OpenBLAS/lapack-netlib/SRC/sgeesx.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__0 = 0;
static integer c_n1 = -1;

/* > \brief <b> SGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors 
for GE matrices</b> */

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

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

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

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

/*       SUBROUTINE SGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, */
/*                          WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, */
/*                          IWORK, LIWORK, BWORK, INFO ) */

/*       CHARACTER          JOBVS, SENSE, SORT */
/*       INTEGER            INFO, LDA, LDVS, LIWORK, LWORK, N, SDIM */
/*       REAL               RCONDE, RCONDV */
/*       LOGICAL            BWORK( * ) */
/*       INTEGER            IWORK( * ) */
/*       REAL               A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ), */
/*      $                   WR( * ) */
/*       LOGICAL            SELECT */
/*       EXTERNAL           SELECT */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGEESX computes for an N-by-N real nonsymmetric matrix A, the */
/* > eigenvalues, the real Schur form T, and, optionally, the matrix of */
/* > Schur vectors Z.  This gives the Schur factorization A = Z*T*(Z**T). */
/* > */
/* > Optionally, it also orders the eigenvalues on the diagonal of the */
/* > real Schur form so that selected eigenvalues are at the top left; */
/* > computes a reciprocal condition number for the average of the */
/* > selected eigenvalues (RCONDE); and computes a reciprocal condition */
/* > number for the right invariant subspace corresponding to the */
/* > selected eigenvalues (RCONDV).  The leading columns of Z form an */
/* > orthonormal basis for this invariant subspace. */
/* > */
/* > For further explanation of the reciprocal condition numbers RCONDE */
/* > and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where */
/* > these quantities are called s and sep respectively). */
/* > */
/* > A real matrix is in real Schur form if it is upper quasi-triangular */
/* > with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in */
/* > the form */
/* >           [  a  b  ] */
/* >           [  c  a  ] */
/* > */
/* > where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc). */
/* > \endverbatim */

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

/* > \param[in] JOBVS */
/* > \verbatim */
/* >          JOBVS is CHARACTER*1 */
/* >          = 'N': Schur vectors are not computed; */
/* >          = 'V': Schur vectors are computed. */
/* > \endverbatim */
/* > */
/* > \param[in] SORT */
/* > \verbatim */
/* >          SORT is CHARACTER*1 */
/* >          Specifies whether or not to order the eigenvalues on the */
/* >          diagonal of the Schur form. */
/* >          = 'N': Eigenvalues are not ordered; */
/* >          = 'S': Eigenvalues are ordered (see SELECT). */
/* > \endverbatim */
/* > */
/* > \param[in] SELECT */
/* > \verbatim */
/* >          SELECT is a LOGICAL FUNCTION of two REAL arguments */
/* >          SELECT must be declared EXTERNAL in the calling subroutine. */
/* >          If SORT = 'S', SELECT is used to select eigenvalues to sort */
/* >          to the top left of the Schur form. */
/* >          If SORT = 'N', SELECT is not referenced. */
/* >          An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if */
/* >          SELECT(WR(j),WI(j)) is true; i.e., if either one of a */
/* >          complex conjugate pair of eigenvalues is selected, then both */
/* >          are.  Note that a selected complex eigenvalue may no longer */
/* >          satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since */
/* >          ordering may change the value of complex eigenvalues */
/* >          (especially if the eigenvalue is ill-conditioned); in this */
/* >          case INFO may be set to N+3 (see INFO below). */
/* > \endverbatim */
/* > */
/* > \param[in] SENSE */
/* > \verbatim */
/* >          SENSE is CHARACTER*1 */
/* >          Determines which reciprocal condition numbers are computed. */
/* >          = 'N': None are computed; */
/* >          = 'E': Computed for average of selected eigenvalues only; */
/* >          = 'V': Computed for selected right invariant subspace only; */
/* >          = 'B': Computed for both. */
/* >          If SENSE = 'E', 'V' or 'B', SORT must equal 'S'. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA, N) */
/* >          On entry, the N-by-N matrix A. */
/* >          On exit, A is overwritten by its real Schur form T. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] SDIM */
/* > \verbatim */
/* >          SDIM is INTEGER */
/* >          If SORT = 'N', SDIM = 0. */
/* >          If SORT = 'S', SDIM = number of eigenvalues (after sorting) */
/* >                         for which SELECT is true. (Complex conjugate */
/* >                         pairs for which SELECT is true for either */
/* >                         eigenvalue count as 2.) */
/* > \endverbatim */
/* > */
/* > \param[out] WR */
/* > \verbatim */
/* >          WR is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] WI */
/* > \verbatim */
/* >          WI is REAL array, dimension (N) */
/* >          WR and WI contain the real and imaginary parts, respectively, */
/* >          of the computed eigenvalues, in the same order that they */
/* >          appear on the diagonal of the output Schur form T.  Complex */
/* >          conjugate pairs of eigenvalues appear consecutively with the */
/* >          eigenvalue having the positive imaginary part first. */
/* > \endverbatim */
/* > */
/* > \param[out] VS */
/* > \verbatim */
/* >          VS is REAL array, dimension (LDVS,N) */
/* >          If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur */
/* >          vectors. */
/* >          If JOBVS = 'N', VS is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVS */
/* > \verbatim */
/* >          LDVS is INTEGER */
/* >          The leading dimension of the array VS.  LDVS >= 1, and if */
/* >          JOBVS = 'V', LDVS >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDE */
/* > \verbatim */
/* >          RCONDE is REAL */
/* >          If SENSE = 'E' or 'B', RCONDE contains the reciprocal */
/* >          condition number for the average of the selected eigenvalues. */
/* >          Not referenced if SENSE = 'N' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDV */
/* > \verbatim */
/* >          RCONDV is REAL */
/* >          If SENSE = 'V' or 'B', RCONDV contains the reciprocal */
/* >          condition number for the selected right invariant subspace. */
/* >          Not referenced if SENSE = 'N' or 'E'. */
/* > \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(1,3*N). */
/* >          Also, if SENSE = 'E' or 'V' or 'B', */
/* >          LWORK >= N+2*SDIM*(N-SDIM), where SDIM is the number of */
/* >          selected eigenvalues computed by this routine.  Note that */
/* >          N+2*SDIM*(N-SDIM) <= N+N*N/2. Note also that an error is only */
/* >          returned if LWORK < f2cmax(1,3*N), but if SENSE = 'E' or 'V' or */
/* >          'B' this may not be large enough. */
/* >          For good performance, LWORK must generally be larger. */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates upper bounds on the optimal sizes of the */
/* >          arrays WORK and IWORK, returns these values as the first */
/* >          entries of the WORK and IWORK arrays, and no error messages */
/* >          related to LWORK or LIWORK are issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
/* >          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LIWORK */
/* > \verbatim */
/* >          LIWORK is INTEGER */
/* >          The dimension of the array IWORK. */
/* >          LIWORK >= 1; if SENSE = 'V' or 'B', LIWORK >= SDIM*(N-SDIM). */
/* >          Note that SDIM*(N-SDIM) <= N*N/4. Note also that an error is */
/* >          only returned if LIWORK < 1, but if SENSE = 'V' or 'B' this */
/* >          may not be large enough. */
/* > */
/* >          If LIWORK = -1, then a workspace query is assumed; the */
/* >          routine only calculates upper bounds on the optimal sizes of */
/* >          the arrays WORK and IWORK, returns these values as the first */
/* >          entries of the WORK and IWORK arrays, and no error messages */
/* >          related to LWORK or LIWORK are issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] BWORK */
/* > \verbatim */
/* >          BWORK is LOGICAL array, dimension (N) */
/* >          Not referenced if SORT = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0: successful exit */
/* >          < 0: if INFO = -i, the i-th argument had an illegal value. */
/* >          > 0: if INFO = i, and i is */
/* >             <= N: the QR algorithm failed to compute all the */
/* >                   eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI */
/* >                   contain those eigenvalues which have converged; if */
/* >                   JOBVS = 'V', VS contains the transformation which */
/* >                   reduces A to its partially converged Schur form. */
/* >             = N+1: the eigenvalues could not be reordered because some */
/* >                   eigenvalues were too close to separate (the problem */
/* >                   is very ill-conditioned); */
/* >             = N+2: after reordering, roundoff changed values of some */
/* >                   complex eigenvalues so that leading eigenvalues in */
/* >                   the Schur form no longer satisfy SELECT=.TRUE.  This */
/* >                   could also be caused by underflow due to scaling. */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup realGEeigen */

