#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 doublereal c_b9 = 0.;

static doublereal c_b10 = 1.;

static integer c__0 = 0;

static integer c__1 = 1;

static integer c__2 = 2;

/* > \brief \b DSTEQR */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download DSTEQR + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) */

/*       CHARACTER          COMPZ */

/*       INTEGER            INFO, LDZ, N */

/*       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > DSTEQR computes all eigenvalues and, optionally, eigenvectors of a */

/* > symmetric tridiagonal matrix using the implicit QL or QR method. */

/* > The eigenvectors of a full or band symmetric matrix can also be found */

/* > if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to */

/* > tridiagonal form. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] COMPZ */

/* > \verbatim */

/* >          COMPZ is CHARACTER*1 */

/* >          = 'N':  Compute eigenvalues only. */

/* >          = 'V':  Compute eigenvalues and eigenvectors of the original */

/* >                  symmetric matrix.  On entry, Z must contain the */

/* >                  orthogonal matrix used to reduce the original matrix */

/* >                  to tridiagonal form. */

/* >          = 'I':  Compute eigenvalues and eigenvectors of the */

/* >                  tridiagonal matrix.  Z is initialized to the identity */

/* >                  matrix. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >          The order of the matrix.  N >= 0. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, the diagonal elements of the tridiagonal matrix. */

/* >          On exit, if INFO = 0, the eigenvalues in ascending order. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          E is DOUBLE PRECISION array, dimension (N-1) */

/* >          On entry, the (n-1) subdiagonal elements of the tridiagonal */

/* >          matrix. */

/* >          On exit, E has been destroyed. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, if  COMPZ = 'V', then Z contains the orthogonal */

/* >          matrix used in the reduction to tridiagonal form. */

/* >          On exit, if INFO = 0, then if  COMPZ = 'V', Z contains the */

/* >          orthonormal eigenvectors of the original symmetric matrix, */

/* >          and if COMPZ = 'I', Z contains the orthonormal eigenvectors */

/* >          of the symmetric tridiagonal matrix. */

/* >          If COMPZ = 'N', then Z is not referenced. */

/* > \endverbatim */

/* > */

/* > \param[in] LDZ */

/* > \verbatim */

/* >          LDZ is INTEGER */

/* >          The leading dimension of the array Z.  LDZ >= 1, and if */

/* >          eigenvectors are desired, then  LDZ >= f2cmax(1,N). */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* >          WORK is DOUBLE PRECISION array, dimension (f2cmax(1,2*N-2)) */

/* >          If COMPZ = 'N', then WORK is not referenced. */

/* > \endverbatim */

/* > */

/* > \param[out] INFO */

/* > \verbatim */

/* >          INFO is INTEGER */

/* >          = 0:  successful exit */

/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */

/* >          > 0:  the algorithm has failed to find all the eigenvalues in */

/* >                a total of 30*N iterations; if INFO = i, then i */

/* >                elements of E have not converged to zero; on exit, D */

/* >                and E contain the elements of a symmetric tridiagonal */

/* >                matrix which is orthogonally similar to the original */

/* >                matrix. */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup auxOTHERcomputational */

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

/* Subroutine */ void dsteqr_(char *compz, integer *n, doublereal *d__, 

  doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 

  integer *info)

{

    /* System generated locals */

    integer z_dim1, z_offset, i__1, i__2;

    doublereal d__1, d__2;

    /* Local variables */

    integer lend, jtot;

    extern /* Subroutine */ void dlae2_(doublereal *, doublereal *, doublereal 

      *, doublereal *, doublereal *);

    doublereal b, c__, f, g;

    integer i__, j, k, l, m;

    doublereal p, r__, s;

    extern logical lsame_(char *, char *);

    extern /* Subroutine */ void dlasr_(char *, char *, char *, integer *, 

      integer *, doublereal *, doublereal *, doublereal *, integer *);

    doublereal anorm;

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

      doublereal *, integer *);

    integer l1;

    extern /* Subroutine */ void dlaev2_(doublereal *, doublereal *, 

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

      doublereal *);

    integer lendm1, lendp1;

    extern doublereal dlapy2_(doublereal *, doublereal *);

    integer ii;

    extern doublereal dlamch_(char *);

    integer mm, iscale;

    extern /* Subroutine */ void dlascl_(char *, integer *, integer *, 

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

      integer *, integer *), dlaset_(char *, integer *, integer 

      *, doublereal *, doublereal *, doublereal *, integer *);

    doublereal safmin;

    extern /* Subroutine */ void dlartg_(doublereal *, doublereal *, 

      doublereal *, doublereal *, doublereal *);

    doublereal safmax;

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

    extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);

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

      integer *);

    integer lendsv;

    doublereal ssfmin;

    integer nmaxit, icompz;

    doublereal ssfmax;

    integer lm1, mm1, nm1;

    doublereal rt1, rt2, eps;

    integer lsv;

    doublereal tst, eps2;

/*  -- 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 parameters. */

    /* Parameter adjustments */

    --d__;

    --e;

    z_dim1 = *ldz;

    z_offset = 1 + z_dim1 * 1;

    z__ -= z_offset;

    --work;

    /* Function Body */

    *info = 0;

    if (lsame_(compz, "N")) {

  icompz = 0;

    } else if (lsame_(compz, "V")) {

  icompz = 1;

    } else if (lsame_(compz, "I")) {

  icompz = 2;

    } else {

  icompz = -1;

    }

    if (icompz < 0) {

  *info = -1;

    } else if (*n < 0) {

  *info = -2;

