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# /home/coin/SVN-release/Cgl-0.55.0/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 269 2009-04-02 05:38:19Z 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. The logical for constraint i
    00549                   is represented as n+i.
    00550                 Otherwise, undefined.
    00551   iters         The number of simplex iterations.
    00552   consys        The constraint system.
    00553   basis         (i) Initial basis.
    00554                 (o) Final basis.
    00555   status        (i) Initial status vector.
    00556                 (o) Final status vector.
    00557   x             (i) No values used, but a vector can be supplied.
    00558                 (o) The values of the basic variables (indexed by basis
    00559                     position).
    00560   y             (i) No values used, but a vector can be supplied.
    00561                 (o) The values of the dual variables (indexed by basis
    00562                     position).
    00563   actvars       There is one entry for each variable, coded TRUE if the
    00564                 variable is active, FALSE otherwise. The vector supplied on
    00565                 input will be overwritten on output.
    00566                 (i) Variables to be activated at startup. Used only for a
    00567                     warm start. Validity is indicated by the lpctlACTVARSIN
    00568                     flag. A vector can be supplied strictly for output use.
    00569                 (o) The current active variables. Will be returned only if
    00570                     requested by the lpctlACTVARSOUT flag. If the vector is
    00571                     valid on return, lpctlACTVARSOUT will remain set,
    00572                     otherwise it will be reset.
    00573
    00574   colsze        Allocated column capacity (length of status vector).
    00575   rowsze        Allocated row capacity (length of basis, x, and y vectors).
    00576
    00577
    00578   Note that dylp will reallocate status, basis->el, actvars, x, and y, if the
    00579   vectors supplied at startup are too small to report the solution. Don't set
    00580   colsze or rowsze to nonzero values without actually allocating space.
    00581 */
    00582
    00583 typedef struct
    00584 { flags ctlopts ;
    00585   dyphase_enum phase ;
    00586   lpret_enum lpret ;
    00587   double obj ;
    00588   int iters ;
    00589   consys_struct *consys ;
    00590   basis_struct *basis ;
    00591   flags *status ;
    00592   double *x ;
    00593   double *y ;
    00594   bool *actvars ;
    00595   int colsze ;
    00596   int rowsze ; } lpprob_struct ;
    00597
    00598
    00599
    00600 /*
    00601   lptols_struct
    00602
    00603   This structure contains phase and tolerance information for the lp algorithm.
    00604
    00605   The philosophy with respect to the separate zero and feasibility tolerances
    00606   for primal and dual variables is that dylp uses the zero tolerance when
    00607   calculating primal or dual variables, and the feasibility tolerance when
    00608   checking for feasibility. This allows us to keep small values for accuracy
    00609   in computation, but not be so fussy when it comes to feasibility.
    00610
    00611   Field         Definition
    00612   -----         ----------
    00613   inf           Infinity. dylp uses IEEE FP infinity, but be careful not to
    00614                 pass it to the basis package.
    00615   zero          Zero tolerance for primal variables, and also the generic
    00616                 zero tolerance for constraint coefficients, right-hand-side
    00617                 values, etc.
    00618   pchk          Primal accuracy check tolerance.
    00619   pfeas         Primal feasibility check tolerance; dynamically scaled from
    00620                 zero in proportion to the 1-norm of the primal basic variables.
    00621   pfeas_scale   Primal feasibility check tolerance multiplier. This provides
    00622                 some user-controllable decoupling of zero and pfeas.
    00623   cost          Base zero tolerance for checks involving objective function
    00624                 coefficients, reduced costs, and related values.
    00625   dchk          Dual accuracy check tolerance. Also used by dy_duenna to
    00626                 test for improvement in the objective.
    00627   dfeas         Dual feasbility check tolerance; dynamically scaled from cost
    00628                 in proportion to the 1-norm of the dual variables. Acts as the
    00629                 zero tolerance for reduced costs.
    00630   dfeas_scale   Dual feasibility check tolerance multiplier. This provides
    00631                 some user-controllable decoupling of cost and dfeas.
    00632   pivot         Simplex pivot selection tolerance, expressed as a multiplier
    00633                 for the pivot selection tolerance used by the basis package
    00634                 when factoring the basis. (I.e., the actual pivot selection
    00635                 criteria will be to accept a simplex pivot a<i,j> if
    00636                 |a<i,j>| > lptols.pivot*basis.pivot*MAX{i}|a<i,j>|.)
    00637   bogus         Multiplier used to identify 'bogus' values, in the range
    00638                 tol < |val| < bogus*tol for the appropriate tolerance.
    00639   swing         Ratio used to identify excessive growth in primal variables
    00640                 (pseudo-unboundedness).
    00641   toobig        Absolute value of primal variables which will cause dual
    00642                 multipivoting to consider primal infeasibility when selecting
    00643                 a flip/pivot sequence.
    00644   purge         Percentage change in objective function required before
    00645                 constraint or variable purging is attempted.
    00646   purgevar      Percentage of maximum reduced cost used to determine the
    00647                 variable purge threshold; nonbasic architectural variables
    00648                 at their optimum bound whose reduced cost exceeds
    00649                 purgevar*MAX{j}cbar<j> are purged.
    00650
    00651   reframe       Multiplier used to trigger a reference framework reset in
    00652                 PSE pricing; reset occurs if
    00653                   |gamma<j> - ||abar<j>||^2| > reframe*||abar<j>||^2.
    00654                 The check is made in pseupdate.
    00655                 Also used to trigger recalculation of the basis inverse row
    00656                 norms used in DSE pricing; reset occurs if
    00657                   |rho<i> - ||beta<i>||^2| > reframe*||beta<i>||^2.
    00658                 The check is made in dseupdate.
    00659 */
    00660
    00661 typedef struct
    00662 { double inf ;
    00663   double zero ;
    00664   double pchk ;
    00665   double pfeas ;
    00666   double pfeas_scale ;
    00667   double cost ;
    00668   double dchk ;
    00669   double dfeas ;
    00670   double dfeas_scale ;
    00671   double pivot ;
    00672   double bogus ;
    00673   double swing ;
    00674   double toobig ;
    00675   double purge ;
    00676   double purgevar ;
    00677   double reframe ; } lptols_struct ;
    00678
    00679 #if defined(DYLP_INTERNAL) || defined(BONSAIG)
    00680 /*
    00681   A few handy macros for testing values against tolerances.
    00682 */
    00683 #ifdef DYLP_INTERNAL
    00684 #  ifdef BND_TOLER
    00685 #    undef BND_TOLER
    00686 #  endif
    00687 #  define BND_TOLER dy_tols->pfeas
    00688 #  ifdef INF_TOLER
    00689 #    undef INF_TOLER
    00690 #  endif
    00691 #  define INF_TOLER dy_tols->inf
    00692 #endif
    00693
    00694 #define withintol(zz_val_zz,zz_tgt_zz,zz_tol_zz) \
    00695   (fabs((zz_val_zz)-(zz_tgt_zz)) <= zz_tol_zz)
    00696
    00697 #define setcleanzero(zz_val_zz,zz_tol_zz) \
    00698   if (fabs(zz_val_zz) < zz_tol_zz) zz_val_zz = 0
    00699
    00700 #define atbnd(zz_val_zz,zz_bnd_zz) \
    00701   ((fabs(zz_bnd_zz) < INF_TOLER) && \
    00702    (fabs((zz_val_zz)-(zz_bnd_zz)) < BND_TOLER*(1.0+fabs(zz_bnd_zz))))
    00703
    00704 #define belowbnd(zz_val_zz,zz_bnd_zz) \
    00705   ((fabs(zz_bnd_zz) < INF_TOLER) ? \
    00706    (((zz_bnd_zz)-(zz_val_zz)) > BND_TOLER*(1.0+fabs(zz_bnd_zz))) : \
    00707    (zz_val_zz < zz_bnd_zz))
    00708
    00709 #define abovebnd(zz_val_zz,zz_bnd_zz) \
    00710   ((fabs(zz_bnd_zz) < INF_TOLER) ? \
    00711    (((zz_val_zz)-(zz_bnd_zz)) > BND_TOLER*(1.0+fabs(zz_bnd_zz))) : \
    00712    (zz_val_zz > zz_bnd_zz))
    00713
    00714 #define withinbnds(zz_lb_zz,zz_val_zz,zz_ub_zz) \
    00715   (!abovebnd(zz_val_zz,zz_ub_zz) && !belowbnd(zz_val_zz,zz_lb_zz))
    00716
    00717 #endif /* DYLP_INTERNAL || BONSAIG */
    00718
    00719 #ifdef DYLP_INTERNAL
    00720 /*
    00721   Finally, a macro to decide if we should snap to a value. The notion here is
    00722   that the accuracy with which one can hit a target value depends on both the
    00723   magnitude of the target and the distance travelled to get there. On a
    00724   64-bit machine, IEEE FP has about 15 decimal digits of accuracy. For
    00725   example, if we're travelling 1.0e7 and trying to hit zero, we only have 8
    00726   decimal places of accuracy remaining. If we're within 1.0e-8, might as well
    00727   snap to 0. In practice, there's already a bit of roundoff in any nontrivial
    00728   calculation, so we start with the zero tolerance and scale from there.
