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#include <math.h>
#include "luksan.h"
#define FALSE_ 0
#define MAX2(a,b) ((a) > (b) ? (a) : (b))
#define MIN2(a,b) ((a) < (b) ? (a) : (b))
#define iabs(a) ((a) < 0 ? -(a) : (a))
/* subroutines extracted from pssubs.for */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PCBS04 ALL SYSTEMS 98/12/01
* PURPOSE :
* INITIATION OF THE VECTOR CONTAINING TYPES OF CONSTRAINTS.
*
* PARAMETERS :
* II NF NUMBER OF VARIABLES.
* RI X(NF) VECTOR OF VARIABLES.
* II IX(NF) VECTOR CONTAINING TYPES OF BOUNDS.
* RI XL(NF) VECTOR CONTAINING LOWER BOUNDS FOR VARIABLES.
* RI XU(NF) VECTOR CONTAINING UPPER BOUNDS FOR VARIABLES.
* RI EPS9 TOLERANCE FOR ACTIVE CONSTRAINTS.
* II KBF SPECIFICATION OF SIMPLE BOUNDS. KBF=0-NO SIMPLE BOUNDS.
* KBF=1-ONE SIDED SIMPLE BOUNDS. KBF=2=TWO SIDED SIMPLE BOUNDS.
*/
void luksan_pcbs04__(int *nf, double *x, int *ix,
double *xl, double *xu, double *eps9, int *kbf)
{
/* System generated locals */
int i__1, i__2;
double d__1, d__2;
/* Local variables */
int i__, ixi;
double temp;
/* Parameter adjustments */
--xu;
--xl;
--ix;
--x;
/* Function Body */
if (*kbf > 0) {
i__1 = *nf;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = 1.;
ixi = (i__2 = ix[i__], iabs(i__2));
/* Computing MAX */
d__2 = (d__1 = xl[i__], fabs(d__1));
if ((ixi == 1 || ixi == 3 || ixi == 4) && x[i__] <= xl[i__] + *
eps9 * MAX2(d__2,temp)) {
x[i__] = xl[i__];
}
/* Computing MAX */
d__2 = (d__1 = xu[i__], fabs(d__1));
if ((ixi == 2 || ixi == 3 || ixi == 4) && x[i__] >= xu[i__] - *
eps9 * MAX2(d__2,temp)) {
x[i__] = xu[i__];
}
/* L1: */
}
}
return;
} /* luksan_pcbs04__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PNINT1 ALL SYSTEMS 91/12/01 */
/* PURPOSE : */
/* EXTRAPOLATION OR INTERPOLATION FOR LINE SEARCH WITH DIRECTIONAL */
/* DERIVATIVES. */
/* PARAMETERS : */
/* RI RL LOWER VALUE OF THE STEPSIZE PARAMETER. */
/* RI RU UPPER VALUE OF THE STEPSIZE PARAMETER. */
/* RI FL VALUE OF THE OBJECTIVE FUNCTION FOR R=RL. */
/* RI FU VALUE OF THE OBJECTIVE FUNCTION FOR R=RU. */
/* RI PL DIRECTIONAL DERIVATIVE FOR R=RL. */
/* RI PU DIRECTIONAL DERIVATIVE FOR R=RU. */
/* RO R VALUE OF THE STEPSIZE PARAMETER OBTAINED. */
/* II MODE MODE OF LINE SEARCH. */
/* II MTYP METHOD SELECTION. MTYP=1-BISECTION. MTYP=2-QUADRATIC */
/* INTERPOLATION (WITH ONE DIRECTIONAL DERIVATIVE). */
/* MTYP=3-QUADRATIC INTERPOLATION (WITH TWO DIRECTIONAL */
/* DERIVATIVES). MTYP=4-CUBIC INTERPOLATION. MTYP=5-CONIC */
/* INTERPOLATION. */
/* IO MERR ERROR INDICATOR. MERR=0 FOR NORMAL RETURN. */
/* METHOD : */
/* EXTRAPOLATION OR INTERPOLATION WITH STANDARD MODEL FUNCTIONS. */
void luksan_pnint1__(double *rl, double *ru, double *fl,
double *fu, double *pl, double *pu, double *r__,
int *mode, int *mtyp, int *merr)
{
/* System generated locals */
double d__1, d__2;
/* Local variables */
double a, b, c__, d__, den, dis;
int ntyp;
*merr = 0;
if (*mode <= 0) {
return;
}
if (*pl >= 0.) {
*merr = 2;
return;
} else if (*ru <= *rl) {
*merr = 3;
return;
}
for (ntyp = *mtyp; ntyp >= 1; --ntyp) {
if (ntyp == 1) {
/* BISECTION */
if (*mode == 1) {
*r__ = *ru * 4.;
return;
} else {
*r__ = (*rl + *ru) * .5;
return;
}
} else if (ntyp == *mtyp) {
a = (*fu - *fl) / (*pl * (*ru - *rl));
b = *pu / *pl;
}
if (ntyp == 2) {
/* QUADRATIC EXTRAPOLATION OR INTERPOLATION WITH ONE DIRECTIONAL */
/* DERIVATIVE */
den = (1. - a) * 2.;
} else if (ntyp == 3) {
/* QUADRATIC EXTRAPOLATION OR INTERPOLATION WITH TWO DIRECTIONAL */
/* DERIVATIVES */
den = 1. - b;
} else if (ntyp == 4) {
/* CUBIC EXTRAPOLATION OR INTERPOLATION */
c__ = b - a * 2. + 1.;
d__ = b - a * 3. + 2.;
dis = d__ * d__ - c__ * 3.;
if (dis < 0.) {
goto L1;
}
den = d__ + sqrt(dis);
} else if (ntyp == 5) {
/* CONIC EXTRAPOLATION OR INTERPOLATION */
dis = a * a - b;
if (dis < 0.) {
goto L1;
}
den = a + sqrt(dis);
if (den <= 0.) {
goto L1;
}
/* Computing 3rd power */
d__1 = 1. / den;
den = 1. - b * (d__1 * (d__1 * d__1));
}
if (*mode == 1 && den > 0. && den < 1.) {
/* EXTRAPOLATION ACCEPTED */
*r__ = *rl + (*ru - *rl) / den;
/* Computing MAX */
d__1 = *r__, d__2 = *ru * 1.1;
*r__ = MAX2(d__1,d__2);
/* Computing MIN */
d__1 = *r__, d__2 = *ru * 1e3;
*r__ = MIN2(d__1,d__2);
return;
} else if (*mode == 2 && den > 1.) {
/* INTERPOLATION ACCEPTED */
*r__ = *rl + (*ru - *rl) / den;
if (*rl == 0.) {
/* Computing MAX */
d__1 = *r__, d__2 = *rl + (*ru - *rl) * .01;
*r__ = MAX2(d__1,d__2);
} else {
/* Computing MAX */
d__1 = *r__, d__2 = *rl + (*ru - *rl) * .1;
*r__ = MAX2(d__1,d__2);
}
/* Computing MIN */
d__1 = *r__, d__2 = *rl + (*ru - *rl) * .9;
*r__ = MIN2(d__1,d__2);
return;
}
L1:
;
}
return;
} /* luksan_pnint1__ */
/* save and restore state, replacing old non-reeentrant implementation
that used static local variables */
#define SS(var) state->var = var
#define SAVE_STATE SS(fl); SS(fu); SS(pl); SS(rl); SS(pu); SS(ru); \
SS(mes1); SS(mes2); SS(mes3); SS(mode); SS(mtyp)
#define RS(var) var = state->var
#define RESTORE_STATE RS(fl); RS(fu); RS(pl); RS(rl); RS(pu); RS(ru); \
RS(mes1); RS(mes2); RS(mes3); RS(mode); RS(mtyp)
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PS1L01 ALL SYSTEMS 97/12/01
* PURPOSE :
* STANDARD LINE SEARCH WITH DIRECTIONAL DERIVATIVES.
