#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 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);}

#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)}

/*  -- translated by f2c (version 20000121).

   You must link the resulting object file with the libraries:

  -lf2c -lm   (in that order)

*/

/* Table of constant values */

static integer c__1 = 1;

static integer c_n1 = -1;

static integer c__3 = 3;

static integer c__2 = 2;

/* > \brief \b SGELQF */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SGELQF + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */

/*       INTEGER            INFO, LDA, LWORK, M, N */

/*       REAL               A( LDA, * ), TAU( * ), WORK( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > SGELQF computes an LQ factorization of a real M-by-N matrix A: */

/* > */

/* >    A = ( L 0 ) *  Q */

/* > */

/* > where: */

/* > */

/* >    Q is a N-by-N orthogonal matrix; */

/* >    L is an lower-triangular M-by-M matrix; */

/* >    0 is a M-by-(N-M) zero matrix, if M < N. */

/* > */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] M */

/* > \verbatim */

/* >          M is INTEGER */

/* >          The number of rows of the matrix A.  M >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >          The number of columns of the matrix A.  N >= 0. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, the M-by-N matrix A. */

/* >          On exit, the elements on and below the diagonal of the array */

/* >          contain the m-by-f2cmin(m,n) lower trapezoidal matrix L (L is */

/* >          lower triangular if m <= n); the elements above 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 >= f2cmax(1,M). */

/* > \endverbatim */

/* > */

/* > \param[out] TAU */

/* > \verbatim */

/* >          TAU is REAL array, dimension (f2cmin(M,N)) */

/* >          The scalar factors of the elementary reflectors (see Further */

/* >          Details). */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* >          WORK is REAL array, dimension (MAX(1,LWORK)) */

/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/* > \endverbatim */

/* > */

/* > \param[in] LWORK */

/* > \verbatim */

/* >          LWORK is INTEGER */

/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,M). */

/* >          For optimum performance LWORK >= M*NB, where NB is the */

/* >          optimal blocksize. */

/* > */

/* >          If LWORK = -1, then a workspace query is assumed; the routine */

/* >          only calculates the optimal size of the WORK array, returns */

/* >          this value as the first entry of the WORK array, and no error */

/* >          message related to LWORK is issued by XERBLA. */

/* > \endverbatim */

/* > */

/* > \param[out] INFO */

/* > \verbatim */

/* >          INFO is INTEGER */

/* >          = 0:  successful exit */

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

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date November 2019 */

/* > \ingroup realGEcomputational */

/* > \par Further Details: */

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

/* > */

/* > \verbatim */

/* > */

/* >  The matrix Q is represented as a product of elementary reflectors */

/* > */

/* >     Q = H(k) . . . H(2) H(1), where k = f2cmin(m,n). */

/* > */

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

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

/* > \endverbatim */

/* > */

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

/* Subroutine */ void sgelqf_(integer *m, integer *n, real *a, integer *lda, 

  real *tau, real *work, integer *lwork, integer *info)

{

    /* System generated locals */

    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;

    /* Local variables */

    integer i__, k, nbmin, iinfo;

    extern /* Subroutine */ void sgelq2_(integer *, integer *, real *, integer 

      *, real *, real *, integer *);

    integer ib, nb, nx;

    extern /* Subroutine */ void slarfb_(char *, char *, char *, char *, 

      integer *, integer *, integer *, real *, integer *, real *, 

      integer *, real *, integer *, real *, integer *);

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

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

      integer *, integer *, ftnlen, ftnlen);

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

      real *, integer *, real *, real *, integer *);

    integer ldwork, lwkopt;

    logical lquery;

    integer iws;

/*  -- LAPACK computational routine (version 3.9.0) -- */

/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */

/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/*     November 2019 */

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

/*     Test the input arguments */

    /* Parameter adjustments */

    a_dim1 = *lda;

    a_offset = 1 + a_dim1 * 1;

    a -= a_offset;

    --tau;

    --work;

    /* Function Body */

    *info = 0;

    nb = ilaenv_(&c__1, "SGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)

      1);

    lwkopt = *m * nb;

    work[1] = (real) lwkopt;

    lquery = *lwork == -1;

    if (*m < 0) {

  *info = -1;

    } else if (*n < 0) {

  *info = -2;

    } else if (*lda < f2cmax(1,*m)) {

  *info = -4;

    } else if (*lwork < f2cmax(1,*m) && ! lquery) {

  *info = -7;

    }

    if (*info != 0) {

  i__1 = -(*info);

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

  return;

    } else if (lquery) {

  return;

    }

/*     Quick return if possible */

    k = f2cmin(*m,*n);

    if (k == 0) {

  work[1] = 1.f;

  return;

    }

    nbmin = 2;

    nx = 0;

    iws = *m;

    if (nb > 1 && nb < k) {

/*        Determine when to cross over from blocked to unblocked code. */

/* Computing MAX */

  i__1 = 0, i__2 = ilaenv_(&c__3, "SGELQF", " ", m, n, &c_n1, &c_n1, (

    ftnlen)6, (ftnlen)1);

  nx = f2cmax(i__1,i__2);

  if (nx < k) {

/*           Determine if workspace is large enough for blocked code. */

      ldwork = *m;

      iws = ldwork * nb;

      if (*lwork < iws) {

/*              Not enough workspace to use optimal NB:  reduce NB and */

/*              determine the minimum value of NB. */

    nb = *lwork / ldwork;

/* Computing MAX */

    i__1 = 2, i__2 = ilaenv_(&c__2, "SGELQF", " ", m, n, &c_n1, &

      c_n1, (ftnlen)6, (ftnlen)1);

    nbmin = f2cmax(i__1,i__2);

      }

  }

    }

    if (nb >= nbmin && nb < k && nx < k) {

/*        Use blocked code initially */

  i__1 = k - nx;

  i__2 = nb;

  for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {

/* Computing MIN */

      i__3 = k - i__ + 1;

      ib = f2cmin(i__3,nb);

/*           Compute the LQ factorization of the current block */

/*           A(i:i+ib-1,i:n) */

      i__3 = *n - i__ + 1;

      sgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[

        1], &iinfo);

      if (i__ + ib <= *m) {

/*              Form the triangular factor of the block reflector */

/*              H = H(i) H(i+1) . . . H(i+ib-1) */

    i__3 = *n - i__ + 1;

    slarft_("Forward", "Rowwise", &i__3, &ib, &a[i__ + i__ * 

      a_dim1], lda, &tau[i__], &work[1], &ldwork);

/*              Apply H to A(i+ib:m,i:n) from the right */

    i__3 = *m - i__ - ib + 1;

    i__4 = *n - i__ + 1;

    slarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3, 

      &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &

      ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + 

      1], &ldwork);

      }

/* L10: */

  }

    } else {

  i__ = 1;

    }

/*     Use unblocked code to factor the last or only block. */

    if (i__ <= k) {

  i__2 = *m - i__ + 1;

  i__1 = *n - i__ + 1;

  sgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]

    , &iinfo);

    }

    work[1] = (real) iws;

    return;

/*     End of SGELQF */

} /* sgelqf_ */