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dylp.h
Go to the documentation of this file.
/*
This file is a part of the Dylp LP distribution.
Copyright (C) 2005 -- 2007 Lou Hafer
School of Computing Science
Simon Fraser University
Burnaby, B.C., V5A 1S6, Canada
lou@cs.sfu.ca
This code is licensed under the terms of the Eclipse Public License (EPL).
*/
#ifndef _DYLP_H
#define _DYLP_H
/*
@(#)dylp.h 4.6 10/15/05
svn/cvs: $Id: dylp.h 407 2010-12-31 20:48:48Z lou $
This file contains definitions related to dylp, a subroutine library which
implements a dynamic (primal-dual) linear programming algorithm based on
the algorithm described by Padberg in Linear Optimisation & Extensions,
Springer-Verlag, 1995. dylp also owes a debt to previous and contemporary
codes the author has worked with --- la05, bandbx, zoom/xmp, ylp, and glpk.
At minimum, dylp requires only a constraint system. Since it manages a
dynamically sized private copy of the constraint system while solving the
LP, there's no point in having the client attach logical variables (they'd
just get in the way, really).
dylp will accept a basis specification. This takes the form of a status
vector giving the status of all variables, and a basis vector specifying
the active constraints and their associated basic variables. From this
dylp will construct an initial active problem which consists of exactly
the given constraints and basic variables, with the logicals for the
constraints making up the nonbasic partition.
dylp returns as a solution the simplex termination code, the objective
value (or related value, appropriate for the termination code), status for
all variables, the active constraints, and the associated primal and dual
variables (put a little differently, a basis, the values of the basic
variables, and the dual variables associated with the active constraints).
The conditional compilation symbol DYLP_INTERNAL is used to delimit
definitions that should be considered internal to dylp. Don't define this
symbol in a client.
*/
#include "dylib_errs.h"
#include "dylib_io.h"
#include "dy_consys.h"
/*
A few words on notation. Traditional matrix and vector notation for LP
suffers a bit when limited to ascii text, but it's readable if you're
familiar with the original. The notation in the comments and code is
loosely based on Chvatal, "Linear Programming", W.H. Freeman, 1983, which
the author happens to like.
A matrix is represented with a capital letter, e.g., B. A vector is
represented with a small letter, e.g., x. A subscript is given in angle
brackets, e.g., x<j> for the jth coefficient of x. An individual element of
a matrix has two subscripts, e.g., a<i,j> for the element in row i, column
j. Column and row vectors are shown with one subscript, e.g., a<j> for the
jth column (or row). Whether the vector is supposed to be a column or a
row should generally be clear from context. A capital letter in the
subscript position indicates a set of elements, e.g., x<N> is the non-basic
variables.
The inverse of a matrix is denoted inv(*), e.g., the basis inverse,
inv(B). The dot product of two vectors is denoted dot(*,*), e.g.,
dot(c,x), or sometimes just written directly, e.g., cx.
The system of constraints is assumed to be Ax <= b, with m rows and n
columns. Once the logical variables (aka slacks and artificials) have been
added, it becomes Ax = b. A is the constraint matrix, x is the vector of
primal variables, and b is the right-hand-side (rhs). NOTE that the
convention for indices is NOT the usual one. Logical variables are assigned
indices 1..m and architectural variables are assigned indices m+1..m+n. It
makes for more efficient addition/deletion of variables; see dy_consys.h for a
little more explanation.
There is an objective function z = cx, where z is the objective value and c
is the vector of coefficients. dylp minimises the objective.
The matrix A is partitioned into the set of basic columns B, and the set of
non-basic columns N (sometimes A<N>). The corresponding partitions of c and
x are c<B>, x<B>, and c<N>, x<N>.
Premultiplication by the basis inverse (e.g., inv(B)a<j>) is referred to as
an `ftran'; postmultiplication (e.g., c<B>inv(B)) as a `btran'. Quantities
that have been transformed using the basis inverse are often (but not
always) renamed as 'barred' quantities.
The basic primal variables are x<B> = inv(B)b. The dual variables are y =
c<B>inv(B). The jth column of A, premultiplied by inv(B), is abar<j> =
inv(B)a<j>. The reduced costs are cbar = c<N> - c<B>inv(B)N = c<N>-yN.
The variable i is used as a row index, j as a column index. Often they will
represent the entering primal variable (j) and the leaving primal variable
(i). Be aware that comments are often written as if the leaving primal
variable x<i> occupies row i of the basis. This simplifies the writing.
But keep in mind that variable x<i> can occupy an arbitrary row k of the
basis.
*/
/*
Termination codes for dy_primal and dy_dual, the top level routines of the
dylp simplex algorithms. Also used by various internal routines. Codes
marked with (*) will never be returned to the client unless dylp has
failed.
lpINV The code is not valid (i.e., not set by an execution of
dy_primal or dy_dual).
lpOPTIMAL The problem has an optimal solution.
lpUNBOUNDED The problem is unbounded.
lpSWING(*) The problem is pseudo-unbounded: Some primal variable grew
excessively in a single pivot.
lpINFEAS The problem is infeasible.
lpACCCHK An accuracy check failed and dylp's internal recovery
algorithms could not recover the situation.
lpSTALLED The problem has been abandoned due to stalling. (We could
in fact actually be cycling, but that's too much trouble
to prove.)
lpITERLIM The problem has been abandoned because it has exceeded an
absolute iteration limit.
lpNOSPACE The problem has been abandoned because the basis package did
not have sufficient space to maintain the basis.
lpLOSTFEAS Feasibility was lost during simplex execution.
lpPUNT The lp has punted because it ran into a pivoting problem.
The next three codes indicate that we're in the middle of
attempting a forced transition for error recovery purposes.
lpFORCEDUAL(*) Force a primal to dual transition.
lpFORCEPRIMAL(*) Force a dual to primal transition.
lpFORCEFULL(*) Force all inactive constraints and variables to be loaded.
lpFATAL Fatal confusion or error of some sort; covers a multitude
of sins.
The dual simplex routine does not have a phase I routine equivalent to
dy_primal1 for the primal simplex. (In the context of dylp, it expects
to run after dy_primal has been used to find an initial optimal solution.)
When using the dual simplex method, internal codes reflect the state of
the dual problem, but dy_dual makes the usual translation back to the
primal problem, as:
Dual Primal Rationale
---- ------ ---------
lpUNBOUNDED lpINFEAS Standard duality theorem.
Note that lpSWING always refers to primal variables.
*/
typedef enum { lpFATAL = -1, lpINV = 0,
lpOPTIMAL, lpUNBOUNDED, lpSWING, lpINFEAS,
lpACCCHK,
lpSTALLED, lpITERLIM, lpNOSPACE,
lpLOSTFEAS, lpPUNT,
lpFORCEDUAL, lpFORCEPRIMAL, lpFORCEFULL } lpret_enum ;
/*
Phase codes for dylp
dyINV Invalid phase
dyINIT Initialisation and setup, including establishing the
initial set of constraints and variables and crashing the
first basis.
dyPRIMAL1 Primal simplex phase I
dyPRIMAL2 Primal simplex phase II
dyDUAL Dual simplex
dyPURGEVAR Deactivation of variables.
dyGENVAR Generation of new variables (not part of original problem).
dyADDVAR Activation of variables.
dyPURGECON Deactivation of constraints.
dyGENCON Generation of new constraints (not part of original problem).
dyADDCON Activation of constraints.
dyFORCEDUAL Force dual feasibility (error recovery)
dyFORCEPRIMAL Force primal feasibility (error recovery)
dyFORCEFULL Force activation of the full system (error recovery)
dyDONE Execution is finished, for one reason or another.
It's true that new variables will be added during dyGENCON -- at the least,
each newly generated constraint will bring with it a logical variable.
dyGENVAR differs in that it is augmenting some subset of the constraints
with new variables (classic column generation, for example).
The main loop states (dyPRIMAL1 -- dyFORCEFULL) must remain a contiguous
block. dy_dumpstats counts on dyPRIMAL1 and dyFORCEPRIMAL being first and
last, respectively, in the block.
dyDONE must remain the last code --- it's used to dimension a statistics
array that tracks the number of times the main loop states are entered.
*/
typedef enum { dyINV = 0, dyINIT,
dyPRIMAL1, dyPRIMAL2, dyDUAL,
dyPURGEVAR, dyGENVAR, dyADDVAR,
dyPURGECON, dyGENCON, dyADDCON,
dyFORCEDUAL, dyFORCEPRIMAL, dyFORCEFULL,
dyDONE } dyphase_enum ;
/*
General return and error codes.
Used by various routines in dylp.
No routine
uses all of these, but there's enough overlap to make one big enum
convenient.
dyrINV Invalid code.
dyrOK Whatever it was that was being done was done without incident.
dyrOPTIMAL The problem is optimal.
dyrUNBOUND The problem is unbounded.
dyrSWING The problem is pseudo-unbounded: Some variable grew by an
excessive amount in a single pivot.
dyrINFEAS The problem is infeasible.
dyrREQCHK Requests a refactor and accuracy check (triggered by various
checks for bogus numbers).
dyrACCCHK An accuracy check has failed.
dyrLOSTPFEAS Primal feasibility has been lost.
dyrLOSTDFEAS Dual feasibility has been lost.
dyrDEGEN Degeneracy has been discovered, or a degenerate pivot has been
taken.
dyrRESELECT Reselect an incoming variable (after an abortive pivot
attempt).
dyrMADPIV The selected pivot coefficient was (numerically) unstable.
dyrPUNT In the context of the dual simplex: the dual simplex has
decided to punt to the primal simplex phase I, for any of
several reasons. Generally this is indicative of the relative
lack of sophistication in the dual simplex.
In the context of the primal simplex: this indicates that all
candidates to enter the basis were flagged with a NOPIVOT
qualifier.
dyrPATCHED The basis package managed to factor the basis after patching
it.
dyrSINGULAR The basis package discovered the basis was singular. (Typically
as a consequence of a pivot gone bad.)
dyrNUMERIC The basis package detected unacceptable growth in the basis
coefficients.
dyrBSPACE The basis package ran out of space for the basis
representation.
dyrSTALLED The LP seems to have stalled (and could possibly be cycling,
but that's too much trouble to prove); triggered by too many
iterations with no change in the objective.
dyrITERLIM The iteration limit has been exceeded.
dyrFATAL Fatal confusion; covers a multitude of sins.
The specific values assigned to some of the codes in the enum come from
earlier use of yla05 as the basis package. It's gone, but there's no
incentive to remove the values.
*/
typedef enum { dyrFATAL = -10, dyrITERLIM, dyrSTALLED,
dyrBSPACE = -7, dyrSINGULAR = -6, dyrNUMERIC = -5,
dyrLOSTPFEAS, dyrLOSTDFEAS, dyrDEGEN, dyrMADPIV,
dyrINV = 0, dyrOK = 1, dyrPATCHED = 2,
dyrRESELECT, dyrREQCHK, dyrACCCHK, dyrPUNT,
dyrOPTIMAL, dyrUNBOUND, dyrSWING, dyrINFEAS } dyret_enum ;
/*
Requests and results for checks and recalculations
Some symbolic names for requesting and reporting on factoring, accuracy
checks and primal and dual variable calculations. These originated with la
Duenna, hence the lad prefix. Interpretation varies subtly from routine to
routine, so check the parameter notes.
ladPRIMALCHK (i) set to request primal accuracy check, Bx<B> = b - Nx<N>,
(o) set to indicate failure of check
ladDUALCHK (i) set to to request dual accuracy check, yB = c<B>
(o) set to indicate failure of check
ladPRIMFEAS (i) set to request primal feasibility check (primal variables
within bounds)
(o) set to indicate loss of primal feasibility
ladDUALFEAS (i) set to request dual feasibility check (reduced costs of
proper sign)
(o) set to indicate loss of dual feasibility
ladPFQUIET (i) set to suppress warnings about variables which are not
primal feasible
ladDFQUIET (i) set to suppress warnings about variables which are not
dual feasible
ladDUALS (i) set to request calculation of the dual variables and
gradient vector
(o) set to indicate calculation of the dual variables and
gradient vector
ladPRIMALS (i) set to request calculation of the primal variables
(o) set to indicate calculation of the primal variables
ladFACTOR (i) set to indicate the basis should be refactored
(o) set to indicate the basis has been factored
ladEXPAND (i) set to force expansion of the space allocated for the
basis representation
(o) set to indicate the space allocated for the basis was
increased
*/
#define ladPRIMFEAS 1<<0
#define ladPRIMALCHK 1<<1
#define ladPFQUIET 1<<2
#define ladDUALFEAS 1<<3
#define ladDUALCHK 1<<4
#define ladDFQUIET 1<<5
#define ladDUALS 1<<6
#define ladPRIMALS 1<<7
#define ladFACTOR 1<<8
#define ladEXPAND 1<<9
␌
/*
Variable status codes
dylp keeps explicit status for both basic and nonbasic variables. These are
set up as flags so that it's easy to test when more than one status will do
for a particular action.
vstatBFX basic, fixed
vstatBUUB basic, above upper bound
vstatBUB basic, at upper bound
vstatB basic, strictly between bounds (a well-behaved basic variable)
vstatBLB basic, at lower bound
vstatBLLB basic, below lower bound
vstatBFR basic, free (unbounded)
vstatNBFX nonbasic, fixed
vstatNBUB nonbasic at upper bound
vstatNBLB nonbasic at lower bound
vstatNBFR nonbasic free
vstatSB superbasic, within bounds
dylp ensures that superbasic variables are, in fact, always strictly within
bounds.