*
* PARAMETERS :
* RO R VALUE OF THE STEPSIZE PARAMETER.
* RO RP PREVIOUS VALUE OF THE STEPSIZE PARAMETER.
* RO F VALUE OF THE OBJECTIVE FUNCTION.
* RI FO INITIAL VALUE OF THE OBJECTIVE FUNCTION.
* RO FP PREVIOUS VALUE OF THE OBJECTIVE FUNCTION.
* RO P VALUE OF THE DIRECTIONAL DERIVATIVE.
* RI PO INITIAL VALUE OF THE DIRECTIONAL DERIVATIVE.
* RO PP PREVIOUS VALUE OF THE DIRECTIONAL DERIVATIVE.
* RI FMIN LOWER BOUND FOR VALUE OF THE OBJECTIVE FUNCTION.
* RI MAXF UPPER BOUND FOR VALUE OF THE OBJECTIVE FUNCTION.
* RI RMIN MINIMUM VALUE OF THE STEPSIZE PARAMETER
* RI RMAX MAXIMUM VALUE OF THE STEPSIZE PARAMETER
* RI TOLS TERMINATION TOLERANCE FOR LINE SEARCH (IN TEST ON THE
* CHANGE OF THE FUNCTION VALUE).
* RI TOLP TERMINATION TOLERANCE FOR LINE SEARCH (IN TEST ON THE
* CHANGE OF THE DIRECTIONAL DERIVATIVE).
* RO PAR1 PARAMETER FOR CONTROLLED SCALING OF VARIABLE METRIC
* UPDATES.
* RO PAR2 PARAMETER FOR CONTROLLED SCALING OF VARIABLE METRIC
* UPDATES.
* II KD DEGREE OF REQUIRED DERIVATIVES.
* IO LD DEGREE OF PREVIOUSLY COMPUTED DERIVATIVES OF OBJECTIVE
* II NIT ACTUAL NUMBER OF ITERATIONS.
* II KIT NUMBER OF THE ITERATION AFTER LAST RESTART.
* IO NRED ACTUAL NUMBER OF EXTRAPOLATIONS OR INTERPOLATIONS.
* II MRED MAXIMUM NUMBER OF EXTRAPOLATIONS OR INTERPOLATIONS.
* IO MAXST MAXIMUM STEPSIZE INDICATOR. MAXST=0 OR MAXST=1 IF MAXIMUM
* STEPSIZE WAS NOT OR WAS REACHED.
* II IEST LOWER BOUND SPECIFICATION. IEST=0 OR IEST=1 IF LOWER BOUND
* IS NOT OR IS GIVEN.
* II INITS CHOICE OF THE INITIAL STEPSIZE. INITS=0-INITIAL STEPSIZE
* IS SPECIFIED IN THE CALLING PROGRAM. INITS=1-UNIT INITIAL
* STEPSIZE. INITS=2-COMBINED UNIT AND QUADRATICALLY ESTIMATED
* INITIAL STEPSIZE. INITS=3-QUADRATICALLY ESTIMATED INITIAL
* STEPSIZE.
* IO ITERS TERMINATION INDICATOR. ITERS=0-ZERO STEP. ITERS=1-PERFECT
* LINE SEARCH. ITERS=2 GOLDSTEIN STEPSIZE. ITERS=3-CURRY
* STEPSIZE. ITERS=4-EXTENDED CURRY STEPSIZE.
* ITERS=5-ARMIJO STEPSIZE. ITERS=6-FIRST STEPSIZE.
* ITERS=7-MAXIMUM STEPSIZE. ITERS=8-UNBOUNDED FUNCTION.
* ITERS=-1-MRED REACHED. ITERS=-2-POSITIVE DIRECTIONAL
* DERIVATIVE. ITERS=-3-ERROR IN INTERPOLATION.
* II KTERS TERMINATION SELECTION. KTERS=1-PERFECT LINE SEARCH.
* KTERS=2-GOLDSTEIN STEPSIZE. KTERS=3-CURRY STEPSIZE.
* KTERS=4-EXTENDED CURRY STEPSIZE. KTERS=5-ARMIJO STEPSIZE.
* KTERS=6-FIRST STEPSIZE.
* II MES METHOD SELECTION. MES=1-BISECTION. MES=2-QUADRATIC
* INTERPOLATION (WITH ONE DIRECTIONAL DERIVATIVE).
* MES=3-QUADRATIC INTERPOLATION (WITH TWO DIRECTIONAL
* DERIVATIVES). MES=4-CUBIC INTERPOLATION. MES=5-CONIC
* INTERPOLATION.
* IU ISYS CONTROL PARAMETER.
