#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 doublereal c_b6 = 1.;

/* > \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download DLARFT + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) */

/*       CHARACTER          DIRECT, STOREV */

/*       INTEGER            K, LDT, LDV, N */

/*       DOUBLE PRECISION   T( LDT, * ), TAU( * ), V( LDV, * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > DLARFT forms the triangular factor T of a real block reflector H */

/* > of order n, which is defined as a product of k elementary reflectors. */

/* > */

/* > If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */

/* > */

/* > If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */

/* > */

/* > If STOREV = 'C', the vector which defines the elementary reflector */

/* > H(i) is stored in the i-th column of the array V, and */

/* > */

/* >    H  =  I - V * T * V**T */

/* > */

/* > If STOREV = 'R', the vector which defines the elementary reflector */

/* > H(i) is stored in the i-th row of the array V, and */

/* > */

/* >    H  =  I - V**T * T * V */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] DIRECT */

/* > \verbatim */

/* >          DIRECT is CHARACTER*1 */

/* >          Specifies the order in which the elementary reflectors are */

/* >          multiplied to form the block reflector: */

/* >          = 'F': H = H(1) H(2) . . . H(k) (Forward) */

/* >          = 'B': H = H(k) . . . H(2) H(1) (Backward) */

/* > \endverbatim */

/* > */

/* > \param[in] STOREV */

/* > \verbatim */

/* >          STOREV is CHARACTER*1 */

/* >          Specifies how the vectors which define the elementary */

/* >          reflectors are stored (see also Further Details): */

/* >          = 'C': columnwise */

/* >          = 'R': rowwise */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >          The order of the block reflector H. N >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] K */

/* > \verbatim */

/* >          K is INTEGER */

/* >          The order of the triangular factor T (= the number of */

/* >          elementary reflectors). K >= 1. */

/* > \endverbatim */

/* > */

/* > \param[in] V */

/* > \verbatim */

/* >          V is DOUBLE PRECISION array, dimension */

/* >                               (LDV,K) if STOREV = 'C' */

/* >                               (LDV,N) if STOREV = 'R' */

/* >          The matrix V. See further details. */

/* > \endverbatim */

/* > */

/* > \param[in] LDV */

/* > \verbatim */

/* >          LDV is INTEGER */

/* >          The leading dimension of the array V. */

/* >          If STOREV = 'C', LDV >= f2cmax(1,N); if STOREV = 'R', LDV >= K. */

/* > \endverbatim */

/* > */

/* > \param[in] TAU */

/* > \verbatim */

/* >          TAU is DOUBLE PRECISION array, dimension (K) */

/* >          TAU(i) must contain the scalar factor of the elementary */

/* >          reflector H(i). */

/* > \endverbatim */

/* > */

/* > \param[out] T */

/* > \verbatim */

/* >          T is DOUBLE PRECISION array, dimension (LDT,K) */

/* >          The k by k triangular factor T of the block reflector. */

/* >          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */

/* >          lower triangular. The rest of the array is not used. */

/* > \endverbatim */

/* > */

/* > \param[in] LDT */

/* > \verbatim */

/* >          LDT is INTEGER */

/* >          The leading dimension of the array T. LDT >= K. */

/* > \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 */

/* > */

/* >  The shape of the matrix V and the storage of the vectors which define */

/* >  the H(i) is best illustrated by the following example with n = 5 and */

/* >  k = 3. The elements equal to 1 are not stored. */

/* > */

/* >  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R': */

/* > */

/* >               V = (  1       )                 V = (  1 v1 v1 v1 v1 ) */

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

/* >                   ( v1 v2  1 )                     (        1 v3 v3 ) */

/* >                   ( v1 v2 v3 ) */

/* >                   ( v1 v2 v3 ) */

/* > */

/* >  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R': */

/* > */

/* >               V = ( v1 v2 v3 )                 V = ( v1 v1  1       ) */

/* >                   ( v1 v2 v3 )                     ( v2 v2 v2  1    ) */

/* >                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 ) */

/* >                   (     1 v3 ) */

/* >                   (        1 ) */

/* > \endverbatim */

/* > */

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

/* Subroutine */ void dlarft_(char *direct, char *storev, integer *n, integer *

  k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, 

  integer *ldt)

{

    /* System generated locals */

    integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;

    doublereal d__1;

    /* Local variables */

    integer i__, j;

    extern logical lsame_(char *, char *);

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

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

      doublereal *, doublereal *, integer *);

    integer lastv;

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

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

    integer prevlastv;