Inactive NBFR variables can be created at startup if dylp is working with a
partial system and there are free variables that are not selected to be in
the initial basis. If the client is forcing a full system, these will be
active NBFR variables. Error recovery may also create active NBFR
variables. By convention, NBFR variables always have a value of zero.
Inactive SB variables should not occur. SB status occurs only as the result
of error recovery and is only valid in primal simplex.
The value of SB variables is lost when they are reported out as part of a
solution. This will only happen if dylp could not find an optimal solution.
The following qualifiers can be added to the status:
vstatNOPIVOT Prevents the variable from being considered as a candidate
for pivoting; used by the pivot rejection machinery.
vstatNOPER Prevents the variable from being perturbed during the
formation of a restricted subproblem.
vstatNOLOAD Prevents the variable from being considered for activation;
used by startup and variable activation/deactivation routines.
*/
#define vstatINV 0
#define vstatBFX 1<<0
#define vstatBUB 1<<1
#define vstatB 1<<2
#define vstatBLB 1<<3
#define vstatBFR 1<<4
#define vstatNBFX 1<<5
#define vstatNBUB 1<<6
#define vstatNBLB 1<<7
#define vstatNBFR 1<<8
#define vstatSB 1<<9
#define vstatBUUB 1<<10
#define vstatBLLB 1<<11
/*
TAKE NOTE: Do not use the msb as a qualifier! The status value, with or
without qualifiers, must be a positive value when cast to a signed integer.
*/
#define vstatNOPIVOT ((flags) 1<<(sizeof(flags)*8-2))
#define vstatNOPER ((flags) 1<<(sizeof(flags)*8-3))
#define vstatNOLOAD ((flags) 1<<(sizeof(flags)*8-4))
#define vstatBASIC \
(vstatBFX|vstatBUUB|vstatBUB|vstatB|vstatBLB|vstatBLLB|vstatBFR)
#define vstatNONBASIC (vstatNBFX|vstatNBUB|vstatNBLB)
#define vstatEXOTIC (vstatSB|vstatNBFR)
#define vstatSTATUS (vstatBASIC|vstatNONBASIC|vstatEXOTIC)
#define vstatQUALS (vstatNOPIVOT|vstatNOPER|vstatNOLOAD)
/*
This macro checks (in a simplistic way) that its parameter encodes one and
only one status. It's intended for mild error checking. See
dylp_utils:dy_chkstatus if you're really feeling paranoid.
*/
#define VALID_STATUS(zz_status_zz) \
(zz_status_zz == vstatBFX || zz_status_zz == vstatBUB || \
zz_status_zz == vstatB || zz_status_zz == vstatBLB || \
zz_status_zz == vstatBFR || \
zz_status_zz == vstatNBFX || zz_status_zz == vstatNBUB || \
zz_status_zz == vstatNBLB || zz_status_zz == vstatNBFR || \
zz_status_zz == vstatSB)
␌
/*
Interface structures: lpprob_struct, lptols_struct, lpopts_struct
*/
/*
basis_struct
This structure is used to describe a basis to dylp, and to return the
final basis at termination. The size of the basis depends on the
number of active constraints, which will be a subset of the constraints
in the system.
The constraint system as supplied to dylp should not have logical variables
(dylp will create them automatically). This presents a problem if the final
basis contains basic logical variables. In this case, vndx is set to the
negative of the index of the constraint which spawned the logical. This
same technique can be used on input to, for example, specify the traditional
all-logical starting basis.
Field Definition
----- ----------
len The number of rows in the basis.
el.cndx Index of the constraint in this basis position.
el.vndx Index of the variable in this basis position.
*/
typedef struct { int cndx ; int vndx ; } basisel_struct ;
typedef struct
{ int len ;
basisel_struct *el ; } basis_struct ;
/*
LP problem control and status flags
lpctlNOFREE (i) Prevents dylp from freeing the problem structures,
in anticipation of a subsequent hot start. If dylp
exits with a state that is not suitable for hot
start, this flag is ignored and the problem data
structures are released.
lpctlONLYFREE (i) In conjunction with an initial phase of dyDONE,
causes dylp to do nothing except free the problem
data structure and return.
lpctlUBNDCHG (i) Indicates that the variable upper bounds (vub) have
been changed.
lpctlLBNDCHG (i) Indicates that the variable lower bounds (lub) have
been changed.
lpctlRHSCHG (i) Indicates that the right-hand side (rhs) has been
changed. Includes the rhslow vector (if it exists).
lpctlOBJCHG (i) Indicates that the objective (obj) has been changed.
lpctlACTVARSIN (i) Indicates that a valid active variable vector has
been supplied.
lpctlINITACTVAR (i) Forces dylp to perform variable activation before
beginning simplex iterations.
lpctlINITACTCON (i) Forces dylp to perform constraint activation before
beginning simplex iterations. (If variable
activation is also requested, constraint activation
occurs first.)
lpctlACTVARSOUT (i) Indicates that an active variable vector is to be
returned.
(o) Indicates that a valid active variable vector has
been returned.
lpctlDYVALID (o) Indicates that dylp exited in a state which can
be restarted with a hot start.
*/
#define lpctlNOFREE 1<<0
#define lpctlONLYFREE 1<<1
#define lpctlUBNDCHG 1<<2
#define lpctlLBNDCHG 1<<3
#define lpctlRHSCHG 1<<4
#define lpctlOBJCHG 1<<5
#define lpctlACTVARSIN 1<<6
#define lpctlINITACTVAR 1<<7
#define lpctlINITACTCON 1<<8
#define lpctlACTVARSOUT 1<<10
#define lpctlDYVALID 1<<11
/*
lpprob_struct
This structure is used to pass an LP problem into dylp and convey the
results back to the client. The allocated size indicated in colsze and
rowsze is assumed to be accurate. If basis, status, x, or y are NULL, they
will be allocated as needed. If they are non-NULL, dylp will reallocate
them if necessary (i.e., when the actual size of the lp exceeds the
allocated size of the vectors).
The status vector has the following coding:
* for nonbasic variables, the normal dylp status flags are used;
* for basic variables, the negative of the basis index is used.
There is one unavoidable problem with this scheme -- the status vector
provides the only information about the value of nonbasic variables. This
is adequate for all but superbasic variables and nonbasic free variables
which are not at zero. Both of these cases are transient anomalies, created
only when the basis package is forced to patch a singular basis, and they
should not persist in the final solution when an optimal solution is found
or when the problem is infeasible. They may, however, occur in the
solution reported for an unbounded problem if the unbounded condition is
discovered before the nonbasic free or superbasic variable is chosen for
pivoting. On input, nonbasic free variables are assumed to take the value
0, and specifying a superbasic variable is illegal.
Field Definition
----- ----------
owner ID of the owner of this problem.
ctlopts Control and status flags.
phase (i) If set to dyDONE, dylp will free any retained data
structures and return. Any other value is ignored.
(o) Termination phase of the dynamic simplex algorithm;
should be dyDONE unless something screws up, in which
case it'll be dyINV.
lpret Return code from the simplex routine.
obj For lpOPTIMAL, the value of the objective function.
For lpINFEAS, the total infeasibility.
For lpUNBOUNDED, the index of the unbounded variable, negated
if the variable can decrease without bound, positive if it
can increase without bound. The logical for constraint i
is represented as n+i.
Otherwise, undefined.
iters The number of simplex iterations.
consys The constraint system.
fullsys True if the active constraint system is the full system, false
otherwise.
basis (i) Initial basis.
(o) Final basis.
status (i) Initial status vector.
(o) Final status vector.
x (i) No values used, but a vector can be supplied.
(o) The values of the basic variables (indexed by basis
position).
y (i) No values used, but a vector can be supplied.
(o) The values of the dual variables (indexed by basis
position).
actvars There is one entry for each variable, coded TRUE if the
variable is active, FALSE otherwise. The vector supplied on
input will be overwritten on output.
(i) Variables to be activated at startup. Used only for a
warm start. Validity is indicated by the lpctlACTVARSIN
flag. A vector can be supplied strictly for output use.
(o) The current active variables. Will be returned only if
requested by the lpctlACTVARSOUT flag. If the vector is
valid on return, lpctlACTVARSOUT will remain set,
otherwise it will be reset.
colsze Allocated column capacity (length of status vector).
rowsze Allocated row capacity (length of basis, x, and y vectors).
Note that dylp will reallocate status, basis->el, actvars, x, and y, if the
vectors supplied at startup are too small to report the solution. Don't set
colsze or rowsze to nonzero values without actually allocating space.
*/
typedef struct
{ void *owner ;
flags ctlopts ;
dyphase_enum phase ;
lpret_enum lpret ;
double obj ;
int iters ;
consys_struct *consys ;
bool fullsys ;
basis_struct *basis ;
flags *status ;
double *x ;
double *y ;
bool *actvars ;
int colsze ;
int rowsze ; } lpprob_struct ;
␌
/*
lptols_struct
This structure contains phase and tolerance information for the lp algorithm.
The philosophy with respect to the separate zero and feasibility tolerances
for primal and dual variables is that dylp uses the zero tolerance when
calculating primal or dual variables, and the feasibility tolerance when
checking for feasibility. This allows us to keep small values for accuracy
in computation, but not be so fussy when it comes to feasibility.
Field Definition
----- ----------
inf Infinity. dylp uses IEEE FP infinity, but be careful not to
pass it to the basis package.
zero Zero tolerance for primal variables, and also the generic
zero tolerance for constraint coefficients, right-hand-side
values, etc.
pchk Primal accuracy check tolerance.
pfeas Primal feasibility check tolerance; dynamically scaled from
zero in proportion to the 1-norm of the primal basic variables.
pfeas_scale Primal feasibility check tolerance multiplier. This provides
some user-controllable decoupling of zero and pfeas.
cost Base zero tolerance for checks involving objective function
coefficients, reduced costs, and related values.
dchk Dual accuracy check tolerance. Also used by dy_duenna to
test for improvement in the objective.
dfeas Dual feasbility check tolerance; dynamically scaled from cost
in proportion to the 1-norm of the dual variables. Acts as the
zero tolerance for reduced costs.
dfeas_scale Dual feasibility check tolerance multiplier. This provides
some user-controllable decoupling of cost and dfeas.
pivot Simplex pivot selection tolerance, expressed as a multiplier
for the pivot selection tolerance used by the basis package
when factoring the basis. (I.e., the actual pivot selection
criteria will be to accept a simplex pivot a<i,j> if
|a<i,j>| > lptols.pivot*basis.pivot*MAX{i}|a<i,j>|.)
bogus Multiplier used to identify 'bogus' values, in the range
tol < |val| < bogus*tol for the appropriate tolerance.
swing Ratio used to identify excessive growth in primal variables
(pseudo-unboundedness).
toobig Absolute value of primal variables which will cause dual
multipivoting to consider primal infeasibility when selecting
a flip/pivot sequence.
purge Percentage change in objective function required before
constraint or variable purging is attempted.
purgevar Percentage of maximum reduced cost used to determine the
variable purge threshold; nonbasic architectural variables
at their optimum bound whose reduced cost exceeds
purgevar*MAX{j}cbar<j> are purged.
reframe Multiplier used to trigger a reference framework reset in
PSE pricing; reset occurs if
|gamma<j> - ||abar<j>||^2| > reframe*||abar<j>||^2.
The check is made in pseupdate.
Also used to trigger recalculation of the basis inverse row
norms used in DSE pricing; reset occurs if
|rho<i> - ||beta<i>||^2| > reframe*||beta<i>||^2.
The check is made in dseupdate.
