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lbfgsb.c
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lbfgsb.c
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/* opt/lbfgsb.f -- translated by f2c (version 20050501).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static doublereal c_b9 = 0.;
static integer c__1 = 1;
static integer c__9 = 9;
static integer c__11 = 11;
static integer c__3 = 3;
static doublereal c_b275 = .001;
static doublereal c_b276 = .9;
static doublereal c_b277 = .1;
static integer c__5 = 5;
/* ================ L-BFGS-B (version 2.1) ========================== */
/*< >*/
/* Subroutine */ int setulb_(integer *n, integer *m, doublereal *x,
doublereal *l, doublereal *u, integer *nbd, doublereal *f, doublereal
*g, doublereal *factr, doublereal *pgtol, doublereal *wa, integer *
iwa, char *task, integer *iprint, char *csave, logical *lsave,
integer *isave, doublereal *dsave, ftnlen task_len, ftnlen csave_len)
{
/* System generated locals */
integer i__1;
/* Builtin functions */
integer s_cmp(char *, char *, ftnlen, ftnlen);
/* Local variables */
integer l1, l2, l3, ld, lr, lt, lz, lwa, lsg, lyg, lwn, lss, lws, lwt,
lsy, lwy, lyy, lsnd, lsgo, lygo;
extern /* Subroutine */ int mainlb_(integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *, integer *,
integer *, char *, integer *, char *, logical *, integer *,
doublereal *, ftnlen, ftnlen);
/*< character*60 task, csave >*/
/*< logical lsave(4) >*/
/*< >*/
/*< >*/
/* ************ */
/* Subroutine setulb */
/* This subroutine partitions the working arrays wa and iwa, and */
/* then uses the limited memory BFGS method to solve the bound */
/* constrained optimization problem by calling mainlb. */
/* (The direct method will be used in the subspace minimization.) */
/* n is an integer variable. */
/* On entry n is the dimension of the problem. */
/* On exit n is unchanged. */
/* m is an integer variable. */
/* On entry m is the maximum number of variable metric corrections */
/* used to define the limited memory matrix. */
/* On exit m is unchanged. */
/* x is a double precision array of dimension n. */
/* On entry x is an approximation to the solution. */
/* On exit x is the current approximation. */
/* l is a double precision array of dimension n. */
/* On entry l is the lower bound on x. */
/* On exit l is unchanged. */
/* u is a double precision array of dimension n. */
/* On entry u is the upper bound on x. */
/* On exit u is unchanged. */
/* nbd is an integer array of dimension n. */
/* On entry nbd represents the type of bounds imposed on the */
/* variables, and must be specified as follows: */
/* nbd(i)=0 if x(i) is unbounded, */
/* 1 if x(i) has only a lower bound, */
/* 2 if x(i) has both lower and upper bounds, and */
/* 3 if x(i) has only an upper bound. */
/* On exit nbd is unchanged. */
/* f is a double precision variable. */
/* On first entry f is unspecified. */
/* On final exit f is the value of the function at x. */
/* g is a double precision array of dimension n. */
/* On first entry g is unspecified. */
/* On final exit g is the value of the gradient at x. */
/* factr is a double precision variable. */
/* On entry factr >= 0 is specified by the user. The iteration */
/* will stop when */
/* (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch */
/* where epsmch is the machine precision, which is automatically */
/* generated by the code. Typical values for factr: 1.d+12 for */
/* low accuracy; 1.d+7 for moderate accuracy; 1.d+1 for extremely */
/* high accuracy. */
/* On exit factr is unchanged. */
/* pgtol is a double precision variable. */
/* On entry pgtol >= 0 is specified by the user. The iteration */
/* will stop when */
/* max{|proj g_i | i = 1, ..., n} <= pgtol */
/* where pg_i is the ith component of the projected gradient. */
/* On exit pgtol is unchanged. */
/* wa is a double precision working array of length */
