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HS90.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HS90
* Problem :
* *********
* A time-optimal heat conduction problem.
* Source: problem 90 in
* W. Hock and K. Schittkowski,
* "Test examples for nonlinear programming codes",
* Lectures Notes in Economics and Mathematical Systems 187, Springer
* Verlag, Heidelberg, 1981.
* SIF input: Nick Gould, September 1991.
* classification QOR2-MN-4-1
* Number of variables
IE N 4
* Constants
RE EPS 0.01
R* EPSSQR EPS EPS
RM -EPSSQR EPSSQR -1.0
* Other useful parameters
IE 1 1
IE 2 2
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N OBJ
G CON
CONSTANTS
Z HS90 CON -EPSSQR
BOUNDS
FR HS90 'DEFAULT'
START POINT
DO I 1 N
DI I 2
X HS90 X(I) 0.5
ND
DO I 2 N
DI I 2
X HS90 X(I) -0.5
ND
HS90SOL X1 8.21443D-01
HS90SOL X2 7.74077D-68
HS90SOL X3 -6.90910D-01
HS90SOL X4 -4.56045D-01
HS90SOL CON -1.03923D+03
ELEMENT TYPE
* SQR
EV SQR X
* H
EV H X1 X2
EV H X3 X4
ELEMENT USES
DO I 1 N
XT O(I) SQR
ZV O(I) X X(I)
ND
XT H H
ZV H X1 X1
ZV H X2 X2
ZV H X3 X3
ZV H X4 X4
GROUP USES
DO I 1 N
XE OBJ O(I)
ND
E CON H -1.0
OBJECT BOUND
* Solution
*XL HS90SOL 1.36010D+00
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HS90
TEMPORARIES
R F
R G(4)
R H(4,4)
R EVAL90
F EVAL90
INDIVIDUALS
* Element type SQR
T SQR
F X * X
G X X + X
H X X 2.0D+0
* Element type H
T H
A F EVAL90( X1, X2, X3, X4,
A+ G, H )
F F
G X1 G(1)
G X2 G(2)
G X3 G(3)
G X4 G(4)
H X1 X1 H(1,1)
H X1 X2 H(1,2)
H X2 X2 H(2,2)
H X1 X3 H(1,3)
H X2 X3 H(2,3)
H X3 X3 H(3,3)
H X1 X4 H(1,4)
H X2 X4 H(2,4)
H X3 X4 H(3,4)
H X4 X4 H(4,4)
ENDATA
DOUBLE PRECISION FUNCTION EVAL90( X1, X2, X3, X4,
* G, H )
DOUBLE PRECISION X1, X2, X3, X4
DOUBLE PRECISION G( 4 ), H( 4, 4 )
INTEGER I , J , K , N , NP1, L
PARAMETER ( N = 4, NP1 = N + 1 )
LOGICAL CALC
DOUBLE PRECISION ALPHA , MUJ2 , T, MUI, MUJ , SMUI , U, SI ,
* RIJ , RHOI , RHOJ , EU, AI, AIMUI2, CMUI
DOUBLE PRECISION X ( N ), P( NP1 ),
* MU ( 30 ), A( 30 ), R( 30, 30 ), S( 30 ),
* RHO( 30 ), DRHO( 30, N ), D2RHO( 30, N, N )
INTRINSIC SIN , COS , EXP
SAVE A, AI, AIMUI2, CMUI, MUI, MUJ, R, S, SMUI, T
C
C Set data.
C
DATA CALC / .TRUE. /
DATA MU / 8.6033358901938017D-01, 3.4256184594817283D+00,
* 6.4372981791719468D+00, 9.5293344053619631D+00,
* 1.2645287223856643D+01, 1.5771284874815882D+01,
* 1.8902409956860023D+01, 2.2036496727938566D+01,
* 2.5172446326646664D+01, 2.8309642854452012D+01,
* 3.1447714637546234D+01, 3.4586424215288922D+01,
* 3.7725612827776501D+01, 4.0865170330488070D+01,
* 4.4005017920830845D+01, 4.7145097736761031D+01,
* 5.0285366337773652D+01, 5.3425790477394663D+01,
* 5.6566344279821521D+01, 5.9707007305335459D+01,
* 6.2847763194454451D+01, 6.5988598698490392D+01,
* 6.9129502973895256D+01, 7.2270467060308960D+01,
* 7.5411483488848148D+01, 7.8552545984242926D+01,
* 8.1693649235601683D+01, 8.4834788718042290D+01,
* 8.7975960552493220D+01, 9.1117161394464745D+01 /
C
C Calculate integration constants.
