OpenBLAS/lapack-netlib/SRC/sggesx.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 blasint logical;

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 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);}
#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++ */


#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#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;
static real c_b42 = 0.f;
static real c_b43 = 1.f;

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

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

/*       SUBROUTINE SGGESX( JOBVSL, JOBVSR, SORT, SELCTG, SENSE, N, A, LDA, */
/*                          B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, */
/*                          VSR, LDVSR, RCONDE, RCONDV, WORK, LWORK, IWORK, */
/*                          LIWORK, BWORK, INFO ) */

/*       CHARACTER          JOBVSL, JOBVSR, SENSE, SORT */
/*       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LIWORK, LWORK, N, */
/*      $                   SDIM */
/*       LOGICAL            BWORK( * ) */
/*       INTEGER            IWORK( * ) */
/*       REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
/*      $                   B( LDB, * ), BETA( * ), RCONDE( 2 ), */
/*      $                   RCONDV( 2 ), VSL( LDVSL, * ), VSR( LDVSR, * ), */
/*      $                   WORK( * ) */
/*       LOGICAL            SELCTG */
/*       EXTERNAL           SELCTG */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGGESX computes for a pair of N-by-N real nonsymmetric matrices */
/* > (A,B), the generalized eigenvalues, the real Schur form (S,T), and, */
/* > optionally, the left and/or right matrices of Schur vectors (VSL and */
/* > VSR).  This gives the generalized Schur factorization */
/* > */
/* >      (A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T ) */
/* > */
/* > Optionally, it also orders the eigenvalues so that a selected cluster */
/* > of eigenvalues appears in the leading diagonal blocks of the upper */
/* > quasi-triangular matrix S and the upper triangular matrix T; computes */
/* > a reciprocal condition number for the average of the selected */
/* > eigenvalues (RCONDE); and computes a reciprocal condition number for */
/* > the right and left deflating subspaces corresponding to the selected */
/* > eigenvalues (RCONDV). The leading columns of VSL and VSR then form */
/* > an orthonormal basis for the corresponding left and right eigenspaces */
/* > (deflating subspaces). */
/* > */
/* > A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */
/* > or a ratio alpha/beta = w, such that  A - w*B is singular.  It is */
/* > usually represented as the pair (alpha,beta), as there is a */
/* > reasonable interpretation for beta=0 or for both being zero. */
/* > */
/* > A pair of matrices (S,T) is in generalized real Schur form if T is */
/* > upper triangular with non-negative diagonal and S is block upper */
/* > triangular with 1-by-1 and 2-by-2 blocks.  1-by-1 blocks correspond */
/* > to real generalized eigenvalues, while 2-by-2 blocks of S will be */
/* > "standardized" by making the corresponding elements of T have the */
/* > form: */
/* >         [  a  0  ] */
/* >         [  0  b  ] */
/* > */
/* > and the pair of corresponding 2-by-2 blocks in S and T will have a */
/* > complex conjugate pair of generalized eigenvalues. */
/* > */
/* > \endverbatim */