    00729
    00730   In some cases, we only know the target, so the best we can do is
    00731   scale to it.
    00732
    00733   The utility of this idea is highly questionable.
    00734 */
    00735
    00736 #define snaptol1(zz_tgt_zz) (dy_tols->zero*(1.0+(zz_tgt_zz)))
    00737
    00738 #define snaptol2(zz_tgt_zz,zz_dst_zz) \
    00739   (dy_tols->zero*(1.0+maxx((zz_tgt_zz),(zz_dst_zz))))
    00740
    00741 #define snaptol3(zz_tol_zz,zz_tgt_zz,zz_dst_zz) \
    00742   ((zz_tol_zz)*(1.0+maxx((zz_tgt_zz),(zz_dst_zz))))
    00743
    00744 #endif /* DYLP_INTERNAL */
    00745
    00746
    00747
    00748 /*
    00749   Enum for initial basis type.
    00750
    00751   This determines the criteria used to select the initial set of basic
    00752   variables during a cold start.
    00753
    00754   ibINV         invalid
    00755   ibLOGICAL     Use only logical (slack and artificial) variables
    00756   ibSLACK       Use slack variables for inequalities. Prefer architectural
    00757                 over artificial variables for equalities.
    00758   ibARCH        Prefer architectural variables over logical variables.
    00759 */
    00760
    00761 typedef enum { ibINV = 0, ibLOGICAL, ibSLACK, ibARCH } ibtype_enum ;
    00762
    00763 /*
    00764   Enum for calling context.
    00765
    00766   As dylp evolves, it may well prove useful to know the context of the
    00767   call. Consider this an experiment. The default context is INITIALLP.
    00768
    00769   cxINV         invalid (context is unknown)
    00770   cxSINGLELP    This is a one-off call to solve a single LP from scratch.
    00771   cxINITIALLP   This is a call to solve a single LP from scratch, but will
    00772                 likely be followed by calls to reoptimise.
    00773   cxBANDC       This call is made in the context of a branch-and-cut
    00774                 algorithm.
    00775 */
    00776
    00777 typedef enum { cxINV = 0, cxSINGLELP, cxINITIALLP, cxBANDC } cxtype_enum ;
    00778
    00779 /*
    00780   lpopts_struct
    00781
    00782   This structure is used to pass option settings to dylp. Default values are
    00783   declared at the beginning of dy_setup.c.
    00784
    00785   Field         Definition
    00786   -----         ----------
    00787   context       The context in which dylp is being called. See comments
    00788                 above for cxtype_enum.
    00789   forcecold     TRUE to force a cold start, FALSE otherwise. If set to TRUE,
    00790                 dominates warm and hot start.
    00791   forcewarm     TRUE to force a warm start, FALSE otherwise. If set to TRUE,
    00792                 dominates hot start.
    00793   fullsys       Forces the use of the full constraint system at all times. The
    00794                 full constraint system is loaded on startup, and all constraint
    00795                 and variable deactivation/activation is skipped. (But see the
    00796                 finpurge option below.) (Also, this will not prevent dylp
    00797                 from resorting to forced phase transitions, which typically
    00798                 involve deactivation of constraints or variables. Arguably
    00799                 this is a bad thing, and may change in the future.)
    00800   active        Used to estimate the initial size of the dylp constraint
    00801                 system relative to the original system.
    00802     vars          Fraction of original variables expected to be active at
    00803                   any time.
    00804     cons          Fraction of original inequalities expected to be active at
    00805                   any time.
    00806   initcons      Specifies how inequalities will be selected to initialize the
    00807                 active system. See extensive comments in dy_coldstart.c.
    00808     frac          Fraction of inequalities to be used.
    00809     i1l           Lower bound on angle to objective, first interval
    00810     i1lopen       TRUE if the bound is open.
    00811     i1u           Upper bound on angle to objective, first interval
    00812     i1uopen       TRUE if the bound is open.
    00813     i2valid       TRUE if the second interval is specified
    00814     i2l           Lower bound on angle to objective, second interval
    00815     i2lopen       TRUE if the bound is open.
    00816     i2u           Upper bound on angle to objective, second interval
    00817     i2uopen       TRUE if the bound is open.
    00818   coldbasis     Code specifying the kind of basis built for a cold start. See
    00819                 comments for ibtype_enum and comments in dy_coldstart.c
    00820   finpurge      Controls whether dylp does a final deactivation of constraints
    00821                 and/or variables. This will occur only an optimal solution is
    00822                 found, and is not suppressed by fullsys.
    00823     cons          TRUE to purge constraints
    00824     vars          TRUE to purge variables
    00825   heroics       Controls behaviour during forced primal <-> dual transitions
    00826     d2p           TRUE to allow deactivation of basic architecturals, FALSE
    00827                   to disallow. FALSE is recommended, and the default.
    00828     p2d           TRUE to allow deactivation of tight constraints, FALSE
    00829                   to disallow. FALSE is recommended, and the default.
    00830     flip          TRUE to allow flips to regain dual feasibility, FALSE to
    00831                   disallow. Tends to cycle; default is false.
    00832   coldvars      If the number of active variables exceeds this value after
    00833                 a cold start, dylp will attempt to purge variables prior to
    00834                 the initial primal simplex run.
    00835   con           Options related to constraint activation/deactivation
    00836     actlvl        The constraint activation strategy
    00837                     0: (strict) activate violated constraints,
    00838                        lhs < rhslow or lhs > rhs
    00839                     1: (tight) activate tight or violated constraints,
    00840                        lhs <= rhslow or lhs >= rhs
    00841     actlim        If non-zero, limits the number of constraints that can be
    00842                   activated in any one call to a constraint activation
    00843                   routine.
    00844     deactlvl    The constraint deactivation strategy:
    00845                   0: (normal) deactivate only inequalities i which are
    00846                      strictly loose (i.e., slk<i> basic, not at bound).
    00847                   1: (aggressive) normal plus inequalities which are tight
    00848                      with y<i> = 0.
    00849                   2: (fanatic) aggressive plus equalities with y<i> = 0
    00850   usedual       TRUE if dual phase II is to be used to regain feasibility after
    00851                 adding constraints, FALSE to force use of primal phase I.
    00852   addvar        If non-zero, at most this many variables will be added in
    00853                 any one pass through phase dyADDVAR.
    00854   dualadd       Controls the types of activation allowed when adding variables
    00855                 during dual simplex.
    00856                   0:    variable activation is disallowed
    00857                   1:    type 1 activation (variables that will be dual feasible
    00858                         when activated into the nonbasic partition)
    00859                   2:    type 2 activation (variables which can be activated
    00860                         if immediately pivoted into the basis)
    00861                   3:    type 3 activation (activate with bound-to-bound pivot)
    00862                 See dy_dualaddvars for more extensive comments.
    00863   scan          Partial pricing parameter. Controls the number of columns to
    00864                 be scanned for a new candidate entering variable when the
    00865                 candidate selected during PSE update is rejected.
    00866   iterlim       The per phase pivot limit for the code; if set to 0, no
    00867                 limit is enforced.
    00868   idlelim       The number of iterations without change in the objective
    00869                 function before the code declares the problem is stalled or
    00870                 cycling.
    00871   dpsel         Options to control dual pivoting. Selection of the leaving
    00872                 variable is always handled by DSE.
    00873     strat:        The strategy used to select the entering variable:
    00874                     0: standard ratio test; may use anti-degen lite
    00875                     1: multipivoting, selecting for maximum dual objective
    00876                        improvement.
    00877                     2: multipivoting, select for minimum predicted
    00878                        infeasibility.
