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MSQRTALS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MSQRTALS
* Problem :
* *********
* The dense matrix square root problem by Nocedal and Liu.
* (Case 0) seen as a nonlinear equation problem.
* This is a least-squares variant of problem MSQRTA.
* Source: problem 201 (p. 93) in
* A.R. Buckley,
* "Test functions for unconstrained minimization",
* TR 1989CS-3, Mathematics, statistics and computing centre,
* Dalhousie University, Halifax (CDN), 1989.
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-V-V
* Dimension of the matrix
*IE P 2 $-PARAMETER n = 4 original value
*IE P 7 $-PARAMETER n = 49
*IE P 10 $-PARAMETER n = 100
*IE P 23 $-PARAMETER n = 529
IE P 32 $-PARAMETER n = 1024
*IE P 70 $-PARAMETER n = 4900
* Number of variables
I* N P P
* other parameter definitions
IE 1 1
* Define the matrix B (solution of the problem)
RE K 0.0
DO I 1 P
DO J 1 P
RA K K 1.0
R* K2 K K
A( B(I,J) SIN K2
ND
* Compute A = B * B
DO I 1 P
DO J 1 P
AE A(I,J) 0.0
DO K 1 P
A* PROD B(I,K) B(K,J)
A+ A(I,J) A(I,J) PROD
ND
VARIABLES
DO I 1 P
DO J 1 P
X X(I,J)
ND
GROUPS
DO I 1 P
DO J 1 P
XN G(I,J)
ND
CONSTANTS
DO I 1 P
DO J 1 P
Z MSQRTALS G(I,J) A(I,J)
ND
BOUNDS
FR MSQRTALS 'DEFAULT'
START POINT
RE K 0.0
DO I 1 P
DO J 1 P
RA K K 1.0
R* K2 K K
R( SK2 SIN K2
RM -4SK2/5 SK2 -0.8
A+ XIJ B(I,J) -4SK2/5
Z MSQRTALS X(I,J) XIJ
ND
ELEMENT TYPE
EV 2PR XIT XTJ
ELEMENT USES
DO I 1 P
DO J 1 P
DO T 1 P
XT E(I,J,T) 2PR
ZV E(I,J,T) XIT X(I,T)
ZV E(I,J,T) XTJ X(T,J)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
T 'DEFAULT' L2
DO I 1 P
DO J 1 P
DO T 1 P
XE G(I,J) E(I,J,T)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MSQRTALS
INDIVIDUALS
T 2PR
F XIT * XTJ
G XIT XTJ
G XTJ XIT
H XIT XTJ 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS MSQRTALS
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA