OpenBLAS/lapack-netlib/SRC/DEPRECATED/sgegs.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__1 = 1;
static integer c_n1 = -1;
static real c_b36 = 0.f;
static real c_b37 = 1.f;

/* > \brief <b> SGEGS computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matr
ices</b> */

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

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

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

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

/*       SUBROUTINE SGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, */
/*                         ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, */
/*                         LWORK, INFO ) */

/*       CHARACTER          JOBVSL, JOBVSR */
/*       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N */
/*       REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
/*      $                   B( LDB, * ), BETA( * ), VSL( LDVSL, * ), */
/*      $                   VSR( LDVSR, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > This routine is deprecated and has been replaced by routine SGGES. */
/* > */
/* > SGEGS computes the eigenvalues, real Schur form, and, optionally, */
/* > left and or/right Schur vectors of a real matrix pair (A,B). */
/* > Given two square matrices A and B, the generalized real Schur */
/* > factorization has the form */
/* > */
/* >   A = Q*S*Z**T,  B = Q*T*Z**T */
/* > */
/* > where Q and Z are orthogonal matrices, T is upper triangular, and S */
/* > is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal */
/* > blocks, the 2-by-2 blocks corresponding to complex conjugate pairs */
/* > of eigenvalues of (A,B).  The columns of Q are the left Schur vectors */
/* > and the columns of Z are the right Schur vectors. */
/* > */
/* > If only the eigenvalues of (A,B) are needed, the driver routine */
/* > SGEGV should be used instead.  See SGEGV for a description of the */
/* > eigenvalues of the generalized nonsymmetric eigenvalue problem */
/* > (GNEP). */
/* > \endverbatim */

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

/* > \param[in] JOBVSL */
/* > \verbatim */
/* >          JOBVSL is CHARACTER*1 */
/* >          = 'N':  do not compute the left Schur vectors; */
/* >          = 'V':  compute the left Schur vectors (returned in VSL). */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVSR */
/* > \verbatim */
/* >          JOBVSR is CHARACTER*1 */
/* >          = 'N':  do not compute the right Schur vectors; */
/* >          = 'V':  compute the right Schur vectors (returned in VSR). */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrices A, B, VSL, and VSR.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA, N) */
/* >          On entry, the matrix A. */
/* >          On exit, the upper quasi-triangular matrix S from the */
/* >          generalized real Schur factorization. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of A.  LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is REAL array, dimension (LDB, N) */
/* >          On entry, the matrix B. */
/* >          On exit, the upper triangular matrix T from the generalized */
/* >          real Schur factorization. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of B.  LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAR */
/* > \verbatim */
/* >          ALPHAR is REAL array, dimension (N) */
/* >          The real parts of each scalar alpha defining an eigenvalue */
/* >          of GNEP. */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAI */
/* > \verbatim */
/* >          ALPHAI is REAL array, dimension (N) */
/* >          The imaginary parts of each scalar alpha defining an */
/* >          eigenvalue of GNEP.  If ALPHAI(j) is zero, then the j-th */
/* >          eigenvalue is real; if positive, then the j-th and (j+1)-st */
/* >          eigenvalues are a complex conjugate pair, with */
/* >          ALPHAI(j+1) = -ALPHAI(j). */
/* > \endverbatim */
/* > */
/* > \param[out] BETA */
/* > \verbatim */
/* >          BETA is REAL array, dimension (N) */
/* >          The scalars beta that define the eigenvalues of GNEP. */
/* >          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */
/* >          beta = BETA(j) represent the j-th eigenvalue of the matrix */
/* >          pair (A,B), in one of the forms lambda = alpha/beta or */
/* >          mu = beta/alpha.  Since either lambda or mu may overflow, */
/* >          they should not, in general, be computed. */
/* > \endverbatim */
/* > */
/* > \param[out] VSL */
/* > \verbatim */
/* >          VSL is REAL array, dimension (LDVSL,N) */
/* >          If JOBVSL = 'V', the matrix of left Schur vectors Q. */
/* >          Not referenced if JOBVSL = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVSL */
/* > \verbatim */
/* >          LDVSL is INTEGER */
/* >          The leading dimension of the matrix VSL. LDVSL >=1, and */
/* >          if JOBVSL = 'V', LDVSL >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] VSR */
/* > \verbatim */
/* >          VSR is REAL array, dimension (LDVSR,N) */
/* >          If JOBVSR = 'V', the matrix of right Schur vectors Z. */
/* >          Not referenced if JOBVSR = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVSR */
/* > \verbatim */
/* >          LDVSR is INTEGER */
/* >          The leading dimension of the matrix VSR. LDVSR >= 1, and */
/* >          if JOBVSR = 'V', LDVSR >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension (MAX(1,LWORK)) */
/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* >          LWORK is INTEGER */
/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,4*N). */
/* >          For good performance, LWORK must generally be larger. */
/* >          To compute the optimal value of LWORK, call ILAENV to get */
/* >          blocksizes (for SGEQRF, SORMQR, and SORGQR.)  Then compute: */
/* >          NB  -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR */
/* >          The optimal LWORK is  2*N + N*(NB+1). */
/* > */
/* >          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. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/* >          = 1,...,N: */
/* >                The QZ iteration failed.  (A,B) are not in Schur */
/* >                form, but ALPHAR(j), ALPHAI(j), and BETA(j) should */
/* >                be correct for j=INFO+1,...,N. */
/* >          > N:  errors that usually indicate LAPACK problems: */
/* >                =N+1: error return from SGGBAL */
/* >                =N+2: error return from SGEQRF */
/* >                =N+3: error return from SORMQR */
/* >                =N+4: error return from SORGQR */
/* >                =N+5: error return from SGGHRD */
/* >                =N+6: error return from SHGEQZ (other than failed */
/* >                                                iteration) */
/* >                =N+7: error return from SGGBAK (computing VSL) */
/* >                =N+8: error return from SGGBAK (computing VSR) */
/* >                =N+9: error return from SLASCL (various places) */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup realGEeigen */

