/
myqld.cc
2122 lines (1891 loc) · 42.5 KB
/
myqld.cc
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#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
/* ************************************************************/
/* -- translated by f2c (version of 22 July 1992 22:54:52).
*/
/* umd
Must include math.h before f2c.h - f2c does a #define abs.
(Thanks go to Martin Wauchope for providing this correction)
We manually included AT&T's f2c.h in this source file, i.e.
it does not have to be present separately in order to compile.
*/
#include <cmath>
#include "bioTypes.h"
/* CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
!!!! NOTICE !!!!
1. The routines contained in this file are due to Prof. K.Schittkowski
of the University of Bayreuth, Germany (modification of routines
due to Prof. MJD Powell at the University of Cambridge). They can
be freely distributed.
2. A few minor modifications were performed at the University of
Maryland. They are marked in the code by "umd".
A.L. Tits, J.L. Zhou, and
Craig Lawrence
University of Maryland
***********************************************************************
SOLUTION OF QUADRATIC PROGRAMMING PROBLEMS
QL0001 SOLVES THE QUADRATIC PROGRAMMING PROBLEM
MINIMIZE .5*X'*C*X + D'*X
SUBJECT TO A(J)*X + B(J) = 0 , J=1,...,ME
A(J)*X + B(J) >= 0 , J=ME+1,...,M
XL <= X <= XU
HERE C MUST BE AN N BY N SYMMETRIC AND POSITIVE MATRIX, D AN N-DIMENSIONAL
VECTOR, A AN M BY N MATRIX AND B AN M-DIMENSIONAL VECTOR. THE ABOVE
SITUATION IS INDICATED BY IWAR(1)=1. ALTERNATIVELY, I.E. IF IWAR(1)=0,
THE OBJECTIVE FUNCTION MATRIX CAN ALSO BE PROVIDED IN FACTORIZED FORM.
IN THIS CASE, C IS AN UPPER TRIANGULAR MATRIX.
THE SUBROUTINE REORGANIZES SOME DATA SO THAT THE PROBLEM CAN BE SOLVED
BY A MODIFICATION OF AN ALGORITHM PROPOSED BY POWELL (1983).
USAGE:
QL0001(M,ME,MMAX,N,NMAX,MNN,C,D,A,B,XL,XU,X,U,IOUT,IFAIL,IPRINT,
WAR,LWAR,IWAR,LIWAR)
DEFINITION OF THE PARAMETERS:
M : TOTAL NUMBER OF CONSTRAINTS.
ME : NUMBER OF EQUALITY CONSTRAINTS.
MMAX : ROW DIMENSION OF A. MMAX MUST BE AT LEAST ONE AND GREATER
THAN M.
N : NUMBER OF VARIABLES.
NMAX : ROW DIMENSION OF C. NMAX MUST BE GREATER OR EQUAL TO N.
MNN : MUST BE EQUAL TO M + N + N.
C(NMAX,NMAX): OBJECTIVE FUNCTION MATRIX WHICH SHOULD BE SYMMETRIC AND
POSITIVE DEFINITE. IF IWAR(1) = 0, C IS SUPPOSED TO BE THE
CHOLESKEY-FACTOR OF ANOTHER MATRIX, I.E. C IS UPPER
TRIANGULAR.
D(NMAX) : CONTAINS THE CONSTANT VECTOR OF THE OBJECTIVE FUNCTION.
A(MMAX,NMAX): CONTAINS THE DATA MATRIX OF THE LINEAR CONSTRAINTS.
B(MMAX) : CONTAINS THE CONSTANT DATA OF THE LINEAR CONSTRAINTS.
XL(N),XU(N): CONTAIN THE LOWER AND UPPER BOUNDS FOR THE VARIABLES.
X(N) : ON RETURN, X CONTAINS THE OPTIMAL SOLUTION VECTOR.
