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lbfgsb.c
executable file
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lbfgsb.c
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/* lbfgsb.f -- translated by f2c (version 20090411).
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
*/
#include "f2c.h"
/* Stephen Becker adding this for the machine epsilon: */
#include <float.h>
/* Stephen Becker adding this for the timer */
#define USE_TIMER
#if defined(_WIN32) || defined(__hpux)
#define FORTRAN_WRAPPER(x) x
#else
#define FORTRAN_WRAPPER(x) x ## _
#endif
/* The fortran file calls dscal, dcopy, ddot, daxpy.
* If we want to use Matlab's 32-bit versions, we must rename these.
* Use this option when you use -lmwblascompat32 (instead of -lmwblas)
* Actually, this doesn't help, since these routines are called from
* fortran, not from this file. However, if you use the f2c version
* and the C files, this might help
* */
#if defined(_BLAS32_)
#define dscal FORTRAN_WRAPPER(dscal32)
#define dcopy FORTRAN_WRAPPER(dcopy32)
#define ddot FORTRAN_WRAPPER(ddot32)
#define daxpy FORTRAN_WRAPPER(daxpy32)
/* #include "blascompat32.h" */ /* this causes problems ... */
extern double ddot(const int *n32, const double *dx, const int *incx32,
const double *dy, const int *incy32);
extern void dcopy(const int *n32, const double *dx, const int *incx32,
double *dy, const int *incy32);
extern void dscal(const int *n32, const double *da, double *dx, const int *incx32);
extern void daxpy(const int *n32, const double *da, const double *dx,
const int *incx32, double *dy, const int *incy32);
#define blas_h
#else
/* add underscores for Windows */
#define dscal FORTRAN_WRAPPER(dscal)
#define dcopy FORTRAN_WRAPPER(dcopy)
#define ddot FORTRAN_WRAPPER(ddot)
#define daxpy FORTRAN_WRAPPER(daxpy)
#endif
/* Stephen: some BLAS expects larger ints for the integer variables
* So, replacing all the "integer" variables with int_F variables,
* which can be defined as either integer or as ptrdiff_t
* */
/* #ifdef _BLAS64_ */
#if defined(_BLAS64_)
#include <stddef.h>
typedef ptrdiff_t int_F;
/* #include "blas.h" */
#define blas_h
extern void dscal(ptrdiff_t *n, double *da, double *dx, ptrdiff_t *incx);
extern void dcopy(ptrdiff_t *n, double *dx, ptrdiff_t *incx, double *dy, ptrdiff_t *incy);
extern double ddot( ptrdiff_t *n, double *dx, ptrdiff_t *incx, double *dy, ptrdiff_t *incy);
extern void daxpy(ptrdiff_t *n, double *da, double *dx, ptrdiff_t *incx, double *dy, ptrdiff_t *incy);
#else
typedef integer int_F;
#endif
/* integer is typically defined by the f2c library */
/* you can also try commenting this line: */
#define timer timer_
/* Table of constant values */
static doublereal c_b9 = 0.;
static int_F c__1 = 1;
static int_F c__9 = 9;
static int_F c__11 = 11;
static int_F c__3 = 3;
static int_F c__5 = 5;
static doublereal c_b280 = .001;
static doublereal c_b281 = .9;
static doublereal c_b282 = .1;
/* =========== L-BFGS-B (version 3.0. April 25, 2011 =================== */
/* This is a modified version of L-BFGS-B. Minor changes in the updated */
/* code appear preceded by a line comment as follows */
/* c-jlm-jn */
/* Major changes are described in the accompanying paper: */
/* Jorge Nocedal and Jose Luis Morales, Remark on "Algorithm 778: */
/* L-BFGS-B: Fortran Subroutines for Large-Scale Bound Constrained */
/* Optimization" (2011). To appear in ACM Transactions on */
/* Mathematical Software, */
/* The paper describes an improvement and a correction to Algorithm 778. */
/* It is shown that the performance of the algorithm can be improved */
/* significantly by making a relatively simple modication to the subspace */
/* minimization phase. The correction concerns an error caused by the use */
