#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]/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);} 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 ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE mat rices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZGEGS + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, */ /* VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, */ /* INFO ) */ /* CHARACTER JOBVSL, JOBVSR */ /* INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N */ /* DOUBLE PRECISION RWORK( * ) */ /* COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ), */ /* $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ), */ /* $ WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > This routine is deprecated and has been replaced by routine ZGGES. */ /* > */ /* > ZGEGS computes the eigenvalues, Schur form, and, optionally, the */ /* > left and or/right Schur vectors of a complex matrix pair (A,B). */ /* > Given two square matrices A and B, the generalized Schur */ /* > factorization has the form */ /* > */ /* > A = Q*S*Z**H, B = Q*T*Z**H */ /* > */ /* > where Q and Z are unitary matrices and S and T are upper triangular. */ /* > The columns of Q are the left Schur vectors */ /* > and the columns of Z are the right Schur vectors. */ /* > */ /* > If only the eigenvalues of (A,B) are needed, the driver routine */ /* > ZGEGV should be used instead. See ZGEGV for a description of the */ /* > eigenvalues of the generalized nonsymmetric eigenvalue problem */ /* > (GNEP). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOBVSL */ /* > \verbatim */ /* > JOBVSL is CHARACTER*1 */ /* > = 'N': do not compute the left Schur vectors; */ /* > = 'V': compute the left Schur vectors (returned in VSL). */ /* > \endverbatim */ /* > */ /* > \param[in] JOBVSR */ /* > \verbatim */ /* > JOBVSR is CHARACTER*1 */ /* > = 'N': do not compute the right Schur vectors; */ /* > = 'V': compute the right Schur vectors (returned in VSR). */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrices A, B, VSL, and VSR. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension (LDA, N) */ /* > On entry, the matrix A. */ /* > On exit, the upper triangular matrix S from the generalized */ /* > Schur factorization. */ /* > \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 COMPLEX*16 array, dimension (LDB, N) */ /* > On entry, the matrix B. */ /* > On exit, the upper triangular matrix T from the generalized */ /* > Schur factorization. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of B. LDB >= 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(j) = S(j,j), the diagonal element of the Schur */ /* > form of A. */ /* > \endverbatim */ /* > */ /* > \param[out] BETA */ /* > \verbatim */ /* > BETA is COMPLEX*16 array, dimension (N) */ /* > The non-negative real scalars beta that define the */ /* > eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element */ /* > of the triangular factor T. */ /* > */ /* > 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[out] VSL */ /* > \verbatim */ /* > VSL is COMPLEX*16 array, dimension (LDVSL,N) */ /* > If JOBVSL = 'V', the matrix of left Schur vectors Q. */ /* > Not referenced if JOBVSL = 'N'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVSL */ /* > \verbatim */ /* > LDVSL is INTEGER */ /* > The leading dimension of the matrix VSL. LDVSL >= 1, and */ /* > if JOBVSL = 'V', LDVSL >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] VSR */ /* > \verbatim */ /* > VSR is COMPLEX*16 array, dimension (LDVSR,N) */ /* > If JOBVSR = 'V', the matrix of right Schur vectors Z. */ /* > Not referenced if JOBVSR = 'N'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVSR */ /* > \verbatim */ /* > LDVSR is INTEGER */ /* > The leading dimension of the matrix VSR. LDVSR >= 1, and */ /* > if JOBVSR = 'V', LDVSR >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] 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(1,2*N). */ /* > For good performance, LWORK must generally be larger. */ /* > To compute the optimal value of LWORK, call ILAENV to get */ /* > blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.) Then