#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++ */



/*
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/




/* Table of constant values */

static integer c__1 = 1;

/* > \brief \b SGEQPF */

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

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

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

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

/*       SUBROUTINE SGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO ) */

/*       INTEGER            INFO, LDA, M, N */
/*       INTEGER            JPVT( * ) */
/*       REAL               A( LDA, * ), TAU( * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > This routine is deprecated and has been replaced by routine SGEQP3. */
/* > */
/* > SGEQPF computes a QR factorization with column pivoting of a */
/* > real M-by-N matrix A: A*P = Q*R. */
/* > \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 upper triangle of the array contains the */
/* >          f2cmin(M,N)-by-N upper triangular matrix R; the elements */
/* >          below the diagonal, together with the array TAU, */
/* >          represent the orthogonal matrix Q as a product of */
/* >          f2cmin(m,n) elementary reflectors. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[in,out] JPVT */
/* > \verbatim */
/* >          JPVT is INTEGER array, dimension (N) */
/* >          On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */
/* >          to the front of A*P (a leading column); if JPVT(i) = 0, */
/* >          the i-th column of A is a free column. */
/* >          On exit, if JPVT(i) = k, then the i-th column of A*P */
/* >          was the k-th column of A. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* >          TAU is REAL array, dimension (f2cmin(M,N)) */
/* >          The scalar factors of the elementary reflectors. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (3*N) */
/* > \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 realGEcomputational */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  The matrix Q is represented as a product of elementary reflectors */
/* > */
/* >     Q = H(1) H(2) . . . H(n) */
/* > */
/* >  Each H(i) has the form */
/* > */
/* >     H = 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:m) is stored on exit in A(i+1:m,i). */
/* > */
/* >  The matrix P is represented in jpvt as follows: If */
/* >     jpvt(j) = i */
/* >  then the jth column of P is the ith canonical unit vector. */
/* > */
/* >  Partial column norm updating strategy modified by */
/* >    Z. Drmac and Z. Bujanovic, Dept. of Mathematics, */
/* >    University of Zagreb, Croatia. */
/* >  -- April 2011                                                      -- */
/* >  For more details see LAPACK Working Note 176. */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void sgeqpf_(integer *m, integer *n, real *a, integer *lda, 
	integer *jpvt, real *tau, real *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    real r__1, r__2;

    /* Local variables */
    real temp, temp2;
    extern real snrm2_(integer *, real *, integer *);
    integer i__, j;
    real tol3z;
    extern /* Subroutine */ void slarf_(char *, integer *, integer *, real *, 
	    integer *, real *, real *, integer *, real *);
    integer itemp;
    extern /* Subroutine */ void sswap_(integer *, real *, integer *, real *, 
	    integer *), sgeqr2_(integer *, integer *, real *, integer *, real 
	    *, real *, integer *);
    integer ma;
    extern /* Subroutine */ void sorm2r_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *);
    integer mn;
    extern real slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern void slarfg_(
	    integer *, real *, real *, integer *, real *);
    extern integer isamax_(integer *, real *, integer *);
    real aii;
    integer pvt;


/*  -- 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 arguments */

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

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

    mn = f2cmin(*m,*n);
    tol3z = sqrt(slamch_("Epsilon"));

/*     Move initial columns up front */

    itemp = 1;
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if (jpvt[i__] != 0) {
	    if (i__ != itemp) {
		sswap_(m, &a[i__ * a_dim1 + 1], &c__1, &a[itemp * a_dim1 + 1],
			 &c__1);
		jpvt[i__] = jpvt[itemp];
		jpvt[itemp] = i__;
	    } else {
		jpvt[i__] = i__;
	    }
	    ++itemp;
	} else {
	    jpvt[i__] = i__;
	}
/* L10: */
    }
    --itemp;

/*     Compute the QR factorization and update remaining columns */

    if (itemp > 0) {
	ma = f2cmin(itemp,*m);
	sgeqr2_(m, &ma, &a[a_offset], lda, &tau[1], &work[1], info);
	if (ma < *n) {
	    i__1 = *n - ma;
	    sorm2r_("Left", "Transpose", m, &i__1, &ma, &a[a_offset], lda, &
		    tau[1], &a[(ma + 1) * a_dim1 + 1], lda, &work[1], info);
	}
    }

    if (itemp < mn) {

/*        Initialize partial column norms. The first n elements of */
/*        work store the exact column norms. */

	i__1 = *n;
	for (i__ = itemp + 1; i__ <= i__1; ++i__) {
	    i__2 = *m - itemp;
	    work[i__] = snrm2_(&i__2, &a[itemp + 1 + i__ * a_dim1], &c__1);
	    work[*n + i__] = work[i__];
/* L20: */
	}

/*        Compute factorization */

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

/*           Determine ith pivot column and swap if necessary */

	    i__2 = *n - i__ + 1;
	    pvt = i__ - 1 + isamax_(&i__2, &work[i__], &c__1);

	    if (pvt != i__) {
		sswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
			c__1);
		itemp = jpvt[pvt];
		jpvt[pvt] = jpvt[i__];
		jpvt[i__] = itemp;
		work[pvt] = work[i__];
		work[*n + pvt] = work[*n + i__];
	    }

/*           Generate elementary reflector H(i) */

	    if (i__ < *m) {
		i__2 = *m - i__ + 1;
		slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + 1 + i__ * 
			a_dim1], &c__1, &tau[i__]);
	    } else {
		slarfg_(&c__1, &a[*m + *m * a_dim1], &a[*m + *m * a_dim1], &
			c__1, &tau[*m]);
	    }

	    if (i__ < *n) {

/*              Apply H(i) to A(i:m,i+1:n) from the left */

		aii = a[i__ + i__ * a_dim1];
		a[i__ + i__ * a_dim1] = 1.f;
		i__2 = *m - i__ + 1;
		i__3 = *n - i__;
		slarf_("LEFT", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
			tau[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[(*
			n << 1) + 1]);
		a[i__ + i__ * a_dim1] = aii;
	    }

/*           Update partial column norms */

	    i__2 = *n;
	    for (j = i__ + 1; j <= i__2; ++j) {
		if (work[j] != 0.f) {

/*                 NOTE: The following 4 lines follow from the analysis in */
/*                 Lapack Working Note 176. */

		    temp = (r__1 = a[i__ + j * a_dim1], abs(r__1)) / work[j];
/* Computing MAX */
		    r__1 = 0.f, r__2 = (temp + 1.f) * (1.f - temp);
		    temp = f2cmax(r__1,r__2);
/* Computing 2nd power */
		    r__1 = work[j] / work[*n + j];
		    temp2 = temp * (r__1 * r__1);
		    if (temp2 <= tol3z) {
			if (*m - i__ > 0) {
			    i__3 = *m - i__;
			    work[j] = snrm2_(&i__3, &a[i__ + 1 + j * a_dim1], 
				    &c__1);
			    work[*n + j] = work[j];
			} else {
			    work[j] = 0.f;
			    work[*n + j] = 0.f;
			}
		    } else {
			work[j] *= sqrt(temp);
		    }
		}
/* L30: */
	    }

/* L40: */
	}
    }
    return;

/*     End of SGEQPF */

} /* sgeqpf_ */