/* (2mmax + 4)nmax + 12mmax^2 + 12mmax. */
/* iwa is an integer working array of length 3nmax. */
/* task is a working string of characters of length 60 indicating */
/* the current job when entering and quitting this subroutine. */
/* iprint is an integer variable that must be set by the user. */
/* It controls the frequency and type of output generated: */
/* iprint<0 no output is generated; */
/* iprint=0 print only one line at the last iteration; */
/* 0<iprint<99 print also f and |proj g| every iprint iterations; */
/* iprint=99 print details of every iteration except n-vectors; */
/* iprint=100 print also the changes of active set and final x; */
/* iprint>100 print details of every iteration including x and g; */
/* When iprint > 0, the file iterate.dat will be created to */
/* summarize the iteration. */
/* csave is a working string of characters of length 60. */
/* lsave is a logical working array of dimension 4. */
/* On exit with 'task' = NEW_X, the following information is */
/* available: */
/* If lsave(1) = .true. then the initial X has been replaced by */
/* its projection in the feasible set; */
/* If lsave(2) = .true. then the problem is constrained; */
/* If lsave(3) = .true. then each variable has upper and lower */
/* bounds; */
/* isave is an integer working array of dimension 44. */
/* On exit with 'task' = NEW_X, the following information is */
/* available: */
/* isave(22) = the total number of intervals explored in the */
/* search of Cauchy points; */
/* isave(26) = the total number of skipped BFGS updates before */
/* the current iteration; */
/* isave(30) = the number of current iteration; */
/* isave(31) = the total number of BFGS updates prior the current */
/* iteration; */
/* isave(33) = the number of intervals explored in the search of */
/* Cauchy point in the current iteration; */
/* isave(34) = the total number of function and gradient */
/* evaluations; */
/* isave(36) = the number of function value or gradient */
/* evaluations in the current iteration; */
/* if isave(37) = 0 then the subspace argmin is within the box; */
/* if isave(37) = 1 then the subspace argmin is beyond the box; */
/* isave(38) = the number of free variables in the current */
/* iteration; */
/* isave(39) = the number of active constraints in the current */
/* iteration; */
/* n + 1 - isave(40) = the number of variables leaving the set of */
/* active constraints in the current iteration; */
/* isave(41) = the number of variables entering the set of active */
/* constraints in the current iteration. */
/* dsave is a double precision working array of dimension 29. */
/* On exit with 'task' = NEW_X, the following information is */
/* available: */
/* dsave(1) = current 'theta' in the BFGS matrix; */
/* dsave(2) = f(x) in the previous iteration; */
/* dsave(3) = factr*epsmch; */
/* dsave(4) = 2-norm of the line search direction vector; */
/* dsave(5) = the machine precision epsmch generated by the code; */
/* dsave(7) = the accumulated time spent on searching for */
/* Cauchy points; */
/* dsave(8) = the accumulated time spent on */
/* subspace minimization; */
/* dsave(9) = the accumulated time spent on line search; */
/* dsave(11) = the slope of the line search function at */
/* the current point of line search; */
/* dsave(12) = the maximum relative step length imposed in */
/* line search; */
/* dsave(13) = the infinity norm of the projected gradient; */
/* dsave(14) = the relative step length in the line search; */
/* dsave(15) = the slope of the line search function at */
/* the starting point of the line search; */
/* dsave(16) = the square of the 2-norm of the line search */
/* direction vector. */
/* Subprograms called: */
/* L-BFGS-B Library ... mainlb. */
/* References: */
/* [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited */
/* memory algorithm for bound constrained optimization'', */
/* SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. */
/* [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: a */
/* limited memory FORTRAN code for solving bound constrained */
/* optimization problems'', Tech. Report, NAM-11, EECS Department, */
/* Northwestern University, 1994. */
/* (Postscript files of these papers are available via anonymous */
/* ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.) */
/* * * * */
/* NEOS, November 1994. (Latest revision June 1996.) */
/* Optimization Technology Center. */
/* Argonne National Laboratory and Northwestern University. */
/* Written by */
/* Ciyou Zhu */
/* in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. */
/* ************ */
/*< >*/
/*< if (task .eq. 'START') then >*/
/* Parameter adjustments */
--iwa;
--g;
--nbd;
--u;
--l;
--x;
--wa;
--lsave;
--isave;
--dsave;
/* Function Body */
if (s_cmp(task, "START", (ftnlen)60, (ftnlen)5) == 0) {
/*< isave(1) = m*n >*/
isave[1] = *m * *n;
/*< isave(2) = m**2 >*/
/* Computing 2nd power */
i__1 = *m;
isave[2] = i__1 * i__1;
/*< isave(3) = 4*m**2 >*/
/* Computing 2nd power */
i__1 = *m;
isave[3] = i__1 * i__1 << 2;
/*< isave(4) = 1 >*/
isave[4] = 1;
/*< isave(5) = isave(4) + isave(1) >*/
isave[5] = isave[4] + isave[1];
/*< isave(6) = isave(5) + isave(1) >*/
isave[6] = isave[5] + isave[1];
/*< isave(7) = isave(6) + isave(2) >*/
isave[7] = isave[6] + isave[2];
/*< isave(8) = isave(7) + isave(2) >*/
isave[8] = isave[7] + isave[2];
/*< isave(9) = isave(8) + isave(2) >*/
isave[9] = isave[8] + isave[2];
/*< isave(10) = isave(9) + isave(2) >*/
isave[10] = isave[9] + isave[2];
/*< isave(11) = isave(10) + isave(3) >*/
isave[11] = isave[10] + isave[3];
/*< isave(12) = isave(11) + isave(3) >*/
isave[12] = isave[11] + isave[3];
/*< isave(13) = isave(12) + n >*/
isave[13] = isave[12] + *n;
/*< isave(14) = isave(13) + n >*/
isave[14] = isave[13] + *n;
/*< isave(15) = isave(14) + n >*/
isave[15] = isave[14] + *n;
/*< isave(16) = isave(15) + n >*/
isave[16] = isave[15] + *n;
/*< isave(17) = isave(16) + 8*m >*/
isave[17] = isave[16] + (*m << 3);
/*< isave(18) = isave(17) + m >*/
isave[18] = isave[17] + *m;
/*< isave(19) = isave(18) + m >*/
isave[19] = isave[18] + *m;
/*< isave(20) = isave(19) + m >*/
isave[20] = isave[19] + *m;
/*< endif >*/
}
/*< l1 = isave(1) >*/
l1 = isave[1];
/*< l2 = isave(2) >*/
l2 = isave[2];
/*< l3 = isave(3) >*/
l3 = isave[3];
/*< lws = isave(4) >*/
lws = isave[4];
/*< lwy = isave(5) >*/
lwy = isave[5];
/*< lsy = isave(6) >*/
lsy = isave[6];
/*< lss = isave(7) >*/
lss = isave[7];
/*< lyy = isave(8) >*/
lyy = isave[8];
/*< lwt = isave(9) >*/
lwt = isave[9];
/*< lwn = isave(10) >*/
lwn = isave[10];
/*< lsnd = isave(11) >*/
lsnd = isave[11];
/*< lz = isave(12) >*/
lz = isave[12];
/*< lr = isave(13) >*/
lr = isave[13];
/*< ld = isave(14) >*/
ld = isave[14];
/*< lt = isave(15) >*/
lt = isave[15];
/*< lwa = isave(16) >*/
lwa = isave[16];
/*< lsg = isave(17) >*/
lsg = isave[17];
/*< lsgo = isave(18) >*/
lsgo = isave[18];
/*< lyg = isave(19) >*/
lyg = isave[19];
/*< lygo = isave(20) >*/
lygo = isave[20];
/*< >*/
mainlb_(n, m, &x[1], &l[1], &u[1], &nbd[1], f, &g[1], factr, pgtol, &wa[
lws], &wa[lwy], &wa[lsy], &wa[lss], &wa[lyy], &wa[lwt], &wa[lwn],
&wa[lsnd], &wa[lz], &wa[lr], &wa[ld], &wa[lt], &wa[lwa], &wa[lsg],
&wa[lsgo], &wa[lyg], &wa[lygo], &iwa[1], &iwa[*n + 1], &iwa[(*n
<< 1) + 1], task, iprint, csave, &lsave[1], &isave[22], &dsave[1],
(ftnlen)60, (ftnlen)60);
/*< return >*/
return 0;
/*< end >*/
} /* setulb_ */
/* ======================= The end of setulb ============================= */
/*< >*/
/* Subroutine */ int mainlb_(integer *n, integer *m, doublereal *x,
doublereal *l, doublereal *u, integer *nbd, doublereal *f, doublereal
*g, doublereal *factr, doublereal *pgtol, doublereal *ws, doublereal *
wy, doublereal *sy, doublereal *ss, doublereal *yy, doublereal *wt,
doublereal *wn, doublereal *snd, doublereal *z__, doublereal *r__,
doublereal *d__, doublereal *t, doublereal *wa, doublereal *sg,
doublereal *sgo, doublereal *yg, doublereal *ygo, integer *index,
integer *iwhere, integer *indx2, char *task, integer *iprint, char *
csave, logical *lsave, integer *isave, doublereal *dsave, ftnlen
task_len, ftnlen csave_len)
{
/* Format strings */
static char fmt_1002[] = "(/,\002At iterate\002,i5,4x,\002f= \002,1p,d12\
.5,4x,\002|proj g|= \002,1p,d12.5)";
static char fmt_1003[] = "(2(1x,i4),5x,\002-\002,5x,\002-\002,3x,\002\
-\002,5x,\002-\002,5x,\002-\002,8x,\002-\002,3x,1p,2(1x,d10.3))";
static char fmt_1001[] = "(//,\002ITERATION \002,i5)";
static char fmt_1005[] = "(/,\002 Singular triangular system detected\
;\002,/,\002 refresh the lbfgs memory and restart the iteration.\002)";
static char fmt_1006[] = "(/,\002 Nonpositive definiteness in Cholesky f\
actorization in formk;\002,/,\002 refresh the lbfgs memory and restart the\
iteration.\002)";
static char fmt_1008[] = "(/,\002 Bad direction in the line search;\002,\
/,\002 refresh the lbfgs memory and restart the iteration.\002)";
static char fmt_1004[] = "(\002 ys=\002,1p,e10.3,\002 -gs=\002,1p,e10.\
3,\002 BFGS update SKIPPED\002)";
static char fmt_1007[] = "(/,\002 Nonpositive definiteness in Cholesky f\
actorization in formt;\002,/,\002 refresh the lbfgs memory and restart the\
iteration.\002)";
/* System generated locals */
integer ws_dim1, ws_offset, wy_dim1, wy_offset, sy_dim1, sy_offset,
ss_dim1, ss_offset, yy_dim1, yy_offset, wt_dim1, wt_offset,
wn_dim1, wn_offset, snd_dim1, snd_offset, i__1;
doublereal d__1, d__2;
olist o__1;
/* Builtin functions */
integer s_cmp(char *, char *, ftnlen, ftnlen);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer f_open(olist *), s_wsfe(cilist *), do_fio(integer *, char *,
ftnlen), e_wsfe();
/* Local variables */
integer i__, k;
doublereal gd, dr, rr, dtd;
integer col;
doublereal tol;
logical wrk;
doublereal stp, cpu1, cpu2;
integer head;
doublereal fold;
integer nact;
doublereal ddum;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
integer info;
doublereal time;
integer nfgv, ifun, iter, nint;
char word[3];
doublereal time1, time2;
integer iback;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal gdold;
integer nfree;
logical boxed;
integer itail;
doublereal theta;
extern /* Subroutine */ int freev_(integer *, integer *, integer *,
integer *, integer *, integer *, integer *, logical *, logical *,
logical *, integer *, integer *), dcopy_(integer *, doublereal *,
integer *, doublereal *, integer *);
doublereal dnorm;
extern /* Subroutine */ int timer_(doublereal *), formk_(integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
logical *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *, integer *,
integer *);
integer nskip, iword;
extern /* Subroutine */ int formt_(integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *), subsm_(integer
*, integer *, integer *, integer *, doublereal *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *, integer *, doublereal *,
doublereal *, integer *, integer *);
doublereal xstep, stpmx;
extern /* Subroutine */ int prn1lb_(integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *, integer *, doublereal *),
prn2lb_(integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *, integer *, integer *, integer *, doublereal
*, integer *, char *, integer *, integer *, doublereal *,
doublereal *, ftnlen), prn3lb_(integer *, doublereal *,
doublereal *, char *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *, doublereal *,
doublereal *, integer *, char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
ftnlen, ftnlen);
integer ileave;
extern /* Subroutine */ int errclb_(integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *, char *, integer *, integer
*, ftnlen);
doublereal cachyt;
integer itfile;
