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GAUSSELM.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GAUSSELM
* Problem :
* *********
* Maximum pivot growth in Gaussian elimination with
* complete pivoting.
* SIF input: Ph.Toint and N. Gould, Dec 1989.
* classification LOR2-AN-V-V
* Size of the matrices = n
*IE N 11 $-PARAMETER matrix dimension
*IE N 12 $-PARAMETER matrix dimension
*IE N 13 $-PARAMETER matrix dimension
*IE N 14 $-PARAMETER matrix dimension
*IE N 15 $-PARAMETER matrix dimension
*IE N 16 $-PARAMETER matrix dimension
*IE N 20 $-PARAMETER matrix dimension
*IE N 25 $-PARAMETER matrix dimension
*IE N 30 $-PARAMETER matrix dimension
*IE N 35 $-PARAMETER matrix dimension
IE N 40 $-PARAMETER matrix dimension
*IE N 45 $-PARAMETER matrix dimension
*IE N 50 $-PARAMETER matrix dimension
* other parameter definitions
IE 1 1
IE 2 2
IA N-1 N -1
RI RN N
RM 6RN RN 6
VARIABLES
DO K 1 N
DO J K N
DO I K N
X X(I,J,K)
ND
GROUPS
* objective function
DO K N N
XN OBJ X(K,K,K) -1.0
ND
* elimination constraints
DO K 1 N-1
IA L K 1
DO I L N
DO J L N
XE E(I,J,K) X(I,J,L) 1.0 X(I,J,K) -1.0
ND
* complete pivoting constraints (submatrices 2 to n-1)
DO K 2 N-1
IA L K 1
DO I L N
XL M(I,K,K) X(I,K,K) 1.0 X(K,K,K) -1.0
XG P(I,K,K) X(I,K,K) 1.0 X(K,K,K) 1.0
XL M(K,I,K) X(K,I,K) 1.0 X(K,K,K) -1.0
XG P(K,I,K) X(K,I,K) 1.0 X(K,K,K) 1.0
DO J L N
XL M(I,J,K) X(I,J,K) 1.0 X(K,K,K) -1.0
XG P(I,J,K) X(I,J,K) 1.0 X(K,K,K) 1.0
ND
BOUNDS
FR GAUSSELM 'DEFAULT'
* complete pivoting constraints (submatrix 1)
DO I 1 N
DO J 1 N
XL GAUSSELM X(I,J,1) -1.0
XU GAUSSELM X(I,J,1) 1.0
ND
* ensure pivotal elements are nonnegative
DO K 1 N
XL GAUSSELM X(K,K,K) 0.0
ND
* normalize first pivot
FX GAUSSELM X1,1,1 1.0
START POINT
* default value for starting point component
V GAUSSELM 'DEFAULT' 0.1
DO K 1 N
DO J K N
DO I K N
I+ I+J I J
I+ I+J+K I+J K
RI RI+J+K I+J+K
RM RI+J+K RI+J+K 0.95
R/ R RI+J+K 6RN
Z GAUSSELM X(I,J,K) R
ND
ELEMENT TYPE
EV ELIM V1 V2
EV ELIM V3
ELEMENT USES
T 'DEFAULT' ELIM
DO K 1 N-1
IA L K 1
DO I L N
DO J L N
ZV A(I,J,K) V1 X(I,K,K)
ZV A(I,J,K) V2 X(K,J,K)
ZV A(I,J,K) V3 X(K,K,K)
ND
GROUP USES
DO K 1 N-1
IA L K 1
DO I L N
DO J L N
XE E(I,J,K) A(I,J,K)
ND
OBJECT BOUND
* Solutions (may be local!)
*LO SOLTN11 -1.06974D+01
*LO SOLTN12 -1.18817D+01
*LO SOLTN13 -1.30205D+01
*LO SOLTN14 -1.45949D+01
*LO SOLTN15 -1.61109D+01
*LO SOLTN16 -1.80598D+01
*LO SOLTN20 -2.42518D+01
*LO SOLTN25 -3.29890D+01
*LO SOLTN30 -4.27435D+01
*LO SOLTN35 -4.58208D+01
*LO SOLTN40 -6.60516D+01
*LO SOLTN45 -7.67437D+01
*LO SOLTN50 -9.46545D+01
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GAUSSELM
TEMPORARIES
R VALUE
R V3SQ
R V3VAL
R V3VAL2
L V3NE0
INDIVIDUALS
T ELIM
A V3NE0 V3 .NE. 0.0
A V3SQ V3 * V3
I V3NE0 VALUE V1 * V2 / V3
E V3NE0 VALUE 1.0D+10
I V3NE0 V3VAL V3
E V3NE0 V3VAL 1.0D-10
I V3NE0 V3VAL2 V3SQ
E V3NE0 V3VAL2 1.0D-10
F VALUE
G V1 V2 / V3VAL
G V2 V1 / V3VAL
G V3 - VALUE / V3VAL
H V1 V2 1.0 / V3VAL
H V1 V3 - V2 / V3VAL2
H V2 V3 - V1 / V3VAL2
H V3 V3 2.0 * VALUE / V3VAL2
ENDATA