#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_b5 = -1.;

static doublereal c_b6 = 1.;

static integer c__1 = 1;

static doublereal c_b16 = 0.;

/* > \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago

nal form by an orthogonal similarity transformation. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download DLATRD + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */

/*       CHARACTER          UPLO */

/*       INTEGER            LDA, LDW, N, NB */

/*       DOUBLE PRECISION   A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > DLATRD reduces NB rows and columns of a real symmetric matrix A to */

/* > symmetric tridiagonal form by an orthogonal similarity */

/* > transformation Q**T * A * Q, and returns the matrices V and W which are */

/* > needed to apply the transformation to the unreduced part of A. */

/* > */

/* > If UPLO = 'U', DLATRD reduces the last NB rows and columns of a */

/* > matrix, of which the upper triangle is supplied; */

/* > if UPLO = 'L', DLATRD reduces the first NB rows and columns of a */

/* > matrix, of which the lower triangle is supplied. */

/* > */

/* > This is an auxiliary routine called by DSYTRD. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] UPLO */

/* > \verbatim */

/* >          UPLO is CHARACTER*1 */

/* >          Specifies whether the upper or lower triangular part of the */

/* >          symmetric matrix A is stored: */

/* >          = 'U': Upper triangular */

/* >          = 'L': Lower triangular */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >          The order of the matrix A. */

/* > \endverbatim */

/* > */

/* > \param[in] NB */

/* > \verbatim */

/* >          NB is INTEGER */

/* >          The number of rows and columns to be reduced. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, the symmetric matrix A.  If UPLO = 'U', the leading */

/* >          n-by-n upper triangular part of A contains the upper */

/* >          triangular part of the matrix A, and the strictly lower */

/* >          triangular part of A is not referenced.  If UPLO = 'L', the */

/* >          leading n-by-n lower triangular part of A contains the lower */

/* >          triangular part of the matrix A, and the strictly upper */

/* >          triangular part of A is not referenced. */

/* >          On exit: */

/* >          if UPLO = 'U', the last NB columns have been reduced to */

/* >            tridiagonal form, with the diagonal elements overwriting */

/* >            the diagonal elements of A; the elements above the diagonal */

/* >            with the array TAU, represent the orthogonal matrix Q as a */

/* >            product of elementary reflectors; */

/* >          if UPLO = 'L', the first NB columns have been reduced to */

/* >            tridiagonal form, with the diagonal elements overwriting */

/* >            the diagonal elements of A; the elements below the diagonal */

/* >            with the array TAU, represent the  orthogonal matrix Q as a */

/* >            product of elementary reflectors. */

/* >          See Further Details. */

/* > \endverbatim */

/* > */

/* > \param[in] LDA */

/* > \verbatim */

/* >          LDA is INTEGER */

/* >          The leading dimension of the array A.  LDA >= (1,N). */

/* > \endverbatim */

/* > */

/* > \param[out] E */

/* > \verbatim */

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

/* >          If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */

/* >          elements of the last NB columns of the reduced matrix; */

/* >          if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */

/* >          the first NB columns of the reduced matrix. */

/* > \endverbatim */

/* > */

/* > \param[out] TAU */

/* > \verbatim */

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

/* >          The scalar factors of the elementary reflectors, stored in */

/* >          TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */

/* >          See Further Details. */

/* > \endverbatim */

/* > */

/* > \param[out] W */

/* > \verbatim */

/* >          W is DOUBLE PRECISION array, dimension (LDW,NB) */

/* >          The n-by-nb matrix W required to update the unreduced part */

/* >          of A. */

/* > \endverbatim */

/* > */

/* > \param[in] LDW */

/* > \verbatim */

/* >          LDW is INTEGER */

/* >          The leading dimension of the array W. LDW >= f2cmax(1,N). */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup doubleOTHERauxiliary */

/* > \par Further Details: */

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

/* > */

/* > \verbatim */

/* > */

/* >  If UPLO = 'U', the matrix Q is represented as a product of elementary */

/* >  reflectors */

/* > */

/* >     Q = H(n) H(n-1) . . . H(n-nb+1). */

/* > */

/* >  Each H(i) has the form */

/* > */

/* >     H(i) = I - tau * v * v**T */

/* > */

/* >  where tau is a real scalar, and v is a real vector with */

/* >  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */

/* >  and tau in TAU(i-1). */

/* > */

/* >  If UPLO = 'L', the matrix Q is represented as a product of elementary */

/* >  reflectors */

/* > */

/* >     Q = H(1) H(2) . . . H(nb). */

/* > */

/* >  Each H(i) has the form */

/* > */

/* >     H(i) = I - tau * v * v**T */

/* > */

/* >  where tau is a real scalar, and v is a real vector with */

/* >  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */

/* >  and tau in TAU(i). */

/* > */

/* >  The elements of the vectors v together form the n-by-nb matrix V */

/* >  which is needed, with W, to apply the transformation to the unreduced */

/* >  part of the matrix, using a symmetric rank-2k update of the form: */

/* >  A := A - V*W**T - W*V**T. */

/* > */

/* >  The contents of A on exit are illustrated by the following examples */

/* >  with n = 5 and nb = 2: */

/* > */

/* >  if UPLO = 'U':                       if UPLO = 'L': */

/* > */

/* >    (  a   a   a   v4  v5 )              (  d                  ) */

/* >    (      a   a   v4  v5 )              (  1   d              ) */

/* >    (          a   1   v5 )              (  v1  1   a          ) */

/* >    (              d   1  )              (  v1  v2  a   a      ) */

/* >    (                  d  )              (  v1  v2  a   a   a  ) */

/* > */

/* >  where d denotes a diagonal element of the reduced matrix, a denotes */

/* >  an element of the original matrix that is unchanged, and vi denotes */

/* >  an element of the vector defining H(i). */

/* > \endverbatim */

/* > */

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

/* Subroutine */ void dlatrd_(char *uplo, integer *n, integer *nb, doublereal *

  a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, 

  integer *ldw)