    00879                     3: multipivoting, select infeasibility reduction if
    00880                        possible, otherwise maximum dual objective improvement.
    00881     flex          If TRUE, dylp will switch between strategies 1 and 3, using
    00882                   strategy 1 unless primal magnitudes become too large.
    00883     allownopiv    If TRUE, sequences of flips with no finishing pivot will be
    00884                   allowed. Defaults to false, very prone to cycling.
    00885   ppsel         Options to control primal pivoting. Selection of the entering
    00886                 variable is always handled by PSE.
    00887     strat:        The strategy used to select the leaving variable:
    00888                     0: standard ratio test; may use anti-degen lite
    00889                     1: multipivoting
    00890   factor        The LP basis will be refactored every factor iterations, in
    00891                 the absence of some compelling reason (typically error
    00892                 recovery) that forces it to occur sooner.
    00893   check         An accuracy check will be forced every check iterations, in
    00894                 the absence of some compelling reason to do it earlier.
    00895   groom         Controls the action taken by the basis grooming routine
    00896                 when it makes a nontrivial status correction:
    00897                   0:    catatonic
    00898                   1:    issue a warning
    00899                   2:    issue an error message and force an abort
    00900                 Numeric codes are related to keywords in dy_setup.c:dy_ctlopt.
    00901   degen         TRUE to allow creation of restricted subproblems to deal with
    00902                 degeneracy, FALSE to disallow it.
    00903   degenpivlim   The number of successive degenerate pivots required before
    00904                 creating a restricted subproblem.
    00905   degenlite     Controls secondary antidegeneracy --- `antidegen lite'
    00906                   0: (pivotabort) break ties using |abar<kj>| and abort when
    00907                      delta<j> = 0
    00908                   1: (pivot) break ties using |abar<kj>| but always scan the
    00909                      full basis
    00910                   2: (alignobj) break ties by examining the alignment of the
    00911                      hyperplane which will become tight on the pivot; choose
    00912                      so that movement in the direction of the objective most
    00913                      nearly lies in the hyperplane
    00914                   3: (alignedge) break ties by examining the alignment of the
    00915                      hyperplane which will become tight on the pivot; choose
    00916                      so that the direction of motion defined by the entering
    00917                      variable most nearly lies in the hyperplane.
    00918                   4: (perpobj) break ties by examining the alignment of the
    00919                      hyperplane which will become tight on the pivot; choose
    00920                      so that the normal of the hyperplane is most nearly
    00921                      aligned with the normal of the objective
    00922                   5: (perpedge) break ties by examining the alignment of the
    00923                      hyperplane which will become tight on the pivot; choose
    00924                      so that the normal of the hyperplane is most nearly
    00925                      aligned with the direction of motion
    00926                 Numeric codes are related to keywords in dy_setup.c:dy_ctlopt.
    00927   patch         TRUE to allow the code to patch a singular basis, FALSE to
    00928                 prevent patching.
    00929   copyorigsys   Controls whether dylp makes a local copy of the original
    00930                 system. If set to TRUE, dylp will always make a local copy.
    00931                 If set to FALSE, a copy will be made only if necessary.
    00932                 Scaling will trigger a local copy.
    00933   scaling       Controls whether dylp attempts to scale the original constraint
    00934                 system for numeric stability.
    00935                   0: scaling is forbidden
    00936                   1: scale the original constraint system using numeric
    00937                      scaling vectors attached to the system
    00938                   2: evaluate the original constraint system and scale it if
    00939                      necessary
    00940                 Note that even if scaling = 0, dylp may install +/-1.0 scaling
    00941                 vectors in order to flip >= constraints to <= constraints. See
    00942                 comments in dy_scaling.c
    00943   print         Substructure for picky printing control. For all print options,
    00944                 a value of 0 suppresses all information messages.
    00945     major         Controls printing of major phase information.
    00946                   1: a message at each phase transition.
    00947     scaling       Controls print level during initial evaluation and scaling of
    00948                   the original constraint system.
    00949                   1: start and finish messages
    00950                   2: stability measures for original and scaled matrices;
    00951                      adjustments to tolerances.
    00952     setup         Controls print level while creating the initial constraint
    00953                   system for dylp.
    00954                   1: start and finish messages.
    00955                   2: summary information about activated constraints
    00956                   3: messages about each constraint included in the initial
    00957                      system.
    00958                   4: messages about each constraint processed for the initial
    00959                      system
    00960                   5: messages about each variable included in the initial
    00961                      system.
    00962                   6: lists value and status of inactive variables with
    00963                      nonzero values
    00964     crash         Controls print level while crashing the basis.
    00965                   1: start & finish messages
    00966                   2: summary counts for logicals, architecturals, artificials
    00967                   3: a dump of the completed basis
    00968                   4: detailed info on the selection of each architectural
    00969                      and artificial variable
    00970     pricing       Controls print level for pricing of columns (rows) in primal
    00971                   (dual) simplex.
    00972                   1: summary messages
    00973                   2: lists candidate list and primal variable selected for
    00974                      entry (exit) at each pivot
    00975                   3: lists each variable as it's added to the candidate list
    00976                      and again when reconsidered for pivoting
    00977     pivoting      Controls print level for selection of the leaving (entering)
    00978                   primal variable in primal (dual) simplex and updating of
    00979                   variables.
    00980                   1: prints result of leaving (entering) variable selection
    00981                   2: information about the selection of the leaving (entering)
    00982                      variable.
    00983                   3: more information about the selection of the leaving
    00984                      (entering) variable.
    00985                   4: prints the pivot column (row) before and after
    00986                      multiplication by the basis inverse, and yet more
    00987                      pivot selection information.
    00988                   5: prints a line for every candidate evaluated
    00989     pivreject     Controls print level for information related to the operation
    00990                   of the pivot rejection mechanism.
    00991                   1: Prints a message for each row/column added to the pivot
    00992                      rejection list, plus other major events.
    00993                   2: Prints a message for each row/column removed from the
    00994                      pivot rejection list.
    00995     degen         Controls print level for information related to the operation
    00996                   of the antidegeneracy mechanism.
    00997                   1: prints a message each time the antidegeneracy level
    00998                      changes
    00999                   2: prints a message when a true degenerate pivot is taken
    01000                      under duress
    01001                   3: prints a message when a degenerate pivot is taken
    01002                   4: prints anomalies as each degenerate set is formed and
    01003                      backed out
    01004                   5: prints details of each degenerate set as it's formed and
    01005                      backed out
    01006     phase1        Controls general print level for phase 1 of primal simplex.
    01007                   1: messages about extraordinary events -- problem pivots, etc.
    01008                   2: messages about 'routine' but infrequent events --
    01009                      termination conditions, refactoring, unboundedness, etc.
    01010                   3: messages with additional details of problems encountered
    01011                   4: a one line log message is printed for each pivot
    01012                   5: summary information about infeasible variables and phase
    01013                      I objective coefficients; information about primal
    01014                      variables updated at each pivot.
    01015                   6: prints the primal variables after each pivot; prints
    01016                      infeasible variables during phase I objective construction
    01017                   7: prints the dual variables after each pivot; prints
    01018                      infeasible variables during phase I objective modification
    01019     phase2        Controls general print level for phase 1 of primal simplex.
    01020                   1: messages about extraordinary events -- problem pivots, etc.
    01021                   2: messages about 'routine' but infrequent events --
    01022                      termination conditions, refactoring, unboundedness, etc.
    01023                   3: messages with additional details of problems encountered
    01024                   4: a one line log message is printed for each pivot
    01025                   5: prints the updated basic primal variables after each pivot
    01026                   6: prints all basic primal variables after each pivot
    01027                   7: prints the dual variables after each pivot.
    01028     dual          Controls general print level for the dual simplex. As
    01029                   phase2.
    01030     basis         Controls print level in routines working with the basis.
    01031                   1: summary warnings about problems: empty rows, singularity,
    01032                      numerical instability, etc.
    01033                   2: information about factoring failures and recovery actions
    01034                   3: warnings about individual empty rows, details of column
    01035                      replacement when patching a singular basis, pivot
    01036                      tolerance adjustments; information about pivoting failures
    01037                      and recovery actions
    01038                   4: basis stability after factoring
    01039                   5: basis stability after pivoting
    01040     conmgmt       Controls print level while dylp is in the purge/generate/
    01041                   activate constraint phases.
    01042                   1: prints the number of constraints purged, generated,
    01043                      & activated, and new size of constraint system.
