OpenBLAS/lapack-netlib/SRC/stgsen.c

/* f2c.h  --  Standard Fortran to C header file */

/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."

	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */

#ifndef F2C_INCLUDE
#define F2C_INCLUDE

#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;
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;}
#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)); }
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#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) = conj(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) (cimag(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;
}
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;
}
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;
}
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;
	_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;
}
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_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;
}	
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_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;
}
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
	_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__2 = 2;
static real c_b28 = 1.f;

/* > \brief \b STGSEN */

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

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

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

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

/*       SUBROUTINE STGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB, */
/*                          ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, M, PL, */
/*                          PR, DIF, WORK, LWORK, IWORK, LIWORK, INFO ) */

/*       LOGICAL            WANTQ, WANTZ */
/*       INTEGER            IJOB, INFO, LDA, LDB, LDQ, LDZ, LIWORK, LWORK, */
/*      $                   M, N */
/*       REAL               PL, PR */
/*       LOGICAL            SELECT( * ) */
/*       INTEGER            IWORK( * ) */
/*       REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
/*      $                   B( LDB, * ), BETA( * ), DIF( * ), Q( LDQ, * ), */
/*      $                   WORK( * ), Z( LDZ, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > STGSEN reorders the generalized real Schur decomposition of a real */
/* > matrix pair (A, B) (in terms of an orthonormal equivalence trans- */
/* > formation Q**T * (A, B) * Z), so that a selected cluster of eigenvalues */
/* > appears in the leading diagonal blocks of the upper quasi-triangular */
/* > matrix A and the upper triangular B. The leading columns of Q and */
/* > Z form orthonormal bases of the corresponding left and right eigen- */
/* > spaces (deflating subspaces). (A, B) must be in generalized real */
/* > Schur canonical form (as returned by SGGES), i.e. A is block upper */
/* > triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper */
/* > triangular. */
/* > */
/* > STGSEN also computes the generalized eigenvalues */
/* > */
/* >             w(j) = (ALPHAR(j) + i*ALPHAI(j))/BETA(j) */
/* > */
/* > of the reordered matrix pair (A, B). */
/* > */
/* > Optionally, STGSEN computes the estimates of reciprocal condition */
/* > numbers for eigenvalues and eigenspaces. These are Difu[(A11,B11), */
/* > (A22,B22)] and Difl[(A11,B11), (A22,B22)], i.e. the separation(s) */
/* > between the matrix pairs (A11, B11) and (A22,B22) that correspond to */
/* > the selected cluster and the eigenvalues outside the cluster, resp., */
/* > and norms of "projections" onto left and right eigenspaces w.r.t. */
/* > the selected cluster in the (1,1)-block. */
/* > \endverbatim */

