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OpenBLAS/lapack-netlib/SRC/DEPRECATED/sgegv.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
#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
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static real c_b27 = 1.f;
static real c_b38 = 0.f;
/* > \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 SGEGV + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgegv.f
"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgegv.f
"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgegv.f
"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, */
/* BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO ) */
/* CHARACTER JOBVL, JOBVR */
/* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N */
/* REAL A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
/* $ B( LDB, * ), BETA( * ), VL( LDVL, * ), */
/* $ VR( LDVR, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > This routine is deprecated and has been replaced by routine SGGEV. */
/* > */
/* > SGEGV computes the eigenvalues and, optionally, the left and/or right */
/* > eigenvectors of a real matrix pair (A,B). */
/* > Given two square matrices A and B, */
/* > the generalized nonsymmetric eigenvalue problem (GNEP) is to find the */
/* > eigenvalues lambda and corresponding (non-zero) eigenvectors x such */
/* > that */
/* > */
/* > A*x = lambda*B*x. */
/* > */
/* > An alternate form is to find the eigenvalues mu and corresponding */
/* > eigenvectors y such that */
/* > */
/* > mu*A*y = B*y. */
/* > */
/* > These two forms are equivalent with mu = 1/lambda and x = y if */
/* > neither lambda nor mu is zero. In order to deal with the case that */
/* > lambda or mu is zero or small, two values alpha and beta are returned */
/* > for each eigenvalue, such that lambda = alpha/beta and */
/* > mu = beta/alpha. */
/* > */
/* > The vectors x and y in the above equations are right eigenvectors of */
/* > the matrix pair (A,B). Vectors u and v satisfying */
/* > */
/* > u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B */
/* > */
/* > are left eigenvectors of (A,B). */
/* > */
/* > Note: this routine performs "full balancing" on A and B */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBVL */
/* > \verbatim */
/* > JOBVL is CHARACTER*1 */
/* > = 'N': do not compute the left generalized eigenvectors; */
/* > = 'V': compute the left generalized eigenvectors (returned */
/* > in VL). */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVR */
/* > \verbatim */
/* > JOBVR is CHARACTER*1 */
/* > = 'N': do not compute the right generalized eigenvectors; */
/* > = 'V': compute the right generalized eigenvectors (returned */
/* > in VR). */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrices A, B, VL, and VR. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA, N) */
/* > On entry, the matrix A. */
/* > If JOBVL = 'V' or JOBVR = 'V', then on exit A */
/* > contains the real Schur form of A from the generalized Schur */
/* > factorization of the pair (A,B) after balancing. */
/* > If no eigenvectors were computed, then only the diagonal */
/* > blocks from the Schur form will be correct. See SGGHRD and */
/* > SHGEQZ for details. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of A. LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* > B is REAL array, dimension (LDB, N) */
/* > On entry, the matrix B. */
/* > If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the */
/* > upper triangular matrix obtained from B in the generalized */
/* > Schur factorization of the pair (A,B) after balancing. */
/* > If no eigenvectors were computed, then only those elements of */
/* > B corresponding to the diagonal blocks from the Schur form of */
/* > A will be correct. See SGGHRD and SHGEQZ for details. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of B. LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAR */
/* > \verbatim */
/* > ALPHAR is REAL array, dimension (N) */
/* > The real parts of each scalar alpha defining an eigenvalue of */
/* > GNEP. */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHAI */
/* > \verbatim */
/* > ALPHAI is REAL array, dimension (N) */
/* > The imaginary parts of each scalar alpha defining an */
/* > eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th */
/* > eigenvalue is real; if positive, then the j-th and */
/* > (j+1)-st eigenvalues are a complex conjugate pair, with */
/* > ALPHAI(j+1) = -ALPHAI(j). */
/* > \endverbatim */
/* > */
/* > \param[out] BETA */
/* > \verbatim */
/* > BETA is REAL array, dimension (N) */
/* > The scalars beta that define the eigenvalues of GNEP. */
/* > */
/* > Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */
/* > beta = BETA(j) represent the j-th eigenvalue of the matrix */
/* > pair (A,B), in one of the forms lambda = alpha/beta or */
/* > mu = beta/alpha. Since either lambda or mu may overflow, */
/* > they should not, in general, be computed. */
/* > \endverbatim */
/* > */
/* > \param[out] VL */
/* > \verbatim */
/* > VL is REAL array, dimension (LDVL,N) */
/* > If JOBVL = 'V', the left eigenvectors u(j) are stored */
/* > in the columns of VL, in the same order as their eigenvalues. */
/* > If the j-th eigenvalue is real, then u(j) = VL(:,j). */
/* > 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). */
/* > */
/* > Each eigenvector is scaled so that its largest component has */
/* > abs(real part) + abs(imag. part) = 1, except for eigenvectors */
/* > corresponding to an eigenvalue with alpha = beta = 0, which */
/* > are set to zero. */
/* > Not referenced if JOBVL = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVL */
/* > \verbatim */
/* > LDVL is INTEGER */
/* > The leading dimension of the matrix VL. LDVL >= 1, and */
/* > if JOBVL = 'V', LDVL >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] VR */
/* > \verbatim */
/* > VR is REAL array, dimension (LDVR,N) */
/* > If JOBVR = 'V', the right eigenvectors x(j) are stored */
/* > in the columns of VR, in the same order as their eigenvalues. */
/* > If the j-th eigenvalue is real, then x(j) = VR(:,j). */
/* > If the j-th and (j+1)-st eigenvalues form a complex conjugate */
/* > pair, then */
/* > x(j) = VR(:,j) + i*VR(:,j+1) */
/* > and */
/* > x(j+1) = VR(:,j) - i*VR(:,j+1). */
/* > */
/* > Each eigenvector is scaled so that its largest component has */
/* > abs(real part) + abs(imag. part) = 1, except for eigenvalues */
/* > corresponding to an eigenvalue with alpha = beta = 0, which */
/* > are set to zero. */
/* > Not referenced if JOBVR = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVR */
/* > \verbatim */
/* > LDVR is INTEGER */
/* > The leading dimension of the matrix VR. LDVR >= 1, and */
/* > if JOBVR = 'V', LDVR >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. LWORK >= f2cmax(1,8*N). */
/* > For good performance, LWORK must generally be larger. */
/* > To compute the optimal value of LWORK, call ILAENV to get */
/* > blocksizes (for SGEQRF, SORMQR, and SORGQR.) Then compute: */
/* > NB -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR; */
/* > The optimal LWORK is: */
/* > 2*N + MAX( 6*N, N*(NB+1) ). */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > = 1,...,N: */
/* > The QZ iteration failed. No eigenvectors have been */
/* > calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) */
/* > should be correct for j=INFO+1,...,N. */
/* > > N: errors that usually indicate LAPACK problems: */
/* > =N+1: error return from SGGBAL */
/* > =N+2: error return from SGEQRF */
/* > =N+3: error return from SORMQR */
/* > =N+4: error return from SORGQR */
/* > =N+5: error return from SGGHRD */
/* > =N+6: error return from SHGEQZ (other than failed */
/* > iteration) */
/* > =N+7: error return from STGEVC */
/* > =N+8: error return from SGGBAK (computing VL) */
/* > =N+9: error return from SGGBAK (computing VR) */
/* > =N+10: error return from SLASCL (various calls) */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup realGEeigen */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > Balancing */
/* > --------- */
/* > */
/* > This driver calls SGGBAL to both permute and scale rows and columns */