compute: */ /* > NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR; */ /* > the optimal LWORK is 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] RWORK */ /* > \verbatim */ /* > RWORK is DOUBLE PRECISION array, dimension (3*N) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > =1,...,N: */ /* > The QZ iteration failed. (A,B) are not in Schur */ /* > form, but ALPHA(j) and BETA(j) should be correct for */ /* > j=INFO+1,...,N. */ /* > > N: errors that usually indicate LAPACK problems: */ /* > =N+1: error return from ZGGBAL */ /* > =N+2: error return from ZGEQRF */ /* > =N+3: error return from ZUNMQR */ /* > =N+4: error return from ZUNGQR */ /* > =N+5: error return from ZGGHRD */ /* > =N+6: error return from ZHGEQZ (other than failed */ /* > iteration) */ /* > =N+7: error return from ZGGBAK (computing VSL) */ /* > =N+8: error return from ZGGBAK (computing VSR) */ /* > =N+9: error return from ZLASCL (various places) */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16GEeigen */ /* ===================================================================== */ /* Subroutine */ int zgegs_(char *jobvsl, char *jobvsr, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, integer *ldvsl, doublecomplex *vsr, integer *ldvsr, doublecomplex * work, integer *lwork, doublereal *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, vsr_dim1, vsr_offset, i__1, i__2, i__3; /* Local variables */ doublereal anrm, bnrm; integer itau, lopt; extern logical lsame_(char *, char *); integer ileft, iinfo, icols; logical ilvsl; integer iwork; logical ilvsr; integer irows, nb; extern doublereal dlamch_(char *); extern /* Subroutine */ int zggbak_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublecomplex *, integer *, integer *), zggbal_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer * , integer *, doublereal *, doublereal *, doublereal *, integer *); logical ilascl, ilbscl; doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); doublereal bignum; integer ijobvl, iright; extern /* Subroutine */ int zgghrd_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer * ), zlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *, integer *); integer ijobvr; extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer * ); doublereal anrmto; integer lwkmin, nb1, nb2, nb3; doublereal bnrmto; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zhgeqz_(char *, char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); doublereal smlnum; integer irwork, lwkopt; logical lquery; extern /* Subroutine */ int zungqr_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zunmqr_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); integer ihi, ilo; doublereal eps; /* -- 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; --alpha; --beta; vsl_dim1 = *ldvsl; vsl_offset = 1 + vsl_dim1 * 1; vsl -= vsl_offset; vsr_dim1 = *ldvsr; vsr_offset = 1 + vsr_dim1 * 1; vsr -= vsr_offset; --work; --rwork; /* Function Body */ if (lsame_(jobvsl, "N")) { ijobvl = 1; ilvsl = FALSE_; } else if (lsame_(jobvsl, "V")) { ijobvl = 2; ilvsl = TRUE_; } else { ijobvl = -1; ilvsl = FALSE_; } if (lsame_(jobvsr, "N")) { ijobvr = 1; ilvsr = FALSE_; } else if (lsame_(jobvsr, "V")) { ijobvr = 2; ilvsr = TRUE_; } else { ijobvr = -1; ilvsr = FALSE_; } /* Test the input arguments */ /* Computing MAX */ i__1 = *n << 1; lwkmin = f2cmax(i__1,1); lwkopt = lwkmin; work[1].r = (doublereal) lwkopt, work[1].i = 0.; 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 (*ldvsl < 1 || ilvsl && *ldvsl < *n) { *info = -11; } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) { *info = -13; } else if (*lwork < lwkmin && ! lquery) { *info = -15; } if (*info == 0) { nb1 = ilaenv_(&c__1, "ZGEQRF", " ", n, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); nb2 = ilaenv_(&c__1, "ZUNMQR", " ", n, n, n, &c_n1, (ftnlen)6, ( ftnlen)1); nb3 = ilaenv_(&c__1, "ZUNGQR", " ", n, n, n, &c_n1, (ftnlen)6, ( ftnlen)1); /* Computing MAX */ i__1 = f2cmax(nb1,nb2); nb = f2cmax(i__1,nb3); lopt = *n * (nb + 1); work[1].r = (doublereal) lopt, work[1].i = 0.; } if (*info != 0) { i__1 = -(*info); xerbla_("ZGEGS ", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Get machine constants */ eps = dlamch_("E") * dlamch_("B"); safmin = dlamch_("S"); smlnum = *n * safmin / eps; bignum = 1. / smlnum; /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */ anrm = zlange_("M", n, n, &a[a_offset], lda, &rwork[1]); ilascl = FALSE_; if (anrm > 0. && anrm < smlnum) { anrmto = smlnum; ilascl = TRUE_; } else if (anrm > bignum) { anrmto = bignum; ilascl = TRUE_; } if (ilascl) { zlascl_("G", &c_n1, &c_n1, &anrm, &anrmto, n, n, &a[a_offset], lda, & iinfo); if (iinfo != 0) { *info = *n + 9; return 0; } } /* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */ bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[1]); ilbscl = FALSE_; if (bnrm > 0. && bnrm < smlnum) { bnrmto = smlnum; ilbscl = TRUE_; } else if (bnrm > bignum) { bnrmto = bignum; ilbscl = TRUE_; } if (ilbscl) { zlascl_("G", &c_n1, &c_n1, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, & iinfo); if (iinfo != 0) { *info = *n + 9; return 0; } } /* Permute the matrix to make it more nearly triangular */ ileft = 1; iright = *n + 1; irwork = iright + *n; iwork = 1; zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[ ileft], &rwork[iright], &rwork[irwork], &iinfo); if (iinfo != 0) { *info = *n + 1; goto L10; } /* Reduce B to triangular form, and initialize VSL and/or VSR */ irows = ihi + 1 - ilo; icols = *n + 1 - ilo; itau = iwork; iwork = itau + irows; i__1 = *lwork + 1 - iwork; zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[ iwork], &i__1, &iinfo); if (iinfo >= 0) { /* Computing MAX */ i__3 = iwork; i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1; lwkopt = f2cmax(i__1,i__2); } if (iinfo != 0) { *info = *n + 2; goto L10; } i__1 = *lwork + 1 - iwork; zunmqr_("L", "C", &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__3 = iwork; i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1; lwkopt = f2cmax(i__1,i__2); } if (iinfo != 0) { *info = *n + 3; goto L10; } if (ilvsl) { zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl); i__1 = irows - 1; i__2 = irows - 1; zlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ilo + 1 + ilo * vsl_dim1], ldvsl); i__1 = *lwork + 1 - iwork; zungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, & work[itau], &work[iwork], &i__1, &iinfo); if (iinfo >= 0) { /* Computing MAX */ i__3 = iwork; i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1; lwkopt = f2cmax(i__1,i__2); } if (iinfo != 0) { *info = *n + 4; goto L10; } } if (ilvsr) { zlaset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr); } /* Reduce to generalized Hessenberg form */ zgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &iinfo); if (iinfo != 0) { *info = *n + 5; goto L10; } /* Perform QZ algorithm, computing Schur vectors if desired */ iwork = itau; i__1 = *lwork + 1 - iwork; zhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[ b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, & vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &rwork[irwork], & iinfo); if (iinfo >= 0) { /* Computing MAX */ i__3 = iwork; i__1 = lwkopt, i__2 = (integer) work[i__3].r + 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 L10; } /* Apply permutation to VSL and VSR */ if (ilvsl) { zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, & vsl[vsl_offset], ldvsl, &iinfo); if (iinfo != 0) { *info = *n + 7; goto L10; } } if (ilvsr) { zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, & vsr[vsr_offset], ldvsr, &iinfo); if (iinfo != 0) { *info = *n + 8; goto L10; } } /* Undo scaling */ if (ilascl) { zlascl_("U", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, & iinfo); if (iinfo != 0) { *info = *n + 9; return 0; } zlascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alpha[1], n, & iinfo); if (iinfo != 0) { *info = *n + 9; return 0; } } if (ilbscl) { zlascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, & iinfo); if (iinfo != 0) { *info = *n + 9; return 0; } zlascl_("G", &c_n1, &c_n1, &bnrmto, &bnrm, n, &c__1, &beta[1], n, & iinfo); if (iinfo != 0) { *info = *n + 9; return 0; } } L10: work[1].r = (doublereal) lwkopt, work[1].i = 0.; return 0; /* End of ZGEGS */ } /* zgegs_ */