extern /* Subroutine */ int active_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *, logical *,
logical *, logical *), cauchy_(integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *);
doublereal epsmch;
extern /* Subroutine */ int cmprlb_(integer *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, integer *, integer *, logical *,
integer *);
logical updatd;
doublereal sbtime;
logical prjctd;
integer iupdat;
extern doublereal dpmeps_();
logical cnstnd;
doublereal sbgnrm;
integer nenter;
doublereal lnscht;
extern /* Subroutine */ int lnsrlb_(integer *, doublereal *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *
, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *, integer *,
integer *, integer *, integer *, char *, logical *, logical *,
char *, integer *, doublereal *, ftnlen, ftnlen), matupd_(integer
*, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *, integer *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *);
integer nintol;
extern /* Subroutine */ int projgr_(integer *, doublereal *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *);
/* Fortran I/O blocks */
static cilist io___62 = { 0, 6, 0, fmt_1002, 0 };
static cilist io___63 = { 0, 0, 0, fmt_1003, 0 };
static cilist io___64 = { 0, 6, 0, fmt_1001, 0 };
static cilist io___66 = { 0, 6, 0, fmt_1005, 0 };
static cilist io___68 = { 0, 6, 0, fmt_1006, 0 };
static cilist io___69 = { 0, 6, 0, fmt_1005, 0 };
static cilist io___71 = { 0, 6, 0, fmt_1008, 0 };
static cilist io___75 = { 0, 6, 0, fmt_1004, 0 };
static cilist io___76 = { 0, 6, 0, fmt_1007, 0 };
/*< character*60 task, csave >*/
/*< logical lsave(4) >*/
/*< >*/
/*< >*/
/* ************ */
/* Subroutine mainlb */
/* This subroutine solves bound constrained optimization problems by */
/* using the compact formula of the limited memory BFGS updates. */
/* n is an integer variable. */
/* On entry n is the number of variables. */
/* On exit n is unchanged. */
/* m is an integer variable. */
/* On entry m is the maximum number of variable metric */
/* corrections allowed in the limited memory matrix. */
/* On exit m is unchanged. */
/* x is a double precision array of dimension n. */
/* On entry x is an approximation to the solution. */
/* On exit x is the current approximation. */
/* l is a double precision array of dimension n. */
/* On entry l is the lower bound of x. */
/* On exit l is unchanged. */
/* u is a double precision array of dimension n. */
/* On entry u is the upper bound of x. */
/* On exit u is unchanged. */
/* nbd is an integer array of dimension n. */
/* On entry nbd represents the type of bounds imposed on the */
/* variables, and must be specified as follows: */
/* nbd(i)=0 if x(i) is unbounded, */
/* 1 if x(i) has only a lower bound, */
/* 2 if x(i) has both lower and upper bounds, */
/* 3 if x(i) has only an upper bound. */
/* On exit nbd is unchanged. */
/* f is a double precision variable. */
/* On first entry f is unspecified. */
/* On final exit f is the value of the function at x. */
/* g is a double precision array of dimension n. */
/* On first entry g is unspecified. */
/* On final exit g is the value of the gradient at x. */
/* factr is a double precision variable. */
/* On entry factr >= 0 is specified by the user. The iteration */
/* will stop when */
/* (f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch */
/* where epsmch is the machine precision, which is automatically */
/* generated by the code. */
/* On exit factr is unchanged. */
/* pgtol is a double precision variable. */
/* On entry pgtol >= 0 is specified by the user. The iteration */
/* will stop when */
/* max{|proj g_i | i = 1, ..., n} <= pgtol */
/* where pg_i is the ith component of the projected gradient. */
/* On exit pgtol is unchanged. */
/* ws, wy, sy, and wt are double precision working arrays used to */
/* store the following information defining the limited memory */
/* BFGS matrix: */
