#include #include #include #include #include #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]/Cd(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);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b ZHGEQZ */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZHGEQZ + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, */ /* ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, */ /* RWORK, INFO ) */ /* CHARACTER COMPQ, COMPZ, JOB */ /* INTEGER IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N */ /* DOUBLE PRECISION RWORK( * ) */ /* COMPLEX*16 ALPHA( * ), BETA( * ), H( LDH, * ), */ /* $ Q( LDQ, * ), T( LDT, * ), WORK( * ), */ /* $ Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZHGEQZ computes the eigenvalues of a complex matrix pair (H,T), */ /* > where H is an upper Hessenberg matrix and T is upper triangular, */ /* > using the single-shift QZ method. */ /* > Matrix pairs of this type are produced by the reduction to */ /* > generalized upper Hessenberg form of a complex matrix pair (A,B): */ /* > */ /* > A = Q1*H*Z1**H, B = Q1*T*Z1**H, */ /* > */ /* > as computed by ZGGHRD. */ /* > */ /* > If JOB='S', then the Hessenberg-triangular pair (H,T) is */ /* > also reduced to generalized Schur form, */ /* > */ /* > H = Q*S*Z**H, T = Q*P*Z**H, */ /* > */ /* > where Q and Z are unitary matrices and S and P are upper triangular. */ /* > */ /* > Optionally, the unitary matrix Q from the generalized Schur */ /* > factorization may be postmultiplied into an input matrix Q1, and the */ /* > unitary matrix Z may be postmultiplied into an input matrix Z1. */ /* > If Q1 and Z1 are the unitary matrices from ZGGHRD that reduced */ /* > the matrix pair (A,B) to generalized Hessenberg form, then the output */ /* > matrices Q1*Q and Z1*Z are the unitary factors from the generalized */ /* > Schur factorization of (A,B): */ /* > */ /* > A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H. */ /* > */ /* > To avoid overflow, eigenvalues of the matrix pair (H,T) */ /* > (equivalently, of (A,B)) are computed as a pair of complex values */ /* > (alpha,beta). 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. */ /* > The values of alpha and beta for the i-th eigenvalue 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': Computer 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 a unitary 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': Q is initialized to the unit matrix and the matrix Z */ /* > of right Schur vectors of (H,T) is returned; */ /* > = 'V': Z must contain a unitary 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 COMPLEX*16 array, dimension (LDH, N) */ /* > On entry, the N-by-N upper Hessenberg matrix H. */ /* > On exit, if JOB = 'S', H contains the upper triangular */ /* > matrix S from the generalized Schur factorization. */ /* > If JOB = 'E', the diagonal of H matches that 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 COMPLEX*16 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. */ /* > If JOB = 'E', the diagonal of T matches that 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] ALPHA */ /* > \verbatim */ /* > ALPHA is COMPLEX*16 array, dimension (N) */ /* > The complex scalars alpha that define the eigenvalues of */ /* > GNEP. ALPHA(i) = S(i,i) in the generalized Schur */ /* > factorization. */ /* > \endverbatim */ /* > */ /* > \param[out] BETA */ /* > \verbatim */ /* > BETA is COMPLEX*16 array, dimension (N) */ /* > The real non-negative scalars beta that define the */ /* > eigenvalues of GNEP. BETA(i) = P(i,i) in