the
    00066   jth column (or row).  Whether the vector is supposed to be a column or a
    00067   row should generally be clear from context. A capital letter in the
    00068   subscript position indicates a set of elements, e.g., x<N> is the non-basic
    00069   variables.
    00070
    00071   The inverse of a matrix is denoted inv(*), e.g., the basis inverse,
    00072   inv(B).  The dot product of two vectors is denoted dot(*,*), e.g.,
    00073   dot(c,x), or sometimes just written directly, e.g., cx.
    00074
    00075   The system of constraints is assumed to be Ax <= b, with m rows and n
    00076   columns. Once the logical variables (aka slacks and artificials) have been
    00077   added, it becomes Ax = b.  A is the constraint matrix, x is the vector of
    00078   primal variables, and b is the right-hand-side (rhs).  NOTE that the
    00079   convention for indices is NOT the usual one. Logical variables are assigned
    00080   indices 1..m and architectural variables are assigned indices m+1..m+n. It
    00081   makes for more efficient addition/deletion of variables; see dy_consys.h for a
    00082   little more explanation.
    00083
    00084   There is an objective function z = cx, where z is the objective value and c
    00085   is the vector of coefficients.  dylp minimises the objective.
    00086
    00087   The matrix A is partitioned into the set of basic columns B, and the set of
    00088   non-basic columns N (sometimes A<N>). The corresponding partitions of c and
    00089   x are c<B>, x<B>, and c<N>, x<N>.
    00090
    00091   Premultiplication by the basis inverse (e.g., inv(B)a<j>) is referred to as
    00092   an `ftran'; postmultiplication (e.g., c<B>inv(B)) as a `btran'.  Quantities
    00093   that have been transformed using the basis inverse are often (but not
    00094   always) renamed as 'barred' quantities.
    00095
    00096   The basic primal variables are x<B> = inv(B)b.  The dual variables are y =
    00097   c<B>inv(B).  The jth column of A, premultiplied by inv(B), is abar<j> =
    00098   inv(B)a<j>. The reduced costs are cbar = c<N> - c<B>inv(B)N = c<N>-yN.
    00099
    00100   The variable i is used as a row index, j as a column index. Often they will
    00101   represent the entering primal variable (j) and the leaving primal variable
    00102   (i). Be aware that comments are often written as if the leaving primal
    00103   variable x<i> occupies row i of the basis. This simplifies the writing.
    00104   But keep in mind that variable x<i> can occupy an arbitrary row k of the
    00105   basis.
    00106 */
    00107
    00108 /*
    00109   Termination codes for dy_primal and dy_dual, the top level routines of the
    00110   dylp simplex algorithms. Also used by various internal routines.  Codes
    00111   marked with (*) will never be returned to the client unless dylp has
    00112   failed.
    00113
    00114   lpINV         The code is not valid (i.e., not set by an execution of
    00115                 dy_primal or dy_dual).
    00116
    00117   lpOPTIMAL     The problem has an optimal solution.
    00118
    00119   lpUNBOUNDED   The problem is unbounded.
    00120
    00121   lpSWING(*)    The problem is pseudo-unbounded: Some primal variable grew
    00122                 excessively in a single pivot.
    00123
    00124   lpINFEAS      The problem is infeasible.
    00125
    00126   lpACCCHK      An accuracy check failed and dylp's internal recovery
    00127                 algorithms could not recover the situation.
    00128
    00129   lpSTALLED     The problem has been abandoned due to stalling. (We could
    00130                 in fact actually be cycling, but that's too much trouble
    00131                 to prove.)
    00132
    00133   lpITERLIM     The problem has been abandoned because it has exceeded an
    00134                 absolute iteration limit.
    00135
    00136   lpNOSPACE     The problem has been abandoned because the basis package did
    00137                 not have sufficient space to maintain the basis.
    00138
    00139   lpLOSTFEAS    Feasibility was lost during simplex execution.
    00140
    00141   lpPUNT        The lp has punted because it ran into a pivoting problem.
    00142
    00143                 The next three codes indicate that we're in the middle of
    00144                 attempting a forced transition for error recovery purposes.
    00145
    00146   lpFORCEDUAL(*) Force a primal to dual transition.
    00147
    00148   lpFORCEPRIMAL(*) Force a dual to primal transition.
    00149
    00150   lpFORCEFULL(*) Force all inactive constraints and variables to be loaded.
    00151
    00152   lpFATAL       Fatal confusion or error of some sort; covers a multitude
    00153                 of sins.
    00154
    00155   The dual simplex routine does not have a phase I routine equivalent to
    00156   dy_primal1 for the primal simplex. (In the context of dylp, it expects
    00157   to run after dy_primal has been used to find an initial optimal solution.)
    00158
    00159   When using the dual simplex method, internal codes reflect the state of
    00160   the dual problem, but dy_dual makes the usual translation back to the
    00161   primal problem, as:
    00162
    00163   Dual          Primal          Rationale
    00164   ----          ------          ---------
    00165   lpUNBOUNDED   lpINFEAS        Standard duality theorem.
    00166
    00167   Note that lpSWING always refers to primal variables.
    00168 */
    00169
    00170 typedef enum { lpFATAL = -1, lpINV = 0,
    00171                lpOPTIMAL, lpUNBOUNDED, lpSWING, lpINFEAS,
    00172                lpACCCHK,
    00173                lpSTALLED, lpITERLIM, lpNOSPACE,
    00174                lpLOSTFEAS, lpPUNT,
    00175                lpFORCEDUAL, lpFORCEPRIMAL, lpFORCEFULL } lpret_enum ;
    00176
    00177
    00178 /*
    00179   Phase codes for dylp
    00180
    00181   dyINV         Invalid phase
    00182   dyINIT        Initialisation and setup, including establishing the
    00183                 initial set of constraints and variables and crashing the
    00184                 first basis.
    00185   dyPRIMAL1     Primal simplex phase I
    00186   dyPRIMAL2     Primal simplex phase II
    00187   dyDUAL        Dual simplex
    00188   dyPURGEVAR    Deactivation of variables.
    00189   dyGENVAR      Generation of new variables (not part of original problem).
    00190   dyADDVAR      Activation of variables.
    00191   dyPURGECON    Deactivation of constraints.
    00192   dyGENCON      Generation of new constraints (not part of original problem).
    00193   dyADDCON      Activation of constraints.
    00194   dyFORCEDUAL   Force dual feasibility (error recovery)
    00195   dyFORCEPRIMAL Force primal feasibility (error recovery)
    00196   dyFORCEFULL   Force activation of the full system (error recovery)
    00197   dyDONE        Execution is finished, for one reason or another.
    00198
    00199   It's true that new variables will be added during dyGENCON -- at the least,
    00200   each newly generated constraint will bring with it a logical variable.
    00201   dyGENVAR differs in that it is augmenting some subset of the constraints
    00202   with new variables (classic column generation, for example).
    00203
    00204   The main loop states (dyPRIMAL1 -- dyFORCEFULL) must remain a contiguous
    00205   block. dy_dumpstats counts on dyPRIMAL1 and dyFORCEPRIMAL being first and
    00206   last, respectively, in the block.
    00207
    00208   dyDONE must remain the last code --- it's used to dimension a statistics
    00209   array that tracks the number of times the main loop states are entered.
    00210 */
    00211
    00212 typedef enum { dyINV = 0, dyINIT,
    00213                dyPRIMAL1, dyPRIMAL2, dyDUAL,
    00214                dyPURGEVAR, dyGENVAR, dyADDVAR,
    00215                dyPURGECON, dyGENCON, dyADDCON,
    00216                dyFORCEDUAL, dyFORCEPRIMAL, dyFORCEFULL,
    00217                dyDONE } dyphase_enum ;
    00218 /*
    00219   General return and error codes.
    00220
    00221   Used by various routines in dylp.
    00222   No routine
    00223   uses all of these, but there's enough overlap to make one big enum
    00224   convenient.
    00225
    00226   dyrINV        Invalid code.
    00227
    00228   dyrOK         Whatever it was that was being done was done without incident.
    00229   dyrOPTIMAL    The problem is optimal.
    00230   dyrUNBOUND    The problem is unbounded.
    00231   dyrSWING      The problem is pseudo-unbounded: Some variable grew by an
    00232                 excessive amount in a single pivot.
    00233   dyrINFEAS     The problem is infeasible.
    00234
    00235   dyrREQCHK     Requests a refactor and accuracy check (triggered by various
    00236                 checks for bogus numbers).
    00237   dyrACCCHK     An accuracy check has failed.
    00238   dyrLOSTPFEAS  Primal feasibility has been lost.
    00239   dyrLOSTDFEAS  Dual feasibility has been lost.
    00240
    00241   dyrDEGEN      Degeneracy has been discovered, or a degenerate pivot has been
    00242                 taken.
    00243   dyrRESELECT   Reselect an incoming variable (after an abortive pivot
    00244                 attempt).
    00245   dyrMADPIV     The selected pivot coefficient was (numerically) unstable.
    00246   dyrPUNT       In the context of the dual simplex: the dual simplex has
    00247                 decided to punt to the primal simplex phase I, for any of
    00248                 several reasons. Generally this is indicative of the relative
    00249                 lack of sophistication in the dual simplex.
    00250                 In the context of the primal simplex: this indicates that all
    00251                 candidates to enter the basis were flagged with a NOPIVOT
    00252                 qualifier.
    00253
    00254   dyrPATCHED    The basis package managed to factor the basis after patching
    00255                 it.
    00256   dyrSINGULAR   The basis package discovered the basis was singular. (Typically
    00257                 as a consequence of a pivot gone bad.)
    00258   dyrNUMERIC    The basis package detected unacceptable growth in the basis
    00259                 coefficients.
    00260   dyrBSPACE     The basis package ran out of space for the basis
    00261                 representation.
    00262   dyrSTALLED    The LP seems to have stalled (and could possibly be cycling,
    00263                 but that's too much trouble to prove); triggered by too many
    00264                 iterations with no change in the objective.
    00265   dyrITERLIM    The iteration limit has been exceeded.
    00266
    00267   dyrFATAL      Fatal confusion; covers a multitude of sins.
    00268
    00269    The specific values assigned to some of the codes in the enum come from
    00270    earlier use of yla05 as the basis package. It's gone, but there's no
    00271    incentive to remove the values.
    00272 */
    00273
    00274 typedef enum { dyrFATAL = -10, dyrITERLIM, dyrSTALLED,
    00275                dyrBSPACE = -7, dyrSINGULAR = -6, dyrNUMERIC = -5,
    00276                dyrLOSTPFEAS, dyrLOSTDFEAS, dyrDEGEN, dyrMADPIV,
    00277                dyrINV = 0, dyrOK = 1, dyrPATCHED = 2,
    00278                dyrRESELECT, dyrREQCHK, dyrACCCHK, dyrPUNT,
    00279                dyrOPTIMAL, dyrUNBOUND, dyrSWING, dyrINFEAS } dyret_enum ;
    00280
    00281 /*
    00282   Requests and results for checks and recalculations
    00283
    00284   Some symbolic names for requesting and reporting on factoring, accuracy
    00285   checks and primal and dual variable calculations. These originated with la
    00286   Duenna, hence the lad prefix. Interpretation varies subtly from routine to
    00287   routine, so check the parameter notes.
