OpenBLAS/lapack-netlib/SRC/ssytrd_sy2sb.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 integer c__4 = 4;
static integer c_n1 = -1;
static integer c__1 = 1;
static real c_b17 = 0.f;
static real c_b23 = 1.f;
static real c_b39 = -.5f;
static real c_b42 = -1.f;

/* > \brief \b SSYTRD_SY2SB */

/*  @generated from zhetrd_he2hb.f, fortran z -> s, Wed Dec  7 08:22:40 2016 */

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

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

/* > \htmlonly */
/* > Download SSYTRD_SY2SB + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssytrd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssytrd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssytrd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE SSYTRD_SY2SB( UPLO, N, KD, A, LDA, AB, LDAB, TAU, */
/*                              WORK, LWORK, INFO ) */

/*       IMPLICIT NONE */

/*       CHARACTER          UPLO */
/*       INTEGER            INFO, LDA, LDAB, LWORK, N, KD */
/*       REAL               A( LDA, * ), AB( LDAB, * ), */
/*                          TAU( * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SSYTRD_SY2SB reduces a real symmetric matrix A to real symmetric */
/* > band-diagonal form AB by a orthogonal similarity transformation: */
/* > Q**T * A * Q = AB. */
/* > \endverbatim */

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

/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          = 'U':  Upper triangle of A is stored; */
/* >          = 'L':  Lower triangle of A is stored. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KD */
/* > \verbatim */
/* >          KD is INTEGER */
/* >          The number of superdiagonals of the reduced matrix if UPLO = 'U', */
/* >          or the number of subdiagonals if UPLO = 'L'.  KD >= 0. */
/* >          The reduced matrix is stored in the array AB. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA,N) */
/* >          On entry, the symmetric matrix A.  If UPLO = 'U', the leading */
/* >          N-by-N upper triangular part of A contains the upper */
/* >          triangular part of the matrix A, and the strictly lower */
/* >          triangular part of A is not referenced.  If UPLO = 'L', the */
/* >          leading N-by-N lower triangular part of A contains the lower */
/* >          triangular part of the matrix A, and the strictly upper */
/* >          triangular part of A is not referenced. */
/* >          On exit, if UPLO = 'U', the diagonal and first superdiagonal */
/* >          of A are overwritten by the corresponding elements of the */
/* >          tridiagonal matrix T, and the elements above the first */
/* >          superdiagonal, with the array TAU, represent the orthogonal */
/* >          matrix Q as a product of elementary reflectors; if UPLO */
/* >          = 'L', the diagonal and first subdiagonal of A are over- */
/* >          written by the corresponding elements of the tridiagonal */
/* >          matrix T, and the elements below the first subdiagonal, 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,N). */
/* > \endverbatim */
/* > */
/* > \param[out] AB */
/* > \verbatim */
/* >          AB is REAL array, dimension (LDAB,N) */
/* >          On exit, the upper or lower triangle of the symmetric band */
/* >          matrix A, stored in the first KD+1 rows of the array.  The */
/* >          j-th column of A is stored in the j-th column of the array AB */
/* >          as follows: */
/* >          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
/* >          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=f2cmin(n,j+kd). */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* >          LDAB is INTEGER */
/* >          The leading dimension of the array AB.  LDAB >= KD+1. */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* >          TAU is REAL array, dimension (N-KD) */
/* >          The scalar factors of the elementary reflectors (see Further */
/* >          Details). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (LWORK) */
/* >          On exit, if INFO = 0, or if LWORK=-1, */
/* >          WORK(1) returns the size of LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* >          LWORK is INTEGER */
/* >          The dimension of the array WORK which should be calculated */
/* >          by a workspace query. LWORK = MAX(1, LWORK_QUERY) */
/* >          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. */
/* >          LWORK_QUERY = N*KD + N*f2cmax(KD,FACTOPTNB) + 2*KD*KD */
/* >          where FACTOPTNB is the blocking used by the QR or LQ */
/* >          algorithm, usually FACTOPTNB=128 is a good choice otherwise */
/* >          putting LWORK=-1 will provide the size of WORK. */
/* > \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 2017 */

