#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)

*/

/* Table of constant values */

static integer c__1 = 1;

static integer c__2 = 2;

static integer c__10 = 10;

static integer c__3 = 3;

static integer c__4 = 4;

static integer c__11 = 11;

/* > \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix assoc

iated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download DLASQ2 + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq2.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq2.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq2.

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE DLASQ2( N, Z, INFO ) */

/*       INTEGER            INFO, N */

/*       DOUBLE PRECISION   Z( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > DLASQ2 computes all the eigenvalues of the symmetric positive */

/* > definite tridiagonal matrix associated with the qd array Z to high */

/* > relative accuracy are computed to high relative accuracy, in the */

/* > absence of denormalization, underflow and overflow. */

/* > */

/* > To see the relation of Z to the tridiagonal matrix, let L be a */

/* > unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and */

/* > let U be an upper bidiagonal matrix with 1's above and diagonal */

/* > Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the */

/* > symmetric tridiagonal to which it is similar. */

/* > */

/* > Note : DLASQ2 defines a logical variable, IEEE, which is true */

/* > on machines which follow ieee-754 floating-point standard in their */

/* > handling of infinities and NaNs, and false otherwise. This variable */

/* > is passed to DLASQ3. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >        The number of rows and columns in the matrix. N >= 0. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          Z is DOUBLE PRECISION array, dimension ( 4*N ) */

/* >        On entry Z holds the qd array. On exit, entries 1 to N hold */

/* >        the eigenvalues in decreasing order, Z( 2*N+1 ) holds the */

/* >        trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If */

/* >        N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) */

/* >        holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of */

/* >        shifts that failed. */

/* > \endverbatim */

/* > */

/* > \param[out] INFO */

/* > \verbatim */

/* >          INFO is INTEGER */

/* >        = 0: successful exit */

/* >        < 0: if the i-th argument is a scalar and had an illegal */

/* >             value, then INFO = -i, if the i-th argument is an */

/* >             array and the j-entry had an illegal value, then */

/* >             INFO = -(i*100+j) */

/* >        > 0: the algorithm failed */

/* >              = 1, a split was marked by a positive value in E */

/* >              = 2, current block of Z not diagonalized after 100*N */

/* >                   iterations (in inner while loop).  On exit Z holds */

/* >                   a qd array with the same eigenvalues as the given Z. */

/* >              = 3, termination criterion of outer while loop not met */

/* >                   (program created more than N unreduced blocks) */

/* > \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 */

/* > */

/* >  Local Variables: I0:N0 defines a current unreduced segment of Z. */

/* >  The shifts are accumulated in SIGMA. Iteration count is in ITER. */

/* >  Ping-pong is controlled by PP (alternates between 0 and 1). */

/* > \endverbatim */

/* > */

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

/* Subroutine */ void dlasq2_(integer *n, doublereal *z__, integer *info)

{

    /* System generated locals */

    integer i__1, i__2, i__3;

    doublereal d__1, d__2;

    /* Local variables */

    logical ieee;

    integer nbig;

    doublereal dmin__, emin, emax;

    integer kmin, ndiv, iter;

    doublereal qmin, temp, qmax, zmax;

    integer splt;

    doublereal dmin1, dmin2, d__, e, g;

    integer k;

    doublereal s, t;

    integer nfail;

    doublereal desig, trace, sigma;

    integer iinfo;

    doublereal tempe, tempq;

    integer i0, i1, i4, n0, n1, ttype;

    extern /* Subroutine */ void dlasq3_(integer *, integer *, doublereal *, 

      integer *, doublereal *, doublereal *, doublereal *, doublereal *,

       integer *, integer *, integer *, logical *, integer *, 

      doublereal *, doublereal *, doublereal *, doublereal *, 

      doublereal *, doublereal *, doublereal *);

    doublereal dn;

    extern doublereal dlamch_(char *);

    integer pp;

    doublereal deemin;

    integer iwhila, iwhilb;

    doublereal oldemn, safmin;

    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);

    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 

      integer *, integer *, ftnlen, ftnlen);

    extern /* Subroutine */ void dlasrt_(char *, integer *, doublereal *, 

      integer *);

    doublereal dn1, dn2, dee, eps, tau, tol;

    integer ipn4;

    doublereal tol2;

/*  -- 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 */

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

/*     Test the input arguments. */

/*     (in case DLASQ2 is not called by DLASQ1) */

    /* Parameter adjustments */

    --z__;

