OpenBLAS/lapack-netlib/SRC/sgeevx.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)}

/*  -- 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> SGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE mat
rices</b> */

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

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

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

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

/*       SUBROUTINE SGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI, */
/*                          VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, */
/*                          RCONDE, RCONDV, WORK, LWORK, IWORK, INFO ) */

/*       CHARACTER          BALANC, JOBVL, JOBVR, SENSE */
/*       INTEGER            IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N */
/*       REAL               ABNRM */
/*       INTEGER            IWORK( * ) */
/*       REAL               A( LDA, * ), RCONDE( * ), RCONDV( * ), */
/*      $                   SCALE( * ), VL( LDVL, * ), VR( LDVR, * ), */
/*      $                   WI( * ), WORK( * ), WR( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGEEVX computes for an N-by-N real nonsymmetric matrix A, the */
/* > eigenvalues and, optionally, the left and/or right eigenvectors. */
/* > */
/* > Optionally also, it computes a balancing transformation to improve */
/* > the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */
/* > SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues */
/* > (RCONDE), and reciprocal condition numbers for the right */
/* > eigenvectors (RCONDV). */
/* > */
/* > The right eigenvector v(j) of A satisfies */
/* >                  A * v(j) = lambda(j) * v(j) */
/* > where lambda(j) is its eigenvalue. */
/* > The left eigenvector u(j) of A satisfies */
/* >               u(j)**H * A = lambda(j) * u(j)**H */
/* > where u(j)**H denotes the conjugate-transpose of u(j). */
/* > */
/* > The computed eigenvectors are normalized to have Euclidean norm */
/* > equal to 1 and largest component real. */
/* > */
/* > Balancing a matrix means permuting the rows and columns to make it */
/* > more nearly upper triangular, and applying a diagonal similarity */
/* > transformation D * A * D**(-1), where D is a diagonal matrix, to */
/* > make its rows and columns closer in norm and the condition numbers */
/* > of its eigenvalues and eigenvectors smaller.  The computed */
/* > reciprocal condition numbers correspond to the balanced matrix. */
/* > Permuting rows and columns will not change the condition numbers */
/* > (in exact arithmetic) but diagonal scaling will.  For further */
/* > explanation of balancing, see section 4.10.2 of the LAPACK */
/* > Users' Guide. */
/* > \endverbatim */

