#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 CGGEVX 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 CGGEVX + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB, */ /* ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI, */ /* LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV, */ /* WORK, LWORK, RWORK, IWORK, BWORK, INFO ) */ /* CHARACTER BALANC, JOBVL, JOBVR, SENSE */ /* INTEGER IHI, ILO, INFO, LDA, LDB, LDVL, LDVR, LWORK, N */ /* REAL ABNRM, BBNRM */ /* LOGICAL BWORK( * ) */ /* INTEGER IWORK( * ) */ /* REAL LSCALE( * ), RCONDE( * ), RCONDV( * ), */ /* $ RSCALE( * ), RWORK( * ) */ /* COMPLEX A( LDA, * ), ALPHA( * ), B( LDB, * ), */ /* $ BETA( * ), VL( LDVL, * ), VR( LDVR, * ), */ /* $ WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CGGEVX computes for a pair of N-by-N complex nonsymmetric matrices */ /* > (A,B) the generalized eigenvalues, and optionally, the left and/or */ /* > right generalized eigenvectors. */ /* > */ /* > Optionally, it also computes a balancing transformation to improve */ /* > the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */ /* > LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for */ /* > the eigenvalues (RCONDE), and reciprocal condition numbers for the */ /* > right eigenvectors (RCONDV). */ /* > */ /* > A generalized eigenvalue for a pair of matrices (A,B) is a scalar */ /* > lambda or a ratio alpha/beta = lambda, such that A - lambda*B is */ /* > singular. It is usually represented as the pair (alpha,beta), as */ /* > there is a reasonable interpretation for beta=0, and even for both */ /* > being zero. */ /* > */ /* > The right eigenvector v(j) corresponding to the eigenvalue lambda(j) */ /* > of (A,B) satisfies */ /* > A * v(j) = lambda(j) * B * v(j) . */ /* > The left eigenvector u(j) corresponding to the eigenvalue lambda(j) */ /* > of (A,B) satisfies */ /* > u(j)**H * A = lambda(j) * u(j)**H * B. */ /* > where u(j)**H is the conjugate-transpose of u(j). */ /* > */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] BALANC */ /* > \verbatim */ /* > BALANC is CHARACTER*1 */ /* > Specifies the balance option to be performed: */ /* > = 'N': do not diagonally scale or permute; */ /* > = 'P': permute only; */ /* > = 'S': scale only; */ /* > = 'B': both permute and scale. */ /* > Computed reciprocal condition numbers will be for the */ /* > matrices after permuting and/or balancing. Permuting does */ /* > not change condition numbers (in exact arithmetic), but */ /* > balancing does. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBVL */ /* > \verbatim */ /* > JOBVL is CHARACTER*1 */ /* > = 'N': do not compute the left generalized eigenvectors; */ /* > = 'V': compute the left generalized eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBVR */ /* > \verbatim */ /* > JOBVR is CHARACTER*1 */ /* > = 'N': do not compute the right generalized eigenvectors; */ /* > = 'V': compute the right generalized eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in] SENSE */ /* > \verbatim */ /* > SENSE is CHARACTER*1 */ /* > Determines which reciprocal condition numbers are computed. */ /* > = 'N': none are computed; */ /* > = 'E': computed for eigenvalues only; */ /* > = 'V': computed for eigenvectors only; */ /* > = 'B': computed for eigenvalues and eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrices A, B, VL, and VR. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA, N) */ /* > On entry, the matrix A in the pair (A,B). */ /* > On exit, A has been overwritten. If JOBVL='V' or JOBVR='V' */ /* > or both, then A contains the first part of the complex Schur */ /* > form of the "balanced" versions of the input A and B. */ /* > \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 array, dimension (LDB, N) */ /* > On entry, the matrix B in the pair (A,B). */ /* > On exit, B has been overwritten. If JOBVL='V' or JOBVR='V' */ /* > or both, then B contains the second part of the complex */ /* > Schur form of the "balanced" versions of the input A and B. */ /* > \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 array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] BETA */ /* > \verbatim */ /* > BETA is COMPLEX array, dimension (N) */ /* > On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized */ /* > eigenvalues. */ /* > */ /* > Note: the quotient ALPHA(j)/BETA(j) ) may easily over- or */ /* > underflow, and BETA(j) may even be zero. Thus, the user */ /* > should avoid naively computing the ratio ALPHA/BETA. */ /* > However, ALPHA will be always less than and usually */ /* > comparable with norm(A) in magnitude, and BETA always less */ /* > than and usually comparable with norm(B). */ /* > \endverbatim */ /* > */ /* > \param[out] VL */ /* > \verbatim */ /* > VL is COMPLEX array, dimension (LDVL,N) */ /* > If JOBVL = 'V', the left generalized eigenvectors u(j) are */ /* > stored one after another in the columns of VL, in the same */ /* > order as their eigenvalues. */ /* > Each eigenvector will be scaled so the largest component */ /* > will have abs(real part) + abs(imag. part) = 1. */ /* > Not referenced if JOBVL = 'N'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVL */ /* > \verbatim */ /* > LDVL is INTEGER */ /* > The leading dimension of the matrix VL. LDVL >= 1, and */ /* > if JOBVL = 'V', LDVL >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] VR */ /* > \verbatim */ /* > VR is COMPLEX array, dimension (LDVR,N) */ /* > If JOBVR = 'V', the right generalized eigenvectors v(j) are */ /* > stored one after another in the columns of VR, in the same */ /* > order as their eigenvalues. */ /* > Each eigenvector will be scaled so the largest component */ /* > will have abs(real part) + abs(imag. part) = 1. */ /* > Not referenced if JOBVR = 'N'. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVR */ /* > \verbatim */ /* > LDVR is INTEGER */ /* > The leading dimension of the matrix VR. LDVR >= 1, and */ /* > if JOBVR = 'V', LDVR >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] ILO */ /* > \verbatim */ /* > ILO is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[out] IHI */ /* > \verbatim */ /* > IHI is INTEGER */ /* > ILO and IHI are integer values such that on exit */ /* > A(i,j) = 0 and B(i,j) = 0 if i > j and */ /* > j = 1,...,ILO-1 or i = IHI+1,...,N. */ /* > If BALANC = 'N' or 'S', ILO = 1 and IHI = N. */ /* > \endverbatim */ /* > */ /* > \param[out] LSCALE */ /* > \verbatim */ /* > LSCALE is REAL array, dimension (N) */ /* > Details of the permutations and scaling factors applied */ /* > to the left side of A and B. If PL(j) is the index of the */ /* > row interchanged with row j, and DL(j) is the scaling */ /* > factor applied to row j, then */ /* > LSCALE(j) = PL(j) for j = 1,...,ILO-1 */ /* > = DL(j) for j = ILO,...,IHI */ /* > = PL(j) for j = IHI+1,...,N. */ /* > The order in which the interchanges are made is N to IHI+1, */ /* > then 1 to ILO-1. */ /* > \endverbatim */ /* > */ /* > \param[out] RSCALE */ /* > \verbatim */ /* > RSCALE is REAL array, dimension (N) */ /* > Details of the permutations and scaling factors applied */ /* > to the right side of A and B. If PR(j) is the index of the */ /* > column interchanged with column j, and DR(j) is the scaling */ /* > factor applied to column j, then */ /* > RSCALE(j) = PR(j) for j = 1,...,ILO-1 */ /* > = DR(j) for j = ILO,...,IHI */ /* > = PR(j) for j = IHI+1,...,N */ /* > The order in which the interchanges are made is N to IHI+1, */ /* > then 1 to ILO-1. */ /* > \endverbatim */ /* > */ /* > \param[out] ABNRM */ /* > \verbatim */ /* > ABNRM is REAL */ /* > The