    00288
    00289   ladPRIMALCHK  (i) set to request primal accuracy check, Bx<B> = b - Nx<N>,
    00290                 (o) set to indicate failure of check
    00291   ladDUALCHK    (i) set to to request dual accuracy check, yB = c<B>
    00292                 (o) set to indicate failure of check
    00293   ladPRIMFEAS   (i) set to request primal feasibility check (primal variables
    00294                     within bounds)
    00295                 (o) set to indicate loss of primal feasibility
    00296   ladDUALFEAS   (i) set to request dual feasibility check (reduced costs of
    00297                     proper sign)
    00298                 (o) set to indicate loss of dual feasibility
    00299   ladPFQUIET    (i) set to suppress warnings about variables which are not
    00300                     primal feasible
    00301   ladDFQUIET    (i) set to suppress warnings about variables which are not
    00302                     dual feasible
    00303   ladDUALS      (i) set to request calculation of the dual variables and
    00304                     gradient vector
    00305                 (o) set to indicate calculation of the dual variables and
    00306                     gradient vector
    00307   ladPRIMALS    (i) set to request calculation of the primal variables
    00308                 (o) set to indicate calculation of the primal variables
    00309   ladFACTOR     (i) set to indicate the basis should be refactored
    00310                 (o) set to indicate the basis has been factored
    00311   ladEXPAND     (i) set to force expansion of the space allocated for the
    00312                     basis representation
    00313                 (o) set to indicate the space allocated for the basis was
    00314                     increased
    00315 */
    00316
    00317 #define ladPRIMFEAS     1<<0
    00318 #define ladPRIMALCHK    1<<1
    00319 #define ladPFQUIET      1<<2
    00320 #define ladDUALFEAS     1<<3
    00321 #define ladDUALCHK      1<<4
    00322 #define ladDFQUIET      1<<5
    00323 #define ladDUALS        1<<6
    00324 #define ladPRIMALS      1<<7
    00325 #define ladFACTOR       1<<8
    00326 #define ladEXPAND       1<<9
    00327
    00328
    00329
    00330 /*
    00331   Variable status codes
    00332
    00333   dylp keeps explicit status for both basic and nonbasic variables. These are
    00334   set up as flags so that it's easy to test when more than one status will do
    00335   for a particular action.
    00336
    00337   vstatBFX      basic, fixed
    00338   vstatBUUB     basic, above upper bound
    00339   vstatBUB      basic, at upper bound
    00340   vstatB        basic, strictly between bounds (a well-behaved basic variable)
    00341   vstatBLB      basic, at lower bound
    00342   vstatBLLB     basic, below lower bound
    00343   vstatBFR      basic, free (unbounded)
    00344
    00345   vstatNBFX     nonbasic, fixed
    00346   vstatNBUB     nonbasic at upper bound
    00347   vstatNBLB     nonbasic at lower bound
    00348   vstatNBFR     nonbasic free
    00349
    00350   vstatSB       superbasic, within bounds
    00351
    00352   dylp ensures that superbasic variables are, in fact, always strictly within
    00353   bounds.
    00354
    00355   Inactive NBFR variables can be created at startup if dylp is working with a
    00356   partial system and there are free variables that are not selected to be in
    00357   the initial basis. If the client is forcing a full system, these will be
    00358   active NBFR variables.  Error recovery may also create active NBFR
    00359   variables. By convention, NBFR variables always have a value of zero.
    00360
    00361   Inactive SB variables should not occur. SB status occurs only as the result
    00362   of error recovery and is only valid in primal simplex.
    00363
    00364   The value of SB variables is lost when they are reported out as part of a
    00365   solution. This will only happen if dylp could not find an optimal solution.
    00366
    00367   The following qualifiers can be added to the status:
    00368
    00369   vstatNOPIVOT  Prevents the variable from being considered as a candidate
    00370                 for pivoting; used by the pivot rejection machinery.
    00371   vstatNOPER    Prevents the variable from being perturbed during the
    00372                 formation of a restricted subproblem.
    00373   vstatNOLOAD   Prevents the variable from being considered for activation;
    00374                 used by startup and variable activation/deactivation routines.
    00375 */
    00376
    00377 #define vstatINV     0
    00378 #define vstatBFX  1<<0
    00379 #define vstatBUB  1<<1
    00380 #define vstatB    1<<2
    00381 #define vstatBLB  1<<3
    00382 #define vstatBFR  1<<4
    00383 #define vstatNBFX 1<<5
    00384 #define vstatNBUB 1<<6
    00385 #define vstatNBLB 1<<7
    00386 #define vstatNBFR 1<<8
    00387 #define vstatSB   1<<9
    00388 #define vstatBUUB  1<<10
    00389 #define vstatBLLB  1<<11
    00390
    00391 /*
    00392   TAKE NOTE: Do not use the msb as a qualifier! The status value, with or
    00393   without qualifiers, must be a positive value when cast to a signed integer.
    00394 */
    00395
    00396 #define vstatNOPIVOT ((flags) 1<<(sizeof(flags)*8-2))
    00397 #define vstatNOPER ((flags) 1<<(sizeof(flags)*8-3))
    00398 #define vstatNOLOAD ((flags) 1<<(sizeof(flags)*8-4))
    00399
    00400 #define vstatBASIC \
    00401         (vstatBFX|vstatBUUB|vstatBUB|vstatB|vstatBLB|vstatBLLB|vstatBFR)
    00402 #define vstatNONBASIC (vstatNBFX|vstatNBUB|vstatNBLB)
    00403 #define vstatEXOTIC (vstatSB|vstatNBFR)
    00404
    00405 #define vstatSTATUS (vstatBASIC|vstatNONBASIC|vstatEXOTIC)
    00406 #define vstatQUALS (vstatNOPIVOT|vstatNOPER|vstatNOLOAD)
    00407
    00408 /*
    00409   This macro checks (in a simplistic way) that its parameter encodes one and
    00410   only one status.  It's intended for mild error checking.  See
    00411   dylp_utils:dy_chkstatus if you're really feeling paranoid.
    00412 */
    00413
    00414 #define VALID_STATUS(zz_status_zz) \
    00415   (zz_status_zz == vstatBFX || zz_status_zz == vstatBUB || \
    00416    zz_status_zz == vstatB   || zz_status_zz == vstatBLB || \
    00417    zz_status_zz == vstatBFR || \
    00418    zz_status_zz == vstatNBFX || zz_status_zz == vstatNBUB || \
    00419    zz_status_zz == vstatNBLB || zz_status_zz == vstatNBFR || \
    00420    zz_status_zz == vstatSB)
    00421
    00422
    00423
    00424 /*
    00425   Interface structures: lpprob_struct, lptols_struct, lpopts_struct
    00426 */
    00427
    00428 /*
    00429   basis_struct
    00430
    00431   This structure is used to describe a basis to dylp, and to return the
    00432   final basis at termination. The size of the basis depends on the
    00433   number of active constraints, which will be a subset of the constraints
    00434   in the system.
    00435
    00436   The constraint system as supplied to dylp should not have logical variables
    00437   (dylp will create them automatically). This presents a problem if the final
    00438   basis contains basic logical variables. In this case, vndx is set to the
    00439   negative of the index of the constraint which spawned the logical. This
    00440   same technique can be used on input to, for example, specify the traditional
    00441   all-logical starting basis.
    00442
    00443   Field         Definition
    00444   -----         ----------
    00445   len           The number of rows in the basis.
    00446   el.cndx       Index of the constraint in this basis position.
    00447   el.vndx       Index of the variable in this basis position.
    00448
    00449 */
    00450
    00451 typedef struct { int cndx ; int vndx ; } basisel_struct ;
    00452
    00453 typedef struct
    00454 { int len ;
    00455   basisel_struct *el ; } basis_struct ;
    00456
    00457
    00458 /*
    00459   LP problem control and status flags
    00460
    00461   lpctlNOFREE           (i) Prevents dylp from freeing the problem structures,
    00462                             in anticipation of a subsequent hot start. If dylp
    00463                             exits with a state that is not suitable for hot
    00464                             start, this flag is ignored and the problem data
    00465                             structures are released.
    00466   lpctlONLYFREE         (i) In conjunction with an initial phase of dyDONE,
    00467                             causes dylp to do nothing except free the problem
    00468                             data structure and return.
    00469   lpctlUBNDCHG          (i) Indicates that the variable upper bounds (vub) have
    00470                             been changed.
    00471   lpctlLBNDCHG          (i) Indicates that the variable lower bounds (lub) have
    00472                             been changed.
    00473   lpctlRHSCHG           (i) Indicates that the right-hand side (rhs) has been
    00474                             changed. Includes the rhslow vector (if it exists).
    00475   lpctlOBJCHG           (i) Indicates that the objective (obj) has been changed.
    00476   lpctlACTVARSIN        (i) Indicates that a valid active variable vector has
    00477                             been supplied.
    00478   lpctlINITACTVAR       (i) Forces dylp to perform variable activation before
    00479                             beginning simplex iterations.
    00480   lpctlINITACTCON       (i) Forces dylp to perform constraint activation before
    00481                             beginning simplex iterations. (If variable
    00482                             activation is also requested, constraint activation
    00483                             occurs first.)
    00484
    00485   lpctlACTVARSOUT       (i) Indicates that an active variable vector is to be
    00486                             returned.
    00487                         (o) Indicates that a valid active variable vector has
    00488                             been returned.
    00489
    00490   lpctlDYVALID          (o) Indicates that dylp exited in a state which can
    00491                             be restarted with a hot start.
    00492
    00493 */
    00494
    00495 #define lpctlNOFREE     1<<0
    00496 #define lpctlONLYFREE   1<<1
    00497 #define lpctlUBNDCHG    1<<2
    00498 #define lpctlLBNDCHG    1<<3
    00499 #define lpctlRHSCHG     1<<4
    00500 #define lpctlOBJCHG     1<<5
    00501 #define lpctlACTVARSIN  1<<6
    00502 #define lpctlINITACTVAR 1<<7
    00503 #define lpctlINITACTCON 1<<8
    00504
    00505 #define lpctlACTVARSOUT 1<<10
    00506
    00507 #define lpctlDYVALID    1<<11
    00508
    00509 /*
    00510   lpprob_struct
    00511
    00512   This structure is used to pass an LP problem into dylp and convey the
    00513   results back to the client. The allocated size indicated in colsze and
    00514   rowsze is assumed to be accurate.  If basis, status, x, or y are NULL, they
    00515   will be allocated as needed. If they are non-NULL, dylp will reallocate
    00516   them if necessary (i.e., when the actual size of the lp exceeds the
    00517   allocated size of the vectors).