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

/* > \param[in] IJOB */
/* > \verbatim */
/* >          IJOB is INTEGER */
/* >          Specifies whether condition numbers are required for the */
/* >          cluster of eigenvalues (PL and PR) or the deflating subspaces */
/* >          (Difu and Difl): */
/* >           =0: Only reorder w.r.t. SELECT. No extras. */
/* >           =1: Reciprocal of norms of "projections" onto left and right */
/* >               eigenspaces w.r.t. the selected cluster (PL and PR). */
/* >           =2: Upper bounds on Difu and Difl. F-norm-based estimate */
/* >               (DIF(1:2)). */
/* >           =3: Estimate of Difu and Difl. 1-norm-based estimate */
/* >               (DIF(1:2)). */
/* >               About 5 times as expensive as IJOB = 2. */
/* >           =4: Compute PL, PR and DIF (i.e. 0, 1 and 2 above): Economic */
/* >               version to get it all. */
/* >           =5: Compute PL, PR and DIF (i.e. 0, 1 and 3 above) */
/* > \endverbatim */
/* > */
/* > \param[in] WANTQ */
/* > \verbatim */
/* >          WANTQ is LOGICAL */
/* >          .TRUE. : update the left transformation matrix Q; */
/* >          .FALSE.: do not update Q. */
/* > \endverbatim */
/* > */
/* > \param[in] WANTZ */
/* > \verbatim */
/* >          WANTZ is LOGICAL */
/* >          .TRUE. : update the right transformation matrix Z; */
/* >          .FALSE.: do not update Z. */
/* > \endverbatim */
/* > */
/* > \param[in] SELECT */
/* > \verbatim */
/* >          SELECT is LOGICAL array, dimension (N) */
/* >          SELECT specifies the eigenvalues in the selected cluster. */
/* >          To select a real eigenvalue w(j), SELECT(j) must be set to */
/* >          .TRUE.. To select a complex conjugate pair of eigenvalues */
/* >          w(j) and w(j+1), corresponding to a 2-by-2 diagonal block, */
/* >          either SELECT(j) or SELECT(j+1) or both must be set to */
/* >          .TRUE.; a complex conjugate pair of eigenvalues must be */
/* >          either both included in the cluster or both excluded. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrices A and B. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension(LDA,N) */
/* >          On entry, the upper quasi-triangular matrix A, with (A, B) in */
/* >          generalized real Schur canonical form. */
/* >          On exit, A is overwritten by the reordered matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is REAL array, dimension(LDB,N) */
/* >          On entry, the upper triangular matrix B, with (A, B) in */
/* >          generalized real Schur canonical form. */
/* >          On exit, B is overwritten by the reordered matrix B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of the array B. LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAR */
/* > \verbatim */
/* >          ALPHAR is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAI */
/* > \verbatim */
/* >          ALPHAI is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] BETA */
/* > \verbatim */
/* >          BETA is REAL array, dimension (N) */
/* > */
/* >          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
/* >          be the generalized eigenvalues.  ALPHAR(j) + ALPHAI(j)*i */
/* >          and BETA(j),j=1,...,N  are the diagonals of the complex Schur */
/* >          form (S,T) that would result if the 2-by-2 diagonal blocks of */
/* >          the real generalized Schur form of (A,B) were further reduced */
/* >          to triangular form using complex unitary transformations. */
/* >          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) negative. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Q */
/* > \verbatim */
/* >          Q is REAL array, dimension (LDQ,N) */
/* >          On entry, if WANTQ = .TRUE., Q is an N-by-N matrix. */
/* >          On exit, Q has been postmultiplied by the left orthogonal */
/* >          transformation matrix which reorder (A, B); The leading M */
/* >          columns of Q form orthonormal bases for the specified pair of */
/* >          left eigenspaces (deflating subspaces). */
/* >          If WANTQ = .FALSE., Q is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* >          LDQ is INTEGER */
/* >          The leading dimension of the array Q.  LDQ >= 1; */
/* >          and if WANTQ = .TRUE., LDQ >= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* >          Z is REAL array, dimension (LDZ,N) */
/* >          On entry, if WANTZ = .TRUE., Z is an N-by-N matrix. */
/* >          On exit, Z has been postmultiplied by the left orthogonal */
/* >          transformation matrix which reorder (A, B); The leading M */
/* >          columns of Z form orthonormal bases for the specified pair of */
/* >          left eigenspaces (deflating subspaces). */
/* >          If WANTZ = .FALSE., Z is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* >          LDZ is INTEGER */
/* >          The leading dimension of the array Z. LDZ >= 1; */
/* >          If WANTZ = .TRUE., LDZ >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The dimension of the specified pair of left and right eigen- */
/* >          spaces (deflating subspaces). 0 <= M <= N. */
/* > \endverbatim */
/* > */
/* > \param[out] PL */
/* > \verbatim */
/* >          PL is REAL */
/* > \endverbatim */
/* > */
/* > \param[out] PR */
/* > \verbatim */
/* >          PR is REAL */
/* > */
/* >          If IJOB = 1, 4 or 5, PL, PR are lower bounds on the */
/* >          reciprocal of the norm of "projections" onto left and right */
/* >          eigenspaces with respect to the selected cluster. */
/* >          0 < PL, PR <= 1. */
/* >          If M = 0 or M = N, PL = PR  = 1. */
/* >          If IJOB = 0, 2 or 3, PL and PR are not referenced. */
/* > \endverbatim */
/* > */
/* > \param[out] DIF */
/* > \verbatim */
/* >          DIF is REAL array, dimension (2). */
/* >          If IJOB >= 2, DIF(1:2) store the estimates of Difu and Difl. */
/* >          If IJOB = 2 or 4, DIF(1:2) are F-norm-based upper bounds on */
/* >          Difu and Difl. If IJOB = 3 or 5, DIF(1:2) are 1-norm-based */
/* >          estimates of Difu and Difl. */