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

/* > \param[in] JOBVSL */
/* > \verbatim */
/* >          JOBVSL is CHARACTER*1 */
/* >          = 'N':  do not compute the left Schur vectors; */
/* >          = 'V':  compute the left Schur vectors. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVSR */
/* > \verbatim */
/* >          JOBVSR is CHARACTER*1 */
/* >          = 'N':  do not compute the right Schur vectors; */
/* >          = 'V':  compute the right Schur vectors. */
/* > \endverbatim */
/* > */
/* > \param[in] SORT */
/* > \verbatim */
/* >          SORT is CHARACTER*1 */
/* >          Specifies whether or not to order the eigenvalues on the */
/* >          diagonal of the generalized Schur form. */
/* >          = 'N':  Eigenvalues are not ordered; */
/* >          = 'S':  Eigenvalues are ordered (see SELCTG). */
/* > \endverbatim */
/* > */
/* > \param[in] SELCTG */
/* > \verbatim */
/* >          SELCTG is a LOGICAL FUNCTION of three REAL arguments */
/* >          SELCTG must be declared EXTERNAL in the calling subroutine. */
/* >          If SORT = 'N', SELCTG is not referenced. */
/* >          If SORT = 'S', SELCTG is used to select eigenvalues to sort */
/* >          to the top left of the Schur form. */
/* >          An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if */
/* >          SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either */
/* >          one of a complex conjugate pair of eigenvalues is selected, */
/* >          then both complex eigenvalues are selected. */
/* >          Note that a selected complex eigenvalue may no longer satisfy */
/* >          SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) = .TRUE. after ordering, */
/* >          since ordering may change the value of complex eigenvalues */
/* >          (especially if the eigenvalue is ill-conditioned), in this */
/* >          case INFO is set to N+3. */
/* > \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 deflating subspaces 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 matrices A, B, VSL, and VSR.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA, N) */
/* >          On entry, the first of the pair of matrices. */
/* >          On exit, A has been overwritten by its generalized Schur */
/* >          form S. */
/* > \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 second of the pair of matrices. */
/* >          On exit, B has been overwritten by its generalized Schur */
/* >          form T. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of B.  LDB >= 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 SELCTG is true.  (Complex conjugate pairs for which */
/* >          SELCTG is true for either eigenvalue count as 2.) */
/* > \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 Schur form of (A,B) were further reduced to */
/* >          triangular form using 2-by-2 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. */
/* > */
/* >          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
/* >          may easily over- or underflow, and BETA(j) may even be zero. */
/* >          Thus, the user should avoid naively computing the ratio. */
/* >          However, ALPHAR and ALPHAI will be always less than and */
/* >          usually comparable with norm(A) in magnitude, and BETA always */
/* >          less than and usually comparable with norm(B). */
/* > \endverbatim */
/* > */
/* > \param[out] VSL */
/* > \verbatim */
/* >          VSL is REAL array, dimension (LDVSL,N) */
/* >          If JOBVSL = 'V', VSL will contain the left Schur vectors. */
/* >          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', VSR will contain the right Schur vectors. */
/* >          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] RCONDE */
/* > \verbatim */
/* >          RCONDE is REAL array, dimension ( 2 ) */
/* >          If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the */
/* >          reciprocal condition numbers for the average of the selected */
/* >          eigenvalues. */
/* >          Not referenced if SENSE = 'N' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDV */
/* > \verbatim */
/* >          RCONDV is REAL array, dimension ( 2 ) */
/* >          If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the */
/* >          reciprocal condition numbers for the selected deflating */
/* >          subspaces. */
/* >          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. */
/* >          If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B', */
/* >          LWORK >= f2cmax( 8*N, 6*N+16, 2*SDIM*(N-SDIM) ), else */
/* >          LWORK >= f2cmax( 8*N, 6*N+16 ). */
/* >          Note that 2*SDIM*(N-SDIM) <= N*N/2. */
/* >          Note also that an error is only returned if */
/* >          LWORK < f2cmax( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B' */
/* >          this may not be large enough. */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates the bound on the optimal size of the WORK */
/* >          array and the minimum size of the IWORK array, returns these */
/* >          values as the first entries of the WORK and IWORK arrays, and */
/* >          no error message related to LWORK or LIWORK 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 minimum LIWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LIWORK */
/* > \verbatim */
/* >          LIWORK is INTEGER */
/* >          The dimension of the array IWORK. */
/* >          If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise */
/* >          LIWORK >= N+6. */
/* > */
/* >          If LIWORK = -1, then a workspace query is assumed; the */
/* >          routine only calculates the bound on the optimal size of the */
/* >          WORK array and the minimum size of the IWORK array, returns */
/* >          these values as the first entries of the WORK and IWORK */
/* >          arrays, and no error message related to LWORK or LIWORK is */
/* >          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. */
/* >          = 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:  =N+1: other than QZ iteration failed in SHGEQZ */
/* >                =N+2: after reordering, roundoff changed values of */
/* >                      some complex eigenvalues so that leading */
/* >                      eigenvalues in the Generalized Schur form no */
/* >                      longer satisfy SELCTG=.TRUE.  This could also */
/* >                      be caused due to scaling. */
/* >                =N+3: reordering failed in STGSEN. */
/* > \endverbatim */