    00518
    00519   The status vector has the following coding:
    00520     * for nonbasic variables, the normal dylp status flags are used;
    00521     * for basic variables, the negative of the basis index is used.
    00522
    00523   There is one unavoidable problem with this scheme -- the status vector
    00524   provides the only information about the value of nonbasic variables. This
    00525   is adequate for all but superbasic variables and nonbasic free variables
    00526   which are not at zero. Both of these cases are transient anomalies, created
    00527   only when the basis package is forced to patch a singular basis, and they
    00528   should not persist in the final solution when an optimal solution is found
    00529   or when the problem is infeasible.  They may, however, occur in the
    00530   solution reported for an unbounded problem if the unbounded condition is
    00531   discovered before the nonbasic free or superbasic variable is chosen for
    00532   pivoting.  On input, nonbasic free variables are assumed to take the value
    00533   0, and specifying a superbasic variable is illegal.
    00534
    00535   Field         Definition
    00536   -----         ----------
    00537   ctlopts       Control and status flags.
    00538   phase         (i) If set to dyDONE, dylp will free any retained data
    00539                     structures and return. Any other value is ignored.
    00540                 (o) Termination phase of the dynamic simplex algorithm;
    00541                     should be dyDONE unless something screws up, in which
    00542                     case it'll be dyINV.
    00543   lpret         Return code from the simplex routine.
    00544   obj           For lpOPTIMAL, the value of the objective function.
    00545                 For lpINFEAS, the total infeasibility.
    00546                 For lpUNBOUNDED, the index of the unbounded variable, negated
    00547                   if the variable can decrease without bound, positive if it
    00548                   can increase without bound.
    00549                 Otherwise, undefined.
    00550   iters         The number of simplex iterations.
    00551   consys        The constraint system.
    00552   basis         (i) Initial basis.
    00553                 (o) Final basis.
    00554   status        (i) Initial status vector.
    00555                 (o) Final status vector.
    00556   x             (i) No values used, but a vector can be supplied.
    00557                 (o) The values of the basic variables (indexed by basis
    00558                     position).
    00559   y             (i) No values used, but a vector can be supplied.
    00560                 (o) The values of the dual variables (indexed by basis
    00561                     position).
    00562   actvars       There is one entry for each variable, coded TRUE if the
    00563                 variable is active, FALSE otherwise. The vector supplied on
    00564                 input will be overwritten on output.
    00565                 (i) Variables to be activated at startup. Used only for a
    00566                     warm start. Validity is indicated by the lpctlACTVARSIN
    00567                     flag. A vector can be supplied strictly for output use.
    00568                 (o) The current active variables. Will be returned only if
    00569                     requested by the lpctlACTVARSOUT flag. If the vector is
    00570                     valid on return, lpctlACTVARSOUT will remain set,
    00571                     otherwise it will be reset.
    00572
    00573   colsze        Allocated column capacity (length of status vector).
    00574   rowsze        Allocated row capacity (length of basis, x, and y vectors).
    00575
    00576
    00577   Note that dylp will reallocate status, basis->el, actvars, x, and y, if the
    00578   vectors supplied at startup are too small to report the solution. Don't set
    00579   colsze or rowsze to nonzero values without actually allocating space.
    00580 */
    00581
    00582 typedef struct
    00583 { flags ctlopts ;
    00584   dyphase_enum phase ;
    00585   lpret_enum lpret ;
    00586   double obj ;
    00587   int iters ;
    00588   consys_struct *consys ;
    00589   basis_struct *basis ;
    00590   flags *status ;
    00591   double *x ;
    00592   double *y ;
    00593   bool *actvars ;
    00594   int colsze ;
    00595   int rowsze ; } lpprob_struct ;
    00596
    00597
    00598
    00599 /*
    00600   lptols_struct
    00601
    00602   This structure contains phase and tolerance information for the lp algorithm.
    00603
    00604   The philosophy with respect to the separate zero and feasibility tolerances
    00605   for primal and dual variables is that dylp uses the zero tolerance when
    00606   calculating primal or dual variables, and the feasibility tolerance when
    00607   checking for feasibility. This allows us to keep small values for accuracy
    00608   in computation, but not be so fussy when it comes to feasibility.
    00609
    00610   Field         Definition
    00611   -----         ----------
    00612   inf           Infinity. dylp uses IEEE FP infinity, but be careful not to
    00613                 pass it to the basis package.
    00614   zero          Zero tolerance for primal variables, and also the generic
    00615                 zero tolerance for constraint coefficients, right-hand-side
    00616                 values, etc.
    00617   pchk          Primal accuracy check tolerance.
    00618   pfeas         Primal feasibility check tolerance; dynamically scaled from
    00619                 zero in proportion to the 1-norm of the primal basic variables.
    00620   pfeas_scale   Primal feasibility check tolerance multiplier. This provides
    00621                 some user-controllable decoupling of zero and pfeas.
    00622   cost          Base zero tolerance for checks involving objective function
    00623                 coefficients, reduced costs, and related values.
    00624   dchk          Dual accuracy check tolerance. Also used by dy_duenna to
    00625                 test for improvement in the objective.
    00626   dfeas         Dual feasbility check tolerance; dynamically scaled from cost
    00627                 in proportion to the 1-norm of the dual variables. Acts as the
    00628                 zero tolerance for reduced costs.
    00629   dfeas_scale   Dual feasibility check tolerance multiplier. This provides
    00630                 some user-controllable decoupling of cost and dfeas.
    00631   pivot         Simplex pivot selection tolerance, expressed as a multiplier
    00632                 for the pivot selection tolerance used by the basis package
    00633                 when factoring the basis. (I.e., the actual pivot selection
    00634                 criteria will be to accept a simplex pivot a<i,j> if
    00635                 |a<i,j>| > lptols.pivot*basis.pivot*MAX{i}|a<i,j>|.)
    00636   bogus         Multiplier used to identify 'bogus' values, in the range
    00637                 tol < |val| < bogus*tol for the appropriate tolerance.
    00638   swing         Ratio used to identify excessive growth in primal variables
    00639                 (pseudo-unboundedness).
    00640   toobig        Absolute value of primal variables which will cause dual
    00641                 multipivoting to consider primal infeasibility when selecting
    00642                 a flip/pivot sequence.
    00643   purge         Percentage change in objective function required before
    00644                 constraint or variable purging is attempted.
    00645   purgevar      Percentage of maximum reduced cost used to determine the
    00646                 variable purge threshold; nonbasic architectural variables
    00647                 at their optimum bound whose reduced cost exceeds
    00648                 purgevar*MAX{j}cbar<j> are purged.
    00649
    00650   reframe       Multiplier used to trigger a reference framework reset in
    00651                 PSE pricing; reset occurs if
    00652                   |gamma<j> - ||abar<j>||^2| > reframe*||abar<j>||^2.
    00653                 The check is made in pseupdate.
    00654                 Also used to trigger recalculation of the basis inverse row
    00655                 norms used in DSE pricing; reset occurs if
    00656                   |rho<i> - ||beta<i>||^2| > reframe*||beta<i>||^2.
    00657                 The check is made in dseupdate.
    00658 */
    00659
    00660 typedef struct
    00661 { double inf ;
    00662   double zero ;
    00663   double pchk ;
    00664   double pfeas ;
    00665   double pfeas_scale ;
    00666   double cost ;
    00667   double dchk ;
    00668   double dfeas ;
    00669   double dfeas_scale ;
    00670   double pivot ;
    00671   double bogus ;
    00672   double swing ;
    00673   double toobig ;
    00674   double purge ;
    00675   double purgevar ;
    00676   double reframe ; } lptols_struct ;
    00677
    00678 #if defined(DYLP_INTERNAL) || defined(BONSAIG)
    00679 /*
    00680   A few handy macros for testing values against tolerances.
    00681 */
    00682 #ifdef DYLP_INTERNAL
    00683 #  ifdef BND_TOLER
    00684 #    undef BND_TOLER
    00685 #  endif
    00686 #  define BND_TOLER dy_tols->pfeas
    00687 #  ifdef INF_TOLER
    00688 #    undef INF_TOLER
    00689 #  endif
    00690 #  define INF_TOLER dy_tols->inf
    00691 #endif
    00692
    00693 #define withintol(zz_val_zz,zz_tgt_zz,zz_tol_zz) \
    00694   (fabs((zz_val_zz)-(zz_tgt_zz)) <= zz_tol_zz)
    00695
    00696 #define setcleanzero(zz_val_zz,zz_tol_zz) \
    00697   if (fabs(zz_val_zz) < zz_tol_zz) zz_val_zz = 0
    00698
    00699 #define atbnd(zz_val_zz,zz_bnd_zz) \
    00700   ((fabs(zz_bnd_zz) < INF_TOLER) && \
    00701    (fabs((zz_val_zz)-(zz_bnd_zz)) < BND_TOLER*(1.0+fabs(zz_bnd_zz))))
    00702
    00703 #define belowbnd(zz_val_zz,zz_bnd_zz) \
    00704   ((fabs(zz_bnd_zz) < INF_TOLER) ? \
    00705    (((zz_bnd_zz)-(zz_val_zz)) > BND_TOLER*(1.0+fabs(zz_bnd_zz))) : \
    00706    (zz_val_zz < zz_bnd_zz))
    00707
    00708 #define abovebnd(zz_val_zz,zz_bnd_zz) \
    00709   ((fabs(zz_bnd_zz) < INF_TOLER) ? \
    00710    (((zz_val_zz)-(zz_bnd_zz)) > BND_TOLER*(1.0+fabs(zz_bnd_zz))) : \
    00711    (zz_val_zz > zz_bnd_zz))
    00712
    00713 #define withinbnds(zz_lb_zz,zz_val_zz,zz_ub_zz) \
    00714   (!abovebnd(zz_val_zz,zz_ub_zz) && !belowbnd(zz_val_zz,zz_lb_zz))
    00715
    00716 #endif /* DYLP_INTERNAL || BONSAIG */
    00717
    00718 #ifdef DYLP_INTERNAL
    00719 /*
    00720   Finally, a macro to decide if we should snap to a value. The notion here is
    00721   that the accuracy with which one can hit a target value depends on both the
    00722   magnitude of the target and the distance travelled to get there. On a
    00723   64-bit machine, IEEE FP has about 15 decimal digits of accuracy. For
    00724   example, if we're travelling 1.0e7 and trying to hit zero, we only have 8
    00725   decimal places of accuracy remaining. If we're within 1.0e-8, might as well
    00726   snap to 0. In practice, there's already a bit of roundoff in any nontrivial
    00727   calculation, so we start with the zero tolerance and scale from there.
