#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 ZTGEVC */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZTGEVC + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, */ /* LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) */ /* CHARACTER HOWMNY, SIDE */ /* INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N */ /* LOGICAL SELECT( * ) */ /* DOUBLE PRECISION RWORK( * ) */ /* COMPLEX*16 P( LDP, * ), S( LDS, * ), VL( LDVL, * ), */ /* $ VR( LDVR, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZTGEVC computes some or all of the right and/or left eigenvectors of */ /* > a pair of complex matrices (S,P), where S and P are upper triangular. */ /* > Matrix pairs of this type are produced by the generalized Schur */ /* > factorization of a complex matrix pair (A,B): */ /* > */ /* > A = Q*S*Z**H, B = Q*P*Z**H */ /* > */ /* > as computed by ZGGHRD + ZHGEQZ. */ /* > */ /* > The right eigenvector x and the left eigenvector y of (S,P) */ /* > corresponding to an eigenvalue w are defined by: */ /* > */ /* > S*x = w*P*x, (y**H)*S = w*(y**H)*P, */ /* > */ /* > where y**H denotes the conjugate tranpose of y. */ /* > The eigenvalues are not input to this routine, but are computed */ /* > directly from the diagonal elements of S and P. */ /* > */ /* > This routine returns the matrices X and/or Y of right and left */ /* > eigenvectors of (S,P), or the products Z*X and/or Q*Y, */ /* > where Z and Q are input matrices. */ /* > If Q and Z are the unitary factors from the generalized Schur */ /* > factorization of a matrix pair (A,B), then Z*X and Q*Y */ /* > are the matrices of right and left eigenvectors of (A,B). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] SIDE */ /* > \verbatim */ /* > SIDE is CHARACTER*1 */ /* > = 'R': compute right eigenvectors only; */ /* > = 'L': compute left eigenvectors only; */ /* > = 'B': compute both right and left eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in] HOWMNY */ /* > \verbatim */ /* > HOWMNY is CHARACTER*1 */ /* > = 'A': compute all right and/or left eigenvectors; */ /* > = 'B': compute all right and/or left eigenvectors, */ /* > backtransformed by the matrices in VR and/or VL; */ /* > = 'S': compute selected right and/or left eigenvectors, */ /* > specified by the logical array SELECT. */ /* > \endverbatim */ /* > */ /* > \param[in] SELECT */ /* > \verbatim */ /* > SELECT is LOGICAL array, dimension (N) */ /* > If HOWMNY='S', SELECT specifies the eigenvectors to be */ /* > computed. The eigenvector corresponding to the j-th */ /* > eigenvalue is computed if SELECT(j) = .TRUE.. */ /* > Not referenced if HOWMNY = 'A' or 'B'. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrices S and P. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] S */ /* > \verbatim */ /* > S is COMPLEX*16 array, dimension (LDS,N) */ /* > The upper triangular matrix S from a generalized Schur */ /* > factorization, as computed by ZHGEQZ. */ /* > \endverbatim */ /* > */ /* > \param[in] LDS */ /* > \verbatim */ /* > LDS is INTEGER */ /* > The leading dimension of array S. LDS >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] P */ /* > \verbatim */ /* > P is COMPLEX*16 array, dimension (LDP,N) */ /* > The upper triangular matrix P from a generalized Schur */ /* > factorization, as computed by ZHGEQZ. P must have real */ /* > diagonal elements. */ /* > \endverbatim */ /* > */ /* > \param[in] LDP */ /* > \verbatim */ /* > LDP is INTEGER */ /* > The leading dimension of array P. LDP >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] VL */ /* > \verbatim */ /* > VL is COMPLEX*16 array, dimension (LDVL,MM) */ /* > On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */ /* > contain an N-by-N matrix Q (usually the unitary matrix Q */ /* > of left Schur vectors returned by ZHGEQZ). */ /* > On exit, if SIDE = 'L' or 'B', VL contains: */ /* > if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */ /* > if HOWMNY = 'B', the matrix Q*Y; */ /* > if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */ /* > SELECT, stored consecutively in the columns of */ /* > VL, in the same order as their eigenvalues. */ /* > Not referenced if SIDE = 'R'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVL */ /* > \verbatim */ /* > LDVL is INTEGER */ /* > The leading dimension of array VL. LDVL >= 1, and if */ /* > SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. */ /* > \endverbatim */ /* > */ /* > \param[in,out] VR */ /* > \verbatim */ /* > VR is COMPLEX*16 array, dimension (LDVR,MM) */ /* > On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */ /* > contain an N-by-N matrix Q (usually the unitary matrix Z */ /* > of right Schur vectors returned by ZHGEQZ). */ /* > On exit, if SIDE = 'R' or 'B', VR contains: */ /* > if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */ /* > if HOWMNY = 'B', the matrix Z*X; */ /* > if HOWMNY = 'S', the right eigenvectors of (S,P) specified by */ /* > SELECT, stored consecutively in the columns of */ /* > VR, in the same order as their eigenvalues. */ /* > Not referenced if SIDE = 'L'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVR */ /* > \verbatim */ /* > LDVR is INTEGER */ /* > The leading dimension of the array VR. LDVR >= 1, and if */ /* > SIDE = 'R' or 'B', LDVR >= N. */ /* > \endverbatim */ /* > */ /* > \param[in] MM */ /* > \verbatim */ /* > MM is INTEGER */ /* > The number of columns in the arrays VL and/or VR. MM >= M. */ /* > \endverbatim */ /* > */ /* > \param[out] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of columns in the arrays VL and/or VR actually */ /* > used to store the eigenvectors. If HOWMNY = 'A' or 'B', M */ /* > is set to N. Each selected eigenvector occupies one column. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX*16 array, dimension (2*N) */ /* > \endverbatim */ /* > */ /* > \param[out] RWORK */ /* > \verbatim */ /* > RWORK is DOUBLE PRECISION array, dimension (2*N) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16GEcomputational */ /* ===================================================================== */ /* Subroutine */ int ztgevc_(char *side, char *howmny, logical *select, integer *n, doublecomplex *s, integer *lds, doublecomplex *p, integer *ldp, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer * ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork, integer *info) { /* System generated locals */ integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2, d__3, d__4, d__5, d__6; doublecomplex z__1, z__2, z__3, z__4; /* Local variables */ integer ibeg, ieig, iend; doublereal dmin__; integer isrc; doublereal temp; doublecomplex suma, sumb; doublereal xmax; doublecomplex d__; integer i__, j; doublereal scale; logical ilall; integer iside; doublereal sbeta; extern logical lsame_(char *, char *); doublereal small; logical compl; doublereal anorm, bnorm; logical compr; extern /* Subroutine */ int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); doublecomplex ca, cb; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); logical ilbbad; doublereal acoefa; integer je; doublereal bcoefa, acoeff; doublecomplex bcoeff; logical ilback; integer im; doublereal ascale, bscale; extern doublereal dlamch_(char *); integer jr; doublecomplex salpha; doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; logical ilcomp; extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, doublecomplex *); integer ihwmny; doublereal big; logical lsa, lsb; doublereal ulp; doublecomplex sum; /* -- 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..