/*  ===================================================================== */
/* Subroutine */ int sgegs_(char *jobvsl, char *jobvsr, integer *n, real *a, 
	integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real 
	*beta, real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *
	work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, 
	    vsr_dim1, vsr_offset, i__1, i__2;

    /* Local variables */
    real anrm, bnrm;
    integer itau, lopt;
    extern logical lsame_(char *, char *);
    integer ileft, iinfo, icols;
    logical ilvsl;
    integer iwork;
    logical ilvsr;
    integer irows, nb;
    extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, integer *
	    ), sggbal_(char *, integer *, real *, integer *, 
	    real *, integer *, integer *, integer *, real *, real *, real *, 
	    integer *);
    logical ilascl, ilbscl;
    extern real slamch_(char *), slange_(char *, integer *, integer *,
	     real *, integer *, real *);
    real safmin;
    extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, integer *, real *, integer *
	    , real *, integer *, integer *), xerbla_(char *, 
	    integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    integer ijobvl, iright;
    extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *);
    integer ijobvr;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *), slaset_(char *, integer *, 
	    integer *, real *, real *, real *, integer *);
    real anrmto;
    integer lwkmin, nb1, nb2, nb3;
    real bnrmto;
    extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *, 
	    integer *, integer *, real *, integer *, real *, integer *, real *
	    , real *, real *, real *, integer *, real *, integer *, real *, 
	    integer *, integer *);
    real smlnum;
    extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *, integer *);
    integer ihi, ilo;
    real eps;


/*  -- LAPACK driver 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 */


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


/*     Decode the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --alphar;
    --alphai;
    --beta;
    vsl_dim1 = *ldvsl;
    vsl_offset = 1 + vsl_dim1 * 1;
    vsl -= vsl_offset;
    vsr_dim1 = *ldvsr;
    vsr_offset = 1 + vsr_dim1 * 1;
    vsr -= vsr_offset;
    --work;

    /* Function Body */
    if (lsame_(jobvsl, "N")) {
	ijobvl = 1;
	ilvsl = FALSE_;
    } else if (lsame_(jobvsl, "V")) {
	ijobvl = 2;
	ilvsl = TRUE_;
    } else {
	ijobvl = -1;
	ilvsl = FALSE_;
    }

    if (lsame_(jobvsr, "N")) {
	ijobvr = 1;
	ilvsr = FALSE_;
    } else if (lsame_(jobvsr, "V")) {
	ijobvr = 2;
	ilvsr = TRUE_;
    } else {
	ijobvr = -1;
	ilvsr = FALSE_;
    }

/*     Test the input arguments */

/* Computing MAX */
    i__1 = *n << 2;
    lwkmin = f2cmax(i__1,1);
    lwkopt = lwkmin;
    work[1] = (real) lwkopt;
    lquery = *lwork == -1;
    *info = 0;
    if (ijobvl <= 0) {
	*info = -1;
    } else if (ijobvr <= 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -5;
    } else if (*ldb < f2cmax(1,*n)) {
	*info = -7;
    } else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
	*info = -12;
    } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
	*info = -14;
    } else if (*lwork < lwkmin && ! lquery) {
	*info = -16;
    }

    if (*info == 0) {
	nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (
		ftnlen)1);
	nb2 = ilaenv_(&c__1, "SORMQR", " ", n, n, n, &c_n1, (ftnlen)6, (
		ftnlen)1);
	nb3 = ilaenv_(&c__1, "SORGQR", " ", n, n, n, &c_n1, (ftnlen)6, (
		ftnlen)1);
/* Computing MAX */
	i__1 = f2cmax(nb1,nb2);
	nb = f2cmax(i__1,nb3);
	lopt = (*n << 1) + *n * (nb + 1);
	work[1] = (real) lopt;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGEGS ", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