the generalized */ /* > Schur factorization. */ /* > */ /* > Together, the quantities alpha = ALPHA(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 COMPLEX*16 array, dimension (LDQ, N) */ /* > On entry, if COMPQ = 'V', the unitary matrix Q1 used in the */ /* > reduction of (A,B) to generalized Hessenberg form. */ /* > On exit, if COMPQ = 'I', the unitary matrix of left Schur */ /* > vectors of (H,T), and if COMPQ = 'V', the unitary 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 COMPLEX*16 array, dimension (LDZ, N) */ /* > On entry, if COMPZ = 'V', the unitary matrix Z1 used in the */ /* > reduction of (A,B) to generalized Hessenberg form. */ /* > On exit, if COMPZ = 'I', the unitary matrix of right Schur */ /* > vectors of (H,T), and if COMPZ = 'V', the unitary 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 COMPLEX*16 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] RWORK */ /* > \verbatim */ /* > RWORK is DOUBLE PRECISION array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > = 1,...,N: the QZ iteration did not converge. (H,T) is not */ /* > in Schur form, but ALPHA(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 ALPHA(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 April 2012 */ /* > \ingroup complex16GEcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > We assume that complex ABS works as long as its value is less than */ /* > overflow. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int zhgeqz_(char *job, char *compq, char *compz, integer *n, integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh, doublecomplex *t, integer *ldt, doublecomplex *alpha, doublecomplex * beta, doublecomplex *q, integer *ldq, doublecomplex *z__, integer * ldz, doublecomplex *work, integer *lwork, doublereal *rwork, 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, i__5, i__6; doublereal d__1, d__2, d__3, d__4, d__5, d__6; doublecomplex z__1, z__2, z__3, z__4, z__5, z__6, z__7; /* Local variables */ doublereal absb, atol, btol, temp; extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublecomplex *); doublereal temp2, c__; integer j; doublecomplex s, x, y; extern logical lsame_(char *, char *); doublecomplex ctemp; integer iiter, ilast, jiter; doublereal anorm, bnorm; integer maxit; doublecomplex shift; extern /* Subroutine */ int zscal_(integer *, doublecomplex *, doublecomplex *, integer *); doublereal tempr; doublecomplex ctemp2, ctemp3; logical ilazr2; integer jc, in; doublereal ascale, bscale; doublecomplex u12; extern doublereal dlamch_(char *); integer jr; doublecomplex signbc; doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublecomplex eshift; logical ilschr; integer icompq, ilastm; extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, doublecomplex *); integer ischur; extern doublereal zlanhs_(char *, integer *, doublecomplex *, integer *, doublereal *); logical ilazro; integer icompz, ifirst; extern /* Subroutine */ int zlartg_(doublecomplex *, doublecomplex *, doublereal *, doublecomplex *, doublecomplex *); integer ifrstm; extern /* Subroutine */ int zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); integer istart; logical lquery; doublecomplex ad11, ad12, ad21, ad22; integer jch; logical ilq, ilz; doublereal ulp; doublecomplex abi12, abi22; /* -- 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..