Access to Index Control Variables

EKKNGET - Request Current Start Indices of Information Stored in dspace

Syntax

On Entry

dspace

is the user-provided work area.

Specified as: a one-dimensional real array of doublewords.

num

is the number of control variables to be retrieved.

Specified as: a fullword integer.
The value of num must be positive and not greater than the length of the array narray.

On Return

rtcod

is the return code for the subroutine, where:

If rtcod = 0, the subroutine completed successfully. Only informational messages were issued.
If rtcod is nonzero, then the value returned is the return code associated with the first occurrence of the highest severity message.
See "Return Codes" for an explanation of return codes.

Returned as: a fullword integer.

dspace

is the user-provided work area.

Returned as: a one-dimensional real array of doublewords.

narray

is an array of FORTRAN indices for the starts of various arrays in dspace. The nth entry of narray is the nth index control variable, documented in table 17 below.

Returned as: a one-dimensional integer array of fullwords.

Notes

1. The number of control variables returned is the minimum of the number requested, num, and the number available.
2. If on return, an entry in narray is zero, it means that the corresponding array was not available when EKKNGET was called. E.g., the "row auxilary solve information" array is dynamically allocated, and if this array is nonexistent at a time when EKKNGET is called, then the value returned for the 29th entry in narray will be zero.
3. If the data array associated with a particular entry of narray is an integer array, then EKKNGET will return a Fortran index into mspace in that entry. Otherwise, EKKNGET will return a Fortran index into dspace. mspace is a user defined fullword integer array that has the same starting location as, and is equivalent to dspace, the floating point workspace. See "Storage Allocation" for more information.
4. Control variables 17 through 22 are created only if you make a call to EKKCOPY. Otherwise, these control variables remain set to zero.
5. Control variables Nrowstat and Ncolstat give the locations (in mspace) of the row and column status vectors respectively. These status vectors are one-dimensional integer arrays of fullwords. The numbering of the bits in these vectors follows the bit numbering conventions for VS FORTRAN. All 32 bits are used internally, but only three of them are important to the user:
• If the 31 bit is set, the variable is basic (row logical for the row status vector and structural variable for the column status vector.) If this bit is set, then the remaining bits are ignored.
• If the 30 bit is set, then the row activity or column activity may go down.
• If the 29 bit is set, then the row activity or column activity may go up.
If one of these bit settings is invalid (for example, if the up bit is set, but the column (variable) is at or above its upper bound), the setting will be ignored.

In practice this translates into the following.

• For basic variables
• The variable will have the basic bit set.
• For nonbasic variables
• A variable at its upper bound will have the down bit set.
• A variable at its lower bound will have the up bit set.
• A fixed variable (and at bound) will have no bits set.
• A free variable at zero will have the up and down bits set.
• Any variable between bounds will have both the up and down bits set.
• A variable above its upper bound will have the down bit set.
• A variable below its lower bound will have the up bit set.
 

Note:

Superbasic variables (that is, variables that are neither basic, nor at bound) are also allowed, although normally library routines set the bits using the primal solution values.

You may set up a basis using this information and then call EKKSSLV with init set to a value other than 3.

When init is set to 3, only the basic bits have meaning. The primal values and bounds bits will be used for other things.

6. The index control variable Nintinfo is an index to information about each integer variable. For each integer variable there are four fields. For example, information for the sixth integer variable would start at mspace ( Nintinfo + ( 5 * 4 )).

The fields for each integer variable are organized as follows:

• Field 1 is the original sequence number of the integer variable.
• Field 2 is reserved.
• Field 3 is the type, where:
• If field 3 = 1 the variable must take on an integer value. Therefore, this is a type 3 special ordered set or an integer variable.
• If field 3 = 2 the variable may take on continuous values. Therefore, this is a type 1 or 2 special ordered set variable.
• Field 4 is reserved.
7. The scaling region contains scale factors that are applied to each matrix element, a _ij, as follows: scaled a _ij = (original a _ij * rowscale _i ) / colscale _j .
8. Indices Nrowaux and Ncolaux give the location of the auxiliary solve information regions. These regions are only set up if:
1. Your model is infeasible or unbounded.
2. EKKSSLV has been stopped at your request and a perturbation is in effect. (Note that this could occur if EKKSSLV was called implicitly during EKKMSLV or EKKBSLV processing. The primal cases are also applicable to EKKNSLV.)
3. EKKQSLV has encountered indefiniteness in the quadratic matrix Q.
• Primal Infeasible (Primal Simplex Algorithm)

