#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 SLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous

 transform. Used by sbdsqr. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SLASQ4 + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasq4.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasq4.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasq4.

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, */

/*                          DN1, DN2, TAU, TTYPE, G ) */

/*       INTEGER            I0, N0, N0IN, PP, TTYPE */

/*       REAL               DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU */

/*       REAL               Z( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > SLASQ4 computes an approximation TAU to the smallest eigenvalue */

/* > using values of d from the previous transform. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] I0 */

/* > \verbatim */

/* >          I0 is INTEGER */

/* >        First index. */

/* > \endverbatim */

/* > */

/* > \param[in] N0 */

/* > \verbatim */

/* >          N0 is INTEGER */

/* >        Last index. */

/* > \endverbatim */

/* > */

/* > \param[in] Z */

/* > \verbatim */

/* >          Z is REAL array, dimension ( 4*N0 ) */

/* >        Z holds the qd array. */

/* > \endverbatim */

/* > */

/* > \param[in] PP */

/* > \verbatim */

/* >          PP is INTEGER */

/* >        PP=0 for ping, PP=1 for pong. */

/* > \endverbatim */

/* > */

/* > \param[in] N0IN */

/* > \verbatim */

/* >          N0IN is INTEGER */

/* >        The value of N0 at start of EIGTEST. */

/* > \endverbatim */

/* > */

/* > \param[in] DMIN */

/* > \verbatim */

/* >          DMIN is REAL */

/* >        Minimum value of d. */

/* > \endverbatim */

/* > */

/* > \param[in] DMIN1 */

/* > \verbatim */

/* >          DMIN1 is REAL */

/* >        Minimum value of d, excluding D( N0 ). */

/* > \endverbatim */

/* > */

/* > \param[in] DMIN2 */

/* > \verbatim */

/* >          DMIN2 is REAL */

/* >        Minimum value of d, excluding D( N0 ) and D( N0-1 ). */

/* > \endverbatim */

/* > */

/* > \param[in] DN */

/* > \verbatim */

/* >          DN is REAL */

/* >        d(N) */

/* > \endverbatim */

/* > */

/* > \param[in] DN1 */

/* > \verbatim */

/* >          DN1 is REAL */

/* >        d(N-1) */

/* > \endverbatim */

/* > */

/* > \param[in] DN2 */

/* > \verbatim */

/* >          DN2 is REAL */

/* >        d(N-2) */

/* > \endverbatim */

/* > */

/* > \param[out] TAU */

/* > \verbatim */

/* >          TAU is REAL */

/* >        This is the shift. */

/* > \endverbatim */

/* > */

/* > \param[out] TTYPE */

/* > \verbatim */

/* >          TTYPE is INTEGER */

/* >        Shift type. */

/* > \endverbatim */

/* > */

/* > \param[in,out] G */

/* > \verbatim */

/* >          G is REAL */

/* >        G is passed as an argument in order to save its value between */

/* >        calls to SLASQ4. */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date June 2016 */

/* > \ingroup auxOTHERcomputational */

/* > \par Further Details: */

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

/* > */

/* > \verbatim */

/* > */

/* >  CNST1 = 9/16 */

/* > \endverbatim */

/* > */

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

/* Subroutine */ void slasq4_(integer *i0, integer *n0, real *z__, integer *pp,

   integer *n0in, real *dmin__, real *dmin1, real *dmin2, real *dn, 

  real *dn1, real *dn2, real *tau, integer *ttype, real *g)

{

    /* System generated locals */

    integer i__1;

    real r__1, r__2;

    /* Local variables */

    real s, a2, b1, b2;

    integer i4, nn, np;

    real gam, gap1, gap2;

/*  -- LAPACK computational routine (version 3.7.1) -- */

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

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

/*     June 2016 */

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

/*     A negative DMIN forces the shift to take that absolute value */

/*     TTYPE records the type of shift. */

    /* Parameter adjustments */

    --z__;