/* ws, of dimension n x m, stores S, the matrix of s-vectors; */
/* wy, of dimension n x m, stores Y, the matrix of y-vectors; */
/* sy, of dimension m x m, stores S'Y; */
/* ss, of dimension m x m, stores S'S; */
/* yy, of dimension m x m, stores Y'Y; */
/* wt, of dimension m x m, stores the Cholesky factorization */
/* of (theta*S'S+LD^(-1)L'); see eq. */
/* (2.26) in [3]. */
/* wn is a double precision working array of dimension 2m x 2m */
/* used to store the LEL^T factorization of the indefinite matrix */
/* K = [-D -Y'ZZ'Y/theta L_a'-R_z' ] */
/* [L_a -R_z theta*S'AA'S ] */
/* where E = [-I 0] */
/* [ 0 I] */
/* snd is a double precision working array of dimension 2m x 2m */
/* used to store the lower triangular part of */
/* N = [Y' ZZ'Y L_a'+R_z'] */
/* [L_a +R_z S'AA'S ] */
/* z(n),r(n),d(n),t(n),wa(8*m) are double precision working arrays. */
/* z is used at different times to store the Cauchy point and */
/* the Newton point. */
/* sg(m),sgo(m),yg(m),ygo(m) are double precision working arrays. */
/* index is an integer working array of dimension n. */
/* In subroutine freev, index is used to store the free and fixed */
/* variables at the Generalized Cauchy Point (GCP). */
/* iwhere is an integer working array of dimension n used to record */
/* the status of the vector x for GCP computation. */
/* iwhere(i)=0 or -3 if x(i) is free and has bounds, */
/* 1 if x(i) is fixed at l(i), and l(i) .ne. u(i) */
/* 2 if x(i) is fixed at u(i), and u(i) .ne. l(i) */
/* 3 if x(i) is always fixed, i.e., u(i)=x(i)=l(i) */
/* -1 if x(i) is always free, i.e., no bounds on it. */
/* indx2 is an integer working array of dimension n. */
/* Within subroutine cauchy, indx2 corresponds to the array iorder. */
/* In subroutine freev, a list of variables entering and leaving */
/* the free set is stored in indx2, and it is passed on to */
/* subroutine formk with this information. */
/* task is a working string of characters of length 60 indicating */
/* the current job when entering and leaving this subroutine. */
/* iprint is an INTEGER variable that must be set by the user. */
/* It controls the frequency and type of output generated: */
/* iprint<0 no output is generated; */
/* iprint=0 print only one line at the last iteration; */
/* 0<iprint<99 print also f and |proj g| every iprint iterations; */
/* iprint=99 print details of every iteration except n-vectors; */
/* iprint=100 print also the changes of active set and final x; */
/* iprint>100 print details of every iteration including x and g; */
/* When iprint > 0, the file iterate.dat will be created to */
/* summarize the iteration. */
/* csave is a working string of characters of length 60. */
/* lsave is a logical working array of dimension 4. */
/* isave is an integer working array of dimension 23. */
/* dsave is a double precision working array of dimension 29. */
/* Subprograms called */
/* L-BFGS-B Library ... cauchy, subsm, lnsrlb, formk, */
/* errclb, prn1lb, prn2lb, prn3lb, active, projgr, */
/* freev, cmprlb, matupd, formt. */
/* Minpack2 Library ... timer, dpmeps. */
/* Linpack Library ... dcopy, ddot. */
/* References: */
/* [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited */
/* memory algorithm for bound constrained optimization'', */
/* SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. */
/* [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: FORTRAN */
/* Subroutines for Large Scale Bound Constrained Optimization'' */
/* Tech. Report, NAM-11, EECS Department, Northwestern University, */
/* 1994. */
/* [3] R. Byrd, J. Nocedal and R. Schnabel "Representations of */
/* Quasi-Newton Matrices and their use in Limited Memory Methods'', */
/* Mathematical Programming 63 (1994), no. 4, pp. 129-156. */
/* (Postscript files of these papers are available via anonymous */
/* ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.) */