    01044                   2: prints a message for each constraint purged or activated.
    01045                      (The cut generation routine is responsible for
    01046                      handling this function when it generates cuts.)
    01047                   3: additional details about refactoring and new values
    01048                      of primal and dual variables.
    01049                   4: prints a message about any variables affected as a side
    01050                      effect of constraint changes, constraints processed
    01051                      but not activated, and information about direction of
    01052                      recession and relative angle of constraints when adding
    01053                      constraints to an unbounded problem.
    01054                   5: prints a running commentary on constraint and variable
    01055                      shifts, inactive variables.
    01056     varmgmt       Controls print level while dylp is in the purge/generate/
    01057                   activate variable phases.
    01058                   1: prints the number of variables purged, generated,
    01059                      & activated, and new size of constraint system.
    01060                   2: prints a message for each variable purged & activated.
    01061                      (The column generation routine is responsible for
    01062                      handling this function when it generates new variables).
    01063                   3: prints a message about any constraints affected as a side
    01064                      effect of variable changes, variables processed but not
    01065                      activated, and information about direction of recession
    01066                      and relative angle of dual constraints when adding
    01067                      variables to an unbounded dual.
    01068                   4: prints a running commentary on constraint and variable
    01069                      shifts.
    01070     force         Controls print level when dylp is attempting to force a
    01071                   transition (primal -> dual, dual -> primal) or force the
    01072                   use of the full constraint system.
    01073                   1: prints a summary message giving the result of the
    01074                      transition attempt
    01075                   2: prints messages about actions taken for individual
    01076                      constraints and variables.
    01077                   3: additional information about variables and constraints
    01078                      examined.
    01079     tableau       Controls print level for routines that generate tableau
    01080                   vectors (beta<i>, beta<j>, abar<i>, abar<j>) for use by
    01081                   external clients.
    01082                   1: prints summary messages about the circumstances
    01083                   4: prints nonzeros in the final vector.
    01084                   5: prints nonzeros in intermediate vectors and (dy_betaj,
    01085                      dy_abarj only) inactive rows
    01086                   6: prints nonzeros of active portion in internal reference
    01087                      frame (dy_betaj only)
    01088     rays          Controls print level for routines that generate primal
    01089                   and dual rays for use by external clients.
    01090                   1: prints summary messages about vectors found.
    01091                   3: print information about columns / rows examined.
    01092                   4: print information about why a column or row was rejected.
    01093     soln          Controls print level for routines that generate primal and
    01094                   dual solutions for use by external clients.
    01095                   1: prints summary messages about the circumstances
    01096                   3: prints nonzeros in the final vector
    01097                   4: prints nonzeros in intermediate vectors
    01098 */
    01099
    01100 typedef struct
    01101 { cxtype_enum context ;
    01102   int scan ;
    01103   int iterlim ;
    01104   int idlelim ;
    01105   struct { int strat ;
    01106            bool flex ;
    01107            bool allownopiv ; } dpsel ;
    01108   struct { int strat ; } ppsel ;
    01109   int factor ;
    01110   int check ;
    01111   int groom ;
    01112   struct { int actlvl ;
    01113            int actlim ;
    01114            int deactlvl ; } con ;
    01115   int addvar ;
    01116   int dualadd ;
    01117   int coldvars ;
    01118   bool forcecold ;
    01119   bool forcewarm ;
    01120   bool usedual ;
    01121   bool degen ;
    01122   int degenpivlim ;
    01123   int degenlite ;
    01124   bool patch ;
    01125   bool fullsys ;
    01126   bool copyorigsys ;
    01127   int scaling ;
    01128   struct { float vars ;
    01129            float cons ; } active ;
    01130   struct { double frac ;
    01131            bool i1lopen ;
    01132            double i1l ;
    01133            bool i1uopen ;
    01134            double i1u ;
    01135            bool i2valid ;
    01136            bool i2lopen ;
    01137            double i2l ;
    01138            bool i2uopen ;
    01139            double i2u ; } initcons ;
    01140   ibtype_enum coldbasis ;
    01141   struct { bool cons ;
    01142            bool vars ; } finpurge ;
    01143   struct { bool d2p ;
    01144            bool p2d ;
    01145            bool flips ; } heroics ;
    01146   struct { int major ;
    01147            int scaling ;
    01148            int setup ;
    01149            int crash ;
    01150            int pricing ;
    01151            int pivoting ;
    01152            int pivreject ;
    01153            int degen ;
    01154            int phase1 ;
    01155            int phase2 ;
    01156            int dual ;
    01157            int basis ;
    01158            int conmgmt ;
    01159            int varmgmt ;
    01160            int force ;
    01161            int tableau ;
    01162            int rays ;
    01163            int soln ; } print ; } lpopts_struct ;
    01164
    01165
    01166
    01167
    01168 /*
    01169   Statistics structure, used to collect information about aspects of dylp
    01170   operation beyond simple pivot counts. The data structure definition is
    01171   always present, but to fill it you have to define DYLP_STATISTICS.
    01172
    01173   Field         Definition
    01174   -----         ----------
    01175   phasecnts[dyDONE] Array with counts for number of times each phase is
    01176                 executed.
    01177   ini_simplex   The initial simplex phase
    01178   cons          A set of arrays with data about individual constraints.
    01179     sze           Allocated capacity of the arrays.
    01180     angle         Angle to the objective function.
    01181     actcnt        Number of times constraint is activated.
    01182     deactcnt      Number of times constraint is deactivated.
    01183     init          True if constraint is active in initial system.
    01184     fin           True if constraint is active in final system.
    01185   vars          A set of arrays with data about individual variables.
    01186     sze           Allocated capacity of the arrays.
    01187     actcnt        Number of times variable is activated.
    01188     deactcnt      Number of times variable is deactivated.
    01189   angle
    01190     max         Maximum angle to the objective function over all constraints.
    01191     min         Minimum angle to the objective function over all constraints.
    01192     hist[*]     Histogram of angles of constraints to the objective function.
    01193                 There are DYSTATS_HISTBINS bins. Currently, 37 bins: 36 bins
    01194                 spanning 5 degrees of angle, and a dedicated 90 degree bin.
    01195
    01196   factor        Tracks how well we're doing with respect to refactoring the
    01197                 basis.
    01198     cnt         Number of time the basis has been refactored.
    01199     prevpiv     Pivot count at last refactorisation.
    01200     avgpivs     Average number of pivots between basis refactorisations.
    01201     maxpivs     Maximum number of pivots between basis refactorisations.
    01202
    01203   pivrej        Statistics about the pivot rejection list and punts.
    01204     max           maximum number of entries on the pivot rejection list
    01205     mad           total number of entries attributed to mad pivots
    01206     sing          total number of entries attributed to singular pivots
    01207     pivtol_red    total number of times the pivot tolerance was reduced
    01208     min_pivtol    the minimum pivot tolerance used
    01209     puntcall      total number of calls to dealWithPunt
    01210     puntret       total number of dyrPUNT returns recommended
    01211
    01212   dmulti        Tracks the dual multipivot algorithm. All fields except cnt are
    01213                 totals; divide by cnt to get averages.
    01214     flippable     Number of flippable variables in the constraint system.
    01215     cnt           Total calls to dualmultiin
    01216     cands         Number of candidates queued for evaluation for entry
    01217     promote       Number of calls that resulted in promoting a sane pivot
    01218                   over an unstable pivot.
    01219     nontrivial    Number of times that the initial scan and sort left
    01220                   multiple candidates for further evaluation.
    01221     evals         Actual number of candidates evaluated (ftran'd column)
    01222     flips         Number of bound-to-bound flips performed
    01223     pivrnk        Index in the list of candidates of the candidate finally
    01224                   selected for pivoting.
    01225     maxrnk        Maximum index selected for pivoting.
    01226
    01227   pmulti        Tracks the primal multipivot algorithm.
    01228     cnt           Total calls to primalmultiin
    01229     cands         Number of candidates queued for evaluation to leave
    01230     nontrivial    Number of times that the candidate list was sorted
    01231     promote       Number of calls that resulted in promoting a sane pivot
    01232                   over an unstable pivot.
    01233
    01234   infeas        Statistics on resolution of infeasibility in primal phase I.
    01235                 Basically, what we're interested in tracking is the number
    01236                 of infeasible variables and the number of pivots between a
    01237                 change in the number of infeasible variables. We're interested
    01238                 in separating the case of 1 variable from 2 or more, because
    01239                 the latter requires vastly more calculation. A little care
    01240                 is required because phase I can run many times.