    /* Function Body */

    if (*dmin__ <= 0.f) {

  *tau = -(*dmin__);

  *ttype = -1;

  return;

    }

    nn = (*n0 << 2) + *pp;

    if (*n0in == *n0) {

/*        No eigenvalues deflated. */

  if (*dmin__ == *dn || *dmin__ == *dn1) {

      b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]);

      b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]);

      a2 = z__[nn - 7] + z__[nn - 5];

/*           Cases 2 and 3. */

      if (*dmin__ == *dn && *dmin1 == *dn1) {

    gap2 = *dmin2 - a2 - *dmin2 * .25f;

    if (gap2 > 0.f && gap2 > b2) {

        gap1 = a2 - *dn - b2 / gap2 * b2;

    } else {

        gap1 = a2 - *dn - (b1 + b2);

    }

    if (gap1 > 0.f && gap1 > b1) {

/* Computing MAX */

        r__1 = *dn - b1 / gap1 * b1, r__2 = *dmin__ * .5f;

        s = f2cmax(r__1,r__2);

        *ttype = -2;

    } else {

        s = 0.f;

        if (*dn > b1) {

      s = *dn - b1;

        }

        if (a2 > b1 + b2) {

/* Computing MIN */

      r__1 = s, r__2 = a2 - (b1 + b2);

      s = f2cmin(r__1,r__2);

        }

/* Computing MAX */

        r__1 = s, r__2 = *dmin__ * .333f;

        s = f2cmax(r__1,r__2);

        *ttype = -3;

    }

      } else {

/*              Case 4. */

    *ttype = -4;

    s = *dmin__ * .25f;

    if (*dmin__ == *dn) {

        gam = *dn;

        a2 = 0.f;

        if (z__[nn - 5] > z__[nn - 7]) {

      return;

        }

        b2 = z__[nn - 5] / z__[nn - 7];

        np = nn - 9;

    } else {

        np = nn - (*pp << 1);

        gam = *dn1;

        if (z__[np - 4] > z__[np - 2]) {

      return;

        }

        a2 = z__[np - 4] / z__[np - 2];

        if (z__[nn - 9] > z__[nn - 11]) {

      return;

        }

        b2 = z__[nn - 9] / z__[nn - 11];

        np = nn - 13;

    }

/*              Approximate contribution to norm squared from I < NN-1. */

    a2 += b2;

    i__1 = (*i0 << 2) - 1 + *pp;

    for (i4 = np; i4 >= i__1; i4 += -4) {

        if (b2 == 0.f) {

      goto L20;

        }

        b1 = b2;

        if (z__[i4] > z__[i4 - 2]) {

      return;

        }

        b2 *= z__[i4] / z__[i4 - 2];

        a2 += b2;

        if (f2cmax(b2,b1) * 100.f < a2 || .563f < a2) {

      goto L20;

        }

/* L10: */

    }

L20:

    a2 *= 1.05f;

/*              Rayleigh quotient residual bound. */

    if (a2 < .563f) {

        s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);

    }

      }

  } else if (*dmin__ == *dn2) {

/*           Case 5. */

      *ttype = -5;

      s = *dmin__ * .25f;

/*           Compute contribution to norm squared from I > NN-2. */

      np = nn - (*pp << 1);

      b1 = z__[np - 2];

      b2 = z__[np - 6];

      gam = *dn2;

      if (z__[np - 8] > b2 || z__[np - 4] > b1) {

    return;

      }

      a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.f);

/*           Approximate contribution to norm squared from I < NN-2. */

      if (*n0 - *i0 > 2) {

    b2 = z__[nn - 13] / z__[nn - 15];

    a2 += b2;

    i__1 = (*i0 << 2) - 1 + *pp;

    for (i4 = nn - 17; i4 >= i__1; i4 += -4) {

        if (b2 == 0.f) {

      goto L40;

        }

        b1 = b2;

        if (z__[i4] > z__[i4 - 2]) {

      return;