/* of routine dpmeps to estimate machine precision. */
/* The total work space **wa** required by the new version is */
/* 2*m*n + 11m*m + 5*n + 8*m */
/* the old version required */
/* 2*m*n + 12m*m + 4*n + 12*m */
/* J. Nocedal Department of Electrical Engineering and */
/* Computer Science. */
/* Northwestern University. Evanston, IL. USA */
/* J.L Morales Departamento de Matematicas, */
/* Instituto Tecnologico Autonomo de Mexico */
/* Mexico D.F. Mexico. */
/* March 2011 */
/* ============================================================================= */
/* Subroutine */ int setulb_(int_F *n, int_F *m, doublereal *x,
doublereal *l, doublereal *u, int_F *nbd, doublereal *f, doublereal
*g, doublereal *factr, doublereal *pgtol, doublereal *wa, int_F *
iwa, char *task, int_F *iprint, char *csave, logical *lsave,
int_F *isave, doublereal *dsave, ftnlen task_len, ftnlen csave_len)
{
/* System generated locals */
int_F i__1;
/* Builtin functions */
int_F s_cmp(char *, char *, ftnlen, ftnlen);
/* Local variables */
static int_F ld, lr, lt, lz, lwa, lwn, lss, lxp, lws, lwt, lsy, lwy,
lsnd;
extern /* Subroutine */ int mainlb_(int_F *, int_F *, doublereal *,
doublereal *, doublereal *, int_F *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, int_F *, int_F *,
int_F *, char *, int_F *, char *, logical *, int_F *,
doublereal *, ftnlen, ftnlen);
/* -jlm-jn */
/* ************ */
/* 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 int_F variable. */
/* On entry n is the dimension of the problem. */
/* On exit n is unchanged. */
/* m is an int_F 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 int_F 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 + 5)nmax + 12mmax^2 + 12mmax. */
/* iwa is an int_F 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 int_F 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 int_F 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. */
/* ************ */
/* -jlm-jn */
/* 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;
/* Computing 2nd power */
i__1 = *m;
isave[2] = i__1 * i__1;
/* Computing 2nd power */
i__1 = *m;
isave[3] = i__1 * i__1 << 2;
isave[4] = 1;
/* ws m*n */
isave[5] = isave[4] + isave[1];
/* wy m*n */
isave[6] = isave[5] + isave[1];
/* wsy m**2 */
isave[7] = isave[6] + isave[2];
/* wss m**2 */
isave[8] = isave[7] + isave[2];
/* wt m**2 */
isave[9] = isave[8] + isave[2];
/* wn 4*m**2 */
isave[10] = isave[9] + isave[3];
/* wsnd 4*m**2 */
isave[11] = isave[10] + isave[3];
/* wz n */
isave[12] = isave[11] + *n;
/* wr n */
isave[13] = isave[12] + *n;
/* wd n */
isave[14] = isave[13] + *n;
/* wt n */
isave[15] = isave[14] + *n;
/* wxp n */
isave[16] = isave[15] + *n;
/* wa 8*m */
}
lws = isave[4];
lwy = isave[5];
lsy = isave[6];
lss = isave[7];
lwt = isave[8];
lwn = isave[9];
lsnd = isave[10];
lz = isave[11];
lr = isave[12];
ld = isave[13];
lt = isave[14];
lxp = isave[15];
lwa = isave[16];
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[lwt], &wa[lwn], &wa[lsnd],
&wa[lz], &wa[lr], &wa[ld], &wa[lt], &wa[lxp], &wa[lwa], &iwa[1],
&iwa[*n + 1], &iwa[(*n << 1) + 1], task, iprint, csave, &lsave[1],
&isave[22], &dsave[1], (ftnlen)60, (ftnlen)60);
return 0;
} /* setulb_ */
/* ======================= The end of setulb ============================= */
/* Subroutine */ int mainlb_(int_F *n, int_F *m, doublereal *x,
doublereal *l, doublereal *u, int_F *nbd, doublereal *f, doublereal
*g, doublereal *factr, doublereal *pgtol, doublereal *ws, doublereal *
wy, doublereal *sy, doublereal *ss, doublereal *wt, doublereal *wn,
doublereal *snd, doublereal *z__, doublereal *r__, doublereal *d__,
doublereal *t, doublereal *xp, doublereal *wa, int_F *index,
int_F *iwhere, int_F *indx2, char *task, int_F *iprint, char *