-- */ /* April 2012 */ /* ===================================================================== */ /* 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; --alpha; --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; --rwork; /* Function Body */ if (lsame_(job, "E")) { ilschr = FALSE_; ischur = 1; } else if (lsame_(job, "S")) { ilschr = TRUE_; ischur = 2; } else { ilschr = TRUE_; 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 { ilq = TRUE_; 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 { ilz = TRUE_; icompz = 0; } /* Check Argument Values */ *info = 0; i__1 = f2cmax(1,*n); work[1].r = (doublereal) i__1, work[1].i = 0.; 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 = -14; } else if (*ldz < 1 || ilz && *ldz < *n) { *info = -16; } else if (*lwork < f2cmax(1,*n) && ! lquery) { *info = -18; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHGEQZ", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ /* WORK( 1 ) = CMPLX( 1 ) */ if (*n <= 0) { work[1].r = 1., work[1].i = 0.; return 0; } /* Initialize Q and Z */ if (icompq == 3) { zlaset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq); } if (icompz == 3) { zlaset_("Full", n, n, &c_b1, &c_b2, &z__[z_offset], ldz); } /* Machine Constants */ in = *ihi + 1 - *ilo; safmin = dlamch_("S"); ulp = dlamch_("E") * dlamch_("B"); anorm = zlanhs_("F", &in, &h__[*ilo + *ilo * h_dim1], ldh, &rwork[1]); bnorm = zlanhs_("F", &in, &t[*ilo + *ilo * t_dim1], ldt, &rwork[1]); /* Computing MAX */ d__1 = safmin, d__2 = ulp * anorm; atol = f2cmax(d__1,d__2); /* Computing MAX */ d__1 = safmin, d__2 = ulp * bnorm; btol = f2cmax(d__1,d__2); ascale = 1. / f2cmax(safmin,anorm); bscale = 1. / f2cmax(safmin,bnorm); /* Set Eigenvalues IHI+1:N */ i__1 = *n; for (j = *ihi + 1; j <= i__1; ++j) { absb = z_abs(&t[j + j * t_dim1]); if (absb > safmin) { i__2 = j + j * t_dim1; z__2.r = t[i__2].r / absb, z__2.i = t[i__2].i / absb; d_cnjg(&z__1, &z__2); signbc.r = z__1.r, signbc.i = z__1.i; i__2 = j + j * t_dim1; t[i__2].r = absb, t[i__2].i = 0.; if (ilschr) { i__2 = j - 1; zscal_(&i__2, &signbc, &t[j * t_dim1 + 1], &c__1); zscal_(&j, &signbc, &h__[j * h_dim1 + 1], &c__1); } else { zscal_(&c__1, &signbc, &h__[j + j * h_dim1], &c__1); } if (ilz) { zscal_(n, &signbc, &z__[j * z_dim1 + 1], &c__1); } } else { i__2 = j + j * t_dim1; t[i__2].r = 0., t[i__2].i = 0.; } i__2 = j; i__3 = j + j * h_dim1; alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i; i__2 = j; i__3 = j + j * t_dim1; beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i; /* L10: */ } /* If IHI < ILO, skip QZ steps */ if (*ihi < *ilo) { goto L190; } /* 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.r = 0., eshift.i = 0.; maxit = (*ihi - *ilo + 1) * 30; i__1 = maxit; for (jiter = 1; jiter <= i__1; ++jiter) { /* Check for too many iterations. */ if (jiter > maxit) { goto L180; } /* Split the matrix if possible. */ /* Two tests: */ /* 1: H(j,j-1)=0 or j=ILO */ /* 2: T(j,j)=0 */ /* Special case: j=ILAST */ if (ilast == *ilo) { goto L60; } else { i__2 = ilast + (ilast - 1) * h_dim1; if ((d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[ilast + (ilast - 1) * h_dim1]), abs(d__2)) <= atol) { i__2 = ilast + (ilast - 1) * h_dim1; h__[i__2].r = 0., h__[i__2].i = 0.; goto L60; } } if (z_abs(&t[ilast + ilast * t_dim1]) <= btol) { i__2 = ilast + ilast * t_dim1; t[i__2].r = 0., t[i__2].i = 0.; goto L50; } /* General case: j= i__2; --j) { /* Test 1: for H(j,j-1)=0 or j=ILO */ if (j == *ilo) { ilazro = TRUE_; } else { i__3 = j + (j - 1) * h_dim1; if ((d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[j + (j - 1) * h_dim1]), abs(d__2)) <= atol) { i__3 = j + (j - 1) * h_dim1; h__[i__3].r = 0., h__[i__3].i = 0.; ilazro = TRUE_; } else { ilazro = FALSE_; } } /* Test 2: for T(j,j)=0 */ if (z_abs(&t[j + j * t_dim1]) < btol) { i__3 = j + j * t_dim1; t[i__3].r = 0., t[i__3].i = 0.; /* Test 1a: Check for 2 consecutive small subdiagonals in A */ ilazr2 = FALSE_; if (! ilazro) { i__3 = j + (j - 1) * h_dim1; i__4 = j + 1 + j * h_dim1; i__5 = j + j * h_dim1; if (((d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(& h__[j + (j - 1) * h_dim1]), abs(d__2))) * (ascale * ((d__3 = h__[i__4].r, abs(d__3)) + (d__4 = d_imag(&h__[j + 1 + j * h_dim1]), abs(d__4)))) <= ((d__5 = h__[i__5].r, abs(d__5)) + (d__6 = d_imag( &h__[j + j * h_dim1]), abs(d__6))) * (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) { i__4 = jch + jch * h_dim1; ctemp.r = h__[i__4].r, ctemp.i = h__[i__4].i; zlartg_(&ctemp, &h__[jch + 1 + jch * h_dim1], &c__, & s, &h__[jch + jch * h_dim1]); i__4 = jch + 1 + jch * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; i__4 = ilastm - jch; zrot_(&i__4, &h__[jch + (jch + 1) * h_dim1], ldh, & h__[jch + 1 + (jch + 1) * h_dim1], ldh, &c__, &s); i__4 = ilastm - jch; zrot_(&i__4, &t[jch + (jch + 1) * t_dim1], ldt, &t[ jch + 1 + (jch + 1) * t_dim1], ldt, &c__, &s); if (ilq) { d_cnjg(&z__1, &s); zrot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1) * q_dim1 + 1], &c__1, &c__, &z__1); } if (ilazr2) { i__4 = jch + (jch - 1) * h_dim1; i__5 = jch + (jch - 1) * h_dim1; z__1.r = c__ * h__[i__5].r, z__1.i = c__ * h__[ i__5].i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; } ilazr2 = FALSE_; i__4 = jch + 1 + (jch + 1) * t_dim1; if ((d__1 = t[i__4].r, abs(d__1)) + (d__2 = d_imag(&t[ jch + 1 + (jch + 1) * t_dim1]), abs(d__2)) >= btol) { if (jch + 1 >= ilast) { goto L60; } else { ifirst = jch + 1; goto L70; } } i__4 = jch + 1 + (jch + 1) * t_dim1; t[i__4].r = 0., t[i__4].i = 0.; /* L20: */ } goto L50; } 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) { i__4 = jch + (jch + 1) * t_dim1; ctemp.r = t[i__4].r, ctemp.i = t[i__4].i; zlartg_(&ctemp, &t[jch + 1 + (jch + 1) * t_dim1], & c__, &s, &t[jch + (jch + 1) * t_dim1]); i__4 = jch + 1 + (jch + 1) * t_dim1; t[i__4].r = 0., t[i__4].i = 0.; if (jch < ilastm - 1) { i__4 = ilastm - jch - 1; zrot_(&i__4, &t[jch + (jch + 2) * t_dim1], ldt, & t[jch + 1 + (jch + 2) * t_dim1], ldt, & c__, &s); } i__4 = ilastm - jch + 2; zrot_(&i__4, &h__[jch + (jch - 1) * h_dim1], ldh, & h__[jch + 1 + (jch - 1) * h_dim1], ldh, &c__, &s); if (ilq) { d_cnjg(&z__1, &s); zrot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1) * q_dim1 + 1], &c__1, &c__, &z__1); } i__4 = jch + 1 + jch * h_dim1; ctemp.r = h__[i__4].r, ctemp.i = h__[i__4].i; zlartg_(&ctemp, &h__[jch + 1 + (jch - 1) * h_dim1], & c__, &s, &h__[jch + 1 + jch * h_dim1]); i__4 = jch + 1 + (jch - 1) * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; i__4 = jch + 1 - ifrstm; zrot_(&i__4, &h__[ifrstm + jch * h_dim1], &c__1, &h__[ ifrstm + (jch - 1) * h_dim1], &c__1, &c__, &s) ; i__4 = jch - ifrstm; zrot_(&i__4, &t[ifrstm + jch * t_dim1], &c__1, &t[ ifrstm + (jch - 1) * t_dim1], &c__1, &c__, &s) ; if (ilz) { zrot_(n, &z__[jch * z_dim1 + 1], &c__1, &z__[(jch - 1) * z_dim1 + 1], &c__1, &c__, &s); } /* L30: */ } goto L50; } } else if (ilazro) { /* Only test 1 passed -- work on J:ILAST */ ifirst = j; goto L70; } /* Neither test passed -- try next J */ /* L40: */ } /* (Drop-through is "impossible") */ *info = (*n << 1) + 1; goto L210; /* T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a */ /* 1x1 block. */ L50: i__2 = ilast + ilast * h_dim1; ctemp.r = h__[i__2].r, ctemp.i = h__[i__2].i; zlartg_(&ctemp, &h__[ilast + (ilast - 