/* > \ingroup realSYcomputational */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  Implemented by Azzam Haidar. */
/* > */
/* >  All details are available on technical report, SC11, SC13 papers. */
/* > */
/* >  Azzam Haidar, Hatem Ltaief, and Jack Dongarra. */
/* >  Parallel reduction to condensed forms for symmetric eigenvalue problems */
/* >  using aggregated fine-grained and memory-aware kernels. In Proceedings */
/* >  of 2011 International Conference for High Performance Computing, */
/* >  Networking, Storage and Analysis (SC '11), New York, NY, USA, */
/* >  Article 8 , 11 pages. */
/* >  http://doi.acm.org/10.1145/2063384.2063394 */
/* > */
/* >  A. Haidar, J. Kurzak, P. Luszczek, 2013. */
/* >  An improved parallel singular value algorithm and its implementation */
/* >  for multicore hardware, In Proceedings of 2013 International Conference */
/* >  for High Performance Computing, Networking, Storage and Analysis (SC '13). */
/* >  Denver, Colorado, USA, 2013. */
/* >  Article 90, 12 pages. */
/* >  http://doi.acm.org/10.1145/2503210.2503292 */
/* > */
/* >  A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. */
/* >  A novel hybrid CPU-GPU generalized eigensolver for electronic structure */
/* >  calculations based on fine-grained memory aware tasks. */
/* >  International Journal of High Performance Computing Applications. */
/* >  Volume 28 Issue 2, Pages 196-209, May 2014. */
/* >  http://hpc.sagepub.com/content/28/2/196 */
/* > */
/* > \endverbatim */
/* > */
/* > \verbatim */
/* > */
/* >  If UPLO = 'U', the matrix Q is represented as a product of elementary */
/* >  reflectors */
/* > */
/* >     Q = H(k)**T . . . H(2)**T H(1)**T, where k = n-kd. */
/* > */
/* >  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+kd-1) = 0 and v(i+kd) = 1; conjg(v(i+kd+1:n)) is stored on exit in */
/* >  A(i,i+kd+1:n), and tau in TAU(i). */
/* > */
/* >  If UPLO = 'L', the matrix Q is represented as a product of elementary */
/* >  reflectors */
/* > */
/* >     Q = H(1) H(2) . . . H(k), where k = n-kd. */
/* > */
/* >  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(kd+1:i) = 0 and v(i+kd+1) = 1; v(i+kd+2:n) is stored on exit in */
/* >  A(i+kd+2:n,i), and tau in TAU(i). */
/* > */
/* >  The contents of A on exit are illustrated by the following examples */
/* >  with n = 5: */
/* > */
/* >  if UPLO = 'U':                       if UPLO = 'L': */
/* > */
/* >    (  ab  ab/v1  v1      v1     v1    )              (  ab                            ) */
/* >    (      ab     ab/v2   v2     v2    )              (  ab/v1  ab                     ) */
/* >    (             ab      ab/v3  v3    )              (  v1     ab/v2  ab              ) */
/* >    (                     ab     ab/v4 )              (  v1     v2     ab/v3  ab       ) */
/* >    (                            ab    )              (  v1     v2     v3     ab/v4 ab ) */
/* > */
/* >  where d and e denote diagonal and off-diagonal elements of T, and vi */
/* >  denotes an element of the vector defining H(i). */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void ssytrd_sy2sb_(char *uplo, integer *n, integer *kd, real 
	*a, integer *lda, real *ab, integer *ldab, real *tau, real *work, 
	integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, ab_dim1, ab_offset, i__1, i__2, i__3, i__4, 
	    i__5;

    /* Local variables */
    extern integer ilaenv2stage_(integer *, char *, char *, integer *, 
	    integer *, integer *, integer *);
    integer tpos, wpos, s1pos, s2pos, i__, j;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    integer lwmin;
    logical upper;
    extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *, 
	    integer *), ssymm_(char *, char *, integer *, integer *, real *, 
	    real *, integer *, real *, integer *, real *, real *, integer *);
    integer lk, pk;
    extern /* Subroutine */ void ssyr2k_(char *, char *, integer *, integer *, 
	    real *, real *, integer *, real *, integer *, real *, real *, 
	    integer *);
    integer pn, lt, lw;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern void sgelqf_(
	    integer *, integer *, real *, integer *, real *, real *, integer *
	    , integer *), sgeqrf_(integer *, integer *, real *, integer *, 
	    real *, real *, integer *, integer *), slarft_(char *, char *, 
	    integer *, integer *, real *, integer *, real *, real *, integer *
	    ), slaset_(char *, integer *, integer *, real *, 
	    real *, real *, integer *);
    integer ls1;
    logical lquery;
    integer ls2, ldt, ldw, lds1, lds2;



/*  -- LAPACK computational routine (version 3.8.0) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     November 2017 */