        }

        b2 *= z__[i4] / z__[i4 - 2];

        a2 += b2;

        if (f2cmax(b2,b1) * 100.f < a2 || .563f < a2) {

      goto L40;

        }

/* L30: */

    }

L40:

    a2 *= 1.05f;

      }

      if (a2 < .563f) {

    s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);

      }

  } else {

/*           Case 6, no information to guide us. */

      if (*ttype == -6) {

    *g += (1.f - *g) * .333f;

      } else if (*ttype == -18) {

    *g = .083250000000000005f;

      } else {

    *g = .25f;

      }

      s = *g * *dmin__;

      *ttype = -6;

  }

    } else if (*n0in == *n0 + 1) {

/*        One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */

  if (*dmin1 == *dn1 && *dmin2 == *dn2) {

/*           Cases 7 and 8. */

      *ttype = -7;

      s = *dmin1 * .333f;

      if (z__[nn - 5] > z__[nn - 7]) {

    return;

      }

      b1 = z__[nn - 5] / z__[nn - 7];

      b2 = b1;

      if (b2 == 0.f) {

    goto L60;

      }

      i__1 = (*i0 << 2) - 1 + *pp;

      for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {

    a2 = b1;

    if (z__[i4] > z__[i4 - 2]) {

        return;

    }

    b1 *= z__[i4] / z__[i4 - 2];

    b2 += b1;

    if (f2cmax(b1,a2) * 100.f < b2) {

        goto L60;

    }

/* L50: */

      }

L60:

      b2 = sqrt(b2 * 1.05f);

/* Computing 2nd power */

      r__1 = b2;

      a2 = *dmin1 / (r__1 * r__1 + 1.f);

      gap2 = *dmin2 * .5f - a2;

      if (gap2 > 0.f && gap2 > b2 * a2) {

/* Computing MAX */

    r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);

    s = f2cmax(r__1,r__2);

      } else {

/* Computing MAX */

    r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);

    s = f2cmax(r__1,r__2);

    *ttype = -8;

      }

  } else {

/*           Case 9. */

      s = *dmin1 * .25f;

      if (*dmin1 == *dn1) {

    s = *dmin1 * .5f;

      }

      *ttype = -9;

  }

    } else if (*n0in == *n0 + 2) {

/*        Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. */

/*        Cases 10 and 11. */

  if (*dmin2 == *dn2 && z__[nn - 5] * 2.f < z__[nn - 7]) {

      *ttype = -10;

      s = *dmin2 * .333f;

      if (z__[nn - 5] > z__[nn - 7]) {

    return;

      }

      b1 = z__[nn - 5] / z__[nn - 7];

      b2 = b1;

      if (b2 == 0.f) {

    goto L80;

      }

      i__1 = (*i0 << 2) - 1 + *pp;

      for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {

    if (z__[i4] > z__[i4 - 2]) {

        return;

    }

    b1 *= z__[i4] / z__[i4 - 2];

    b2 += b1;

    if (b1 * 100.f < b2) {

        goto L80;

    }

/* L70: */

      }

L80:

      b2 = sqrt(b2 * 1.05f);

/* Computing 2nd power */

      r__1 = b2;

      a2 = *dmin2 / (r__1 * r__1 + 1.f);

      gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[

        nn - 9]) - a2;

      if (gap2 > 0.f && gap2 > b2 * a2) {

/* Computing MAX */

    r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);

    s = f2cmax(r__1,r__2);

      } else {

/* Computing MAX */

    r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);

    s = f2cmax(r__1,r__2);

      }

  } else {

      s = *dmin2 * .25f;

      *ttype = -11;

  }

    } else if (*n0in > *n0 + 2) {

/*        Case 12, more than two eigenvalues deflated. No information. */

  s = 0.f;

  *ttype = -12;

    }

    *tau = s;

    return;

/*     End of SLASQ4 */

} /* slasq4_ */