    01241
    01242     prevpiv     The pivot count (tot.iters) at the previous change.
    01243     maxcnt      The maximum number of infeasible variables encountered (this
    01244                 is not strictly monotonic, as dylp may enter phase I many
    01245                 times due to activating violated constraints).
    01246     totpivs     The total number of pivots expended in phase I.
    01247     maxpivs     The maximum number of pivots with no change in the number of
    01248                 feasible variables.
    01249     chgcnt1     The number of times that the number of infeasible variables
    01250                 changed and reduced costs did not have to be recalculated
    01251                 (specifically, exactly one variable became feasible, and it
    01252                 left the basis as it did so).
    01253     chgcnt2     The number of times that the number of infeasible variables
    01254                 changed in such a way as to require recalculation of the
    01255                 reduced costs.
    01256
    01257   [dp]degen[*]  Array of stats for each restricted subproblem nesting level,
    01258                 with separate arrays for dual (ddegen) and primal (pdegen).
    01259                 degen[0].cnt is used to hold the maximum nesting level.
    01260     cnt         Number of times this nesting level was entered.
    01261     avgsiz      The average number of variables in a restricted subproblem.
    01262                 Kept by iterative update, as avg<k+1> = (avg<k>*k+size)/(k+1).
    01263                 Suffers from cumulative loss of accuracy, but it'll do for
    01264                 our purposes.
    01265     maxsiz      The maximum number of variables in a restricted subproblem.
    01266     totpivs     Total number of pivots at or above this nesting level.
    01267     avgpivs     Average number of pivots at or above this nesting level.
    01268     maxpivs     Maximum number of pivots for any one instance at or above
    01269                 this nesting level.
    01270
    01271   tot, p1, p2, d2       Iteration and pivot counts, total and for each
    01272                         individual phase. These are copied over from
    01273                         dy_lp (lp_struct) at the end of the run, so that
    01274                         they can be printed by dumpstats.
    01275
    01276   DYSTATS_MAXDEGEN is the maximum number of levels of nesting accommodated by
    01277   antidegeneracy statistics and debugging structures. The actual algorithm
    01278   has no inherent limitation.
    01279
    01280   DYSTATS_HISTBINS is the number of bins for constraint angles. It should be an
    01281   odd number. Each bin will span 180/(DYSTATS_HISTBINS-1) degrees, with the
    01282   final bin reserved for constraints at 90 degrees. For example, a value of 37
    01283   gives 180/(37-1) = 5 degrees per bin.
    01284 */
    01285
    01286 #define DYSTATS_MAXDEGEN 25
    01287 #define DYSTATS_HISTBINS 37
    01288
    01289 typedef struct {
    01290   int phasecnts[dyDONE+1] ;
    01291   dyphase_enum ini_simplex ;
    01292   struct { int sze ;
    01293            double *angle ;
    01294            int *actcnt ;
    01295            int *deactcnt ;
    01296            bool *init ;
    01297            bool *fin ; } cons ;
    01298   struct { int sze ;
    01299            int *actcnt ;
    01300            int *deactcnt ; } vars ;
    01301   struct { float max ;
    01302            float min ;
    01303            int hist[DYSTATS_HISTBINS] ; } angle ;
    01304   struct { int cnt ;
    01305            int prevpiv ;
    01306            float avgpivs ;
    01307            int maxpivs ; } factor ;
    01308   struct { int max ;
    01309            int mad ;
    01310            int sing ;
    01311            int pivtol_red ;
    01312            double min_pivtol ;
    01313            int puntcall ;
    01314            int puntret ; } pivrej ;
    01315   struct { int flippable ;
    01316            int cnt ;
    01317            int cands ;
    01318            int promote ;
    01319            int nontrivial ;
    01320            int evals ;
    01321            int flips ;
    01322            int pivrnks ;
    01323            int maxrnk ; } dmulti ;
    01324   struct { int cnt ;
    01325            int cands ;
    01326            int nontrivial ;
    01327            int promote ; } pmulti ;
    01328   struct { int prevpiv ;
    01329            int maxcnt ;
    01330            int totpivs ;
    01331            int maxpivs ;
    01332            int chgcnt1 ;
    01333            int chgcnt2 ; } infeas ;
    01334   struct { int cnt ;
    01335            float avgsiz ;
    01336            int maxsiz ;
    01337            int totpivs ;
    01338            float avgpivs ;
    01339            int maxpivs ; } pdegen[DYSTATS_MAXDEGEN] ;
    01340   struct { int cnt ;
    01341            float avgsiz ;
    01342            int maxsiz ;
    01343            int totpivs ;
    01344            float avgpivs ;
    01345            int maxpivs ; } ddegen[DYSTATS_MAXDEGEN] ;
    01346   struct { int iters ;
    01347            int pivs ; } tot ;
    01348   struct { int iters ;
    01349            int pivs ; } p1 ;
    01350   struct { int iters ;
    01351            int pivs ; } p2 ;
    01352   struct { int iters ;
    01353            int pivs ; } d2 ; } lpstats_struct ;
    01354
    01355
    01356
    01357 #ifdef DYLP_INTERNAL
    01358
    01359 /*
    01360   Macros to determine whether a constraint or variable is active, and whether
    01361   it's eligible for activation. Coding is explained below for dy_origcons and
    01362   dy_origvars. The main purpose served by these macros is to make it easy to
    01363   find activiation/deactivation points in the code, should the conventions ever
    01364   change.
    01365 */
    01366
    01367 #define ACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] > 0)
    01368 #define INACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] <= 0)
    01369 #define LOADABLE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] == 0)
    01370 #define MARK_UNLOADABLE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] = -1)
    01371 #define MARK_INACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] = 0)
    01372
    01373 #define ACTIVE_VAR(zz_vndx_zz) (dy_origvars[(zz_vndx_zz)] > 0)
    01374 #define INACTIVE_VAR(zz_vndx_zz) (dy_origvars[(zz_vndx_zz)] <= 0)
    01375 #define LOADABLE_VAR(zz_vndx_zz) \
    01376   ((dy_origvars[(zz_vndx_zz)] < 0) && \
    01377    flgoff(((flags) -dy_origvars[(zz_vndx_zz)]),vstatNOLOAD|vstatNBFX))
    01378 #define MARK_INACTIVE_VAR(zz_vndx_zz,zz_val_zz) \
    01379   (dy_origvars[(zz_vndx_zz)] = (zz_val_zz))
    01380
    01381
    01382 /*
    01383   dy_logchn             i/o id for the execution log file
    01384   dy_gtxecho            controls echoing of generated text to stdout
    01385 */
    01386
    01387 extern ioid dy_logchn ;
    01388 extern bool dy_gtxecho ;
    01389
    01390
    01391 /*
    01392   lp_struct
    01393
    01394   This structure is the control structure for an LP problem within dylp.
    01395
    01396   Field         Definition
    01397   -----         ----------
    01398   phase         Current phase of the dynamic simplex algorithm.
    01399   lpret         Return code from the most recent simplex execution.
    01400
    01401   z             Value of the objective function (includes inactzcorr).
    01402   inactzcorr    Correction to the objective function due to inactive variables
    01403                 with non-zero values.
    01404
    01405   simplex       Simplex algorithm status and control
    01406     active        currently active or most recently completed
    01407     next          currently active or to be started
    01408     init_pse      TRUE if the PSE structures need to be reinitialised,
    01409                   FALSE otherwise
    01410     init_dse      TRUE if the DSE structures need to be reinitialised,
    01411                   FALSE otherwise
    01412                 These fields are used to determine when to update or
    01413                 reinitialise the PSE and DSE data structures. Active and next
    01414                 must be valid during the purge/gen/add variable/constraint
    01415                 cycles.
    01416
    01417                 A word on infeas and infeascnt: They are guaranteed accurate
    01418                 only immediately after initialisation and following a primal
    01419                 feasibility check.
    01420
    01421   infeas        Total infeasibility = SUM{j} max(0,x<j>-ub<j>,lb<j>-x<j>)
    01422   infeascnt     The number of infeasible variables; refreshed when dy_accchk
    01423                 is asked to do a primal feasibility check.
    01424
    01425   ubnd          Substructure for information on unbounded or pseudo-unbounded
    01426                 problems.