U(MNN) : ON RETURN, U CONTAINS THE LAGRANGE MULTIPLIERS. THE FIRST
M POSITIONS ARE RESERVED FOR THE MULTIPLIERS OF THE M
LINEAR CONSTRAINTS AND THE SUBSEQUENT ONES FOR THE
MULTIPLIERS OF THE LOWER AND UPPER BOUNDS. ON SUCCESSFUL
TERMINATION, ALL VALUES OF U WITH RESPECT TO INEQUALITIES
AND BOUNDS SHOULD BE GREATER OR EQUAL TO ZERO.
IOUT : INTEGER INDICATING THE DESIRED OUTPUT UNIT NUMBER, I.E.
ALL WRITE-STATEMENTS START WITH 'WRITE(IOUT,... '.
IFAIL : SHOWS THE TERMINATION REASON.
IFAIL = 0 : SUCCESSFUL RETURN.
IFAIL = 1 : TOO MANY ITERATIONS (MORE THAN 40*(N+M)).
IFAIL = 2 : ACCURACY INSUFFICIENT TO SATISFY CONVERGENCE
CRITERION.
IFAIL = 5 : LENGTH OF A WORKING ARRAY IS TOO SHORT.
IFAIL > 10 : THE CONSTRAINTS ARE INCONSISTENT.
IPRINT : OUTPUT CONTROL.
IPRINT = 0 : NO OUTPUT OF QL0001.
IPRINT > 0 : BRIEF OUTPUT IN ERROR CASES.
WAR(LWAR) : REAL WORKING ARRAY. THE LENGTH LWAR SHOULD BE GRATER THAN
3*NMAX*NMAX/2 + 10*NMAX + 2*MMAX.
IWAR(LIWAR): INTEGER WORKING ARRAY. THE LENGTH LIWAR SHOULD BE AT
LEAST N.
IF IWAR(1)=0 INITIALLY, THEN THE CHOLESKY DECOMPOSITION
WHICH IS REQUIRED BY THE DUAL ALGORITHM TO GET THE FIRST
UNCONSTRAINED MINIMUM OF THE OBJECTIVE FUNCTION, IS
PERFORMED INTERNALLY. OTHERWISE, I.E. IF IWAR(1)=1, THEN
IT IS ASSUMED THAT THE USER PROVIDES THE INITIAL FAC-
TORIZATION BY HIMSELF AND STORES IT IN THE UPPER TRIAN-
GULAR PART OF THE ARRAY C.
A NAMED COMMON-BLOCK /CMACHE/EPS MUST BE PROVIDED BY THE USER,
WHERE EPS DEFINES A GUESS FOR THE UNDERLYING MACHINE PRECISION.
AUTHOR: K. SCHITTKOWSKI,
MATHEMATISCHES INSTITUT,
UNIVERSITAET BAYREUTH,
8580 BAYREUTH,
GERMANY, F.R.
VERSION: 1.4 (MARCH, 1987)
*/
/* f2c.h -- Standard Fortran to C header file */
/** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
#ifndef F2C_INCLUDE
#define F2C_INCLUDE
typedef int integer;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef bioReal doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
typedef long int logical;
typedef short int shortlogical;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
#ifdef f2c_i2
/* for -i2 */
typedef short flag;
typedef short ftnlen;
typedef short ftnint;
#else
typedef long flag;
typedef long ftnlen;
typedef long ftnint;
#endif
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
shortint h;
integer i;
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
typedef long Long;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
Long *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define my_abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (doublereal)my_abs(x)
#define dmin(a,b) (doublereal)((a) <= (b) ? (a) : (b))
#define dmax(a,b) (doublereal)((a) >= (b) ? (a) : (b))
//#define dmin(a,b) (doublereal)dmin(a,b)
//#define dmax(a,b) (doublereal)patMax(a,b)
/* procedure parameter types for -A and -C++ */
#define F2C_proc_par_types 1
#ifdef __cplusplus