/*     Get machine constants */

    eps = slamch_("E") * slamch_("B");
    safmin = slamch_("S");
    smlnum = *n * safmin / eps;
    bignum = 1.f / smlnum;

/*     Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */

    anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
    ilascl = FALSE_;
    if (anrm > 0.f && anrm < smlnum) {
	anrmto = smlnum;
	ilascl = TRUE_;
    } else if (anrm > bignum) {
	anrmto = bignum;
	ilascl = TRUE_;
    }

    if (ilascl) {
	slascl_("G", &c_n1, &c_n1, &anrm, &anrmto, n, n, &a[a_offset], lda, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
    }

/*     Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */

    bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
    ilbscl = FALSE_;
    if (bnrm > 0.f && bnrm < smlnum) {
	bnrmto = smlnum;
	ilbscl = TRUE_;
    } else if (bnrm > bignum) {
	bnrmto = bignum;
	ilbscl = TRUE_;
    }

    if (ilbscl) {
	slascl_("G", &c_n1, &c_n1, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
    }

/*     Permute the matrix to make it more nearly triangular */
/*     Workspace layout:  (2*N words -- "work..." not actually used) */
/*        left_permutation, right_permutation, work... */

    ileft = 1;
    iright = *n + 1;
    iwork = iright + *n;
    sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
	    ileft], &work[iright], &work[iwork], &iinfo);
    if (iinfo != 0) {
	*info = *n + 1;
	goto L10;
    }

/*     Reduce B to triangular form, and initialize VSL and/or VSR */
/*     Workspace layout:  ("work..." must have at least N words) */
/*        left_permutation, right_permutation, tau, work... */

    irows = ihi + 1 - ilo;
    icols = *n + 1 - ilo;
    itau = iwork;
    iwork = itau + irows;
    i__1 = *lwork + 1 - iwork;
    sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
	    iwork], &i__1, &iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
	i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
	lwkopt = f2cmax(i__1,i__2);
    }
    if (iinfo != 0) {
	*info = *n + 2;
	goto L10;
    }

    i__1 = *lwork + 1 - iwork;
    sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
	    work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
	    iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
	i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
	lwkopt = f2cmax(i__1,i__2);
    }
    if (iinfo != 0) {
	*info = *n + 3;
	goto L10;
    }

    if (ilvsl) {
	slaset_("Full", n, n, &c_b36, &c_b37, &vsl[vsl_offset], ldvsl);
	i__1 = irows - 1;
	i__2 = irows - 1;
	slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ilo 
		+ 1 + ilo * vsl_dim1], ldvsl);
	i__1 = *lwork + 1 - iwork;
	sorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
		work[itau], &work[iwork], &i__1, &iinfo);
	if (iinfo >= 0) {
/* Computing MAX */
	    i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
	    lwkopt = f2cmax(i__1,i__2);
	}
	if (iinfo != 0) {
	    *info = *n + 4;
	    goto L10;
	}
    }

    if (ilvsr) {
	slaset_("Full", n, n, &c_b36, &c_b37, &vsr[vsr_offset], ldvsr);
    }

/*     Reduce to generalized Hessenberg form */

    sgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
	    ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &iinfo);
    if (iinfo != 0) {
	*info = *n + 5;
	goto L10;
    }

/*     Perform QZ algorithm, computing Schur vectors if desired */
/*     Workspace layout:  ("work..." must have at least 1 word) */
/*        left_permutation, right_permutation, work... */

    iwork = itau;
    i__1 = *lwork + 1 - iwork;
    shgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
	    b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
	    , ldvsl, &vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
	i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
	lwkopt = f2cmax(i__1,i__2);
    }
    if (iinfo != 0) {
	if (iinfo > 0 && iinfo <= *n) {
	    *info = iinfo;
	} else if (iinfo > *n && iinfo <= *n << 1) {
	    *info = iinfo - *n;
	} else {
	    *info = *n + 6;
	}
	goto L10;
    }

/*     Apply permutation to VSL and VSR */

    if (ilvsl) {
	sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
		vsl_offset], ldvsl, &iinfo);
	if (iinfo != 0) {
	    *info = *n + 7;
	    goto L10;
	}
    }
    if (ilvsr) {
	sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
		vsr_offset], ldvsr, &iinfo);
	if (iinfo != 0) {
	    *info = *n + 8;
	    goto L10;
	}
    }

/*     Undo scaling */

    if (ilascl) {
	slascl_("H", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
	slascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
	slascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
    }

    if (ilbscl) {
	slascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
	slascl_("G", &c_n1, &c_n1, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
		iinfo);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
    }

L10:
    work[1] = (real) lwkopt;

    return 0;

/*     End of SGEGS */

} /* sgegs_ */