*/
typedef struct
{ double inf ;
double zero ;
double pchk ;
double pfeas ;
double pfeas_scale ;
double cost ;
double dchk ;
double dfeas ;
double dfeas_scale ;
double pivot ;
double bogus ;
double swing ;
double toobig ;
double purge ;
double purgevar ;
double reframe ; } lptols_struct ;
#if defined(DYLP_INTERNAL) || defined(BONSAIG)
/*
A few handy macros for testing values against tolerances.
*/
#ifdef DYLP_INTERNAL
# ifdef BND_TOLER
# undef BND_TOLER
# endif
# define BND_TOLER dy_tols->pfeas
# ifdef INF_TOLER
# undef INF_TOLER
# endif
# define INF_TOLER dy_tols->inf
#endif
#define withintol(zz_val_zz,zz_tgt_zz,zz_tol_zz) \
(fabs((zz_val_zz)-(zz_tgt_zz)) <= zz_tol_zz)
#define setcleanzero(zz_val_zz,zz_tol_zz) \
if (fabs(zz_val_zz) < zz_tol_zz) zz_val_zz = 0
#define atbnd(zz_val_zz,zz_bnd_zz) \
((fabs(zz_bnd_zz) < INF_TOLER) && \
(fabs((zz_val_zz)-(zz_bnd_zz)) < BND_TOLER*(1.0+fabs(zz_bnd_zz))))
#define belowbnd(zz_val_zz,zz_bnd_zz) \
((fabs(zz_bnd_zz) < INF_TOLER) ? \
(((zz_bnd_zz)-(zz_val_zz)) > BND_TOLER*(1.0+fabs(zz_bnd_zz))) : \
(zz_val_zz < zz_bnd_zz))
#define abovebnd(zz_val_zz,zz_bnd_zz) \
((fabs(zz_bnd_zz) < INF_TOLER) ? \
(((zz_val_zz)-(zz_bnd_zz)) > BND_TOLER*(1.0+fabs(zz_bnd_zz))) : \
(zz_val_zz > zz_bnd_zz))
#define withinbnds(zz_lb_zz,zz_val_zz,zz_ub_zz) \
(!abovebnd(zz_val_zz,zz_ub_zz) && !belowbnd(zz_val_zz,zz_lb_zz))
#endif /* DYLP_INTERNAL || BONSAIG */
#ifdef DYLP_INTERNAL
/*
Finally, a macro to decide if we should snap to a value. The notion here is
that the accuracy with which one can hit a target value depends on both the
magnitude of the target and the distance travelled to get there. On a
64-bit machine, IEEE FP has about 15 decimal digits of accuracy. For
example, if we're travelling 1.0e7 and trying to hit zero, we only have 8
decimal places of accuracy remaining. If we're within 1.0e-8, might as well
snap to 0. In practice, there's already a bit of roundoff in any nontrivial
calculation, so we start with the zero tolerance and scale from there.
In some cases, we only know the target, so the best we can do is
scale to it.
The utility of this idea is highly questionable.
*/
#define snaptol1(zz_tgt_zz) (dy_tols->zero*(1.0+(zz_tgt_zz)))
#define snaptol2(zz_tgt_zz,zz_dst_zz) \
(dy_tols->zero*(1.0+maxx((zz_tgt_zz),(zz_dst_zz))))
#define snaptol3(zz_tol_zz,zz_tgt_zz,zz_dst_zz) \
((zz_tol_zz)*(1.0+maxx((zz_tgt_zz),(zz_dst_zz))))
#endif /* DYLP_INTERNAL */
␌
/*
Enum for initial basis type.
This determines the criteria used to select the initial set of basic
variables during a cold start.
ibINV invalid
ibLOGICAL Use only logical (slack and artificial) variables
ibSLACK Use slack variables for inequalities. Prefer architectural
over artificial variables for equalities.
ibARCH Prefer architectural variables over logical variables.
*/
typedef enum { ibINV = 0, ibLOGICAL, ibSLACK, ibARCH } ibtype_enum ;
/*
Enum for calling context.
As dylp evolves, it has proven useful to know the context of the
call. Consider this a work in progress. The default context is INITIALLP.
cxINV invalid (context is unknown)
cxLOAD This call is only to (re)load data structures. Returns after
one iteration of dual or primal simplex, but shows problem
status rather than lpITERLIM.
cxUNLOAD This call is solely for the purpose of freeing the problem
data structures. (Replaces dyDONE/lpctlONLYFREE hack.)
cxSINGLELP This is a one-off call to solve a single LP from scratch.
cxINITIALLP This is a call to solve a single LP from scratch, but will
likely be followed by calls to reoptimise.
cxBANDC This call is made in the context of a branch-and-cut
algorithm.
cxUSERPIV This call is in the context of user control of pivoting.
*/
typedef enum { cxINV = 0, cxLOAD, cxUNLOAD,
cxSINGLELP, cxINITIALLP, cxBANDC, cxUSERPIV } cxtype_enum ;
/*
lpopts_struct
This structure is used to pass option settings to dylp. Default values are
declared at the beginning of dy_setup.c.
Field Definition
----- ----------
context The context in which dylp is being called. See comments
above for cxtype_enum.
forcecold TRUE to force a cold start, FALSE otherwise. If set to TRUE,
dominates warm and hot start.
forcewarm TRUE to force a warm start, FALSE otherwise. If set to TRUE,
dominates hot start.
fullsys Forces the use of the full constraint system at all times. The
full constraint system is loaded on startup, and all constraint
and variable deactivation/activation is skipped. (But see the
finpurge option below.) (Also, this will not prevent dylp
from resorting to forced phase transitions, which typically
involve deactivation of constraints or variables. Arguably
this is a bad thing, and may change in the future.)
active Used to estimate the initial size of the dylp constraint
system relative to the original system.
vars Fraction of original variables expected to be active at
any time.
cons Fraction of original inequalities expected to be active at
any time.
initcons Specifies how inequalities will be selected to initialize the
active system. See extensive comments in dy_coldstart.c.
frac Fraction of inequalities to be used.
i1l Lower bound on angle to objective, first interval
i1lopen TRUE if the bound is open.
i1u Upper bound on angle to objective, first interval
i1uopen TRUE if the bound is open.
i2valid TRUE if the second interval is specified
i2l Lower bound on angle to objective, second interval
i2lopen TRUE if the bound is open.
i2u Upper bound on angle to objective, second interval
i2uopen TRUE if the bound is open.
coldbasis Code specifying the kind of basis built for a cold start. See
comments for ibtype_enum and comments in dy_coldstart.c
finpurge Controls whether dylp does a final deactivation of constraints
and/or variables. This will occur only an optimal solution is
found, and is not suppressed by fullsys.
cons TRUE to purge constraints
vars TRUE to purge variables
heroics Controls behaviour during forced primal <-> dual transitions
d2p TRUE to allow deactivation of basic architecturals, FALSE
to disallow. FALSE is recommended, and the default.
p2d TRUE to allow deactivation of tight constraints, FALSE
to disallow. FALSE is recommended, and the default.
flip TRUE to allow flips to regain dual feasibility, FALSE to
disallow. Tends to cycle; default is false.
coldvars If the number of active variables exceeds this value after
a cold start, dylp will attempt to purge variables prior to
the initial primal simplex run.
con Options related to constraint activation/deactivation
actlvl The constraint activation strategy
0: (strict) activate violated constraints,
lhs < rhslow or lhs > rhs
1: (tight) activate tight or violated constraints,
lhs <= rhslow or lhs >= rhs
actlim If non-zero, limits the number of constraints that can be
activated in any one call to a constraint activation
routine.
deactlvl The constraint deactivation strategy:
0: (normal) deactivate only inequalities i which are
strictly loose (i.e., slk<i> basic, not at bound).
1: (aggressive) normal plus inequalities which are tight
with y<i> = 0.
2: (fanatic) aggressive plus equalities with y<i> = 0
usedual TRUE if dual phase II is to be used to regain feasibility after
adding constraints, FALSE to force use of primal phase I.
addvar If non-zero, at most this many variables will be added in
any one pass through phase dyADDVAR.
dualadd Controls the types of activation allowed when adding variables
during dual simplex.
0: variable activation is disallowed
1: type 1 activation (variables that will be dual feasible
when activated into the nonbasic partition)
2: type 2 activation (variables which can be activated
if immediately pivoted into the basis)
3: type 3 activation (activate with bound-to-bound pivot)
See dy_dualaddvars for more extensive comments.
scan Partial pricing parameter. Controls the number of columns to
be scanned for a new candidate entering variable when the
candidate selected during PSE update is rejected.
iterlim The per phase pivot limit for the code; if set to 0, no
limit is enforced.
idlelim The number of iterations without change in the objective
function before the code declares the problem is stalled or
cycling.
dpsel Options to control dual pivoting. Selection of the leaving
variable is always handled by DSE.
strat: The strategy used to select the entering variable:
0: standard ratio test; may use anti-degen lite
1: multipivoting, selecting for maximum dual objective
improvement.
2: multipivoting, select for minimum predicted
infeasibility.
3: multipivoting, select infeasibility reduction if
possible, otherwise maximum dual objective improvement.
flex If TRUE, dylp will switch between strategies 1 and 3, using
strategy 1 unless primal magnitudes become too large.
allownopiv If TRUE, sequences of flips with no finishing pivot will be
allowed. Defaults to false, very prone to cycling.
ppsel Options to control primal pivoting. Selection of the entering
variable is always handled by PSE.
strat: The strategy used to select the leaving variable:
0: standard ratio test; may use anti-degen lite
1: multipivoting
factor The LP basis will be refactored every factor iterations, in
the absence of some compelling reason (typically error
recovery) that forces it to occur sooner.
check An accuracy check will be forced every check iterations, in
the absence of some compelling reason to do it earlier.
groom Controls the action taken by the basis grooming routine
when it makes a nontrivial status correction:
0: catatonic
1: issue a warning
2: issue an error message and force an abort
Numeric codes should match keywords in dy_options.c:dy_ctlopt.
degen TRUE to allow creation of restricted subproblems to deal with
degeneracy, FALSE to disallow it.
degenpivlim The number of successive degenerate pivots required before
creating a restricted subproblem.
degenlite Controls secondary antidegeneracy --- `antidegen lite'
0: (pivotabort) break ties using |abar<kj>| and abort when
delta<j> = 0
1: (pivot) break ties using |abar<kj>| but always scan the
full basis
2: (alignobj) break ties by examining the alignment of the
hyperplane which will become tight on the pivot; choose
so that movement in the direction of the objective most
nearly lies in the hyperplane
3: (alignedge) break ties by examining the alignment of the
hyperplane which will become tight on the pivot; choose
so that the direction of motion defined by the entering
variable most nearly lies in the hyperplane.
4: (perpobj) break ties by examining the alignment of the
hyperplane which will become tight on the pivot; choose
so that the normal of the hyperplane is most nearly
aligned with the normal of the objective
5: (perpedge) break ties by examining the alignment of the
hyperplane which will become tight on the pivot; choose
so that the normal of the hyperplane is most nearly
aligned with the direction of motion
Numeric codes should match keywords in dy_options.c:dy_ctlopt.
patch TRUE to allow the code to patch a singular basis, FALSE to
prevent patching.
copyorigsys Controls whether dylp makes a local copy of the original
system. If set to TRUE, dylp will always make a local copy.
If set to FALSE, a copy will be made only if necessary.
Scaling will trigger a local copy.
scaling Controls whether dylp attempts to scale the original constraint
system for numeric stability.
0: scaling is forbidden
1: scale the original constraint system using numeric
scaling vectors attached to the system
2: evaluate the original constraint system and scale it if
necessary
Note that even if scaling = 0, dylp may install +/-1.0 scaling
vectors in order to flip >= constraints to <= constraints. See
comments in dy_scaling.c
print Substructure for picky printing control. For all print options,
a value of 0 suppresses all information messages.
major Controls printing of major phase information.
1: a message at each phase transition.
scaling Controls print level during initial evaluation and scaling of
the original constraint system.
1: start and finish messages
2: stability measures for original and scaled matrices;
adjustments to tolerances.
setup Controls print level while creating the initial constraint
system for dylp.
1: start and finish messages.
2: summary information about activated constraints
3: messages about each constraint included in the initial
system.
4: messages about each constraint processed for the initial
system
5: messages about each variable included in the initial
system.
6: lists value and status of inactive variables with
nonzero values
crash Controls print level while crashing the basis.
1: start & finish messages
2: summary counts for logicals, architecturals, artificials
3: a dump of the completed basis
4: detailed info on the selection of each architectural
and artificial variable
pricing Controls print level for pricing of columns (rows) in primal
(dual) simplex.