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


/*     Determine the minimal workspace size required */
/*     and test the input parameters */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    --tau;
    --work;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    lquery = *lwork == -1;
    lwmin = ilaenv2stage_(&c__4, "SSYTRD_SY2SB", "", n, kd, &c_n1, &c_n1);
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*kd < 0) {
	*info = -3;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -5;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = 1, i__2 = *kd + 1;
	if (*ldab < f2cmax(i__1,i__2)) {
	    *info = -7;
	} else if (*lwork < lwmin && ! lquery) {
	    *info = -10;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SSYTRD_SY2SB", &i__1, (ftnlen)12);
	return;
    } else if (lquery) {
	work[1] = (real) lwmin;
	return;
    }

/*     Quick return if possible */
/*     Copy the upper/lower portion of A into AB */

    if (*n <= *kd + 1) {
	if (upper) {
	    i__1 = *n;
	    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
		i__2 = *kd + 1;
		lk = f2cmin(i__2,i__);
		scopy_(&lk, &a[i__ - lk + 1 + i__ * a_dim1], &c__1, &ab[*kd + 
			1 - lk + 1 + i__ * ab_dim1], &c__1);
/* L100: */
	    }
	} else {
	    i__1 = *n;
	    for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
		i__2 = *kd + 1, i__3 = *n - i__ + 1;
		lk = f2cmin(i__2,i__3);
		scopy_(&lk, &a[i__ + i__ * a_dim1], &c__1, &ab[i__ * ab_dim1 
			+ 1], &c__1);
/* L110: */
	    }
	}
	work[1] = 1.f;
	return;
    }

/*     Determine the pointer position for the workspace */

    ldt = *kd;
    lds1 = *kd;
    lt = ldt * *kd;
    lw = *n * *kd;
    ls1 = lds1 * *kd;
    ls2 = lwmin - lt - lw - ls1;
/*      LS2 = N*MAX(KD,FACTOPTNB) */
    tpos = 1;
    wpos = tpos + lt;
    s1pos = wpos + lw;
    s2pos = s1pos + ls1;
    if (upper) {
	ldw = *kd;
	lds2 = *kd;
    } else {
	ldw = *n;
	lds2 = *n;
    }


/*     Set the workspace of the triangular matrix T to zero once such a */
/*     way every time T is generated the upper/lower portion will be always zero */

    slaset_("A", &ldt, kd, &c_b17, &c_b17, &work[tpos], &ldt);

    if (upper) {
	i__1 = *n - *kd;
	i__2 = *kd;
	for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
	    pn = *n - i__ - *kd + 1;
/* Computing MIN */
	    i__3 = *n - i__ - *kd + 1;
	    pk = f2cmin(i__3,*kd);

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

	    sgelqf_(kd, &pn, &a[i__ + (i__ + *kd) * a_dim1], lda, &tau[i__], &
		    work[s2pos], &ls2, &iinfo);

/*            Copy the upper portion of A into AB */

	    i__3 = i__ + pk - 1;
	    for (j = i__; j <= i__3; ++j) {
/* Computing MIN */
		i__4 = *kd, i__5 = *n - j;
		lk = f2cmin(i__4,i__5) + 1;
		i__4 = *ldab - 1;
		scopy_(&lk, &a[j + j * a_dim1], lda, &ab[*kd + 1 + j * 
			ab_dim1], &i__4);
/* L20: */
	    }

	    slaset_("Lower", &pk, &pk, &c_b17, &c_b23, &a[i__ + (i__ + *kd) * 
		    a_dim1], lda);

/*            Form the matrix T */

	    slarft_("Forward", "Rowwise", &pn, &pk, &a[i__ + (i__ + *kd) * 
		    a_dim1], lda, &tau[i__], &work[tpos], &ldt);

/*            Compute W: */

	    sgemm_("Conjugate", "No transpose", &pk, &pn, &pk, &c_b23, &work[
		    tpos], &ldt, &a[i__ + (i__ + *kd) * a_dim1], lda, &c_b17, 
		    &work[s2pos], &lds2);

	    ssymm_("Right", uplo, &pk, &pn, &c_b23, &a[i__ + *kd + (i__ + *kd)
		     * a_dim1], lda, &work[s2pos], &lds2, &c_b17, &work[wpos],
		     &ldw);

	    sgemm_("No transpose", "Conjugate", &pk, &pk, &pn, &c_b23, &work[
		    wpos], &ldw, &work[s2pos], &lds2, &c_b17, &work[s1pos], &
		    lds1);

	    sgemm_("No transpose", "No transpose", &pk, &pn, &pk, &c_b39, &
		    work[s1pos], &lds1, &a[i__ + (i__ + *kd) * a_dim1], lda, &
		    c_b23, &work[wpos], &ldw);


