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OpenBLAS/lapack-netlib/SRC/shgeqz.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 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 real c_b12 = 0.f;
static real c_b13 = 1.f;
static integer c__1 = 1;
static integer c__3 = 3;
/* > \brief \b SHGEQZ */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SHGEQZ + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/shgeqz.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/shgeqz.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/shgeqz.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, */
/* ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK, */
/* LWORK, INFO ) */
/* CHARACTER COMPQ, COMPZ, JOB */
/* INTEGER IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N */
/* REAL ALPHAI( * ), ALPHAR( * ), BETA( * ), */
/* $ H( LDH, * ), Q( LDQ, * ), T( LDT, * ), */
/* $ WORK( * ), Z( LDZ, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SHGEQZ computes the eigenvalues of a real matrix pair (H,T), */
/* > where H is an upper Hessenberg matrix and T is upper triangular, */
/* > using the double-shift QZ method. */
/* > Matrix pairs of this type are produced by the reduction to */
/* > generalized upper Hessenberg form of a real matrix pair (A,B): */
/* > */
/* > A = Q1*H*Z1**T, B = Q1*T*Z1**T, */
/* > */
/* > as computed by SGGHRD. */
/* > */
/* > If JOB='S', then the Hessenberg-triangular pair (H,T) is */
/* > also reduced to generalized Schur form, */
/* > */
/* > H = Q*S*Z**T, T = Q*P*Z**T, */
/* > */
/* > where Q and Z are orthogonal matrices, P is an upper triangular */
/* > matrix, and S is a quasi-triangular matrix with 1-by-1 and 2-by-2 */
/* > diagonal blocks. */
/* > */
/* > The 1-by-1 blocks correspond to real eigenvalues of the matrix pair */
/* > (H,T) and the 2-by-2 blocks correspond to complex conjugate pairs of */
/* > eigenvalues. */
/* > */
/* > Additionally, the 2-by-2 upper triangular diagonal blocks of P */
/* > corresponding to 2-by-2 blocks of S are reduced to positive diagonal */
/* > form, i.e., if S(j+1,j) is non-zero, then P(j+1,j) = P(j,j+1) = 0, */
/* > P(j,j) > 0, and P(j+1,j+1) > 0. */
/* > */
/* > Optionally, the orthogonal matrix Q from the generalized Schur */
/* > factorization may be postmultiplied into an input matrix Q1, and the */
/* > orthogonal matrix Z may be postmultiplied into an input matrix Z1. */
/* > If Q1 and Z1 are the orthogonal matrices from SGGHRD that reduced */
/* > the matrix pair (A,B) to generalized upper Hessenberg form, then the */
/* > output matrices Q1*Q and Z1*Z are the orthogonal factors from the */
/* > generalized Schur factorization of (A,B): */
/* > */
/* > A = (Q1*Q)*S*(Z1*Z)**T, B = (Q1*Q)*P*(Z1*Z)**T. */
/* > */
/* > To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently, */
/* > of (A,B)) are computed as a pair of values (alpha,beta), where alpha is */
/* > complex and beta real. */
/* > If beta is nonzero, lambda = alpha / beta is an eigenvalue of the */
/* > generalized nonsymmetric eigenvalue problem (GNEP) */
/* > A*x = lambda*B*x */
/* > and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the */
/* > alternate form of the GNEP */
/* > mu*A*y = B*y. */
/* > Real eigenvalues can be read directly from the generalized Schur */
/* > form: */
/* > alpha = S(i,i), beta = P(i,i). */
/* > */
/* > Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix */
/* > Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), */
/* > pp. 241--256. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOB */
/* > \verbatim */
/* > JOB is CHARACTER*1 */
/* > = 'E': Compute eigenvalues only; */
/* > = 'S': Compute eigenvalues and the Schur form. */
/* > \endverbatim */
/* > */
/* > \param[in] COMPQ */
/* > \verbatim */
/* > COMPQ is CHARACTER*1 */
/* > = 'N': Left Schur vectors (Q) are not computed; */
/* > = 'I': Q is initialized to the unit matrix and the matrix Q */
/* > of left Schur vectors of (H,T) is returned; */
/* > = 'V': Q must contain an orthogonal matrix Q1 on entry and */
/* > the product Q1*Q is returned. */
/* > \endverbatim */
/* > */
/* > \param[in] COMPZ */
/* > \verbatim */
/* > COMPZ is CHARACTER*1 */
/* > = 'N': Right Schur vectors (Z) are not computed; */
/* > = 'I': Z is initialized to the unit matrix and the matrix Z */
/* > of right Schur vectors of (H,T) is returned; */
/* > = 'V': Z must contain an orthogonal matrix Z1 on entry and */
/* > the product Z1*Z is returned. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrices H, T, Q, and Z. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] ILO */
/* > \verbatim */
/* > ILO is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[in] IHI */