-- */ /* December 2016 */ /* ===================================================================== */ /* Decode and Test the input parameters */ /* Parameter adjustments */ --select; s_dim1 = *lds; s_offset = 1 + s_dim1 * 1; s -= s_offset; p_dim1 = *ldp; p_offset = 1 + p_dim1 * 1; p -= p_offset; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1 * 1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1 * 1; vr -= vr_offset; --work; --rwork; /* Function Body */ if (lsame_(howmny, "A")) { ihwmny = 1; ilall = TRUE_; ilback = FALSE_; } else if (lsame_(howmny, "S")) { ihwmny = 2; ilall = FALSE_; ilback = FALSE_; } else if (lsame_(howmny, "B")) { ihwmny = 3; ilall = TRUE_; ilback = TRUE_; } else { ihwmny = -1; } if (lsame_(side, "R")) { iside = 1; compl = FALSE_; compr = TRUE_; } else if (lsame_(side, "L")) { iside = 2; compl = TRUE_; compr = FALSE_; } else if (lsame_(side, "B")) { iside = 3; compl = TRUE_; compr = TRUE_; } else { iside = -1; } *info = 0; if (iside < 0) { *info = -1; } else if (ihwmny < 0) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*lds < f2cmax(1,*n)) { *info = -6; } else if (*ldp < f2cmax(1,*n)) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_("ZTGEVC", &i__1, (ftnlen)6); return 0; } /* Count the number of eigenvectors */ if (! ilall) { im = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (select[j]) { ++im; } /* L10: */ } } else { im = *n; } /* Check diagonal of B */ ilbbad = FALSE_; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (d_imag(&p[j + j * p_dim1]) != 0.) { ilbbad = TRUE_; } /* L20: */ } if (ilbbad) { *info = -7; } else if (compl && *ldvl < *n || *ldvl < 1) { *info = -10; } else if (compr && *ldvr < *n || *ldvr < 1) { *info = -12; } else if (*mm < im) { *info = -13; } if (*info != 0) { i__1 = -(*info); xerbla_("ZTGEVC", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ *m = im; if (*n == 0) { return 0; } /* Machine Constants */ safmin = dlamch_("Safe minimum"); big = 1. / safmin; dlabad_(&safmin, &big); ulp = dlamch_("Epsilon") * dlamch_("Base"); small = safmin * *n / ulp; big = 1. / small; bignum = 1. / (safmin * *n); /* Compute the 1-norm of each column of the strictly upper triangular */ /* part of A and B to check for possible overflow in the triangular */ /* solver. */ i__1 = s_dim1 + 1; anorm = (d__1 = s[i__1].r, abs(d__1)) + (d__2 = d_imag(&s[s_dim1 + 1]), abs(d__2)); i__1 = p_dim1 + 1; bnorm = (d__1 = p[i__1].r, abs(d__1)) + (d__2 = d_imag(&p[p_dim1 + 1]), abs(d__2)); rwork[1] = 0.; rwork[*n + 1] = 0.; i__1 = *n; for (j = 2; j <= i__1; ++j) { rwork[j] = 0.; rwork[*n + j] = 0.; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * s_dim1; rwork[j] += (d__1 = s[i__3].r, abs(d__1)) + (d__2 = d_imag(&s[i__ + j * s_dim1]), abs(d__2)); i__3 = i__ + j * p_dim1; rwork[*n + j] += (d__1 = p[i__3].r, abs(d__1)) + (d__2 = d_imag(& p[i__ + j * p_dim1]), abs(d__2)); /* L30: */ } /* Computing MAX */ i__2 = j + j * s_dim1; d__3 = anorm, d__4 = rwork[j] + ((d__1 = s[i__2].r, abs(d__1)) + ( d__2 = d_imag(&s[j + j * s_dim1]), abs(d__2))); anorm = f2cmax(d__3,d__4); /* Computing MAX */ i__2 = j + j * p_dim1; d__3 = bnorm, d__4 = rwork[*n + j] + ((d__1 = p[i__2].r, abs(d__1)) + (d__2 = d_imag(&p[j + j * p_dim1]), abs(d__2))); bnorm = f2cmax(d__3,d__4); /* L40: */ } ascale = 1. / f2cmax(anorm,safmin); bscale = 1. / f2cmax(bnorm,safmin); /* Left eigenvectors */ if (compl) { ieig = 0; /* Main loop over eigenvalues */ i__1 = *n; for (je = 1; je <= i__1; ++je) { if (ilall) { ilcomp = TRUE_; } else { ilcomp = select[je]; } if (ilcomp) { ++ieig; i__2 = je + je * s_dim1; i__3 = je + je * p_dim1; if ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__3].r, abs(d__1)) <= safmin) { /* Singular matrix pencil -- return unit eigenvector */ i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr + ieig * vl_dim1; vl[i__3].r = 0., vl[i__3].i = 0.; /* L50: */ } i__2 = ieig + ieig * vl_dim1; vl[i__2].r = 1., vl[i__2].i = 0.; goto L140; } /* Non-singular eigenvalue: */ /* Compute coefficients a and b in */ /* H */ /* y ( a A - b B ) = 0 */ /* Computing MAX */ i__2 = je + je * s_dim1; i__3 = je + je * p_dim1; d__4 = ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 = p[i__3].r, abs(d__1)) * bscale, d__4 = f2cmax(d__4,d__5); temp = 1. / f2cmax(d__4,safmin); i__2 = je + je * s_dim1; z__2.r = temp * s[i__2].r, z__2.i = temp * s[i__2].i; z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i; salpha.r = z__1.r, salpha.i = z__1.i; i__2 = je + je * p_dim1; sbeta = temp * p[i__2].r * bscale; acoeff = sbeta * ascale; z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; /* Scale to avoid underflow */ lsa = abs(sbeta) >= safmin && abs(acoeff) < small; lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3)) + (d__4 = d_imag(&bcoeff), abs(d__4)) < small; scale = 1.; if (lsa) { scale = small / abs(sbeta) * f2cmin(anorm,big); } if (lsb) { /* Computing MAX */ d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), abs(d__2))) * f2cmin( bnorm,big); scale = f2cmax(d__3,d__4); } if (lsa || lsb) { /* Computing MIN */ /* Computing MAX */ d__5 = 1., d__6 = abs(acoeff), d__5 = f2cmax(d__5,d__6), d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&bcoeff), abs(d__2)); d__3 = scale, d__4 = 1. / (safmin * f2cmax(d__5,d__6)); scale = f2cmin(d__3,d__4); if (lsa) { acoeff = ascale * (scale * sbeta); } else { acoeff = scale * acoeff; } if (lsb) { z__2.r = scale * salpha.r, z__2.i = scale * salpha.i; z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; } else { z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; } } acoefa = abs(acoeff); bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(& bcoeff), abs(d__2)); xmax = 1.; i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr; work[i__3].r = 0., work[i__3].i = 0.; /* L60: */ } i__2 = je; work[i__2].r = 1., work[i__2].i = 0.; /* Computing MAX */ d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 = f2cmax(d__1,d__2); dmin__ = f2cmax(d__1,safmin); /* H */ /* Triangular solve of (a A - b B) y = 0 */ /* H */ /* (rowwise in (a A - b B) , or columnwise in a A - b B) */ i__2 = *n; for (j = je + 1; j <= i__2; ++j) { /* Compute */ /* j-1 */ /* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */ /* k=je */ /* (Scale if necessary) */ temp = 1. / xmax; if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum * temp) { i__3 = j - 1; for (jr = je; jr <= i__3; ++jr) { i__4 = jr; i__5 = jr; z__1.r = temp * work[i__5].r, z__1.i = temp * work[i__5].i; work[i__4].r = z__1.r, work[i__4].i = z__1.i; /* L70: */ } xmax = 1.; } suma.r = 0., suma.i = 0.; sumb.r = 0., sumb.i = 0.; i__3 = j - 1; for (jr = je; jr <= i__3; ++jr) { d_cnjg(&z__3, &s[jr + j * s_dim1]); i__4 = jr; z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4] .i, z__2.i = z__3.r * work[i__4].i + z__3.i * work[i__4].r; z__1.r = suma.r + z__2.r, z__1.i = suma.i + z__2.i; suma.r = z__1.r, suma.i = z__1.i; d_cnjg(&z__3, &p[jr + j * p_dim1]); i__4 = jr; z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4] .i, z__2.i = z__3.r * work[i__4].i + z__3.i * work[i__4].r; z__1.r = sumb.r + z__2.r, z__1.i = sumb.i + z__2.i; sumb.r = z__1.r, sumb.i = z__1.i; /* L80: */ } z__2.r = acoeff * suma.r, z__2.i = acoeff * suma.i; d_cnjg(&z__4, &bcoeff); z__3.r = z__4.r * sumb.r - z__4.i * sumb.i, z__3.i = z__4.r * sumb.i + z__4.i * sumb.r; z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; sum.r = z__1.r, sum.i = z__1.i; /* Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) */ /* with scaling and perturbation of the denominator */ i__3 = j + j * s_dim1; z__3.r = acoeff * s[i__3].r, z__3.i = acoeff * s[i__3].i; i__4 = j + j * p_dim1; z__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i, z__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4] .r; z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i; d_cnjg(&z__1, &z__2); d__.r = z__1.r, d__.i = z__1.i; if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs( d__2)) <= dmin__) { z__1.r = dmin__, z__1.i = 0.; d__.r = z__1.r, d__.i = z__1.i; } if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs( d__2)) < 1.) { if ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum), abs(d__2)) >= bignum * ((d__3 = d__.r, abs( d__3)) + (d__4 = d_imag(&d__), abs(d__4)))) { temp = 1. / ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum), abs(d__2))); i__3 = j - 1; for (jr = je; jr <= i__3; ++jr) { i__4 = jr; i__5 = jr; z__1.r = temp * work[i__5].r, z__1.i = temp * work[i__5].i; work[i__4].r = z__1.r, work[i__4].i = z__1.i; /* L90: */ } xmax = temp * xmax; z__1.r = temp * sum.r, z__1.i = temp * sum.i; sum.r = z__1.r, sum.i = z__1.i; } } i__3 = j; z__2.r = -sum.r, z__2.i = -sum.i; zladiv_(&z__1, &z__2, &d__); work[i__3].r = z__1.r, work[i__3].i = z__1.i; /* Computing MAX */ i__3 = j; d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + ( d__2 = d_imag(&work[j]), abs(d__2)); xmax = f2cmax(d__3,d__4); /* L100: */ } /* Back transform eigenvector if HOWMNY='B'. */ if (ilback) { i__2 = *n + 1 - je; zgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], ldvl, &work[je], &c__1, &c_b1, &work[*n + 1], &c__1); isrc = 2; ibeg = 1; } else { isrc = 1; ibeg = je; } /* Copy and scale eigenvector into column of VL */ xmax = 0.; i__2 = *n; for (jr = ibeg; jr <= i__2; ++jr) { /* Computing MAX */ i__3 = (isrc - 1) * *n + jr; d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + ( d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs( d__2)); xmax = f2cmax(d__3,d__4); /* L110: */ } if (xmax > safmin) { temp = 1. / xmax; i__2 = *n; for (jr = ibeg; jr <= i__2; ++jr) { i__3 = jr + ieig * vl_dim1; i__4 = (isrc - 1) * *n + jr; z__1.r = temp * work[i__4].r, z__1.i = temp * work[ i__4].i; vl[i__3].r = z__1.r, vl[i__3].i = z__1.i; /* L120: */ } } else { ibeg = *n + 1; } i__2 = ibeg - 1; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr + ieig * vl_dim1; vl[i__3].r = 0., vl[i__3].i = 0.; /* L130: */ } } L140: ; } } /* Right eigenvectors */ if (compr) { ieig = im + 1; /* Main loop over eigenvalues */ for (je = *n; je >= 1; --je) { if (ilall) { ilcomp = TRUE_; } else { ilcomp = select[je]; } if (ilcomp) { --ieig; i__1 = je + je * s_dim1; i__2 = je + je * p_dim1; if ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__2].r, abs(d__1)) <= safmin) { /* Singular matrix pencil -- return unit eigenvector */ i__1 = *n; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr + ieig * vr_dim1; vr[i__2].r = 0., vr[i__2].i = 0.; /* L150: */ } i__1 = ieig + ieig * vr_dim1; vr[i__1].r = 1., vr[i__1].i = 0.; goto L250; } /* Non-singular eigenvalue: */ /* Compute coefficients a and b in */ /* ( a A - b B ) x = 0 */ /* Computing MAX */ i__1 = je + je * s_dim1; i__2 = je + je * p_dim1; d__4 = ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 = p[i__2].r, abs(d__1)) * bscale, d__4 = f2cmax(d__4,d__5); temp = 1. / f2cmax(d__4,safmin); i__1 = je + je * s_dim1; z__2.r = temp * s[i__1].r, z__2.i = temp * s[i__1].i; z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i; salpha.r = z__1.r, salpha.i = z__1.i; i__1 = je + je * p_dim1; sbeta = temp * p[i__1].r * bscale; acoeff = sbeta * ascale; z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; /* Scale to avoid underflow */ lsa = abs(sbeta) >= safmin && abs(acoeff) < small; lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3)) + (d__4 = d_imag(&bcoeff), abs(d__4)) < small; scale = 1.; if (lsa) { scale = small / abs(sbeta) * f2cmin(anorm,big); } if (lsb) { /* Computing MAX */ d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha), abs(d__2))) * f2cmin( bnorm,big); scale = f2cmax(d__3,d__4); } if (lsa || lsb) { /* Computing MIN */ /* Computing MAX */ d__5 = 1., d__6 = abs(acoeff), d__5 = f2cmax(d__5,d__6), d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&bcoeff), abs(d__2)); d__3 = scale, d__4 = 1. / (safmin * f2cmax(d__5,d__6)); scale = f2cmin(d__3,d__4); if (lsa) { acoeff = ascale * (scale * sbeta); } else { acoeff = scale * acoeff; } if (lsb) { z__2.r = scale * salpha.r, z__2.i = scale * salpha.i; z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; } else { z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i; bcoeff.r = z__1.r, bcoeff.i = z__1.i; } } acoefa = abs(acoeff); bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(& bcoeff), abs(d__2)); xmax = 1.; i__1 = *n; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; work[i__2].r = 0., work[i__2].i = 0.; /* L160: */ } i__1 = je; work[i__1].r = 1., work[i__1].i = 0.; /* Computing MAX */ d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 = f2cmax(d__1,d__2); dmin__ = f2cmax(d__1,safmin); /* Triangular solve of (a A - b B) x = 0 (columnwise) */ /* WORK(1:j-1) contains