/* > of A and B. The permutations PL and PR are chosen so that PL*A*PR */
/* > and PL*B*R will be upper triangular except for the diagonal blocks */
/* > A(i:j,i:j) and B(i:j,i:j), with i and j as close together as */
/* > possible. The diagonal scaling matrices DL and DR are chosen so */
/* > that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to */
/* > one (except for the elements that start out zero.) */
/* > */
/* > After the eigenvalues and eigenvectors of the balanced matrices */
/* > have been computed, SGGBAK transforms the eigenvectors back to what */
/* > they would have been (in perfect arithmetic) if they had not been */
/* > balanced. */
/* > */
/* > Contents of A and B on Exit */
/* > -------- -- - --- - -- ---- */
/* > */
/* > If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or */
/* > both), then on exit the arrays A and B will contain the real Schur */
/* > form[*] of the "balanced" versions of A and B. If no eigenvectors */
/* > are computed, then only the diagonal blocks will be correct. */
/* > */
/* > [*] See SHGEQZ, SGEGS, or read the book "Matrix Computations", */
/* > by Golub & van Loan, pub. by Johns Hopkins U. Press. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void sgegv_(char *jobvl, char *jobvr, integer *n, real *a,
integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real
*beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work,
integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2;
real r__1, r__2, r__3, r__4;
/* Local variables */
real absb, anrm, bnrm;
integer itau;
real temp;
logical ilvl, ilvr;
integer lopt;
real anrm1, anrm2, bnrm1, bnrm2, absai, scale, absar, sbeta;
extern logical lsame_(char *, char *);
integer ileft, iinfo, icols, iwork, irows, jc, nb, in, jr;
real salfai;
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 salfar;
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;
char chtemp[1];
logical ldumma[1];
extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer ijobvl, iright;
logical ilimit;
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 *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *), stgevc_(
char *, char *, logical *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *, integer *,
integer *, real *, integer *);
real onepls;
integer lwkmin, nb1, nb2, nb3;
extern /* Subroutine */ void shgeqz_(char *, char *, char *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *,
integer *, integer *), sorgqr_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
integer ihi, ilo;
real eps;
logical ilv;
/* -- LAPACK driver routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* December 2016 */
/* ===================================================================== */
/* Decode the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--alphar;
--alphai;
--beta;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
--work;
/* Function Body */
if (lsame_(jobvl, "N")) {
ijobvl = 1;
ilvl = FALSE_;
} else if (lsame_(jobvl, "V")) {
ijobvl = 2;
ilvl = TRUE_;
} else {
ijobvl = -1;
ilvl = FALSE_;
}
if (lsame_(jobvr, "N")) {
ijobvr = 1;
ilvr = FALSE_;
} else if (lsame_(jobvr, "V")) {
ijobvr = 2;
ilvr = TRUE_;
} else {
ijobvr = -1;
ilvr = FALSE_;
}
ilv = ilvl || ilvr;
/* Test the input arguments */
/* Computing MAX */
i__1 = *n << 3;
lwkmin = f2cmax(i__1,1);
lwkopt = lwkmin;
work[1] = (real) lwkopt;
lquery = *lwork == -1;
*info = 0;
if (ijobvl <= 0) {
*info = -1;
} else if (ijobvr <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < f2cmax(1,*n)) {
*info = -5;
} else if (*ldb < f2cmax(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || ilvl && *ldvl < *n) {
*info = -12;
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
*info = -14;
} else if (*lwork < lwkmin && ! lquery) {
*info = -16;
}
if (*info == 0) {
nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb2 = ilaenv_(&c__1, "SORMQR", " ", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)1);
nb3 = ilaenv_(&c__1, "SORGQR", " ", n, n, n, &c_n1, (ftnlen)6, (
ftnlen)1);
/* Computing MAX */
i__1 = f2cmax(nb1,nb2);
nb = f2cmax(i__1,nb3);
/* Computing MAX */
i__1 = *n * 6, i__2 = *n * (nb + 1);