1) * h_dim1], &c__, &s, &h__[ ilast + ilast * h_dim1]); i__2 = ilast + (ilast - 1) * h_dim1; h__[i__2].r = 0., h__[i__2].i = 0.; i__2 = ilast - ifrstm; zrot_(&i__2, &h__[ifrstm + ilast * h_dim1], &c__1, &h__[ifrstm + ( ilast - 1) * h_dim1], &c__1, &c__, &s); i__2 = ilast - ifrstm; zrot_(&i__2, &t[ifrstm + ilast * t_dim1], &c__1, &t[ifrstm + (ilast - 1) * t_dim1], &c__1, &c__, &s); if (ilz) { zrot_(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 ALPHA and BETA */ L60: absb = z_abs(&t[ilast + ilast * t_dim1]); if (absb > safmin) { i__2 = ilast + ilast * t_dim1; z__2.r = t[i__2].r / absb, z__2.i = t[i__2].i / absb; d_cnjg(&z__1, &z__2); signbc.r = z__1.r, signbc.i = z__1.i; i__2 = ilast + ilast * t_dim1; t[i__2].r = absb, t[i__2].i = 0.; if (ilschr) { i__2 = ilast - ifrstm; zscal_(&i__2, &signbc, &t[ifrstm + ilast * t_dim1], &c__1); i__2 = ilast + 1 - ifrstm; zscal_(&i__2, &signbc, &h__[ifrstm + ilast * h_dim1], &c__1); } else { zscal_(&c__1, &signbc, &h__[ilast + ilast * h_dim1], &c__1); } if (ilz) { zscal_(n, &signbc, &z__[ilast * z_dim1 + 1], &c__1); } } else { i__2 = ilast + ilast * t_dim1; t[i__2].r = 0., t[i__2].i = 0.; } i__2 = ilast; i__3 = ilast + ilast * h_dim1; alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i; i__2 = ilast; i__3 = ilast + ilast * t_dim1; beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i; /* Go to next block -- exit if finished. */ --ilast; if (ilast < *ilo) { goto L190; } /* Reset counters */ iiter = 0; eshift.r = 0., eshift.i = 0.; if (! ilschr) { ilastm = ilast; if (ifrstm > ilast) { ifrstm = *ilo; } } goto L160; /* QZ step */ /* This iteration only involves rows/columns IFIRST:ILAST. We */ /* assume IFIRST < ILAST, and that the diagonal of B is non-zero. */ L70: ++iiter; if (! ilschr) { ifrstm = ifirst; } /* Compute the Shift. */ /* 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) { /* The Wilkinson shift (AEP p.512), i.e., the eigenvalue of */ /* the bottom-right 2x2 block of A inv(B) which is nearest to */ /* the bottom-right element. */ /* We factor B as U*D, where U has unit diagonals, and */ /* compute (A*inv(D))*inv(U). */ i__2 = ilast - 1 + ilast * t_dim1; z__2.r = bscale * t[i__2].r, z__2.i = bscale * t[i__2].i; i__3 = ilast + ilast * t_dim1; z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i; z_div(&z__1, &z__2, &z__3); u12.r = z__1.r, u12.i = z__1.i; i__2 = ilast - 1 + (ilast - 1) * h_dim1; z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i; i__3 = ilast - 1 + (ilast - 1) * t_dim1; z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i; z_div(&z__1, &z__2, &z__3); ad11.r = z__1.r, ad11.i = z__1.i; i__2 = ilast + (ilast - 1) * h_dim1; z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i; i__3 = ilast - 1 + (ilast - 1) * t_dim1; z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i; z_div(&z__1, &z__2, &z__3); ad21.r = z__1.r, ad21.i = z__1.i; i__2 = ilast - 1 + ilast * h_dim1; z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i; i__3 = ilast + ilast * t_dim1; z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i; z_div(&z__1, &z__2, &z__3); ad12.r = z__1.r, ad12.i = z__1.i; i__2 = ilast + ilast * h_dim1; z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i; i__3 = ilast + ilast * t_dim1; z__3.r = bscale * t[i__3].r, z__3.i = bscale * t[i__3].i; z_div(&z__1, &z__2, &z__3); ad22.r = z__1.r, ad22.i = z__1.i; z__2.r = u12.r * ad21.r - u12.i * ad21.i, z__2.i = u12.r * ad21.i + u12.i * ad21.r; z__1.r = ad22.r - z__2.r, z__1.i = ad22.i - z__2.i; abi22.r = z__1.r, abi22.i = z__1.i; z__2.r = u12.r * ad11.r - u12.i * ad11.i, z__2.i = u12.r * ad11.i + u12.i * ad11.r; z__1.r = ad12.r - z__2.r, z__1.i = ad12.i - z__2.i; abi12.r = z__1.r, abi12.i = z__1.i; shift.r = abi22.r, shift.i = abi22.i; z_sqrt(&z__2, &abi12); z_sqrt(&z__3, &ad21); z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; ctemp.r = z__1.r, ctemp.i = z__1.i; temp = (d__1 = ctemp.r, abs(d__1)) + (d__2 = d_imag(&ctemp), abs( d__2)); if (ctemp.r != 0. || ctemp.i != 0.) { z__2.r = ad11.r - shift.r, z__2.i = ad11.i - shift.i; z__1.r = z__2.r * .5, z__1.i = z__2.i * .5; x.r = z__1.r, x.i = z__1.i; temp2 = (d__1 = x.r, abs(d__1)) + (d__2 = d_imag(&x), abs( d__2)); /* Computing MAX */ d__3 = temp, d__4 = (d__1 = x.r, abs(d__1)) + (d__2 = d_imag(& x), abs(d__2)); temp = f2cmax(d__3,d__4); z__5.r = x.r / temp, z__5.i = x.i / temp; pow_zi(&z__4, &z__5, &c__2); z__7.r = ctemp.r / temp, z__7.i = ctemp.i / temp; pow_zi(&z__6, &z__7, &c__2); z__3.r = z__4.r + z__6.r, z__3.i = z__4.i + z__6.i; z_sqrt(&z__2, &z__3); z__1.r = temp * z__2.r, z__1.i = temp * z__2.i; y.r = z__1.r, y.i = z__1.i; if (temp2 > 0.) { z__1.r = x.r / temp2, z__1.i = x.i / temp2; z__2.r = x.r / temp2, z__2.i = x.i / temp2; if (z__1.r * y.r + d_imag(&z__2) * d_imag(&y) < 0.) { z__3.r = -y.r, z__3.i = -y.i; y.r = z__3.r, y.i = z__3.i; } } z__4.r = x.r + y.r, z__4.i = x.i + y.i; zladiv_(&z__3, &ctemp, &z__4); z__2.r = ctemp.r * z__3.r - ctemp.i * z__3.i, z__2.i = ctemp.r * z__3.i + ctemp.i * z__3.r; z__1.r = shift.r - z__2.r, z__1.i = shift.i - z__2.i; shift.r = z__1.r, shift.i = z__1.i; } } else { /* Exceptional shift. Chosen for no particularly good reason. */ i__2 = ilast + ilast * t_dim1; if (iiter / 20 * 20 == iiter && bscale * ((d__1 = t[i__2].r, abs( d__1)) + (d__2 = d_imag(&t[ilast + ilast * t_dim1]), abs( d__2))) > safmin) { i__2 = ilast + ilast * h_dim1; z__3.r = ascale * h__[i__2].r, z__3.i = ascale * h__[i__2].i; i__3 = ilast + ilast * t_dim1; z__4.r = bscale * t[i__3].r, z__4.i = bscale * t[i__3].i; z_div(&z__2, &z__3, &z__4); z__1.r = eshift.r + z__2.r, z__1.i = eshift.i + z__2.i; eshift.r = z__1.r, eshift.i = z__1.i; } else { i__2 = ilast + (ilast - 1) * h_dim1; z__3.r = ascale * h__[i__2].r, z__3.i = ascale * h__[i__2].i; i__3 = ilast - 1 + (ilast - 1) * t_dim1; z__4.r = bscale * t[i__3].r, z__4.i = bscale * t[i__3].i; z_div(&z__2, &z__3, &z__4); z__1.r = eshift.r + z__2.r, z__1.i = eshift.i + z__2.i; eshift.r = z__1.r, eshift.i = z__1.i; } shift.r = eshift.r, shift.i = eshift.i; } /* Now check for two consecutive small subdiagonals. */ i__2 = ifirst + 1; for (j = ilast - 1; j >= i__2; --j) { istart = j; i__3 = j + j * h_dim1; z__2.r = ascale * h__[i__3].r, z__2.i = ascale * h__[i__3].i; i__4 = j + j * t_dim1; z__4.r = bscale * t[i__4].r, z__4.i = bscale * t[i__4].i; z__3.r = shift.r * z__4.r - shift.i * z__4.i, z__3.i = shift.r * z__4.i + shift.i * z__4.r; z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; ctemp.r = z__1.r, ctemp.i = z__1.i; temp = (d__1 = ctemp.r, abs(d__1)) + (d__2 = d_imag(&ctemp), abs( d__2)); i__3 = j + 1 + j * h_dim1; temp2 = ascale * ((d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[j + 1 + j * h_dim1]), abs(d__2))); tempr = f2cmax(temp,temp2); if (tempr < 1. && tempr != 0.) { temp /= tempr; temp2 /= tempr; } i__3 = j + (j - 1) * h_dim1; if (((d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[j + (j - 1) * h_dim1]), abs(d__2))) * temp2 <= temp * atol) { goto L90; } /* L80: */ } istart = ifirst; i__2 = ifirst + ifirst * h_dim1; z__2.r = ascale * h__[i__2].r, z__2.i = ascale * h__[i__2].i; i__3 = ifirst + ifirst * t_dim1; z__4.r = bscale * t[i__3].r, z__4.i = bscale * t[i__3].i; z__3.r = shift.r * z__4.r - shift.i * z__4.i, z__3.i = shift.r * z__4.i + shift.i * z__4.r; z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; ctemp.r = z__1.r, ctemp.i = z__1.i; L90: /* Do an implicit-shift QZ sweep. */ /* Initial Q */ i__2 = istart + 1 + istart * h_dim1; z__1.r = ascale * h__[i__2].r, z__1.i = ascale * h__[i__2].i; ctemp2.r = z__1.r, ctemp2.i = z__1.i; zlartg_(&ctemp, &ctemp2, &c__, &s, &ctemp3); /* Sweep */ i__2 = ilast - 1; for (j = istart; j <= i__2; ++j) { if (j > istart) { i__3 = j + (j - 1) * h_dim1; ctemp.r = h__[i__3].r, ctemp.i = h__[i__3].i; zlartg_(&ctemp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, & h__[j + (j - 1) * h_dim1]); i__3 = j + 1 + (j - 1) * h_dim1; h__[i__3].r = 0., h__[i__3].i = 0.; } i__3 = ilastm; for (jc = j; jc <= i__3; ++jc) { i__4 = j + jc * h_dim1; z__2.r = c__ * h__[i__4].r, z__2.i = c__ * h__[i__4].i; i__5 = j + 1 + jc * h_dim1; z__3.r = s.r * h__[i__5].r - s.i * h__[i__5].i, z__3.i = s.r * h__[i__5].i + s.i * h__[i__5].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; ctemp.r = z__1.r, ctemp.i = z__1.i; i__4 = j + 1 + jc * h_dim1; d_cnjg(&z__4, &s); z__3.r = -z__4.r, z__3.i = -z__4.i; i__5 = j + jc * h_dim1; z__2.r = z__3.r * h__[i__5].r - z__3.i * h__[i__5].i, z__2.i = z__3.r * h__[i__5].i + z__3.i * h__[i__5].r; i__6 = j + 1 + jc * h_dim1; z__5.r = c__ * h__[i__6].r, z__5.i = c__ * h__[i__6].i; z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = j + jc * h_dim1; h__[i__4].r = ctemp.r, h__[i__4].i = ctemp.i; i__4 = j + jc * t_dim1; z__2.r = c__ * t[i__4].r, z__2.i = c__ * t[i__4].i; i__5 = j + 1 + jc * t_dim1; z__3.r = s.r * t[i__5].r - s.i * t[i__5].i, z__3.i = s.r * t[ i__5].i + s.i * t[i__5].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; ctemp2.r = z__1.r, ctemp2.i = z__1.i; i__4 = j + 1 + jc * t_dim1; d_cnjg(&z__4, &s); z__3.r = -z__4.r, z__3.i = -z__4.i; i__5 = j + jc * t_dim1; z__2.r = z__3.r * t[i__5].r - z__3.i * t[i__5].i, z__2.i = z__3.r * t[i__5].i + z__3.i * t[i__5].r; i__6 = j + 1 + jc * t_dim1; z__5.r = c__ * t[i__6].r, z__5.i = c__ * t[i__6].i; z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; t[i__4].r = z__1.r, t[i__4].i = z__1.i; i__4 = j + jc * t_dim1; t[i__4].r = ctemp2.r, t[i__4].i = ctemp2.i; /* L100: */ } if (ilq) { i__3 = *n; for (jr = 1; jr <= i__3; ++jr) { i__4 = jr + j * q_dim1; z__2.r = c__ * q[i__4].r, z__2.i = c__ * q[i__4].i; d_cnjg(&z__4, &s); i__5 = jr + (j + 1) * q_dim1; z__3.r = z__4.r * q[i__5].r - z__4.i * q[i__5].i, z__3.i = z__4.r * q[i__5].i + z__4.i * q[i__5].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; ctemp.r = z__1.r, ctemp.i = z__1.i; i__4 = jr + (j + 1) * q_dim1; z__3.r = -s.r, z__3.i = -s.i; i__5 = jr + j * q_dim1; z__2.r = z__3.r * q[i__5].r - z__3.i * q[i__5].i, z__2.i = z__3.r * q[i__5].i + z__3.i * q[i__5].r; i__6 = jr + (j + 1) * q_dim1; z__4.r = c__ * q[i__6].r, z__4.i = c__ * q[i__6].i; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; q[i__4].r = z__1.r, q[i__4].i = z__1.i; i__4 = jr + j * q_dim1; q[i__4].r = ctemp.r, q[i__4].i = ctemp.i; /* L110: */ } } i__3 = j + 1 + (j + 1) * t_dim1; ctemp.r = t[i__3].r, ctemp.i = t[i__3].i; zlartg_(&ctemp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j + 1) * t_dim1]); i__3 = j + 1 + j * t_dim1; t[i__3].r = 0., t[i__3].i = 0.; /* Computing MIN */ i__4 = j + 2; i__3 = f2cmin(i__4,ilast); for (jr = ifrstm; jr <= i__3; ++jr) { i__4 = jr + (j + 1) * h_dim1; z__2.r = c__ * h__[i__4].r, z__2.i = c__ * h__[i__4].i; i__5 = jr + j * h_dim1; z__3.r = s.r * h__[i__5].r - s.i * h__[i__5].i, z__3.i = s.r * h__[i__5].i + s.i * h__[i__5].