/*  ===================================================================== */
/* Subroutine */ int sgeesx_(char *jobvs, char *sort, L_fp select, char *
	sense, integer *n, real *a, integer *lda, integer *sdim, real *wr, 
	real *wi, real *vs, integer *ldvs, real *rconde, real *rcondv, real *
	work, integer *lwork, integer *iwork, integer *liwork, logical *bwork,
	 integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3;

    /* Local variables */
    integer ibal;
    real anrm;
    integer ierr, itau, iwrk, lwrk, inxt, i__, icond, ieval;
    extern logical lsame_(char *, char *);
    logical cursl;
    integer liwrk, i1, i2;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *), sswap_(integer *, real *, integer *, real *, integer *
	    );
    logical lst2sl;
    extern /* Subroutine */ int slabad_(real *, real *);
    logical scalea;
    integer ip;
    real cscale;
    extern /* Subroutine */ int sgebak_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, integer *, integer *), sgebal_(char *, integer *, real *, integer *, 
	    integer *, integer *, real *, integer *);
    extern real slamch_(char *);
    extern /* Subroutine */ int sgehrd_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *), xerbla_(char 
	    *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern real slange_(char *, integer *, integer *, real *, integer *, real 
	    *);
    real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, 
	    real *, integer *);
    logical wantsb, wantse, lastsl;
    extern /* Subroutine */ int sorghr_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *), shseqr_(char 
	    *, char *, integer *, integer *, integer *, real *, integer *, 
	    real *, real *, real *, integer *, real *, integer *, integer *);
    integer minwrk, maxwrk;
    logical wantsn;
    real smlnum;
    integer hswork;
    extern /* Subroutine */ int strsen_(char *, char *, logical *, integer *, 
	    real *, integer *, real *, integer *, real *, real *, integer *, 
	    real *, real *, real *, integer *, integer *, integer *, integer *
	    );
    logical wantst, lquery, wantsv, wantvs;
    integer ihi, ilo;
    real dum[1], 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..-- */
/*     June 2016 */


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


/*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --wr;
    --wi;
    vs_dim1 = *ldvs;
    vs_offset = 1 + vs_dim1 * 1;
    vs -= vs_offset;
    --work;
    --iwork;
    --bwork;

    /* Function Body */
    *info = 0;
    wantvs = lsame_(jobvs, "V");
    wantst = lsame_(sort, "S");
    wantsn = lsame_(sense, "N");
    wantse = lsame_(sense, "E");
    wantsv = lsame_(sense, "V");
    wantsb = lsame_(sense, "B");
    lquery = *lwork == -1 || *liwork == -1;

    if (! wantvs && ! lsame_(jobvs, "N")) {
	*info = -1;
    } else if (! wantst && ! lsame_(sort, "N")) {
	*info = -2;
    } else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && ! 
	    wantsn) {
	*info = -4;
    } else if (*n < 0) {
	*info = -5;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -7;
    } else if (*ldvs < 1 || wantvs && *ldvs < *n) {
	*info = -12;
    }

/*     Compute workspace */
/*      (Note: Comments in the code beginning "RWorkspace:" describe the */
/*       minimal amount of real workspace needed at that point in the */
/*       code, as well as the preferred amount for good performance. */
/*       IWorkspace refers to integer workspace. */
/*       NB refers to the optimal block size for the immediately */
/*       following subroutine, as returned by ILAENV. */
/*       HSWORK refers to the workspace preferred by SHSEQR, as */
/*       calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/*       the worst case. */
/*       If SENSE = 'E', 'V' or 'B', then the amount of workspace needed */
/*       depends on SDIM, which is computed by the routine STRSEN later */
/*       in the code.) */

    if (*info == 0) {
	liwrk = 1;
	if (*n == 0) {
	    minwrk = 1;
	    lwrk = 1;
	} else {
	    maxwrk = (*n << 1) + *n * ilaenv_(&c__1, "SGEHRD", " ", n, &c__1, 
		    n, &c__0, (ftnlen)6, (ftnlen)1);
	    minwrk = *n * 3;