/* * * * */
/* NEOS, November 1994. (Latest revision June 1996.) */
/* Optimization Technology Center. */
/* Argonne National Laboratory and Northwestern University. */
/* Written by */
/* Ciyou Zhu */
/* in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. */
/* ************ */
/*< logical prjctd,cnstnd,boxed,updatd,wrk >*/
/*< character*3 word >*/
/*< >*/
/*< >*/
/*< double precision one,zero >*/
/*< parameter (one=1.0d0,zero=0.0d0) >*/
/*< if (task .eq. 'START') then >*/
/* Parameter adjustments */
--indx2;
--iwhere;
--index;
--t;
--d__;
--r__;
--z__;
--g;
--nbd;
--u;
--l;
--x;
--ygo;
--yg;
--sgo;
--sg;
--wa;
snd_dim1 = 2 * *m;
snd_offset = 1 + snd_dim1;
snd -= snd_offset;
wn_dim1 = 2 * *m;
wn_offset = 1 + wn_dim1;
wn -= wn_offset;
wt_dim1 = *m;
wt_offset = 1 + wt_dim1;
wt -= wt_offset;
yy_dim1 = *m;
yy_offset = 1 + yy_dim1;
yy -= yy_offset;
ss_dim1 = *m;
ss_offset = 1 + ss_dim1;
ss -= ss_offset;
sy_dim1 = *m;
sy_offset = 1 + sy_dim1;
sy -= sy_offset;
wy_dim1 = *n;
wy_offset = 1 + wy_dim1;
wy -= wy_offset;
ws_dim1 = *n;
ws_offset = 1 + ws_dim1;
ws -= ws_offset;
--lsave;
--isave;
--dsave;
/* Function Body */
if (s_cmp(task, "START", (ftnlen)60, (ftnlen)5) == 0) {
/*< call timer(time1) >*/
timer_(&time1);
/* Generate the current machine precision. */
/*< epsmch = dpmeps() >*/
epsmch = dpmeps_();
/* Initialize counters and scalars when task='START'. */
/* for the limited memory BFGS matrices: */
/*< col = 0 >*/
col = 0;
/*< head = 1 >*/
head = 1;
/*< theta = one >*/
theta = 1.;
/*< iupdat = 0 >*/
iupdat = 0;
/*< updatd = .false. >*/
updatd = FALSE_;
/* for operation counts: */
/*< iter = 0 >*/
iter = 0;
/*< nfgv = 0 >*/
nfgv = 0;
/*< nint = 0 >*/
nint = 0;
/*< nintol = 0 >*/
nintol = 0;
/*< nskip = 0 >*/
nskip = 0;
/*< nfree = n >*/
nfree = *n;
/* for stopping tolerance: */
/*< tol = factr*epsmch >*/
tol = *factr * epsmch;
/* for measuring running time: */
/*< cachyt = 0 >*/
cachyt = 0.;
/*< sbtime = 0 >*/
sbtime = 0.;
/*< lnscht = 0 >*/
lnscht = 0.;
/* 'word' records the status of subspace solutions. */
/*< word = '---' >*/
s_copy(word, "---", (ftnlen)3, (ftnlen)3);
/* 'info' records the termination information. */
/*< info = 0 >*/
info = 0;
/*< if (iprint .ge. 1) then >*/
if (*iprint >= 1) {
/* open a summary file 'iterate.dat' */
/*< open (8, file = 'iterate.dat', status = 'unknown') >*/
o__1.oerr = 0;
o__1.ounit = 8;
o__1.ofnmlen = 11;
o__1.ofnm = "iterate.dat";
o__1.orl = 0;
o__1.osta = "unknown";
o__1.oacc = 0;
o__1.ofm = 0;
o__1.oblnk = 0;
f_open(&o__1);
/*< itfile = 8 >*/
itfile = 8;
/*< endif >*/
}
/* Check the input arguments for errors. */
/*< call errclb(n,m,factr,l,u,nbd,task,info,k) >*/
errclb_(n, m, factr, &l[1], &u[1], &nbd[1], task, &info, &k, (ftnlen)
60);
/*< if (task(1:5) .eq. 'ERROR') then >*/
if (s_cmp(task, "ERROR", (ftnlen)5, (ftnlen)5) == 0) {
/*< >*/
prn3lb_(n, &x[1], f, task, iprint, &info, &itfile, &iter, &nfgv, &
nintol, &nskip, &nact, &sbgnrm, &c_b9, &nint, word, &
iback, &stp, &xstep, &k, &cachyt, &sbtime, &lnscht, (
ftnlen)60, (ftnlen)3);
/*< return >*/
return 0;
/*< endif >*/
}
/*< call prn1lb(n,m,l,u,x,iprint,itfile,epsmch) >*/
prn1lb_(n, m, &l[1], &u[1], &x[1], iprint, &itfile, &epsmch);
/* Initialize iwhere & project x onto the feasible set. */
/*< call active(n,l,u,nbd,x,iwhere,iprint,prjctd,cnstnd,boxed) >*/
active_(n, &l[1], &u[1], &nbd[1], &x[1], &iwhere[1], iprint, &prjctd,
&cnstnd, &boxed);
/* The end of the initialization. */
/*< else >*/
} else {
/* restore local variables. */
/*< prjctd = lsave(1) >*/
prjctd = lsave[1];
/*< cnstnd = lsave(2) >*/
cnstnd = lsave[2];
/*< boxed = lsave(3) >*/
boxed = lsave[3];
/*< updatd = lsave(4) >*/
updatd = lsave[4];
/*< nintol = isave(1) >*/
nintol = isave[1];
/*< itfile = isave(3) >*/
itfile = isave[3];
/*< iback = isave(4) >*/
iback = isave[4];
/*< nskip = isave(5) >*/
nskip = isave[5];
/*< head = isave(6) >*/
head = isave[6];