/* > \verbatim */
/* > IHI is INTEGER */
/* > ILO and IHI mark the rows and columns of H which are in */
/* > Hessenberg form. It is assumed that A is already upper */
/* > triangular in rows and columns 1:ILO-1 and IHI+1:N. */
/* > If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] H */
/* > \verbatim */
/* > H is REAL array, dimension (LDH, N) */
/* > On entry, the N-by-N upper Hessenberg matrix H. */
/* > On exit, if JOB = 'S', H contains the upper quasi-triangular */
/* > matrix S from the generalized Schur factorization. */
/* > If JOB = 'E', the diagonal blocks of H match those of S, but */
/* > the rest of H is unspecified. */
/* > \endverbatim */
/* > */
/* > \param[in] LDH */
/* > \verbatim */
/* > LDH is INTEGER */
/* > The leading dimension of the array H. LDH >= f2cmax( 1, N ). */
/* > \endverbatim */
/* > */
/* > \param[in,out] T */
/* > \verbatim */
/* > T is REAL array, dimension (LDT, N) */
/* > On entry, the N-by-N upper triangular matrix T. */
/* > On exit, if JOB = 'S', T contains the upper triangular */
/* > matrix P from the generalized Schur factorization; */
/* > 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks of S */
/* > are reduced to positive diagonal form, i.e., if H(j+1,j) is */
/* > non-zero, then T(j+1,j) = T(j,j+1) = 0, T(j,j) > 0, and */
/* > T(j+1,j+1) > 0. */
/* > If JOB = 'E', the diagonal blocks of T match those of P, but */
/* > the rest of T is unspecified. */
/* > \endverbatim */
/* > */
/* > \param[in] LDT */
/* > \verbatim */
/* > LDT is INTEGER */
/* > The leading dimension of the array T. LDT >= 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[in,out] Q */
/* > \verbatim */
/* > Q is REAL array, dimension (LDQ, N) */
/* > On entry, if COMPQ = 'V', the orthogonal matrix Q1 used in */
/* > the reduction of (A,B) to generalized Hessenberg form. */
/* > On exit, if COMPQ = 'I', the orthogonal matrix of left Schur */
/* > vectors of (H,T), and if COMPQ = 'V', the orthogonal matrix */
/* > of left Schur vectors of (A,B). */
/* > Not referenced if COMPQ = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* > LDQ is INTEGER */
/* > The leading dimension of the array Q. LDQ >= 1. */
/* > If COMPQ='V' or 'I', then LDQ >= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* > Z is REAL array, dimension (LDZ, N) */
/* > On entry, if COMPZ = 'V', the orthogonal matrix Z1 used in */
/* > the reduction of (A,B) to generalized Hessenberg form. */
/* > On exit, if COMPZ = 'I', the orthogonal matrix of */
/* > right Schur vectors of (H,T), and if COMPZ = 'V', the */
/* > orthogonal matrix of right Schur vectors of (A,B). */
/* > Not referenced if COMPZ = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* > LDZ is INTEGER */
/* > The leading dimension of the array Z. LDZ >= 1. */
/* > If COMPZ='V' or 'I', then LDZ >= 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,N). */
/* > */
/* > 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 did not converge. (H,T) is not */
/* > in Schur form, but ALPHAR(i), ALPHAI(i), and */
/* > BETA(i), i=INFO+1,...,N should be correct. */
/* > = N+1,...,2*N: the shift calculation failed. (H,T) is not */
/* > in Schur form, but ALPHAR(i), ALPHAI(i), and */
/* > BETA(i), i=INFO-N+1,...,N should be correct. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* > \ingroup realGEcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > Iteration counters: */
/* > */
/* > JITER -- counts iterations. */
/* > IITER -- counts iterations run since ILAST was last */
/* > changed. This is therefore reset only when a 1-by-1 or */
/* > 2-by-2 block deflates off the bottom. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void shgeqz_(char *job, char *compq, char *compz, integer *n,
integer *ilo, integer *ihi, real *h__, integer *ldh, real *t, integer
*ldt, real *alphar, real *alphai, real *beta, real *q, integer *ldq,
real *z__, integer *ldz, real *work, integer *lwork, integer *info)
{
/* System generated locals */
integer h_dim1, h_offset, q_dim1, q_offset, t_dim1, t_offset, z_dim1,
z_offset, i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4;
/* Local variables */
real ad11l, ad12l, ad21l, ad22l, ad32l, wabs, atol, btol, temp;
extern /* Subroutine */ void srot_(integer *, real *, integer *, real *,
integer *, real *, real *), slag2_(real *, integer *, real *,
integer *, real *, real *, real *, real *, real *, real *);
real temp2, s1inv, c__;
integer j;
real s, v[3], scale;
extern logical lsame_(char *, char *);
integer iiter, ilast, jiter;
real anorm, bnorm;
integer maxit;
real tempi, tempr, s1, s2, t1, u1, u2;
logical ilazr2;
real a11, a12, a21, a22, b11, b22, c12, c21;
