OpenBLAS/lapack-netlib/SRC/slabrd.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 int logical;
typedef short int shortlogical;
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++ */

#define F2C_proc_par_types 1
#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 real c_b4 = -1.f;
static real c_b5 = 1.f;
static integer c__1 = 1;
static real c_b16 = 0.f;

/* > \brief \b SLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. */

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

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

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

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

/*       SUBROUTINE SLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, */
/*                          LDY ) */

/*       INTEGER            LDA, LDX, LDY, M, N, NB */
/*       REAL               A( LDA, * ), D( * ), E( * ), TAUP( * ), */
/*      $                   TAUQ( * ), X( LDX, * ), Y( LDY, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SLABRD reduces the first NB rows and columns of a real general */
/* > m by n matrix A to upper or lower bidiagonal form by an orthogonal */
/* > transformation Q**T * A * P, and returns the matrices X and Y which */
/* > are needed to apply the transformation to the unreduced part of A. */
/* > */
/* > If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */
/* > bidiagonal form. */
/* > */
/* > This is an auxiliary routine called by SGEBRD */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The number of rows in the matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of columns in the matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] NB */
/* > \verbatim */
/* >          NB is INTEGER */
/* >          The number of leading rows and columns of A to be reduced. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA,N) */
/* >          On entry, the m by n general matrix to be reduced. */
/* >          On exit, the first NB rows and columns of the matrix are */
/* >          overwritten; the rest of the array is unchanged. */
/* >          If m >= n, elements on and below the diagonal in the first NB */
/* >            columns, with the array TAUQ, represent the orthogonal */
/* >            matrix Q as a product of elementary reflectors; and */
/* >            elements above the diagonal in the first NB rows, with the */
/* >            array TAUP, represent the orthogonal matrix P as a product */
/* >            of elementary reflectors. */
/* >          If m < n, elements below the diagonal in the first NB */
/* >            columns, with the array TAUQ, represent the orthogonal */
/* >            matrix Q as a product of elementary reflectors, and */
/* >            elements on and above the diagonal in the first NB rows, */
/* >            with the array TAUP, represent the orthogonal matrix P 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] D */
/* > \verbatim */
/* >          D is REAL array, dimension (NB) */
/* >          The diagonal elements of the first NB rows and columns of */
/* >          the reduced matrix.  D(i) = A(i,i). */
/* > \endverbatim */
/* > */
/* > \param[out] E */
/* > \verbatim */
/* >          E is REAL array, dimension (NB) */
/* >          The off-diagonal elements of the first NB rows and columns of */
/* >          the reduced matrix. */
/* > \endverbatim */
/* > */
/* > \param[out] TAUQ */
/* > \verbatim */
/* >          TAUQ is REAL array, dimension (NB) */
/* >          The scalar factors of the elementary reflectors which */
/* >          represent the orthogonal matrix Q. See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[out] TAUP */
/* > \verbatim */
/* >          TAUP is REAL array, dimension (NB) */
/* >          The scalar factors of the elementary reflectors which */
/* >          represent the orthogonal matrix P. See Further Details. */
/* > \endverbatim */
/* > */
/* > \param[out] X */
/* > \verbatim */
/* >          X is REAL array, dimension (LDX,NB) */
/* >          The m-by-nb matrix X required to update the unreduced part */
/* >          of A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDX */
/* > \verbatim */
/* >          LDX is INTEGER */
/* >          The leading dimension of the array X. LDX >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] Y */
/* > \verbatim */
/* >          Y is REAL array, dimension (LDY,NB) */
/* >          The n-by-nb matrix Y required to update the unreduced part */
/* >          of A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDY */
/* > \verbatim */
/* >          LDY is INTEGER */
/* >          The leading dimension of the array Y. LDY >= f2cmax(1,N). */
/* > \endverbatim */

