#include <math.h>

#include <stdlib.h>

#include <string.h>

#include <stdio.h>

#include <complex.h>

#ifdef complex

#undef complex

#endif

#ifdef I

#undef I

#endif

#if defined(_WIN64)

typedef long long BLASLONG;

typedef unsigned long long BLASULONG;

#else

typedef long BLASLONG;

typedef unsigned long BLASULONG;

#endif

#ifdef LAPACK_ILP64

typedef BLASLONG blasint;

#if defined(_WIN64)

#define blasabs(x) llabs(x)

#else

#define blasabs(x) labs(x)

#endif

#else

typedef int blasint;

#define blasabs(x) abs(x)

#endif

typedef blasint integer;

typedef unsigned int uinteger;

typedef char *address;

typedef short int shortint;

typedef float real;

typedef double doublereal;

typedef struct { real r, i; } complex;

typedef struct { doublereal r, i; } doublecomplex;

#ifdef _MSC_VER

static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}

static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}

static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}

static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}

#else

static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}

static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}

static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}

static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}

#endif

#define pCf(z) (*_pCf(z))

#define pCd(z) (*_pCd(z))

typedef blasint logical;

typedef char logical1;

typedef char integer1;

#define TRUE_ (1)

#define FALSE_ (0)

/* Extern is for use with -E */

#ifndef Extern

#define Extern extern

#endif

/* I/O stuff */

typedef int flag;

typedef int ftnlen;

typedef int ftnint;

/*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 */

  integer1 g;

  shortint h;

  integer i;

  /* longint j; */

  real r;

  doublereal d;

  complex c;

  doublecomplex z;

  };

typedef union Multitype Multitype;

struct Vardesc {  /* for Namelist */

  char *name;

  char *addr;

  ftnlen *dims;

  int  type;

  };

typedef struct Vardesc Vardesc;

struct Namelist {

  char *name;

  Vardesc **vars;

  int nvars;

  };

typedef struct Namelist Namelist;

#define abs(x) ((x) >= 0 ? (x) : -(x))

#define dabs(x) (fabs(x))

#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))

#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))

#define dmin(a,b) (f2cmin(a,b))

#define dmax(a,b) (f2cmax(a,b))

#define bit_test(a,b) ((a) >> (b) & 1)

#define bit_clear(a,b)  ((a) & ~((uinteger)1 << (b)))

#define bit_set(a,b)  ((a) |  ((uinteger)1 << (b)))

#define abort_() { sig_die("Fortran abort routine called", 1); }

#define c_abs(z) (cabsf(Cf(z)))

#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }

#ifdef _MSC_VER

#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}

#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}

#else

#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}

#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}

#endif

#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}

#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}

#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}

//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}

#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}

#define d_abs(x) (fabs(*(x)))

#define d_acos(x) (acos(*(x)))

#define d_asin(x) (asin(*(x)))

#define d_atan(x) (atan(*(x)))

#define d_atn2(x, y) (atan2(*(x),*(y)))

#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }

#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }

#define d_cos(x) (cos(*(x)))

#define d_cosh(x) (cosh(*(x)))

#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )

#define d_exp(x) (exp(*(x)))

#define d_imag(z) (cimag(Cd(z)))

#define r_imag(z) (cimagf(Cf(z)))

#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))

#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))

#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )

#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )

#define d_log(x) (log(*(x)))

#define d_mod(x, y) (fmod(*(x), *(y)))

#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))

#define d_nint(x) u_nint(*(x))

#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))

#define d_sign(a,b) u_sign(*(a),*(b))

#define r_sign(a,b) u_sign(*(a),*(b))

#define d_sin(x) (sin(*(x)))

#define d_sinh(x) (sinh(*(x)))

#define d_sqrt(x) (sqrt(*(x)))

#define d_tan(x) (tan(*(x)))

#define d_tanh(x) (tanh(*(x)))

#define i_abs(x) abs(*(x))

#define i_dnnt(x) ((integer)u_nint(*(x)))

#define i_len(s, n) (n)

#define i_nint(x) ((integer)u_nint(*(x)))

#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))

#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))

#define pow_si(B,E) spow_ui(*(B),*(E))

#define pow_ri(B,E) spow_ui(*(B),*(E))

#define pow_di(B,E) dpow_ui(*(B),*(E))