*
* SUBPROGRAM USED :
* S PNINT1 EXTRAPOLATION OR INTERPOLATION WITH DIRECTIONAL
* DERIVATIVES.
*
* METHOD :
* SAFEGUARDED EXTRAPOLATION AND INTERPOLATION WITH STANDARD TERMINATION
* CRITERIA.
*/
void luksan_ps1l01__(double *r__, double *rp,
double *f, double *fo, double *fp, double *p,
double *po, double *pp, double *minf, double *maxf,
double *rmin, double *rmax, double *tols, double *
tolp, double *par1, double *par2, int *kd, int *ld,
int *nit, int *kit, int *nred, int *mred, int *
maxst, int *iest, int *inits, int *iters, int *kters,
int *mes, int *isys, ps1l01_state *state)
{
/* System generated locals */
double d__1, d__2;
/* Local variables */
unsigned l1, l2, l3, m1, l5, m2, l7, m3;
double fl, fu, pl, rl, pu, ru;
int mes1, mes2, mes3, mode;
int merr;
int mtyp;
int init1;
double rtemp;
RESTORE_STATE;
if (*isys == 1) {
goto L3;
}
mes1 = 2;
mes2 = 2;
mes3 = 2;
*iters = 0;
if (*po >= 0.) {
*r__ = 0.;
*iters = -2;
goto L4;
}
if (*rmax <= 0.) {
*iters = 0;
goto L4;
}
/* INITIAL STEPSIZE SELECTION */
if (*inits > 0) {
rtemp = *minf - *f;
} else if (*iest == 0) {
rtemp = *f - *fp;
} else {
/* Computing MAX */
d__1 = *f - *fp, d__2 = *minf - *f;
rtemp = MAX2(d__1,d__2);
}
init1 = iabs(*inits);
*rp = 0.;
*fp = *fo;
*pp = *po;
if (init1 == 0) {
} else if (init1 == 1 || (*inits >= 1 && *iest == 0)) {
*r__ = 1.;
} else if (init1 == 2) {
/* Computing MIN */
d__1 = 1., d__2 = rtemp * 4. / *po;
*r__ = MIN2(d__1,d__2);
} else if (init1 == 3) {
/* Computing MIN */
d__1 = 1., d__2 = rtemp * 2. / *po;
*r__ = MIN2(d__1,d__2);
} else if (init1 == 4) {
*r__ = rtemp * 2. / *po;
}
*r__ = MAX2(*r__,*rmin);
*r__ = MIN2(*r__,*rmax);
mode = 0;
ru = 0.;
fu = *fo;
pu = *po;
/* NEW STEPSIZE SELECTION (EXTRAPOLATION OR INTERPOLATION) */
L2:
luksan_pnint1__(&rl, &ru, &fl, &fu, &pl, &pu, r__, &mode, &mtyp, &merr);
if (merr > 0) {
*iters = -merr;
goto L4;
} else if (mode == 1) {
--(*nred);
*r__ = MIN2(*r__,*rmax);
} else if (mode == 2) {
++(*nred);
}
/* COMPUTATION OF THE NEW FUNCTION VALUE AND THE NEW DIRECTIONAL */
/* DERIVATIVE */
*kd = 1;
*ld = -1;
*isys = 1;
SAVE_STATE;
return;
L3:
if (mode == 0) {
*par1 = *p / *po;
*par2 = *f - *fo;
}
if (*iters != 0) {
goto L4;
}
if (*f <= *minf) {
*iters = 7;
goto L4;
} else {
l1 = *r__ <= *rmin && *nit != *kit;
l2 = *r__ >= *rmax;
l3 = *f - *fo <= *tols * *r__ * *po;
l5 = *p >= *tolp * *po || (mes2 == 2 && mode == 2);
l7 = mes2 <= 2 || mode != 0;
m1 = FALSE_;
m2 = FALSE_;
m3 = l3;
if (mes3 >= 1) {
m1 = fabs(*p) <= fabs(*po) * .01 && *fo - *f >= fabs(*fo) *
9.9999999999999994e-12;
l3 = l3 || m1;
}
if (mes3 >= 2) {
m2 = fabs(*p) <= fabs(*po) * .5 && (d__1 = *fo - *f, fabs(d__1)) <=
fabs(*fo) * 2.0000000000000001e-13;
l3 = l3 || m2;
}
*maxst = 0;
if (l2) {
*maxst = 1;
}
}
/* TEST ON TERMINATION */
if (l1 && ! l3) {
*iters = 0;
goto L4;
} else if (l2 && l3 && ! l5) {
*iters = 7;
goto L4;
} else if (m3 && mes1 == 3) {
*iters = 5;
goto L4;
} else if (l3 && l5 && l7) {
*iters = 4;
goto L4;
} else if (*kters < 0 || (*kters == 6 && l7)) {
*iters = 6;
goto L4;
} else if (iabs(*nred) >= *mred) {
*iters = -1;
goto L4;
} else {
*rp = *r__;
*fp = *f;
*pp = *p;
mode = MAX2(mode,1);
mtyp = iabs(*mes);
if (*f >= *maxf) {
mtyp = 1;
}
}
if (mode == 1) {
/* INTERVAL CHANGE AFTER EXTRAPOLATION */
rl = ru;
fl = fu;
pl = pu;
ru = *r__;
fu = *f;
pu = *p;
if (! l3) {
*nred = 0;
mode = 2;
} else if (mes1 == 1) {
mtyp = 1;
}
} else {
/* INTERVAL CHANGE AFTER INTERPOLATION */
if (! l3) {
ru = *r__;
fu = *f;
pu = *p;
} else {
rl = *r__;
fl = *f;
pl = *p;
}
}
goto L2;
L4:
*isys = 0;
SAVE_STATE;
return;
} /* luksan_ps1l01__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PULSP3 ALL SYSTEMS 02/12/01
* PURPOSE :
* LIMITED STORAGE VARIABLE METRIC UPDATE.
*
* PARAMETERS :
* II N NUMBER OF VARIABLES (NUMBER OF ROWS OF XM).
* II M NUMBER OF COLUMNS OF XM.
* II MF MAXIMUM NUMBER OF COLUMNS OF XM.
* RI XM(N*M) RECTANGULAR MATRIX IN THE PRODUCT FORM SHIFTED BROYDEN
* METHOD (STORED COLUMNWISE): H-SIGMA*I=XM*TRANS(XM)
* RO GR(M) MATRIX TRANS(XM)*GO.