If you are using the primal algorithm, and the model is primal infeasible, then Nrowaux and Ncolaux are the Phase 1 reduced costs. The Phase 1 reduced costs are similar to the data referenced by Nrowslacks and Ncolrcosts. These costs are set as if an objective coefficient of +1.0 has been given to each variable above its upper bound, and an objective coefficient of -1.0 has been given to each variable below its lower bound.
• Primal Unbounded (Primal Simplex Algorithm)

If you are using the primal algorithm, and the model is primal unbounded, the values pointed to by Nrowaux and Ncolaux give a direction of unboundedness. (For example, for a minimization problem, a direction of unboundedness would be a vector you could travel along and continually decrease the objective function value.)
• Primal Infeasible (Dual Simplex Algorithm)

If you are using the dual algorithm and the model is primal infeasible (which is equivalent to dual unbounded), then Nrowaux and Ncolaux point to the updated row of the tableau for which the infeasibility was found. Nrowaux points to the entries associated with the logical variables, and Ncolaux points to the entries associated with the structural variables.
• Primal Unbounded (Dual Simplex Algorithm)

If you are using the dual algorithm and the model is primal unbounded, the values pointed to by Nrowaux and Ncolaux give a direction of unboundedness. (For example, for a minimization problem, a direction of unboundedness would be a vector you could travel along and continually decrease the objective function value.)
• Primal Infeasible (Quadratic Simplex)

If your model is primal infeasible, then the values pointed to by Nrowaux and Ncolaux contain information about where the infeasibility was detected. Nrowaux points to row multipliers to prove primal infeasibility. Rows with nonzero multipliers are the rows you should focus on when examining your model formulation. The value pointed to by Ncolaux contains the product of the row multipliers and the matrix A. This product represents the implied inconsistent constraint.
• Dual Infeasible (Quadratic Simplex)

If your model is dual infeasible (primal unbounded), then the values pointed to by Nrowaux and Ncolaux contain information related to the direction of unboundedness. The values pointed to by Nrowaux contain row activity changes that result from following the direction of unboundedness pointed to by Ncolaux. The value pointed to by Ncolaux contains a direction that can be traveled along indefinitely in the primal solution space. Traveling along this ray improves the linear part of the objective function and maintains a zero inner product with the quadratic part of the objective function.
• If EKKSSLV Is Stopped

If you stopped the solve (either in EKKITRU or by setting Imaxiter or Istopmask), and a perturbation is in effect, then the value pointed to by Nrowaux is the perturbation to be applied to the rows and the value pointed to by Ncolaux is the perturbation to be applied to the columns.
• Indefiniteness

If indefiniteness has been detected in the quadratic matrix Q, then only Ncolaux is set. The value pointed to by Ncolaux contains a direction z that can be followed indefinitely in the primal solution space where z ^T Q z < 0.
9. If EKKNGET is called from a program written in C, the indices returned by this routine have to be adjusted by 1 when used to index C arrays. This is because in C the first element of dspace is referred to as dspace[0], while in FORTRAN the first element of dspace is referred to as dspace(1). For more information, see "Sample C Program EXNAME".

Examples

• "Sample FORTRAN Program EXCOPY"
• "Sample FORTRAN Program EXDANWOL"
• "Sample FORTRAN Program EXDSCM2"
• "Sample FORTRAN Program EXDUAL"
• "Sample FORTRAN Program EXFRONT"
• "Sample FORTRAN Program EXGES"
• "Sample FORTRAN Program EXLPDC2"
• "Sample FORTRAN Program EXMPRSL"
• "Sample FORTRAN Program EXMSLV3"
• "Sample FORTRAN Program EXNAME"
• "Sample FORTRAN Program EXNAME2"
• "Sample FORTRAN Program EXNCRSH"
• "Sample FORTRAN Program EXNGET"
• "Sample FORTRAN Program EXOSLBAS"
• "Sample FORTRAN Program EXROW"
• "Sample FORTRAN Program EXRPTB"
• "Sample FORTRAN Program EXRVIS"
• "Sample FORTRAN Program EXSELNM2"
• "Sample FORTRAN Program EXSENS2"
• "Sample FORTRAN Program EXTOMPSX"
• "Sample C Program EXNAME"
• "Sample C Program EXROW"