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

/* > \param[in] BALANC */
/* > \verbatim */
/* >          BALANC is CHARACTER*1 */
/* >          Indicates how the input matrix should be diagonally scaled */
/* >          and/or permuted to improve the conditioning of its */
/* >          eigenvalues. */
/* >          = 'N': Do not diagonally scale or permute; */
/* >          = 'P': Perform permutations to make the matrix more nearly */
/* >                 upper triangular. Do not diagonally scale; */
/* >          = 'S': Diagonally scale the matrix, i.e. replace A by */
/* >                 D*A*D**(-1), where D is a diagonal matrix chosen */
/* >                 to make the rows and columns of A more equal in */
/* >                 norm. Do not permute; */
/* >          = 'B': Both diagonally scale and permute A. */
/* > */
/* >          Computed reciprocal condition numbers will be for the matrix */
/* >          after balancing and/or permuting. Permuting does not change */
/* >          condition numbers (in exact arithmetic), but balancing does. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVL */
/* > \verbatim */
/* >          JOBVL is CHARACTER*1 */
/* >          = 'N': left eigenvectors of A are not computed; */
/* >          = 'V': left eigenvectors of A are computed. */
/* >          If SENSE = 'E' or 'B', JOBVL must = 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVR */
/* > \verbatim */
/* >          JOBVR is CHARACTER*1 */
/* >          = 'N': right eigenvectors of A are not computed; */
/* >          = 'V': right eigenvectors of A are computed. */
/* >          If SENSE = 'E' or 'B', JOBVR must = 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] SENSE */
/* > \verbatim */
/* >          SENSE is CHARACTER*1 */
/* >          Determines which reciprocal condition numbers are computed. */
/* >          = 'N': None are computed; */
/* >          = 'E': Computed for eigenvalues only; */
/* >          = 'V': Computed for right eigenvectors only; */
/* >          = 'B': Computed for eigenvalues and right eigenvectors. */
/* > */
/* >          If SENSE = 'E' or 'B', both left and right eigenvectors */
/* >          must also be computed (JOBVL = 'V' and JOBVR = 'V'). */
/* > \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 has been overwritten.  If JOBVL = 'V' or */
/* >          JOBVR = 'V', A contains the real Schur form of the balanced */
/* >          version of the input matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
/* > \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.  Complex */
/* >          conjugate pairs of eigenvalues will appear consecutively */
/* >          with the eigenvalue having the positive imaginary part */
/* >          first. */
/* > \endverbatim */
/* > */
/* > \param[out] VL */
/* > \verbatim */
/* >          VL is REAL array, dimension (LDVL,N) */
/* >          If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* >          after another in the columns of VL, in the same order */
/* >          as their eigenvalues. */
/* >          If JOBVL = 'N', VL is not referenced. */
/* >          If the j-th eigenvalue is real, then u(j) = VL(:,j), */
/* >          the j-th column of VL. */
/* >          If the j-th and (j+1)-st eigenvalues form a complex */
/* >          conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and */
/* >          u(j+1) = VL(:,j) - i*VL(:,j+1). */
/* > \endverbatim */
/* > */
/* > \param[in] LDVL */
/* > \verbatim */
/* >          LDVL is INTEGER */
/* >          The leading dimension of the array VL.  LDVL >= 1; if */
/* >          JOBVL = 'V', LDVL >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] VR */
/* > \verbatim */
/* >          VR is REAL array, dimension (LDVR,N) */
/* >          If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* >          after another in the columns of VR, in the same order */
/* >          as their eigenvalues. */
/* >          If JOBVR = 'N', VR is not referenced. */
/* >          If the j-th eigenvalue is real, then v(j) = VR(:,j), */
/* >          the j-th column of VR. */
/* >          If the j-th and (j+1)-st eigenvalues form a complex */
/* >          conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and */
/* >          v(j+1) = VR(:,j) - i*VR(:,j+1). */
/* > \endverbatim */
/* > */
/* > \param[in] LDVR */
/* > \verbatim */
/* >          LDVR is INTEGER */
/* >          The leading dimension of the array VR.  LDVR >= 1, and if */
/* >          JOBVR = 'V', LDVR >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] ILO */
/* > \verbatim */
/* >          ILO is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[out] IHI */
/* > \verbatim */
/* >          IHI is INTEGER */
/* >          ILO and IHI are integer values determined when A was */
/* >          balanced.  The balanced A(i,j) = 0 if I > J and */
/* >          J = 1,...,ILO-1 or I = IHI+1,...,N. */
/* > \endverbatim */
/* > */
/* > \param[out] SCALE */
/* > \verbatim */
/* >          SCALE is REAL array, dimension (N) */
/* >          Details of the permutations and scaling factors applied */
/* >          when balancing A.  If P(j) is the index of the row and column */
/* >          interchanged with row and column j, and D(j) is the scaling */
/* >          factor applied to row and column j, then */
/* >          SCALE(J) = P(J),    for J = 1,...,ILO-1 */
/* >                   = D(J),    for J = ILO,...,IHI */
/* >                   = P(J)     for J = IHI+1,...,N. */
/* >          The order in which the interchanges are made is N to IHI+1, */
/* >          then 1 to ILO-1. */
/* > \endverbatim */
/* > */
/* > \param[out] ABNRM */
/* > \verbatim */
/* >          ABNRM is REAL */
/* >          The one-norm of the balanced matrix (the maximum */
/* >          of the sum of absolute values of elements of any column). */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDE */
/* > \verbatim */
/* >          RCONDE is REAL array, dimension (N) */
/* >          RCONDE(j) is the reciprocal condition number of the j-th */
/* >          eigenvalue. */
/* > \endverbatim */
/* > */
/* > \param[out] RCONDV */
/* > \verbatim */
/* >          RCONDV is REAL array, dimension (N) */
/* >          RCONDV(j) is the reciprocal condition number of the j-th */
/* >          right eigenvector. */
/* > \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 SENSE = 'N' or 'E', */
/* >          LWORK >= f2cmax(1,2*N), and if JOBVL = 'V' or JOBVR = 'V', */
/* >          LWORK >= 3*N.  If SENSE = 'V' or 'B', LWORK >= N*(N+6). */
/* >          For good performance, LWORK must generally be larger. */
/* > */
/* >          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 (2*N-2) */
/* >          If SENSE = 'N' or 'E', not referenced. */
/* > \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, the QR algorithm failed to compute all the */
/* >                eigenvalues, and no eigenvectors or condition numbers */
/* >                have been computed; elements 1:ILO-1 and i+1:N of WR */
/* >                and WI contain eigenvalues which have converged. */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/*  @generated from dgeevx.f, fortran d -> s, Tue Apr 19 01:47:44 2016 */