{

    /* System generated locals */

    integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;

    /* Local variables */

    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 

      integer *);

    integer i__;

    doublereal alpha;

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

      integer *);

    extern logical lsame_(char *, char *);

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

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

      doublereal *, doublereal *, integer *), daxpy_(integer *, 

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

      dsymv_(char *, integer *, doublereal *, doublereal *, integer *, 

      doublereal *, integer *, doublereal *, doublereal *, integer *), dlarfg_(integer *, doublereal *, doublereal *, integer *,

       doublereal *);

    integer iw;

/*  -- LAPACK auxiliary 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 */

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

/*     Quick return if possible */

    /* Parameter adjustments */

    a_dim1 = *lda;

    a_offset = 1 + a_dim1 * 1;

    a -= a_offset;

    --e;

    --tau;

    w_dim1 = *ldw;

    w_offset = 1 + w_dim1 * 1;

    w -= w_offset;

    /* Function Body */

    if (*n <= 0) {

  return;

    }

    if (lsame_(uplo, "U")) {

/*        Reduce last NB columns of upper triangle */

  i__1 = *n - *nb + 1;

  for (i__ = *n; i__ >= i__1; --i__) {

      iw = i__ - *n + *nb;

      if (i__ < *n) {

/*              Update A(1:i,i) */

    i__2 = *n - i__;

    dgemv_("No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * 

      a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, &

      c_b6, &a[i__ * a_dim1 + 1], &c__1);

    i__2 = *n - i__;

    dgemv_("No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * 

      w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, &

      c_b6, &a[i__ * a_dim1 + 1], &c__1);

      }

      if (i__ > 1) {

/*              Generate elementary reflector H(i) to annihilate */

/*              A(1:i-2,i) */

    i__2 = i__ - 1;

    dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + 

      1], &c__1, &tau[i__ - 1]);

    e[i__ - 1] = a[i__ - 1 + i__ * a_dim1];

    a[i__ - 1 + i__ * a_dim1] = 1.;

/*              Compute W(1:i-1,i) */

    i__2 = i__ - 1;

    dsymv_("Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * 

      a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], &

      c__1);

    if (i__ < *n) {

        i__2 = i__ - 1;

        i__3 = *n - i__;

        dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * 

          w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, &

          c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);

        i__2 = i__ - 1;

        i__3 = *n - i__;

        dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *

           a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], &

          c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);

        i__2 = i__ - 1;

        i__3 = *n - i__;

        dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * 

          a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, &

          c_b16, &w[i__ + 1 + iw * w_dim1], &c__1);

        i__2 = i__ - 1;

        i__3 = *n - i__;

        dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * 

          w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], &

          c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1);

    }

    i__2 = i__ - 1;

    dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1);

    i__2 = i__ - 1;

    alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1],

       &c__1, &a[i__ * a_dim1 + 1], &c__1);

    i__2 = i__ - 1;

    daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * 

      w_dim1 + 1], &c__1);

      }

/* L10: */

  }

    } else {

/*        Reduce first NB columns of lower triangle */

  i__1 = *nb;

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

/*           Update A(i:n,i) */

      i__2 = *n - i__ + 1;

      i__3 = i__ - 1;

      dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda,

         &w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], &

        c__1);

      i__2 = *n - i__ + 1;

      i__3 = i__ - 1;

      dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw,

         &a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], &

        c__1);

      if (i__ < *n) {

/*              Generate elementary reflector H(i) to annihilate */

/*              A(i+2:n,i) */

    i__2 = *n - i__;

/* Computing MIN */

    i__3 = i__ + 2;

    dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[f2cmin(i__3,*n) + 

      i__ * a_dim1], &c__1, &tau[i__]);

    e[i__] = a[i__ + 1 + i__ * a_dim1];

    a[i__ + 1 + i__ * a_dim1] = 1.;

/*              Compute W(i+1:n,i) */

    i__2 = *n - i__;

    dsymv_("Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1]

      , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[

      i__ + 1 + i__ * w_dim1], &c__1);

    i__2 = *n - i__;

    i__3 = i__ - 1;

    dgemv_("Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1],

       ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[

      i__ * w_dim1 + 1], &c__1);

    i__2 = *n - i__;

    i__3 = i__ - 1;

    dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + 

      a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[

      i__ + 1 + i__ * w_dim1], &c__1);

    i__2 = *n - i__;

    i__3 = i__ - 1;

    dgemv_("Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1],

       lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[

      i__ * w_dim1 + 1], &c__1);

    i__2 = *n - i__;

    i__3 = i__ - 1;

    dgemv_("No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + 

      w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[

      i__ + 1 + i__ * w_dim1], &c__1);

    i__2 = *n - i__;

    dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1);

    i__2 = *n - i__;

    alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ * 

      w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1);

    i__2 = *n - i__;

    daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[

      i__ + 1 + i__ * w_dim1], &c__1);

      }

/* L20: */

  }

    }

    return;

/*     End of DLATRD */

} /* dlatrd_ */