#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 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);}
#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++ */




/* Table of constant values */

static doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;

/* > \brief \b ZTZRQF */

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

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download ZTZRQF + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztzrqf.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztzrqf.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztzrqf.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO ) */

/*       INTEGER            INFO, LDA, M, N */
/*       COMPLEX*16         A( LDA, * ), TAU( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > This routine is deprecated and has been replaced by routine ZTZRZF. */
/* > */
/* > ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A */
/* > to upper triangular form by means of unitary transformations. */
/* > */
/* > The upper trapezoidal matrix A is factored as */
/* > */
/* >    A = ( R  0 ) * Z, */
/* > */
/* > where Z is an N-by-N unitary matrix and R is an M-by-M upper */
/* > triangular matrix. */
/* > \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 >= M. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is COMPLEX*16 array, dimension (LDA,N) */
/* >          On entry, the leading M-by-N upper trapezoidal part of the */
/* >          array A must contain the matrix to be factorized. */
/* >          On exit, the leading M-by-M upper triangular part of A */
/* >          contains the upper triangular matrix R, and elements M+1 to */
/* >          N of the first M rows of A, with the array TAU, represent the */
/* >          unitary matrix Z as a product of M elementary reflectors. */
/* > \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 COMPLEX*16 array, dimension (M) */
/* >          The scalar factors of the elementary reflectors. */
/* > \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 December 2016 */

/* > \ingroup complex16OTHERcomputational */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  The  factorization is obtained by Householder's method.  The kth */
/* >  transformation matrix, Z( k ), whose conjugate transpose is used to */
/* >  introduce zeros into the (m - k + 1)th row of A, is given in the form */
/* > */
/* >     Z( k ) = ( I     0   ), */
/* >              ( 0  T( k ) ) */
/* > */
/* >  where */
/* > */
/* >     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ), */
/* >                                                   (   0    ) */
/* >                                                   ( z( k ) ) */
/* > */
/* >  tau is a scalar and z( k ) is an ( n - m ) element vector. */
/* >  tau and z( k ) are chosen to annihilate the elements of the kth row */
/* >  of X. */
/* > */
/* >  The scalar tau is returned in the kth element of TAU and the vector */
/* >  u( k ) in the kth row of A, such that the elements of z( k ) are */
/* >  in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in */
/* >  the upper triangular part of A. */
/* > */
/* >  Z is given by */
/* > */
/* >     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ). */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void ztzrqf_(integer *m, integer *n, doublecomplex *a, 
	integer *lda, doublecomplex *tau, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    doublecomplex z__1, z__2;

    /* Local variables */
    integer i__, k;
    doublecomplex alpha;
    extern /* Subroutine */ void zgerc_(integer *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *), zgemv_(char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, doublecomplex *, integer *);
    integer m1;
    extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    extern int xerbla_(char *, integer *, ftnlen);
    extern void zlarfg_(integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *), zlacgv_(integer *, 
	    doublecomplex *, integer *);


/*  -- LAPACK computational routine (version 3.7.0) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     December 2016 */


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


/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --tau;

    /* Function Body */
    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < *m) {
	*info = -2;
    } else if (*lda < f2cmax(1,*m)) {
	*info = -4;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZTZRQF", &i__1, 6);
	return;
    }

/*     Perform the factorization. */

    if (*m == 0) {
	return;
    }
    if (*m == *n) {
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    i__2 = i__;
	    tau[i__2].r = 0., tau[i__2].i = 0.;
/* L10: */
	}
    } else {
/* Computing MIN */
	i__1 = *m + 1;
	m1 = f2cmin(i__1,*n);
	for (k = *m; k >= 1; --k) {

/*           Use a Householder reflection to zero the kth row of A. */
/*           First set up the reflection. */

	    i__1 = k + k * a_dim1;
	    d_cnjg(&z__1, &a[k + k * a_dim1]);
	    a[i__1].r = z__1.r, a[i__1].i = z__1.i;
	    i__1 = *n - *m;
	    zlacgv_(&i__1, &a[k + m1 * a_dim1], lda);
	    i__1 = k + k * a_dim1;
	    alpha.r = a[i__1].r, alpha.i = a[i__1].i;
	    i__1 = *n - *m + 1;
	    zlarfg_(&i__1, &alpha, &a[k + m1 * a_dim1], lda, &tau[k]);
	    i__1 = k + k * a_dim1;
	    a[i__1].r = alpha.r, a[i__1].i = alpha.i;
	    i__1 = k;
	    d_cnjg(&z__1, &tau[k]);
	    tau[i__1].r = z__1.r, tau[i__1].i = z__1.i;

	    i__1 = k;
	    if ((tau[i__1].r != 0. || tau[i__1].i != 0.) && k > 1) {

/*              We now perform the operation  A := A*P( k )**H. */

/*              Use the first ( k - 1 ) elements of TAU to store  a( k ), */
/*              where  a( k ) consists of the first ( k - 1 ) elements of */
/*              the  kth column  of  A.  Also  let  B  denote  the  first */
/*              ( k - 1 ) rows of the last ( n - m ) columns of A. */

		i__1 = k - 1;
		zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &tau[1], &c__1);

/*              Form   w = a( k ) + B*z( k )  in TAU. */

		i__1 = k - 1;
		i__2 = *n - *m;
		zgemv_("No transpose", &i__1, &i__2, &c_b1, &a[m1 * a_dim1 + 
			1], lda, &a[k + m1 * a_dim1], lda, &c_b1, &tau[1], &
			c__1);

/*              Now form  a( k ) := a( k ) - conjg(tau)*w */
/*              and       B      := B      - conjg(tau)*w*z( k )**H. */

		i__1 = k - 1;
		d_cnjg(&z__2, &tau[k]);
		z__1.r = -z__2.r, z__1.i = -z__2.i;
		zaxpy_(&i__1, &z__1, &tau[1], &c__1, &a[k * a_dim1 + 1], &
			c__1);
		i__1 = k - 1;
		i__2 = *n - *m;
		d_cnjg(&z__2, &tau[k]);
		z__1.r = -z__2.r, z__1.i = -z__2.i;
		zgerc_(&i__1, &i__2, &z__1, &tau[1], &c__1, &a[k + m1 * 
			a_dim1], lda, &a[m1 * a_dim1 + 1], lda);
	    }
/* L20: */
	}
    }

    return;

/*     End of ZTZRQF */

} /* ztzrqf_ */