/*  -- 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 */

    v_dim1 = *ldv;

    v_offset = 1 + v_dim1 * 1;

    v -= v_offset;

    --tau;

    t_dim1 = *ldt;

    t_offset = 1 + t_dim1 * 1;

    t -= t_offset;

    /* Function Body */

    if (*n == 0) {

  return;

    }

    if (lsame_(direct, "F")) {

  prevlastv = *n;

  i__1 = *k;

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

      prevlastv = f2cmax(i__,prevlastv);

      if (tau[i__] == 0.) {

/*              H(i)  =  I */

    i__2 = i__;

    for (j = 1; j <= i__2; ++j) {

        t[j + i__ * t_dim1] = 0.;

    }

      } else {

/*              general case */

    if (lsame_(storev, "C")) {

/*                 Skip any trailing zeros. */

        i__2 = i__ + 1;

        for (lastv = *n; lastv >= i__2; --lastv) {

      if (v[lastv + i__ * v_dim1] != 0.) {

          myexit_();

      }

        }

        i__2 = i__ - 1;

        for (j = 1; j <= i__2; ++j) {

      t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1];

        }

        j = f2cmin(lastv,prevlastv);

/*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) */

        i__2 = j - i__;

        i__3 = i__ - 1;

        d__1 = -tau[i__];

        dgemv_("Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 + 

          v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, &

          c_b6, &t[i__ * t_dim1 + 1], &c__1);

    } else {

/*                 Skip any trailing zeros. */

        i__2 = i__ + 1;

        for (lastv = *n; lastv >= i__2; --lastv) {

      if (v[i__ + lastv * v_dim1] != 0.) {

          myexit_();

      }

        }

        i__2 = i__ - 1;

        for (j = 1; j <= i__2; ++j) {

      t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1];

        }

        j = f2cmin(lastv,prevlastv);

/*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T */

        i__2 = i__ - 1;

        i__3 = j - i__;

        d__1 = -tau[i__];

        dgemv_("No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) *

           v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], 

          ldv, &c_b6, &t[i__ * t_dim1 + 1], &c__1);

    }

/*              T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */

    i__2 = i__ - 1;

    dtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[

      t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);

    t[i__ + i__ * t_dim1] = tau[i__];

    if (i__ > 1) {

        prevlastv = f2cmax(prevlastv,lastv);

    } else {

        prevlastv = lastv;

    }

      }

  }

    } else {

  prevlastv = 1;

  for (i__ = *k; i__ >= 1; --i__) {

      if (tau[i__] == 0.) {

/*              H(i)  =  I */

    i__1 = *k;

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

        t[j + i__ * t_dim1] = 0.;

    }

      } else {

/*              general case */

    if (i__ < *k) {

        if (lsame_(storev, "C")) {

/*                    Skip any leading zeros. */

      i__1 = i__ - 1;

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

          if (v[lastv + i__ * v_dim1] != 0.) {

        myexit_();

          }

      }

      i__1 = *k;

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

          t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__ 

            + j * v_dim1];

      }

      j = f2cmax(lastv,prevlastv);

/*                    T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) */

      i__1 = *n - *k + i__ - j;

      i__2 = *k - i__;

      d__1 = -tau[i__];

      dgemv_("Transpose", &i__1, &i__2, &d__1, &v[j + (i__ 

        + 1) * v_dim1], ldv, &v[j + i__ * v_dim1], &

        c__1, &c_b6, &t[i__ + 1 + i__ * t_dim1], &

        c__1);

        } else {

/*                    Skip any leading zeros. */

      i__1 = i__ - 1;

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

          if (v[i__ + lastv * v_dim1] != 0.) {

        myexit_();

          }

      }

      i__1 = *k;

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

          t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k 

            + i__) * v_dim1];

      }

      j = f2cmax(lastv,prevlastv);

/*                    T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T */

      i__1 = *k - i__;

      i__2 = *n - *k + i__ - j;

      d__1 = -tau[i__];

      dgemv_("No transpose", &i__1, &i__2, &d__1, &v[i__ + 

        1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], 

        ldv, &c_b6, &t[i__ + 1 + i__ * t_dim1], &c__1);

        }

/*                 T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */

        i__1 = *k - i__;

        dtrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__ 

          + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *

           t_dim1], &c__1)

          ;

        if (i__ > 1) {

      prevlastv = f2cmin(prevlastv,lastv);

        } else {

      prevlastv = lastv;

        }

    }

    t[i__ + i__ * t_dim1] = tau[i__];

      }

  }

    }

    return;

/*     End of DLARFT */

} /* dlarft_ */