#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}

#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}

#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}

#define s_cat(lpp, rpp, rnp, np, llp) {   ftnlen i, nc, ll; char *f__rp, *lp;   ll = (llp); lp = (lpp);   for(i=0; i < (int)*(np); ++i) {           nc = ll;          if((rnp)[i] < nc) nc = (rnp)[i];          ll -= nc;           f__rp = (rpp)[i];           while(--nc >= 0) *lp++ = *(f__rp)++;         }  while(--ll >= 0) *lp++ = ' '; }

#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))

#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }

#define sig_die(s, kill) { exit(1); }

#define s_stop(s, n) {exit(0);}

static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";

#define z_abs(z) (cabs(Cd(z)))

#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}

#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}

#define myexit_() break;

#define mycycle() continue;

#define myceiling(w) {ceil(w)}

#define myhuge(w) {HUGE_VAL}

//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}

#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/* procedure parameter types for -A and -C++ */

#ifdef __cplusplus

typedef logical (*L_fp)(...);

#else

typedef logical (*L_fp)();

#endif

static float spow_ui(float x, integer n) {

  float pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

static double dpow_ui(double x, integer n) {

  double pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#ifdef _MSC_VER

static _Fcomplex cpow_ui(complex x, integer n) {

  complex pow={1.0,0.0}; unsigned long int u;

    if(n != 0) {

    if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;

    for(u = n; ; ) {

      if(u & 01) pow.r *= x.r, pow.i *= x.i;

      if(u >>= 1) x.r *= x.r, x.i *= x.i;

      else break;

    }

  }

  _Fcomplex p={pow.r, pow.i};

  return p;

}

#else

static _Complex float cpow_ui(_Complex float x, integer n) {

  _Complex float pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#endif

#ifdef _MSC_VER

static _Dcomplex zpow_ui(_Dcomplex x, integer n) {

  _Dcomplex pow={1.0,0.0}; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];

    for(u = n; ; ) {

      if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];

      if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];

      else break;

    }

  }

  _Dcomplex p = {pow._Val[0], pow._Val[1]};

  return p;

}

#else

static _Complex double zpow_ui(_Complex double x, integer n) {

  _Complex double pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#endif

static integer pow_ii(integer x, integer n) {

  integer pow; unsigned long int u;

  if (n <= 0) {

    if (n == 0 || x == 1) pow = 1;

    else if (x != -1) pow = x == 0 ? 1/x : 0;

    else n = -n;

  }

  if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {

    u = n;

    for(pow = 1; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

static integer dmaxloc_(double *w, integer s, integer e, integer *n)

{

  double m; integer i, mi;

  for(m=w[s-1], mi=s, i=s+1; i<=e; i++)

    if (w[i-1]>m) mi=i ,m=w[i-1];

  return mi-s+1;

}

static integer smaxloc_(float *w, integer s, integer e, integer *n)

{

  float m; integer i, mi;

  for(m=w[s-1], mi=s, i=s+1; i<=e; i++)

    if (w[i-1]>m) mi=i ,m=w[i-1];

  return mi-s+1;

}

static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Fcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];

      zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];

      zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];

    }

  }

  pCf(z) = zdotc;

}

#else

  _Complex float zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);

    }

  }

  pCf(z) = zdotc;

}

#endif

static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Dcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];

      zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];

      zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];

    }

  }

  pCd(z) = zdotc;

}

#else

  _Complex double zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conj(Cd(&x[i])) * Cd(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);

    }

  }

  pCd(z) = zdotc;

}

#endif  

static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Fcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];

      zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];

      zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];

    }

  }

  pCf(z) = zdotc;

}

#else

  _Complex float zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cf(&x[i]) * Cf(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);

    }

  }

  pCf(z) = zdotc;

}

#endif

static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Dcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];

      zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];

      zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];

    }

  }

  pCd(z) = zdotc;

}

#else

  _Complex double zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cd(&x[i]) * Cd(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);

    }

  }

  pCd(z) = zdotc;

}

#endif

/*  -- translated by f2c (version 20000121).