typedef int /* Unknown procedure type */ (*U_fp)(...);
typedef shortint (*J_fp)(...);
typedef integer (*I_fp)(...);
typedef real (*R_fp)(...);
typedef doublereal (*D_fp)(...), (*E_fp)(...);
typedef /* Complex */ VOID (*C_fp)(...);
typedef /* Double Complex */ VOID (*Z_fp)(...);
typedef logical (*L_fp)(...);
typedef shortlogical (*K_fp)(...);
typedef /* Character */ VOID (*H_fp)(...);
typedef /* Subroutine */ int (*S_fp)(...);
#else
typedef int /* Unknown procedure type */ (*U_fp)();
typedef shortint (*J_fp)();
typedef integer (*I_fp)();
typedef real (*R_fp)();
typedef doublereal (*D_fp)(), (*E_fp)();
typedef /* Complex */ VOID (*C_fp)();
typedef /* Double Complex */ VOID (*Z_fp)();
typedef logical (*L_fp)();
typedef shortlogical (*K_fp)();
typedef /* Character */ VOID (*H_fp)();
typedef /* Subroutine */ int (*S_fp)();
#endif
/* E_fp is for real functions when -R is not specified */
typedef VOID C_f; /* complex function */
typedef VOID H_f; /* character function */
typedef VOID Z_f; /* double complex function */
typedef doublereal E_f; /* real function with -R not specified */
/* undef any lower-case symbols that your C compiler predefines, e.g.: */
#ifndef Skip_f2c_Undefs
#undef cray
#undef gcos
#undef mc68010
#undef mc68020
#undef mips
#undef pdp11
#undef sgi
#undef sparc
#undef sun
#undef sun2
#undef sun3
#undef sun4
#undef u370
#undef u3b
#undef u3b2
#undef u3b5
#undef unix
#undef vax
#endif
#endif
/* Common Block Declarations */
struct cfsqp_cmache_{
doublereal eps;
} cmache_;
#define cmache_1 cmache_
/* Table of constant values */
//static integer c__1 = 1;
/* umd */
/*
ql0002_ is declared here to provide ANSI C compliance.
(Thanks got to Martin Wauchope for providing this correction)
*/
#ifdef __STDC__
int ql0002_(integer *n,integer *m,integer *meq,integer *mmax,
integer *mn,integer *mnn,integer *nmax,
logical *lql,
doublereal *a,doublereal *b,doublereal *grad,
doublereal *g,doublereal *xl,doublereal *xu,doublereal *x,
integer *nact,integer *iact,integer *maxit,
doublereal *vsmall,
integer *info,
doublereal *diag, doublereal *w,
integer *lw);
#else
int ql0002_();
#endif
/* umd */
/*
When the fortran code was f2c converted, the use of fortran COMMON
blocks was no longer available. Thus an additional variable, eps1,
was added to the parameter list to account for this.
*/
/* umd */
/*
Two alternative definitions are provided in order to give ANSI
compliance.
*/
#ifdef __STDC__
int ql0001_(int *m,int *me,int *mmax,int *n,int *nmax,int *mnn,
bioReal *c,bioReal *d,bioReal *a,bioReal *b,bioReal *xl,
bioReal *xu,bioReal *x,bioReal *u,int *iout,int *ifail,
int *iprint,bioReal *war,int *lwar,int *iwar,int *liwar,
bioReal *eps1)
#else
/* Subroutine */
int ql0001_(m, me, mmax, n, nmax, mnn, c, d, a, b, xl, xu, x,
u, iout, ifail, iprint, war, lwar, iwar, liwar, eps1)
integer *m, *me, *mmax, *n, *nmax, *mnn;