/* >          If M = 0 or N, DIF(1:2) = F-norm([A, B]). */
/* >          If IJOB = 0 or 1, DIF is not referenced. */
/* > \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 >=  4*N+16. */
/* >          If IJOB = 1, 2 or 4, LWORK >= MAX(4*N+16, 2*M*(N-M)). */
/* >          If IJOB = 3 or 5, LWORK >= MAX(4*N+16, 4*M*(N-M)). */
/* > */
/* >          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] 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 IJOB = 1, 2 or 4, LIWORK >=  N+6. */
/* >          If IJOB = 3 or 5, LIWORK >= MAX(2*M*(N-M), N+6). */
/* > */
/* >          If LIWORK = -1, then a workspace query is assumed; the */
/* >          routine only calculates the optimal size of the IWORK array, */
/* >          returns this value as the first entry of the IWORK array, and */
/* >          no error message related to LIWORK 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: Reordering of (A, B) failed because the transformed */
/* >                matrix pair (A, B) would be too far from generalized */
/* >                Schur form; the problem is very ill-conditioned. */
/* >                (A, B) may have been partially reordered. */
/* >                If requested, 0 is returned in DIF(*), PL and PR. */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup realOTHERcomputational */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  STGSEN first collects the selected eigenvalues by computing */
/* >  orthogonal U and W that move them to the top left corner of (A, B). */
/* >  In other words, the selected eigenvalues are the eigenvalues of */
/* >  (A11, B11) in: */
/* > */
/* >              U**T*(A, B)*W = (A11 A12) (B11 B12) n1 */
/* >                              ( 0  A22),( 0  B22) n2 */
/* >                                n1  n2    n1  n2 */
/* > */
/* >  where N = n1+n2 and U**T means the transpose of U. The first n1 columns */
/* >  of U and W span the specified pair of left and right eigenspaces */
/* >  (deflating subspaces) of (A, B). */
/* > */
/* >  If (A, B) has been obtained from the generalized real Schur */
/* >  decomposition of a matrix pair (C, D) = Q*(A, B)*Z**T, then the */
/* >  reordered generalized real Schur form of (C, D) is given by */
/* > */
/* >           (C, D) = (Q*U)*(U**T*(A, B)*W)*(Z*W)**T, */
/* > */
/* >  and the first n1 columns of Q*U and Z*W span the corresponding */
/* >  deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.). */
/* > */
/* >  Note that if the selected eigenvalue is sufficiently ill-conditioned, */
/* >  then its value may differ significantly from its value before */
/* >  reordering. */
/* > */
/* >  The reciprocal condition numbers of the left and right eigenspaces */
/* >  spanned by the first n1 columns of U and W (or Q*U and Z*W) may */
/* >  be returned in DIF(1:2), corresponding to Difu and Difl, resp. */
/* > */
/* >  The Difu and Difl are defined as: */
/* > */
/* >       Difu[(A11, B11), (A22, B22)] = sigma-f2cmin( Zu ) */
/* >  and */
/* >       Difl[(A11, B11), (A22, B22)] = Difu[(A22, B22), (A11, B11)], */
/* > */
/* >  where sigma-f2cmin(Zu) is the smallest singular value of the */
/* >  (2*n1*n2)-by-(2*n1*n2) matrix */
/* > */
/* >       Zu = [ kron(In2, A11)  -kron(A22**T, In1) ] */
/* >            [ kron(In2, B11)  -kron(B22**T, In1) ]. */
/* > */
/* >  Here, Inx is the identity matrix of size nx and A22**T is the */
/* >  transpose of A22. kron(X, Y) is the Kronecker product between */
/* >  the matrices X and Y. */
/* > */
/* >  When DIF(2) is small, small changes in (A, B) can cause large changes */
/* >  in the deflating subspace. An approximate (asymptotic) bound on the */
/* >  maximum angular error in the computed deflating subspaces is */
/* > */
/* >       EPS * norm((A, B)) / DIF(2), */
/* > */
/* >  where EPS is the machine precision. */
/* > */
/* >  The reciprocal norm of the projectors on the left and right */
/* >  eigenspaces associated with (A11, B11) may be returned in PL and PR. */
/* >  They are computed as follows. First we compute L and R so that */
/* >  P*(A, B)*Q is block diagonal, where */
/* > */
/* >       P = ( I -L ) n1           Q = ( I R ) n1 */
/* >           ( 0  I ) n2    and        ( 0 I ) n2 */
/* >             n1 n2                    n1 n2 */
/* > */
/* >  and (L, R) is the solution to the generalized Sylvester equation */
/* > */
/* >       A11*R - L*A22 = -A12 */
/* >       B11*R - L*B22 = -B12 */
/* > */
/* >  Then PL = (F-norm(L)**2+1)**(-1/2) and PR = (F-norm(R)**2+1)**(-1/2). */
/* >  An approximate (asymptotic) bound on the average absolute error of */
/* >  the selected eigenvalues is */
/* > */
/* >       EPS * norm((A, B)) / PL. */
/* > */
/* >  There are also global error bounds which valid for perturbations up */
/* >  to a certain restriction:  A lower bound (x) on the smallest */
/* >  F-norm(E,F) for which an eigenvalue of (A11, B11) may move and */
/* >  coalesce with an eigenvalue of (A22, B22) under perturbation (E,F), */
/* >  (i.e. (A + E, B + F), is */
/* > */
/* >   x = f2cmin(Difu,Difl)/((1/(PL*PL)+1/(PR*PR))**(1/2)+2*f2cmax(1/PL,1/PR)). */
/* > */
/* >  An approximate bound on x can be computed from DIF(1:2), PL and PR. */
/* > */
/* >  If y = ( F-norm(E,F) / x) <= 1, the angles between the perturbed */
/* >  (L', R') and unperturbed (L, R) left and right deflating subspaces */
/* >  associated with the selected cluster in the (1,1)-blocks can be */
/* >  bounded as */
/* > */
/* >   f2cmax-angle(L, L') <= arctan( y * PL / (1 - y * (1 - PL * PL)**(1/2)) */
/* >   f2cmax-angle(R, R') <= arctan( y * PR / (1 - y * (1 - PR * PR)**(1/2)) */
/* > */
/* >  See LAPACK User's Guide section 4.11 or the following references */
/* >  for more information. */
/* > */
/* >  Note that if the default method for computing the Frobenius-norm- */
/* >  based estimate DIF is not wanted (see SLATDF), then the parameter */
/* >  IDIFJB (see below) should be changed from 3 to 4 (routine SLATDF */
/* >  (IJOB = 2 will be used)). See STGSYL for more details. */
/* > \endverbatim */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* >     Umea University, S-901 87 Umea, Sweden. */