extern real slapy2_(real *, real *);
integer jc;
extern real slapy3_(real *, real *, real *);
real an, bn, cl;
extern /* Subroutine */ void slasv2_(real *, real *, real *, real *, real *
, real *, real *, real *, real *);
real cq, cr;
integer in;
real ascale, bscale, u12, w11;
integer jr;
real cz, sl, w12, w21, w22, wi, sr;
extern real slamch_(char *);
real vs, wr, safmin;
extern /* Subroutine */ void slarfg_(integer *, real *, real *, integer *,
real *);
real safmax;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
real eshift;
logical ilschr;
real b1a, b2a;
integer icompq, ilastm;
extern real slanhs_(char *, integer *, real *, integer *, real *);
real a1i;
integer ischur;
real a2i, b1i;
logical ilazro;
integer icompz, ifirst, ifrstm;
real a1r;
integer istart;
logical ilpivt;
real a2r, b1r, b2i, b2r;
extern /* Subroutine */ void slartg_(real *, real *, real *, real *, real *
), slaset_(char *, integer *, integer *, real *, real *, real *,
integer *);
logical lquery;
real wr2, ad11, ad12, ad21, ad22, c11i, c22i;
integer jch;
real c11r, c22r;
logical ilq;
real u12l, tau, sqi;
logical ilz;
real ulp, sqr, szi, szr;
/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2016 */
/* ===================================================================== */
/* $ SAFETY = 1.0E+0 ) */
/* Decode JOB, COMPQ, COMPZ */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1 * 1;
h__ -= h_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
--alphar;
--alphai;
--beta;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
/* Function Body */
if (lsame_(job, "E")) {
ilschr = FALSE_;
ischur = 1;
} else if (lsame_(job, "S")) {
ilschr = TRUE_;
ischur = 2;
} else {
ischur = 0;
}
if (lsame_(compq, "N")) {
ilq = FALSE_;
icompq = 1;
} else if (lsame_(compq, "V")) {
ilq = TRUE_;
icompq = 2;
} else if (lsame_(compq, "I")) {
ilq = TRUE_;
icompq = 3;
} else {
icompq = 0;
}
if (lsame_(compz, "N")) {
ilz = FALSE_;
icompz = 1;
} else if (lsame_(compz, "V")) {
ilz = TRUE_;
icompz = 2;
} else if (lsame_(compz, "I")) {
ilz = TRUE_;
icompz = 3;
} else {
icompz = 0;
}
/* Check Argument Values */
*info = 0;
work[1] = (real) f2cmax(1,*n);
lquery = *lwork == -1;
if (ischur == 0) {
*info = -1;
} else if (icompq == 0) {
*info = -2;
} else if (icompz == 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*ilo < 1) {
*info = -5;
} else if (*ihi > *n || *ihi < *ilo - 1) {
*info = -6;
} else if (*ldh < *n) {
*info = -8;
} else if (*ldt < *n) {
*info = -10;
} else if (*ldq < 1 || ilq && *ldq < *n) {
*info = -15;
} else if (*ldz < 1 || ilz && *ldz < *n) {
*info = -17;
} else if (*lwork < f2cmax(1,*n) && ! lquery) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SHGEQZ", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*n <= 0) {
work[1] = 1.f;
return;
}
/* Initialize Q and Z */
if (icompq == 3) {
slaset_("Full", n, n, &c_b12, &c_b13, &q[q_offset], ldq);
}
if (icompz == 3) {
slaset_("Full", n, n, &c_b12, &c_b13, &z__[z_offset], ldz);
}
/* Machine Constants */
in = *ihi + 1 - *ilo;
safmin = slamch_("S");
safmax = 1.f / safmin;
ulp = slamch_("E") * slamch_("B");
anorm = slanhs_("F", &in, &h__[*ilo + *ilo * h_dim1], ldh, &work[1]);
bnorm = slanhs_("F", &in, &t[*ilo + *ilo * t_dim1], ldt, &work[1]);
/* Computing MAX */
r__1 = safmin, r__2 = ulp * anorm;
atol = f2cmax(r__1,r__2);
/* Computing MAX */
r__1 = safmin, r__2 = ulp * bnorm;
btol = f2cmax(r__1,r__2);
ascale = 1.f / f2cmax(safmin,anorm);
bscale = 1.f / f2cmax(safmin,bnorm);
/* Set Eigenvalues IHI+1:N */
i__1 = *n;
for (j = *ihi + 1; j <= i__1; ++j) {
if (t[j + j * t_dim1] < 0.f) {
if (ilschr) {
i__2 = j;
for (jr = 1; jr <= i__2; ++jr) {
h__[jr + j * h_dim1] = -h__[jr + j * h_dim1];
t[jr + j * t_dim1] = -t[jr + j * t_dim1];
/* L10: */
}
} else {
h__[j + j * h_dim1] = -h__[j + j * h_dim1];
t[j + j * t_dim1] = -t[j + j * t_dim1];
}
if (ilz) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
z__[jr + j * z_dim1] = -z__[jr + j * z_dim1];
/* L20: */
}
}
}
alphar[j] = h__[j + j * h_dim1];
alphai[j] = 0.f;
beta[j] = t[j + j * t_dim1];
/* L30: */
}
/* If IHI < ILO, skip QZ steps */
if (*ihi < *ilo) {
goto L380;
}
/* MAIN QZ ITERATION LOOP */
/* Initialize dynamic indices */
/* Eigenvalues ILAST+1:N have been found. */
/* Column operations modify rows IFRSTM:whatever. */
/* Row operations modify columns whatever:ILASTM. */
/* If only eigenvalues are being computed, then */
/* IFRSTM is the row of the last splitting row above row ILAST; */
/* this is always at least ILO. */
/* IITER counts iterations since the last eigenvalue was found, */
/* to tell when to use an extraordinary shift. */
/* MAXIT is the maximum number of QZ sweeps allowed. */
ilast = *ihi;
if (ilschr) {
ifrstm = 1;