1: summary messages
2: lists candidate list and primal variable selected for
entry (exit) at each pivot
3: lists each variable as it's added to the candidate list
and again when reconsidered for pivoting
pivoting Controls print level for selection of the leaving (entering)
primal variable in primal (dual) simplex and updating of
variables.
1: prints result of leaving (entering) variable selection
2: information about the selection of the leaving (entering)
variable.
3: more information about the selection of the leaving
(entering) variable.
4: prints the pivot column (row) before and after
multiplication by the basis inverse, and yet more
pivot selection information.
5: prints a line for every candidate evaluated
pivreject Controls print level for information related to the operation
of the pivot rejection mechanism.
1: Prints a message for each row/column added to the pivot
rejection list, plus other major events.
2: Prints a message for each row/column removed from the
pivot rejection list.
degen Controls print level for information related to the operation
of the antidegeneracy mechanism.
1: prints a message each time the antidegeneracy level
changes
2: prints a message when a true degenerate pivot is taken
under duress
3: prints a message when a degenerate pivot is taken
4: prints anomalies as each degenerate set is formed and
backed out
5: prints details of each degenerate set as it's formed and
backed out
phase1 Controls general print level for phase 1 of primal simplex.
1: messages about extraordinary events -- problem pivots, etc.
2: messages about 'routine' but infrequent events --
termination conditions, refactoring, unboundedness, etc.
3: messages with additional details of problems encountered
4: a one line log message is printed for each pivot
5: summary information about infeasible variables and phase
I objective coefficients; information about primal
variables updated at each pivot.
6: prints the primal variables after each pivot; prints
infeasible variables during phase I objective construction
7: prints the dual variables after each pivot; prints
infeasible variables during phase I objective modification
phase2 Controls general print level for phase 1 of primal simplex.
1: messages about extraordinary events -- problem pivots, etc.
2: messages about 'routine' but infrequent events --
termination conditions, refactoring, unboundedness, etc.
3: messages with additional details of problems encountered
4: a one line log message is printed for each pivot
5: prints the updated basic primal variables after each pivot
6: prints all basic primal variables after each pivot
7: prints the dual variables after each pivot.
dual Controls general print level for the dual simplex. As
phase2.
basis Controls print level in routines working with the basis.
1: summary warnings about problems: empty rows, singularity,
numerical instability, etc.
2: information about factoring failures and recovery actions
3: warnings about individual empty rows, details of column
replacement when patching a singular basis, pivot
tolerance adjustments; information about pivoting failures
and recovery actions
4: basis stability after factoring
5: basis stability after pivoting
conmgmt Controls print level while dylp is in the purge/generate/
activate constraint phases.
1: prints the number of constraints purged, generated,
& activated, and new size of constraint system.
2: prints a message for each constraint purged or activated.
(The cut generation routine is responsible for
handling this function when it generates cuts.)
3: additional details about refactoring and new values
of primal and dual variables.
4: prints a message about any variables affected as a side
effect of constraint changes, constraints processed
but not activated, and information about direction of
recession and relative angle of constraints when adding
constraints to an unbounded problem.
5: prints a running commentary on constraint and variable
shifts, inactive variables.
varmgmt Controls print level while dylp is in the purge/generate/
activate variable phases.
1: prints the number of variables purged, generated,
& activated, and new size of constraint system.
2: prints a message for each variable purged & activated.
(The column generation routine is responsible for
handling this function when it generates new variables).
3: prints a message about any constraints affected as a side
effect of variable changes, variables processed but not
activated, and information about direction of recession
and relative angle of dual constraints when adding
variables to an unbounded dual.
4: prints a running commentary on constraint and variable
shifts.
force Controls print level when dylp is attempting to force a
transition (primal -> dual, dual -> primal) or force the
use of the full constraint system.
1: prints a summary message giving the result of the
transition attempt
2: prints messages about actions taken for individual
constraints and variables.
3: additional information about variables and constraints
examined.
tableau Controls print level for routines that generate tableau
vectors (beta<i>, beta<j>, abar<i>, abar<j>) for use by
external clients.
1: prints summary messages about the circumstances
4: prints nonzeros in the final vector.
5: prints nonzeros in intermediate vectors and (dy_betaj,
dy_abarj only) inactive rows
6: prints nonzeros of active portion in internal reference
frame (dy_betaj only)
rays Controls print level for routines that generate primal
and dual rays for use by external clients.
1: prints summary messages about vectors found.
3: print information about columns / rows examined.
4: print information about why a column or row was rejected.
5: print nonzeros for each ray
soln Controls print level for routines that generate primal and
dual solutions for use by external clients.
1: prints summary messages about the circumstances
3: prints nonzeros in the final vector
4: prints nonzeros in intermediate vectors
*/
typedef struct
{ cxtype_enum context ;
int scan ;
int iterlim ;
int idlelim ;
struct { int strat ;
bool flex ;
bool allownopiv ; } dpsel ;
struct { int strat ; } ppsel ;
int factor ;
int check ;
int groom ;
struct { int actlvl ;
int actlim ;
int deactlvl ; } con ;
int addvar ;
int dualadd ;
int coldvars ;
bool forcecold ;
bool forcewarm ;
bool usedual ;
bool degen ;
int degenpivlim ;
int degenlite ;
bool patch ;
bool fullsys ;
bool copyorigsys ;
int scaling ;
struct { float vars ;
float cons ; } active ;
struct { double frac ;
bool i1lopen ;
double i1l ;
bool i1uopen ;
double i1u ;
bool i2valid ;
bool i2lopen ;
double i2l ;
bool i2uopen ;
double i2u ; } initcons ;
ibtype_enum coldbasis ;
struct { bool cons ;
bool vars ; } finpurge ;
struct { bool d2p ;
bool p2d ;
bool flips ; } heroics ;
struct { int major ;
int scaling ;
int setup ;
int crash ;
int pricing ;
int pivoting ;
int pivreject ;
int degen ;
int phase1 ;
int phase2 ;
int dual ;
int basis ;
int conmgmt ;
int varmgmt ;
int force ;
int tableau ;
int rays ;
int soln ; } print ; } lpopts_struct ;
␌
/*
Statistics structure, used to collect information about aspects of dylp
operation beyond simple pivot counts. The data structure definition is
always present, but to fill it you have to define DYLP_STATISTICS.
Field Definition
----- ----------
phasecnts[dyDONE] Array with counts for number of times each phase is
executed.
ini_simplex The initial simplex phase
cons A set of arrays with data about individual constraints.
sze Allocated capacity of the arrays.
angle Angle to the objective function.
actcnt Number of times constraint is activated.
deactcnt Number of times constraint is deactivated.
init True if constraint is active in initial system.
fin True if constraint is active in final system.
vars A set of arrays with data about individual variables.
sze Allocated capacity of the arrays.
actcnt Number of times variable is activated.
deactcnt Number of times variable is deactivated.
angle
max Maximum angle to the objective function over all constraints.
min Minimum angle to the objective function over all constraints.
hist[*] Histogram of angles of constraints to the objective function.
There are DYSTATS_HISTBINS bins. Currently, 37 bins: 36 bins
spanning 5 degrees of angle, and a dedicated 90 degree bin.
factor Tracks how well we're doing with respect to refactoring the
basis.
cnt Number of time the basis has been refactored.
prevpiv Pivot count at last refactorisation.
avgpivs Average number of pivots between basis refactorisations.
maxpivs Maximum number of pivots between basis refactorisations.
pivrej Statistics about the pivot rejection list and punts.
max maximum number of entries on the pivot rejection list
mad total number of entries attributed to mad pivots
sing total number of entries attributed to singular pivots
pivtol_red total number of times the pivot tolerance was reduced
min_pivtol the minimum pivot tolerance used
puntcall total number of calls to dealWithPunt
puntret total number of dyrPUNT returns recommended
dmulti Tracks the dual multipivot algorithm. All fields except cnt are
totals; divide by cnt to get averages.
flippable Number of flippable variables in the constraint system.
cnt Total calls to dualmultiin
cands Number of candidates queued for evaluation for entry
promote Number of calls that resulted in promoting a sane pivot
over an unstable pivot.
nontrivial Number of times that the initial scan and sort left
multiple candidates for further evaluation.
evals Actual number of candidates evaluated (ftran'd column)
flips Number of bound-to-bound flips performed
pivrnk Index in the list of candidates of the candidate finally
selected for pivoting.
maxrnk Maximum index selected for pivoting.
pmulti Tracks the primal multipivot algorithm.
cnt Total calls to primalmultiin
cands Number of candidates queued for evaluation to leave
nontrivial Number of times that the candidate list was sorted
promote Number of calls that resulted in promoting a sane pivot
over an unstable pivot.
infeas Statistics on resolution of infeasibility in primal phase I.
Basically, what we're interested in tracking is the number
of infeasible variables and the number of pivots between a
change in the number of infeasible variables. We're interested
in separating the case of 1 variable from 2 or more, because
the latter requires vastly more calculation. A little care
is required because phase I can run many times.
prevpiv The pivot count (tot.iters) at the previous change.
maxcnt The maximum number of infeasible variables encountered (this
is not strictly monotonic, as dylp may enter phase I many
times due to activating violated constraints).
totpivs The total number of pivots expended in phase I.
maxpivs The maximum number of pivots with no change in the number of
feasible variables.
chgcnt1 The number of times that the number of infeasible variables
changed and reduced costs did not have to be recalculated
(specifically, exactly one variable became feasible, and it
left the basis as it did so).
chgcnt2 The number of times that the number of infeasible variables
changed in such a way as to require recalculation of the
reduced costs.
[dp]degen[*] Array of stats for each restricted subproblem nesting level,
with separate arrays for dual (ddegen) and primal (pdegen).
degen[0].cnt is used to hold the maximum nesting level.
cnt Number of times this nesting level was entered.
avgsiz The average number of variables in a restricted subproblem.
Kept by iterative update, as avg<k+1> = (avg<k>*k+size)/(k+1).
Suffers from cumulative loss of accuracy, but it'll do for
our purposes.
maxsiz The maximum number of variables in a restricted subproblem.
totpivs Total number of pivots at or above this nesting level.
avgpivs Average number of pivots at or above this nesting level.
maxpivs Maximum number of pivots for any one instance at or above
this nesting level.
tot, p1, p2, d2 Iteration and pivot counts, total and for each
individual phase. These are copied over from
dy_lp (lp_struct) at the end of the run, so that
they can be printed by dumpstats.
DYSTATS_MAXDEGEN is the maximum number of levels of nesting accommodated by
antidegeneracy statistics and debugging structures. The actual algorithm
has no inherent limitation.
DYSTATS_HISTBINS is the number of bins for constraint angles. It should be an
odd number. Each bin will span 180/(DYSTATS_HISTBINS-1) degrees, with the
final bin reserved for constraints at 90 degrees. For example, a value of 37
gives 180/(37-1) = 5 degrees per bin.
*/
#define DYSTATS_MAXDEGEN 25
#define DYSTATS_HISTBINS 37
typedef struct {
int phasecnts[dyDONE+1] ;
dyphase_enum ini_simplex ;
struct { int sze ;
double *angle ;
int *actcnt ;
int *deactcnt ;
bool *init ;
bool *fin ; } cons ;
struct { int sze ;
int *actcnt ;
int *deactcnt ; } vars ;
struct { float max ;
float min ;
int hist[DYSTATS_HISTBINS] ; } angle ;
struct { int cnt ;
int prevpiv ;
float avgpivs ;
int maxpivs ; } factor ;
struct { int max ;
int mad ;
int sing ;
int pivtol_red ;
double min_pivtol ;
int puntcall ;
int puntret ; } pivrej ;
struct { int flippable ;
int cnt ;
int cands ;
int promote ;
int nontrivial ;
int evals ;
int flips ;
int pivrnks ;
int maxrnk ; } dmulti ;
struct { int cnt ;
int cands ;
int nontrivial ;
int promote ; } pmulti ;
struct { int prevpiv ;
int maxcnt ;
int totpivs ;
int maxpivs ;
int chgcnt1 ;
int chgcnt2 ; } infeas ;
struct { int cnt ;
float avgsiz ;
int maxsiz ;
int totpivs ;
float avgpivs ;
int maxpivs ; } pdegen[DYSTATS_MAXDEGEN] ;
struct { int cnt ;
float avgsiz ;
int maxsiz ;
int totpivs ;
float avgpivs ;
int maxpivs ; } ddegen[DYSTATS_MAXDEGEN] ;
struct { int iters ;
int pivs ; } tot ;
struct { int iters ;
int pivs ; } p1 ;
struct { int iters ;
int pivs ; } p2 ;
struct { int iters ;
int pivs ; } d2 ; } lpstats_struct ;
␌
#ifdef DYLP_INTERNAL
/*
Macros to determine whether a constraint or variable is active, and whether
it's eligible for activation. Coding is explained below for dy_origcons and
dy_origvars. The main purpose served by these macros is to make it easy to
find activiation/deactivation points in the code, should the conventions ever
change.