    01427     ndx           The index of the variable fingered for causing unboundedness
    01428                   or pseudo-unboundedness (swing).
    01429     ratio         The growth ratio.
    01430
    01431   p1obj         The following fields relate to handling of the phase I
    01432                 objective function.
    01433     installed   TRUE if the phase I objective is currently installed
    01434     infcnt      Tracks the number of variables incorporated in p1obj which
    01435                 remain infeasible.
    01436     infvars_sze Allocated size of the infvars vector.
    01437     infvars     Vector of indices of infeasible variables incorporated in the
    01438                 phase I objective.
    01439     p1obj       Pointer to the phase I objective (temporary storage while
    01440                 the phase II objective is installed).
    01441     p2obj       Pointer to the phase II objective (temporary storage while
    01442                 the phase I objective is installed).
    01443
    01444                 A word on pivot and iteration counts: Iteration counts tally
    01445                 iterations of the pivoting loop, successful or not. Pivot
    01446                 counts tally successful bound-to-bound or change-of-basis
    01447                 pivots. Pretty much all messages will give tot.iters, so that
    01448                 it's possible to track the progress of an LP. Iterf has an
    01449                 entirely different function -- it's tracking the accumulation
    01450                 of eta matrices in the basis representation.
    01451
    01452   sys           Substructure for dynamic system modification status.
    01453     forcedfull    Set to TRUE if the full system has been forced in state
    01454                   dyFORCEFULL. This should happen at most once, so if we
    01455                   enter dyFORCEFULL and forcedfull == TRUE, it's fatal.
    01456     cons
    01457       loadable    Count of constraints which could be activated
    01458       unloadable  Count of constraints which are ineligible for activation
    01459                   (empty constraints and nonbinding rows)
    01460     vars
    01461       loadable    Count of variables which could be activated
    01462       unloadable  Count of variables which are ineligible for activation
    01463                   (nonbasic fixed)
    01464
    01465   tot           Total simplex iterations and pivots, all phases
    01466     iters
    01467     pivs
    01468   p1            Primal phase I iterations and pivots.
    01469     iters
    01470     pivs
    01471   p2            Primal phase II iterations and pivots.
    01472     iters
    01473     pivs
    01474   d2            Dual phase II iterations and pivots.
    01475     iters
    01476     pivs
    01477
    01478   pivok         Set to TRUE in dy_{primal|dual}pivot if the current iteration
    01479                 is a  successful pivot. Cleared to FALSE at the head of
    01480                 dy_duenna.
    01481   prev_pivok    Set to pivok at head of dy_duenna. Provides status of just
    01482                 completed pivot for post-Duenna decisions.
    01483
    01484   basis         Various fields related to basis change, refactoring, etc.
    01485
    01486     etas        The number of basis changes (hence eta matrices) since the
    01487                 the basis was last factored. Used to schedule periodic
    01488                 factoring of the basis. Reset to 0 each time the basis is
    01489                 factored.
    01490     pivs        The number of basis pivots since entry into a primal or dual
    01491                 simplex phase (excludes bound-to-bound simplex `pivots').
    01492                 Used when deciding whether to remove variables from the pivot
    01493                 reject list, and whether to pop out of a simplex phase due to
    01494                 excessive swing.
    01495     dinf        Number of successive refactors with dual infeasibility.
    01496                 Cleared at the start of a simplex phase.
    01497                 Incremented/cleared in dy_accchk iff a dual feasibility check
    01498                 is performed.
    01499
    01500   degen         Activation level of antidegeneracy algorithm. Held at 0 when
    01501                 the antidegeneracy algorithm is not active. Incremented each
    01502                 time a restricted subproblem is formed, and decremented when
    01503                 the restriction is backed out. (Values > 1 indicate that
    01504                 degeneracy recurred while working on a restricted subproblem,
    01505                 resulting in further restriction.)
    01506   degenpivcnt   The number of successive degenerate pivots.
    01507
    01508   idlecnt       The number of cycles since the objective has changed.
    01509
    01510   lastz         Previous objective value for various activities; used to
    01511                 detect and suppress loops.
    01512     piv           Objective at last pivot (detects stalling)
    01513     cd            Objective at last entry into constraint deactivation
    01514                   (dyPURGECON) (detects constraint activate/deactivate loops)
    01515     vd            Objective at last entry into variable deactivation
    01516                   (dyPURGEVAR) (detects variable activate/deactivate loops)
    01517     fp            Objective at last entry into force primal (dyFORCEPRIMAL)
    01518                   (detects constraint activate/deactivate loops)
    01519     fd            Objective at last entry into force dual (dyFORCEDUAL)
    01520                   (detects variable activate/deactivate loops)
    01521
    01522   prim          Primal variable information
    01523     norm1         1-norm of basic primal variables inv(B)b
    01524     norm2         2-norm of basic primal variables
    01525     max           inf-norm (max) of basic primal variables
    01526     maxndx        index of max primal variable
    01527
    01528   dual          Dual variable information
    01529     norm1         1-norm of dual variables c<B>inv(B)
    01530     norm2         2-norm of dual variables
    01531     max           inf-norm (max) of dual variables
    01532     maxndx        index of max dual variable
    01533
    01534 */
    01535
    01536 typedef struct
    01537 { dyphase_enum phase ;
    01538   lpret_enum lpret ;
    01539   double z ;
    01540   double inactzcorr ;
    01541   struct { dyphase_enum active ;
    01542            dyphase_enum next ;
    01543            bool init_pse ;
    01544            bool init_dse ; } simplex ;
    01545   double infeas ;
    01546   int infeascnt ;
    01547   struct { int ndx ;
    01548            double ratio ; } ubnd ;
    01549   struct { bool installed ;
    01550            int infcnt ;
    01551            int infvars_sze ;
    01552            int *infvars ;
    01553            double *p1obj ;
    01554            double *p2obj ; } p1obj ;
    01555   struct { struct { int loadable ;
    01556                     int unloadable ; } cons ;
    01557            struct { int loadable ;
    01558                     int unloadable ; } vars ;
    01559            bool forcedfull ; } sys ;
    01560   struct { int iters ;
    01561            int pivs ; } tot ;
    01562   struct { int iters ;
    01563            int pivs ; } p1 ;
    01564   struct { int iters ;
    01565            int pivs ; } p2 ;
    01566   struct { int iters ;
    01567            int pivs ; } d2 ;
    01568   bool pivok ;
    01569   bool prev_pivok ;
    01570   struct { int etas ;
    01571            int pivs ;
    01572            int dinf ; } basis ;
    01573   int degen ;
    01574   int degenpivcnt ;
    01575   int idlecnt ;
    01576   struct { double piv ;
    01577            double cd ;
    01578            double vd ;
    01579            double fp ;
    01580            double fd ; } lastz ;
    01581   struct { double norm1 ;
    01582            double norm2 ;
    01583            double max ;
    01584            int maxndx ; } prim ;
    01585   struct { double norm1 ;
    01586            double norm2 ;
    01587            double max ;
    01588            int maxndx ; } dual ;
    01589   } lp_struct ;
    01590
    01591
    01592 /*
    01593   Declarations global to the dylp implementation but not visible outside of
    01594   it. With this we can avoid passing huge numbers of parameters and/or
    01595   unpacking a structure on a regular basis. Unless otherwise indicated, indices
    01596   are in the dy_sys (active system) frame of reference.
    01597
    01598   dy_retained   TRUE if dylp thinks that the structures below are valid, FALSE
    01599                 otherwise.
    01600
    01601   Main structures
    01602   ---------------
    01603   dy_lp:        The lp control structure for dylp.
    01604   dy_sys:       The active constraint system; initialised in dylp:startup
    01605   dy_tols:      Tolerances in effect for dylp; initialised in
    01606                 dylp:dylp from orig_tols.
    01607   dy_opts:      Options in effect for dylp; initialised in
    01608                 dylp:dylp to point to same structure as orig_opts.
    01609   dy_stats      Statistics structure for dylp; initialised in dylp:dylp to
    01610                 point ot the same structure as orig_stats.
    01611
    01612   Constraint & Variable Management
    01613   --------------------------------
    01614   dy_actvars:   The active variables. Indexed in dy_sys frame, contains
    01615                 indices in orig_sys frame. Attached to dy_sys.
    01616                 Entries for logical variables (1 <= j <= concnt) are
    01617                 meaningless.