ilastm = *n;
} else {
ifrstm = *ilo;
ilastm = *ihi;
}
iiter = 0;
eshift = 0.f;
maxit = (*ihi - *ilo + 1) * 30;
i__1 = maxit;
for (jiter = 1; jiter <= i__1; ++jiter) {
/* Split the matrix if possible. */
/* Two tests: */
/* 1: H(j,j-1)=0 or j=ILO */
/* 2: T(j,j)=0 */
if (ilast == *ilo) {
/* Special case: j=ILAST */
goto L80;
} else {
if ((r__1 = h__[ilast + (ilast - 1) * h_dim1], abs(r__1)) <= atol)
{
h__[ilast + (ilast - 1) * h_dim1] = 0.f;
goto L80;
}
}
if ((r__1 = t[ilast + ilast * t_dim1], abs(r__1)) <= btol) {
t[ilast + ilast * t_dim1] = 0.f;
goto L70;
}
/* General case: j<ILAST */
i__2 = *ilo;
for (j = ilast - 1; j >= i__2; --j) {
/* Test 1: for H(j,j-1)=0 or j=ILO */
if (j == *ilo) {
ilazro = TRUE_;
} else {
if ((r__1 = h__[j + (j - 1) * h_dim1], abs(r__1)) <= atol) {
h__[j + (j - 1) * h_dim1] = 0.f;
ilazro = TRUE_;
} else {
ilazro = FALSE_;
}
}
/* Test 2: for T(j,j)=0 */
if ((r__1 = t[j + j * t_dim1], abs(r__1)) < btol) {
t[j + j * t_dim1] = 0.f;
/* Test 1a: Check for 2 consecutive small subdiagonals in A */
ilazr2 = FALSE_;
if (! ilazro) {
temp = (r__1 = h__[j + (j - 1) * h_dim1], abs(r__1));
temp2 = (r__1 = h__[j + j * h_dim1], abs(r__1));
tempr = f2cmax(temp,temp2);
if (tempr < 1.f && tempr != 0.f) {
temp /= tempr;
temp2 /= tempr;
}
if (temp * (ascale * (r__1 = h__[j + 1 + j * h_dim1], abs(
r__1))) <= temp2 * (ascale * atol)) {
ilazr2 = TRUE_;
}
}
/* If both tests pass (1 & 2), i.e., the leading diagonal */
/* element of B in the block is zero, split a 1x1 block off */
/* at the top. (I.e., at the J-th row/column) The leading */
/* diagonal element of the remainder can also be zero, so */
/* this may have to be done repeatedly. */
if (ilazro || ilazr2) {
i__3 = ilast - 1;
for (jch = j; jch <= i__3; ++jch) {
temp = h__[jch + jch * h_dim1];
slartg_(&temp, &h__[jch + 1 + jch * h_dim1], &c__, &s,
&h__[jch + jch * h_dim1]);
h__[jch + 1 + jch * h_dim1] = 0.f;
i__4 = ilastm - jch;
srot_(&i__4, &h__[jch + (jch + 1) * h_dim1], ldh, &
h__[jch + 1 + (jch + 1) * h_dim1], ldh, &c__,
&s);
i__4 = ilastm - jch;
srot_(&i__4, &t[jch + (jch + 1) * t_dim1], ldt, &t[
jch + 1 + (jch + 1) * t_dim1], ldt, &c__, &s);
if (ilq) {
srot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1)
* q_dim1 + 1], &c__1, &c__, &s);
}
if (ilazr2) {
h__[jch + (jch - 1) * h_dim1] *= c__;
}
ilazr2 = FALSE_;
if ((r__1 = t[jch + 1 + (jch + 1) * t_dim1], abs(r__1)
) >= btol) {
if (jch + 1 >= ilast) {
goto L80;
} else {
ifirst = jch + 1;
goto L110;
}
}
t[jch + 1 + (jch + 1) * t_dim1] = 0.f;
/* L40: */
}
goto L70;
} else {
/* Only test 2 passed -- chase the zero to T(ILAST,ILAST) */
/* Then process as in the case T(ILAST,ILAST)=0 */
i__3 = ilast - 1;
for (jch = j; jch <= i__3; ++jch) {
temp = t[jch + (jch + 1) * t_dim1];
slartg_(&temp, &t[jch + 1 + (jch + 1) * t_dim1], &c__,
&s, &t[jch + (jch + 1) * t_dim1]);
t[jch + 1 + (jch + 1) * t_dim1] = 0.f;
if (jch < ilastm - 1) {
i__4 = ilastm - jch - 1;
srot_(&i__4, &t[jch + (jch + 2) * t_dim1], ldt, &
t[jch + 1 + (jch + 2) * t_dim1], ldt, &
c__, &s);
}
i__4 = ilastm - jch + 2;
srot_(&i__4, &h__[jch + (jch - 1) * h_dim1], ldh, &
h__[jch + 1 + (jch - 1) * h_dim1], ldh, &c__,
&s);
if (ilq) {
srot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1)
* q_dim1 + 1], &c__1, &c__, &s);
}
temp = h__[jch + 1 + jch * h_dim1];
slartg_(&temp, &h__[jch + 1 + (jch - 1) * h_dim1], &
c__, &s, &h__[jch + 1 + jch * h_dim1]);
h__[jch + 1 + (jch - 1) * h_dim1] = 0.f;
i__4 = jch + 1 - ifrstm;
srot_(&i__4, &h__[ifrstm + jch * h_dim1], &c__1, &h__[
ifrstm + (jch - 1) * h_dim1], &c__1, &c__, &s)
;
i__4 = jch - ifrstm;
srot_(&i__4, &t[ifrstm + jch * t_dim1], &c__1, &t[
ifrstm + (jch - 1) * t_dim1], &c__1, &c__, &s)
;
if (ilz) {
srot_(n, &z__[jch * z_dim1 + 1], &c__1, &z__[(jch
- 1) * z_dim1 + 1], &c__1, &c__, &s);
}
/* L50: */
}
goto L70;
}
} else if (ilazro) {
/* Only test 1 passed -- work on J:ILAST */
ifirst = j;
goto L110;
}
/* Neither test passed -- try next J */
/* L60: */
}
/* (Drop-through is "impossible") */
*info = *n + 1;
goto L420;
/* T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a */
/* 1x1 block. */
L70:
temp = h__[ilast + ilast * h_dim1];
slartg_(&temp, &h__[ilast + (ilast - 1) * h_dim1], &c__, &s, &h__[
ilast + ilast * h_dim1]);
h__[ilast + (ilast - 1) * h_dim1] = 0.f;
i__2 = ilast - ifrstm;
srot_(&i__2, &h__[ifrstm + ilast * h_dim1], &c__1, &h__[ifrstm + (
ilast - 1) * h_dim1], &c__1, &c__, &s);
i__2 = ilast - ifrstm;
srot_(&i__2, &t[ifrstm + ilast * t_dim1], &c__1, &t[ifrstm + (ilast -
1) * t_dim1], &c__1, &c__, &s);
if (ilz) {
srot_(n, &z__[ilast * z_dim1 + 1], &c__1, &z__[(ilast - 1) *
z_dim1 + 1], &c__1, &c__, &s);
}
/* H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHAR, ALPHAI, */