    /* Function Body */

    *info = 0;

    eps = dlamch_("Precision");

    safmin = dlamch_("Safe minimum");

    tol = eps * 100.;

/* Computing 2nd power */

    d__1 = tol;

    tol2 = d__1 * d__1;

    if (*n < 0) {

  *info = -1;

  xerbla_("DLASQ2", &c__1, (ftnlen)6);

  return;

    } else if (*n == 0) {

  return;

    } else if (*n == 1) {

/*        1-by-1 case. */

  if (z__[1] < 0.) {

      *info = -201;

      xerbla_("DLASQ2", &c__2, (ftnlen)6);

  }

  return;

    } else if (*n == 2) {

/*        2-by-2 case. */

  if (z__[1] < 0.) {

      *info = -201;

      xerbla_("DLASQ2", &c__2, (ftnlen)6);

      return;

  } else if (z__[2] < 0.) {

      *info = -202;

      xerbla_("DLASQ2", &c__2, (ftnlen)6);

      return;

  } else if (z__[3] < 0.) {

      *info = -203;

      xerbla_("DLASQ2", &c__2, (ftnlen)6);

      return;

  } else if (z__[3] > z__[1]) {

      d__ = z__[3];

      z__[3] = z__[1];

      z__[1] = d__;

  }

  z__[5] = z__[1] + z__[2] + z__[3];

  if (z__[2] > z__[3] * tol2) {

      t = (z__[1] - z__[3] + z__[2]) * .5;

      s = z__[3] * (z__[2] / t);

      if (s <= t) {

    s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.) + 1.)));

      } else {

    s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s)));

      }

      t = z__[1] + (s + z__[2]);

      z__[3] *= z__[1] / t;

      z__[1] = t;

  }

  z__[2] = z__[3];

  z__[6] = z__[2] + z__[1];

  return;

    }

/*     Check for negative data and compute sums of q's and e's. */

    z__[*n * 2] = 0.;

    emin = z__[2];

    qmax = 0.;

    zmax = 0.;

    d__ = 0.;

    e = 0.;

    i__1 = *n - 1 << 1;

    for (k = 1; k <= i__1; k += 2) {

  if (z__[k] < 0.) {

      *info = -(k + 200);

      xerbla_("DLASQ2", &c__2, (ftnlen)6);

      return;

  } else if (z__[k + 1] < 0.) {

      *info = -(k + 201);

      xerbla_("DLASQ2", &c__2, (ftnlen)6);

      return;

  }

  d__ += z__[k];

  e += z__[k + 1];

/* Computing MAX */

  d__1 = qmax, d__2 = z__[k];

  qmax = f2cmax(d__1,d__2);

/* Computing MIN */

  d__1 = emin, d__2 = z__[k + 1];

  emin = f2cmin(d__1,d__2);

/* Computing MAX */

  d__1 = f2cmax(qmax,zmax), d__2 = z__[k + 1];

  zmax = f2cmax(d__1,d__2);

/* L10: */

    }

    if (z__[(*n << 1) - 1] < 0.) {

  *info = -((*n << 1) + 199);

  xerbla_("DLASQ2", &c__2, (ftnlen)6);

  return;

    }

    d__ += z__[(*n << 1) - 1];

/* Computing MAX */

    d__1 = qmax, d__2 = z__[(*n << 1) - 1];

    qmax = f2cmax(d__1,d__2);

    zmax = f2cmax(qmax,zmax);

/*     Check for diagonality. */

    if (e == 0.) {

  i__1 = *n;

  for (k = 2; k <= i__1; ++k) {

      z__[k] = z__[(k << 1) - 1];

/* L20: */

  }

  dlasrt_("D", n, &z__[1], &iinfo);

  z__[(*n << 1) - 1] = d__;

  return;

    }

    trace = d__ + e;

/*     Check for zero data. */

    if (trace == 0.) {

  z__[(*n << 1) - 1] = 0.;

  return;

    }

/*     Check whether the machine is IEEE conformable. */

    ieee = ilaenv_(&c__10, "DLASQ2", "N", &c__1, &c__2, &c__3, &c__4, (ftnlen)

      6, (ftnlen)1) == 1 && ilaenv_(&c__11, "DLASQ2", "N", &c__1, &c__2,

       &c__3, &c__4, (ftnlen)6, (ftnlen)1) == 1;

/*     Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */

    for (k = *n << 1; k >= 2; k += -2) {

  z__[k * 2] = 0.;

  z__[(k << 1) - 1] = z__[k];

  z__[(k << 1) - 2] = 0.;

  z__[(k << 1) - 3] = z__[k - 1];