*/
#define ACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] > 0)
#define INACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] <= 0)
#define LOADABLE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] == 0)
#define MARK_UNLOADABLE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] = -1)
#define MARK_INACTIVE_CON(zz_cndx_zz) (dy_origcons[(zz_cndx_zz)] = 0)
#define ACTIVE_VAR(zz_vndx_zz) (dy_origvars[(zz_vndx_zz)] > 0)
#define INACTIVE_VAR(zz_vndx_zz) (dy_origvars[(zz_vndx_zz)] <= 0)
#define LOADABLE_VAR(zz_vndx_zz) \
((dy_origvars[(zz_vndx_zz)] < 0) && \
flgoff(((flags) -dy_origvars[(zz_vndx_zz)]),vstatNOLOAD|vstatNBFX))
#define MARK_INACTIVE_VAR(zz_vndx_zz,zz_val_zz) \
(dy_origvars[(zz_vndx_zz)] = (zz_val_zz))
/*
dy_logchn i/o id for the execution log file
dy_gtxecho controls echoing of generated text to stdout
*/
extern ioid dy_logchn ;
extern bool dy_gtxecho ;
/*
lp_struct
This structure is the control structure for an LP problem within dylp.
Field Definition
----- ----------
phase Current phase of the dynamic simplex algorithm.
lpret Return code from the most recent simplex execution.
z Value of the objective function (includes inactzcorr).
inactzcorr Correction to the objective function due to inactive variables
with non-zero values.
simplex Simplex algorithm status and control
active currently active or most recently completed
next currently active or to be started
init_pse TRUE if the PSE structures need to be reinitialised,
FALSE otherwise
init_dse TRUE if the DSE structures need to be reinitialised,
FALSE otherwise
These fields are used to determine when to update or
reinitialise the PSE and DSE data structures. Active and next
must be valid during the purge/gen/add variable/constraint
cycles.
A word on infeas and infeascnt: They are guaranteed accurate
only immediately after initialisation and following a primal
feasibility check.
infeas Total infeasibility = SUM{j} max(0,x<j>-ub<j>,lb<j>-x<j>)
infeascnt The number of infeasible variables; refreshed when dy_accchk
is asked to do a primal feasibility check.
ubnd Substructure for information on unbounded or pseudo-unbounded
problems.
ndx The index of the variable fingered for causing unboundedness
or pseudo-unboundedness (swing).
ratio The growth ratio.
p1obj The following fields relate to handling of the phase I
objective function.
installed TRUE if the phase I objective is currently installed
infcnt Tracks the number of variables incorporated in p1obj which
remain infeasible.
infvars_sze Allocated size of the infvars vector.
infvars Vector of indices of infeasible variables incorporated in the
phase I objective.
p1obj Pointer to the phase I objective (temporary storage while
the phase II objective is installed).
p2obj Pointer to the phase II objective (temporary storage while
the phase I objective is installed).
A word on pivot and iteration counts: Iteration counts tally
iterations of the pivoting loop, successful or not. Pivot
counts tally successful bound-to-bound or change-of-basis
pivots. Pretty much all messages will give tot.iters, so that
it's possible to track the progress of an LP. Iterf has an
entirely different function -- it's tracking the accumulation
of eta matrices in the basis representation.
sys Substructure for dynamic system modification status.
forcedfull Set to TRUE if the full system has been forced in state
dyFORCEFULL. This should happen at most once, so if we
enter dyFORCEFULL and forcedfull == TRUE, it's fatal.
cons
loadable Count of constraints which could be activated
unloadable Count of constraints which are ineligible for activation
(empty constraints and nonbinding rows)
vars
loadable Count of variables which could be activated
unloadable Count of variables which are ineligible for activation
(nonbasic fixed)
tot Total simplex iterations and pivots, all phases
iters
pivs
p1 Primal phase I iterations and pivots.
iters
pivs
p2 Primal phase II iterations and pivots.
iters
pivs
d2 Dual phase II iterations and pivots.
iters
pivs
pivok Set to TRUE in dy_{primal|dual}pivot if the current iteration
is a successful pivot. Cleared to FALSE at the head of
dy_duenna.
prev_pivok Set to pivok at head of dy_duenna. Provides status of just
completed pivot for post-Duenna decisions.
basis Various fields related to basis change, refactoring, etc.
etas The number of basis changes (hence eta matrices) since the
the basis was last factored. Used to schedule periodic
factoring of the basis. Reset to 0 each time the basis is
factored.
pivs The number of basis pivots since entry into a primal or dual
simplex phase (excludes bound-to-bound simplex `pivots').
Used when deciding whether to remove variables from the pivot
reject list, and whether to pop out of a simplex phase due to
excessive swing.
dinf Number of successive refactors with dual infeasibility.
Cleared at the start of a simplex phase.
Incremented/cleared in dy_accchk iff a dual feasibility check
is performed.
degen Activation level of antidegeneracy algorithm. Held at 0 when
the antidegeneracy algorithm is not active. Incremented each
time a restricted subproblem is formed, and decremented when
the restriction is backed out. (Values > 1 indicate that
degeneracy recurred while working on a restricted subproblem,
resulting in further restriction.)
degenpivcnt The number of successive degenerate pivots.
idlecnt The number of cycles since the objective has changed.
lastz Previous objective value for various activities; used to
detect and suppress loops.
piv Objective at last pivot (detects stalling)
cd Objective at last entry into constraint deactivation
(dyPURGECON) (detects constraint activate/deactivate loops)
vd Objective at last entry into variable deactivation
(dyPURGEVAR) (detects variable activate/deactivate loops)
fp Objective at last entry into force primal (dyFORCEPRIMAL)
(detects constraint activate/deactivate loops)
fd Objective at last entry into force dual (dyFORCEDUAL)
(detects variable activate/deactivate loops)
prim Primal variable information
norm1 1-norm of basic primal variables inv(B)b
norm2 2-norm of basic primal variables
max inf-norm (max) of basic primal variables
maxndx index of max primal variable
dual Dual variable information
norm1 1-norm of dual variables c<B>inv(B)
norm2 2-norm of dual variables
max inf-norm (max) of dual variables
maxndx index of max dual variable
*/
typedef struct
{ dyphase_enum phase ;
lpret_enum lpret ;
double z ;
double inactzcorr ;
struct { dyphase_enum active ;
dyphase_enum next ;
bool init_pse ;
bool init_dse ; } simplex ;
double infeas ;
int infeascnt ;
struct { int ndx ;
double ratio ; } ubnd ;
struct { bool installed ;
int infcnt ;
int infvars_sze ;
int *infvars ;
double *p1obj ;
double *p2obj ; } p1obj ;
struct { struct { int loadable ;
int unloadable ; } cons ;
struct { int loadable ;
int unloadable ; } vars ;
bool forcedfull ; } sys ;
struct { int iters ;
int pivs ; } tot ;
struct { int iters ;
int pivs ; } p1 ;
struct { int iters ;
int pivs ; } p2 ;
struct { int iters ;
int pivs ; } d2 ;
bool pivok ;
bool prev_pivok ;
struct { int etas ;
int pivs ;
int dinf ; } basis ;
int degen ;
int degenpivcnt ;
int idlecnt ;
struct { double piv ;
double cd ;
double vd ;
double fp ;
double fd ; } lastz ;
struct { double norm1 ;
double norm2 ;
double max ;
int maxndx ; } prim ;
struct { double norm1 ;
double norm2 ;
double max ;
int maxndx ; } dual ;
} lp_struct ;
/*
Declarations global to the dylp implementation but not visible outside of
it. With this we can avoid passing huge numbers of parameters and/or
unpacking a structure on a regular basis. Unless otherwise indicated, indices
are in the dy_sys (active system) frame of reference.
dy_owner Null if there's no active problem. Contains the ID of the
current owner if there's an active problem. Passed in as
part of the lpprob_struct.
Main structures
---------------
dy_lp: The lp control structure for dylp.
dy_sys: The active constraint system; initialised in dylp:startup
dy_tols: Tolerances in effect for dylp; initialised in
dylp:dylp from orig_tols.
dy_opts: Options in effect for dylp; initialised in
dylp:dylp to point to same structure as orig_opts.
dy_stats Statistics structure for dylp; initialised in dylp:dylp to
point ot the same structure as orig_stats.
Constraint & Variable Management
--------------------------------
dy_actvars: The active variables. Indexed in dy_sys frame, contains
indices in orig_sys frame. Attached to dy_sys.
Entries for logical variables (1 <= j <= concnt) are
meaningless.
dy_actcons: The active constraints. Indexed in dy_sys frame, contains
indices in orig_sys frame. Attached to dy_sys.
dy_origvars: Status of the original architectural variables.
* A value of 0 indicates the entry hasn't been processed.
Should never happen.
* If the variable is active, the entry contains the index
of the variable in the dy_sys frame.
* If the variable is inactive, the coding is the negative of
the vstat flags, limited to the nonbasic status values
vstatNBFR, vstatNBFX, vstatNBLB, or vstatNBUB, and the
qualifier vstatNOLOAD.
Indexed in orig_sys frame. Attached to orig_sys.
dy_origcons: Status of the original constraints.
* If the constraint is active, the entry contains the index
of the constraint in the dy_sys frame.
* If the constraint is inactive, contains 0.
* If the constraint cannot be activated, contains a negative
value.
Indexed in orig_sys frame. Attached to orig_sys.
Note that there are macros defined to test whether a variable or constraint
is inactive, and whether it's eligible for activation. Use them!
Basis Management
----------------
dy_basis: The basis vector. Indexed by basis position, attached to
dy_sys.
dy_var2basis: Translates a variable index to a basis pos'n. Indexed by
column, attached to dy_sys. Entries for nonbasic variables
must be kept at 0.
dy_status: The status vector. Indexed by column, attached to dy_sys.
Primal and Dual Variables
-------------------------
dy_x: The values of all primal variables. Indexed by column,
attached to dy_sys. Values of nonbasic variables must always
be correct (to allow uniform handling of normal nonbasic
variables and superbasic variables). Values of basic
variables will retain unperturbed values while the
antidegeneracy mechanism is active -- this allows the
perturbation to be quickly backed out.
dy_xbasic: The values of the basic variables. Indexed by basis pos'n,
attached to dy_sys.
dy_y: The dual variables. Indexed by basis pos'n, attached to
dy_sys.
Projected Steepest Edge (PSE) Pricing
-------------------------------------
dy_cbar: Iteratively updated vector of reduced costs. Indexed by column,
attached to dy_sys.
dy_gamma: Iteratively updated vector of column norms ||abar<j>||^2.
Indexed by column, attached to dy_sys.
dy_frame: Boolean vector which indicates if a given variable is in the
current frame of reference. Indexed by column, attached to
dy_sys.
Dual Steepest Edge (DSE) Pricing
--------------------------------
dy_rho: Iteratively updated vector of row norms ||beta<i>||^2.
Indexed by basis position, attached to dy_sys.
DSE pricing also makes use of dy_xbasic (the reduced costs of the dual
variables), and maintains dy_cbar.
Antidegeneracy
--------------
dy_brkout: Specifies the direction a variable needs to move to escape
from a degenerate vertex. Indexed by basis pos'n, attached
to dy_sys.
dy_degenset: Specifies the set of constraints (equivalently, basic
variables) perturbed at each level of the antidegeneracy
algorithm. Indexed by basis pos'n, attached to dy_sys. The
entry for a constraint is the highest level of degenerate set
which includes the constraint. If the entry is 0, the
constraint is not involved in degeneracy.
dy_ddegenset: Specifies the set of dual constraints (equivalently, reduced
costs) perturbed at each level of the antidegeneracy
algorithm. Indexed by variable index, attached to dy_sys.
The entry for a dual constraint is the highest level of
degenerate set which includes the constraint. If the entry is
0, the constraint is not involved in degeneracy.