/* and BETA */
L80:
if (t[ilast + ilast * t_dim1] < 0.f) {
if (ilschr) {
i__2 = ilast;
for (j = ifrstm; j <= i__2; ++j) {
h__[j + ilast * h_dim1] = -h__[j + ilast * h_dim1];
t[j + ilast * t_dim1] = -t[j + ilast * t_dim1];
/* L90: */
}
} else {
h__[ilast + ilast * h_dim1] = -h__[ilast + ilast * h_dim1];
t[ilast + ilast * t_dim1] = -t[ilast + ilast * t_dim1];
}
if (ilz) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
z__[j + ilast * z_dim1] = -z__[j + ilast * z_dim1];
/* L100: */
}
}
}
alphar[ilast] = h__[ilast + ilast * h_dim1];
alphai[ilast] = 0.f;
beta[ilast] = t[ilast + ilast * t_dim1];
/* Go to next block -- exit if finished. */
--ilast;
if (ilast < *ilo) {
goto L380;
}
/* Reset counters */
iiter = 0;
eshift = 0.f;
if (! ilschr) {
ilastm = ilast;
if (ifrstm > ilast) {
ifrstm = *ilo;
}
}
goto L350;
/* QZ step */
/* This iteration only involves rows/columns IFIRST:ILAST. We */
/* assume IFIRST < ILAST, and that the diagonal of B is non-zero. */
L110:
++iiter;
if (! ilschr) {
ifrstm = ifirst;
}
/* Compute single shifts. */
/* At this point, IFIRST < ILAST, and the diagonal elements of */
/* T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in */
/* magnitude) */
if (iiter / 10 * 10 == iiter) {
/* Exceptional shift. Chosen for no particularly good reason. */
/* (Single shift only.) */
if ((real) maxit * safmin * (r__1 = h__[ilast + (ilast - 1) *
h_dim1], abs(r__1)) < (r__2 = t[ilast - 1 + (ilast - 1) *
t_dim1], abs(r__2))) {
eshift = h__[ilast + (ilast - 1) * h_dim1] / t[ilast - 1 + (
ilast - 1) * t_dim1];
} else {
eshift += 1.f / (safmin * (real) maxit);
}
s1 = 1.f;
wr = eshift;
} else {
/* Shifts based on the generalized eigenvalues of the */
/* bottom-right 2x2 block of A and B. The first eigenvalue */
/* returned by SLAG2 is the Wilkinson shift (AEP p.512), */
r__1 = safmin * 100.f;
slag2_(&h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &t[ilast - 1
+ (ilast - 1) * t_dim1], ldt, &r__1, &s1, &s2, &wr, &wr2,
&wi);
if ((r__1 = wr / s1 * t[ilast + ilast * t_dim1] - h__[ilast +
ilast * h_dim1], abs(r__1)) > (r__2 = wr2 / s2 * t[ilast
+ ilast * t_dim1] - h__[ilast + ilast * h_dim1], abs(r__2)
)) {
temp = wr;
wr = wr2;
wr2 = temp;
temp = s1;
s1 = s2;
s2 = temp;
}
/* Computing MAX */
/* Computing MAX */
r__3 = 1.f, r__4 = abs(wr), r__3 = f2cmax(r__3,r__4), r__4 = abs(wi);
r__1 = s1, r__2 = safmin * f2cmax(r__3,r__4);
temp = f2cmax(r__1,r__2);
if (wi != 0.f) {
goto L200;
}
}
/* Fiddle with shift to avoid overflow */
temp = f2cmin(ascale,1.f) * (safmax * .5f);
if (s1 > temp) {
scale = temp / s1;
} else {
scale = 1.f;
}
temp = f2cmin(bscale,1.f) * (safmax * .5f);
if (abs(wr) > temp) {
/* Computing MIN */
r__1 = scale, r__2 = temp / abs(wr);
scale = f2cmin(r__1,r__2);
}
s1 = scale * s1;
wr = scale * wr;
/* Now check for two consecutive small subdiagonals. */
i__2 = ifirst + 1;
for (j = ilast - 1; j >= i__2; --j) {
istart = j;
temp = (r__1 = s1 * h__[j + (j - 1) * h_dim1], abs(r__1));
temp2 = (r__1 = s1 * h__[j + j * h_dim1] - wr * t[j + j * t_dim1],
abs(r__1));
tempr = f2cmax(temp,temp2);
if (tempr < 1.f && tempr != 0.f) {
temp /= tempr;
temp2 /= tempr;
}
if ((r__1 = ascale * h__[j + 1 + j * h_dim1] * temp, abs(r__1)) <=
ascale * atol * temp2) {
goto L130;
}
/* L120: */
}
istart = ifirst;
L130:
/* Do an implicit single-shift QZ sweep. */
/* Initial Q */
temp = s1 * h__[istart + istart * h_dim1] - wr * t[istart + istart *
t_dim1];
temp2 = s1 * h__[istart + 1 + istart * h_dim1];
slartg_(&temp, &temp2, &c__, &s, &tempr);
/* Sweep */
i__2 = ilast - 1;
for (j = istart; j <= i__2; ++j) {
if (j > istart) {
temp = h__[j + (j - 1) * h_dim1];
slartg_(&temp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, &h__[
j + (j - 1) * h_dim1]);
h__[j + 1 + (j - 1) * h_dim1] = 0.f;
}
i__3 = ilastm;
for (jc = j; jc <= i__3; ++jc) {
temp = c__ * h__[j + jc * h_dim1] + s * h__[j + 1 + jc *
h_dim1];
h__[j + 1 + jc * h_dim1] = -s * h__[j + jc * h_dim1] + c__ *
h__[j + 1 + jc * h_dim1];
h__[j + jc * h_dim1] = temp;
temp2 = c__ * t[j + jc * t_dim1] + s * t[j + 1 + jc * t_dim1];
t[j + 1 + jc * t_dim1] = -s * t[j + jc * t_dim1] + c__ * t[j
+ 1 + jc * t_dim1];
t[j + jc * t_dim1] = temp2;
/* L140: */
}
if (ilq) {
i__3 = *n;
for (jr = 1; jr <= i__3; ++jr) {
temp = c__ * q[jr + j * q_dim1] + s * q[jr + (j + 1) *
q_dim1];
q[jr + (j + 1) * q_dim1] = -s * q[jr + j * q_dim1] + c__ *
q[jr + (j + 1) * q_dim1];
q[jr + j * q_dim1] = temp;
/* L150: */
}
}
temp = t[j + 1 + (j + 1) * t_dim1];
slartg_(&temp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j +
1) * t_dim1]);
t[j + 1 + j * t_dim1] = 0.f;
/* Computing MIN */
i__4 = j + 2;
i__3 = f2cmin(i__4,ilast);
for (jr = ifrstm; jr <= i__3; ++jr) {