doublereal *c, *d, *a, *b, *xl, *xu, *x, *u;
integer *iout, *ifail, *iprint;
doublereal *war;
integer *lwar, *iwar, *liwar;
doublereal *eps1;
#endif
{
/* Format strings */
// static char fmt_1000[] = "(/8x,/002***QL: MATRIX G WAS ENLARGED/002,i3,/002-TIMES BY UNITMATRIX/002)";
// static char fmt_1100[] = "(/8x,/002***QL: CONSTRAINT /002,i5,/002 NOT CONSISTENT TO /002,/,(10x,10i5))";
// static char fmt_1200[] = "(/8x,/002***QL: LWAR TOO SMALL/002)";
// static char fmt_1210[] = "(/8x,/002***QL: LIWAR TOO SMALL/002)";
// static char fmt_1220[] = "(/8x,/002***QL: MNN TOO SMALL/002)";
// static char fmt_1300[] = "(/8x,/002***QL: TOO MANY ITERATIONS (MORE THAN/002,i6,/002)/002)";
// static char fmt_1400[] = "(/8x,/002***QL: ACCURACY INSUFFICIENT TO ATTAIN CONVERGENCE/002)";
/* System generated locals */
// integer c_dim1, c_offset, a_dim1, a_offset, i__1, i__2;
integer c_dim1, c_offset, a_dim1, a_offset, i__1 ;
/* Builtin functions */
/* integer s_wsfe(), do_fio(), e_wsfe(); */
/* Local variables */
static doublereal diag;
/* extern int ql0002_(); */
static integer nact, info;
static doublereal zero;
static integer i, j, idiag, maxit;
static doublereal qpeps;
static integer in, mn, lw;
static doublereal ten;
static logical lql;
static integer inw1, inw2;
/* Fortran I/O blocks */
// static cilist io___16 = { 0, 0, 0, fmt_1000, 0 };
// static cilist io___18 = { 0, 0, 0, fmt_1100, 0 };
// static cilist io___19 = { 0, 0, 0, fmt_1200, 0 };
// static cilist io___20 = { 0, 0, 0, fmt_1210, 0 };
// static cilist io___21 = { 0, 0, 0, fmt_1220, 0 };
// static cilist io___22 = { 0, 0, 0, fmt_1300, 0 };
// static cilist io___23 = { 0, 0, 0, fmt_1400, 0 };
/* INTRINSIC FUNCTIONS: DSQRT */
/* Parameter adjustments */
--iwar;
--war;
--u;
--x;
--xu;
--xl;
--b;
a_dim1 = *mmax;
a_offset = a_dim1 + 1;
a -= a_offset;
--d;
c_dim1 = *nmax;
c_offset = c_dim1 + 1;
c -= c_offset;
/* Function Body */
cmache_1.eps = *eps1;
/* CONSTANT DATA */
/* ################################################################# */
if (fabs(c[*nmax + *nmax * c_dim1]) == 0.e0) {
c[*nmax + *nmax * c_dim1] = cmache_1.eps;
}
/* umd */
/* This prevents a subsequent more major modification of the Hessian */
/* matrix in the important case when a minmax problem (yielding a */
/* singular Hessian matrix) is being solved. */
/* ----UMCP, April 1991, Jian L. Zhou */
/* ################################################################# */
lql = FALSE_;
if (iwar[1] == 1) {
lql = TRUE_;
}
zero = 0.;
ten = 10.;
maxit = (*m + *n) * 40;
qpeps = cmache_1.eps;
inw1 = 1;
inw2 = inw1 + *mmax;
/* PREPARE PROBLEM DATA FOR EXECUTION */
if (*m <= 0) {
goto L20;
}
in = inw1;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
war[in] = -b[j];
/* L10: */
++in;
}
L20:
lw = *nmax * 3 * *nmax / 2 + *nmax * 10 + *m;
if (inw2 + lw > *lwar) {
goto L80;
}