/* > \ingroup realGEeigen */

/*  ===================================================================== */
/* Subroutine */ void sgeevx_(char *balanc, char *jobvl, char *jobvr, char *
	sense, integer *n, real *a, integer *lda, real *wr, real *wi, real *
	vl, integer *ldvl, real *vr, integer *ldvr, integer *ilo, integer *
	ihi, real *scale, real *abnrm, real *rconde, real *rcondv, real *work,
	 integer *lwork, integer *iwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, 
	    i__2, i__3;
    real r__1, r__2;

    /* Local variables */
    char side[1];
    real anrm;
    integer ierr, itau, iwrk, nout;
    extern /* Subroutine */ void srot_(integer *, real *, integer *, real *, 
	    integer *, real *, real *);
    extern real snrm2_(integer *, real *, integer *);
    integer i__, k;
    real r__;
    integer icond;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
    extern real slapy2_(real *, real *);
    real cs;
    extern /* Subroutine */ void slabad_(real *, real *);
    logical scalea;
    real cscale;
    extern /* Subroutine */ void sgebak_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, integer *, integer *), sgebal_(char *, integer *, real *, integer *, 
	    integer *, integer *, real *, integer *);
    real sn;
    extern real slamch_(char *), slange_(char *, integer *, integer *,
	     real *, integer *, real *);
    extern /* Subroutine */ void sgehrd_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *);
    extern int xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    logical select[1];
    real bignum;
    extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    extern integer isamax_(integer *, real *, integer *);
    extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *), slartg_(real *, real *, 
	    real *, real *, real *), 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;
    extern /* Subroutine */ void strsna_(char *, char *, logical *, integer *, 
	    real *, integer *, real *, integer *, real *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *, 
	    integer *);
    logical wantvl, wntsnb;
    integer hswork;
    logical wntsne;
    real smlnum;
    logical lquery, wantvr, wntsnn, wntsnv;
    extern /* Subroutine */ void strevc3_(char *, char *, logical *, integer *,
	     real *, integer *, real *, integer *, real *, integer *, integer 
	    *, integer *, real *, integer *, integer *);
    char job[1];
    real scl, dum[1], eps;
    integer lwork_trevc__;


/*  -- 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 2016 */


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


/*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --wr;
    --wi;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1 * 1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1 * 1;
    vr -= vr_offset;
    --scale;
    --rconde;
    --rcondv;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1;
    wantvl = lsame_(jobvl, "V");
    wantvr = lsame_(jobvr, "V");
    wntsnn = lsame_(sense, "N");
    wntsne = lsame_(sense, "E");
    wntsnv = lsame_(sense, "V");
    wntsnb = lsame_(sense, "B");
    if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P") 
	    || lsame_(balanc, "B"))) {
	*info = -1;
    } else if (! wantvl && ! lsame_(jobvl, "N")) {
	*info = -2;
    } else if (! wantvr && ! lsame_(jobvr, "N")) {
	*info = -3;
    } else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb) 
	    && ! (wantvl && wantvr)) {
	*info = -4;
    } else if (*n < 0) {
	*info = -5;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -7;
    } else if (*ldvl < 1 || wantvl && *ldvl < *n) {
	*info = -11;
    } else if (*ldvr < 1 || wantvr && *ldvr < *n) {
	*info = -13;
    }

/*     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. */
/*       HSWORK refers to the workspace preferred by SHSEQR, as */
/*       calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/*       the worst case.) */