* RU XO(N) VECTORS OF VARIABLES DIFFERENCE XO AND VECTOR XO-TILDE.
* RU GO(N) GRADIENT DIFFERENCE GO AND VECTOR XM*TRANS(XM)*GO.
* RI R STEPSIZE PARAMETER.
* RI PO OLD DIRECTIONAL DERIVATIVE (MULTIPLIED BY R)
* RU SIG SCALING PARAMETER (ZETA AND SIGMA).
* IO ITERH TERMINATION INDICATOR. ITERH<0-BAD DECOMPOSITION.
* ITERH=0-SUCCESSFUL UPDATE. ITERH>0-NONPOSITIVE PARAMETERS.
* II MET3 CHOICE OF SIGMA (1-CONSTANT, 2-QUADRATIC EQUATION).
*
* SUBPROGRAMS USED :
* S MXDRMM MULTIPLICATION OF A ROWWISE STORED DENSE RECTANGULAR
* MATRIX BY A VECTOR.
* S MXDCMU UPDATE OF A COLUMNWISE STORED DENSE RECTANGULAR MATRIX.
* WITH CONTROLLING OF POSITIVE DEFINITENESS.
* S MXVDIR VECTOR AUGMENTED BY A SCALED VECTOR.
* RF MXVDOT DOT PRODUCT OF VECTORS.
* S MXVSCL SCALING OF A VECTOR.
*
* METHOD :
* SHIFTED BFGS METHOD IN THE PRODUCT FORM.
*/
void luksan_pulsp3__(int *n, int *m, int *mf,
double *xm, double *gr, double *xo, double *go,
double *r__, double *po, double *sig, int *iterh,
int *met3)
{
/* System generated locals */
double d__1, d__2, d__3, d__4;
/* Builtin functions */
/* Local variables */
double a, b, c__, aa, bb, ah, den, par, pom;
/* Parameter adjustments */
--go;
--xo;
--gr;
--xm;
/* Function Body */
if (*m >= *mf) {
return;
}
b = luksan_mxvdot__(n, &xo[1], &go[1]);
if (b <= 0.) {
*iterh = 2;
goto L22;
}
luksan_mxdrmm__(n, m, &xm[1], &go[1], &gr[1]);
ah = luksan_mxvdot__(n, &go[1], &go[1]);
aa = luksan_mxvdot__(m, &gr[1], &gr[1]);
a = aa + ah * *sig;
c__ = -(*r__) * *po;
/* DETERMINATION OF THE PARAMETER SIG (SHIFT) */
par = 1.;
pom = b / ah;
if (a > 0.) {
den = luksan_mxvdot__(n, &xo[1], &xo[1]);
if (*met3 <= 4) {
/* Computing MAX */
d__1 = 0., d__2 = 1. - aa / a;
/* Computing MAX */
d__3 = 0., d__4 = 1. - b * b / (den * ah);
*sig = sqrt((MAX2(d__1,d__2))) / (sqrt((MAX2(d__3,d__4))) + 1.) *
pom;
} else {
/* Computing MAX */
d__1 = 0., d__2 = *sig * ah / a;
/* Computing MAX */
d__3 = 0., d__4 = 1. - b * b / (den * ah);
*sig = sqrt((MAX2(d__1,d__2))) / (sqrt((MAX2(d__3,d__4))) + 1.) *
pom;
}
/* Computing MAX */
d__1 = *sig, d__2 = pom * .2;
*sig = MAX2(d__1,d__2);
/* Computing MIN */
d__1 = *sig, d__2 = pom * .8;
*sig = MIN2(d__1,d__2);
} else {
*sig = pom * .25;
}
/* COMPUTATION OF SHIFTED XO AND SHIFTED B */
bb = b - ah * *sig;
d__1 = -(*sig);
luksan_mxvdir__(n, &d__1, &go[1], &xo[1], &xo[1]);
/* BFGS-BASED SHIFTED BFGS UPDATE */
pom = 1.;
d__1 = -1. / bb;
luksan_mxdcmu__(n, m, &xm[1], &d__1, &xo[1], &gr[1]);
d__1 = sqrt(par / bb);
luksan_mxvscl__(n, &d__1, &xo[1], &xm[*n * *m + 1]);
++(*m);
L22:
*iterh = 0;
return;
} /* luksan_pulsp3__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PULVP3 ALL SYSTEMS 03/12/01
* PURPOSE :
* RANK-TWO LIMITED-STORAGE VARIABLE-METRIC METHODS IN THE PRODUCT FORM.
*
* PARAMETERS :
* II N NUMBER OF VARIABLES (NUMBER OF ROWS OF XM).
* II M NUMBER OF COLUMNS OF XM.
* RI XM(N*M) RECTANGULAR MATRIX IN THE PRODUCT FORM SHIFTED BROYDEN
* METHOD (STORED COLUMNWISE): H-SIGMA*I=XM*TRANS(XM)
* RO XR(M) VECTOR TRANS(XM)*H**(-1)*XO.
* RO GR(M) MATRIX TRANS(XM)*GO.
* RA S(N) AUXILIARY VECTORS (H**(-1)*XO AND U).
* RA SO(N) AUXILIARY VECTORS ((H-SIGMA*I)*H**(-1)*XO AND V).
* RU XO(N) VECTORS OF VARIABLES DIFFERENCE XO AND VECTOR XO-TILDE.
* RU GO(N) GRADIENT DIFFERENCE GO AND VECTOR XM*TRANS(XM)*GO.
* RI R STEPSIZE PARAMETER.
* RI PO OLD DIRECTIONAL DERIVATIVE (MULTIPLIED BY R)
* RU SIG SCALING PARAMETER (ZETA AND SIGMA).
* IO ITERH TERMINATION INDICATOR. ITERH<0-BAD DECOMPOSITION.
* ITERH=0-SUCCESSFUL UPDATE. ITERH>0-NONPOSITIVE PARAMETERS.
* II MET2 CHOICE OF THE CORRECTION PARAMETER (1-THE UNIT VALUE,
* 2-THE BALANCING VALUE, 3-THE SQUARE ROOT, 4-THE GEOMETRIC
* MEAN).
* II MET3 CHOICE OF THE SHIFT PARAMETER (4-THE FIRST FORMULA,
* 5-THE SECOND FORMULA).