Table 17. Index control variables
 

sequence number	Variable Name	Description
1	Nrowlower	The Fortran index into  dspace  for the first element of row lower bounds.
2	Nrowacts	The Fortran index into  dspace  for the first element of row activities.
3	Nrowupper	The Fortran index into  dspace  for the first element of row upper bounds.
4	Nrowduals	The Fortran index into  dspace  for the first element of row slacks.
5	Nrowstat	The Fortran index into  mspace  for the first element of the row status vector.
6	Ncollower	The Fortran index into  dspace  for the first element of column lower bounds.
7	Ncolsol	The Fortran index into  dspace  for the first element of the solution (column activities).
8	Ncolupper	The Fortran index into  dspace  for the first element of column upper bounds.
9	Ncolrcosts	The Fortran index into  dspace  for the first element of reduced costs.
10	Ncolstat	The Fortran index into  mspace  for the first element of the column status vector.
11	Nobjective	The Fortran index into  dspace  for the first element of column costs (objective function coefficients).
12	Nrownames	The Fortran index into  dspace  for the first element of row names.
13	Ncolnames	The Fortran index into  dspace  for the first element of column names.
14	Nrowscales	The Fortran index into  dspace  for the first element of row scale factors.
15	Ncolscales	The Fortran index into  dspace  for the first element of column scale factors.
16	Npresolve	The Fortran index into  mspace  for the first element of the presolve region.
17	Nrowcc	The Fortran index into  mspace  for the first element of rows for matrix (column copy).
18	Ncolrc	The Fortran index into  mspace  for the first element of columns for matrix (row copy).
19	Nelemcc	The Fortran index into  dspace  for the first element of elements for matrix (column copy).
20	Nelemrc	The Fortran index into  dspace  for the first element of columns for matrix (row copy).
21	Nrowrc	The Fortran index into  mspace  for the first element of row starts (row copy).
22	Ncolcc	The Fortran index into  mspace  for the first element of column starts (column copy).
23	Nfirstfree	The Fortran index into  dspace  of the first element of free space.
24	Nlastfree	The Fortran index into  dspace  of the last element of free space.
25	Nblockcol	The Fortran index into  mspace  for the first element of column entries for the latest block.
26	Nblockrow	The Fortran index into  mspace  for the first element of row entries for the latest block.
27	Nblockelem	The Fortran index into  dspace  for the first element of elements for the latest block.
28	Nintinfo	The Fortran index into  mspace  for the first element of integer information.
29	Nrowaux	The Fortran index into  dspace  for the first element of row auxiliary solve information.
30	Ncolaux	The Fortran index into  dspace  for the first element of column auxiliary solve information.
31	Nsobjupc	The Fortran index into  dspace  created by EKKSOBJ for the first element of the array of cost upper limits.
32	Nsobjdnc	The Fortran index into  dspace  created by EKKSOBJ for the first element of the array of cost lower limits.
33	Nsobjupv	The Fortran index into  dspace  created by EKKSOBJ for the first element of ranges of the objective function values corresponding to the upper limits on cost coefficients indexed by   Nsobjupc .
34	Nsobjdnv	The Fortran index into  dspace  created by EKKSOBJ for the first element of ranges of the objective function values corresponding to the lower limits on cost coefficients indexed by   Nsobjdnc .
35	Nsobjupe	The Fortran index into  mspace  created by EKKSOBJ for the first element of the array of entering rows or columns corresponding to the increased cost coefficients indexed by   Nsobjupc .
36	Nsobjdne	The Fortran index into  mspace  created by EKKSOBJ for the first element of the array of entering rows or columns corresponding to the decreased cost coefficients indexed by   Nsobjdnc .
37	Nsobjupl	The Fortran index into  mspace  created by EKKSOBJ for the first element of the array of leaving rows or columns corresponding to the increased cost coefficients indexed by   Nsobjupc .
38	Nsobjdnl	The Fortran index into  mspace  created by EKKSOBJ for the first element of the array of leaving rows or columns corresponding to the decreased cost coefficients indexed by   Nsobjdnc .
39	Nsbndcupb	The Fortran index into  dspace  created by EKKSBND for the first element of the upper limits on column bounds.
