OpenBLAS/lapack-netlib/SRC/slaqps.c

#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 real c_b8 = -1.f;
static real c_b9 = 1.f;
static real c_b16 = 0.f;

/* > \brief \b SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by us
ing BLAS level 3. */

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

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

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

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

/*       SUBROUTINE SLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, */
/*                          VN2, AUXV, F, LDF ) */

/*       INTEGER            KB, LDA, LDF, M, N, NB, OFFSET */
/*       INTEGER            JPVT( * ) */
/*       REAL               A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ), */
/*      $                   VN1( * ), VN2( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SLAQPS computes a step of QR factorization with column pivoting */
/* > of a real M-by-N matrix A by using Blas-3.  It tries to factorize */
/* > NB columns from A starting from the row OFFSET+1, and updates all */
/* > of the matrix with Blas-3 xGEMM. */
/* > */
/* > In some cases, due to catastrophic cancellations, it cannot */
/* > factorize NB columns.  Hence, the actual number of factorized */
/* > columns is returned in KB. */
/* > */
/* > Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. */
/* > \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] OFFSET */
/* > \verbatim */
/* >          OFFSET is INTEGER */
/* >          The number of rows of A that have been factorized in */
/* >          previous steps. */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* >          NB is INTEGER */
/* >          The number of columns to factorize. */
/* > \endverbatim */
/* > */
/* > \param[out] KB */
/* > \verbatim */
/* >          KB is INTEGER */
/* >          The number of columns actually factorized. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA,N) */
/* >          On entry, the M-by-N matrix A. */
/* >          On exit, block A(OFFSET+1:M,1:KB) is the triangular */
/* >          factor obtained and block A(1:OFFSET,1:N) has been */
/* >          accordingly pivoted, but no factorized. */
/* >          The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has */
/* >          been updated. */
/* > \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) */
/* >          JPVT(I) = K <==> Column K of the full matrix A has been */
/* >          permuted into position I in AP. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* >          TAU is REAL array, dimension (KB) */
/* >          The scalar factors of the elementary reflectors. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VN1 */
/* > \verbatim */
/* >          VN1 is REAL array, dimension (N) */
/* >          The vector with the partial column norms. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VN2 */
/* > \verbatim */
/* >          VN2 is REAL array, dimension (N) */
/* >          The vector with the exact column norms. */
/* > \endverbatim */
/* > */
/* > \param[in,out] AUXV */
/* > \verbatim */
/* >          AUXV is REAL array, dimension (NB) */
/* >          Auxiliary vector. */
/* > \endverbatim */
/* > */
/* > \param[in,out] F */
/* > \verbatim */
/* >          F is REAL array, dimension (LDF,NB) */
/* >          Matrix F**T = L*Y**T*A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDF */
/* > \verbatim */
/* >          LDF is INTEGER */
/* >          The leading dimension of the array F. LDF >= f2cmax(1,N). */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup realOTHERauxiliary */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
/* >    X. Sun, Computer Science Dept., Duke University, USA */
/* > */
/* > \n */
/* >  Partial column norm updating strategy modified on April 2011 */
/* >    Z. Drmac and Z. Bujanovic, Dept. of Mathematics, */
/* >    University of Zagreb, Croatia. */

/* > \par References: */
/*  ================ */
/* > */
/* > LAPACK Working Note 176 */

/* > \htmlonly */
/* > <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a> */
/* > \endhtmlonly */

/*  ===================================================================== */
/* Subroutine */ void slaqps_(integer *m, integer *n, integer *offset, integer 
	*nb, integer *kb, real *a, integer *lda, integer *jpvt, real *tau, 
	real *vn1, real *vn2, real *auxv, real *f, integer *ldf)
{
    /* System generated locals */
    integer a_dim1, a_offset, f_dim1, f_offset, i__1, i__2;
    real r__1, r__2;

    /* Local variables */
    real temp, temp2;
    extern real snrm2_(integer *, real *, integer *);
    integer j, k;
    real tol3z;
    extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    integer itemp;
    extern /* Subroutine */ void sgemv_(char *, integer *, integer *, real *, 
	    real *, integer *, real *, integer *, real *, real *, integer *), sswap_(integer *, real *, integer *, real *, integer *);
    integer rk;
    extern real slamch_(char *);
    extern /* Subroutine */ void slarfg_(integer *, real *, real *, integer *, 
	    real *);
    integer lsticc;
    extern integer isamax_(integer *, real *, integer *);
    integer lastrk;
    real akk;
    integer pvt;


/*  -- 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 */


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


    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --jpvt;
    --tau;
    --vn1;
    --vn2;
    --auxv;
    f_dim1 = *ldf;
    f_offset = 1 + f_dim1 * 1;
    f -= f_offset;

    /* Function Body */
/* Computing MIN */
    i__1 = *m, i__2 = *n + *offset;
    lastrk = f2cmin(i__1,i__2);
    lsticc = 0;
    k = 0;
    tol3z = sqrt(slamch_("Epsilon"));

/*     Beginning of while loop. */

L10:
    if (k < *nb && lsticc == 0) {
	++k;
	rk = *offset + k;