    00728
    00729   In some cases, we only know the target, so the best we can do is
    00730   scale to it.
    00731
    00732   The utility of this idea is highly questionable.
    00733 */
    00734
    00735 #define snaptol1(zz_tgt_zz) (dy_tols->zero*(1.0+(zz_tgt_zz)))
    00736
    00737 #define snaptol2(zz_tgt_zz,zz_dst_zz) \
    00738   (dy_tols->zero*(1.0+maxx((zz_tgt_zz),(zz_dst_zz))))
    00739
    00740 #define snaptol3(zz_tol_zz,zz_tgt_zz,zz_dst_zz) \
    00741   ((zz_tol_zz)*(1.0+maxx((zz_tgt_zz),(zz_dst_zz))))
    00742
    00743 #endif /* DYLP_INTERNAL */
    00744
    00745
    00746
    00747 /*
    00748   Enum for initial basis type.
    00749
    00750   This determines the criteria used to select the initial set of basic
    00751   variables during a cold start.
    00752
    00753   ibINV         invalid
    00754   ibLOGICAL     Use only logical (slack and artificial) variables
    00755   ibSLACK       Use slack variables for inequalities. Prefer architectural
    00756                 over artificial variables for equalities.
    00757   ibARCH        Prefer architectural variables over logical variables.
    00758 */
    00759
    00760 typedef enum { ibINV = 0, ibLOGICAL, ibSLACK, ibARCH } ibtype_enum ;
    00761
    00762 /*
    00763   Enum for calling context.
    00764
    00765   As dylp evolves, it may well prove useful to know the context of the
    00766   call. Consider this an experiment. The default context is INITIALLP.
    00767
    00768   cxINV         invalid (context is unknown)
    00769   cxSINGLELP    This is a one-off call to solve a single LP from scratch.
    00770   cxINITIALLP   This is a call to solve a single LP from scratch, but will
    00771                 likely be followed by calls to reoptimise.
    00772   cxBANDC       This call is made in the context of a branch-and-cut
    00773                 algorithm.
    00774 */
    00775
    00776 typedef enum { cxINV = 0, cxSINGLELP, cxINITIALLP, cxBANDC } cxtype_enum ;
    00777
    00778 /*
    00779   lpopts_struct
    00780
    00781   This structure is used to pass option settings to dylp. Default values are
    00782   declared at the beginning of dy_setup.c.
    00783
    00784   Field         Definition
    00785   -----         ----------
    00786   context       The context in which dylp is being called. See comments
    00787                 above for cxtype_enum.
    00788   forcecold     TRUE to force a cold start, FALSE otherwise. If set to TRUE,
    00789                 dominates warm and hot start.
    00790   forcewarm     TRUE to force a warm start, FALSE otherwise. If set to TRUE,
    00791                 dominates hot start.
    00792   fullsys       Forces the use of the full constraint system at all times. The
    00793                 full constraint system is loaded on startup, and all constraint
    00794                 and variable deactivation/activation is skipped. (But see the
    00795                 finpurge option below.) (Also, this will not prevent dylp
    00796                 from resorting to forced phase transitions, which typically
    00797                 involve deactivation of constraints or variables. Arguably
    00798                 this is a bad thing, and may change in the future.)
    00799   active        Used to estimate the initial size of the dylp constraint
    00800                 system relative to the original system.
    00801     vars          Fraction of original variables expected to be active at
    00802                   any time.
    00803     cons          Fraction of original inequalities expected to be active at
    00804                   any time.
    00805   initcons      Specifies how inequalities will be selected to initialize the
    00806                 active system. See extensive comments in dy_coldstart.c.
    00807     frac          Fraction of inequalities to be used.
    00808     i1l           Lower bound on angle to objective, first interval
    00809     i1lopen       TRUE if the bound is open.
    00810     i1u           Upper bound on angle to objective, first interval
    00811     i1uopen       TRUE if the bound is open.
    00812     i2valid       TRUE if the second interval is specified
    00813     i2l           Lower bound on angle to objective, second interval
    00814     i2lopen       TRUE if the bound is open.
    00815     i2u           Upper bound on angle to objective, second interval
    00816     i2uopen       TRUE if the bound is open.
    00817   coldbasis     Code specifying the kind of basis built for a cold start. See
    00818                 comments for ibtype_enum and comments in dy_coldstart.c
    00819   finpurge      Controls whether dylp does a final deactivation of constraints
    00820                 and/or variables. This will occur only an optimal solution is
    00821                 found, and is not suppressed by fullsys.
    00822     cons          TRUE to purge constraints
    00823     vars          TRUE to purge variables
    00824   heroics       Controls behaviour during forced primal <-> dual transitions
    00825     d2p           TRUE to allow deactivation of basic architecturals, FALSE
    00826                   to disallow. FALSE is recommended, and the default.
    00827     p2d           TRUE to allow deactivation of tight constraints, FALSE
    00828                   to disallow. FALSE is recommended, and the default.
    00829     flip          TRUE to allow flips to regain dual feasibility, FALSE to
    00830                   disallow. Tends to cycle; default is false.
    00831   coldvars      If the number of active variables exceeds this value after
    00832                 a cold start, dylp will attempt to purge variables prior to
    00833                 the initial primal simplex run.
    00834   con           Options related to constraint activation/deactivation
    00835     actlvl        The constraint activation strategy
    00836                     0: (strict) activate violated constraints,
    00837                        lhs < rhslow or lhs > rhs
    00838                     1: (tight) activate tight or violated constraints,
    00839                        lhs <= rhslow or lhs >= rhs
    00840     actlim        If non-zero, limits the number of constraints that can be
    00841                   activated in any one call to a constraint activation
    00842                   routine.
    00843     deactlvl    The constraint deactivation strategy:
    00844                   0: (normal) deactivate only inequalities i which are
    00845                      strictly loose (i.e., slk<i> basic, not at bound).
    00846                   1: (aggressive) normal plus inequalities which are tight
    00847                      with y<i> = 0.
    00848                   2: (fanatic) aggressive plus equalities with y<i> = 0
    00849   usedual       TRUE if dual phase II is to be used to regain feasibility after
    00850                 adding constraints, FALSE to force use of primal phase I.
    00851   addvar        If non-zero, at most this many variables will be added in
    00852                 any one pass through phase dyADDVAR.
    00853   dualadd       Controls the types of activation allowed when adding variables
    00854                 during dual simplex.
    00855                   0:    variable activation is disallowed
    00856                   1:    type 1 activation (variables that will be dual feasible
    00857                         when activated into the nonbasic partition)
    00858                   2:    type 2 activation (variables which can be activated
    00859                         if immediately pivoted into the basis)
    00860                   3:    type 3 activation (activate with bound-to-bound pivot)
    00861                 See dy_dualaddvars for more extensive comments.
    00862   scan          Partial pricing parameter. Controls the number of columns to
    00863                 be scanned for a new candidate entering variable when the
    00864                 candidate selected during PSE update is rejected.
    00865   iterlim       The per phase pivot limit for the code; if set to 0, no
    00866                 limit is enforced.
    00867   idlelim       The number of iterations without change in the objective
    00868                 function before the code declares the problem is stalled or
    00869                 cycling.
    00870   dpsel         Options to control dual pivoting. Selection of the leaving
    00871                 variable is always handled by DSE.
    00872     strat:        The strategy used to select the entering variable:
    00873                     0: standard ratio test; may use anti-degen lite
    00874                     1: multipivoting, selecting for maximum dual objective
    00875                        improvement.
    00876                     2: multipivoting, select for minimum predicted
    00877                        infeasibility.
    00878                     3: multipivoting, select infeasibility reduction if
    00879                        possible, otherwise maximum dual objective improvement.
    00880     flex          If TRUE, dylp will switch between strategies 1 and 3, using
    00881                   strategy 1 unless primal magnitudes become too large.
    00882     allownopiv    If TRUE, sequences of flips with no finishing pivot will be
    00883                   allowed. Defaults to false, very prone to cycling.
    00884   ppsel         Options to control primal pivoting. Selection of the entering
    00885                 variable is always handled by PSE.
    00886     strat:        The strategy used to select the leaving variable:
    00887                     0: standard ratio test; may use anti-degen lite
    00888                     1: multipivoting
    00889   factor        The LP basis will be refactored every factor iterations, in
    00890                 the absence of some compelling reason (typically error
    00891                 recovery) that forces it to occur sooner.
    00892   check         An accuracy check will be forced every check iterations, in
    00893                 the absence of some compelling reason to do it earlier.
    00894   groom         Controls the action taken by the basis grooming routine
    00895                 when it makes a nontrivial status correction:
    00896                   0:    catatonic
    00897                   1:    issue a warning
    00898                   2:    issue an error message and force an abort
    00899                 Numeric codes are related to keywords in dy_setup.c:dy_ctlopt.
    00900   degen         TRUE to allow creation of restricted subproblems to deal with
    00901                 degeneracy, FALSE to disallow it.
    00902   degenpivlim   The number of successive degenerate pivots required before
    00903                 creating a restricted subproblem.
    00904   degenlite     Controls secondary antidegeneracy --- `antidegen lite'
    00905                   0: (pivotabort) break ties using |abar<kj>| and abort when
    00906                      delta<j> = 0
    00907                   1: (pivot) break ties using |abar<kj>| but always scan the
    00908                      full basis
    00909                   2: (alignobj) break ties by examining the alignment of the
    00910                      hyperplane which will become tight on the pivot; choose
    00911                      so that movement in the direction of the objective most
    00912                      nearly lies in the hyperplane
    00913                   3: (alignedge) break ties by examining the alignment of the
    00914                      hyperplane which will become tight on the pivot; choose
    00915                      so that the direction of motion defined by the entering
    00916                      variable most nearly lies in the hyperplane.
    00917                   4: (perpobj) break ties by examining the alignment of the
    00918                      hyperplane which will become tight on the pivot; choose
    00919                      so that the normal of the hyperplane is most nearly
    00920                      aligned with the normal of the objective
    00921                   5: (perpedge) break ties by examining the alignment of the
    00922                      hyperplane which will become tight on the pivot; choose
    00923                      so that the normal of the hyperplane is most nearly
    00924                      aligned with the direction of motion
    00925                 Numeric codes are related to keywords in dy_setup.c:dy_ctlopt.
    00926   patch         TRUE to allow the code to patch a singular basis, FALSE to
    00927                 prevent patching.
    00928   copyorigsys   Controls whether dylp makes a local copy of the original
    00929                 system. If set to TRUE, dylp will always make a local copy.
    00930                 If set to FALSE, a copy will be made only if necessary.
    00931                 Scaling will trigger a local copy.
    00932   scaling       Controls whether dylp attempts to scale the original constraint
    00933                 system.