	    shseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[1]
		    , &vs[vs_offset], ldvs, &work[1], &c_n1, &ieval);
	    hswork = work[1];

	    if (! wantvs) {
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n + hswork;
		maxwrk = f2cmax(i__1,i__2);
	    } else {
/* Computing MAX */
		i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1, 
			"SORGHR", " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)
			1);
		maxwrk = f2cmax(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n + hswork;
		maxwrk = f2cmax(i__1,i__2);
	    }
	    lwrk = maxwrk;
	    if (! wantsn) {
/* Computing MAX */
		i__1 = lwrk, i__2 = *n + *n * *n / 2;
		lwrk = f2cmax(i__1,i__2);
	    }
	    if (wantsv || wantsb) {
		liwrk = *n * *n / 4;
	    }
	}
	iwork[1] = liwrk;
	work[1] = (real) lwrk;

	if (*lwork < minwrk && ! lquery) {
	    *info = -16;
	} else if (*liwork < 1 && ! lquery) {
	    *info = -18;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGEESX", &i__1, (ftnlen)6);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

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

/*     Get machine constants */

    eps = slamch_("P");
    smlnum = slamch_("S");
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1.f / smlnum;

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

    anrm = slange_("M", n, n, &a[a_offset], lda, dum);
    scalea = FALSE_;
    if (anrm > 0.f && anrm < smlnum) {
	scalea = TRUE_;
	cscale = smlnum;
    } else if (anrm > bignum) {
	scalea = TRUE_;
	cscale = bignum;
    }
    if (scalea) {
	slascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
		ierr);
    }

/*     Permute the matrix to make it more nearly triangular */
/*     (RWorkspace: need N) */

    ibal = 1;
    sgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr);

/*     Reduce to upper Hessenberg form */
/*     (RWorkspace: need 3*N, prefer 2*N+N*NB) */

    itau = *n + ibal;
    iwrk = *n + itau;
    i__1 = *lwork - iwrk + 1;
    sgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
	     &ierr);

    if (wantvs) {

/*        Copy Householder vectors to VS */

	slacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
		;

/*        Generate orthogonal matrix in VS */
/*        (RWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */

	i__1 = *lwork - iwrk + 1;
	sorghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
		 &i__1, &ierr);
    }

    *sdim = 0;

/*     Perform QR iteration, accumulating Schur vectors in VS if desired */
/*     (RWorkspace: need N+1, prefer N+HSWORK (see comments) ) */

    iwrk = itau;
    i__1 = *lwork - iwrk + 1;
    shseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[1], &vs[
	    vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
    if (ieval > 0) {
	*info = ieval;
    }

/*     Sort eigenvalues if desired */

    if (wantst && *info == 0) {
	if (scalea) {
	    slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wr[1], n, &
		    ierr);
	    slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wi[1], n, &
		    ierr);
	}
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    bwork[i__] = (*select)(&wr[i__], &wi[i__]);
/* L10: */
	}

/*        Reorder eigenvalues, transform Schur vectors, and compute */
/*        reciprocal condition numbers */
/*        (RWorkspace: if SENSE is not 'N', need N+2*SDIM*(N-SDIM) */
/*                     otherwise, need N ) */
/*        (IWorkspace: if SENSE is 'V' or 'B', need SDIM*(N-SDIM) */
/*                     otherwise, need 0 ) */

	i__1 = *lwork - iwrk + 1;
	strsen_(sense, jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
		 ldvs, &wr[1], &wi[1], sdim, rconde, rcondv, &work[iwrk], &
		i__1, &iwork[1], liwork, &icond);
	if (! wantsn) {
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + (*sdim << 1) * (*n - *sdim);
	    maxwrk = f2cmax(i__1,i__2);
	}
	if (icond == -15) {