/* > \par References: */
/*  ================ */
/* > */
/* > \verbatim */
/* > */
/* >  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
/* >      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
/* >      M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
/* >      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
/* > */
/* >  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
/* >      Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
/* >      Estimation: Theory, Algorithms and Software, */
/* >      Report UMINF - 94.04, Department of Computing Science, Umea */
/* >      University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working */
/* >      Note 87. To appear in Numerical Algorithms, 1996. */
/* > */
/* >  [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
/* >      for Solving the Generalized Sylvester Equation and Estimating the */
/* >      Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
/* >      Department of Computing Science, Umea University, S-901 87 Umea, */
/* >      Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
/* >      Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, */
/* >      1996. */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ int stgsen_(integer *ijob, logical *wantq, logical *wantz, 
	logical *select, integer *n, real *a, integer *lda, real *b, integer *
	ldb, real *alphar, real *alphai, real *beta, real *q, integer *ldq, 
	real *z__, integer *ldz, integer *m, real *pl, real *pr, real *dif, 
	real *work, integer *lwork, integer *iwork, integer *liwork, integer *
	info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, 
	    z_offset, i__1, i__2;
    real r__1;

    /* Local variables */
    integer kase;
    logical pair;
    integer ierr;
    real dsum;
    logical swap;
    extern /* Subroutine */ int slag2_(real *, integer *, real *, integer *, 
	    real *, real *, real *, real *, real *, real *);
    integer i__, k, isave[3];
    logical wantd;
    integer lwmin;
    logical wantp;
    integer n1, n2;
    extern /* Subroutine */ int slacn2_(integer *, real *, real *, integer *, 
	    real *, integer *, integer *);
    logical wantd1, wantd2;
    integer kk;
    real dscale;
    integer ks;
    real rdscal;
    extern real slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slacpy_(
	    char *, integer *, integer *, real *, integer *, real *, integer *
	    ), stgexc_(logical *, logical *, integer *, real *, 
	    integer *, real *, integer *, real *, integer *, real *, integer *
	    , integer *, integer *, real *, integer *, integer *);
    integer liwmin;
    extern /* Subroutine */ int slassq_(integer *, real *, integer *, real *, 
	    real *);
    real smlnum;
    integer mn2;
    logical lquery;
    extern /* Subroutine */ int stgsyl_(char *, integer *, integer *, integer 
	    *, real *, integer *, real *, integer *, real *, integer *, real *
	    , integer *, real *, integer *, real *, integer *, real *, real *,
	     real *, integer *, integer *, integer *);
    integer ijb;
    real eps;