* II MET5 CHOICE OF THE METHOD (1-RANK-ONE METHOD, 2-RANK-TWO
* METHOD).
*
* SUBPROGRAMS USED :
* S MXDRMM MULTIPLICATION OF A ROWWISE STORED DENSE RECTANGULAR
* MATRIX BY A VECTOR.
* S MXDCMU UPDATE OF A COLUMNWISE STORED DENSE RECTANGULAR MATRIX.
* WITH CONTROLLING OF POSITIVE DEFINITENESS. RANK-ONE FORMULA.
* S MXDCMV UPDATE OF A COLUMNWISE STORED DENSE RECTANGULAR MATRIX.
* WITH CONTROLLING OF POSITIVE DEFINITENESS. RANK-TWO FORMULA.
* S MXVDIR VECTOR AUGMENTED BY A SCALED VECTOR.
* RF MXVDOT DOT PRODUCT OF VECTORS.
* S MXVLIN LINEAR COMBINATION OF TWO VECTORS.
* S MXVSCL SCALING OF A VECTOR.
*
* METHOD :
* RANK-ONE LIMITED-STORAGE VARIABLE-METRIC METHOD IN THE PRODUCT FORM.
*/
void luksan_pulvp3__(int *n, int *m, double *xm,
double *xr, double *gr, double *s, double *so,
double *xo, double *go, double *r__, double *po,
double *sig, int *iterh, int *met2, int *met3,
int *met5)
{
/* System generated locals */
double d__1, d__2, d__3, d__4;
/* Builtin functions */
/* Local variables */
double a, b, c__, aa, bb, cc, ah, den, par, pom, zet;
/* Parameter adjustments */
--go;
--xo;
--so;
--s;
--gr;
--xr;
--xm;
/* Function Body */
zet = *sig;
/* COMPUTATION OF B */
b = luksan_mxvdot__(n, &xo[1], &go[1]);
if (b <= 0.) {
*iterh = 2;
goto L22;
}
/* COMPUTATION OF GR=TRANS(XM)*GO, XR=TRANS(XM)*H**(-1)*XO */
/* AND S=H**(-1)*XO, SO=(H-SIGMA*I)*H**(-1)*XO. COMPUTATION */
/* OF AA=GR*GR, BB=GR*XR, CC=XR*XR. COMPUTATION OF A AND C. */
luksan_mxdrmm__(n, m, &xm[1], &go[1], &gr[1]);
luksan_mxvscl__(n, r__, &s[1], &s[1]);
luksan_mxdrmm__(n, m, &xm[1], &s[1], &xr[1]);
d__1 = -(*sig);
luksan_mxvdir__(n, &d__1, &s[1], &xo[1], &so[1]);
ah = luksan_mxvdot__(n, &go[1], &go[1]);
aa = luksan_mxvdot__(m, &gr[1], &gr[1]);
bb = luksan_mxvdot__(m, &gr[1], &xr[1]);
cc = luksan_mxvdot__(m, &xr[1], &xr[1]);
a = aa + ah * *sig;
c__ = -(*r__) * *po;
/* DETERMINATION OF THE PARAMETER SIG (SHIFT) */
pom = b / ah;
if (a > 0.) {
den = luksan_mxvdot__(n, &xo[1], &xo[1]);
if (*met3 <= 4) {
/* Computing MAX */
d__1 = 0., d__2 = 1. - aa / a;
/* Computing MAX */
d__3 = 0., d__4 = 1. - b * b / (den * ah);
*sig = sqrt((MAX2(d__1,d__2))) / (sqrt((MAX2(d__3,d__4))) + 1.) *
pom;
} else {
/* Computing MAX */
d__1 = 0., d__2 = *sig * ah / a;
/* Computing MAX */
d__3 = 0., d__4 = 1. - b * b / (den * ah);
*sig = sqrt((MAX2(d__1,d__2))) / (sqrt((MAX2(d__3,d__4))) + 1.) *
pom;
}
/* Computing MAX */
d__1 = *sig, d__2 = pom * .2;
*sig = MAX2(d__1,d__2);
/* Computing MIN */
d__1 = *sig, d__2 = pom * .8;
*sig = MIN2(d__1,d__2);
} else {
*sig = pom * .25;
}
/* COMPUTATION OF SHIFTED XO AND SHIFTED B */
b -= ah * *sig;
d__1 = -(*sig);
luksan_mxvdir__(n, &d__1, &go[1], &xo[1], &xo[1]);
/* COMPUTATION OF THE PARAMETER RHO (CORRECTION) */
if (*met2 <= 1) {
par = 1.;
} else if (*met2 == 2) {
par = *sig * ah / b;
} else if (*met2 == 3) {
par = sqrt(1. - aa / a);
} else if (*met2 == 4) {
par = sqrt(sqrt(1. - aa / a) * (*sig * ah / b));
} else {
par = zet / (zet + *sig);
}
/* COMPUTATION OF THE PARAMETER THETA (BFGS) */
d__1 = sqrt(par * b / cc);
pom = copysign(d__1, bb);
/* COMPUTATION OF Q AND P */
if (*met5 == 1) {
/* RANK ONE UPDATE OF XM */
luksan_mxvdir__(m, &pom, &xr[1], &gr[1], &xr[1]);
luksan_mxvlin__(n, &par, &xo[1], &pom, &so[1], &s[1]);
d__1 = -1. / (par * b + pom * bb);
luksan_mxdcmu__(n, m, &xm[1], &d__1, &s[1], &xr[1]);
} else {
/* RANK TWO UPDATE OF XM */
d__1 = par / pom - bb / b;
luksan_mxvdir__(n, &d__1, &xo[1], &so[1], &s[1]);
d__1 = -1. / b;
d__2 = -1. / cc;
luksan_mxdcmv__(n, m, &xm[1], &d__1, &xo[1], &gr[1], &d__2, &s[1], &xr[1]);
}
L22:
*iterh = 0;
return;
} /* luksan_pulvp3__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PYADC0 ALL SYSTEMS 98/12/01
* PURPOSE :
* NEW SIMPLE BOUNDS ARE ADDED TO THE ACTIVE SET.
*
* PARAMETERS :
* II NF DECLARED NUMBER OF VARIABLES.
* II N REDUCED NUMBER OF VARIABLES.