/*           Not enough real workspace */

	    *info = -16;
	} else if (icond == -17) {

/*           Not enough integer workspace */

	    *info = -18;
	} else if (icond > 0) {

/*           STRSEN failed to reorder or to restore standard Schur form */

	    *info = icond + *n;
	}
    }

    if (wantvs) {

/*        Undo balancing */
/*        (RWorkspace: need N) */

	sgebak_("P", "R", n, &ilo, &ihi, &work[ibal], n, &vs[vs_offset], ldvs,
		 &ierr);
    }

    if (scalea) {

/*        Undo scaling for the Schur form of A */

	slascl_("H", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
		ierr);
	i__1 = *lda + 1;
	scopy_(n, &a[a_offset], &i__1, &wr[1], &c__1);
	if ((wantsv || wantsb) && *info == 0) {
	    dum[0] = *rcondv;
	    slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &
		    c__1, &ierr);
	    *rcondv = dum[0];
	}
	if (cscale == smlnum) {

/*           If scaling back towards underflow, adjust WI if an */
/*           offdiagonal element of a 2-by-2 block in the Schur form */
/*           underflows. */

	    if (ieval > 0) {
		i1 = ieval + 1;
		i2 = ihi - 1;
		i__1 = ilo - 1;
		slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[
			1], n, &ierr);
	    } else if (wantst) {
		i1 = 1;
		i2 = *n - 1;
	    } else {
		i1 = ilo;
		i2 = ihi - 1;
	    }
	    inxt = i1 - 1;
	    i__1 = i2;
	    for (i__ = i1; i__ <= i__1; ++i__) {
		if (i__ < inxt) {
		    goto L20;
		}
		if (wi[i__] == 0.f) {
		    inxt = i__ + 1;
		} else {
		    if (a[i__ + 1 + i__ * a_dim1] == 0.f) {
			wi[i__] = 0.f;
			wi[i__ + 1] = 0.f;
		    } else if (a[i__ + 1 + i__ * a_dim1] != 0.f && a[i__ + (
			    i__ + 1) * a_dim1] == 0.f) {
			wi[i__] = 0.f;
			wi[i__ + 1] = 0.f;
			if (i__ > 1) {
			    i__2 = i__ - 1;
			    sswap_(&i__2, &a[i__ * a_dim1 + 1], &c__1, &a[(
				    i__ + 1) * a_dim1 + 1], &c__1);
			}
			if (*n > i__ + 1) {
			    i__2 = *n - i__ - 1;
			    sswap_(&i__2, &a[i__ + (i__ + 2) * a_dim1], lda, &
				    a[i__ + 1 + (i__ + 2) * a_dim1], lda);
			}
			if (wantvs) {
			    sswap_(n, &vs[i__ * vs_dim1 + 1], &c__1, &vs[(i__ 
				    + 1) * vs_dim1 + 1], &c__1);
			}
			a[i__ + (i__ + 1) * a_dim1] = a[i__ + 1 + i__ * 
				a_dim1];
			a[i__ + 1 + i__ * a_dim1] = 0.f;
		    }
		    inxt = i__ + 2;
		}
L20:
		;
	    }
	}
	i__1 = *n - ieval;
/* Computing MAX */
	i__3 = *n - ieval;
	i__2 = f2cmax(i__3,1);
	slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ieval + 
		1], &i__2, &ierr);
    }

    if (wantst && *info == 0) {

/*        Check if reordering successful */

	lastsl = TRUE_;
	lst2sl = TRUE_;
	*sdim = 0;
	ip = 0;
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    cursl = (*select)(&wr[i__], &wi[i__]);
	    if (wi[i__] == 0.f) {
		if (cursl) {
		    ++(*sdim);
		}
		ip = 0;
		if (cursl && ! lastsl) {
		    *info = *n + 2;
		}
	    } else {
		if (ip == 1) {

/*                 Last eigenvalue of conjugate pair */

		    cursl = cursl || lastsl;
		    lastsl = cursl;
		    if (cursl) {
			*sdim += 2;
		    }
		    ip = -1;
		    if (cursl && ! lst2sl) {
			*info = *n + 2;
		    }
		} else {

/*                 First eigenvalue of conjugate pair */

		    ip = 1;
		}
	    }
	    lst2sl = lastsl;
	    lastsl = cursl;
/* L30: */
	}
    }

    work[1] = (real) maxwrk;
    if (wantsv || wantsb) {
	iwork[1] = *sdim * (*n - *sdim);
    } else {
	iwork[1] = 1;
    }

    return 0;

/*     End of SGEESX */

} /* sgeesx_ */