one-norm of the balanced matrix A. */ /* > \endverbatim */ /* > */ /* > \param[out] BBNRM */ /* > \verbatim */ /* > BBNRM is REAL */ /* > The one-norm of the balanced matrix B. */ /* > \endverbatim */ /* > */ /* > \param[out] RCONDE */ /* > \verbatim */ /* > RCONDE is REAL array, dimension (N) */ /* > If SENSE = 'E' or 'B', the reciprocal condition numbers of */ /* > the eigenvalues, stored in consecutive elements of the array. */ /* > If SENSE = 'N' or 'V', RCONDE is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] RCONDV */ /* > \verbatim */ /* > RCONDV is REAL array, dimension (N) */ /* > If SENSE = 'V' or 'B', the estimated reciprocal condition */ /* > numbers of the eigenvectors, stored in consecutive elements */ /* > of the array. If the eigenvalues cannot be reordered to */ /* > compute RCONDV(j), RCONDV(j) is set to 0; this can only occur */ /* > when the true value would be very small anyway. */ /* > If SENSE = 'N' or 'E', RCONDV is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX 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). */ /* > If SENSE = 'E', LWORK >= f2cmax(1,4*N). */ /* > If SENSE = 'V' or 'B', LWORK >= f2cmax(1,2*N*N+2*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 REAL array, dimension (lrwork) */ /* > lrwork must be at least f2cmax(1,6*N) if BALANC = 'S' or 'B', */ /* > and at least f2cmax(1,2*N) otherwise. */ /* > Real workspace. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (N+2) */ /* > If SENSE = 'E', IWORK is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] BWORK */ /* > \verbatim */ /* > BWORK is LOGICAL array, dimension (N) */ /* > If SENSE = 'N', BWORK is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > = 1,...,N: */ /* > The QZ iteration failed. No eigenvectors have been */ /* > calculated, but ALPHA(j) and BETA(j) should be correct */ /* > for j=INFO+1,...,N. */ /* > > N: =N+1: other than QZ iteration failed in CHGEQZ. */ /* > =N+2: error return from CTGEVC. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date April 2012 */ /* > \ingroup complexGEeigen */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > Balancing a matrix pair (A,B) includes, first, permuting rows and */ /* > columns to isolate eigenvalues, second, applying diagonal similarity */ /* > transformation to the rows and columns to make the rows and columns */ /* > as close in norm as possible. The computed reciprocal condition */ /* > numbers correspond to the balanced matrix. Permuting rows and columns */ /* > will not change the condition numbers (in exact arithmetic) but */ /* > diagonal scaling will. For further explanation of balancing, see */ /* > section 4.11.1.2 of LAPACK Users' Guide. */ /* > */ /* > An approximate error bound on the chordal distance between the i-th */ /* > computed generalized eigenvalue w and the corresponding exact */ /* > eigenvalue lambda is */ /* > */ /* > chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I) */ /* > */ /* > An approximate error bound for the angle between the i-th computed */ /* > eigenvector VL(i) or VR(i) is given by */ /* > */ /* > EPS * norm(ABNRM, BBNRM) / DIF(i). */ /* > */ /* > For further explanation of the reciprocal condition numbers RCONDE */ /* > and RCONDV, see section 4.11 of LAPACK User's Guide. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int cggevx_(char *balanc, char *jobvl, char *jobvr, char * sense, integer *n, complex *a, integer *lda, complex *b, integer *ldb, complex *alpha, complex *beta, complex *vl, integer *ldvl, complex * vr, integer *ldvr, integer *ilo, integer *ihi, real *lscale, real * rscale, real *abnrm, real *bbnrm, real *rconde, real *rcondv, complex *work, integer *lwork, real *rwork, integer *iwork, logical *bwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3, i__4; real r__1, r__2, r__3, r__4; complex q__1; /* Local variables */ real anrm, bnrm; integer ierr, itau; real temp; logical ilvl, ilvr; integer iwrk, iwrk1, i__, j, m; extern logical lsame_(char *, char *); integer icols; logical noscl; integer irows, jc; extern /* Subroutine */ int cggbak_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, complex *, integer *, integer *), cggbal_(char *, integer *, complex *, integer *, complex *, integer *, integer *, integer *, real *, real *, real *, integer *), slabad_(real *, real *); integer in; extern real clange_(char *, integer *, integer *, complex *, integer *, real *); integer jr; extern /* Subroutine */ int cgghrd_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, integer *), clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *); logical ilascl, ilbscl; extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), clacpy_( char *, integer *, integer *, complex *, integer *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *); logical ldumma[1]; char chtemp[1]; real bignum; extern /* Subroutine */ int chgeqz_(char *, char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, complex *, complex *, integer *, complex *, integer *, complex *, integer *, real *, integer *), ctgevc_(char *, char *, logical *, integer *, complex *, integer * , complex *, integer *, complex *, integer *, complex *, integer * , integer *, integer *, complex *, real *, integer *); integer ijobvl; extern /* Subroutine */ int ctgsna_(char *, char *, logical *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *, integer *), slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern real slamch_(char *); integer ijobvr; logical wantsb; extern /* Subroutine */ int cungqr_(integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *); real anrmto; logical wantse; real bnrmto; extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *); integer minwrk, maxwrk; logical wantsn; real smlnum; logical lquery, wantsv; real eps; logical ilv; /* -- LAPACK driver routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* April 2012 */ /* ===================================================================== */ /* 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; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1 * 1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1 * 1; vr -= vr_offset; --lscale; --rscale; --rconde; --rcondv; --work; --rwork; --iwork; --bwork; /* Function Body */ if (lsame_(jobvl, "N")) { ijobvl = 1; ilvl = FALSE_; } else if (lsame_(jobvl, "V")) { ijobvl = 2; ilvl = TRUE_; } else { ijobvl = -1; ilvl = FALSE_; } if (lsame_(jobvr, "N")) { ijobvr = 1; ilvr = FALSE_; } else if (lsame_(jobvr, "V")) { ijobvr = 2; ilvr = TRUE_; } else { ijobvr = -1; ilvr = FALSE_; } ilv = ilvl || ilvr; noscl = lsame_(balanc, "N") || lsame_(balanc, "P"); wantsn = lsame_(sense, "N"); wantse = lsame_(sense, "E"); wantsv = lsame_(sense, "V"); wantsb = lsame_(sense, "B"); /* Test the input arguments */ *info = 0; lquery = *lwork == -1; if (! (noscl || lsame_(balanc, "S") || lsame_( balanc, "B"))) { *info = -1; } else if (ijobvl <= 0) { *info = -2; } else if (ijobvr <= 0) { *info = -3; } else if (! (wantsn || wantse || wantsb || wantsv)) { *info = -4; } else if (*n < 0) { *info = -5; } else if (*lda < f2cmax(1,*n)) { *info = -7; } else if (*ldb < f2cmax(1,*n)) { *info = -9; } else if (*ldvl < 1 || ilvl && *ldvl < *n) { *info = -13; } else if (*ldvr < 1 || ilvr && *ldvr < *n) { *info = -15; } /* Compute workspace */ /* (Note: Comments in the code beginning "Workspace:" describe the */ /* minimal amount of workspace needed at that point in the code, */ /* as well as the preferred amount for good performance. */ /* NB refers to the optimal block size for the immediately */ /* following subroutine, as returned by