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BROYDN7D.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BROYDN7D
* Problem :
* *********
* A seven diagonal variant of the Broyden tridiagonal system,
* featuring a band far away from the diagonal.
* Source:
* Ph.L. Toint,
* "Some numerical results using a sparse matrix updating formula in
* unconstrained optimization",
* Mathematics of Computation, vol. 32(114), pp. 839-852, 1978.
* See also Buckley#84
* SIF input: Ph. Toint, Dec 1989.
* classification OUR2-AN-V-0
* N/2 is half the number of variables
*IE N/2 5 $-PARAMETER n=10 original value
*IE N/2 25 $-PARAMETER n=50
*IE N/2 50 $-PARAMETER n=100
*IE N/2 250 $-PARAMETER n=500
*IE N/2 500 $-PARAMETER n=1000
IE N/2 2500 $-PARAMETER n=5000
*IE N/2 5000 $-PARAMETER n=10000
* Number of variables
IM N N/2 2
* Other parameters
IE 1 1
IE 2 2
IA N-1 N -1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N E1 X2 - 2.0
DO I 2 N-1
IA I-1 I -1
IA I+1 I 1
XN E(I) X(I-1) -1.0 X(I+1) - 2.0
ND
XN E(N) X(N-1) -1.0
DO I 1 N/2
I+ IPN2 I N/2
XN S(I) X(I) 1.0 X(IPN2) 1.0
ND
CONSTANTS
DO I 1 N
X BROYDN7D E(I) -1.0
ND
BOUNDS
FR BROYDN7D 'DEFAULT'
START POINT
XV BROYDN7D 'DEFAULT' 1.0
ELEMENT TYPE
EV BROY V1
ELEMENT USES
XT 'DEFAULT' BROY
DO I 1 N
ZV B(I) V1 X(I)
ND
GROUP TYPE
GV L7/3 GVAR
GROUP USES
XT 'DEFAULT' L7/3
DO I 1 N
XE E(I) B(I)
ND
OBJECT BOUND
LO BROYDN7D 0.0
* Solution
*LO SOLTN 1.2701
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BROYDN7D
TEMPORARIES
R TEMP1
R TEMP2
INDIVIDUALS
T BROY
A TEMP1 - 2.0 * V1
A TEMP2 3.0 + TEMP1
F TEMP2 * V1
G V1 TEMP2 + TEMP1
H V1 V1 - 4.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS BROYDN7D
TEMPORARIES
R Z
M ABS
M SIGN
INDIVIDUALS
T L7/3
A Z ABS( GVAR )
F Z**(7.0/3.0)
G 7.0 * SIGN( Z**(4.0/3.0), GVAR ) / 3.0
H 28.0 * Z**(1.0/3.0) / 9.0
ENDATA