    } else if (*ldz < 1 || icompz > 0 && *ldz < f2cmax(1,*n)) {

  *info = -6;

    }

    if (*info != 0) {

  i__1 = -(*info);

  xerbla_("DSTEQR", &i__1, (ftnlen)6);

  return;

    }

/*     Quick return if possible */

    if (*n == 0) {

  return;

    }

    if (*n == 1) {

  if (icompz == 2) {

      z__[z_dim1 + 1] = 1.;

  }

  return;

    }

/*     Determine the unit roundoff and over/underflow thresholds. */

    eps = dlamch_("E");

/* Computing 2nd power */

    d__1 = eps;

    eps2 = d__1 * d__1;

    safmin = dlamch_("S");

    safmax = 1. / safmin;

    ssfmax = sqrt(safmax) / 3.;

    ssfmin = sqrt(safmin) / eps2;

/*     Compute the eigenvalues and eigenvectors of the tridiagonal */

/*     matrix. */

    if (icompz == 2) {

  dlaset_("Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz);

    }

    nmaxit = *n * 30;

    jtot = 0;

/*     Determine where the matrix splits and choose QL or QR iteration */

/*     for each block, according to whether top or bottom diagonal */

/*     element is smaller. */

    l1 = 1;

    nm1 = *n - 1;

L10:

    if (l1 > *n) {

  goto L160;

    }

    if (l1 > 1) {

  e[l1 - 1] = 0.;

    }

    if (l1 <= nm1) {

  i__1 = nm1;

  for (m = l1; m <= i__1; ++m) {

      tst = (d__1 = e[m], abs(d__1));

      if (tst == 0.) {

    goto L30;

      }

      if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m 

        + 1], abs(d__2))) * eps) {

    e[m] = 0.;

    goto L30;

      }

/* L20: */

  }

    }

    m = *n;

L30:

    l = l1;

    lsv = l;

    lend = m;

    lendsv = lend;

    l1 = m + 1;

    if (lend == l) {

  goto L10;

    }

/*     Scale submatrix in rows and columns L to LEND */

    i__1 = lend - l + 1;

    anorm = dlanst_("M", &i__1, &d__[l], &e[l]);

    iscale = 0;

    if (anorm == 0.) {

  goto L10;

    }

    if (anorm > ssfmax) {

  iscale = 1;

  i__1 = lend - l + 1;

  dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, 

    info);

  i__1 = lend - l;

  dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, 

    info);

    } else if (anorm < ssfmin) {

  iscale = 2;

  i__1 = lend - l + 1;

  dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, 

    info);

  i__1 = lend - l;

  dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, 

    info);

    }

/*     Choose between QL and QR iteration */

    if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {

  lend = lsv;

  l = lendsv;

    }

    if (lend > l) {

/*        QL Iteration */

/*        Look for small subdiagonal element. */

L40:

  if (l != lend) {

      lendm1 = lend - 1;

      i__1 = lendm1;

      for (m = l; m <= i__1; ++m) {

/* Computing 2nd power */

    d__2 = (d__1 = e[m], abs(d__1));

    tst = d__2 * d__2;

    if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m 

      + 1], abs(d__2)) + safmin) {

        goto L60;

    }

/* L50: */

      }

  }

  m = lend;

L60:

  if (m < lend) {

      e[m] = 0.;

  }

  p = d__[l];

  if (m == l) {

      goto L80;

  }

/*        If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */

/*        to compute its eigensystem. */

  if (m == l + 1) {

      if (icompz > 0) {

    dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s);

    work[l] = c__;

    work[*n - 1 + l] = s;

    dlasr_("R", "V", "B", n, &c__2, &work[l], &work[*n - 1 + l], &

      z__[l * z_dim1 + 1], ldz);

      } else {

    dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2);

      }

      d__[l] = rt1;

      d__[l + 1] = rt2;

      e[l] = 0.;

      l += 2;

      if (l <= lend) {

    goto L40;

      }

      goto L140;

  }

  if (jtot == nmaxit) {

      goto L140;

  }

  ++jtot;

/*        Form shift. */

  g = (d__[l + 1] - p) / (e[l] * 2.);

  r__ = dlapy2_(&g, &c_b10);

  g = d__[m] - p + e[l] / (g + d_sign(&r__, &g));

  s = 1.;

  c__ = 1.;

  p = 0.;

/*        Inner loop */

  mm1 = m - 1;

  i__1 = l;

  for (i__ = mm1; i__ >= i__1; --i__) {

      f = s * e[i__];

      b = c__ * e[i__];

      dlartg_(&g, &f, &c__, &s, &r__);

      if (i__ != m - 1) {

    e[i__ + 1] = r__;

      }

      g = d__[i__ + 1] - p;

      r__ = (d__[i__] - g) * s + c__ * 2. * b;

      p = s * r__;

      d__[i__ + 1] = g + p;

      g = c__ * r__ - b;

/*           If eigenvectors are desired, then save rotations. */

      if (icompz > 0) {

    work[i__] = c__;

    work[*n - 1 + i__] = -s;

      }

/* L70: */

  }

/*        If eigenvectors are desired, then apply saved rotations. */

  if (icompz > 0) {

      mm = m - l + 1;

      dlasr_("R", "V", "B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l 

        * z_dim1 + 1], ldz);

  }

  d__[l] -= p;

  e[l] = g;

  goto L40;

/*        Eigenvalue found. */

L80:

  d__[l] = p;

  ++l;

  if (l <= lend) {

      goto L40;

  }

  goto L140;

    } else {

/*        QR Iteration */