    00934                   0: scaling is forbidden
    00935                   1: scale the original constraint system using scaling vectors
    00936                      attached to the system
    00937                   2: evaluate the original constraint system and scale it if
    00938                      necessary
    00939   print         Substructure for picky printing control. For all print options,
    00940                 a value of 0 suppresses all information messages.
    00941     major         Controls printing of major phase information.
    00942                   1: a message at each phase transition.
    00943     scaling       Controls print level during initial evaluation and scaling of
    00944                   the original constraint system.
    00945                   1: start and finish messages
    00946                   2: stability measures for original and scaled matrices;
    00947                      adjustments to tolerances.
    00948     setup         Controls print level while creating the initial constraint
    00949                   system for dylp.
    00950                   1: start and finish messages.
    00951                   2: summary information about activated constraints
    00952                   3: messages about each constraint included in the initial
    00953                      system.
    00954                   4: messages about each constraint processed for the initial
    00955                      system
    00956                   5: messages about each variable included in the initial
    00957                      system.
    00958                   6: lists value and status of inactive variables with
    00959                      nonzero values
    00960     crash         Controls print level while crashing the basis.
    00961                   1: start & finish messages
    00962                   2: summary counts for logicals, architecturals, artificials
    00963                   3: a dump of the completed basis
    00964                   4: detailed info on the selection of each architectural
    00965                      and artificial variable
    00966     pricing       Controls print level for pricing of columns (rows) in primal
    00967                   (dual) simplex.
    00968                   1: summary messages
    00969                   2: lists candidate list and primal variable selected for
    00970                      entry (exit) at each pivot
    00971                   3: lists each variable as it's added to the candidate list
    00972                      and again when reconsidered for pivoting
    00973     pivoting      Controls print level for selection of the leaving (entering)
    00974                   primal variable in primal (dual) simplex and updating of
    00975                   variables.
    00976                   1: prints result of leaving (entering) variable selection
    00977                   2: information about the selection of the leaving (entering)
    00978                      variable.
    00979                   3: more information about the selection of the leaving
    00980                      (entering) variable.
    00981                   4: prints the pivot column (row) before and after
    00982                      multiplication by the basis inverse, and yet more
    00983                      pivot selection information.
    00984                   5: prints a line for every candidate evaluated
    00985     pivreject     Controls print level for information related to the operation
    00986                   of the pivot rejection mechanism.
    00987                   1: Prints a message for each row/column added to the pivot
    00988                      rejection list, plus other major events.
    00989                   2: Prints a message for each row/column removed from the
    00990                      pivot rejection list.
    00991     degen         Controls print level for information related to the operation
    00992                   of the antidegeneracy mechanism.
    00993                   1: prints a message each time the antidegeneracy level
    00994                      changes
    00995                   2: prints a message when a true degenerate pivot is taken
    00996                      under duress
    00997                   3: prints a message when a degenerate pivot is taken
    00998                   4: prints anomalies as each degenerate set is formed and
    00999                      backed out
    01000                   5: prints details of each degenerate set as it's formed and
    01001                      backed out
    01002     phase1        Controls general print level for phase 1 of primal simplex.
    01003                   1: messages about extraordinary events -- problem pivots, etc.
    01004                   2: messages about 'routine' but infrequent events --
    01005                      termination conditions, refactoring, unboundedness, etc.
    01006                   3: messages with additional details of problems encountered
    01007                   4: a one line log message is printed for each pivot
    01008                   5: summary information about infeasible variables and phase
    01009                      I objective coefficients; information about primal
    01010                      variables updated at each pivot.
    01011                   6: prints the primal variables after each pivot; prints
    01012                      infeasible variables during phase I objective construction
    01013                   7: prints the dual variables after each pivot; prints
    01014                      infeasible variables during phase I objective modification
    01015     phase2        Controls general print level for phase 1 of primal simplex.
    01016                   1: messages about extraordinary events -- problem pivots, etc.
    01017                   2: messages about 'routine' but infrequent events --
    01018                      termination conditions, refactoring, unboundedness, etc.
    01019                   3: messages with additional details of problems encountered
    01020                   4: a one line log message is printed for each pivot
    01021                   5: prints the updated basic primal variables after each pivot
    01022                   6: prints all basic primal variables after each pivot
    01023                   7: prints the dual variables after each pivot.
    01024     dual          Controls general print level for the dual simplex. As
    01025                   phase2.
    01026     basis         Controls print level in routines working with the basis.
    01027                   1: summary warnings about problems: empty rows, singularity,
    01028                      numerical instability, etc.
    01029                   2: information about factoring failures and recovery actions
    01030                   3: warnings about individual empty rows, details of column
    01031                      replacement when patching a singular basis, pivot
    01032                      tolerance adjustments; information about pivoting failures
    01033                      and recovery actions
    01034                   4: basis stability after factoring
    01035                   5: basis stability after pivoting
    01036     conmgmt       Controls print level while dylp is in the purge/generate/
    01037                   activate constraint phases.
    01038                   1: prints the number of constraints purged, generated,
    01039                      & activated, and new size of constraint system.
    01040                   2: prints a message for each constraint purged or activated.
    01041                      (The cut generation routine is responsible for
    01042                      handling this function when it generates cuts.)
    01043                   3: additional details about refactoring and new values
    01044                      of primal and dual variables.
    01045                   4: prints a message about any variables affected as a side
    01046                      effect of constraint changes, constraints processed
    01047                      but not activated, and information about direction of
    01048                      recession and relative angle of constraints when adding
    01049                      constraints to an unbounded problem.
    01050                   5: prints a running commentary on constraint and variable
    01051                      shifts, inactive variables.
    01052     varmgmt       Controls print level while dylp is in the purge/generate/
    01053                   activate variable phases.
    01054                   1: prints the number of variables purged, generated,
    01055                      & activated, and new size of constraint system.
    01056                   2: prints a message for each variable purged & activated.
    01057                      (The column generation routine is responsible for
    01058                      handling this function when it generates new variables).
    01059                   3: prints a message about any constraints affected as a side
    01060                      effect of variable changes, variables processed but not
    01061                      activated, and information about direction of recession
    01062                      and relative angle of dual constraints when adding
    01063                      variables to an unbounded dual.
    01064                   4: prints a running commentary on constraint and variable
    01065                      shifts.
    01066     force         Controls print level when dylp is attempting to force a
    01067                   transition (primal -> dual, dual -> primal) or force the
    01068                   use of the full constraint system.
    01069                   1: prints a summary message giving the result of the
    01070                      transition attempt
    01071                   2: prints messages about actions taken for individual
    01072                      constraints and variables.
    01073                   3: additional information about variables and constraints
    01074                      examined.
    01075 */
    01076
    01077 typedef struct
    01078 { cxtype_enum context ;
    01079   int scan ;
    01080   int iterlim ;
    01081   int idlelim ;
    01082   struct { int strat ;
    01083            bool flex ;
    01084            bool allownopiv ; } dpsel ;
    01085   struct { int strat ; } ppsel ;
    01086   int factor ;
    01087   int check ;
    01088   int groom ;
    01089   struct { int actlvl ;
    01090            int actlim ;
    01091            int deactlvl ; } con ;
    01092   int addvar ;
    01093   int dualadd ;
    01094   int coldvars ;
    01095   bool forcecold ;
    01096   bool forcewarm ;
    01097   bool usedual ;
    01098   bool degen ;
    01099   int degenpivlim ;
    01100   int degenlite ;
    01101   bool patch ;
    01102   bool fullsys ;
    01103   bool copyorigsys ;
    01104   int scaling ;
    01105   struct { float vars ;
    01106            float cons ; } active ;
    01107   struct { double frac ;
    01108            bool i1lopen ;
    01109            double i1l ;
    01110            bool i1uopen ;
    01111            double i1u ;
    01112            bool i2valid ;
    01113            bool i2lopen ;
    01114            double i2l ;
    01115            bool i2uopen ;
    01116            double i2u ; } initcons ;
    01117   ibtype_enum coldbasis ;
    01118   struct { bool cons ;
    01119            bool vars ; } finpurge ;
    01120   struct { bool d2p ;
    01121            bool p2d ;
    01122            bool flips ; } heroics ;
    01123   struct { int major ;
    01124            int scaling ;
    01125            int setup ;
    01126            int crash ;
    01127            int pricing ;
    01128            int pivoting ;
    01129            int pivreject ;
    01130            int degen ;
    01131            int phase1 ;
    01132            int phase2 ;
    01133            int dual ;
    01134            int basis ;
    01135            int conmgmt ;
    01136            int varmgmt ;
    01137            int force ; } print ; } lpopts_struct ;
    01138
    01139
    01140
    01141
    01142 /*
    01143   Statistics structure, used to collect information about aspects of dylp
    01144   operation beyond simple pivot counts. The data structure definition is
    01145   always present, but to fill it you have to define DYLP_STATISTICS.
    01146
    01147   Field         Definition
    01148   -----         ----------
    01149   phasecnts[dyDONE] Array with counts for number of times each phase is
    01150                 executed.
    01151   ini_simplex   The initial simplex phase
    01152   cons          A set of arrays with data about individual constraints.
    01153     sze           Allocated capacity of the arrays.
    01154     angle         Angle to the objective function.
    01155     actcnt        Number of times constraint is activated.
    01156     deactcnt      Number of times constraint is deactivated.
    01157     init          True if constraint is active in initial system.
    01158     fin           True if constraint is active in final system.
    01159   vars          A set of arrays with data about individual variables.
    01160     sze           Allocated capacity of the arrays.
    01161     actcnt        Number of times variable is activated.
    01162     deactcnt      Number of times variable is deactivated.
    01163   angle
    01164     max         Maximum angle to the objective function over all constraints.
    01165     min         Minimum angle to the objective function over all constraints.
    01166     hist[*]     Histogram of angles of constraints to the objective function.
    01167                 There are DYSTATS_HISTBINS bins. Currently, 37 bins: 36 bins
    01168                 spanning 5 degrees of angle, and a dedicated 90 degree bin.
    01169
    01170   factor        Tracks how well we're doing with respect to refactoring the
    01171                 basis.
    01172     cnt         Number of time the basis has been refactored.
    01173     prevpiv     Pivot count at last refactorisation.
    01174     avgpivs     Average number of pivots between basis refactorisations.
    01175     maxpivs     Maximum number of pivots between basis refactorisations.
    01176
    01177   pivrej        Statistics about the pivot rejection list and punts.
    01178     max           maximum number of entries on the pivot rejection list
    01179     mad           total number of entries attributed to mad pivots
    01180     sing          total number of entries attributed to singular pivots
    01181     pivtol_red    total number of times the pivot tolerance was reduced
    01182     min_pivtol    the minimum pivot tolerance used
    01183     puntcall      total number of calls to dealWithPunt
    01184     puntret       total number of dyrPUNT returns recommended
    01185
    01186   dmulti        Tracks the dual multipivot algorithm. All fields except cnt are
    01187                 totals; divide by cnt to get averages.