/*  -- LAPACK computational 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 */


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


/*     Decode and test the input parameters */

    /* Parameter adjustments */
    --select;
    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;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --dif;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1 || *liwork == -1;

    if (*ijob < 0 || *ijob > 5) {
	*info = -1;
    } else if (*n < 0) {
	*info = -5;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -7;
    } else if (*ldb < f2cmax(1,*n)) {
	*info = -9;
    } else if (*ldq < 1 || *wantq && *ldq < *n) {
	*info = -14;
    } else if (*ldz < 1 || *wantz && *ldz < *n) {
	*info = -16;
    }

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

/*     Get machine constants */

    eps = slamch_("P");
    smlnum = slamch_("S") / eps;
    ierr = 0;

    wantp = *ijob == 1 || *ijob >= 4;
    wantd1 = *ijob == 2 || *ijob == 4;
    wantd2 = *ijob == 3 || *ijob == 5;
    wantd = wantd1 || wantd2;

/*     Set M to the dimension of the specified pair of deflating */
/*     subspaces. */

    *m = 0;
    pair = FALSE_;
    if (! lquery || *ijob != 0) {
	i__1 = *n;
	for (k = 1; k <= i__1; ++k) {
	    if (pair) {
		pair = FALSE_;
	    } else {
		if (k < *n) {
		    if (a[k + 1 + k * a_dim1] == 0.f) {
			if (select[k]) {
			    ++(*m);
			}
		    } else {
			pair = TRUE_;
			if (select[k] || select[k + 1]) {
			    *m += 2;
			}
		    }
		} else {
		    if (select[*n]) {
			++(*m);
		    }
		}
	    }
/* L10: */
	}
    }

    if (*ijob == 1 || *ijob == 2 || *ijob == 4) {
/* Computing MAX */
	i__1 = 1, i__2 = (*n << 2) + 16, i__1 = f2cmax(i__1,i__2), i__2 = (*m << 
		1) * (*n - *m);
	lwmin = f2cmax(i__1,i__2);
/* Computing MAX */
	i__1 = 1, i__2 = *n + 6;
	liwmin = f2cmax(i__1,i__2);
    } else if (*ijob == 3 || *ijob == 5) {
/* Computing MAX */
	i__1 = 1, i__2 = (*n << 2) + 16, i__1 = f2cmax(i__1,i__2), i__2 = (*m << 
		2) * (*n - *m);
	lwmin = f2cmax(i__1,i__2);
/* Computing MAX */
	i__1 = 1, i__2 = (*m << 1) * (*n - *m), i__1 = f2cmax(i__1,i__2), i__2 = 
		*n + 6;
	liwmin = f2cmax(i__1,i__2);
    } else {
/* Computing MAX */
	i__1 = 1, i__2 = (*n << 2) + 16;
	lwmin = f2cmax(i__1,i__2);
	liwmin = 1;
    }

    work[1] = (real) lwmin;
    iwork[1] = liwmin;

    if (*lwork < lwmin && ! lquery) {
	*info = -22;
    } else if (*liwork < liwmin && ! lquery) {
	*info = -24;
    }

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

/*     Quick return if possible. */

    if (*m == *n || *m == 0) {
	if (wantp) {
	    *pl = 1.f;
	    *pr = 1.f;
	}
	if (wantd) {
	    dscale = 0.f;
	    dsum = 1.f;
	    i__1 = *n;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		slassq_(n, &a[i__ * a_dim1 + 1], &c__1, &dscale, &dsum);
		slassq_(n, &b[i__ * b_dim1 + 1], &c__1, &dscale, &dsum);
/* L20: */
	    }
	    dif[1] = dscale * sqrt(dsum);
	    dif[2] = dif[1];
	}
	goto L60;
    }