    01618   dy_actcons:   The active constraints. Indexed in dy_sys frame, contains
    01619                 indices in orig_sys frame. Attached to dy_sys.
    01620   dy_origvars:  Status of the original architectural variables.
    01621                  * A value of 0 indicates the entry hasn't been processed.
    01622                    Should never happen.
    01623                  * If the variable is active, the entry contains the index
    01624                    of the variable in the dy_sys frame.
    01625                  * If the variable is inactive, the coding is the negative of
    01626                    the vstat flags, limited to the nonbasic status values
    01627                    vstatNBFR, vstatNBFX, vstatNBLB, or vstatNBUB, and the
    01628                    qualifier vstatNOLOAD.
    01629                 Indexed in orig_sys frame. Attached to orig_sys.
    01630   dy_origcons:  Status of the original constraints.
    01631                  * If the constraint is active, the entry contains the index
    01632                    of the constraint in the dy_sys frame.
    01633                  * If the constraint is inactive, contains 0.
    01634                  * If the constraint cannot be activated, contains a negative
    01635                    value.
    01636                 Indexed in orig_sys frame. Attached to orig_sys.
    01637
    01638   Note that there are macros defined to test whether a variable or constraint
    01639   is inactive, and whether it's eligible for activation. Use them!
    01640
    01641   Basis Management
    01642   ----------------
    01643   dy_basis:     The basis vector. Indexed by basis position, attached to
    01644                 dy_sys.
    01645   dy_var2basis: Translates a variable index to a basis pos'n. Indexed by
    01646                 column, attached to dy_sys. Entries for nonbasic variables
    01647                 must be kept at 0.
    01648   dy_status:    The status vector. Indexed by column, attached to dy_sys.
    01649
    01650   Primal and Dual Variables
    01651   -------------------------
    01652   dy_x:         The values of all primal variables. Indexed by column,
    01653                 attached to dy_sys. Values of nonbasic variables must always
    01654                 be correct (to allow uniform handling of normal nonbasic
    01655                 variables and superbasic variables). Values of basic
    01656                 variables will retain unperturbed values while the
    01657                 antidegeneracy mechanism is active -- this allows the
    01658                 perturbation to be quickly backed out.
    01659   dy_xbasic:    The values of the basic variables. Indexed by basis pos'n,
    01660                 attached to dy_sys.
    01661   dy_y:         The dual variables. Indexed by basis pos'n, attached to
    01662                 dy_sys.
    01663
    01664   Projected Steepest Edge (PSE) Pricing
    01665   -------------------------------------
    01666   dy_cbar:      Iteratively updated vector of reduced costs. Indexed by column,
    01667                 attached to dy_sys.
    01668   dy_gamma:     Iteratively updated vector of column norms ||abar<j>||^2.
    01669                 Indexed by column, attached to dy_sys.
    01670   dy_frame:     Boolean vector which indicates if a given variable is in the
    01671                 current frame of reference. Indexed by column, attached to
    01672                 dy_sys.
    01673
    01674   Dual Steepest Edge (DSE) Pricing
    01675   --------------------------------
    01676   dy_rho:       Iteratively updated vector of row norms ||beta<i>||^2.
    01677                 Indexed by basis position, attached to dy_sys.
    01678
    01679   DSE pricing also makes use of dy_xbasic (the reduced costs of the dual
    01680   variables), and maintains dy_cbar.
    01681
    01682   Antidegeneracy
    01683   --------------
    01684   dy_brkout:    Specifies the direction a variable needs to move to escape
    01685                 from a degenerate vertex.  Indexed by basis pos'n, attached
    01686                 to dy_sys.
    01687   dy_degenset:  Specifies the set of constraints (equivalently, basic
    01688                 variables) perturbed at each level of the antidegeneracy
    01689                 algorithm. Indexed by basis pos'n, attached to dy_sys.  The
    01690                 entry for a constraint is the highest level of degenerate set
    01691                 which includes the constraint. If the entry is 0, the
    01692                 constraint is not involved in degeneracy.
    01693   dy_ddegenset: Specifies the set of dual constraints (equivalently, reduced
    01694                 costs) perturbed at each level of the antidegeneracy
    01695                 algorithm. Indexed by variable index, attached to dy_sys.
    01696                 The entry for a dual constraint is the highest level of
    01697                 degenerate set which includes the constraint. If the entry is
    01698                 0, the constraint is not involved in degeneracy.
    01699 */
    01700
    01701 extern bool dy_retained ;
    01702
    01703 extern lp_struct *dy_lp ;
    01704 extern consys_struct *dy_sys ;
    01705 extern lptols_struct *dy_tols ;
    01706 extern lpopts_struct *dy_opts ;
    01707 extern int *dy_actvars,*dy_actcons,*dy_origvars,*dy_origcons,
    01708            *dy_basis,*dy_var2basis,
    01709            *dy_brkout,*dy_degenset,*dy_ddegenset ;
    01710 extern flags *dy_status ;
    01711 extern double *dy_x,*dy_xbasic,*dy_y,*dy_cbar,*dy_gamma,*dy_rho ;
    01712 extern bool *dy_frame ;
    01713
    01714 extern lpstats_struct *dy_stats ;
    01715
    01716 /*
    01717   dy_scaling.c
    01718 */
    01719
    01720 extern bool dy_initlclsystem(lpprob_struct *orig_lp, bool hotstart) ;
    01721 extern void dy_freelclsystem(lpprob_struct *orig_lp, bool freesys) ;
    01722 extern bool dy_isscaled(void) ;
    01723 extern void dy_scaling_vectors(const double **rscale, const double **cscale) ;
    01724 extern consys_struct *dy_scaled_origsys() ;
    01725
    01726 /*
    01727   dy_coldstart.c
    01728 */
    01729
    01730 extern dyret_enum dy_coldstart(consys_struct *orig_sys),
    01731                   dy_crash(void) ;
    01732
    01733 /*
    01734   dy_warmstart.c
    01735 */
    01736
    01737 extern dyret_enum dy_warmstart(lpprob_struct *orig_lp) ;
    01738
    01739 /*
    01740   dy_hotstart.c
    01741 */
    01742
    01743 extern dyret_enum dy_hotstart(lpprob_struct *orig_lp) ;
    01744
    01745 /*
    01746   dy_basis.c
    01747 */
    01748
    01749 extern dyret_enum dy_factor(flags *calcflgs),
    01750                   dy_pivot(int xipos, double abarij, double maxabarj) ;
    01751 extern double dy_chkpiv(double abarij, double maxabarj) ;
    01752 extern void dy_btran(double *col), dy_ftran(double *col, bool save) ;
    01753 extern bool dy_setpivparms(int curdelta, int mindelta) ;
    01754 extern char *dy_prtpivparms(int lvl) ;
    01755
    01756 /*
    01757   dy_bound.c
    01758 */
    01759
    01760 extern int dy_activateBndCons(consys_struct *orig_sys) ;
    01761 extern int dy_dualaddvars(consys_struct *orig_sys) ;
    01762
    01763 /*
    01764   dy_conmgmt.c
    01765 */
    01766
    01767 extern bool dy_loadcon(consys_struct *orig_sys, int orig_ndx,
    01768                        bool genvars, int *inactndxs) ;
    01769 extern bool dy_deactNBLogPrimCon(consys_struct *orig_sys, int i),
    01770             dy_deactBLogPrimCon(consys_struct *orig_sys, int i),
    01771             dy_actBLogPrimCon(consys_struct *orig_sys, int i,
    01772                               int *inactvars),
    01773             dy_actBLogPrimConList(consys_struct *orig_sys,
    01774                                   int cnt, int *ocndxs, int **inactvars) ;
    01775 extern int dy_deactivateCons(consys_struct *orig_sys),
    01776            dy_activateCons(consys_struct *orig_sys, bool with_vars) ;