40	Nsbndcdnb	The Fortran index into  dspace  created by EKKSBND for the first element of the lower limits on column bounds.
41	Nsbndcupv	The Fortran index into  dspace  created by EKKSBND for the first element of the ranges of the objective function values corresponding to the upper limits on column bounds indexed by  Nsbndcupb .
42	Nsbndcdnv	The Fortran index into  dspace  created by EKKSBND for the first element of ranges of the objective function values corresponding to the lower limits on column bounds indexed by   Nsbndcdnb .
43	Nsbndcupe	The Fortran index into  mspace  created by EKKSBND for the first element of the array of entering rows or columns corresponding to the upper limits on column bounds indexed by   Nsbndcupb.
44	Nsbndcdne	The Fortran index into  mspace  created by EKKSBND for the first element of the array of entering rows or columns corresponding to the lower limits on column bounds indexed by   Nsbndcdnb .
45	Nsbndcupl	The Fortran index into  mspace  created by EKKSBND for the first element of the array of leaving rows or columns corresponding to the upper limits on column bounds indexed by   Nsbndcupb .
46	Nsbndcdnl	The Fortran index into  mspace  created by EKKSBND for the first element of the array of leaving rows or columns corresponding to the lower limits on column bounds indexed by   Nsbndcdnb .
47	Nsbndrupb	The Fortran index into  dspace  created by EKKSBND for the first element of the upper limits on row bounds.
48	Nsbndrdnb	The Fortran index into  dspace  created by EKKSBND for the first element of the lower limits on row bounds.
49	Nsbndrupv	The Fortran index into  dspace  created by EKKSBND for the first element of the ranges of the objective function values corresponding to the upper limits on row bounds indexed by  Nsbndrupb .
50	Nsbndrdnv	The Fortran index into  dspace  created by EKKSBND for the first element of ranges of the objective function values corresponding to the lower limits on row bounds indexed by   Nsbndrdnb .
51	Nsbndrupe	The Fortran index into  mspace  created by EKKSBND for the first element of the array of entering rows or columns corresponding to the upper limits on row bounds indexed by   Nsbndrupb .
52	Nsbndrdne	The Fortran index into  mspace  created by EKKSBND for the first element of the array of entering rows or columns corresponding to the lower limits on row bounds indexed by   Nsbndrdnb .
53	Nsbndrupl	The Fortran index into  mspace  created by EKKSBND for the first element of the array of leaving rows or columns corresponding to the upper limits on row bounds indexed by   Nsbndrupb .
54	Nsbndrdnl	The Fortran index into  mspace  created by EKKSBND for the first element of the array of leaving rows or columns corresponding to the lower limits on row bounds indexed by   Nsbndrdnb .
55	Nsellistcol	The Fortran index into  mspace  for the column selection list.
56	Nsellistrow	The Fortran index into  mspace  for the row selection list.
57	Nsparcost	The Fortran index into  dspace  for the parametric cost (objective) change vector created for EKKSPAR.
58	Nsparrlo	The Fortran index into  dspace  for the row lower bounds parametric change vector created for EKKSPAR.
59	Nsparrup	The Fortran index into  dspace  for the row upper bounds parametric change vector created for EKKSPAR.
60	Nsparclo	The Fortran index into  dspace  for the column lower bounds parametric change vector created for EKKSPAR.
61	Nsparcup	The Fortran index into  dspace  for the column upper bounds parametric change vector created for EKKSPAR.
62	Narcid	The Fortran index into  mspace  for the first element of the indices of the arcs in the basis.
63	Nlevel	The Fortran index into  mspace  for the first element of the array of node levels.
64	Nparent	The Fortran index into  mspace  for the first element of the array of parent nodes.
65	Npreorder	The Fortran index into  mspace  for the first element of the preorder traversal array.
66	Nrevpreorder	The Fortran index into  mspace  for the first element of the reverse preorder traversal array.
67	Nqrow	The Fortran index into mspace for the first element of rows for quadratic matrix (column copy) or the index into mspace for the first element of row entries for quadratic matrix (index copy).
68	Nqcol	The Fortran index into mspace for the first element of column starts for quadratic matrix (column copy) or the Fortran index into mspace for the first element of column entries for quadratic matrix (index copy).
69	Nqelem	The Fortran index into dspace for the first element of elements quadratic matrix (column or index copy).