C
IF ( CALC ) THEN
T = 2.0D+0 / 1.5D+1
DO 20 I = 1, 30
MUI = MU( I )
SMUI = SIN( MUI )
CMUI = COS( MUI )
AI = 2.0D+0 * SMUI / ( MUI + SMUI * CMUI )
A( I ) = AI
S( I ) = 2.0D+0 * AI * ( CMUI - SMUI / MUI )
AIMUI2 = AI * MUI ** 2
DO 10 J = 1, I
IF ( I .NE. J ) THEN
MUJ = MU( J )
R( I, J ) = 5.0D-1 * (
* SIN( MUI + MUJ ) / ( MUI + MUJ ) +
* SIN( MUI - MUJ ) / ( MUI - MUJ ) ) *
* AIMUI2 * A( J ) * MUJ ** 2
R( J, I ) = R( I, J )
ELSE
R( I, I ) = 5.0D-1 * ( 1.0D+0 + 5.0D-1 *
* SIN( MUI + MUI ) / MUI ) *
* AIMUI2 ** 2
END IF
10 CONTINUE
20 CONTINUE
CALC = .FALSE.
END IF
C
C Assign values to variables.
C
X( 1 ) = X1
X( 2 ) = X2
X( 3 ) = X3
X( 4 ) = X4
C
C n 2
C Calculate the functions p(x) = SUM x .
C j i=j i
C
P( NP1 ) = 0.0D+0
DO 100 K = N, 1, - 1
P( K ) = P( K + 1 ) + X( K ) ** 2
100 CONTINUE
C
C Calculate the functions rho.
C
DO 190 J = 1, 30
MUJ2 = MU( J ) * MU( J )
U = EXP( - MUJ2 * P( 1 ) )
DO 120 K = 1, N
DRHO( J, K ) = 2.0D+0 * U * X( K )
DO 110 L = K, N
D2RHO( J, K, L ) = - 4.0D+0 * MUJ2 * U * X( K ) * X( L )
IF ( L .EQ. K ) D2RHO( J, K, L ) = D2RHO( J, K, L ) +
* 2.0D+0 * U
110 CONTINUE
120 CONTINUE
ALPHA = - 2.0D+0
DO 180 I = 2, N
EU = ALPHA * EXP( - MUJ2 * P( I ) )
U = U + EU
DO 140 K = I, N
DRHO( J, K ) = DRHO( J, K ) + 2.0D+0 * EU * X( K )
DO 130 L = K, N
D2RHO( J, K, L ) = D2RHO( J, K, L ) -
* 4.0D+0 * MUJ2 * EU * X( K ) * X( L )
IF ( L .EQ. K )
* D2RHO( J, K, L ) = D2RHO( J, K, L ) + 2.0D+0 * EU
130 CONTINUE
140 CONTINUE
ALPHA = - ALPHA
180 CONTINUE
U = U + 5.0D-1 * ALPHA
RHO( J ) = - U / MUJ2
190 CONTINUE
C
C Evaluate the function and derivatives.
C
EVAL90 = T
DO 320 K = 1, N
G( K ) = 0.0D+0
DO 310 L = K, N
H( K, L ) = 0.0D+0
310 CONTINUE
320 CONTINUE
DO 490 I = 1, 30
SI = S( I )
RHOI = RHO( I )
EVAL90 = EVAL90 + SI * RHOI
DO 420 K = 1, N
G( K ) = G( K ) + SI * DRHO( I, K )
DO 410 L = K, N
H( K, L ) = H( K, L ) + SI * D2RHO( I, K, L )
410 CONTINUE
420 CONTINUE
DO 480 J = 1, 30
RIJ = R( I, J )
RHOJ = RHO( J )
EVAL90 = EVAL90 + RIJ * RHOI * RHOJ
DO 440 K = 1, N
G( K ) = G( K ) + RIJ * ( RHOI * DRHO( J, K ) +
* RHOJ * DRHO( I, K ) )
DO 430 L = K, N
H( K, L ) = H( K, L ) + RIJ * (
* RHOI * D2RHO( J, K, L ) +
* RHOJ * D2RHO( I, K, L ) +
* DRHO( I, K ) * DRHO( J, L ) +
* DRHO( J, K ) * DRHO( I, L ) )
430 CONTINUE
440 CONTINUE
480 CONTINUE
490 CONTINUE
RETURN
END