    01777
    01778 /*
    01779   dy_varmgmt.c
    01780 */
    01781
    01782 extern bool dy_actNBPrimArch(consys_struct *orig_sys, int ovndx),
    01783             dy_actNBPrimArchList(consys_struct *orig_sys,
    01784                                  int cnt, int *ovndxs),
    01785             dy_deactBPrimArch(consys_struct *orig_sys, int ovndx),
    01786             dy_deactNBPrimArch(consys_struct *orig_sys, int ovndx) ;
    01787 extern int dy_deactivateVars(consys_struct *orig_sys),
    01788            dy_activateVars(consys_struct *orig_sys, int *candidates) ;
    01789
    01790 /*
    01791   dy_primalpivot.c
    01792 */
    01793
    01794 extern dyret_enum dy_primalin(int initcol, int scan, int *xjndx, int *nextcol),
    01795                   dy_primalpivot(int xjndx, int indir, int *xindx, int *outdir,
    01796                                  double *abarij, double *delta, int *xjcand),
    01797                   dy_degenout(int level) ;
    01798
    01799 /*
    01800   dy_duenna.c
    01801 */
    01802
    01803 extern dyret_enum dy_duenna(dyret_enum pivresult, int xjndx, int xindx,
    01804                             int xjcand, int xicand),
    01805                   dy_accchk(flags *checks) ;
    01806
    01807 /*
    01808   dy_pivreject.c
    01809 */
    01810
    01811 extern dyret_enum dy_addtopivrej(int xkndx, dyret_enum why,
    01812                                  double abarij, double maxabarij),
    01813                   dy_dealWithPunt(void) ;
    01814 extern bool dy_clrpivrej(int *entries) ;
    01815 extern void dy_checkpivtol(void) ;
    01816 extern void dy_initpivrej(int sze), dy_freepivrej(void) ;
    01817
    01818
    01819 /*
    01820   dy_primal.c
    01821 */
    01822
    01823 extern lpret_enum dy_primal(void) ;
    01824 extern bool dy_initp1obj(void),dy_swapobjs(dyphase_enum phase) ;
    01825
    01826 /*
    01827   dy_dualpivot.c
    01828 */
    01829
    01830 extern dyret_enum
    01831   dy_dualout(int *xindx),
    01832   dy_dualpivot(int xindx, int outdir,
    01833                int *p_xjndx, int *p_indir, double *p_cbarj,
    01834                double *p_abarij, double *p_delta, int *xicand),
    01835   dy_dualdegenout(int level) ;
    01836
    01837 /*
    01838   dy_dual.c
    01839 */
    01840
    01841 extern lpret_enum dy_dual(void) ;
    01842
    01843 #endif /* DYLP_INTERNAL */
    01844
    01845 /*
    01846   dy_setup.c
    01847 */
    01848
    01849 extern void dy_defaults(lpopts_struct **opts, lptols_struct **tols),
    01850             dy_checkdefaults(consys_struct *sys,
    01851                              lpopts_struct *opts, lptols_struct *tols),
    01852             dy_setprintopts(int lvl, lpopts_struct *opts) ;
    01853
    01854
    01855 /*
    01856   dylp.c
    01857 */
    01858
    01859 extern lpret_enum dylp(lpprob_struct *orig_lp, lpopts_struct *orig_opts,
    01860                        lptols_struct *orig_tols, lpstats_struct *orig_stats) ;
    01861
    01862 /*
    01863   dylp_utils.c
    01864 */
    01865
    01866 #ifdef DYLP_INTERNAL
    01867
    01868 extern lpret_enum dyret2lpret(dyret_enum dyret) ;
    01869 extern dyret_enum dy_updateprimals(int j, double deltaj, double *p_abarj) ;
    01870 extern bool dy_reducerhs(double *rhs, bool init),
    01871             dy_calcprimals(void),dy_calccbar(void) ;
    01872 extern void dy_calcduals(void),dy_setbasicstatus(void),
    01873             dy_dseinit(void),dy_pseinit(void) ;
    01874 extern double dy_calcobj(void),dy_calcdualobj(void),dy_calcpinfeas(void) ;
    01875 extern void dy_finishup(lpprob_struct *orig_lp, dyphase_enum phase) ;
    01876
    01877 #ifdef DYLP_PARANOIA
    01878
    01879 extern bool dy_chkstatus(int vndx),
    01880             dy_chkdysys(consys_struct *orig_sys) ;
    01881 extern void dy_chkdual(int lvl) ;
    01882
    01883 #endif
    01884
    01885 #endif /* DYLP_INTERNAL */
    01886
    01887 extern bool dy_dupbasis(int dst_basissze, basis_struct **p_dst_basis,
    01888                         basis_struct *src_basis, int dst_statussze,
    01889                         flags **p_dst_status,
    01890                         int src_statuslen, flags *src_status) ;
    01891 extern void dy_freesoln(lpprob_struct *lpprob) ;
    01892
    01893 /*
    01894   dy_penalty.c
    01895 */
    01896
    01897 extern bool dy_pricenbvars(lpprob_struct *orig_lp, flags priceme,
    01898                            double **p_ocbar, int *p_nbcnt, int **p_nbvars),
    01899             dy_pricedualpiv(lpprob_struct *orig_lp, int oxindx,
    01900                             double nubi, double xi, double nlbi,
    01901                             int nbcnt, int *nbvars,
    01902                             double *cbar, double *p_upeni, double *p_dpeni) ;
    01903
    01904 /*
    01905   dy_tableau.c
    01906 */
    01907
    01908 extern bool dy_abarj(lpprob_struct *orig_lp, int tgt_j, double **p_abarj) ;
    01909 extern bool dy_betaj(lpprob_struct *orig_lp, int tgt_j, double **p_betaj) ;
    01910 extern bool dy_betai(lpprob_struct *orig_lp, int tgt_i, double **p_betai) ;
    01911 extern bool dy_abari(lpprob_struct *orig_lp, int tgt_i, double **p_abari,
    01912                      double **p_betai) ;
    01913
    01914 /*
    01915   dy_rays.c
    01916 */
    01917
    01918 extern bool dy_primalRays(lpprob_struct *orig_lp,
    01919                           int *p_numRays, double ***p_rays) ;
    01920 extern bool dy_dualRays(lpprob_struct *orig_lp,
    01921                         int *p_numRays, double ***p_rays) ;
    01922
    01923 /*
    01924   dy_solutions.c
    01925 */
    01926
    01927 extern void dy_colDuals(lpprob_struct *orig_lp, double **p_cbar) ;
    01928 extern void dy_rowDuals(lpprob_struct *orig_lp, double **p_y) ;
    01929
    01930 extern void dy_colPrimals(lpprob_struct *orig_lp, double **p_x) ;
    01931 extern void dy_rowPrimals(lpprob_struct *orig_lp,
    01932                           double **p_xB, int **p_indB) ;
    01933 extern void dy_logPrimals(lpprob_struct *orig_lp, double **p_logx) ;
    01934
    01935 extern void dy_colStatus(lpprob_struct *orig_lp, flags **p_colstat) ;
    01936 extern void dy_logStatus(lpprob_struct *orig_lp, flags **p_logstat) ;
    01937
    01938 extern bool dy_expandxopt(lpprob_struct *lp, double **p_xopt) ;
    01939
    01940 /*
    01941   dylp_io.c
    01942 */
    01943
    01944 #include <dylib_io.h>
    01945
    01946 #ifdef DYLP_INTERNAL
    01947
    01948 extern void dy_logpivot(dyret_enum result, int xjndx, int indir, double cbarj,
    01949                         int xindx, int outdir, double abarij, double delta) ;
    01950 extern const char *dy_prtdyret(dyret_enum retcode) ;
    01951
    01952 #endif /* DYLP_INTERNAL */
    01953
    01954 extern const char *dy_prtlpret(lpret_enum lpret),
    01955                   *dy_prtlpphase(dyphase_enum phase, bool abbrv) ;
    01956 extern char *dy_prtvstat(flags status) ;
    01957 extern bool dy_dumpcompact(ioid chn, bool echo, lpprob_struct *soln,
    01958                            bool nbzeros) ;
    01959
    01960 /*
    01961   dy_statistics.c
    01962
    01963   These routines are compiled unconditionally, but note that the compile-time
    01964   symbol DYLP_STATISTICS must be defined before dylp will actually take the
    01965   time to collect detailed statistics. See dy_statistics.c for additional
    01966   instructions.
    01967 */
    01968
    01969 extern void dy_initstats(lpstats_struct **p_lpstats, consys_struct *orig_sys),
    01970             dy_dumpstats(ioid chn, bool echo, lpstats_struct *lpstats,
    01971                          consys_struct *orig_sys),
    01972             dy_freestats(lpstats_struct **p_lpstats) ;
    01973
    01974 #ifdef DYLP_INTERNAL
    01975
    01976 extern void dy_finalstats(lpstats_struct *lpstats) ;
    01977
    01978 #endif /* DYLP_INTERNAL */
    01979
    01980
    01981 #endif /* _DYLP_H */