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

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

/* > \date June 2017 */

/* > \ingroup realGEeigen */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  An approximate (asymptotic) bound on the average absolute error of */
/* >  the selected eigenvalues is */
/* > */
/* >       EPS * norm((A, B)) / RCONDE( 1 ). */
/* > */
/* >  An approximate (asymptotic) bound on the maximum angular error in */
/* >  the computed deflating subspaces is */
/* > */
/* >       EPS * norm((A, B)) / RCONDV( 2 ). */
/* > */
/* >  See LAPACK User's Guide, section 4.11 for more information. */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void sggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp 
	selctg, char *sense, integer *n, real *a, integer *lda, real *b, 
	integer *ldb, integer *sdim, real *alphar, real *alphai, real *beta, 
	real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *rconde, 
	real *rcondv, real *work, integer *lwork, integer *iwork, integer *
	liwork, logical *bwork, 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;
    real r__1;

    /* Local variables */
    integer ijob;
    real anrm, bnrm;
    integer ierr, itau, iwrk, lwrk, i__;
    extern logical lsame_(char *, char *);
    integer ileft, icols;
    logical cursl, ilvsl, ilvsr;
    integer irows;
    logical lst2sl;
    extern /* Subroutine */ void slabad_(real *, real *);
    integer ip;
    real pl;
    extern /* Subroutine */ void 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 *);
    real pr;
    logical ilascl, ilbscl;
    extern real slamch_(char *), slange_(char *, integer *, integer *,
	     real *, integer *, real *);
    real safmin;
    extern /* Subroutine */ void sgghrd_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, integer *, real *, integer *
	    , real *, integer *, integer *);
    real safmax;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    real bignum;
    extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    integer ijobvl, iright;
    extern /* Subroutine */ void sgeqrf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *);
    integer ijobvr;
    extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *);
    logical wantsb, wantse, lastsl;
    integer liwmin;
    real anrmto, bnrmto;
    integer minwrk, maxwrk;
    logical wantsn;
    real smlnum;
    extern /* Subroutine */ void shgeqz_(char *, char *, char *, integer *, 
	    integer *, integer *, real *, integer *, real *, integer *, real *
	    , real *, real *, real *, integer *, real *, integer *, real *, 
	    integer *, integer *), slaset_(char *, 
	    integer *, integer *, real *, real *, real *, integer *), 
	    sorgqr_(integer *, integer *, integer *, real *, integer *, real *
	    , real *, integer *, integer *), stgsen_(integer *, logical *, 
	    logical *, logical *, integer *, real *, integer *, real *, 
	    integer *, real *, real *, real *, real *, integer *, real *, 
	    integer *, integer *, real *, real *, real *, real *, integer *, 
	    integer *, integer *, integer *);
    logical wantst, lquery, wantsv;
    extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    integer *, integer *);
    real dif[2];
    integer ihi, ilo;
    real eps;


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


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


/*     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;
    --rconde;
    --rcondv;
    --work;
    --iwork;
    --bwork;

    /* 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_;
    }

    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 (wantsn) {
	ijob = 0;
    } else if (wantse) {
	ijob = 1;
    } else if (wantsv) {
	ijob = 2;
    } else if (wantsb) {
	ijob = 4;
    }

/*     Test the input arguments */

    *info = 0;
    if (ijobvl <= 0) {
	*info = -1;
    } else if (ijobvr <= 0) {
	*info = -2;
    } else if (! wantst && ! lsame_(sort, "N")) {
	*info = -3;
    } else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && ! 
	    wantsn) {
	*info = -5;
    } else if (*n < 0) {
	*info = -6;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -8;
    } else if (*ldb < f2cmax(1,*n)) {
	*info = -10;
    } else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
	*info = -16;
    } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
	*info = -18;
    }