* RI X(NF) VECTOR OF VARIABLES.
* II IX(NF) VECTOR CONTAINING TYPES OF BOUNDS.
* RI XL(NF) VECTOR CONTAINING LOWER BOUNDS FOR VARIABLES.
* RI XU(NF) VECTOR CONTAINING UPPER BOUNDS FOR VARIABLES.
* IO INEW NUMBER OF ACTIVE CONSTRAINTS.
*/
void luksan_pyadc0__(int *nf, int *n, double *x,
int *ix, double *xl, double *xu, int *inew)
{
/* System generated locals */
int i__1;
/* Local variables */
int i__, ii, ixi;
/* Parameter adjustments */
--ix;
--x;
--xl;
--xu;
/* Function Body */
*n = *nf;
*inew = 0;
i__1 = *nf;
for (i__ = 1; i__ <= i__1; ++i__) {
ii = ix[i__];
ixi = iabs(ii);
if (ixi >= 5) {
ix[i__] = -ixi;
} else if ((ixi == 1 || ixi == 3 || ixi == 4) && x[i__] <= xl[i__]) {
x[i__] = xl[i__];
if (ixi == 4) {
ix[i__] = -3;
} else {
ix[i__] = -ixi;
}
--(*n);
if (ii > 0) {
++(*inew);
}
} else if ((ixi == 2 || ixi == 3 || ixi == 4) && x[i__] >= xu[i__]) {
x[i__] = xu[i__];
if (ixi == 3) {
ix[i__] = -4;
} else {
ix[i__] = -ixi;
}
--(*n);
if (ii > 0) {
++(*inew);
}
}
/* L1: */
}
return;
} /* luksan_pyadc0__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PYFUT1 ALL SYSTEMS 98/12/01
* PURPOSE :
* TERMINATION CRITERIA AND TEST ON RESTART.
*
* PARAMETERS :
* II N ACTUAL NUMBER OF VARIABLES.
* RI F NEW VALUE OF THE OBJECTIVE FUNCTION.
* RI FO OLD VALUE OF THE OBJECTIVE FUNCTION.
* RI UMAX MAXIMUM ABSOLUTE VALUE OF THE NEGATIVE LAGRANGE MULTIPLIER.
* RO GMAX NORM OF THE TRANSFORMED GRADIENT.
* RI DMAX MAXIMUM RELATIVE DIFFERENCE OF VARIABLES.
* RI TOLX LOWER BOUND FOR STEPLENGTH.
* RI TOLF LOWER BOUND FOR FUNCTION DECREASE.
* RI TOLB LOWER BOUND FOR FUNCTION VALUE.
* RI TOLG LOWER BOUND FOR GRADIENT.
* II KD DEGREE OF REQUIRED DERIVATIVES.
* IU NIT ACTUAL NUMBER OF ITERATIONS.
* II KIT NUMBER OF THE ITERATION AFTER RESTART.
* II MIT MAXIMUM NUMBER OF ITERATIONS.
* IU NFV ACTUAL NUMBER OF COMPUTED FUNCTION VALUES.
* II MFV MAXIMUM NUMBER OF COMPUTED FUNCTION VALUES.
* IU NFG ACTUAL NUMBER OF COMPUTED GRADIENT VALUES.
* II MFG MAXIMUM NUMBER OF COMPUTED GRADIENT VALUES.
* IU NTESX ACTUAL NUMBER OF TESTS ON STEPLENGTH.
* II MTESX MAXIMUM NUMBER OF TESTS ON STEPLENGTH.
* IU NTESF ACTUAL NUMBER OF TESTS ON FUNCTION DECREASE.
* II MTESF MAXIMUM NUMBER OF TESTS ON FUNCTION DECREASE.
* II IRES1 RESTART SPECIFICATION. RESTART IS PERFORMED AFTER
* IRES1*N+IRES2 ITERATIONS.
* II IRES2 RESTART SPECIFICATION. RESTART IS PERFORMED AFTER
* IRES1*N+IRES2 ITERATIONS.
* IU IREST RESTART INDICATOR. RESTART IS PERFORMED IF IREST>0.
* II ITERS TERMINATION INDICATOR FOR STEPLENGTH DETERMINATION.
* ITERS=0 FOR ZERO STEP.
* IO ITERM TERMINATION INDICATOR. ITERM=1-TERMINATION AFTER MTESX
* UNSUFFICIENT STEPLENGTHS. ITERM=2-TERMINATION AFTER MTESF
* UNSUFFICIENT FUNCTION DECREASES. ITERM=3-TERMINATION ON LOWER
* BOUND FOR FUNCTION VALUE. ITERM=4-TERMINATION ON LOWER BOUND
* FOR GRADIENT. ITERM=11-TERMINATION AFTER MAXIMUM NUMBER OF
* ITERATIONS. ITERM=12-TERMINATION AFTER MAXIMUM NUMBER OF
* COMPUTED FUNCTION VALUES.
*/
void luksan_pyfut1__(int *n, double *f, double *fo, double *umax,
double *gmax, int xstop, /* double *dmax__, */
const nlopt_stopping *stop,
double *tolg, int *kd, int *nit, int *kit, int *mit,
int *nfg, int *mfg, int *ntesx,
int *mtesx, int *ntesf, int *mtesf, int *ites,
int *ires1, int *ires2, int *irest, int *iters,
int *iterm)
{
/* System generated locals */
double d__1, d__2;
/* Builtin functions */
if (*iterm < 0) {
return;
}
if (*ites <= 0) {
goto L1;
}
if (*iters == 0) {
goto L1;
}
if (*nit <= 0) {
/* Computing MIN */
d__1 = sqrt((fabs(*f))), d__2 = fabs(*f) / 10.;
*fo = *f + MIN2(d__1,d__2);
}
if (nlopt_stop_forced(stop)) {
*iterm = -999;
return;
}
if (*f <= stop->minf_max /* *tolb */) {
*iterm = 3;
return;
}
if (*kd > 0) {
if (*gmax <= *tolg && *umax <= *tolg) {
*iterm = 4;
return;
}
}
if (*nit <= 0) {
*ntesx = 0;
*ntesf = 0;
}
if (xstop) /* (*dmax__ <= *tolx) */ {
*iterm = 1;
++(*ntesx);
if (*ntesx >= *mtesx) {
return;
}
} else {
*ntesx = 0;
}
if (nlopt_stop_ftol(stop, *f, *fo)) {
*iterm = 2;
++(*ntesf);
if (*ntesf >= *mtesf) {
return;
}
} else {
*ntesf = 0;
}
L1:
if (*nit >= *mit) {
*iterm = 11;
return;
}
if (nlopt_stop_evals(stop)) /* (*nfv >= *mfv) */ {
*iterm = 12;
return;
}
if (*nfg >= *mfg) {
*iterm = 13;
return;
}
*iterm = 0;
if (*n > 0 && *nit - *kit >= *ires1 * *n + *ires2) {
*irest = MAX2(*irest,1);
}
++(*nit);
return;
} /* luksan_pyfut1__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PYRMC0 ALL SYSTEMS 98/12/01
* PURPOSE :
* OLD SIMPLE BOUND IS REMOVED FROM THE ACTIVE SET. TRANSFORMED
* GRADIENT OF THE OBJECTIVE FUNCTION IS UPDATED.