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; ctemp.r = z__1.r, ctemp.i = z__1.i; i__4 = jr + j * h_dim1; d_cnjg(&z__4, &s); z__3.r = -z__4.r, z__3.i = -z__4.i; i__5 = jr + (j + 1) * h_dim1; z__2.r = z__3.r * h__[i__5].r - z__3.i * h__[i__5].i, z__2.i = z__3.r * h__[i__5].i + z__3.i * h__[i__5].r; i__6 = jr + j * h_dim1; z__5.r = c__ * h__[i__6].r, z__5.i = c__ * h__[i__6].i; z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = jr + (j + 1) * h_dim1; h__[i__4].r = ctemp.r, h__[i__4].i = ctemp.i; /* L120: */ } i__3 = j; for (jr = ifrstm; jr <= i__3; ++jr) { i__4 = jr + (j + 1) * t_dim1; z__2.r = c__ * t[i__4].r, z__2.i = c__ * t[i__4].i; i__5 = jr + j * t_dim1; z__3.r = s.r * t[i__5].r - s.i * t[i__5].i, z__3.i = s.r * t[ i__5].i + s.i * t[i__5].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; ctemp.r = z__1.r, ctemp.i = z__1.i; i__4 = jr + j * t_dim1; d_cnjg(&z__4, &s); z__3.r = -z__4.r, z__3.i = -z__4.i; i__5 = jr + (j + 1) * t_dim1; z__2.r = z__3.r * t[i__5].r - z__3.i * t[i__5].i, z__2.i = z__3.r * t[i__5].i + z__3.i * t[i__5].r; i__6 = jr + j * t_dim1; z__5.r = c__ * t[i__6].r, z__5.i = c__ * t[i__6].i; z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; t[i__4].r = z__1.r, t[i__4].i = z__1.i; i__4 = jr + (j + 1) * t_dim1; t[i__4].r = ctemp.r, t[i__4].i = ctemp.i; /* L130: */ } if (ilz) { i__3 = *n; for (jr = 1; jr <= i__3; ++jr) { i__4 = jr + (j + 1) * z_dim1; z__2.r = c__ * z__[i__4].r, z__2.i = c__ * z__[i__4].i; i__5 = jr + j * z_dim1; z__3.r = s.r * z__[i__5].r - s.i * z__[i__5].i, z__3.i = s.r * z__[i__5].i + s.i * z__[i__5].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; ctemp.r = z__1.r, ctemp.i = z__1.i; i__4 = jr + j * z_dim1; d_cnjg(&z__4, &s); z__3.r = -z__4.r, z__3.i = -z__4.i; i__5 = jr + (j + 1) * z_dim1; z__2.r = z__3.r * z__[i__5].r - z__3.i * z__[i__5].i, z__2.i = z__3.r * z__[i__5].i + z__3.i * z__[i__5] .r; i__6 = jr + j * z_dim1; z__5.r = c__ * z__[i__6].r, z__5.i = c__ * z__[i__6].i; z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; z__[i__4].r = z__1.r, z__[i__4].i = z__1.i; i__4 = jr + (j + 1) * z_dim1; z__[i__4].r = ctemp.r, z__[i__4].i = ctemp.i; /* L140: */ } } /* L150: */ } L160: /* L170: */ ; } /* Drop-through = non-convergence */ L180: *info = ilast; goto L210; /* Successful completion of all QZ steps */ L190: /* Set Eigenvalues 1:ILO-1 */ i__1 = *ilo - 1; for (j = 1; j <= i__1; ++j) { absb = z_abs(&t[j + j * t_dim1]); if (absb > safmin) { i__2 = j + j * t_dim1; z__2.r = t[i__2].r / absb, z__2.i = t[i__2].i / absb; d_cnjg(&z__1, &z__2); signbc.r = z__1.r, signbc.i = z__1.i; i__2 = j + j * t_dim1; t[i__2].r = absb, t[i__2].i = 0.; if (ilschr) { i__2 = j - 1; zscal_(&i__2, &signbc, &t[j * t_dim1 + 1], &c__1); zscal_(&j, &signbc, &h__[j * h_dim1 + 1], &c__1); } else { zscal_(&c__1, &signbc, &h__[j + j * h_dim1], &c__1); } if (ilz) { zscal_(n, &signbc, &z__[j * z_dim1 + 1], &c__1); } } else { i__2 = j + j * t_dim1; t[i__2].r = 0., t[i__2].i = 0.; } i__2 = j; i__3 = j + j * h_dim1; alpha[i__2].r = h__[i__3].r, alpha[i__2].i = h__[i__3].i; i__2 = j; i__3 = j + j * t_dim1; beta[i__2].r = t[i__3].r, beta[i__2].i = t[i__3].i; /* L200: */ } /* Normal Termination */ *info = 0; /* Exit (other than argument error) -- return optimal workspace size */ L210: z__1.r = (doublereal) (*n), z__1.i = 0.; work[1].r = z__1.r, work[1].i = z__1.i; return 0; /* End of ZHGEQZ */ } /* zhgeqz_ */