csave, logical *lsave, int_F *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 iteratio"
"n.\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 */
int_F ws_dim1, ws_offset, wy_dim1, wy_offset, sy_dim1, sy_offset,
ss_dim1, ss_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 */
int_F s_cmp(char *, char *, ftnlen, ftnlen);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
int_F f_open(olist *), s_wsfe(cilist *), do_fio(int_F *, char *,
ftnlen), e_wsfe(void);
/* Local variables */
static int_F i__, k;
static doublereal gd, dr, rr, dtd;
static int_F col;
static doublereal tol;
static logical wrk;
static doublereal stp, cpu1, cpu2;
static int_F head;
static doublereal fold;
static int_F nact;
static doublereal ddum;
#ifndef blas_h
extern doublereal ddot(int_F *, doublereal *, int_F *, doublereal *,
int_F *);
#endif
static int_F info, nseg;
static doublereal time;
static int_F nfgv, ifun, iter;
static char word[3];
static doublereal time1, time2;
static int_F iback;
#ifndef blas_h
extern /* Subroutine */ int dscal(int_F *, doublereal *, doublereal *,
int_F *);
#endif
static doublereal gdold;
static int_F nfree;
static logical boxed;
static int_F itail;
static doublereal theta;
/*extern int freev_(int_F *, int_F *, int_F *,
int_F *, int_F *, int_F *, int_F *, logical *, logical *,
logical *, int_F *, int_F *), dcopy(int_F *, doublereal *,
int_F *, doublereal *, int_F *);*/
extern /* Subroutine */ int freev_(int_F *, int_F *, int_F *,
int_F *, int_F *, int_F *, int_F *, logical *, logical *,
logical *, int_F *, int_F *);
#ifndef blas_h
extern /* Subroutine */ int dcopy(int_F *, doublereal *,
int_F *, doublereal *, int_F *);
#endif
static doublereal dnorm;
#ifdef USE_TIMER
extern int timer(doublereal *), formk_(int_F *,
int_F *, int_F *, int_F *, int_F *, int_F *, int_F *,
logical *, doublereal *, doublereal *, int_F *, doublereal *,
doublereal *, doublereal *, doublereal *, int_F *, int_F *,
int_F *);
#endif
static int_F nskip, iword;
extern /* Subroutine */ int formt_(int_F *, doublereal *, doublereal *,
doublereal *, int_F *, doublereal *, int_F *), subsm_(int_F
*, int_F *, int_F *, int_F *, doublereal *, doublereal *,
int_F *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, int_F *
, int_F *, int_F *, doublereal *, doublereal *, int_F *,
int_F *);
static doublereal xstep, stpmx;
extern /* Subroutine */ int prn1lb_(int_F *, int_F *, doublereal *,
doublereal *, doublereal *, int_F *, int_F *, doublereal *),
prn2lb_(int_F *, doublereal *, doublereal *, doublereal *,
int_F *, int_F *, int_F *, int_F *, int_F *, doublereal
*, int_F *, char *, int_F *, int_F *, doublereal *,
doublereal *, ftnlen), prn3lb_(int_F *, doublereal *,
doublereal *, char *, int_F *, int_F *, int_F *, int_F *,
int_F *, int_F *, int_F *, int_F *, doublereal *,
doublereal *, int_F *, char *, int_F *, doublereal *,
doublereal *, int_F *, doublereal *, doublereal *, doublereal *,
ftnlen, ftnlen);
static int_F ileave;
extern /* Subroutine */ int errclb_(int_F *, int_F *, doublereal *,
doublereal *, doublereal *, int_F *, char *, int_F *, int_F
*, ftnlen);
static doublereal cachyt;
static int_F itfile;
extern /* Subroutine */ int active_(int_F *, doublereal *, doublereal *,
int_F *, doublereal *, int_F *, int_F *, logical *,
logical *, logical *), cauchy_(int_F *, doublereal *,
doublereal *, doublereal *, int_F *, doublereal *, int_F *,
int_F *, doublereal *, doublereal *, doublereal *, int_F *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, int_F *, int_F *, doublereal *, doublereal *,
doublereal *, doublereal *, int_F *, int_F *, doublereal *,
int_F *, doublereal *);
static doublereal epsmch;
extern /* Subroutine */ int cmprlb_(int_F *, int_F *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, int_F *,