/*            Update the unreduced submatrix A(i+kd:n,i+kd:n), using */
/*            an update of the form:  A := A - V'*W - W'*V */

	    ssyr2k_(uplo, "Conjugate", &pn, &pk, &c_b42, &a[i__ + (i__ + *kd) 
		    * a_dim1], lda, &work[wpos], &ldw, &c_b23, &a[i__ + *kd + 
		    (i__ + *kd) * a_dim1], lda);
/* L10: */
	}

/*        Copy the upper band to AB which is the band storage matrix */

	i__2 = *n;
	for (j = *n - *kd + 1; j <= i__2; ++j) {
/* Computing MIN */
	    i__1 = *kd, i__3 = *n - j;
	    lk = f2cmin(i__1,i__3) + 1;
	    i__1 = *ldab - 1;
	    scopy_(&lk, &a[j + j * a_dim1], lda, &ab[*kd + 1 + j * ab_dim1], &
		    i__1);
/* L30: */
	}

    } else {

/*         Reduce the lower triangle of A to lower band matrix */

	i__2 = *n - *kd;
	i__1 = *kd;
	for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
	    pn = *n - i__ - *kd + 1;
/* Computing MIN */
	    i__3 = *n - i__ - *kd + 1;
	    pk = f2cmin(i__3,*kd);

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

	    sgeqrf_(&pn, kd, &a[i__ + *kd + i__ * a_dim1], lda, &tau[i__], &
		    work[s2pos], &ls2, &iinfo);

/*            Copy the upper portion of A into AB */

	    i__3 = i__ + pk - 1;
	    for (j = i__; j <= i__3; ++j) {
/* Computing MIN */
		i__4 = *kd, i__5 = *n - j;
		lk = f2cmin(i__4,i__5) + 1;
		scopy_(&lk, &a[j + j * a_dim1], &c__1, &ab[j * ab_dim1 + 1], &
			c__1);
/* L50: */
	    }

	    slaset_("Upper", &pk, &pk, &c_b17, &c_b23, &a[i__ + *kd + i__ * 
		    a_dim1], lda);

/*            Form the matrix T */

	    slarft_("Forward", "Columnwise", &pn, &pk, &a[i__ + *kd + i__ * 
		    a_dim1], lda, &tau[i__], &work[tpos], &ldt);

/*            Compute W: */

	    sgemm_("No transpose", "No transpose", &pn, &pk, &pk, &c_b23, &a[
		    i__ + *kd + i__ * a_dim1], lda, &work[tpos], &ldt, &c_b17,
		     &work[s2pos], &lds2);

	    ssymm_("Left", uplo, &pn, &pk, &c_b23, &a[i__ + *kd + (i__ + *kd) 
		    * a_dim1], lda, &work[s2pos], &lds2, &c_b17, &work[wpos], 
		    &ldw);

	    sgemm_("Conjugate", "No transpose", &pk, &pk, &pn, &c_b23, &work[
		    s2pos], &lds2, &work[wpos], &ldw, &c_b17, &work[s1pos], &
		    lds1);

	    sgemm_("No transpose", "No transpose", &pn, &pk, &pk, &c_b39, &a[
		    i__ + *kd + i__ * a_dim1], lda, &work[s1pos], &lds1, &
		    c_b23, &work[wpos], &ldw);


/*            Update the unreduced submatrix A(i+kd:n,i+kd:n), using */
/*            an update of the form:  A := A - V*W' - W*V' */

	    ssyr2k_(uplo, "No transpose", &pn, &pk, &c_b42, &a[i__ + *kd + 
		    i__ * a_dim1], lda, &work[wpos], &ldw, &c_b23, &a[i__ + *
		    kd + (i__ + *kd) * a_dim1], lda);
/*            ================================================================== */
/*            RESTORE A FOR COMPARISON AND CHECKING TO BE REMOVED */
/*             DO 45 J = I, I+PK-1 */
/*                LK = MIN( KD, N-J ) + 1 */
/*                CALL SCOPY( LK, AB( 1, J ), 1, A( J, J ), 1 ) */
/*   45        CONTINUE */
/*            ================================================================== */
/* L40: */
	}

/*        Copy the lower band to AB which is the band storage matrix */

	i__1 = *n;
	for (j = *n - *kd + 1; j <= i__1; ++j) {
/* Computing MIN */
	    i__2 = *kd, i__3 = *n - j;
	    lk = f2cmin(i__2,i__3) + 1;
	    scopy_(&lk, &a[j + j * a_dim1], &c__1, &ab[j * ab_dim1 + 1], &
		    c__1);
/* L60: */
	}
    }

    work[1] = (real) lwmin;
    return;

/*     End of SSYTRD_SY2SB */

} /* ssytrd_sy2sb__ */