    01188     flippable     Number of flippable variables in the constraint system.
    01189     cnt           Total calls to dualmultiin
    01190     cands         Number of candidates queued for evaluation for entry
    01191     promote       Number of calls that resulted in promoting a sane pivot
    01192                   over an unstable pivot.
    01193     nontrivial    Number of times that the initial scan and sort left
    01194                   multiple candidates for further evaluation.
    01195     evals         Actual number of candidates evaluated (ftran'd column)
    01196     flips         Number of bound-to-bound flips performed
    01197     pivrnk        Index in the list of candidates of the candidate finally
    01198                   selected for pivoting.
    01199     maxrnk        Maximum index selected for pivoting.
    01200
    01201   pmulti        Tracks the primal multipivot algorithm.
    01202     cnt           Total calls to primalmultiin
    01203     cands         Number of candidates queued for evaluation to leave
    01204     nontrivial    Number of times that the candidate list was sorted
    01205     promote       Number of calls that resulted in promoting a sane pivot
    01206                   over an unstable pivot.
    01207
    01208   infeas        Statistics on resolution of infeasibility in primal phase I.
    01209                 Basically, what we're interested in tracking is the number
    01210                 of infeasible variables and the number of pivots between a
    01211                 change in the number of infeasible variables. We're interested
    01212                 in separating the case of 1 variable from 2 or more, because
    01213                 the latter requires vastly more calculation. A little care
    01214                 is required because phase I can run many times.
    01215
    01216     prevpiv     The pivot count (tot.iters) at the previous change.
    01217     maxcnt      The maximum number of infeasible variables encountered (this
    01218                 is not strictly monotonic, as dylp may enter phase I many
    01219                 times due to activating violated constraints).
    01220     totpivs     The total number of pivots expended in phase I.
    01221     maxpivs     The maximum number of pivots with no change in the number of
    01222                 feasible variables.
    01223     chgcnt1     The number of times that the number of infeasible variables
    01224                 changed and reduced costs did not have to be recalculated
    01225                 (specifically, exactly one variable became feasible, and it
    01226                 left the basis as it did so).
    01227     chgcnt2     The number of times that the number of infeasible variables
    01228                 changed in such a way as to require recalculation of the
    01229                 reduced costs.
    01230
    01231   [dp]degen[*]  Array of stats for each restricted subproblem nesting level,
    01232                 with separate arrays for dual (ddegen) and primal (pdegen).
    01233                 degen[0].cnt is used to hold the maximum nesting level.
    01234     cnt         Number of times this nesting level was entered.
    01235     avgsiz      The average number of variables in a restricted subproblem.
    01236                 Kept by iterative update, as avg<k+1> = (avg<k>*k+size)/(k+1).
    01237                 Suffers from cumulative loss of accuracy, but it'll do for
    01238                 our purposes.
    01239     maxsiz      The maximum number of variables in a restricted subproblem.
    01240     totpivs     Total number of pivots at or above this nesting level.
    01241     avgpivs     Average number of pivots at or above this nesting level.
    01242     maxpivs     Maximum number of pivots for any one instance at or above
    01243                 this nesting level.
    01244
    01245   tot, p1, p2, d2       Iteration and pivot counts, total and for each
    01246                         individual phase. These are copied over from
    01247                         dy_lp (lp_struct) at the end of the run, so that
    01248                         they can be printed by dumpstats.
    01249
    01250   DYSTATS_MAXDEGEN is the maximum number of levels of nesting accommodated by
    01251   antidegeneracy statistics and debugging structures. The actual algorithm
    01252   has no inherent limitation.
    01253
    01254   DYSTATS_HISTBINS is the number of bins for constraint angles. It should be an
    01255   odd number. Each bin will span 180/(DYSTATS_HISTBINS-1) degrees, with the
    01256   final bin reserved for constraints at 90 degrees. For example, a value of 37
    01257   gives 180/(37-1) = 5 degrees per bin.
    01258 */
    01259
    01260 #define DYSTATS_MAXDEGEN 25
    01261 #define DYSTATS_HISTBINS 37
    01262
    01263 typedef struct {
    01264   int phasecnts[dyDONE+1] ;
    01265   dyphase_enum ini_simplex ;
    01266   struct { int sze ;
    01267            double *angle ;
    01268            int *actcnt ;
    01269            int *deactcnt ;
    01270            bool *init ;
    01271            bool *fin ; } cons ;
    01272   struct { int sze ;
    01273            int *actcnt ;
    01274            int *deactcnt ; } vars ;
    01275   struct { float max ;
    01276            float min ;
    01277            int hist[DYSTATS_HISTBINS] ; } angle ;
    01278   struct { int cnt ;
    01279            int prevpiv ;
    01280            float avgpivs ;
    01281            int maxpivs ; } factor ;
    01282   struct { int max ;
    01283            int mad ;
    01284            int sing ;
    01285            int pivtol_red ;
    01286            double min_pivtol ;
    01287            int puntcall ;
    01288            int puntret ; } pivrej ;
    01289   struct { int flippable ;
    01290            int cnt ;
    01291            int cands ;
    01292            int promote ;
    01293            int nontrivial ;
    01294            int evals ;
    01295            int flips ;
    01296            int pivrnks ;
    01297            int maxrnk ; } dmulti ;
    01298   struct { int cnt ;
    01299            int cands ;
    01300            int nontrivial ;
    01301            int promote ; } pmulti ;
    01302   struct { int prevpiv ;
    01303            int maxcnt ;
    01304            int totpivs ;
    01305            int maxpivs ;
    01306            int chgcnt1 ;
    01307            int chgcnt2 ; } infeas ;
    01308   struct { int cnt ;
    01309            float avgsiz ;
    01310            int maxsiz ;
    01311            int totpivs ;
    01312            float avgpivs ;
    01313            int maxpivs ; } pdegen[DYSTATS_MAXDEGEN] ;
    01314   struct { int cnt ;
    01315            float avgsiz ;
    01316            int maxsiz ;
    01317            int totpivs ;
    01318            float avgpivs ;
    01319            int maxpivs ; } ddegen[DYSTATS_MAXDEGEN] ;
    01320   struct { int iters ;
    01321            int pivs ; } tot ;
    01322   struct { int iters ;
    01323            int pivs ; } p1 ;
    01324   struct { int iters ;
    01325            int pivs ; } p2 ;
    01326   struct { int iters ;
    01327            int pivs ; } d2 ; } lpstats_struct ;
    01328
    01329
    01330
    01331 #ifdef DYLP_INTERNAL
    01332
    01333 /*
    01334   Macros to determine whether a constraint or variable is active, and whether
    01335   it's eligible for activation. Coding is explained below for dy_origcons and
    01336   dy_origvars. The main purpose served by these macros is to make it easy to
    01337   find activiation/deactivation points in the code, should the conventions ever
    01338   change.
    01339 */
    01340
    01341 #define ACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] > 0)
    01342 #define INACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] <= 0)
    01343 #define LOADABLE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] == 0)
    01344 #define MARK_UNLOADABLE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] = -1)
    01345 #define MARK_INACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] = 0)
    01346
    01347 #define ACTIVE_VAR(zz_vndx_zz) (dy_origvars[(zz_vndx_zz)] > 0)
    01348 #define INACTIVE_VAR(zz_vndx_zz) (dy_origvars[(zz_vndx_zz)] <= 0)
    01349 #define LOADABLE_VAR(zz_vndx_zz) \
    01350   ((dy_origvars[(zz_vndx_zz)] < 0) && \
    01351    flgoff(((flags) -dy_origvars[(zz_vndx_zz)]),vstatNOLOAD|vstatNBFX))
    01352 #define MARK_INACTIVE_VAR(zz_vndx_zz,zz_val_zz) \
    01353   (dy_origvars[(zz_vndx_zz)] = (zz_val_zz))
    01354
    01355
    01356 /*
    01357   dy_logchn             i/o id for the execution log file
    01358   dy_gtxecho            controls echoing of generated text to stdout
    01359 */
    01360
    01361 extern ioid dy_logchn ;
    01362 extern bool dy_gtxecho ;
    01363
    01364
    01365 /*
    01366   lp_struct
    01367
    01368   This structure is the control structure for an LP problem within dylp.
    01369
    01370   Field         Definition
    01371   -----         ----------
    01372   phase         Current phase of the dynamic simplex algorithm.
    01373   lpret         Return code from the most recent simplex execution.
    01374
    01375   z             Value of the objective function (includes inactzcorr).
    01376   inactzcorr    Correction to the objective function due to inactive variables
    01377                 with non-zero values.
    01378
    01379   simplex       Simplex algorithm status and control
    01380     active        currently active or most recently completed
    01381     next          currently active or to be started
    01382     init_pse      TRUE if the PSE structures need to be reinitialised,
    01383                   FALSE otherwise
    01384     init_dse      TRUE if the DSE structures need to be reinitialised,
    01385                   FALSE otherwise
    01386                 These fields are used to determine when to update or
    01387                 reinitialise the PSE and DSE data structures. Active and next
    01388                 must be valid during the purge/gen/add variable/constraint
    01389                 cycles.
    01390
    01391                 A word on infeas and infeascnt: They are guaranteed accurate
    01392                 only immediately after initialisation and following a primal
    01393                 feasibility check.
    01394
    01395   infeas        Total infeasibility = SUM{j} max(0,x<j>-ub<j>,lb<j>-x<j>)
    01396   infeascnt     The number of infeasible variables; refreshed when dy_accchk
    01397                 is asked to do a primal feasibility check.
    01398
    01399   ubnd          Substructure for information on unbounded or pseudo-unbounded
    01400                 problems.
    01401     ndx           The index of the variable fingered for causing unboundedness
    01402                   or pseudo-unboundedness (swing).
    01403     ratio         The growth ratio.
    01404
    01405   p1obj         The following fields relate to handling of the phase I
    01406                 objective function.
    01407     installed   TRUE if the phase I objective is currently installed
    01408     infcnt      Tracks the number of variables incorporated in p1obj which
    01409                 remain infeasible.
    01410     infvars_sze Allocated size of the infvars vector.
    01411     infvars     Vector of indices of infeasible variables incorporated in the
    01412                 phase I objective.
    01413     p1obj       Pointer to the phase I objective (temporary storage while
    01414                 the phase II objective is installed).
    01415     p2obj       Pointer to the phase II objective (temporary storage while
    01416                 the phase I objective is installed).
    01417
    01418                 A word on pivot and iteration counts: Iteration counts tally
    01419                 iterations of the pivoting loop, successful or not. Pivot
    01420                 counts tally successful bound-to-bound or change-of-basis
    01421                 pivots. Pretty much all messages will give tot.iters, so that
    01422                 it's possible to track the progress of an LP. Iterf has an
    01423                 entirely different function -- it's tracking the accumulation
    01424                 of eta matrices in the basis representation.
    01425
    01426   sys           Substructure for dynamic system modification status.