doublereal *, int_F *, int_F *, int_F *, logical *,
int_F *);
static logical updatd;
static doublereal sbtime;
static logical prjctd;
static int_F iupdat;
static doublereal sbgnrm;
static logical cnstnd;
extern /* Subroutine */ int matupd_(int_F *, int_F *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, int_F *, int_F *, int_F *, int_F *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
static int_F nenter;
static doublereal lnscht;
extern /* Subroutine */ int lnsrlb_(int_F *, doublereal *, doublereal *,
int_F *, doublereal *, doublereal *, doublereal *, doublereal *
, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, int_F *, int_F *,
int_F *, int_F *, int_F *, char *, logical *, logical *,
char *, int_F *, doublereal *, ftnlen, ftnlen);
static int_F nintol;
extern /* Subroutine */ int projgr_(int_F *, doublereal *, doublereal *,
int_F *, doublereal *, doublereal *, doublereal *);
/* Fortran I/O blocks */
static cilist io___55 = { 0, 6, 0, fmt_1002, 0 };
static cilist io___56 = { 0, 0, 0, fmt_1003, 0 };
static cilist io___57 = { 0, 6, 0, fmt_1001, 0 };
static cilist io___59 = { 0, 6, 0, fmt_1005, 0 };
static cilist io___61 = { 0, 6, 0, fmt_1006, 0 };
static cilist io___62 = { 0, 6, 0, fmt_1005, 0 };
static cilist io___64 = { 0, 6, 0, fmt_1008, 0 };
static cilist io___68 = { 0, 6, 0, fmt_1004, 0 };
static cilist io___69 = { 0, 6, 0, fmt_1007, 0 };
/* -jlm-jn */
/* ************ */
/* Subroutine mainlb */
/* This subroutine solves bound constrained optimization problems by */
/* using the compact formula of the limited memory BFGS updates. */
/* n is an int_F variable. */
/* On entry n is the number of variables. */
/* On exit n is unchanged. */
/* m is an int_F 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 int_F 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), xp(n),wa(8*m) are double precision working arrays. */
/* z is used at different times to store the Cauchy point and */
/* the Newton point. */
/* xp is used to safeguard the projected Newton direction */
/* sg(m),sgo(m),yg(m),ygo(m) are double precision working arrays. */
/* index is an int_F 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 int_F 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 int_F 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 int_F 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 */
/* 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. */
/* ************ */
/* Parameter adjustments */
--indx2;
--iwhere;
--index;
--xp;
--t;
--d__;
--r__;
--z__;
--g;
--nbd;
--u;
--l;
--x;
--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;
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) {
/* epsmch = epsilon(one) */
/* Stephen changing this, just for the f2c conversion. Must */
/* edit C file by hand, and use DBL_EPSILON from float.h */
/* epsmch = 1.f; */
epsmch = DBL_EPSILON;
#ifdef USE_TIMER
timer(&time1);
#endif
/* Initialize counters and scalars when task='START'. */
/* for the limited memory BFGS matrices: */
col = 0;
head = 1;
theta = 1.;
iupdat = 0;
updatd = FALSE_;
iback = 0;
itail = 0;
iword = 0;
nact = 0;
ileave = 0;
nenter = 0;
fold = 0.;
dnorm = 0.;
cpu1 = 0.;
gd = 0.;
stpmx = 0.;
sbgnrm = 0.;
stp = 0.;
gdold = 0.;
dtd = 0.;
/* for operation counts: */
iter = 0;
nfgv = 0;
nseg = 0;
nintol = 0;
nskip = 0;
nfree = *n;
ifun = 0;
/* for stopping tolerance: */
tol = *factr * epsmch;
/* for measuring running time: */
cachyt = 0.;
sbtime = 0.;
lnscht = 0.;
/* 'word' records the status of subspace solutions. */
s_copy(word, "---", (ftnlen)3, (ftnlen)3);
/* 'info' records the termination information. */
info = 0;
itfile = 8;
if (*iprint >= 1) {
/* open a summary file 'iterate.dat' */
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);