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

	    if (wantvl) {
		strevc3_("L", "B", select, n, &a[a_offset], lda, &vl[
			vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &
			work[1], &c_n1, &ierr);
		lwork_trevc__ = (integer) work[1];
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n + lwork_trevc__;
		maxwrk = f2cmax(i__1,i__2);
		shseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
			1], &vl[vl_offset], ldvl, &work[1], &c_n1, info);
	    } else if (wantvr) {
		strevc3_("R", "B", select, n, &a[a_offset], lda, &vl[
			vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &
			work[1], &c_n1, &ierr);
		lwork_trevc__ = (integer) work[1];
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n + lwork_trevc__;
		maxwrk = f2cmax(i__1,i__2);
		shseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
			1], &vr[vr_offset], ldvr, &work[1], &c_n1, info);
	    } else {
		if (wntsnn) {
		    shseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &wr[1], 
			    &wi[1], &vr[vr_offset], ldvr, &work[1], &c_n1, 
			    info);
		} else {
		    shseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &wr[1], 
			    &wi[1], &vr[vr_offset], ldvr, &work[1], &c_n1, 
			    info);
		}
	    }
	    hswork = (integer) work[1];

	    if (! wantvl && ! wantvr) {
		minwrk = *n << 1;
		if (! wntsnn) {
/* Computing MAX */
		    i__1 = minwrk, i__2 = *n * *n + *n * 6;
		    minwrk = f2cmax(i__1,i__2);
		}
		maxwrk = f2cmax(maxwrk,hswork);
		if (! wntsnn) {
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *n * *n + *n * 6;
		    maxwrk = f2cmax(i__1,i__2);
		}
	    } else {
		minwrk = *n * 3;
		if (! wntsnn && ! wntsne) {
/* Computing MAX */
		    i__1 = minwrk, i__2 = *n * *n + *n * 6;
		    minwrk = f2cmax(i__1,i__2);
		}
		maxwrk = f2cmax(maxwrk,hswork);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "SORGHR",
			 " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
		maxwrk = f2cmax(i__1,i__2);
		if (! wntsnn && ! wntsne) {
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *n * *n + *n * 6;
		    maxwrk = f2cmax(i__1,i__2);
		}
/* Computing MAX */
		i__1 = maxwrk, i__2 = *n * 3;
		maxwrk = f2cmax(i__1,i__2);
	    }
	    maxwrk = f2cmax(maxwrk,minwrk);
	}
	work[1] = (real) maxwrk;

	if (*lwork < minwrk && ! lquery) {
	    *info = -21;
	}
    }

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

/*     Quick return if possible */

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

/*     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] */

    icond = 0;
    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);
    }

/*     Balance the matrix and compute ABNRM */

    sgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
    *abnrm = slange_("1", n, n, &a[a_offset], lda, dum);
    if (scalea) {
	dum[0] = *abnrm;
	slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
		ierr);
	*abnrm = dum[0];
    }

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

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

    if (wantvl) {

/*        Want left eigenvectors */
/*        Copy Householder vectors to VL */

	*(unsigned char *)side = 'L';
	slacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
		;

/*        Generate orthogonal matrix in VL */
/*        (Workspace: need 2*N-1, prefer N+(N-1)*NB) */

	i__1 = *lwork - iwrk + 1;
	sorghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
		i__1, &ierr);

/*        Perform QR iteration, accumulating Schur vectors in VL */
/*        (Workspace: need 1, prefer HSWORK (see comments) ) */

	iwrk = itau;
	i__1 = *lwork - iwrk + 1;
	shseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[1], &vl[
		vl_offset], ldvl, &work[iwrk], &i__1, info);

	if (wantvr) {

/*           Want left and right eigenvectors */
/*           Copy Schur vectors to VR */

	    *(unsigned char *)side = 'B';
	    slacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
	}

    } else if (wantvr) {

/*        Want right eigenvectors */
/*        Copy Householder vectors to VR */

	*(unsigned char *)side = 'R';
	slacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
		;

/*        Generate orthogonal matrix in VR */
/*        (Workspace: need 2*N-1, prefer N+(N-1)*NB) */

	i__1 = *lwork - iwrk + 1;
	sorghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], &
		i__1, &ierr);

/*        Perform QR iteration, accumulating Schur vectors in VR */
/*        (Workspace: need 1, prefer HSWORK (see comments) ) */

	iwrk = itau;
	i__1 = *lwork - iwrk + 1;
	shseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[1], &vr[
		vr_offset], ldvr, &work[iwrk], &i__1, info);

    } else {

/*        Compute eigenvalues only */
/*        If condition numbers desired, compute Schur form */

	if (wntsnn) {
	    *(unsigned char *)job = 'E';
	} else {
	    *(unsigned char *)job = 'S';
	}