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

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

/* > \date June 2017 */

/* > \ingroup realOTHERauxiliary */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  The matrices Q and P are represented as products of elementary */
/* >  reflectors: */
/* > */
/* >     Q = H(1) H(2) . . . H(nb)  and  P = G(1) G(2) . . . G(nb) */
/* > */
/* >  Each H(i) and G(i) has the form: */
/* > */
/* >     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T */
/* > */
/* >  where tauq and taup are real scalars, and v and u are real vectors. */
/* > */
/* >  If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */
/* >  A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */
/* >  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
/* > */
/* >  If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */
/* >  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */
/* >  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
/* > */
/* >  The elements of the vectors v and u together form the m-by-nb matrix */
/* >  V and the nb-by-n matrix U**T which are needed, with X and Y, to apply */
/* >  the transformation to the unreduced part of the matrix, using a block */
/* >  update of the form:  A := A - V*Y**T - X*U**T. */
/* > */
/* >  The contents of A on exit are illustrated by the following examples */
/* >  with nb = 2: */
/* > */
/* >  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n): */
/* > */
/* >    (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 ) */
/* >    (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 ) */
/* >    (  v1  v2  a   a   a  )           (  v1  1   a   a   a   a  ) */
/* >    (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  ) */
/* >    (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  ) */
/* >    (  v1  v2  a   a   a  ) */
/* > */
/* >  where a denotes an element of the original matrix which is unchanged, */
/* >  vi denotes an element of the vector defining H(i), and ui an element */
/* >  of the vector defining G(i). */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void slabrd_(integer *m, integer *n, integer *nb, real *a, 
	integer *lda, real *d__, real *e, real *tauq, real *taup, real *x, 
	integer *ldx, real *y, integer *ldy)
{
    /* System generated locals */
    integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, 
	    i__3;

    /* Local variables */
    integer i__;
    extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *), 
	    sgemv_(char *, integer *, integer *, real *, real *, integer *, 
	    real *, integer *, real *, real *, integer *), slarfg_(
	    integer *, real *, real *, integer *, real *);


/*  -- LAPACK auxiliary routine (version 3.7.1) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     June 2017 */


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


/*     Quick return if possible */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --d__;
    --e;
    --tauq;
    --taup;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1 * 1;
    x -= x_offset;
    y_dim1 = *ldy;
    y_offset = 1 + y_dim1 * 1;
    y -= y_offset;

    /* Function Body */
    if (*m <= 0 || *n <= 0) {
	return;
    }

    if (*m >= *n) {

/*        Reduce to upper bidiagonal form */

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

/*           Update A(i:m,i) */

	    i__2 = *m - i__ + 1;
	    i__3 = i__ - 1;
	    sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda,
		     &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], &
		    c__1);
	    i__2 = *m - i__ + 1;
	    i__3 = i__ - 1;
	    sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx,
		     &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * 
		    a_dim1], &c__1);

/*           Generate reflection Q(i) to annihilate A(i+1:m,i) */

	    i__2 = *m - i__ + 1;
/* Computing MIN */
	    i__3 = i__ + 1;
	    slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[f2cmin(i__3,*m) + i__ * 
		    a_dim1], &c__1, &tauq[i__]);
	    d__[i__] = a[i__ + i__ * a_dim1];
	    if (i__ < *n) {
		a[i__ + i__ * a_dim1] = 1.f;

/*              Compute Y(i+1:n,i) */

		i__2 = *m - i__ + 1;
		i__3 = *n - i__;
		sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * 
			a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &
			y[i__ + 1 + i__ * y_dim1], &c__1);
		i__2 = *m - i__ + 1;
		i__3 = i__ - 1;
		sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], 
			lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * 
			y_dim1 + 1], &c__1);
		i__2 = *n - i__;
		i__3 = i__ - 1;
		sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + 
			y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
			i__ + 1 + i__ * y_dim1], &c__1);
		i__2 = *m - i__ + 1;
		i__3 = i__ - 1;
		sgemv_("Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], 
			ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * 
			y_dim1 + 1], &c__1);
		i__2 = i__ - 1;
		i__3 = *n - i__;
		sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * 
			a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, 
			&y[i__ + 1 + i__ * y_dim1], &c__1);
		i__2 = *n - i__;
		sscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);

/*              Update A(i,i+1:n) */

		i__2 = *n - i__;
		sgemv_("No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + 
			y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + (
			i__ + 1) * a_dim1], lda);
		i__2 = i__ - 1;
		i__3 = *n - i__;
		sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * 
			a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[
			i__ + (i__ + 1) * a_dim1], lda);

/*              Generate reflection P(i) to annihilate A(i,i+2:n) */

		i__2 = *n - i__;
/* Computing MIN */
		i__3 = i__ + 2;
		slarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + f2cmin(
			i__3,*n) * a_dim1], lda, &taup[i__]);
		e[i__] = a[i__ + (i__ + 1) * a_dim1];
		a[i__ + (i__ + 1) * a_dim1] = 1.f;