lopt = (*n << 1) + f2cmax(i__1,i__2);
work[1] = (real) lopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGEGV ", &i__1, 6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*n == 0) {
return;
}
/* Get machine constants */
eps = slamch_("E") * slamch_("B");
safmin = slamch_("S");
safmin += safmin;
safmax = 1.f / safmin;
onepls = eps * 4 + 1.f;
/* Scale A */
anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
anrm1 = anrm;
anrm2 = 1.f;
if (anrm < 1.f) {
if (safmax * anrm < 1.f) {
anrm1 = safmin;
anrm2 = safmax * anrm;
}
}
if (anrm > 0.f) {
slascl_("G", &c_n1, &c_n1, &anrm, &c_b27, n, n, &a[a_offset], lda, &
iinfo);
if (iinfo != 0) {
*info = *n + 10;
return;
}
}
/* Scale B */
bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
bnrm1 = bnrm;
bnrm2 = 1.f;
if (bnrm < 1.f) {
if (safmax * bnrm < 1.f) {
bnrm1 = safmin;
bnrm2 = safmax * bnrm;
}
}
if (bnrm > 0.f) {
slascl_("G", &c_n1, &c_n1, &bnrm, &c_b27, n, n, &b[b_offset], ldb, &
iinfo);
if (iinfo != 0) {
*info = *n + 10;
return;
}
}
/* Permute the matrix to make it more nearly triangular */
/* Workspace layout: (8*N words -- "work" requires 6*N words) */
/* left_permutation, right_permutation, work... */
ileft = 1;
iright = *n + 1;
iwork = iright + *n;
sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
ileft], &work[iright], &work[iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 1;
goto L120;
}
/* Reduce B to triangular form, and initialize VL and/or VR */
/* Workspace layout: ("work..." must have at least N words) */
/* left_permutation, right_permutation, tau, work... */
irows = ihi + 1 - ilo;
if (ilv) {
icols = *n + 1 - ilo;
} else {
icols = irows;
}
itau = iwork;
iwork = itau + irows;
i__1 = *lwork + 1 - iwork;
sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = f2cmax(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 2;
goto L120;
}
i__1 = *lwork + 1 - iwork;
sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = f2cmax(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 3;
goto L120;
}
if (ilvl) {
slaset_("Full", n, n, &c_b38, &c_b27, &vl[vl_offset], ldvl)
;
i__1 = irows - 1;
i__2 = irows - 1;
slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[ilo +
1 + ilo * vl_dim1], ldvl);
i__1 = *lwork + 1 - iwork;
sorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
itau], &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = f2cmax(i__1,i__2);
}
if (iinfo != 0) {
*info = *n + 4;
goto L120;
}
}
if (ilvr) {
slaset_("Full", n, n, &c_b38, &c_b27, &vr[vr_offset], ldvr)
;
}
/* Reduce to generalized Hessenberg form */
if (ilv) {
/* Eigenvectors requested -- work on whole matrix. */
sgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &iinfo);
} else {
sgghrd_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda,
&b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
vr_offset], ldvr, &iinfo);
}
if (iinfo != 0) {
*info = *n + 5;
goto L120;
}
/* Perform QZ algorithm */
/* Workspace layout: ("work..." must have at least 1 word) */
/* left_permutation, right_permutation, work... */
iwork = itau;
if (ilv) {
*(unsigned char *)chtemp = 'S';
} else {
*(unsigned char *)chtemp = 'E';
}
i__1 = *lwork + 1 - iwork;
shgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &work[iwork], &i__1, &iinfo);
if (iinfo >= 0) {
/* Computing MAX */
i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
lwkopt = f2cmax(i__1,i__2);
}
if (iinfo != 0) {
if (iinfo > 0 && iinfo <= *n) {
*info = iinfo;
} else if (iinfo > *n && iinfo <= *n << 1) {
*info = iinfo - *n;
} else {
*info = *n + 6;
}
goto L120;
}
if (ilv) {
/* Compute Eigenvectors (STGEVC requires 6*N words of workspace) */
if (ilvl) {
if (ilvr) {
*(unsigned char *)chtemp = 'B';
} else {
*(unsigned char *)chtemp = 'L';
}
} else {
*(unsigned char *)chtemp = 'R';
}
stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
&vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
iwork], &iinfo);
if (iinfo != 0) {
*info = *n + 7;
goto L120;
}
/* Undo balancing on VL and VR, rescale */
if (ilvl) {
sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vl[vl_offset], ldvl, &iinfo);
if (iinfo != 0) {