   You must link the resulting object file with the libraries:

  -lf2c -lm   (in that order)

*/

/* > \brief \b SLAED6 used by sstedc. Computes one Newton step in solution of the secular equation. */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */

/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */

/* > Download SLAED6 + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaed6.

f"> */

/* > [TGZ]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaed6.

f"> */

/* > [ZIP]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaed6.

f"> */

/* > [TXT]</a> */

/* > \endhtmlonly */

/*  Definition: */

/*  =========== */

/*       SUBROUTINE SLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO ) */

/*       LOGICAL            ORGATI */

/*       INTEGER            INFO, KNITER */

/*       REAL               FINIT, RHO, TAU */

/*       REAL               D( 3 ), Z( 3 ) */

/* > \par Purpose: */

/*  ============= */

/* > */

/* > \verbatim */

/* > */

/* > SLAED6 computes the positive or negative root (closest to the origin) */

/* > of */

/* >                  z(1)        z(2)        z(3) */

/* > f(x) =   rho + --------- + ---------- + --------- */

/* >                 d(1)-x      d(2)-x      d(3)-x */

/* > */

/* > It is assumed that */

/* > */

/* >       if ORGATI = .true. the root is between d(2) and d(3); */

/* >       otherwise it is between d(1) and d(2) */

/* > */

/* > This routine will be called by SLAED4 when necessary. In most cases, */

/* > the root sought is the smallest in magnitude, though it might not be */

/* > in some extremely rare situations. */

/* > \endverbatim */

/*  Arguments: */

/*  ========== */

/* > \param[in] KNITER */

/* > \verbatim */

/* >          KNITER is INTEGER */

/* >               Refer to SLAED4 for its significance. */

/* > \endverbatim */

/* > */

/* > \param[in] ORGATI */

/* > \verbatim */

/* >          ORGATI is LOGICAL */

/* >               If ORGATI is true, the needed root is between d(2) and */

/* >               d(3); otherwise it is between d(1) and d(2).  See */

/* >               SLAED4 for further details. */

/* > \endverbatim */

/* > */

/* > \param[in] RHO */

/* > \verbatim */

/* >          RHO is REAL */

/* >               Refer to the equation f(x) above. */

/* > \endverbatim */

/* > */

/* > \param[in] D */

/* > \verbatim */

/* >          D is REAL array, dimension (3) */

/* >               D satisfies d(1) < d(2) < d(3). */

/* > \endverbatim */

/* > */

/* > \param[in] Z */

/* > \verbatim */

/* >          Z is REAL array, dimension (3) */

/* >               Each of the elements in z must be positive. */

/* > \endverbatim */

/* > */

/* > \param[in] FINIT */

/* > \verbatim */

/* >          FINIT is REAL */

/* >               The value of f at 0. It is more accurate than the one */

/* >               evaluated inside this routine (if someone wants to do */

/* >               so). */

/* > \endverbatim */

/* > */

/* > \param[out] TAU */

/* > \verbatim */

/* >          TAU is REAL */

/* >               The root of the equation f(x). */

/* > \endverbatim */

/* > */

/* > \param[out] INFO */

/* > \verbatim */

/* >          INFO is INTEGER */

/* >               = 0: successful exit */

/* >               > 0: if INFO = 1, failure to converge */

/* > \endverbatim */

/*  Authors: */

/*  ======== */

/* > \author Univ. of Tennessee */

/* > \author Univ. of California Berkeley */

/* > \author Univ. of Colorado Denver */

/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup auxOTHERcomputational */

/* > \par Further Details: */

/*  ===================== */

/* > */

/* > \verbatim */

/* > */

/* >  10/02/03: This version has a few statements commented out for thread */

/* >  safety (machine parameters are computed on each entry). SJH. */

/* > */

/* >  05/10/06: Modified from a new version of Ren-Cang Li, use */

/* >     Gragg-Thornton-Warner cubic convergent scheme for better stability. */

/* > \endverbatim */

/* > \par Contributors: */

/*  ================== */

/* > */

/* >     Ren-Cang Li, Computer Science Division, University of California */

/* >     at Berkeley, USA */

/* > */

/*  ===================================================================== */

/* Subroutine */ void slaed6_(integer *kniter, logical *orgati, real *rho, 

  real *d__, real *z__, real *finit, real *tau, integer *info)

{

    /* System generated locals */

    integer i__1;

    real r__1, r__2, r__3, r__4;