if (*liwar < *n) {
goto L81;
}
if (*mnn < *m + *n + *n) {
goto L82;
}
mn = *m + *n;
/* CALL OF QL0002 */
ql0002_(n, m, me, mmax, &mn, mnn, nmax, &lql, &a[a_offset], &war[inw1], &
d[1], &c[c_offset], &xl[1], &xu[1], &x[1], &nact, &iwar[1], &
maxit, &qpeps, &info, &diag, &war[inw2], &lw);
/* TEST OF MATRIX CORRECTIONS */
*ifail = 0;
if (info == 1) {
goto L40;
}
if (info == 2) {
goto L90;
}
idiag = 0;
if (diag > zero && diag < 1e3) {
idiag = (integer) diag;
}
/*
if (*iprint > 0 && idiag > 0) {
io___16.ciunit = *iout;
s_wsfe(&io___16);
do_fio(&c__1, (char *)&idiag, (ftnlen)sizeof(integer));
e_wsfe();
}
*/
if (info < 0) {
goto L70;
}
/* REORDER MULTIPLIER */
i__1 = *mnn;
for (j = 1; j <= i__1; ++j) {
/* L50: */
u[j] = zero;
}
in = inw2 - 1;
if (nact == 0) {
goto L30;
}
i__1 = nact;
for (i = 1; i <= i__1; ++i) {
j = iwar[i];
u[j] = war[in + i];
/* L60: */
}
L30:
return 0;
/* ERROR MESSAGES */
L70:
*ifail = -info + 10;
/*
if (*iprint > 0 && nact > 0) {
io___18.ciunit = *iout;
s_wsfe(&io___18);
i__1 = -info;
do_fio(&c__1, (char *)&i__1, (ftnlen)sizeof(integer));
i__2 = nact;
for (i = 1; i <= i__2; ++i) {
do_fio(&c__1, (char *)&iwar[i], (ftnlen)sizeof(integer));
}
e_wsfe();
}
*/
return 0;
L80:
*ifail = 5;
/*
if (*iprint > 0) {
io___19.ciunit = *iout;
s_wsfe(&io___19);
e_wsfe();
}
*/
return 0;
L81:
*ifail = 5;
/*
if (*iprint > 0) {
io___20.ciunit = *iout;
s_wsfe(&io___20);
e_wsfe();
}
*/
return 0;
L82:
*ifail = 5;
/*
if (*iprint > 0) {
io___21.ciunit = *iout;
s_wsfe(&io___21);
e_wsfe();
}
*/
return 0;
L40:
*ifail = 1;
/*
if (*iprint > 0) {
io___22.ciunit = *iout;
s_wsfe(&io___22);
do_fio(&c__1, (char *)&maxit, (ftnlen)sizeof(integer));
e_wsfe();
}
*/
return 0;
L90:
*ifail = 2;
/*
if (*iprint > 0) {
io___23.ciunit = *iout;
s_wsfe(&io___23);
e_wsfe();
}
*/
return 0;
/* FORMAT-INSTRUCTIONS */
} /* ql0001_ */
/* umd
Two alternative definitions are provided in order to give ANSI
compliance.
(Thanks got to Martin Wauchope for providing this correction)
*/
#ifdef __STDC__
int ql0002_(integer *n,integer *m,integer *meq,integer *mmax,
integer *mn,integer *mnn,integer *nmax,
logical *lql,
doublereal *a,doublereal *b,doublereal *grad,
doublereal *g,doublereal *xl,doublereal *xu,doublereal *x,
integer *nact,integer *iact,integer *maxit,
doublereal *vsmall,
integer *info,
doublereal *diag, doublereal *w,
integer *lw)
#else
/* Subroutine */ int ql0002_(n, m, meq, mmax, mn, mnn, nmax, lql, a, b, grad,
g, xl, xu, x, nact, iact, maxit, vsmall, info, diag, w, lw)
integer *n, *m, *meq, *mmax, *mn, *mnn, *nmax;
logical *lql;
doublereal *a, *b, *grad, *g, *xl, *xu, *x;
integer *nact, *iact, *maxit;
doublereal *vsmall;
integer *info;
doublereal *diag, *w;
integer *lw;
#endif
{
/* System generated locals */
integer a_dim1, a_offset, g_dim1, g_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3, d__4;
/* Builtin functions */