*/
extern void *dy_owner ;
extern lp_struct *dy_lp ;
extern consys_struct *dy_sys ;
extern lptols_struct *dy_tols ;
extern lpopts_struct *dy_opts ;
extern int *dy_actvars,*dy_actcons,*dy_origvars,*dy_origcons,
*dy_basis,*dy_var2basis,
*dy_brkout,*dy_degenset,*dy_ddegenset ;
extern flags *dy_status ;
extern double *dy_x,*dy_xbasic,*dy_y,*dy_cbar,*dy_gamma,*dy_rho ;
extern bool *dy_frame ;
extern lpstats_struct *dy_stats ;
/*
dy_scaling.c
*/
extern bool dy_initlclsystem(lpprob_struct *orig_lp, bool hotstart) ;
extern void dy_freelclsystem(lpprob_struct *orig_lp, bool freesys) ;
extern bool dy_isscaled(void) ;
extern void dy_scaling_vectors(const double **rscale, const double **cscale) ;
extern consys_struct *dy_scaled_origsys() ;
/*
dy_coldstart.c
*/
extern dyret_enum dy_coldstart(consys_struct *orig_sys),
dy_crash(void) ;
/*
dy_warmstart.c
*/
extern dyret_enum dy_warmstart(lpprob_struct *orig_lp) ;
/*
dy_hotstart.c
*/
extern dyret_enum dy_hotstart(lpprob_struct *orig_lp) ;
/*
dy_basis.c
*/
extern dyret_enum dy_factor(flags *calcflgs),
dy_pivot(int xipos, double abarij, double maxabarj) ;
extern double dy_chkpiv(double abarij, double maxabarj) ;
extern void dy_btran(double *col), dy_ftran(double *col, bool save) ;
extern bool dy_setpivparms(int curdelta, int mindelta) ;
extern char *dy_prtpivparms(int lvl) ;
/*
dy_bound.c
*/
extern int dy_activateBndCons(consys_struct *orig_sys) ;
extern int dy_dualaddvars(consys_struct *orig_sys) ;
/*
dy_conmgmt.c
*/
extern bool dy_loadcon(consys_struct *orig_sys, int orig_ndx,
bool genvars, int *inactndxs) ;
extern bool dy_deactNBLogPrimCon(consys_struct *orig_sys, int i),
dy_deactBLogPrimCon(consys_struct *orig_sys, int i),
dy_actBLogPrimCon(consys_struct *orig_sys, int i,
int *inactvars),
dy_actBLogPrimConList(consys_struct *orig_sys,
int cnt, int *ocndxs, int **inactvars) ;
extern int dy_deactivateCons(consys_struct *orig_sys),
dy_activateCons(consys_struct *orig_sys, bool with_vars) ;
/*
dy_varmgmt.c
*/
extern bool dy_actNBPrimArch(consys_struct *orig_sys, int ovndx),
dy_actNBPrimArchList(consys_struct *orig_sys,
int cnt, int *ovndxs),
dy_deactBPrimArch(consys_struct *orig_sys, int ovndx),
dy_deactNBPrimArch(consys_struct *orig_sys, int ovndx) ;
extern int dy_deactivateVars(consys_struct *orig_sys),
dy_activateVars(consys_struct *orig_sys, int *candidates) ;
/*
dy_primalpivot.c
*/
extern dyret_enum dy_primalin(int initcol, int scan, int *xjndx, int *nextcol),
dy_primalpivot(int xjndx, int indir, int *xindx, int *outdir,
double *abarij, double *delta, int *xjcand),
dy_degenout(int level) ;
/*
dy_duenna.c
*/
extern dyret_enum dy_duenna(dyret_enum pivresult, int xjndx, int xindx,
int xjcand, int xicand),
dy_accchk(flags *checks) ;
/*
dy_pivreject.c
*/
extern dyret_enum dy_addtopivrej(int xkndx, dyret_enum why,
double abarij, double maxabarij),
dy_dealWithPunt(void) ;
extern bool dy_clrpivrej(int *entries) ;
extern void dy_checkpivtol(void) ;
extern void dy_initpivrej(int sze), dy_freepivrej(void) ;
/*
dy_primal.c
*/
extern lpret_enum dy_primal(void) ;
extern bool dy_initp1obj(void),dy_swapobjs(dyphase_enum phase) ;
/*
dy_dualpivot.c
*/
extern dyret_enum
dy_dualout(int *xindx),
dy_dualpivot(int xindx, int outdir,
int *p_xjndx, int *p_indir, double *p_cbarj,
double *p_abarij, double *p_delta, int *xicand),
dy_dualdegenout(int level) ;
/*
dy_dual.c
*/
extern lpret_enum dy_dual(void) ;
#endif /* DYLP_INTERNAL */
/*
dy_setup.c
*/
extern void dy_defaults(lpopts_struct **opts, lptols_struct **tols),
dy_checkdefaults(consys_struct *sys,
lpopts_struct *opts, lptols_struct *tols),
dy_setprintopts(int lvl, lpopts_struct *opts) ;
/*
dylp.c
*/
extern lpret_enum dylp(lpprob_struct *orig_lp, lpopts_struct *orig_opts,
lptols_struct *orig_tols, lpstats_struct *orig_stats) ;
extern void *dy_getOwner() ;
/*
dylp_utils.c
*/
#ifdef DYLP_INTERNAL
extern lpret_enum dyret2lpret(dyret_enum dyret) ;
extern dyret_enum dy_updateprimals(int j, double deltaj, double *p_abarj) ;
extern bool dy_reducerhs(double *rhs, bool init),
dy_calcprimals(void),dy_calccbar(void) ;
extern void dy_calcduals(void),dy_setbasicstatus(void),
dy_dseinit(void),dy_pseinit(void) ;
extern double dy_calcobj(void),dy_calcdualobj(void),dy_calcpinfeas(void) ;
extern void dy_finishup(lpprob_struct *orig_lp, dyphase_enum phase) ;
#ifdef DYLP_PARANOIA
extern bool dy_chkstatus(int vndx),
dy_chkdysys(consys_struct *orig_sys) ;
extern void dy_chkdual(int lvl) ;
#endif
#endif /* DYLP_INTERNAL */
extern bool dy_dupbasis(int dst_basissze, basis_struct **p_dst_basis,
basis_struct *src_basis, int dst_statussze,
flags **p_dst_status,
int src_statuslen, flags *src_status) ;
extern void dy_freesoln(lpprob_struct *lpprob) ;
/*
dy_penalty.c
*/
extern bool dy_pricenbvars(lpprob_struct *orig_lp, flags priceme,
double **p_ocbar, int *p_nbcnt, int **p_nbvars),
dy_pricedualpiv(lpprob_struct *orig_lp, int oxindx,
double nubi, double xi, double nlbi,
int nbcnt, int *nbvars,
double *cbar, double *p_upeni, double *p_dpeni) ;
/*
dy_tableau.c
*/
extern bool dy_abarj(lpprob_struct *orig_lp, int tgt_j, double **p_abarj) ;
extern bool dy_betaj(lpprob_struct *orig_lp, int tgt_j, double **p_betaj) ;
extern bool dy_betak(lpprob_struct *orig_lp, int col_k, double **p_betaj) ;
extern bool dy_betai(lpprob_struct *orig_lp, int tgt_i, double **p_betai) ;
extern bool dy_abari(lpprob_struct *orig_lp, int tgt_i, double **p_abari,
double **p_betai) ;
/*
dy_rays.c
*/
extern bool dy_primalRays(lpprob_struct *orig_lp,
int *p_numRays, double ***p_rays) ;
extern bool dy_dualRays(lpprob_struct *orig_lp, bool fullRay,
int *p_numRays, double ***p_rays, bool trueDuals) ;
/*
dy_solutions.c
*/
extern void dy_colDuals(lpprob_struct *orig_lp, double **p_cbar,
bool trueDuals) ;
extern void dy_rowDuals(lpprob_struct *orig_lp, double **p_y,
bool trueDuals) ;
extern void dy_rowDualsGivenC(lpprob_struct *orig_lp, double **p_y,
const double *c, bool trueDuals) ;
extern void dy_colPrimals(lpprob_struct *orig_lp, double **p_x) ;
extern void dy_rowPrimals(lpprob_struct *orig_lp,
double **p_xB, int **p_indB) ;
extern void dy_logPrimals(lpprob_struct *orig_lp, double **p_logx) ;
extern void dy_colStatus(lpprob_struct *orig_lp, flags **p_colstat) ;
extern void dy_logStatus(lpprob_struct *orig_lp, flags **p_logstat) ;
extern bool dy_expandxopt(lpprob_struct *lp, double **p_xopt) ;
/*
dylp_io.c
*/
#include <dylib_io.h>
#ifdef DYLP_INTERNAL
extern void dy_logpivot(dyret_enum result, int xjndx, int indir, double cbarj,
int xindx, int outdir, double abarij, double delta) ;
extern const char *dy_prtdyret(dyret_enum retcode) ;
#endif /* DYLP_INTERNAL */
extern const char *dy_prtlpret(lpret_enum lpret),
*dy_prtlpphase(dyphase_enum phase, bool abbrv) ;
extern char *dy_prtvstat(flags status) ;
extern bool dy_dumpcompact(ioid chn, bool echo, lpprob_struct *soln,
bool nbzeros) ;
extern void dy_setlogchn (ioid chn) ;
extern void dy_setgtxecho (bool echo) ;
/*
dy_statistics.c
These routines are compiled unconditionally, but note that the compile-time
symbol DYLP_STATISTICS must be defined before dylp will actually take the
time to collect detailed statistics. See dy_statistics.c for additional
instructions.
*/
extern void dy_initstats(lpstats_struct **p_lpstats, consys_struct *orig_sys),
dy_dumpstats(ioid chn, bool echo, lpstats_struct *lpstats,
consys_struct *orig_sys),
dy_freestats(lpstats_struct **p_lpstats) ;
#ifdef DYLP_INTERNAL
extern void dy_finalstats(lpstats_struct *lpstats) ;
#endif /* DYLP_INTERNAL */
#endif /* _DYLP_H */
dy_consys.h
dylib_errs.h
dylib_io.h
ioid
int ioid
Definition dylib_io.h:39
flags
unsigned int flags
Definition dylib_std.h:97
dy_actvars
int * dy_actvars
dy_stats
lpstats_struct * dy_stats
dy_prtpivparms
char * dy_prtpivparms(int lvl)
dy_abarj
bool dy_abarj(lpprob_struct *orig_lp, int tgt_j, double **p_abarj)
dy_actNBPrimArch
bool dy_actNBPrimArch(consys_struct *orig_sys, int ovndx)
dy_checkpivtol
void dy_checkpivtol(void)
dy_brkout
int * dy_brkout
Definition dylp.h:1724
dy_freelclsystem
void dy_freelclsystem(lpprob_struct *orig_lp, bool freesys)
dy_duenna
dyret_enum dy_duenna(dyret_enum pivresult, int xjndx, int xindx, int xjcand, int xicand)
dy_y
double * dy_y
Definition dylp.h:1726
dy_colStatus
void dy_colStatus(lpprob_struct *orig_lp, flags **p_colstat)
dy_pivot
dyret_enum dy_pivot(int xipos, double abarij, double maxabarj)
dy_dumpcompact
bool dy_dumpcompact(ioid chn, bool echo, lpprob_struct *soln, bool nbzeros)
dy_degenset
int * dy_degenset
Definition dylp.h:1724
dy_lp
lp_struct * dy_lp
dy_setgtxecho
void dy_setgtxecho(bool echo)
dy_pseinit
void dy_pseinit(void)
DYSTATS_HISTBINS
#define DYSTATS_HISTBINS
Definition dylp.h:1301
dy_btran
void dy_btran(double *col)
dy_primal
lpret_enum dy_primal(void)
dy_xbasic
double * dy_xbasic
Definition dylp.h:1726
dy_updateprimals
dyret_enum dy_updateprimals(int j, double deltaj, double *p_abarj)
ibtype_enum
ibtype_enum
Definition dylp.h:766
ibINV
@ ibINV
Definition dylp.h:766
ibARCH
@ ibARCH
Definition dylp.h:766
ibLOGICAL
@ ibLOGICAL
Definition dylp.h:766
ibSLACK
@ ibSLACK
Definition dylp.h:766
dy_factor
dyret_enum dy_factor(flags *calcflgs)
dy_coldstart
dyret_enum dy_coldstart(consys_struct *orig_sys)
dy_opts
lpopts_struct * dy_opts
dy_dual
lpret_enum dy_dual(void)
dy_dualdegenout
dyret_enum dy_dualdegenout(int level)
dy_actcons
int * dy_actcons
Definition dylp.h:1722
dy_warmstart
dyret_enum dy_warmstart(lpprob_struct *orig_lp)
dy_isscaled
bool dy_isscaled(void)
dy_calcdualobj
double dy_calcdualobj(void)
dy_dupbasis
bool dy_dupbasis(int dst_basissze, basis_struct **p_dst_basis, basis_struct *src_basis, int dst_statussze, flags **p_dst_status, int src_statuslen, flags *src_status)
dy_deactBLogPrimCon
bool dy_deactBLogPrimCon(consys_struct *orig_sys, int i)
dy_activateCons
int dy_activateCons(consys_struct *orig_sys, bool with_vars)
dy_logStatus
void dy_logStatus(lpprob_struct *orig_lp, flags **p_logstat)
dy_crash
dyret_enum dy_crash(void)
dy_abari
bool dy_abari(lpprob_struct *orig_lp, int tgt_i, double **p_abari, double **p_betai)
dy_dealWithPunt
dyret_enum dy_dealWithPunt(void)
dy_setprintopts
void dy_setprintopts(int lvl, lpopts_struct *opts)
dy_sys
consys_struct * dy_sys
cxtype_enum
cxtype_enum
Definition dylp.h:788
cxINITIALLP
@ cxINITIALLP
Definition dylp.h:789
cxUSERPIV
@ cxUSERPIV
Definition dylp.h:789
cxINV
@ cxINV
Definition dylp.h:788
cxBANDC
@ cxBANDC
Definition dylp.h:789
cxSINGLELP
@ cxSINGLELP
Definition dylp.h:789
cxUNLOAD
@ cxUNLOAD
Definition dylp.h:788
cxLOAD
@ cxLOAD
Definition dylp.h:788
dy_checkdefaults
void dy_checkdefaults(consys_struct *sys, lpopts_struct *opts, lptols_struct *tols)
dy_setbasicstatus
void dy_setbasicstatus(void)
dy_betak
bool dy_betak(lpprob_struct *orig_lp, int col_k, double **p_betaj)
dy_dualpivot
dyret_enum dy_dualpivot(int xindx, int outdir, int *p_xjndx, int *p_indir, double *p_cbarj, double *p_abarij, double *p_delta, int *xicand)
dylp
lpret_enum dylp(lpprob_struct *orig_lp, lpopts_struct *orig_opts, lptols_struct *orig_tols, lpstats_struct *orig_stats)
dy_primalpivot
dyret_enum dy_primalpivot(int xjndx, int indir, int *xindx, int *outdir, double *abarij, double *delta, int *xjcand)
dy_loadcon
bool dy_loadcon(consys_struct *orig_sys, int orig_ndx, bool genvars, int *inactndxs)
dy_finishup
void dy_finishup(lpprob_struct *orig_lp, dyphase_enum phase)
dy_freesoln
void dy_freesoln(lpprob_struct *lpprob)
dy_prtvstat
char * dy_prtvstat(flags status)
dy_ftran
void dy_ftran(double *col, bool save)
dy_freepivrej
void dy_freepivrej(void)
dy_expandxopt
bool dy_expandxopt(lpprob_struct *lp, double **p_xopt)
dy_rowDualsGivenC
void dy_rowDualsGivenC(lpprob_struct *orig_lp, double **p_y, const double *c, bool trueDuals)
dy_deactBPrimArch
bool dy_deactBPrimArch(consys_struct *orig_sys, int ovndx)
dy_pricedualpiv
bool dy_pricedualpiv(lpprob_struct *orig_lp, int oxindx, double nubi, double xi, double nlbi, int nbcnt, int *nbvars, double *cbar, double *p_upeni, double *p_dpeni)
dy_ddegenset
int * dy_ddegenset
Definition dylp.h:1724
dy_calcduals
void dy_calcduals(void)
dy_initpivrej
void dy_initpivrej(int sze)
dy_reducerhs
bool dy_reducerhs(double *rhs, bool init)
DYSTATS_MAXDEGEN
#define DYSTATS_MAXDEGEN
Definition dylp.h:1300
dy_actBLogPrimConList
bool dy_actBLogPrimConList(consys_struct *orig_sys, int cnt, int *ocndxs, int **inactvars)
dy_deactNBLogPrimCon
bool dy_deactNBLogPrimCon(consys_struct *orig_sys, int i)
dy_initp1obj
bool dy_initp1obj(void)
dy_tols
lptols_struct * dy_tols
dy_frame
bool * dy_frame
dy_prtlpret
const char * dy_prtlpret(lpret_enum lpret)
dy_activateVars
int dy_activateVars(consys_struct *orig_sys, int *candidates)
dy_calccbar
bool dy_calccbar(void)
dy_dumpstats
void dy_dumpstats(ioid chn, bool echo, lpstats_struct *lpstats, consys_struct *orig_sys)
dy_calcprimals
bool dy_calcprimals(void)
dyret_enum
dyret_enum
Definition dylp.h:274
dyrSTALLED
@ dyrSTALLED
Definition dylp.h:274
dyrRESELECT
@ dyrRESELECT
Definition dylp.h:278
dyrSINGULAR
@ dyrSINGULAR
Definition dylp.h:275
dyrPATCHED
@ dyrPATCHED
Definition dylp.h:277
dyrOPTIMAL
@ dyrOPTIMAL
Definition dylp.h:279
dyrPUNT
@ dyrPUNT
Definition dylp.h:278
dyrLOSTPFEAS
@ dyrLOSTPFEAS
Definition dylp.h:276
dyrDEGEN
@ dyrDEGEN
Definition dylp.h:276
dyrMADPIV
@ dyrMADPIV
Definition dylp.h:276
dyrBSPACE
@ dyrBSPACE
Definition dylp.h:275
dyrACCCHK
@ dyrACCCHK
Definition dylp.h:278
dyrSWING
@ dyrSWING
Definition dylp.h:279
dyrITERLIM
@ dyrITERLIM
Definition dylp.h:274
dyrREQCHK
@ dyrREQCHK
Definition dylp.h:278
dyrUNBOUND
@ dyrUNBOUND
Definition dylp.h:279
dyrLOSTDFEAS
@ dyrLOSTDFEAS
Definition dylp.h:276
dyrOK
@ dyrOK
Definition dylp.h:277
dyrFATAL
@ dyrFATAL
Definition dylp.h:274
dyrINFEAS
@ dyrINFEAS
Definition dylp.h:279
dyrNUMERIC
@ dyrNUMERIC
Definition dylp.h:275
dyrINV
@ dyrINV
Definition dylp.h:277
dy_initlclsystem
bool dy_initlclsystem(lpprob_struct *orig_lp, bool hotstart)
dy_actNBPrimArchList
bool dy_actNBPrimArchList(consys_struct *orig_sys, int cnt, int *ovndxs)
dy_betaj
bool dy_betaj(lpprob_struct *orig_lp, int tgt_j, double **p_betaj)
dy_swapobjs
bool dy_swapobjs(dyphase_enum phase)
dy_origcons
int * dy_origcons
Definition dylp.h:1722
dy_var2basis
int * dy_var2basis
Definition dylp.h:1723
dy_origvars
int * dy_origvars
Definition dylp.h:1722
dy_actBLogPrimCon
bool dy_actBLogPrimCon(consys_struct *orig_sys, int i, int *inactvars)
dy_clrpivrej
bool dy_clrpivrej(int *entries)
dy_getOwner
void * dy_getOwner()
dy_addtopivrej
dyret_enum dy_addtopivrej(int xkndx, dyret_enum why, double abarij, double maxabarij)
dy_rowDuals
void dy_rowDuals(lpprob_struct *orig_lp, double **p_y, bool trueDuals)
dyphase_enum
dyphase_enum
Definition dylp.h:212
dyFORCEDUAL
@ dyFORCEDUAL
Definition dylp.h:216
dyPRIMAL1
@ dyPRIMAL1
Definition dylp.h:213
dyGENCON
@ dyGENCON
Definition dylp.h:215
dyFORCEFULL
@ dyFORCEFULL
Definition dylp.h:216
dyPURGECON
@ dyPURGECON
Definition dylp.h:215
dyGENVAR
@ dyGENVAR
Definition dylp.h:214
dyDONE
@ dyDONE
Definition dylp.h:217
dyPRIMAL2
@ dyPRIMAL2
Definition dylp.h:213
dyADDCON
@ dyADDCON
Definition dylp.h:215
dyINV
@ dyINV
Definition dylp.h:212
dyPURGEVAR
@ dyPURGEVAR
Definition dylp.h:214
dyDUAL
@ dyDUAL
Definition dylp.h:213
dyFORCEPRIMAL
@ dyFORCEPRIMAL
Definition dylp.h:216
dyINIT
@ dyINIT
Definition dylp.h:212
dyADDVAR
@ dyADDVAR
Definition dylp.h:214
dy_primalin
dyret_enum dy_primalin(int initcol, int scan, int *xjndx, int *nextcol)
dy_setlogchn
void dy_setlogchn(ioid chn)
dy_scaling_vectors
void dy_scaling_vectors(const double **rscale, const double **cscale)
dy_logpivot
void dy_logpivot(dyret_enum result, int xjndx, int indir, double cbarj, int xindx, int outdir, double abarij, double delta)
dy_logchn
ioid dy_logchn
dy_freestats
void dy_freestats(lpstats_struct **p_lpstats)
dy_x
double * dy_x
dy_setpivparms
bool dy_setpivparms(int curdelta, int mindelta)
dy_gamma
double * dy_gamma
Definition dylp.h:1726
dy_basis
int * dy_basis
Definition dylp.h:1723
dy_defaults
void dy_defaults(lpopts_struct **opts, lptols_struct **tols)
dy_deactivateCons
int dy_deactivateCons(consys_struct *orig_sys)
dy_cbar
double * dy_cbar
Definition dylp.h:1726
lpret_enum
lpret_enum
Definition dylp.h:170
lpPUNT
@ lpPUNT
Definition dylp.h:174
lpFATAL
@ lpFATAL
Definition dylp.h:170
lpACCCHK
@ lpACCCHK
Definition dylp.h:172
lpINFEAS
@ lpINFEAS
Definition dylp.h:171
lpFORCEFULL
@ lpFORCEFULL
Definition dylp.h:175
lpITERLIM
@ lpITERLIM
Definition dylp.h:173
lpLOSTFEAS
@ lpLOSTFEAS
Definition dylp.h:174
lpFORCEDUAL
@ lpFORCEDUAL
Definition dylp.h:175
lpOPTIMAL
@ lpOPTIMAL
Definition dylp.h:171
lpNOSPACE
@ lpNOSPACE
Definition dylp.h:173
lpSWING
@ lpSWING
Definition dylp.h:171
lpUNBOUNDED
@ lpUNBOUNDED
Definition dylp.h:171
lpINV
@ lpINV
Definition dylp.h:170
lpSTALLED
@ lpSTALLED
Definition dylp.h:173
lpFORCEPRIMAL
@ lpFORCEPRIMAL
Definition dylp.h:175
dy_gtxecho
bool dy_gtxecho
dy_status
flags * dy_status
dy_scaled_origsys
consys_struct * dy_scaled_origsys()
dy_deactivateVars
int dy_deactivateVars(consys_struct *orig_sys)
dy_primalRays
bool dy_primalRays(lpprob_struct *orig_lp, int *p_numRays, double ***p_rays)
dy_dualaddvars
int dy_dualaddvars(consys_struct *orig_sys)
dy_rowPrimals
void dy_rowPrimals(lpprob_struct *orig_lp, double **p_xB, int **p_indB)
dy_deactNBPrimArch
bool dy_deactNBPrimArch(consys_struct *orig_sys, int ovndx)
dyret2lpret
lpret_enum dyret2lpret(dyret_enum dyret)
dy_colPrimals
void dy_colPrimals(lpprob_struct *orig_lp, double **p_x)
dy_dseinit
void dy_dseinit(void)
dy_hotstart
dyret_enum dy_hotstart(lpprob_struct *orig_lp)
dy_colDuals
void dy_colDuals(lpprob_struct *orig_lp, double **p_cbar, bool trueDuals)
dy_degenout