/* L30: */

    }

    i0 = 1;

    n0 = *n;

/*     Reverse the qd-array, if warranted. */

    if (z__[(i0 << 2) - 3] * 1.5 < z__[(n0 << 2) - 3]) {

  ipn4 = i0 + n0 << 2;

  i__1 = i0 + n0 - 1 << 1;

  for (i4 = i0 << 2; i4 <= i__1; i4 += 4) {

      temp = z__[i4 - 3];

      z__[i4 - 3] = z__[ipn4 - i4 - 3];

      z__[ipn4 - i4 - 3] = temp;

      temp = z__[i4 - 1];

      z__[i4 - 1] = z__[ipn4 - i4 - 5];

      z__[ipn4 - i4 - 5] = temp;

/* L40: */

  }

    }

/*     Initial split checking via dqd and Li's test. */

    pp = 0;

    for (k = 1; k <= 2; ++k) {

  d__ = z__[(n0 << 2) + pp - 3];

  i__1 = (i0 << 2) + pp;

  for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) {

      if (z__[i4 - 1] <= tol2 * d__) {

    z__[i4 - 1] = 0.;

    d__ = z__[i4 - 3];

      } else {

    d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1]));

      }

/* L50: */

  }

/*        dqd maps Z to ZZ plus Li's test. */

  emin = z__[(i0 << 2) + pp + 1];

  d__ = z__[(i0 << 2) + pp - 3];

  i__1 = (n0 - 1 << 2) + pp;

  for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) {

      z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1];

      if (z__[i4 - 1] <= tol2 * d__) {

    z__[i4 - 1] = 0.;

    z__[i4 - (pp << 1) - 2] = d__;

    z__[i4 - (pp << 1)] = 0.;

    d__ = z__[i4 + 1];

      } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] && 

        safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) {

    temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2];

    z__[i4 - (pp << 1)] = z__[i4 - 1] * temp;

    d__ *= temp;

      } else {

    z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - (

      pp << 1) - 2]);

    d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]);

      }

/* Computing MIN */

      d__1 = emin, d__2 = z__[i4 - (pp << 1)];

      emin = f2cmin(d__1,d__2);

/* L60: */

  }

  z__[(n0 << 2) - pp - 2] = d__;

/*        Now find qmax. */

  qmax = z__[(i0 << 2) - pp - 2];

  i__1 = (n0 << 2) - pp - 2;

  for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) {

/* Computing MAX */

      d__1 = qmax, d__2 = z__[i4];

      qmax = f2cmax(d__1,d__2);

/* L70: */

  }

/*        Prepare for the next iteration on K. */

  pp = 1 - pp;

/* L80: */

    }

/*     Initialise variables to pass to DLASQ3. */

    ttype = 0;

    dmin1 = 0.;

    dmin2 = 0.;

    dn = 0.;

    dn1 = 0.;

    dn2 = 0.;

    g = 0.;

    tau = 0.;

    iter = 2;

    nfail = 0;

    ndiv = n0 - i0 << 1;

    i__1 = *n + 1;

    for (iwhila = 1; iwhila <= i__1; ++iwhila) {

  if (n0 < 1) {

      goto L170;

  }

/*        While array unfinished do */

/*        E(N0) holds the value of SIGMA when submatrix in I0:N0 */

/*        splits from the rest of the array, but is negated. */

  desig = 0.;

  if (n0 == *n) {

      sigma = 0.;

  } else {

      sigma = -z__[(n0 << 2) - 1];

  }

  if (sigma < 0.) {

      *info = 1;

      return;

  }

/*        Find last unreduced submatrix's top index I0, find QMAX and */

/*        EMIN. Find Gershgorin-type bound if Q's much greater than E's. */

  emax = 0.;

  if (n0 > i0) {

      emin = (d__1 = z__[(n0 << 2) - 5], abs(d__1));

  } else {

      emin = 0.;

  }

  qmin = z__[(n0 << 2) - 3];

  qmax = qmin;

  for (i4 = n0 << 2; i4 >= 8; i4 += -4) {

      if (z__[i4 - 5] <= 0.) {

    goto L100;

      }

      if (qmin >= emax * 4.) {

/* Computing MIN */

    d__1 = qmin, d__2 = z__[i4 - 3];

    qmin = f2cmin(d__1,d__2);

/* Computing MAX */