*
* PARAMETERS :
* II NF DECLARED NUMBER OF VARIABLES.
* II N REDUCED NUMBER OF VARIABLES.
* II IX(NF) VECTOR CONTAINING TYPES OF BOUNDS.
* RI G(NF) GRADIENT OF THE OBJECTIVE FUNCTION.
* RI EPS8 TOLERANCE FOR CONSTRAINT TO BE REMOVED.
* RI UMAX MAXIMUM ABSOLUTE VALUE OF THE NEGATIVE LAGRANGE MULTIPLIER.
* RI GMAX NORM OF THE TRANSFORMED GRADIENT.
* RO RMAX MAXIMUM VALUE OF THE STEPSIZE PARAMETER.
* II IOLD NUMBER OF REMOVED CONSTRAINTS.
* IU IREST RESTART INDICATOR.
*/
void luksan_pyrmc0__(int *nf, int *n, int *ix,
double *g, double *eps8, double *umax, double *gmax,
double *rmax, int *iold, int *irest)
{
/* System generated locals */
int i__1, i__2, i__3;
/* Local variables */
int i__, ixi;
/* Parameter adjustments */
--g;
--ix;
/* Function Body */
if (*n == 0 || *rmax > 0.) {
if (*umax > *eps8 * *gmax) {
*iold = 0;
i__1 = *nf;
for (i__ = 1; i__ <= i__1; ++i__) {
ixi = ix[i__];
if (ixi >= 0) {
} else if (ixi <= -5) {
} else if ((ixi == -1 || ixi == -3) && -g[i__] <= 0.) {
} else if ((ixi == -2 || ixi == -4) && g[i__] <= 0.) {
} else {
++(*iold);
/* Computing MIN */
i__3 = (i__2 = ix[i__], iabs(i__2));
ix[i__] = MIN2(i__3,3);
if (*rmax == 0.) {
goto L2;
}
}
/* L1: */
}
L2:
if (*iold > 1) {
*irest = MAX2(*irest,1);
}
}
}
return;
} /* luksan_pyrmc0__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PYTRCD ALL SYSTEMS 98/12/01
* PURPOSE :
* VECTORS OF VARIABLES DIFFERENCE AND GRADIENTS DIFFERENCE ARE COMPUTED
* AND SCALED AND REDUCED. TEST VALUE DMAX IS DETERMINED.
*
* PARAMETERS :
* II NF DECLARED NUMBER OF VARIABLES.
* RI X(NF) VECTOR OF VARIABLES.
* II IX(NF) VECTOR CONTAINING TYPES OF BOUNDS.
* RU XO(NF) VECTORS OF VARIABLES DIFFERENCE.
* RI G(NF) GRADIENT OF THE OBJECTIVE FUNCTION.
* RU GO(NF) GRADIENTS DIFFERENCE.
* RO R VALUE OF THE STEPSIZE PARAMETER.
* RO F NEW VALUE OF THE OBJECTIVE FUNCTION.
* RI FO OLD VALUE OF THE OBJECTIVE FUNCTION.
* RO P NEW VALUE OF THE DIRECTIONAL DERIVATIVE.
* RI PO OLD VALUE OF THE DIRECTIONAL DERIVATIVE.
* RO DMAX MAXIMUM RELATIVE DIFFERENCE OF VARIABLES.
* II KBF SPECIFICATION OF SIMPLE BOUNDS. KBF=0-NO SIMPLE BOUNDS.
* KBF=1-ONE SIDED SIMPLE BOUNDS. KBF=2=TWO SIDED SIMPLE BOUNDS.
* IO KD DEGREE OF REQUIRED DERIVATIVES.
* IO LD DEGREE OF COMPUTED DERIVATIVES.
* II ITERS TERMINATION INDICATOR FOR STEPLENGTH DETERMINATION.
* ITERS=0 FOR ZERO STEP.
*
* SUBPROGRAMS USED :
* S MXVDIF DIFFERENCE OF TWO VECTORS.
* S MXVSAV DIFFERENCE OF TWO VECTORS WITH COPYING AND SAVING THE
* SUBSTRACTED ONE.
*/
void luksan_pytrcd__(int *nf, double *x, int *ix,
double *xo, double *g, double *go, double *r__,
double *f, double *fo, double *p, double *po,
double *dmax__, int *kbf, int *kd, int *ld, int *
iters)
{
/* System generated locals */
int i__1;
double d__1, d__2, d__3, d__4, d__5;
/* Local variables */
int i__;
/* Parameter adjustments */
--go;
--g;
--xo;
--ix;
--x;
/* Function Body */
if (*iters > 0) {
luksan_mxvdif__(nf, &x[1], &xo[1], &xo[1]);
luksan_mxvdif__(nf, &g[1], &go[1], &go[1]);
*po = *r__ * *po;
*p = *r__ * *p;
} else {
*f = *fo;
*p = *po;
luksan_mxvsav__(nf, &x[1], &xo[1]);
luksan_mxvsav__(nf, &g[1], &go[1]);
*ld = *kd;
}
*dmax__ = 0.;
i__1 = *nf;
for (i__ = 1; i__ <= i__1; ++i__) {
if (*kbf > 0) {
if (ix[i__] < 0) {
xo[i__] = 0.;
go[i__] = 0.;
goto L1;
}
}
/* Computing MAX */
/* Computing MAX */
d__5 = (d__2 = x[i__], fabs(d__2));
d__3 = *dmax__, d__4 = (d__1 = xo[i__], fabs(d__1)) / MAX2(d__5,1.);
*dmax__ = MAX2(d__3,d__4);
L1:
;
}
return;
} /* luksan_pytrcd__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PYTRCG ALL SYSTEMS 99/12/01
* PURPOSE :
* GRADIENT OF THE OBJECTIVE FUNCTION IS SCALED AND REDUCED. TEST VALUES
* GMAX AND UMAX ARE COMPUTED.
