#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_b4 = -1.;

static doublereal c_b5 = 1.;

static integer c__1 = 1;

static doublereal c_b16 = 0.;

/* > \brief \b DLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download DLABRD + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, */

/*                          LDY ) */

/*       INTEGER            LDA, LDX, LDY, M, N, NB */

/*       DOUBLE PRECISION   A( LDA, * ), D( * ), E( * ), TAUP( * ), */

/*      $                   TAUQ( * ), X( LDX, * ), Y( LDY, * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > DLABRD reduces the first NB rows and columns of a real general */

/* > m by n matrix A to upper or lower bidiagonal form by an orthogonal */

/* > transformation Q**T * A * P, and returns the matrices X and Y which */

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

/* > */

/* > If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */

/* > bidiagonal form. */

/* > */

/* > This is an auxiliary routine called by DGEBRD */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] M */

/* > \verbatim */

/* >          M is INTEGER */

/* >          The number of rows in the matrix A. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >          The number of columns in the matrix A. */

/* > \endverbatim */

/* > */

/* > \param[in] NB */

/* > \verbatim */

/* >          NB is INTEGER */

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

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, the m by n general matrix to be reduced. */

/* >          On exit, the first NB rows and columns of the matrix are */

/* >          overwritten; the rest of the array is unchanged. */

/* >          If m >= n, elements on and below the diagonal in the first NB */

/* >            columns, with the array TAUQ, represent the orthogonal */

/* >            matrix Q as a product of elementary reflectors; and */

/* >            elements above the diagonal in the first NB rows, with the */

/* >            array TAUP, represent the orthogonal matrix P as a product */

/* >            of elementary reflectors. */

/* >          If m < n, elements below the diagonal in the first NB */

/* >            columns, with the array TAUQ, represent the orthogonal */

/* >            matrix Q as a product of elementary reflectors, and */

/* >            elements on and above the diagonal in the first NB rows, */

/* >            with the array TAUP, represent the orthogonal matrix P 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 >= f2cmax(1,M). */

/* > \endverbatim */

/* > */

/* > \param[out] D */

/* > \verbatim */

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

/* >          The diagonal elements of the first NB rows and columns of */

/* >          the reduced matrix.  D(i) = A(i,i). */

/* > \endverbatim */

/* > */

/* > \param[out] E */

/* > \verbatim */

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

/* >          The off-diagonal elements of the first NB rows and columns of */

/* >          the reduced matrix. */

/* > \endverbatim */

/* > */

/* > \param[out] TAUQ */

/* > \verbatim */

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

/* >          The scalar factors of the elementary reflectors which */

/* >          represent the orthogonal matrix Q. See Further Details. */

/* > \endverbatim */

/* > */

/* > \param[out] TAUP */

/* > \verbatim */

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

/* >          The scalar factors of the elementary reflectors which */

/* >          represent the orthogonal matrix P. See Further Details. */

/* > \endverbatim */

/* > */

/* > \param[out] X */

/* > \verbatim */

/* >          X is DOUBLE PRECISION array, dimension (LDX,NB) */

/* >          The m-by-nb matrix X required to update the unreduced part */

/* >          of A. */

/* > \endverbatim */

/* > */

/* > \param[in] LDX */

/* > \verbatim */

/* >          LDX is INTEGER */

/* >          The leading dimension of the array X. LDX >= f2cmax(1,M). */

/* > \endverbatim */

/* > */

/* > \param[out] Y */

/* > \verbatim */

/* >          Y is DOUBLE PRECISION array, dimension (LDY,NB) */

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

/* >          of A. */

/* > \endverbatim */

/* > */

/* > \param[in] LDY */

/* > \verbatim */

/* >          LDY is INTEGER */

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

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date June 2017 */

/* > \ingroup doubleOTHERauxiliary */

/* > \par Further Details: */

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

/* > */

/* > \verbatim */

/* > */

/* >  The matrices Q and P are represented as products of elementary */

/* >  reflectors: */

/* > */

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

/* > */

/* >  Each H(i) and G(i) has the form: */

/* > */

/* >     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T */

/* > */

/* >  where tauq and taup are real scalars, and v and u are real vectors. */

/* > */

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

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

/* >  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */

/* > */

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

/* >  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */

/* >  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */

/* > */

/* >  The elements of the vectors v and u together form the m-by-nb matrix */

/* >  V and the nb-by-n matrix U**T which are needed, with X and Y, to apply */

/* >  the transformation to the unreduced part of the matrix, using a block */

/* >  update of the form:  A := A - V*Y**T - X*U**T. */

/* > */

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

/* >  with nb = 2: */

/* > */

/* >  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n): */

/* > */

/* >    (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 ) */

/* >    (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 ) */

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

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

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

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

/* > */

/* >  where a denotes an element of the original matrix which is unchanged, */

/* >  vi denotes an element of the vector defining H(i), and ui an element */

/* >  of the vector defining G(i). */

/* > \endverbatim */

/* > */

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

/* Subroutine */ void dlabrd_(integer *m, integer *n, integer *nb, doublereal *

  a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, 

  doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer 

  *ldy)

{

    /* System generated locals */

    integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, 

      i__3;

    /* Local variables */

    integer i__;

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

      integer *), dgemv_(char *, integer *, integer *, doublereal *, 

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

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

       doublereal *, integer *, doublereal *);

/*  -- LAPACK auxiliary 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 2017 */

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

/*     Quick return if possible */

    /* Parameter adjustments */

    a_dim1 = *lda;

    a_offset = 1 + a_dim1 * 1;

    a -= a_offset;

    --d__;

    --e;

    --tauq;