temp = c__ * h__[jr + (j + 1) * h_dim1] + s * h__[jr + j *
h_dim1];
h__[jr + j * h_dim1] = -s * h__[jr + (j + 1) * h_dim1] + c__ *
h__[jr + j * h_dim1];
h__[jr + (j + 1) * h_dim1] = temp;
/* L160: */
}
i__3 = j;
for (jr = ifrstm; jr <= i__3; ++jr) {
temp = c__ * t[jr + (j + 1) * t_dim1] + s * t[jr + j * t_dim1]
;
t[jr + j * t_dim1] = -s * t[jr + (j + 1) * t_dim1] + c__ * t[
jr + j * t_dim1];
t[jr + (j + 1) * t_dim1] = temp;
/* L170: */
}
if (ilz) {
i__3 = *n;
for (jr = 1; jr <= i__3; ++jr) {
temp = c__ * z__[jr + (j + 1) * z_dim1] + s * z__[jr + j *
z_dim1];
z__[jr + j * z_dim1] = -s * z__[jr + (j + 1) * z_dim1] +
c__ * z__[jr + j * z_dim1];
z__[jr + (j + 1) * z_dim1] = temp;
/* L180: */
}
}
/* L190: */
}
goto L350;
/* Use Francis double-shift */
/* Note: the Francis double-shift should work with real shifts, */
/* but only if the block is at least 3x3. */
/* This code may break if this point is reached with */
/* a 2x2 block with real eigenvalues. */
L200:
if (ifirst + 1 == ilast) {
/* Special case -- 2x2 block with complex eigenvectors */
/* Step 1: Standardize, that is, rotate so that */
/* ( B11 0 ) */
/* B = ( ) with B11 non-negative. */
/* ( 0 B22 ) */
slasv2_(&t[ilast - 1 + (ilast - 1) * t_dim1], &t[ilast - 1 +
ilast * t_dim1], &t[ilast + ilast * t_dim1], &b22, &b11, &
sr, &cr, &sl, &cl);
if (b11 < 0.f) {
cr = -cr;
sr = -sr;
b11 = -b11;
b22 = -b22;
}
i__2 = ilastm + 1 - ifirst;
srot_(&i__2, &h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &h__[
ilast + (ilast - 1) * h_dim1], ldh, &cl, &sl);
i__2 = ilast + 1 - ifrstm;
srot_(&i__2, &h__[ifrstm + (ilast - 1) * h_dim1], &c__1, &h__[
ifrstm + ilast * h_dim1], &c__1, &cr, &sr);
if (ilast < ilastm) {
i__2 = ilastm - ilast;
srot_(&i__2, &t[ilast - 1 + (ilast + 1) * t_dim1], ldt, &t[
ilast + (ilast + 1) * t_dim1], ldt, &cl, &sl);
}
if (ifrstm < ilast - 1) {
i__2 = ifirst - ifrstm;
srot_(&i__2, &t[ifrstm + (ilast - 1) * t_dim1], &c__1, &t[
ifrstm + ilast * t_dim1], &c__1, &cr, &sr);
}
if (ilq) {
srot_(n, &q[(ilast - 1) * q_dim1 + 1], &c__1, &q[ilast *
q_dim1 + 1], &c__1, &cl, &sl);
}
if (ilz) {
srot_(n, &z__[(ilast - 1) * z_dim1 + 1], &c__1, &z__[ilast *
z_dim1 + 1], &c__1, &cr, &sr);
}
t[ilast - 1 + (ilast - 1) * t_dim1] = b11;
t[ilast - 1 + ilast * t_dim1] = 0.f;
t[ilast + (ilast - 1) * t_dim1] = 0.f;
t[ilast + ilast * t_dim1] = b22;
/* If B22 is negative, negate column ILAST */
if (b22 < 0.f) {
i__2 = ilast;
for (j = ifrstm; j <= i__2; ++j) {
h__[j + ilast * h_dim1] = -h__[j + ilast * h_dim1];
t[j + ilast * t_dim1] = -t[j + ilast * t_dim1];
/* L210: */
}
if (ilz) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
z__[j + ilast * z_dim1] = -z__[j + ilast * z_dim1];
/* L220: */
}
}
b22 = -b22;
}
/* Step 2: Compute ALPHAR, ALPHAI, and BETA (see refs.) */
/* Recompute shift */
r__1 = safmin * 100.f;
slag2_(&h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &t[ilast - 1
+ (ilast - 1) * t_dim1], ldt, &r__1, &s1, &temp, &wr, &
temp2, &wi);
/* If standardization has perturbed the shift onto real line, */
/* do another (real single-shift) QR step. */
if (wi == 0.f) {
goto L350;
}
s1inv = 1.f / s1;
/* Do EISPACK (QZVAL) computation of alpha and beta */
a11 = h__[ilast - 1 + (ilast - 1) * h_dim1];
a21 = h__[ilast + (ilast - 1) * h_dim1];
a12 = h__[ilast - 1 + ilast * h_dim1];
a22 = h__[ilast + ilast * h_dim1];
/* Compute complex Givens rotation on right */
/* (Assume some element of C = (sA - wB) > unfl ) */
/* __ */
/* (sA - wB) ( CZ -SZ ) */
/* ( SZ CZ ) */
c11r = s1 * a11 - wr * b11;
c11i = -wi * b11;
c12 = s1 * a12;
c21 = s1 * a21;
c22r = s1 * a22 - wr * b22;
c22i = -wi * b22;
if (abs(c11r) + abs(c11i) + abs(c12) > abs(c21) + abs(c22r) + abs(
c22i)) {
t1 = slapy3_(&c12, &c11r, &c11i);
cz = c12 / t1;
szr = -c11r / t1;
szi = -c11i / t1;
} else {
cz = slapy2_(&c22r, &c22i);
if (cz <= safmin) {
cz = 0.f;
szr = 1.f;
szi = 0.f;
} else {
tempr = c22r / cz;
tempi = c22i / cz;
t1 = slapy2_(&cz, &c21);
cz /= t1;
szr = -c21 * tempr / t1;
szi = c21 * tempi / t1;
}
}
/* Compute Givens rotation on left */
/* ( CQ SQ ) */
/* ( __ ) A or B */
/* ( -SQ CQ ) */
an = abs(a11) + abs(a12) + abs(a21) + abs(a22);
bn = abs(b11) + abs(b22);
wabs = abs(wr) + abs(wi);
if (s1 * an > wabs * bn) {
cq = cz * b11;
sqr = szr * b22;
sqi = -szi * b22;
} else {
a1r = cz * a11 + szr * a12;
a1i = szi * a12;
a2r = cz * a21 + szr * a22;
a2i = szi * a22;
cq = slapy2_(&a1r, &a1i);
if (cq <= safmin) {
cq = 0.f;
sqr = 1.f;
sqi = 0.f;
} else {
tempr = a1r / cq;
tempi = a1i / cq;
sqr = tempr * a2r + tempi * a2i;
sqi = tempi * a2r - tempr * a2i;
}
}
t1 = slapy3_(&cq, &sqr, &sqi);
cq /= t1;
sqr /= t1;
sqi /= t1;
/* Compute diagonal elements of QBZ */