    01427     forcedfull    Set to TRUE if the full system has been forced in state
    01428                   dyFORCEFULL. This should happen at most once, so if we
    01429                   enter dyFORCEFULL and forcedfull == TRUE, it's fatal.
    01430     cons
    01431       loadable    Count of constraints which could be activated
    01432       unloadable  Count of constraints which are ineligible for activation
    01433                   (empty constraints and nonbinding rows)
    01434     vars
    01435       loadable    Count of variables which could be activated
    01436       unloadable  Count of variables which are ineligible for activation
    01437                   (nonbasic fixed)
    01438
    01439   tot           Total simplex iterations and pivots, all phases
    01440     iters
    01441     pivs
    01442   p1            Primal phase I iterations and pivots.
    01443     iters
    01444     pivs
    01445   p2            Primal phase II iterations and pivots.
    01446     iters
    01447     pivs
    01448   d2            Dual phase II iterations and pivots.
    01449     iters
    01450     pivs
    01451
    01452   pivok         Set to TRUE in dy_{primal|dual}pivot if the current iteration
    01453                 is a  successful pivot. Cleared to FALSE at the head of
    01454                 dy_duenna.
    01455   prev_pivok    Set to pivok at head of dy_duenna. Provides status of just
    01456                 completed pivot for post-Duenna decisions.
    01457
    01458   basis         Various fields related to basis change, refactoring, etc.
    01459
    01460     etas        The number of basis changes (hence eta matrices) since the
    01461                 the basis was last factored. Used to schedule periodic
    01462                 factoring of the basis. Reset to 0 each time the basis is
    01463                 factored.
    01464     pivs        The number of basis pivots since entry into a primal or dual
    01465                 simplex phase (excludes bound-to-bound simplex `pivots').
    01466                 Used when deciding whether to remove variables from the pivot
    01467                 reject list, and whether to pop out of a simplex phase due to
    01468                 excessive swing.
    01469     dinf        Number of successive refactors with dual infeasibility.
    01470                 Cleared at the start of a simplex phase.
    01471                 Incremented/cleared in dy_accchk iff a dual feasibility check
    01472                 is performed.
    01473
    01474   degen         Activation level of antidegeneracy algorithm. Held at 0 when
    01475                 the antidegeneracy algorithm is not active. Incremented each
    01476                 time a restricted subproblem is formed, and decremented when
    01477                 the restriction is backed out. (Values > 1 indicate that
    01478                 degeneracy recurred while working on a restricted subproblem,
    01479                 resulting in further restriction.)
    01480   degenpivcnt   The number of successive degenerate pivots.
    01481
    01482   idlecnt       The number of cycles since the objective has changed.
    01483
    01484   lastz         Previous objective value for various activities; used to
    01485                 detect and suppress loops.
    01486     piv           Objective at last pivot (detects stalling)
    01487     cd            Objective at last entry into constraint deactivation
    01488                   (dyPURGECON) (detects constraint activate/deactivate loops)
    01489     vd            Objective at last entry into variable deactivation
    01490                   (dyPURGEVAR) (detects variable activate/deactivate loops)
    01491     fp            Objective at last entry into force primal (dyFORCEPRIMAL)
    01492                   (detects constraint activate/deactivate loops)
    01493     fd            Objective at last entry into force dual (dyFORCEDUAL)
    01494                   (detects variable activate/deactivate loops)
    01495
    01496   prim          Primal variable information
    01497     norm1         1-norm of basic primal variables inv(B)b
    01498     norm2         2-norm of basic primal variables
    01499     max           inf-norm (max) of basic primal variables
    01500     maxndx        index of max primal variable
    01501
    01502   dual          Dual variable information
    01503     norm1         1-norm of dual variables c<B>inv(B)
    01504     norm2         2-norm of dual variables
    01505     max           inf-norm (max) of dual variables
    01506     maxndx        index of max dual variable
    01507
    01508 */
    01509
    01510 typedef struct
    01511 { dyphase_enum phase ;
    01512   lpret_enum lpret ;
    01513   double z ;
    01514   double inactzcorr ;
    01515   struct { dyphase_enum active ;
    01516            dyphase_enum next ;
    01517            bool init_pse ;
    01518            bool init_dse ; } simplex ;
    01519   double infeas ;
    01520   int infeascnt ;
    01521   struct { int ndx ;
    01522            double ratio ; } ubnd ;
    01523   struct { bool installed ;
    01524            int infcnt ;
    01525            int infvars_sze ;
    01526            int *infvars ;
    01527            double *p1obj ;
    01528            double *p2obj ; } p1obj ;
    01529   struct { struct { int loadable ;
    01530                     int unloadable ; } cons ;
    01531            struct { int loadable ;
    01532                     int unloadable ; } vars ;
    01533            bool forcedfull ; } sys ;
    01534   struct { int iters ;
    01535            int pivs ; } tot ;
    01536   struct { int iters ;
    01537            int pivs ; } p1 ;
    01538   struct { int iters ;
    01539            int pivs ; } p2 ;
    01540   struct { int iters ;
    01541            int pivs ; } d2 ;
    01542   bool pivok ;
    01543   bool prev_pivok ;
    01544   struct { int etas ;
    01545            int pivs ;
    01546            int dinf ; } basis ;
    01547   int degen ;
    01548   int degenpivcnt ;
    01549   int idlecnt ;
    01550   struct { double piv ;
    01551            double cd ;
    01552            double vd ;
    01553            double fp ;
    01554            double fd ; } lastz ;
    01555   struct { double norm1 ;
    01556            double norm2 ;
    01557            double max ;
    01558            int maxndx ; } prim ;
    01559   struct { double norm1 ;
    01560            double norm2 ;
    01561            double max ;
    01562            int maxndx ; } dual ;
    01563   } lp_struct ;
    01564
    01565
    01566 /*
    01567   Declarations global to the dylp implementation but not visible outside of
    01568   it. With this we can avoid passing huge numbers of parameters and/or
    01569   unpacking a structure on a regular basis. Unless otherwise indicated, indices
    01570   are in the dy_sys (active system) frame of reference.
    01571
    01572   Main structures
    01573   ---------------
    01574   dy_lp:        The lp control structure for dylp.
    01575   dy_sys:       The active constraint system; initialised in dylp:startup
    01576   dy_tols:      Tolerances in effect for dylp; initialised in
    01577                 dylp:dylp from orig_tols.
    01578   dy_opts:      Options in effect for dylp; initialised in
    01579                 dylp:dylp to point to same structure as orig_opts.
    01580   dy_stats      Statistics structure for dylp; initialised in dylp:dylp to
    01581                 point ot the same structure as orig_stats.
    01582
    01583   Constraint & Variable Management
    01584   --------------------------------
    01585   dy_actvars:   The active variables. Indexed in dy_sys frame, contains
    01586                 indices in orig_sys frame. Attached to dy_sys.
    01587                 Entries for logical variables (1 <= j <= concnt) are
    01588                 meaningless.
    01589   dy_actcons:   The active constraints. Indexed in dy_sys frame, contains
    01590                 indices in orig_sys frame. Attached to dy_sys.
    01591   dy_origvars:  Status of the original architectural variables.
    01592                  * A value of 0 indicates the entry hasn't been processed.
    01593                    Should never happen.
    01594                  * If the variable is active, the entry contains the index
    01595                    of the variable in the dy_sys frame.
    01596                  * If the variable is inactive, the coding is the negative of
    01597                    the vstat flags, limited to the nonbasic status values
    01598                    vstatNBFR, vstatNBFX, vstatNBLB, or vstatNBUB, and the
    01599                    qualifier vstatNOLOAD.
    01600                 Indexed in orig_sys frame. Attached to orig_sys.
    01601   dy_origcons:  Status of the original constraints.
    01602                  * If the constraint is active, the entry contains the index
    01603                    of the constraint in the dy_sys frame.
    01604                  * If the constraint is inactive, contains 0.
    01605                  * If the constraint cannot be activated, contains a negative
    01606                    value.
    01607                 Indexed in orig_sys frame. Attached to orig_sys.
    01608
    01609   Note that there are macros defined to test whether a variable or constraint
    01610   is inactive, and whether it's eligible for activation. Use them!
    01611
    01612   Basis Management
    01613   ----------------
    01614   dy_basis:     The basis vector. Indexed by basis position, attached to
    01615                 dy_sys.
    01616   dy_var2basis: Translates a variable index to a basis pos'n. Indexed by
    01617                 column, attached to dy_sys. Entries for nonbasic variables
    01618                 must be kept at 0.
    01619   dy_status:    The status vector. Indexed by column, attached to dy_sys.
    01620
    01621   Primal and Dual Variables
    01622   -------------------------
    01623   dy_x:         The values of all primal variables. Indexed by column,
    01624                 attached to dy_sys. Values of nonbasic variables must always
    01625                 be correct (to allow uniform handling of normal nonbasic
    01626                 variables and superbasic variables). Values of basic
    01627                 variables will retain unperturbed values while the
    01628                 antidegeneracy mechanism is active -- this allows the
    01629                 perturbation to be quickly backed out.
    01630   dy_xbasic:    The values of the basic variables. Indexed by basis pos'n,
    01631                 attached to dy_sys.
    01632   dy_y:         The dual variables. Indexed by basis pos'n, attached to
    01633                 dy_sys.
    01634
    01635   Projected Steepest Edge (PSE) Pricing
    01636   -------------------------------------
    01637   dy_cbar:      Iteratively updated vector of reduced costs. Indexed by column,
    01638                 attached to dy_sys.
    01639   dy_gamma:     Iteratively updated vector of column norms ||abar<j>||^2.
    01640                 Indexed by column, attached to dy_sys.
    01641   dy_frame:     Boolean vector which indicates if a given variable is in the
    01642                 current frame of reference. Indexed by column, attached to
    01643                 dy_sys.
    01644
    01645   Dual Steepest Edge (DSE) Pricing
    01646   --------------------------------
    01647   dy_rho:       Iteratively updated vector of row norms ||beta<i>||^2.
    01648                 Indexed by basis position, attached to dy_sys.
    01649
    01650   DSE pricing also makes use of dy_xbasic (the reduced costs of the dual
    01651   variables), and maintains dy_cbar.
    01652
    01653   Antidegeneracy
    01654   --------------
    01655   dy_brkout:    Specifies the direction a variable needs to move to escape
    01656                 from a degenerate vertex.  Indexed by basis pos'n, attached
    01657                 to dy_sys.
    01658   dy_degenset:  Specifies the set of constraints (equivalently, basic
    01659                 variables) perturbed at each level of the antidegeneracy
    01660                 algorithm. Indexed by basis pos'n, attached to dy_sys.  The
    01661                 entry for a constraint is the highest level of degenerate set
    01662                 which includes the constraint. If the entry is 0, the
    01663                 constraint is not involved in degeneracy.