sums w, */ /* WORK(j+1:JE) contains x */ i__1 = je - 1; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr + je * s_dim1; z__2.r = acoeff * s[i__3].r, z__2.i = acoeff * s[i__3].i; i__4 = jr + je * p_dim1; z__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i, z__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4] .r; z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L170: */ } i__1 = je; work[i__1].r = 1., work[i__1].i = 0.; for (j = je - 1; j >= 1; --j) { /* Form x(j) := - w(j) / d */ /* with scaling and perturbation of the denominator */ i__1 = j + j * s_dim1; z__2.r = acoeff * s[i__1].r, z__2.i = acoeff * s[i__1].i; i__2 = j + j * p_dim1; z__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i, z__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2] .r; z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; d__.r = z__1.r, d__.i = z__1.i; if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs( d__2)) <= dmin__) { z__1.r = dmin__, z__1.i = 0.; d__.r = z__1.r, d__.i = z__1.i; } if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs( d__2)) < 1.) { i__1 = j; if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag( &work[j]), abs(d__2)) >= bignum * ((d__3 = d__.r, abs(d__3)) + (d__4 = d_imag(&d__), abs( d__4)))) { i__1 = j; temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + ( d__2 = d_imag(&work[j]), abs(d__2))); i__1 = je; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr; z__1.r = temp * work[i__3].r, z__1.i = temp * work[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L180: */ } } } i__1 = j; i__2 = j; z__2.r = -work[i__2].r, z__2.i = -work[i__2].i; zladiv_(&z__1, &z__2, &d__); work[i__1].r = z__1.r, work[i__1].i = z__1.i; if (j > 1) { /* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */ i__1 = j; if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag( &work[j]), abs(d__2)) > 1.) { i__1 = j; temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + ( d__2 = d_imag(&work[j]), abs(d__2))); if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >= bignum * temp) { i__1 = je; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr; z__1.r = temp * work[i__3].r, z__1.i = temp * work[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L190: */ } } } i__1 = j; z__1.r = acoeff * work[i__1].r, z__1.i = acoeff * work[i__1].i; ca.r = z__1.r, ca.i = z__1.i; i__1 = j; z__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[ i__1].i, z__1.i = bcoeff.r * work[i__1].i + bcoeff.i * work[i__1].r; cb.r = z__1.r, cb.i = z__1.i; i__1 = j - 1; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr; i__3 = jr; i__4 = jr + j * s_dim1; z__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i, z__3.i = ca.r * s[i__4].i + ca.i * s[i__4] .r; z__2.r = work[i__3].r + z__3.r, z__2.i = work[ i__3].i + z__3.i; i__5 = jr + j * p_dim1; z__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i, z__4.i = cb.r * p[i__5].i + cb.i * p[i__5] .r; z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - z__4.i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L200: */ } } /* L210: */ } /* Back transform eigenvector if HOWMNY='B'. */ if (ilback) { zgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1); isrc = 2; iend = *n; } else { isrc = 1; iend = je; } /* Copy and scale eigenvector into column of VR */ xmax = 0.; i__1 = iend; for (jr = 1; jr <= i__1; ++jr) { /* Computing MAX */ i__2 = (isrc - 1) * *n + jr; d__3 = xmax, d__4 = (d__1 = work[i__2].r, abs(d__1)) + ( d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs( d__2)); xmax = f2cmax(d__3,d__4); /* L220: */ } if (xmax > safmin) { temp = 1. / xmax; i__1 = iend; for (jr = 1; jr <= i__1; ++jr) { i__2 = jr + ieig * vr_dim1; i__3 = (isrc - 1) * *n + jr; z__1.r = temp * work[i__3].r, z__1.i = temp * work[ i__3].i; vr[i__2].r = z__1.r, vr[i__2].i = z__1.i; /* L230: */ } } else { iend = 0; } i__1 = *n; for (jr = iend + 1; jr <= i__1; ++jr) { i__2 = jr + ieig * vr_dim1; vr[i__2].r = 0., vr[i__2].i = 0.; /* L240: */ } } L250: ; } } return 0; /* End of ZTGEVC */ } /* ztgevc_ */