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

	i__1 = *n - k + 1;
	pvt = k - 1 + isamax_(&i__1, &vn1[k], &c__1);
	if (pvt != k) {
	    sswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
	    i__1 = k - 1;
	    sswap_(&i__1, &f[pvt + f_dim1], ldf, &f[k + f_dim1], ldf);
	    itemp = jpvt[pvt];
	    jpvt[pvt] = jpvt[k];
	    jpvt[k] = itemp;
	    vn1[pvt] = vn1[k];
	    vn2[pvt] = vn2[k];
	}

/*        Apply previous Householder reflectors to column K: */
/*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**T. */

	if (k > 1) {
	    i__1 = *m - rk + 1;
	    i__2 = k - 1;
	    sgemv_("No transpose", &i__1, &i__2, &c_b8, &a[rk + a_dim1], lda, 
		    &f[k + f_dim1], ldf, &c_b9, &a[rk + k * a_dim1], &c__1);
	}

/*        Generate elementary reflector H(k). */

	if (rk < *m) {
	    i__1 = *m - rk + 1;
	    slarfg_(&i__1, &a[rk + k * a_dim1], &a[rk + 1 + k * a_dim1], &
		    c__1, &tau[k]);
	} else {
	    slarfg_(&c__1, &a[rk + k * a_dim1], &a[rk + k * a_dim1], &c__1, &
		    tau[k]);
	}

	akk = a[rk + k * a_dim1];
	a[rk + k * a_dim1] = 1.f;

/*        Compute Kth column of F: */

/*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**T*A(RK:M,K). */

	if (k < *n) {
	    i__1 = *m - rk + 1;
	    i__2 = *n - k;
	    sgemv_("Transpose", &i__1, &i__2, &tau[k], &a[rk + (k + 1) * 
		    a_dim1], lda, &a[rk + k * a_dim1], &c__1, &c_b16, &f[k + 
		    1 + k * f_dim1], &c__1);
	}

/*        Padding F(1:K,K) with zeros. */

	i__1 = k;
	for (j = 1; j <= i__1; ++j) {
	    f[j + k * f_dim1] = 0.f;
/* L20: */
	}

/*        Incremental updating of F: */
/*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**T */
/*                    *A(RK:M,K). */

	if (k > 1) {
	    i__1 = *m - rk + 1;
	    i__2 = k - 1;
	    r__1 = -tau[k];
	    sgemv_("Transpose", &i__1, &i__2, &r__1, &a[rk + a_dim1], lda, &a[
		    rk + k * a_dim1], &c__1, &c_b16, &auxv[1], &c__1);

	    i__1 = k - 1;
	    sgemv_("No transpose", n, &i__1, &c_b9, &f[f_dim1 + 1], ldf, &
		    auxv[1], &c__1, &c_b9, &f[k * f_dim1 + 1], &c__1);
	}

/*        Update the current row of A: */
/*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**T. */

	if (k < *n) {
	    i__1 = *n - k;
	    sgemv_("No transpose", &i__1, &k, &c_b8, &f[k + 1 + f_dim1], ldf, 
		    &a[rk + a_dim1], lda, &c_b9, &a[rk + (k + 1) * a_dim1], 
		    lda);
	}

/*        Update partial column norms. */

	if (rk < lastrk) {
	    i__1 = *n;
	    for (j = k + 1; j <= i__1; ++j) {
		if (vn1[j] != 0.f) {

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

		    temp = (r__1 = a[rk + j * a_dim1], abs(r__1)) / vn1[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 = vn1[j] / vn2[j];
		    temp2 = temp * (r__1 * r__1);
		    if (temp2 <= tol3z) {
			vn2[j] = (real) lsticc;
			lsticc = j;
		    } else {
			vn1[j] *= sqrt(temp);
		    }
		}
/* L30: */
	    }
	}

	a[rk + k * a_dim1] = akk;

/*        End of while loop. */

	goto L10;
    }
    *kb = k;
    rk = *offset + *kb;

/*     Apply the block reflector to the rest of the matrix: */
/*     A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - */
/*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**T. */

/* Computing MIN */
    i__1 = *n, i__2 = *m - *offset;
    if (*kb < f2cmin(i__1,i__2)) {
	i__1 = *m - rk;
	i__2 = *n - *kb;
	sgemm_("No transpose", "Transpose", &i__1, &i__2, kb, &c_b8, &a[rk + 
		1 + a_dim1], lda, &f[*kb + 1 + f_dim1], ldf, &c_b9, &a[rk + 1 
		+ (*kb + 1) * a_dim1], lda);
    }

/*     Recomputation of difficult columns. */

L40:
    if (lsticc > 0) {
	itemp = i_nint(&vn2[lsticc]);
	i__1 = *m - rk;
	vn1[lsticc] = snrm2_(&i__1, &a[rk + 1 + lsticc * a_dim1], &c__1);

/*        NOTE: The computation of VN1( LSTICC ) relies on the fact that */
/*        SNRM2 does not fail on vectors with norm below the value of */
/*        SQRT(DLAMCH('S')) */

	vn2[lsticc] = vn1[lsticc];
	lsticc = itemp;
	goto L40;
    }

    return;

/*     End of SLAQPS */

} /* slaqps_ */