    01664   dy_ddegenset: Specifies the set of dual constraints (equivalently, reduced
    01665                 costs) perturbed at each level of the antidegeneracy
    01666                 algorithm. Indexed by variable index, attached to dy_sys.
    01667                 The entry for a dual constraint is the highest level of
    01668                 degenerate set which includes the constraint. If the entry is
    01669                 0, the constraint is not involved in degeneracy.
    01670 */
    01671
    01672 extern lp_struct *dy_lp ;
    01673 extern consys_struct *dy_sys ;
    01674 extern lptols_struct *dy_tols ;
    01675 extern lpopts_struct *dy_opts ;
    01676 extern int *dy_actvars,*dy_actcons,*dy_origvars,*dy_origcons,
    01677            *dy_basis,*dy_var2basis,
    01678            *dy_brkout,*dy_degenset,*dy_ddegenset ;
    01679 extern flags *dy_status ;
    01680 extern double *dy_x,*dy_xbasic,*dy_y,*dy_cbar,*dy_gamma,*dy_rho ;
    01681 extern bool *dy_frame ;
    01682
    01683 extern lpstats_struct *dy_stats ;
    01684
    01685 /*
    01686   dy_scaling.c
    01687 */
    01688
    01689 extern bool dy_initlclsystem(lpprob_struct *orig_lp, bool hotstart) ;
    01690 extern void dy_freelclsystem(lpprob_struct *orig_lp, bool freesys) ;
    01691 extern bool dy_isscaled(void) ;
    01692
    01693 /*
    01694   dy_coldstart.c
    01695 */
    01696
    01697 extern dyret_enum dy_coldstart(consys_struct *orig_sys),
    01698                   dy_crash(void) ;
    01699
    01700 /*
    01701   dy_warmstart.c
    01702 */
    01703
    01704 extern dyret_enum dy_warmstart(lpprob_struct *orig_lp) ;
    01705
    01706 /*
    01707   dy_hotstart.c
    01708 */
    01709
    01710 extern dyret_enum dy_hotstart(lpprob_struct *orig_lp) ;
    01711
    01712 /*
    01713   dy_basis.c
    01714 */
    01715
    01716 extern dyret_enum dy_factor(flags *calcflgs),
    01717                   dy_pivot(int xipos, double abarij, double maxabarj) ;
    01718 extern double dy_chkpiv(double abarij, double maxabarj) ;
    01719 extern void dy_btran(double *col), dy_ftran(double *col, bool save) ;
    01720 extern bool dy_setpivparms(int curdelta, int mindelta) ;
    01721 extern char *dy_prtpivparms(int lvl) ;
    01722
    01723 /*
    01724   dy_bound.c
    01725 */
    01726
    01727 extern int dy_activateBndCons(consys_struct *orig_sys) ;
    01728 extern int dy_dualaddvars(consys_struct *orig_sys) ;
    01729
    01730 /*
    01731   dy_conmgmt.c
    01732 */
    01733
    01734 extern bool dy_loadcon(consys_struct *orig_sys, int orig_ndx,
    01735                        bool genvars, int *inactndxs) ;
    01736 extern bool dy_deactNBLogPrimCon(consys_struct *orig_sys, int i),
    01737             dy_deactBLogPrimCon(consys_struct *orig_sys, int i),
    01738             dy_actBLogPrimCon(consys_struct *orig_sys, int i,
    01739                               int *inactvars),
    01740             dy_actBLogPrimConList(consys_struct *orig_sys,
    01741                                   int cnt, int *ocndxs, int **inactvars) ;
    01742 extern int dy_deactivateCons(consys_struct *orig_sys),
    01743            dy_activateCons(consys_struct *orig_sys, bool with_vars) ;
    01744
    01745 /*
    01746   dy_varmgmt.c
    01747 */
    01748
    01749 extern bool dy_actNBPrimArch(consys_struct *orig_sys, int ovndx),
    01750             dy_actNBPrimArchList(consys_struct *orig_sys,
    01751                                  int cnt, int *ovndxs),
    01752             dy_deactBPrimArch(consys_struct *orig_sys, int ovndx),
    01753             dy_deactNBPrimArch(consys_struct *orig_sys, int ovndx) ;
    01754 extern int dy_deactivateVars(consys_struct *orig_sys),
    01755            dy_activateVars(consys_struct *orig_sys, int *candidates) ;
    01756
    01757 /*
    01758   dy_primalpivot.c
    01759 */
    01760
    01761 extern dyret_enum dy_primalin(int initcol, int scan, int *xjndx, int *nextcol),
    01762                   dy_primalpivot(int xjndx, int indir, int *xindx, int *outdir,
    01763                                  double *abarij, double *delta, int *xjcand),
    01764                   dy_degenout(int level) ;
    01765
    01766 /*
    01767   dy_duenna.c
    01768 */
    01769
    01770 extern dyret_enum dy_duenna(dyret_enum pivresult, int xjndx, int xindx,
    01771                             int xjcand, int xicand),
    01772                   dy_accchk(flags *checks) ;
    01773
    01774 /*
    01775   dy_pivreject.c
    01776 */
    01777
    01778 extern dyret_enum dy_addtopivrej(int xkndx, dyret_enum why,
    01779                                  double abarij, double maxabarij),
    01780                   dy_dealWithPunt(void) ;
    01781 extern bool dy_clrpivrej(int *entries) ;
    01782 extern void dy_checkpivtol(void) ;
    01783 extern void dy_initpivrej(int sze), dy_freepivrej(void) ;
    01784
    01785
    01786 /*
    01787   dy_primal.c
    01788 */
    01789
    01790 extern lpret_enum dy_primal(void) ;
    01791 extern bool dy_initp1obj(void),dy_swapobjs(dyphase_enum phase) ;
    01792
    01793 /*
    01794   dy_dualpivot.c
    01795 */
    01796
    01797 extern dyret_enum
    01798   dy_dualout(int *xindx),
    01799   dy_dualpivot(int xindx, int outdir,
    01800                int *p_xjndx, int *p_indir, double *p_cbarj,
    01801                double *p_abarij, double *p_delta, int *xicand),
    01802   dy_dualdegenout(int level) ;
    01803
    01804 /*
    01805   dy_dual.c
    01806 */
    01807
    01808 extern lpret_enum dy_dual(void) ;
    01809
    01810 #endif /* DYLP_INTERNAL */
    01811
    01812 /*
    01813   dy_setup.c
    01814 */
    01815
    01816 extern void dy_defaults(lpopts_struct **opts, lptols_struct **tols),
    01817             dy_checkdefaults(consys_struct *sys,
    01818                              lpopts_struct *opts, lptols_struct *tols),
    01819             dy_setprintopts(int lvl, lpopts_struct *opts) ;
    01820
    01821
    01822 /*
    01823   dylp.c
    01824 */
    01825
    01826 extern lpret_enum dylp(lpprob_struct *orig_lp, lpopts_struct *orig_opts,
    01827                        lptols_struct *orig_tols, lpstats_struct *orig_stats) ;
    01828
    01829 /*
    01830   dylp_utils.c
    01831 */
    01832
    01833 #ifdef DYLP_INTERNAL
    01834
    01835 extern lpret_enum dyret2lpret(dyret_enum dyret) ;
    01836 extern dyret_enum dy_updateprimals(int j, double deltaj, double *p_abarj) ;
    01837 extern bool dy_reducerhs(double *rhs, bool init),
    01838             dy_calcprimals(void),dy_calccbar(void) ;
    01839 extern void dy_calcduals(void),dy_setbasicstatus(void),
    01840             dy_dseinit(void),dy_pseinit(void) ;
    01841 extern double dy_calcobj(void),dy_calcdualobj(void),dy_calcpinfeas(void) ;
    01842 extern void dy_finishup(lpprob_struct *orig_lp, dyphase_enum phase) ;
    01843
    01844 #ifdef PARANOIA
    01845
    01846 extern bool dy_chkstatus(int vndx),
    01847             dy_chkdysys(consys_struct *orig_sys) ;
    01848 extern void dy_chkdual(int lvl) ;
    01849
    01850 #endif
    01851
    01852 #endif /* DYLP_INTERNAL */
    01853
    01854 extern bool dy_dupbasis(int dst_basissze, basis_struct **p_dst_basis,
    01855                         basis_struct *src_basis, int dst_statussze,
    01856                         flags **p_dst_status,
    01857                         int src_statuslen, flags *src_status),
    01858             dy_expandxopt(lpprob_struct *lp, double **p_xopt) ;
    01859 extern void dy_freesoln(lpprob_struct *lpprob) ;
    01860
    01861 /*
    01862   dy_penalty.c
    01863 */
    01864
    01865 extern bool dy_pricenbvars(lpprob_struct *orig_lp, flags priceme,
    01866                            double **p_ocbar, int *p_nbcnt, int **p_nbvars),
    01867             dy_pricedualpiv(lpprob_struct *orig_lp, int oxindx,
    01868                             double nubi, double xi, double nlbi,
    01869                             int nbcnt, int *nbvars,
    01870                             double *cbar, double *p_upeni, double *p_dpeni) ;
    01871
    01872 /*
    01873   dylp_io.c
    01874 */
    01875
    01876 #include <dylib_io.h>
    01877
    01878 #ifdef DYLP_INTERNAL
    01879
    01880 extern void dy_logpivot(dyret_enum result, int xjndx, int indir, double cbarj,
    01881                         int xindx, int outdir, double abarij, double delta) ;
    01882 extern const char *dy_prtdyret(dyret_enum retcode) ;
    01883
    01884 #endif /* DYLP_INTERNAL */
    01885
    01886 extern const char *dy_prtlpret(lpret_enum lpret),
    01887                   *dy_prtlpphase(dyphase_enum phase, bool abbrv) ;
    01888 extern char *dy_prtvstat(flags status) ;
    01889 extern bool dy_dumpcompact(ioid chn, bool echo, lpprob_struct *soln,
    01890                            bool nbzeros) ;
    01891
    01892 /*
    01893   dy_statistics.c
    01894
    01895   These routines are compiled unconditionally, but note that the compile-time
    01896   symbol DYLP_STATISTICS must be defined before dylp will actually take the
    01897   time to collect detailed statistics. See dy_statistics.c for additional
    01898   instructions.
    01899 */
    01900
    01901 extern void dy_initstats(lpstats_struct **p_lpstats, consys_struct *orig_sys),
    01902             dy_dumpstats(ioid chn, bool echo, lpstats_struct *lpstats,
    01903                          consys_struct *orig_sys),
    01904             dy_freestats(lpstats_struct **p_lpstats) ;
    01905
    01906 #ifdef DYLP_INTERNAL
    01907
    01908 extern void dy_finalstats(lpstats_struct *lpstats) ;
    01909
    01910 #endif /* DYLP_INTERNAL */
    01911
    01912
    01913 #endif /* _DYLP_H */