/*     Compute workspace */
/*      (Note: Comments in the code beginning "Workspace:" describe the */
/*       minimal amount of workspace needed at that point in the code, */
/*       as well as the preferred amount for good performance. */
/*       NB refers to the optimal block size for the immediately */
/*       following subroutine, as returned by ILAENV.) */

    if (*info == 0) {
	if (*n > 0) {
/* Computing MAX */
	    i__1 = *n << 3, i__2 = *n * 6 + 16;
	    minwrk = f2cmax(i__1,i__2);
	    maxwrk = minwrk - *n + *n * ilaenv_(&c__1, "SGEQRF", " ", n, &
		    c__1, n, &c__0, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = minwrk - *n + *n * ilaenv_(&c__1, "SORMQR", 
		    " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = f2cmax(i__1,i__2);
	    if (ilvsl) {
/* Computing MAX */
		i__1 = maxwrk, i__2 = minwrk - *n + *n * ilaenv_(&c__1, "SOR"
			"GQR", " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
		maxwrk = f2cmax(i__1,i__2);
	    }
	    lwrk = maxwrk;
	    if (ijob >= 1) {
/* Computing MAX */
		i__1 = lwrk, i__2 = *n * *n / 2;
		lwrk = f2cmax(i__1,i__2);
	    }
	} else {
	    minwrk = 1;
	    maxwrk = 1;
	    lwrk = 1;
	}
	work[1] = (real) lwrk;
	if (wantsn || *n == 0) {
	    liwmin = 1;
	} else {
	    liwmin = *n + 6;
	}
	iwork[1] = liwmin;

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

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

/*     Quick return if possible */

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

/*     Get machine constants */

    eps = slamch_("P");
    safmin = slamch_("S");
    safmax = 1.f / safmin;
    slabad_(&safmin, &safmax);
    smlnum = sqrt(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__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
		ierr);
    }

/*     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__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
		ierr);
    }

/*     Permute the matrix to make it more nearly triangular */
/*     (Workspace: need 6*N + 2*N for permutation parameters) */

    ileft = 1;
    iright = *n + 1;
    iwrk = iright + *n;
    sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
	    ileft], &work[iright], &work[iwrk], &ierr);

/*     Reduce B to triangular form (QR decomposition of B) */
/*     (Workspace: need N, prefer N*NB) */

    irows = ihi + 1 - ilo;
    icols = *n + 1 - ilo;
    itau = iwrk;
    iwrk = itau + irows;
    i__1 = *lwork + 1 - iwrk;
    sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
	    iwrk], &i__1, &ierr);

/*     Apply the orthogonal transformation to matrix A */
/*     (Workspace: need N, prefer N*NB) */

    i__1 = *lwork + 1 - iwrk;
    sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
	    work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
	    ierr);

/*     Initialize VSL */
/*     (Workspace: need N, prefer N*NB) */

    if (ilvsl) {
	slaset_("Full", n, n, &c_b42, &c_b43, &vsl[vsl_offset], ldvsl);
	if (irows > 1) {
	    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 - iwrk;
	sorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
		work[itau], &work[iwrk], &i__1, &ierr);
    }

/*     Initialize VSR */

    if (ilvsr) {
	slaset_("Full", n, n, &c_b42, &c_b43, &vsr[vsr_offset], ldvsr);
    }

/*     Reduce to generalized Hessenberg form */
/*     (Workspace: none needed) */

    sgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
	    ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);

    *sdim = 0;

/*     Perform QZ algorithm, computing Schur vectors if desired */
/*     (Workspace: need N) */

    iwrk = itau;
    i__1 = *lwork + 1 - iwrk;
    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[iwrk], &i__1, &ierr);
    if (ierr != 0) {
	if (ierr > 0 && ierr <= *n) {
	    *info = ierr;
	} else if (ierr > *n && ierr <= *n << 1) {
	    *info = ierr - *n;
	} else {
	    *info = *n + 1;
	}
	goto L50;
    }