/*< col = isave(7) >*/
col = isave[7];
/*< itail = isave(8) >*/
itail = isave[8];
/*< iter = isave(9) >*/
iter = isave[9];
/*< iupdat = isave(10) >*/
iupdat = isave[10];
/*< nint = isave(12) >*/
nint = isave[12];
/*< nfgv = isave(13) >*/
nfgv = isave[13];
/*< info = isave(14) >*/
info = isave[14];
/*< ifun = isave(15) >*/
ifun = isave[15];
/*< iword = isave(16) >*/
iword = isave[16];
/*< nfree = isave(17) >*/
nfree = isave[17];
/*< nact = isave(18) >*/
nact = isave[18];
/*< ileave = isave(19) >*/
ileave = isave[19];
/*< nenter = isave(20) >*/
nenter = isave[20];
/*< theta = dsave(1) >*/
theta = dsave[1];
/*< fold = dsave(2) >*/
fold = dsave[2];
/*< tol = dsave(3) >*/
tol = dsave[3];
/*< dnorm = dsave(4) >*/
dnorm = dsave[4];
/*< epsmch = dsave(5) >*/
epsmch = dsave[5];
/*< cpu1 = dsave(6) >*/
cpu1 = dsave[6];
/*< cachyt = dsave(7) >*/
cachyt = dsave[7];
/*< sbtime = dsave(8) >*/
sbtime = dsave[8];
/*< lnscht = dsave(9) >*/
lnscht = dsave[9];
/*< time1 = dsave(10) >*/
time1 = dsave[10];
/*< gd = dsave(11) >*/
gd = dsave[11];
/*< stpmx = dsave(12) >*/
stpmx = dsave[12];
/*< sbgnrm = dsave(13) >*/
sbgnrm = dsave[13];
/*< stp = dsave(14) >*/
stp = dsave[14];
/*< gdold = dsave(15) >*/
gdold = dsave[15];
/*< dtd = dsave(16) >*/
dtd = dsave[16];
/* After returning from the driver go to the point where execution */
/* is to resume. */
/*< if (task(1:5) .eq. 'FG_LN') goto 666 >*/
if (s_cmp(task, "FG_LN", (ftnlen)5, (ftnlen)5) == 0) {
goto L666;
}
/*< if (task(1:5) .eq. 'NEW_X') goto 777 >*/
if (s_cmp(task, "NEW_X", (ftnlen)5, (ftnlen)5) == 0) {
goto L777;
}
/*< if (task(1:5) .eq. 'FG_ST') goto 111 >*/
if (s_cmp(task, "FG_ST", (ftnlen)5, (ftnlen)5) == 0) {
goto L111;
}
/*< if (task(1:4) .eq. 'STOP') then >*/
if (s_cmp(task, "STOP", (ftnlen)4, (ftnlen)4) == 0) {
/*< if (task(7:9) .eq. 'CPU') then >*/
if (s_cmp(task + 6, "CPU", (ftnlen)3, (ftnlen)3) == 0) {
/* restore the previous iterate. */
/*< call dcopy(n,t,1,x,1) >*/
dcopy_(n, &t[1], &c__1, &x[1], &c__1);
/*< call dcopy(n,r,1,g,1) >*/
dcopy_(n, &r__[1], &c__1, &g[1], &c__1);
/*< f = fold >*/
*f = fold;
/*< endif >*/
}
/*< goto 999 >*/
goto L999;
/*< endif >*/
}
/*< endif >*/
}
/* Compute f0 and g0. */
/*< task = 'FG_START' >*/
s_copy(task, "FG_START", (ftnlen)60, (ftnlen)8);
/* return to the driver to calculate f and g; reenter at 111. */
/*< goto 1000 >*/
goto L1000;
/*< 111 continue >*/
L111:
/*< nfgv = 1 >*/
nfgv = 1;
/* Compute the infinity norm of the (-) projected gradient. */
/*< call projgr(n,l,u,nbd,x,g,sbgnrm) >*/
projgr_(n, &l[1], &u[1], &nbd[1], &x[1], &g[1], &sbgnrm);
/*< if (iprint .ge. 1) then >*/
if (*iprint >= 1) {
/*< write (6,1002) iter,f,sbgnrm >*/
s_wsfe(&io___62);
do_fio(&c__1, (char *)&iter, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*f), (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&sbgnrm, (ftnlen)sizeof(doublereal));
e_wsfe();
/*< write (itfile,1003) iter,nfgv,sbgnrm,f >*/
io___63.ciunit = itfile;
s_wsfe(&io___63);
do_fio(&c__1, (char *)&iter, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nfgv, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&sbgnrm, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&(*f), (ftnlen)sizeof(doublereal));
e_wsfe();
/*< endif >*/
}
/*< if (sbgnrm .le. pgtol) then >*/
if (sbgnrm <= *pgtol) {
/* terminate the algorithm. */
/*< task = 'CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL' >*/
s_copy(task, "CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL", (
ftnlen)60, (ftnlen)48);
/*< goto 999 >*/
goto L999;
/*< endif >*/
}
/* ----------------- the beginning of the loop -------------------------- */
/*< 222 continue >*/
L222:
/*< if (iprint .ge. 99) write (6,1001) iter + 1 >*/
if (*iprint >= 99) {
s_wsfe(&io___64);
i__1 = iter + 1;
do_fio(&c__1, (char *)&i__1, (ftnlen)sizeof(integer));
e_wsfe();
}
/*< iword = -1 >*/
iword = -1;
/*< if (.not. cnstnd .and. col .gt. 0) then >*/