/*     Collect the selected blocks at the top-left corner of (A, B). */

    ks = 0;
    pair = FALSE_;
    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {
	if (pair) {
	    pair = FALSE_;
	} else {

	    swap = select[k];
	    if (k < *n) {
		if (a[k + 1 + k * a_dim1] != 0.f) {
		    pair = TRUE_;
		    swap = swap || select[k + 1];
		}
	    }

	    if (swap) {
		++ks;

/*              Swap the K-th block to position KS. */
/*              Perform the reordering of diagonal blocks in (A, B) */
/*              by orthogonal transformation matrices and update */
/*              Q and Z accordingly (if requested): */

		kk = k;
		if (k != ks) {
		    stgexc_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], 
			    ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &kk, 
			    &ks, &work[1], lwork, &ierr);
		}

		if (ierr > 0) {

/*                 Swap is rejected: exit. */

		    *info = 1;
		    if (wantp) {
			*pl = 0.f;
			*pr = 0.f;
		    }
		    if (wantd) {
			dif[1] = 0.f;
			dif[2] = 0.f;
		    }
		    goto L60;
		}

		if (pair) {
		    ++ks;
		}
	    }
	}
/* L30: */
    }
    if (wantp) {

/*        Solve generalized Sylvester equation for R and L */
/*        and compute PL and PR. */

	n1 = *m;
	n2 = *n - *m;
	i__ = n1 + 1;
	ijb = 0;
	slacpy_("Full", &n1, &n2, &a[i__ * a_dim1 + 1], lda, &work[1], &n1);
	slacpy_("Full", &n1, &n2, &b[i__ * b_dim1 + 1], ldb, &work[n1 * n2 + 
		1], &n1);
	i__1 = *lwork - (n1 << 1) * n2;
	stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ * a_dim1]
		, lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ + i__ * 
		b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &dif[1], &
		work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], &ierr);

/*        Estimate the reciprocal of norms of "projections" onto left */
/*        and right eigenspaces. */

	rdscal = 0.f;
	dsum = 1.f;
	i__1 = n1 * n2;
	slassq_(&i__1, &work[1], &c__1, &rdscal, &dsum);
	*pl = rdscal * sqrt(dsum);
	if (*pl == 0.f) {
	    *pl = 1.f;
	} else {
	    *pl = dscale / (sqrt(dscale * dscale / *pl + *pl) * sqrt(*pl));
	}
	rdscal = 0.f;
	dsum = 1.f;
	i__1 = n1 * n2;
	slassq_(&i__1, &work[n1 * n2 + 1], &c__1, &rdscal, &dsum);
	*pr = rdscal * sqrt(dsum);
	if (*pr == 0.f) {
	    *pr = 1.f;
	} else {
	    *pr = dscale / (sqrt(dscale * dscale / *pr + *pr) * sqrt(*pr));
	}
    }

    if (wantd) {

/*        Compute estimates of Difu and Difl. */

	if (wantd1) {
	    n1 = *m;
	    n2 = *n - *m;
	    i__ = n1 + 1;
	    ijb = 3;

/*           Frobenius norm-based Difu-estimate. */

	    i__1 = *lwork - (n1 << 1) * n2;
	    stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ * 
		    a_dim1], lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ + 
		    i__ * b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &
		    dif[1], &work[(n1 << 1) * n2 + 1], &i__1, &iwork[1], &
		    ierr);

/*           Frobenius norm-based Difl-estimate. */

	    i__1 = *lwork - (n1 << 1) * n2;
	    stgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, &a[
		    a_offset], lda, &work[1], &n2, &b[i__ + i__ * b_dim1], 
		    ldb, &b[b_offset], ldb, &work[n1 * n2 + 1], &n2, &dscale, 
		    &dif[2], &work[(n1 << 1) * n2 + 1], &i__1, &iwork[1], &
		    ierr);
	} else {


/*           Compute 1-norm-based estimates of Difu and Difl using */
/*           reversed communication with SLACN2. In each step a */
/*           generalized Sylvester equation or a transposed variant */
/*           is solved. */

	    kase = 0;
	    n1 = *m;
	    n2 = *n - *m;
	    i__ = n1 + 1;
	    ijb = 0;
	    mn2 = (n1 << 1) * n2;