/*     Sort eigenvalues ALPHA/BETA and compute the reciprocal of */
/*     condition number(s) */
/*     (Workspace: If IJOB >= 1, need MAX( 8*(N+1), 2*SDIM*(N-SDIM) ) */
/*                 otherwise, need 8*(N+1) ) */

    if (wantst) {

/*        Undo scaling on eigenvalues before SELCTGing */

	if (ilascl) {
	    slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], 
		    n, &ierr);
	    slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], 
		    n, &ierr);
	}
	if (ilbscl) {
	    slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, 
		    &ierr);
	}

/*        Select eigenvalues */

	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    bwork[i__] = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
/* L10: */
	}

/*        Reorder eigenvalues, transform Generalized Schur vectors, and */
/*        compute reciprocal condition numbers */

	i__1 = *lwork - iwrk + 1;
	stgsen_(&ijob, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
		b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[
		vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pl, &pr, 
		dif, &work[iwrk], &i__1, &iwork[1], liwork, &ierr);

	if (ijob >= 1) {
/* Computing MAX */
	    i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
	    maxwrk = f2cmax(i__1,i__2);
	}
	if (ierr == -22) {

/*            not enough real workspace */

	    *info = -22;
	} else {
	    if (ijob == 1 || ijob == 4) {
		rconde[1] = pl;
		rconde[2] = pr;
	    }
	    if (ijob == 2 || ijob == 4) {
		rcondv[1] = dif[0];
		rcondv[2] = dif[1];
	    }
	    if (ierr == 1) {
		*info = *n + 3;
	    }
	}

    }

/*     Apply permutation to VSL and VSR */
/*     (Workspace: none needed) */

    if (ilvsl) {
	sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
		vsl_offset], ldvsl, &ierr);
    }

    if (ilvsr) {
	sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
		vsr_offset], ldvsr, &ierr);
    }

/*     Check if unscaling would cause over/underflow, if so, rescale */
/*     (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of */
/*     B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) */

    if (ilascl) {
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (alphai[i__] != 0.f) {
		if (alphar[i__] / safmax > anrmto / anrm || safmin / alphar[
			i__] > anrm / anrmto) {
		    work[1] = (r__1 = a[i__ + i__ * a_dim1] / alphar[i__], 
			    abs(r__1));
		    beta[i__] *= work[1];
		    alphar[i__] *= work[1];
		    alphai[i__] *= work[1];
		} else if (alphai[i__] / safmax > anrmto / anrm || safmin / 
			alphai[i__] > anrm / anrmto) {
		    work[1] = (r__1 = a[i__ + (i__ + 1) * a_dim1] / alphai[
			    i__], abs(r__1));
		    beta[i__] *= work[1];
		    alphar[i__] *= work[1];
		    alphai[i__] *= work[1];
		}
	    }
/* L20: */
	}
    }

    if (ilbscl) {
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (alphai[i__] != 0.f) {
		if (beta[i__] / safmax > bnrmto / bnrm || safmin / beta[i__] 
			> bnrm / bnrmto) {
		    work[1] = (r__1 = b[i__ + i__ * b_dim1] / beta[i__], abs(
			    r__1));
		    beta[i__] *= work[1];
		    alphar[i__] *= work[1];
		    alphai[i__] *= work[1];
		}
	    }
/* L25: */
	}
    }

/*     Undo scaling */

    if (ilascl) {
	slascl_("H", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
		ierr);
	slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
		ierr);
	slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
		ierr);
    }

    if (ilbscl) {
	slascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
		ierr);
	slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
		ierr);
    }

    if (wantst) {

/*        Check if reordering is correct */

	lastsl = TRUE_;
	lst2sl = TRUE_;
	*sdim = 0;
	ip = 0;
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    cursl = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
	    if (alphai[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;
/* L40: */
	}

    }

L50:

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

    return;

/*     End of SGGESX */

} /* sggesx_ */