tempr = sqr * szr - sqi * szi;
tempi = sqr * szi + sqi * szr;
b1r = cq * cz * b11 + tempr * b22;
b1i = tempi * b22;
b1a = slapy2_(&b1r, &b1i);
b2r = cq * cz * b22 + tempr * b11;
b2i = -tempi * b11;
b2a = slapy2_(&b2r, &b2i);
/* Normalize so beta > 0, and Im( alpha1 ) > 0 */
beta[ilast - 1] = b1a;
beta[ilast] = b2a;
alphar[ilast - 1] = wr * b1a * s1inv;
alphai[ilast - 1] = wi * b1a * s1inv;
alphar[ilast] = wr * b2a * s1inv;
alphai[ilast] = -(wi * b2a) * s1inv;
/* Step 3: Go to next block -- exit if finished. */
ilast = ifirst - 1;
if (ilast < *ilo) {
goto L380;
}
/* Reset counters */
iiter = 0;
eshift = 0.f;
if (! ilschr) {
ilastm = ilast;
if (ifrstm > ilast) {
ifrstm = *ilo;
}
}
goto L350;
} else {
/* Usual case: 3x3 or larger block, using Francis implicit */
/* double-shift */
/* 2 */
/* Eigenvalue equation is w - c w + d = 0, */
/* -1 2 -1 */
/* so compute 1st column of (A B ) - c A B + d */
/* using the formula in QZIT (from EISPACK) */
/* We assume that the block is at least 3x3 */
ad11 = ascale * h__[ilast - 1 + (ilast - 1) * h_dim1] / (bscale *
t[ilast - 1 + (ilast - 1) * t_dim1]);
ad21 = ascale * h__[ilast + (ilast - 1) * h_dim1] / (bscale * t[
ilast - 1 + (ilast - 1) * t_dim1]);
ad12 = ascale * h__[ilast - 1 + ilast * h_dim1] / (bscale * t[
ilast + ilast * t_dim1]);
ad22 = ascale * h__[ilast + ilast * h_dim1] / (bscale * t[ilast +
ilast * t_dim1]);
u12 = t[ilast - 1 + ilast * t_dim1] / t[ilast + ilast * t_dim1];
ad11l = ascale * h__[ifirst + ifirst * h_dim1] / (bscale * t[
ifirst + ifirst * t_dim1]);
ad21l = ascale * h__[ifirst + 1 + ifirst * h_dim1] / (bscale * t[
ifirst + ifirst * t_dim1]);
ad12l = ascale * h__[ifirst + (ifirst + 1) * h_dim1] / (bscale *
t[ifirst + 1 + (ifirst + 1) * t_dim1]);
ad22l = ascale * h__[ifirst + 1 + (ifirst + 1) * h_dim1] / (
bscale * t[ifirst + 1 + (ifirst + 1) * t_dim1]);
ad32l = ascale * h__[ifirst + 2 + (ifirst + 1) * h_dim1] / (
bscale * t[ifirst + 1 + (ifirst + 1) * t_dim1]);
u12l = t[ifirst + (ifirst + 1) * t_dim1] / t[ifirst + 1 + (ifirst
+ 1) * t_dim1];
v[0] = (ad11 - ad11l) * (ad22 - ad11l) - ad12 * ad21 + ad21 * u12
* ad11l + (ad12l - ad11l * u12l) * ad21l;
v[1] = (ad22l - ad11l - ad21l * u12l - (ad11 - ad11l) - (ad22 -
ad11l) + ad21 * u12) * ad21l;
v[2] = ad32l * ad21l;
istart = ifirst;
slarfg_(&c__3, v, &v[1], &c__1, &tau);
v[0] = 1.f;
/* Sweep */
i__2 = ilast - 2;
for (j = istart; j <= i__2; ++j) {
/* All but last elements: use 3x3 Householder transforms. */
/* Zero (j-1)st column of A */
if (j > istart) {
v[0] = h__[j + (j - 1) * h_dim1];
v[1] = h__[j + 1 + (j - 1) * h_dim1];
v[2] = h__[j + 2 + (j - 1) * h_dim1];
slarfg_(&c__3, &h__[j + (j - 1) * h_dim1], &v[1], &c__1, &
tau);
v[0] = 1.f;
h__[j + 1 + (j - 1) * h_dim1] = 0.f;
h__[j + 2 + (j - 1) * h_dim1] = 0.f;
}
i__3 = ilastm;
for (jc = j; jc <= i__3; ++jc) {
temp = tau * (h__[j + jc * h_dim1] + v[1] * h__[j + 1 +
jc * h_dim1] + v[2] * h__[j + 2 + jc * h_dim1]);
h__[j + jc * h_dim1] -= temp;
h__[j + 1 + jc * h_dim1] -= temp * v[1];
h__[j + 2 + jc * h_dim1] -= temp * v[2];
temp2 = tau * (t[j + jc * t_dim1] + v[1] * t[j + 1 + jc *
t_dim1] + v[2] * t[j + 2 + jc * t_dim1]);
t[j + jc * t_dim1] -= temp2;
t[j + 1 + jc * t_dim1] -= temp2 * v[1];
t[j + 2 + jc * t_dim1] -= temp2 * v[2];
/* L230: */
}
if (ilq) {
i__3 = *n;
for (jr = 1; jr <= i__3; ++jr) {
temp = tau * (q[jr + j * q_dim1] + v[1] * q[jr + (j +
1) * q_dim1] + v[2] * q[jr + (j + 2) * q_dim1]
);
q[jr + j * q_dim1] -= temp;
q[jr + (j + 1) * q_dim1] -= temp * v[1];
q[jr + (j + 2) * q_dim1] -= temp * v[2];
/* L240: */
}
}
/* Zero j-th column of B (see SLAGBC for details) */
/* Swap rows to pivot */
ilpivt = FALSE_;
/* Computing MAX */
r__3 = (r__1 = t[j + 1 + (j + 1) * t_dim1], abs(r__1)), r__4 =
(r__2 = t[j + 1 + (j + 2) * t_dim1], abs(r__2));
temp = f2cmax(r__3,r__4);
/* Computing MAX */
r__3 = (r__1 = t[j + 2 + (j + 1) * t_dim1], abs(r__1)), r__4 =
(r__2 = t[j + 2 + (j + 2) * t_dim1], abs(r__2));
temp2 = f2cmax(r__3,r__4);
if (f2cmax(temp,temp2) < safmin) {
scale = 0.f;
u1 = 1.f;
u2 = 0.f;
goto L250;
} else if (temp >= temp2) {
w11 = t[j + 1 + (j + 1) * t_dim1];
w21 = t[j + 2 + (j + 1) * t_dim1];
w12 = t[j + 1 + (j + 2) * t_dim1];
w22 = t[j + 2 + (j + 2) * t_dim1];
u1 = t[j + 1 + j * t_dim1];
u2 = t[j + 2 + j * t_dim1];
} else {
w21 = t[j + 1 + (j + 1) * t_dim1];
w11 = t[j + 2 + (j + 1) * t_dim1];
w22 = t[j + 1 + (j + 2) * t_dim1];
w12 = t[j + 2 + (j + 2) * t_dim1];
u2 = t[j + 1 + j * t_dim1];
u1 = t[j + 2 + j * t_dim1];
}
/* Swap columns if nec. */
if (abs(w12) > abs(w11)) {
ilpivt = TRUE_;
temp = w12;
temp2 = w22;
w12 = w11;
w22 = w21;
w11 = temp;
w21 = temp2;
}
/* LU-factor */
temp = w21 / w11;
u2 -= temp * u1;
w22 -= temp * w12;