*
* PARAMETERS :
* II NF DECLARED NUMBER OF VARIABLES.
* II N ACTUAL NUMBER OF VARIABLES.
* II IX(NF) VECTOR CONTAINING TYPES OF BOUNDS.
* RI G(NF) GRADIENT OF THE OBJECTIVE FUNCTION.
* RI UMAX MAXIMUM ABSOLUTE VALUE OF THE NEGATIVE LAGRANGE MULTIPLIER.
* RI GMAX NORM OF THE TRANSFORMED GRADIENT.
* II KBF SPECIFICATION OF SIMPLE BOUNDS. KBF=0-NO SIMPLE BOUNDS.
* KBF=1-ONE SIDED SIMPLE BOUNDS. KBF=2=TWO SIDED SIMPLE BOUNDS.
* II IOLD INDEX OF THE REMOVED CONSTRAINT.
*
* SUBPROGRAMS USED :
* RF MXVMAX L-INFINITY NORM OF A VECTOR.
*/
void luksan_pytrcg__(int *nf, int *n, int *ix,
double *g, double *umax, double *gmax, int *kbf,
int *iold)
{
/* System generated locals */
int i__1;
double d__1, d__2;
/* Local variables */
int i__;
double temp;
/* Parameter adjustments */
--g;
--ix;
/* Function Body */
if (*kbf > 0) {
*gmax = 0.;
*umax = 0.;
*iold = 0;
i__1 = *nf;
for (i__ = 1; i__ <= i__1; ++i__) {
temp = g[i__];
if (ix[i__] >= 0) {
/* Computing MAX */
d__1 = *gmax, d__2 = fabs(temp);
*gmax = MAX2(d__1,d__2);
} else if (ix[i__] <= -5) {
} else if ((ix[i__] == -1 || ix[i__] == -3) && *umax + temp >= 0.)
{
} else if ((ix[i__] == -2 || ix[i__] == -4) && *umax - temp >= 0.)
{
} else {
*iold = i__;
*umax = fabs(temp);
}
/* L1: */
}
} else {
*umax = 0.;
*gmax = luksan_mxvmax__(nf, &g[1]);
}
*n = *nf;
return;
} /* luksan_pytrcg__ */
/* cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* SUBROUTINE PYTRCS ALL SYSTEMS 98/12/01
* PURPOSE :
* SCALED AND REDUCED DIRECTION VECTOR IS BACK TRANSFORMED. VECTORS
* X,G AND VALUES F,P ARE SAVED.
*
* PARAMETERS :
* II NF DECLARED NUMBER OF VARIABLES.
* RI X(NF) VECTOR OF VARIABLES.
* II IX(NF) VECTOR CONTAINING TYPES OF BOUNDS.
* RO XO(NF) SAVED VECTOR OF VARIABLES.
* RI XL(NF) VECTOR CONTAINING LOWER BOUNDS FOR VARIABLES.
* RI XU(NF) VECTOR CONTAINING UPPER BOUNDS FOR VARIABLES.
* RI G(NF) GRADIENT OF THE OBJECTIVE FUNCTION.
* RO GO(NF) SAVED GRADIENT OF THE OBJECTIVE FUNCTION.
* RO S(NF) DIRECTION VECTOR.
* RO RO SAVED VALUE OF THE STEPSIZE PARAMETER.
* RO FP PREVIOUS VALUE OF THE OBJECTIVE FUNCTION.
* RU FO SAVED VALUE OF THE OBJECTIVE FUNCTION.
* RI F VALUE OF THE OBJECTIVE FUNCTION.
* RO PO SAVED VALUE OF THE DIRECTIONAL DERIVATIVE.
* RI P VALUE OF THE DIRECTIONAL DERIVATIVE.
* RO RMAX MAXIMUM VALUE OF THE STEPSIZE PARAMETER.
* RI ETA9 MAXIMUM FOR REAL NUMBERS.
* II KBF SPECIFICATION OF SIMPLE BOUNDS. KBF=0-NO SIMPLE BOUNDS.
* KBF=1-ONE SIDED SIMPLE BOUNDS. KBF=2=TWO SIDED SIMPLE BOUNDS.
*
* SUBPROGRAMS USED :
* S MXVCOP COPYING OF A VECTOR.
*/
void luksan_pytrcs__(int *nf, double *x, int *ix,
double *xo, double *xl, double *xu, double *g,
double *go, double *s, double *ro, double *fp,
double *fo, double *f, double *po, double *p,
double *rmax, double *eta9, int *kbf)
{
/* System generated locals */
int i__1;
double d__1, d__2;
/* Local variables */
int i__;
/* Parameter adjustments */
--s;
--go;
--g;
--xu;
--xl;
--xo;
--ix;
--x;
/* Function Body */
*fp = *fo;
*ro = 0.;
*fo = *f;
*po = *p;
luksan_mxvcop__(nf, &x[1], &xo[1]);
luksan_mxvcop__(nf, &g[1], &go[1]);
if (*kbf > 0) {
i__1 = *nf;
for (i__ = 1; i__ <= i__1; ++i__) {
if (ix[i__] < 0) {
s[i__] = 0.;
} else {
if (ix[i__] == 1 || ix[i__] >= 3) {
if (s[i__] < -1. / *eta9) {
/* Computing MIN */
d__1 = *rmax, d__2 = (xl[i__] - x[i__]) / s[i__];
*rmax = MIN2(d__1,d__2);
}
}
if (ix[i__] == 2 || ix[i__] >= 3) {
if (s[i__] > 1. / *eta9) {
/* Computing MIN */
d__1 = *rmax, d__2 = (xu[i__] - x[i__]) / s[i__];
*rmax = MIN2(d__1,d__2);
}
}
}
/* L1: */
}
}
return;
} /* luksan_pytrcs__ */
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