/*           1-norm-based estimate of Difu. */

L40:
	    slacn2_(&mn2, &work[mn2 + 1], &work[1], &iwork[1], &dif[1], &kase,
		     isave);
	    if (kase != 0) {
		if (kase == 1) {

/*                 Solve generalized Sylvester equation. */

		    i__1 = *lwork - (n1 << 1) * n2;
		    stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + 
			    i__ * a_dim1], lda, &work[1], &n1, &b[b_offset], 
			    ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 + 
			    1], &n1, &dscale, &dif[1], &work[(n1 << 1) * n2 + 
			    1], &i__1, &iwork[1], &ierr);
		} else {

/*                 Solve the transposed variant. */

		    i__1 = *lwork - (n1 << 1) * n2;
		    stgsyl_("T", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + 
			    i__ * a_dim1], lda, &work[1], &n1, &b[b_offset], 
			    ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 + 
			    1], &n1, &dscale, &dif[1], &work[(n1 << 1) * n2 + 
			    1], &i__1, &iwork[1], &ierr);
		}
		goto L40;
	    }
	    dif[1] = dscale / dif[1];

/*           1-norm-based estimate of Difl. */

L50:
	    slacn2_(&mn2, &work[mn2 + 1], &work[1], &iwork[1], &dif[2], &kase,
		     isave);
	    if (kase != 0) {
		if (kase == 1) {

/*                 Solve generalized Sylvester equation. */

		    i__1 = *lwork - (n1 << 1) * n2;
		    stgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, 
			    &a[a_offset], lda, &work[1], &n2, &b[i__ + i__ * 
			    b_dim1], ldb, &b[b_offset], ldb, &work[n1 * n2 + 
			    1], &n2, &dscale, &dif[2], &work[(n1 << 1) * n2 + 
			    1], &i__1, &iwork[1], &ierr);
		} else {

/*                 Solve the transposed variant. */

		    i__1 = *lwork - (n1 << 1) * n2;
		    stgsyl_("T", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, 
			    &a[a_offset], lda, &work[1], &n2, &b[i__ + i__ * 
			    b_dim1], ldb, &b[b_offset], ldb, &work[n1 * n2 + 
			    1], &n2, &dscale, &dif[2], &work[(n1 << 1) * n2 + 
			    1], &i__1, &iwork[1], &ierr);
		}
		goto L50;
	    }
	    dif[2] = dscale / dif[2];

	}
    }

L60:

/*     Compute generalized eigenvalues of reordered pair (A, B) and */
/*     normalize the generalized Schur form. */

    pair = FALSE_;
    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {
	if (pair) {
	    pair = FALSE_;
	} else {

	    if (k < *n) {
		if (a[k + 1 + k * a_dim1] != 0.f) {
		    pair = TRUE_;
		}
	    }

	    if (pair) {

/*             Compute the eigenvalue(s) at position K. */

		work[1] = a[k + k * a_dim1];
		work[2] = a[k + 1 + k * a_dim1];
		work[3] = a[k + (k + 1) * a_dim1];
		work[4] = a[k + 1 + (k + 1) * a_dim1];
		work[5] = b[k + k * b_dim1];
		work[6] = b[k + 1 + k * b_dim1];
		work[7] = b[k + (k + 1) * b_dim1];
		work[8] = b[k + 1 + (k + 1) * b_dim1];
		r__1 = smlnum * eps;
		slag2_(&work[1], &c__2, &work[5], &c__2, &r__1, &beta[k], &
			beta[k + 1], &alphar[k], &alphar[k + 1], &alphai[k]);
		alphai[k + 1] = -alphai[k];

	    } else {

		if (r_sign(&c_b28, &b[k + k * b_dim1]) < 0.f) {

/*                 If B(K,K) is negative, make it positive */

		    i__2 = *n;
		    for (i__ = 1; i__ <= i__2; ++i__) {
			a[k + i__ * a_dim1] = -a[k + i__ * a_dim1];
			b[k + i__ * b_dim1] = -b[k + i__ * b_dim1];
			if (*wantq) {
			    q[i__ + k * q_dim1] = -q[i__ + k * q_dim1];
			}
/* L80: */
		    }
		}

		alphar[k] = a[k + k * a_dim1];
		alphai[k] = 0.f;
		beta[k] = b[k + k * b_dim1];

	    }
	}
/* L70: */
    }

    work[1] = (real) lwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of STGSEN */

} /* stgsen_ */