w21 = 0.f;
/* Compute SCALE */
scale = 1.f;
if (abs(w22) < safmin) {
scale = 0.f;
u2 = 1.f;
u1 = -w12 / w11;
goto L250;
}
if (abs(w22) < abs(u2)) {
scale = (r__1 = w22 / u2, abs(r__1));
}
if (abs(w11) < abs(u1)) {
/* Computing MIN */
r__2 = scale, r__3 = (r__1 = w11 / u1, abs(r__1));
scale = f2cmin(r__2,r__3);
}
/* Solve */
u2 = scale * u2 / w22;
u1 = (scale * u1 - w12 * u2) / w11;
L250:
if (ilpivt) {
temp = u2;
u2 = u1;
u1 = temp;
}
/* Compute Householder Vector */
/* Computing 2nd power */
r__1 = scale;
/* Computing 2nd power */
r__2 = u1;
/* Computing 2nd power */
r__3 = u2;
t1 = sqrt(r__1 * r__1 + r__2 * r__2 + r__3 * r__3);
tau = scale / t1 + 1.f;
vs = -1.f / (scale + t1);
v[0] = 1.f;
v[1] = vs * u1;
v[2] = vs * u2;
/* Apply transformations from the right. */
/* Computing MIN */
i__4 = j + 3;
i__3 = f2cmin(i__4,ilast);
for (jr = ifrstm; jr <= i__3; ++jr) {
temp = tau * (h__[jr + j * h_dim1] + v[1] * h__[jr + (j +
1) * h_dim1] + v[2] * h__[jr + (j + 2) * h_dim1]);
h__[jr + j * h_dim1] -= temp;
h__[jr + (j + 1) * h_dim1] -= temp * v[1];
h__[jr + (j + 2) * h_dim1] -= temp * v[2];
/* L260: */
}
i__3 = j + 2;
for (jr = ifrstm; jr <= i__3; ++jr) {
temp = tau * (t[jr + j * t_dim1] + v[1] * t[jr + (j + 1) *
t_dim1] + v[2] * t[jr + (j + 2) * t_dim1]);
t[jr + j * t_dim1] -= temp;
t[jr + (j + 1) * t_dim1] -= temp * v[1];
t[jr + (j + 2) * t_dim1] -= temp * v[2];
/* L270: */
}
if (ilz) {
i__3 = *n;
for (jr = 1; jr <= i__3; ++jr) {
temp = tau * (z__[jr + j * z_dim1] + v[1] * z__[jr + (
j + 1) * z_dim1] + v[2] * z__[jr + (j + 2) *
z_dim1]);
z__[jr + j * z_dim1] -= temp;
z__[jr + (j + 1) * z_dim1] -= temp * v[1];
z__[jr + (j + 2) * z_dim1] -= temp * v[2];
/* L280: */
}
}
t[j + 1 + j * t_dim1] = 0.f;
t[j + 2 + j * t_dim1] = 0.f;
/* L290: */
}
/* Last elements: Use Givens rotations */
/* Rotations from the left */
j = ilast - 1;
temp = h__[j + (j - 1) * h_dim1];
slartg_(&temp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, &h__[j +
(j - 1) * h_dim1]);
h__[j + 1 + (j - 1) * h_dim1] = 0.f;
i__2 = ilastm;
for (jc = j; jc <= i__2; ++jc) {
temp = c__ * h__[j + jc * h_dim1] + s * h__[j + 1 + jc *
h_dim1];
h__[j + 1 + jc * h_dim1] = -s * h__[j + jc * h_dim1] + c__ *
h__[j + 1 + jc * h_dim1];
h__[j + jc * h_dim1] = temp;
temp2 = c__ * t[j + jc * t_dim1] + s * t[j + 1 + jc * t_dim1];
t[j + 1 + jc * t_dim1] = -s * t[j + jc * t_dim1] + c__ * t[j
+ 1 + jc * t_dim1];
t[j + jc * t_dim1] = temp2;
/* L300: */
}
if (ilq) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
temp = c__ * q[jr + j * q_dim1] + s * q[jr + (j + 1) *
q_dim1];
q[jr + (j + 1) * q_dim1] = -s * q[jr + j * q_dim1] + c__ *
q[jr + (j + 1) * q_dim1];
q[jr + j * q_dim1] = temp;
/* L310: */
}
}
/* Rotations from the right. */
temp = t[j + 1 + (j + 1) * t_dim1];
slartg_(&temp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j +
1) * t_dim1]);
t[j + 1 + j * t_dim1] = 0.f;
i__2 = ilast;
for (jr = ifrstm; jr <= i__2; ++jr) {
temp = c__ * h__[jr + (j + 1) * h_dim1] + s * h__[jr + j *
h_dim1];
h__[jr + j * h_dim1] = -s * h__[jr + (j + 1) * h_dim1] + c__ *
h__[jr + j * h_dim1];
h__[jr + (j + 1) * h_dim1] = temp;
/* L320: */
}
i__2 = ilast - 1;
for (jr = ifrstm; jr <= i__2; ++jr) {
temp = c__ * t[jr + (j + 1) * t_dim1] + s * t[jr + j * t_dim1]
;
t[jr + j * t_dim1] = -s * t[jr + (j + 1) * t_dim1] + c__ * t[
jr + j * t_dim1];
t[jr + (j + 1) * t_dim1] = temp;
/* L330: */
}
if (ilz) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
temp = c__ * z__[jr + (j + 1) * z_dim1] + s * z__[jr + j *
z_dim1];
z__[jr + j * z_dim1] = -s * z__[jr + (j + 1) * z_dim1] +
c__ * z__[jr + j * z_dim1];
z__[jr + (j + 1) * z_dim1] = temp;
/* L340: */
}
}
/* End of Double-Shift code */
}
goto L350;
/* End of iteration loop */
L350:
/* L360: */
;
}
/* Drop-through = non-convergence */
*info = ilast;
goto L420;
/* Successful completion of all QZ steps */
L380:
/* Set Eigenvalues 1:ILO-1 */
i__1 = *ilo - 1;
for (j = 1; j <= i__1; ++j) {
if (t[j + j * t_dim1] < 0.f) {
if (ilschr) {
i__2 = j;
for (jr = 1; jr <= i__2; ++jr) {
h__[jr + j * h_dim1] = -h__[jr + j * h_dim1];
t[jr + j * t_dim1] = -t[jr + j * t_dim1];
/* L390: */
}
} else {
h__[j + j * h_dim1] = -h__[j + j * h_dim1];
t[j + j * t_dim1] = -t[j + j * t_dim1];
}
if (ilz) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
z__[jr + j * z_dim1] = -z__[jr + j * z_dim1];
/* L400: */
}
}
}
alphar[j] = h__[j + j * h_dim1];
alphai[j] = 0.f;
beta[j] = t[j + j * t_dim1];
/* L410: */
}
/* Normal Termination */
*info = 0;
/* Exit (other than argument error) -- return optimal workspace size */
L420:
work[1] = (real) (*n);
return;
/* End of SHGEQZ */
} /* shgeqz_ */
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