dyret_enum dy_degenout(int level)
dy_accchk
dyret_enum dy_accchk(flags *checks)
dy_pricenbvars
bool dy_pricenbvars(lpprob_struct *orig_lp, flags priceme, double **p_ocbar, int *p_nbcnt, int **p_nbvars)
dy_dualout
dyret_enum dy_dualout(int *xindx)
dy_calcpinfeas
double dy_calcpinfeas(void)
dy_owner
void * dy_owner
dy_betai
bool dy_betai(lpprob_struct *orig_lp, int tgt_i, double **p_betai)
dy_rho
double * dy_rho
Definition dylp.h:1726
dy_calcobj
double dy_calcobj(void)
dy_prtdyret
const char * dy_prtdyret(dyret_enum retcode)
dy_dualRays
bool dy_dualRays(lpprob_struct *orig_lp, bool fullRay, int *p_numRays, double ***p_rays, bool trueDuals)
dy_chkpiv
double dy_chkpiv(double abarij, double maxabarj)
dy_activateBndCons
int dy_activateBndCons(consys_struct *orig_sys)
dy_logPrimals
void dy_logPrimals(lpprob_struct *orig_lp, double **p_logx)
dy_prtlpphase
const char * dy_prtlpphase(dyphase_enum phase, bool abbrv)
dy_finalstats
void dy_finalstats(lpstats_struct *lpstats)
dy_initstats
void dy_initstats(lpstats_struct **p_lpstats, consys_struct *orig_sys)
print
#define print
Definition glplib.h:28
basis_struct
Definition dylp.h:454
basis_struct::el
basisel_struct * el
Definition dylp.h:455
basis_struct::len
int len
Definition dylp.h:454
basisel_struct
Definition dylp.h:451
basisel_struct::cndx
int cndx
Definition dylp.h:451
consys_struct
Definition dy_consys.h:461
lp_struct
Definition dylp.h:1551
lp_struct::installed
bool installed
Definition dylp.h:1563
lp_struct::infeas
double infeas
Definition dylp.h:1559
lp_struct::infvars_sze
int infvars_sze
Definition dylp.h:1565
lp_struct::iters
int iters
Definition dylp.h:1574
lp_struct::infvars
int * infvars
Definition dylp.h:1566
lp_struct::init_dse
bool init_dse
Definition dylp.h:1558
lp_struct::forcedfull
bool forcedfull
Definition dylp.h:1573
lp_struct::cd
double cd
Definition dylp.h:1591
lp_struct::fd
double fd
Definition dylp.h:1594
lp_struct::ndx
int ndx
Definition dylp.h:1561
lp_struct::idlecnt
int idlecnt
Definition dylp.h:1589
lp_struct::fp
double fp
Definition dylp.h:1593
lp_struct::norm1
double norm1
Definition dylp.h:1595
lp_struct::max
double max
Definition dylp.h:1597
lp_struct::phase
dyphase_enum phase
Definition dylp.h:1551
lp_struct::z
double z
Definition dylp.h:1553
lp_struct::vd
double vd
Definition dylp.h:1592
lp_struct::degenpivcnt
int degenpivcnt
Definition dylp.h:1588
lp_struct::next
dyphase_enum next
Definition dylp.h:1556
lp_struct::infcnt
int infcnt
Definition dylp.h:1564
lp_struct::piv
double piv
Definition dylp.h:1590
lp_struct::active
dyphase_enum active
Definition dylp.h:1555
lp_struct::init_pse
bool init_pse
Definition dylp.h:1557
lp_struct::ratio
double ratio
Definition dylp.h:1562
lp_struct::loadable
int loadable
Definition dylp.h:1569
lp_struct::maxndx
int maxndx
Definition dylp.h:1598
lp_struct::norm2
double norm2
Definition dylp.h:1596
lp_struct::lpret
lpret_enum lpret
Definition dylp.h:1552
lp_struct::etas
int etas
Definition dylp.h:1584
lp_struct::pivs
int pivs
Definition dylp.h:1575
lp_struct::inactzcorr
double inactzcorr
Definition dylp.h:1554
lp_struct::prev_pivok
bool prev_pivok
Definition dylp.h:1583
lp_struct::degen
int degen
Definition dylp.h:1587
lp_struct::pivok
bool pivok
Definition dylp.h:1582
lp_struct::p1obj
double * p1obj
Definition dylp.h:1567
lp_struct::infeascnt
int infeascnt
Definition dylp.h:1560
lpopts_struct
Definition dylp.h:1115
lpopts_struct::phase2
int phase2
Definition dylp.h:1169
lpopts_struct::cons
bool cons
Definition dylp.h:1155
lpopts_struct::degen
bool degen
Definition dylp.h:1135
lpopts_struct::pricing
int pricing
Definition dylp.h:1164
lpopts_struct::degenpivlim
int degenpivlim
Definition dylp.h:1136
lpopts_struct::degenlite
int degenlite
Definition dylp.h:1137
lpopts_struct::i2u
double i2u
Definition dylp.h:1153
lpopts_struct::actlim
int actlim
Definition dylp.h:1127
lpopts_struct::i2lopen
bool i2lopen
Definition dylp.h:1150
lpopts_struct::dual
int dual
Definition dylp.h:1170
lpopts_struct::setup
int setup
Definition dylp.h:1162
lpopts_struct::flex
bool flex
Definition dylp.h:1120
lpopts_struct::i1u
double i1u
Definition dylp.h:1148
lpopts_struct::p2d
bool p2d
Definition dylp.h:1158
lpopts_struct::copyorigsys
bool copyorigsys
Definition dylp.h:1140
lpopts_struct::i1lopen
bool i1lopen
Definition dylp.h:1145
lpopts_struct::forcewarm
bool forcewarm
Definition dylp.h:1133
lpopts_struct::phase1
int phase1
Definition dylp.h:1168
lpopts_struct::factor
int factor
Definition dylp.h:1123
lpopts_struct::flips
bool flips
Definition dylp.h:1159
lpopts_struct::actlvl
int actlvl
Definition dylp.h:1126
lpopts_struct::strat
int strat
Definition dylp.h:1119
lpopts_struct::frac
double frac
Definition dylp.h:1144
lpopts_struct::rays
int rays
Definition dylp.h:1176
lpopts_struct::d2p
bool d2p
Definition dylp.h:1157
lpopts_struct::i2valid
bool i2valid
Definition dylp.h:1149
lpopts_struct::scan
int scan
Definition dylp.h:1116
lpopts_struct::groom
int groom
Definition dylp.h:1125
lpopts_struct::pivreject
int pivreject
Definition dylp.h:1166
lpopts_struct::conmgmt
int conmgmt
Definition dylp.h:1172
lpopts_struct::coldvars
int coldvars
Definition dylp.h:1131
lpopts_struct::pivoting
int pivoting
Definition dylp.h:1165
lpopts_struct::major
int major
Definition dylp.h:1160
lpopts_struct::forcecold
bool forcecold
Definition dylp.h:1132
lpopts_struct::fullsys
bool fullsys
Definition dylp.h:1139
lpopts_struct::i1l
double i1l
Definition dylp.h:1146
lpopts_struct::i2l
double i2l
Definition dylp.h:1151
lpopts_struct::patch
bool patch
Definition dylp.h:1138
lpopts_struct::idlelim
int idlelim
Definition dylp.h:1118
lpopts_struct::context
cxtype_enum context
Definition dylp.h:1115
lpopts_struct::basis
int basis
Definition dylp.h:1171
lpopts_struct::i1uopen
bool i1uopen
Definition dylp.h:1147
lpopts_struct::vars
float vars
Definition dylp.h:1142
lpopts_struct::force
int force
Definition dylp.h:1174
lpopts_struct::i2uopen
bool i2uopen
Definition dylp.h:1152
lpopts_struct::scaling
int scaling
Definition dylp.h:1141
lpopts_struct::coldbasis
ibtype_enum coldbasis
Definition dylp.h:1154
lpopts_struct::iterlim
int iterlim
Definition dylp.h:1117
lpopts_struct::allownopiv
bool allownopiv
Definition dylp.h:1121
lpopts_struct::usedual
bool usedual
Definition dylp.h:1134
lpopts_struct::tableau
int tableau
Definition dylp.h:1175
lpopts_struct::degen
int degen
Definition dylp.h:1167
lpopts_struct::dualadd
int dualadd
Definition dylp.h:1130
lpopts_struct::crash
int crash
Definition dylp.h:1163
lpopts_struct::check
int check
Definition dylp.h:1124
lpopts_struct::addvar
int addvar
Definition dylp.h:1129
lpopts_struct::varmgmt
int varmgmt
Definition dylp.h:1173
lpprob_struct
Definition dylp.h:587
lpprob_struct::basis
basis_struct * basis
Definition dylp.h:595
lpprob_struct::fullsys
bool fullsys
Definition dylp.h:594
lpprob_struct::owner
void * owner
Definition dylp.h:587
lpprob_struct::colsze
int colsze
Definition dylp.h:600
lpprob_struct::obj
double obj
Definition dylp.h:591
lpprob_struct::x
double * x
Definition dylp.h:597
lpprob_struct::ctlopts
flags ctlopts
Definition dylp.h:588
lpprob_struct::iters
int iters
Definition dylp.h:592
lpprob_struct::phase
dyphase_enum phase
Definition dylp.h:589
lpprob_struct::rowsze
int rowsze
Definition dylp.h:601
lpprob_struct::actvars
bool * actvars
Definition dylp.h:599
lpprob_struct::lpret
lpret_enum lpret
Definition dylp.h:590
lpprob_struct::consys
consys_struct * consys
Definition dylp.h:593
lpprob_struct::y
double * y
Definition dylp.h:598
lpprob_struct::status
flags * status
Definition dylp.h:596
lpstats_struct
Definition dylp.h:1303
lpstats_struct::min
float min
Definition dylp.h:1316
lpstats_struct::max
float max
Definition dylp.h:1315
lpstats_struct::flippable
int flippable
Definition dylp.h:1329
lpstats_struct::iters
int iters
Definition dylp.h:1360
lpstats_struct::max
int max
Definition dylp.h:1322
lpstats_struct::chgcnt1
int chgcnt1
Definition dylp.h:1346
lpstats_struct::totpivs
int totpivs
Definition dylp.h:1344
lpstats_struct::pivtol_red
int pivtol_red
Definition dylp.h:1325
lpstats_struct::chgcnt2
int chgcnt2
Definition dylp.h:1347
lpstats_struct::flips
int flips
Definition dylp.h:1335
lpstats_struct::maxcnt
int maxcnt
Definition dylp.h:1343
lpstats_struct::maxsiz
int maxsiz
Definition dylp.h:1350
lpstats_struct::ini_simplex
dyphase_enum ini_simplex
Definition dylp.h:1305
lpstats_struct::pivs
int pivs
Definition dylp.h:1361
lpstats_struct::prevpiv
int prevpiv
Definition dylp.h:1319
lpstats_struct::avgpivs
float avgpivs
Definition dylp.h:1320
lpstats_struct::puntcall
int puntcall
Definition dylp.h:1327
lpstats_struct::cands
int cands
Definition dylp.h:1331
lpstats_struct::avgsiz
float avgsiz
Definition dylp.h:1349
lpstats_struct::deactcnt
int * deactcnt
Definition dylp.h:1309
lpstats_struct::nontrivial
int nontrivial
Definition dylp.h:1333
lpstats_struct::pivrnks
int pivrnks
Definition dylp.h:1336
lpstats_struct::angle
double * angle
Definition dylp.h:1307
lpstats_struct::sing
int sing
Definition dylp.h:1324
lpstats_struct::min_pivtol
double min_pivtol
Definition dylp.h:1326
lpstats_struct::cnt
int cnt
Definition dylp.h:1318
lpstats_struct::actcnt
int * actcnt
Definition dylp.h:1308
lpstats_struct::evals
int evals
Definition dylp.h:1334
lpstats_struct::mad
int mad
Definition dylp.h:1323
lpstats_struct::promote
int promote
Definition dylp.h:1332
lpstats_struct::init
bool * init
Definition dylp.h:1310
lpstats_struct::sze
int sze
Definition dylp.h:1306
lptols_struct
Definition dylp.h:667
lptols_struct::swing
double swing
Definition dylp.h:678
lptols_struct::toobig
double toobig
Definition dylp.h:679
lptols_struct::purgevar
double purgevar
Definition dylp.h:681
lptols_struct::reframe
double reframe
Definition dylp.h:682
lptols_struct::dchk
double dchk
Definition dylp.h:673
lptols_struct::pchk
double pchk
Definition dylp.h:669
lptols_struct::dfeas_scale
double dfeas_scale
Definition dylp.h:675
lptols_struct::pfeas_scale
double pfeas_scale
Definition dylp.h:671
lptols_struct::purge
double purge
Definition dylp.h:680
lptols_struct::pivot
double pivot
Definition dylp.h:676
lptols_struct::bogus
double bogus
Definition dylp.h:677
lptols_struct::cost
double cost
Definition dylp.h:672
lptols_struct::zero
double zero
Definition dylp.h:668
lptols_struct::dfeas
double dfeas
Definition dylp.h:674
lptols_struct::inf
double inf
Definition dylp.h:667
lptols_struct::pfeas
double pfeas
Definition dylp.h:670