/*        (Workspace: need 1, prefer HSWORK (see comments) ) */

	iwrk = itau;
	i__1 = *lwork - iwrk + 1;
	shseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[1], &vr[
		vr_offset], ldvr, &work[iwrk], &i__1, info);
    }

/*     If INFO .NE. 0 from SHSEQR, then quit */

    if (*info != 0) {
	goto L50;
    }

    if (wantvl || wantvr) {

/*        Compute left and/or right eigenvectors */
/*        (Workspace: need 3*N, prefer N + 2*N*NB) */

	i__1 = *lwork - iwrk + 1;
	strevc3_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], 
		ldvl, &vr[vr_offset], ldvr, n, &nout, &work[iwrk], &i__1, &
		ierr);
    }

/*     Compute condition numbers if desired */
/*     (Workspace: need N*N+6*N unless SENSE = 'E') */

    if (! wntsnn) {
	strsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset], 
		ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout, 
		&work[iwrk], n, &iwork[1], &icond);
    }

    if (wantvl) {

/*        Undo balancing of left eigenvectors */

	sgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl, 
		&ierr);

/*        Normalize left eigenvectors and make largest component real */

	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (wi[i__] == 0.f) {
		scl = 1.f / snrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
		sscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
	    } else if (wi[i__] > 0.f) {
		r__1 = snrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
		r__2 = snrm2_(n, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
		scl = 1.f / slapy2_(&r__1, &r__2);
		sscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
		sscal_(n, &scl, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
		i__2 = *n;
		for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
		    r__1 = vl[k + i__ * vl_dim1];
/* Computing 2nd power */
		    r__2 = vl[k + (i__ + 1) * vl_dim1];
		    work[k] = r__1 * r__1 + r__2 * r__2;
/* L10: */
		}
		k = isamax_(n, &work[1], &c__1);
		slartg_(&vl[k + i__ * vl_dim1], &vl[k + (i__ + 1) * vl_dim1], 
			&cs, &sn, &r__);
		srot_(n, &vl[i__ * vl_dim1 + 1], &c__1, &vl[(i__ + 1) * 
			vl_dim1 + 1], &c__1, &cs, &sn);
		vl[k + (i__ + 1) * vl_dim1] = 0.f;
	    }
/* L20: */
	}
    }

    if (wantvr) {

/*        Undo balancing of right eigenvectors */

	sgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr, 
		&ierr);

/*        Normalize right eigenvectors and make largest component real */

	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    if (wi[i__] == 0.f) {
		scl = 1.f / snrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
		sscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
	    } else if (wi[i__] > 0.f) {
		r__1 = snrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
		r__2 = snrm2_(n, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
		scl = 1.f / slapy2_(&r__1, &r__2);
		sscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
		sscal_(n, &scl, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
		i__2 = *n;
		for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
		    r__1 = vr[k + i__ * vr_dim1];
/* Computing 2nd power */
		    r__2 = vr[k + (i__ + 1) * vr_dim1];
		    work[k] = r__1 * r__1 + r__2 * r__2;
/* L30: */
		}
		k = isamax_(n, &work[1], &c__1);
		slartg_(&vr[k + i__ * vr_dim1], &vr[k + (i__ + 1) * vr_dim1], 
			&cs, &sn, &r__);
		srot_(n, &vr[i__ * vr_dim1 + 1], &c__1, &vr[(i__ + 1) * 
			vr_dim1 + 1], &c__1, &cs, &sn);
		vr[k + (i__ + 1) * vr_dim1] = 0.f;
	    }
/* L40: */
	}
    }

/*     Undo scaling if necessary */

L50:
    if (scalea) {
	i__1 = *n - *info;
/* Computing MAX */
	i__3 = *n - *info;
	i__2 = f2cmax(i__3,1);
	slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[*info + 
		1], &i__2, &ierr);
	i__1 = *n - *info;
/* Computing MAX */
	i__3 = *n - *info;
	i__2 = f2cmax(i__3,1);
	slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[*info + 
		1], &i__2, &ierr);
	if (*info == 0) {
	    if ((wntsnv || wntsnb) && icond == 0) {
		slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[
			1], n, &ierr);
	    }
	} else {
	    i__1 = *ilo - 1;
	    slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[1], 
		    n, &ierr);
	    i__1 = *ilo - 1;
	    slascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[1], 
		    n, &ierr);
	}
    }

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

/*     End of SGEEVX */

} /* sgeevx_ */