}
/* Check the input arguments for errors. */
errclb_(n, m, factr, &l[1], &u[1], &nbd[1], task, &info, &k, (ftnlen)
60);
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, &nseg, word, &
iback, &stp, &xstep, &k, &cachyt, &sbtime, &lnscht, (
ftnlen)60, (ftnlen)3);
return 0;
}
prn1lb_(n, m, &l[1], &u[1], &x[1], iprint, &itfile, &epsmch);
/* Initialize iwhere & project x onto the feasible set. */
active_(n, &l[1], &u[1], &nbd[1], &x[1], &iwhere[1], iprint, &prjctd,
&cnstnd, &boxed);
/* The end of the initialization. */
} else {
/* restore local variables. */
prjctd = lsave[1];
cnstnd = lsave[2];
boxed = lsave[3];
updatd = lsave[4];
nintol = isave[1];
itfile = isave[3];
iback = isave[4];
nskip = isave[5];
head = isave[6];
col = isave[7];
itail = isave[8];
iter = isave[9];
iupdat = isave[10];
nseg = isave[12];
nfgv = isave[13];
info = isave[14];
ifun = isave[15];
iword = isave[16];
nfree = isave[17];
nact = isave[18];
ileave = isave[19];
nenter = isave[20];
theta = dsave[1];
fold = dsave[2];
tol = dsave[3];
dnorm = dsave[4];
epsmch = dsave[5];
cpu1 = dsave[6];
cachyt = dsave[7];
sbtime = dsave[8];
lnscht = dsave[9];
time1 = dsave[10];
gd = dsave[11];
stpmx = dsave[12];
sbgnrm = dsave[13];
stp = dsave[14];
gdold = dsave[15];
dtd = dsave[16];
/* After returning from the driver go to the point where execution */
/* is to resume. */
if (s_cmp(task, "FG_LN", (ftnlen)5, (ftnlen)5) == 0) {
goto L666;
}
if (s_cmp(task, "NEW_X", (ftnlen)5, (ftnlen)5) == 0) {
goto L777;
}
if (s_cmp(task, "FG_ST", (ftnlen)5, (ftnlen)5) == 0) {
goto L111;
}
if (s_cmp(task, "STOP", (ftnlen)4, (ftnlen)4) == 0) {
if (s_cmp(task + 6, "CPU", (ftnlen)3, (ftnlen)3) == 0) {
/* restore the previous iterate. */
dcopy(n, &t[1], &c__1, &x[1], &c__1);
dcopy(n, &r__[1], &c__1, &g[1], &c__1);
*f = fold;
}
goto L999;
}
}
/* Compute f0 and g0. */
s_copy(task, "FG_START", (ftnlen)60, (ftnlen)8);
/* return to the driver to calculate f and g; reenter at 111. */
goto L1000;
L111:
nfgv = 1;
/* Compute the infinity norm of the (-) projected gradient. */
projgr_(n, &l[1], &u[1], &nbd[1], &x[1], &g[1], &sbgnrm);
if (*iprint >= 1) {
s_wsfe(&io___55);
do_fio(&c__1, (char *)&iter, (ftnlen)sizeof(int_F));
do_fio(&c__1, (char *)&(*f), (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&sbgnrm, (ftnlen)sizeof(doublereal));
e_wsfe();
io___56.ciunit = itfile;
s_wsfe(&io___56);
do_fio(&c__1, (char *)&iter, (ftnlen)sizeof(int_F));
do_fio(&c__1, (char *)&nfgv, (ftnlen)sizeof(int_F));
do_fio(&c__1, (char *)&sbgnrm, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&(*f), (ftnlen)sizeof(doublereal));
e_wsfe();
}
if (sbgnrm <= *pgtol) {
/* terminate the algorithm. */
s_copy(task, "CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL", (
ftnlen)60, (ftnlen)48);
goto L999;
}
/* ----------------- the beginning of the loop -------------------------- */
L222:
if (*iprint >= 99) {
s_wsfe(&io___57);
i__1 = iter + 1;
do_fio(&c__1, (char *)&i__1, (ftnlen)sizeof(int_F));
e_wsfe();
}
iword = -1;
if (! cnstnd && col > 0) {
/* skip the search for GCP. */
dcopy(n, &x[1], &c__1, &z__[1], &c__1);
wrk = updatd;
nseg = 0;
goto L333;
}
/* ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
/* Compute the Generalized Cauchy Point (GCP). */
/* ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc */
#ifdef USE_TIMER
timer(&cpu1);
#endif
cauchy_(n, &x[1], &l[1], &u[1], &nbd[1], &g[1], &indx2[1], &iwhere[1], &t[
1], &d__[1], &z__[1], m, &wy[wy_offset], &ws[ws_offset], &sy[
sy_offset], &wt[wt_offset], &theta, &col, &head, &wa[1], &wa[(*m
<< 1) + 1], &wa[(*m << 2) + 1], &wa[*m * 6 + 1], &nseg, iprint, &
sbgnrm, &info, &epsmch);
if (info != 0) {
/* singular triangular system detected; refresh the lbfgs memory. */
if (*iprint >= 1) {
s_wsfe(&io___59);