/* umd */
/* double sqrt(); */
/* Local variables */
static doublereal onha, xmag, suma, sumb, sumc, temp, step, zero;
static integer iwwn;
static doublereal sumx, sumy;
static integer i, j, k;
static doublereal fdiff;
static integer iflag, jflag, kflag, lflag;
static doublereal diagr;
static integer ifinc, kfinc, jfinc, mflag, nflag;
static doublereal vfact, tempa;
static integer iterc, itref;
static doublereal cvmax, ratio, xmagr;
static integer kdrop;
static logical lower;
static integer knext, k1;
static doublereal ga, gb;
static integer ia, id;
static doublereal fdiffa;
static integer ii, il, kk, jl, ip, ir, nm, is, iu, iw, ju, ix, iz, nu, iy;
static doublereal parinc, parnew;
static integer ira, irb, iwa;
static doublereal one;
static integer iwd, iza;
static doublereal res;
static integer ipp, iwr, iws;
static doublereal sum;
static integer iww, iwx, iwy;
static doublereal two;
static integer iwz;
/* WHETHER THE CONSTRAINT IS ACTIVE. */
/* AUTHOR: K. SCHITTKOWSKI, */
/* MATHEMATISCHES INSTITUT, */
/* UNIVERSITAET BAYREUTH, */
/* 8580 BAYREUTH, */
/* GERMANY, F.R. */
/* AUTHOR OF ORIGINAL VERSION: */
/* M.J.D. POWELL, DAMTP, */
/* UNIVERSITY OF CAMBRIDGE, SILVER STREET */
/* CAMBRIDGE, */
/* ENGLAND */
/* REFERENCE: M.J.D. POWELL: ZQPCVX, A FORTRAN SUBROUTINE FOR CONVEX */
/* PROGRAMMING, REPORT DAMTP/1983/NA17, UNIVERSITY OF */
/* CAMBRIDGE, ENGLAND, 1983. */
/* VERSION : 2.0 (MARCH, 1987) */
/************************************************************************
***/
/* INTRINSIC FUNCTIONS: DMAX1,DSQRT,DABS,DMIN1 */
/* INITIAL ADDRESSES */
/* Parameter adjustments */
--w;
--iact;
--x;
--xu;
--xl;
g_dim1 = *nmax;
g_offset = g_dim1 + 1;
g -= g_offset;
--grad;
--b;
a_dim1 = *mmax;
a_offset = a_dim1 + 1;
a -= a_offset;
/* Function Body */
iwz = *nmax;
iwr = iwz + *nmax * *nmax;
iww = iwr + *nmax * (*nmax + 3) / 2;
iwd = iww + *nmax;
iwx = iwd + *nmax;
iwa = iwx + *nmax;
/* SET SOME CONSTANTS. */
zero = 0.;
one = 1.;
two = 2.;
onha = 1.5;
vfact = 1.;
/* SET SOME PARAMETERS. */
/* NUMBER LESS THAN VSMALL ARE ASSUMED TO BE NEGLIGIBLE. */
/* THE MULTIPLE OF I THAT IS ADDED TO G IS AT MOST DIAGR TIMES */
/* THE LEAST MULTIPLE OF I THAT GIVES POSITIVE DEFINITENESS. */
/* X IS RE-INITIALISED IF ITS MAGNITUDE IS REDUCED BY THE */
/* FACTOR XMAGR. */
/* A CHECK IS MADE FOR AN INCREASE IN F EVERY IFINC ITERATIONS, */
/* AFTER KFINC ITERATIONS ARE COMPLETED. */
diagr = two;
xmagr = .01;
ifinc = 3;
kfinc = (*n > 10) ? *n : 10 ;
/* FIND THE RECIPROCALS OF THE LENGTHS OF THE CONSTRAINT NORMALS. */
/* RETURN IF A CONSTRAINT IS INFEASIBLE DUE TO A ZERO NORMAL. */
*nact = 0;
if (*m <= 0) {
goto L45;
}
i__1 = *m;
for (k = 1; k <= i__1; ++k) {
sum = zero;
i__2 = *n;
for (i = 1; i <= i__2; ++i) {
/* L10: */
/* Computing 2nd power */
d__1 = a[k + i * a_dim1];
sum += d__1 * d__1;
}
if (sum > zero) {