/*              Compute X(i+1:m,i) */

		i__2 = *m - i__;
		i__3 = *n - i__;
		sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ 
			+ 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1], 
			lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1);
		i__2 = *n - i__;
		sgemv_("Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], 
			ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[
			i__ * x_dim1 + 1], &c__1);
		i__2 = *m - i__;
		sgemv_("No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + 
			a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
			i__ + 1 + i__ * x_dim1], &c__1);
		i__2 = i__ - 1;
		i__3 = *n - i__;
		sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * 
			a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, &
			c_b16, &x[i__ * x_dim1 + 1], &c__1);
		i__2 = *m - i__;
		i__3 = i__ - 1;
		sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + 
			x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
			i__ + 1 + i__ * x_dim1], &c__1);
		i__2 = *m - i__;
		sscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
	    }
/* L10: */
	}
    } else {

/*        Reduce to lower bidiagonal form */

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

/*           Update A(i,i:n) */

	    i__2 = *n - i__ + 1;
	    i__3 = i__ - 1;
	    sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy,
		     &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], 
		    lda);
	    i__2 = i__ - 1;
	    i__3 = *n - i__ + 1;
	    sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], 
		    lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1],
		     lda);

/*           Generate reflection P(i) to annihilate A(i,i+1:n) */

	    i__2 = *n - i__ + 1;
/* Computing MIN */
	    i__3 = i__ + 1;
	    slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + f2cmin(i__3,*n) * 
		    a_dim1], lda, &taup[i__]);
	    d__[i__] = a[i__ + i__ * a_dim1];
	    if (i__ < *m) {
		a[i__ + i__ * a_dim1] = 1.f;

/*              Compute X(i+1:m,i) */

		i__2 = *m - i__;
		i__3 = *n - i__ + 1;
		sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ *
			 a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &
			x[i__ + 1 + i__ * x_dim1], &c__1);
		i__2 = *n - i__ + 1;
		i__3 = i__ - 1;
		sgemv_("Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], 
			ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * 
			x_dim1 + 1], &c__1);
		i__2 = *m - i__;
		i__3 = i__ - 1;
		sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + 
			a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
			i__ + 1 + i__ * x_dim1], &c__1);
		i__2 = i__ - 1;
		i__3 = *n - i__ + 1;
		sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + 
			1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ *
			 x_dim1 + 1], &c__1);
		i__2 = *m - i__;
		i__3 = i__ - 1;
		sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + 
			x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
			i__ + 1 + i__ * x_dim1], &c__1);
		i__2 = *m - i__;
		sscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);

/*              Update A(i+1:m,i) */

		i__2 = *m - i__;
		i__3 = i__ - 1;
		sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + 
			a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + 
			1 + i__ * a_dim1], &c__1);
		i__2 = *m - i__;
		sgemv_("No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + 
			x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[
			i__ + 1 + i__ * a_dim1], &c__1);

/*              Generate reflection Q(i) to annihilate A(i+2:m,i) */

		i__2 = *m - i__;
/* Computing MIN */
		i__3 = i__ + 2;
		slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[f2cmin(i__3,*m) + 
			i__ * a_dim1], &c__1, &tauq[i__]);
		e[i__] = a[i__ + 1 + i__ * a_dim1];
		a[i__ + 1 + i__ * a_dim1] = 1.f;

/*              Compute Y(i+1:n,i) */

		i__2 = *m - i__;
		i__3 = *n - i__;
		sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + 
			1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, 
			&c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1);
		i__2 = *m - i__;
		i__3 = i__ - 1;
		sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1],
			 lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
			i__ * y_dim1 + 1], &c__1);
		i__2 = *n - i__;
		i__3 = i__ - 1;
		sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + 
			y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
			i__ + 1 + i__ * y_dim1], &c__1);
		i__2 = *m - i__;
		sgemv_("Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], 
			ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
			i__ * y_dim1 + 1], &c__1);
		i__2 = *n - i__;
		sgemv_("Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 
			+ 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ 
			+ 1 + i__ * y_dim1], &c__1);
		i__2 = *n - i__;
		sscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
	    }
/* L20: */
	}
    }
    return;

/*     End of SLABRD */

} /* slabrd_ */