    /* Local variables */

    real base;

    integer iter;

    real temp, temp1, temp2, temp3, temp4, a, b, c__, f;

    integer i__;

    logical scale;

    integer niter;

    real small1, small2, fc, df, sminv1, sminv2, dscale[3], sclfac;

    extern real slamch_(char *);

    real zscale[3], erretm, sclinv, ddf, lbd, eta, ubd, eps;

/*  -- LAPACK computational routine (version 3.7.0) -- */

/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */

/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/*     December 2016 */

/*  ===================================================================== */

    /* Parameter adjustments */

    --z__;

    --d__;

    /* Function Body */

    *info = 0;

    if (*orgati) {

  lbd = d__[2];

  ubd = d__[3];

    } else {

  lbd = d__[1];

  ubd = d__[2];

    }

    if (*finit < 0.f) {

  lbd = 0.f;

    } else {

  ubd = 0.f;

    }

    niter = 1;

    *tau = 0.f;

    if (*kniter == 2) {

  if (*orgati) {

      temp = (d__[3] - d__[2]) / 2.f;

      c__ = *rho + z__[1] / (d__[1] - d__[2] - temp);

      a = c__ * (d__[2] + d__[3]) + z__[2] + z__[3];

      b = c__ * d__[2] * d__[3] + z__[2] * d__[3] + z__[3] * d__[2];

  } else {

      temp = (d__[1] - d__[2]) / 2.f;

      c__ = *rho + z__[3] / (d__[3] - d__[2] - temp);

      a = c__ * (d__[1] + d__[2]) + z__[1] + z__[2];

      b = c__ * d__[1] * d__[2] + z__[1] * d__[2] + z__[2] * d__[1];

  }

/* Computing MAX */

  r__1 = abs(a), r__2 = abs(b), r__1 = f2cmax(r__1,r__2), r__2 = abs(c__);

  temp = f2cmax(r__1,r__2);

  a /= temp;

  b /= temp;

  c__ /= temp;

  if (c__ == 0.f) {

      *tau = b / a;

  } else if (a <= 0.f) {

      *tau = (a - sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)))) / (

        c__ * 2.f);

  } else {

      *tau = b * 2.f / (a + sqrt((r__1 = a * a - b * 4.f * c__, abs(

        r__1))));

  }

  if (*tau < lbd || *tau > ubd) {

      *tau = (lbd + ubd) / 2.f;

  }

  if (d__[1] == *tau || d__[2] == *tau || d__[3] == *tau) {

      *tau = 0.f;

  } else {

      temp = *finit + *tau * z__[1] / (d__[1] * (d__[1] - *tau)) + *tau 

        * z__[2] / (d__[2] * (d__[2] - *tau)) + *tau * z__[3] / (

        d__[3] * (d__[3] - *tau));

      if (temp <= 0.f) {

    lbd = *tau;

      } else {

    ubd = *tau;

      }

      if (abs(*finit) <= abs(temp)) {

    *tau = 0.f;

      }

  }

    }

/*     get machine parameters for possible scaling to avoid overflow */

/*     modified by Sven: parameters SMALL1, SMINV1, SMALL2, */

/*     SMINV2, EPS are not SAVEd anymore between one call to the */

/*     others but recomputed at each call */

    eps = slamch_("Epsilon");

    base = slamch_("Base");

    i__1 = (integer) (log(slamch_("SafMin")) / log(base) / 3.f);

    small1 = pow_ri(&base, &i__1);

    sminv1 = 1.f / small1;

    small2 = small1 * small1;

    sminv2 = sminv1 * sminv1;

/*     Determine if scaling of inputs necessary to avoid overflow */

/*     when computing 1/TEMP**3 */

    if (*orgati) {

/* Computing MIN */

  r__3 = (r__1 = d__[2] - *tau, abs(r__1)), r__4 = (r__2 = d__[3] - *

    tau, abs(r__2));

  temp = f2cmin(r__3,r__4);

    } else {

/* Computing MIN */

  r__3 = (r__1 = d__[1] - *tau, abs(r__1)), r__4 = (r__2 = d__[2] - *

    tau, abs(r__2));

  temp = f2cmin(r__3,r__4);

    }

    scale = FALSE_;

    if (temp <= small1) {

  scale = TRUE_;

  if (temp <= small2) {

/*        Scale up by power of radix nearest 1/SAFMIN**(2/3) */

      sclfac = sminv2;

      sclinv = small2;