goto L20;
}
if (b[k] == zero) {
goto L30;
}
*info = -k;
if (k <= *meq) {
goto L730;
}
if (b[k] <= 0.) {
goto L30;
} else {
goto L730;
}
L20:
sum = one / sqrt(sum);
L30:
ia = iwa + k;
/* L40: */
w[ia] = sum;
}
L45:
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
ia = iwa + *m + k;
/* L50: */
w[ia] = one;
}
/* IF NECESSARY INCREASE THE DIAGONAL ELEMENTS OF G. */
if (! (*lql)) {
goto L165;
}
*diag = zero;
i__1 = *n;
for (i = 1; i <= i__1; ++i) {
id = iwd + i;
w[id] = g[i + i * g_dim1];
/* Computing MAX */
d__1 = *diag, d__2 = *vsmall - w[id];
*diag = dmax(d__1,d__2) ;
if (i == *n) {
goto L60;
}
ii = i + 1;
i__2 = *n;
for (j = ii; j <= i__2; ++j) {
/* Computing MIN */
d__1 = w[id], d__2 = g[j + j * g_dim1];
ga = -dmin(d__1,d__2);
gb = (d__1 = w[id] - g[j + j * g_dim1], my_abs(d__1)) + (d__2 = g[i
+ j * g_dim1], my_abs(d__2));
if (gb > zero) {
/* Computing 2nd power */
d__1 = g[i + j * g_dim1];
ga += d__1 * d__1 / gb;
}
/* L55: */
*diag = dmax(*diag,ga);
}
L60:
;
}
if (*diag <= zero) {
goto L90;
}
L70:
*diag = diagr * *diag;
i__1 = *n;
for (i = 1; i <= i__1; ++i) {
id = iwd + i;
/* L80: */
g[i + i * g_dim1] = *diag + w[id];
}
/* FORM THE CHOLESKY FACTORISATION OF G. THE TRANSPOSE */
/* OF THE FACTOR WILL BE PLACED IN THE R-PARTITION OF W. */
L90:
ir = iwr;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
ira = iwr;
irb = ir + 1;
i__2 = j;
for (i = 1; i <= i__2; ++i) {
temp = g[i + j * g_dim1];
if (i == 1) {
goto L110;
}
i__3 = ir;
for (k = irb; k <= i__3; ++k) {
++ira;
/* L100: */
temp -= w[k] * w[ira];
}
L110:
++ir;
++ira;
if (i < j) {
w[ir] = temp / w[ira];
}
/* L120: */
}
if (temp < *vsmall) {
goto L140;
}
/* L130: */
w[ir] = sqrt(temp);
}
goto L170;
/* INCREASE FURTHER THE DIAGONAL ELEMENT OF G. */
L140:
w[j] = one;
sumx = one;
k = j;
L150:
sum = zero;
ira = ir - 1;
i__1 = j;
for (i = k; i <= i__1; ++i) {
sum -= w[ira] * w[i];
/* L160: */
ira += i;
}
ir -= k;
--k;
w[k] = sum / w[ir];
/* Computing 2nd power */
d__1 = w[k];
sumx += d__1 * d__1;
if (k >= 2) {
goto L150;
}
*diag = *diag + *vsmall - temp / sumx;
goto L70;
/* STORE THE CHOLESKY FACTORISATION IN THE R-PARTITION */
/* OF W. */
L165:
ir = iwr;
i__1 = *n;
for (i = 1; i <= i__1; ++i) {
i__2 = i;
for (j = 1; j <= i__2; ++j) {
++ir;
/* L166: */
w[ir] = g[j + i * g_dim1];
}
}
/* SET Z THE INVERSE OF THE MATRIX IN R. */
L170:
nm = *n - 1;
i__2 = *n;
for (i = 1; i <= i__2; ++i) {
iz = iwz + i;
if (i == 1) {
goto L190;
}
i__1 = i;
for (j = 2; j <= i__1; ++j) {
w[iz] = zero;
/* L180: */
iz += *n;
}
L190:
ir = iwr + (i + i * i) / 2;
w[iz] = one / w[ir];
if (i == *n) {
goto L220;
}
iza = iz;
i__1 = nm;
for (j = i; j <= i__1; ++j) {
ir += i;
sum = zero;
i__3 = iz;
i__4 = *n;
for (k = iza; i__4 < 0 ? k >= i__3 : k <= i__3; k += i__4) {
sum += w[k] * w[ir];
/* L200: */
++ir;
}
iz += *n;
/* L210: */
w[iz] = -sum / w[ir];
}
L220:
;
}