    --taup;

    x_dim1 = *ldx;

    x_offset = 1 + x_dim1 * 1;

    x -= x_offset;

    y_dim1 = *ldy;

    y_offset = 1 + y_dim1 * 1;

    y -= y_offset;

    /* Function Body */

    if (*m <= 0 || *n <= 0) {

  return;

    }

    if (*m >= *n) {

/*        Reduce to upper bidiagonal form */

  i__1 = *nb;

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

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

      i__2 = *m - i__ + 1;

      i__3 = i__ - 1;

      dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda,

         &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], &

        c__1);

      i__2 = *m - i__ + 1;

      i__3 = i__ - 1;

      dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx,

         &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * 

        a_dim1], &c__1);

/*           Generate reflection Q(i) to annihilate A(i+1:m,i) */

      i__2 = *m - i__ + 1;

/* Computing MIN */

      i__3 = i__ + 1;

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

        a_dim1], &c__1, &tauq[i__]);

      d__[i__] = a[i__ + i__ * a_dim1];

      if (i__ < *n) {

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

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

    i__2 = *m - i__ + 1;

    i__3 = *n - i__;

    dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * 

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

      y[i__ + 1 + i__ * y_dim1], &c__1);

    i__2 = *m - i__ + 1;

    i__3 = i__ - 1;

    dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], 

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

      y_dim1 + 1], &c__1);

    i__2 = *n - i__;

    i__3 = i__ - 1;

    dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + 

      y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[

      i__ + 1 + i__ * y_dim1], &c__1);

    i__2 = *m - i__ + 1;

    i__3 = i__ - 1;

    dgemv_("Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], 

      ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * 

      y_dim1 + 1], &c__1);

    i__2 = i__ - 1;

    i__3 = *n - i__;

    dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * 

      a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, 

      &y[i__ + 1 + i__ * y_dim1], &c__1);

    i__2 = *n - i__;

    dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);

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

    i__2 = *n - i__;

    dgemv_("No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + 

      y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + (

      i__ + 1) * a_dim1], lda);

    i__2 = i__ - 1;

    i__3 = *n - i__;

    dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * 

      a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[

      i__ + (i__ + 1) * a_dim1], lda);

/*              Generate reflection P(i) to annihilate A(i,i+2:n) */

    i__2 = *n - i__;

/* Computing MIN */

    i__3 = i__ + 2;

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

      i__3,*n) * a_dim1], lda, &taup[i__]);

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

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

/*              Compute X(i+1:m,i) */

    i__2 = *m - i__;

    i__3 = *n - i__;

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

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

      lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1);

    i__2 = *n - i__;

    dgemv_("Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], 

      ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[

      i__ * x_dim1 + 1], &c__1);

    i__2 = *m - i__;

    dgemv_("No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + 

      a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[

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

      c_b16, &x[i__ * x_dim1 + 1], &c__1);

    i__2 = *m - i__;

    i__3 = i__ - 1;

    dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + 

      x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[

      i__ + 1 + i__ * x_dim1], &c__1);

    i__2 = *m - i__;

    dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);

      }

/* L10: */

  }

    } else {

/*        Reduce to lower bidiagonal form */

  i__1 = *nb;

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

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

      i__2 = *n - i__ + 1;

      i__3 = i__ - 1;

      dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy,

         &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], 

        lda);

      i__2 = i__ - 1;

      i__3 = *n - i__ + 1;

      dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], 

        lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1],

         lda);

/*           Generate reflection P(i) to annihilate A(i,i+1:n) */

      i__2 = *n - i__ + 1;

/* Computing MIN */

      i__3 = i__ + 1;

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

        a_dim1], lda, &taup[i__]);

      d__[i__] = a[i__ + i__ * a_dim1];

      if (i__ < *m) {

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

/*              Compute X(i+1:m,i) */

    i__2 = *m - i__;

    i__3 = *n - i__ + 1;

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

       a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &

      x[i__ + 1 + i__ * x_dim1], &c__1);

    i__2 = *n - i__ + 1;

    i__3 = i__ - 1;

    dgemv_("Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], 

      ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * 

      x_dim1 + 1], &c__1);

    i__2 = *m - i__;

    i__3 = i__ - 1;

    dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + 

      a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[

      i__ + 1 + i__ * x_dim1], &c__1);

    i__2 = i__ - 1;

    i__3 = *n - i__ + 1;

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

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

       x_dim1 + 1], &c__1);

    i__2 = *m - i__;

    i__3 = i__ - 1;

    dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + 

      x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[

      i__ + 1 + i__ * x_dim1], &c__1);

    i__2 = *m - i__;

    dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);

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

    i__2 = *m - i__;

    i__3 = i__ - 1;

    dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + 

      a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + 

      1 + i__ * a_dim1], &c__1);

    i__2 = *m - i__;

    dgemv_("No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + 

      x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[

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

/*              Generate reflection Q(i) to annihilate A(i+2:m,i) */

    i__2 = *m - i__;

/* Computing MIN */

    i__3 = i__ + 2;

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

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

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

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

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

    i__2 = *m - i__;

    i__3 = *n - i__;

    dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + 

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

      &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1);

    i__2 = *m - i__;

    i__3 = i__ - 1;

    dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1],

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

      i__ * y_dim1 + 1], &c__1);

    i__2 = *n - i__;

    i__3 = i__ - 1;

    dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + 

      y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[

      i__ + 1 + i__ * y_dim1], &c__1);

    i__2 = *m - i__;

    dgemv_("Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], 

      ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[

      i__ * y_dim1 + 1], &c__1);

    i__2 = *n - i__;

    dgemv_("Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 

      + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ 

      + 1 + i__ * y_dim1], &c__1);

    i__2 = *n - i__;

    dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);

      }

/* L20: */

  }

    }

    return;

/*     End of DLABRD */

} /* dlabrd_ */