  } else {

/*        Scale up by power of radix nearest 1/SAFMIN**(1/3) */

      sclfac = sminv1;

      sclinv = small1;

  }

/*        Scaling up safe because D, Z, TAU scaled elsewhere to be O(1) */

  for (i__ = 1; i__ <= 3; ++i__) {

      dscale[i__ - 1] = d__[i__] * sclfac;

      zscale[i__ - 1] = z__[i__] * sclfac;

/* L10: */

  }

  *tau *= sclfac;

  lbd *= sclfac;

  ubd *= sclfac;

    } else {

/*        Copy D and Z to DSCALE and ZSCALE */

  for (i__ = 1; i__ <= 3; ++i__) {

      dscale[i__ - 1] = d__[i__];

      zscale[i__ - 1] = z__[i__];

/* L20: */

  }

    }

    fc = 0.f;

    df = 0.f;

    ddf = 0.f;

    for (i__ = 1; i__ <= 3; ++i__) {

  temp = 1.f / (dscale[i__ - 1] - *tau);

  temp1 = zscale[i__ - 1] * temp;

  temp2 = temp1 * temp;

  temp3 = temp2 * temp;

  fc += temp1 / dscale[i__ - 1];

  df += temp2;

  ddf += temp3;

/* L30: */

    }

    f = *finit + *tau * fc;

    if (abs(f) <= 0.f) {

  goto L60;

    }

    if (f <= 0.f) {

  lbd = *tau;

    } else {

  ubd = *tau;

    }

/*        Iteration begins -- Use Gragg-Thornton-Warner cubic convergent */

/*                            scheme */

/*     It is not hard to see that */

/*           1) Iterations will go up monotonically */

/*              if FINIT < 0; */

/*           2) Iterations will go down monotonically */

/*              if FINIT > 0. */

    iter = niter + 1;

    for (niter = iter; niter <= 40; ++niter) {

  if (*orgati) {

      temp1 = dscale[1] - *tau;

      temp2 = dscale[2] - *tau;

  } else {

      temp1 = dscale[0] - *tau;

      temp2 = dscale[1] - *tau;

  }

  a = (temp1 + temp2) * f - temp1 * temp2 * df;

  b = temp1 * temp2 * f;

  c__ = f - (temp1 + temp2) * df + temp1 * temp2 * ddf;

/* Computing MAX */

  r__1 = abs(a), r__2 = abs(b), r__1 = f2cmax(r__1,r__2), r__2 = abs(c__);

  temp = f2cmax(r__1,r__2);

  a /= temp;

  b /= temp;

  c__ /= temp;

  if (c__ == 0.f) {

      eta = b / a;

  } else if (a <= 0.f) {

      eta = (a - sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)))) / (

        c__ * 2.f);

  } else {

      eta = b * 2.f / (a + sqrt((r__1 = a * a - b * 4.f * c__, abs(r__1)

        )));

  }

  if (f * eta >= 0.f) {

      eta = -f / df;

  }

  *tau += eta;

  if (*tau < lbd || *tau > ubd) {

      *tau = (lbd + ubd) / 2.f;

  }

  fc = 0.f;

  erretm = 0.f;

  df = 0.f;

  ddf = 0.f;

  for (i__ = 1; i__ <= 3; ++i__) {

      if (dscale[i__ - 1] - *tau != 0.f) {

    temp = 1.f / (dscale[i__ - 1] - *tau);

    temp1 = zscale[i__ - 1] * temp;

    temp2 = temp1 * temp;

    temp3 = temp2 * temp;

    temp4 = temp1 / dscale[i__ - 1];

    fc += temp4;

    erretm += abs(temp4);

    df += temp2;

    ddf += temp3;

      } else {

    goto L60;

      }

/* L40: */

  }

  f = *finit + *tau * fc;

  erretm = (abs(*finit) + abs(*tau) * erretm) * 8.f + abs(*tau) * df;

  if (abs(f) <= eps * 4.f * erretm || ubd - lbd <= eps * 4.f * abs(*tau)

    ) {

      goto L60;

  }

  if (f <= 0.f) {

      lbd = *tau;

  } else {

      ubd = *tau;

  }

/* L50: */

    }

    *info = 1;

L60:

/*     Undo scaling */

    if (scale) {

  *tau *= sclinv;

    }

    return;

/*     End of SLAED6 */

} /* slaed6_ */