*info = *n + 8;
goto L120;
}
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L50;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vl[jr + jc * vl_dim1],
abs(r__1));
temp = f2cmax(r__2,r__3);
/* L10: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vl[jr + jc * vl_dim1],
abs(r__1)) + (r__2 = vl[jr + (jc + 1) *
vl_dim1], abs(r__2));
temp = f2cmax(r__3,r__4);
/* L20: */
}
}
if (temp < safmin) {
goto L50;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
/* L30: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + jc * vl_dim1] *= temp;
vl[jr + (jc + 1) * vl_dim1] *= temp;
/* L40: */
}
}
L50:
;
}
}
if (ilvr) {
sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
vr[vr_offset], ldvr, &iinfo);
if (iinfo != 0) {
*info = *n + 9;
goto L120;
}
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
if (alphai[jc] < 0.f) {
goto L100;
}
temp = 0.f;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = vr[jr + jc * vr_dim1],
abs(r__1));
temp = f2cmax(r__2,r__3);
/* L60: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
r__3 = temp, r__4 = (r__1 = vr[jr + jc * vr_dim1],
abs(r__1)) + (r__2 = vr[jr + (jc + 1) *
vr_dim1], abs(r__2));
temp = f2cmax(r__3,r__4);
/* L70: */
}
}
if (temp < safmin) {
goto L100;
}
temp = 1.f / temp;
if (alphai[jc] == 0.f) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
/* L80: */
}
} else {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + jc * vr_dim1] *= temp;
vr[jr + (jc + 1) * vr_dim1] *= temp;
/* L90: */
}
}
L100:
;
}
}
/* End of eigenvector calculation */
}
/* Undo scaling in alpha, beta */
/* Note: this does not give the alpha and beta for the unscaled */
/* problem. */
/* Un-scaling is limited to avoid underflow in alpha and beta */
/* if they are significant. */
i__1 = *n;
for (jc = 1; jc <= i__1; ++jc) {
absar = (r__1 = alphar[jc], abs(r__1));
absai = (r__1 = alphai[jc], abs(r__1));
absb = (r__1 = beta[jc], abs(r__1));
salfar = anrm * alphar[jc];
salfai = anrm * alphai[jc];
sbeta = bnrm * beta[jc];
ilimit = FALSE_;
scale = 1.f;
/* Check for significant underflow in ALPHAI */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absar, r__1 = f2cmax(r__1,r__2), r__2 = eps *
absb;
if (abs(salfai) < safmin && absai >= f2cmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX */
r__1 = onepls * safmin, r__2 = anrm2 * absai;
scale = onepls * safmin / anrm1 / f2cmax(r__1,r__2);
} else if (salfai == 0.f) {
/* If insignificant underflow in ALPHAI, then make the */
/* conjugate eigenvalue real. */
if (alphai[jc] < 0.f && jc > 1) {
alphai[jc - 1] = 0.f;
} else if (alphai[jc] > 0.f && jc < *n) {
alphai[jc + 1] = 0.f;
}
}
/* Check for significant underflow in ALPHAR */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absai, r__1 = f2cmax(r__1,r__2), r__2 = eps *
absb;
if (abs(salfar) < safmin && absar >= f2cmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX */
/* Computing MAX */
r__3 = onepls * safmin, r__4 = anrm2 * absar;
r__1 = scale, r__2 = onepls * safmin / anrm1 / f2cmax(r__3,r__4);
scale = f2cmax(r__1,r__2);
}
/* Check for significant underflow in BETA */
/* Computing MAX */
r__1 = safmin, r__2 = eps * absar, r__1 = f2cmax(r__1,r__2), r__2 = eps *
absai;
if (abs(sbeta) < safmin && absb >= f2cmax(r__1,r__2)) {
ilimit = TRUE_;
/* Computing MAX */
/* Computing MAX */
r__3 = onepls * safmin, r__4 = bnrm2 * absb;
r__1 = scale, r__2 = onepls * safmin / bnrm1 / f2cmax(r__3,r__4);
scale = f2cmax(r__1,r__2);
}
/* Check for possible overflow when limiting scaling */
if (ilimit) {
/* Computing MAX */
r__1 = abs(salfar), r__2 = abs(salfai), r__1 = f2cmax(r__1,r__2),
r__2 = abs(sbeta);
temp = scale * safmin * f2cmax(r__1,r__2);
if (temp > 1.f) {
scale /= temp;
}
if (scale < 1.f) {
ilimit = FALSE_;
}
}
/* Recompute un-scaled ALPHAR, ALPHAI, BETA if necessary. */
if (ilimit) {
salfar = scale * alphar[jc] * anrm;
salfai = scale * alphai[jc] * anrm;
sbeta = scale * beta[jc] * bnrm;
}
alphar[jc] = salfar;
alphai[jc] = salfai;
beta[jc] = sbeta;
/* L110: */
}
L120:
work[1] = (real) lwkopt;
return;
/* End of SGEGV */
} /* sgegv_ */
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