ILAENV. The workspace is */ /* computed assuming ILO = 1 and IHI = N, the worst case.) */ if (*info == 0) { if (*n == 0) { minwrk = 1; maxwrk = 1; } else { minwrk = *n << 1; if (wantse) { minwrk = *n << 2; } else if (wantsv || wantsb) { minwrk = (*n << 1) * (*n + 1); } maxwrk = minwrk; /* Computing MAX */ i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "CGEQRF", " ", n, & c__1, n, &c__0, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__1,i__2); /* Computing MAX */ i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "CUNMQR", " ", n, & c__1, n, &c__0, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__1,i__2); if (ilvl) { /* Computing MAX */ i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "CUNGQR", " ", n, &c__1, n, &c__0, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__1,i__2); } } work[1].r = (real) maxwrk, work[1].i = 0.f; if (*lwork < minwrk && ! lquery) { *info = -25; } } if (*info != 0) { i__1 = -(*info); xerbla_("CGGEVX", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Get machine constants */ eps = slamch_("P"); smlnum = slamch_("S"); bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); smlnum = sqrt(smlnum) / eps; bignum = 1.f / smlnum; /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */ anrm = clange_("M", n, n, &a[a_offset], lda, &rwork[1]); ilascl = FALSE_; if (anrm > 0.f && anrm < smlnum) { anrmto = smlnum; ilascl = TRUE_; } else if (anrm > bignum) { anrmto = bignum; ilascl = TRUE_; } if (ilascl) { clascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, & ierr); } /* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */ bnrm = clange_("M", n, n, &b[b_offset], ldb, &rwork[1]); ilbscl = FALSE_; if (bnrm > 0.f && bnrm < smlnum) { bnrmto = smlnum; ilbscl = TRUE_; } else if (bnrm > bignum) { bnrmto = bignum; ilbscl = TRUE_; } if (ilbscl) { clascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, & ierr); } /* Permute and/or balance the matrix pair (A,B) */ /* (Real Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise) */ cggbal_(balanc, n, &a[a_offset], lda, &b[b_offset], ldb, ilo, ihi, & lscale[1], &rscale[1], &rwork[1], &ierr); /* Compute ABNRM and BBNRM */ *abnrm = clange_("1", n, n, &a[a_offset], lda, &rwork[1]); if (ilascl) { rwork[1] = *abnrm; slascl_("G", &c__0, &c__0, &anrmto, &anrm, &c__1, &c__1, &rwork[1], & c__1, &ierr); *abnrm = rwork[1]; } *bbnrm = clange_("1", n, n, &b[b_offset], ldb, &rwork[1]); if (ilbscl) { rwork[1] = *bbnrm; slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, &c__1, &c__1, &rwork[1], & c__1, &ierr); *bbnrm = rwork[1]; } /* Reduce B to triangular form (QR decomposition of B) */ /* (Complex Workspace: need N, prefer N*NB ) */ irows = *ihi + 1 - *ilo; if (ilv || ! wantsn) { icols = *n + 1 - *ilo; } else { icols = irows; } itau = 1; iwrk = itau + irows; i__1 = *lwork + 1 - iwrk; cgeqrf_(&irows, &icols, &b[*ilo + *ilo * b_dim1], ldb, &work[itau], &work[ iwrk], &i__1, &ierr); /* Apply the unitary transformation to A */ /* (Complex Workspace: need N, prefer N*NB) */ i__1 = *lwork + 1 - iwrk; cunmqr_("L", "C", &irows, &icols, &irows, &b[*ilo + *ilo * b_dim1], ldb, & work[itau], &a[*ilo + *ilo * a_dim1], lda, &work[iwrk], &i__1, & ierr); /* Initialize VL and/or VR */ /* (Workspace: need N, prefer N*NB) */ if (ilvl) { claset_("Full", n, n, &c_b1, &c_b2, &vl[vl_offset], ldvl); if (irows > 1) { i__1 = irows - 1; i__2 = irows - 1; clacpy_("L", &i__1, &i__2, &b[*ilo + 1 + *ilo * b_dim1], ldb, &vl[ *ilo + 1 + *ilo * vl_dim1], ldvl); } i__1 = *lwork + 1 - iwrk; cungqr_(&irows, &irows, &irows, &vl[*ilo + *ilo * vl_dim1], ldvl, & work[itau], &work[iwrk], &i__1, &ierr); } if (ilvr) { claset_("Full", n, n, &c_b1, &c_b2, &vr[vr_offset], ldvr); } /* Reduce to generalized Hessenberg form */ /* (Workspace: none needed) */ if (ilv || ! wantsn) { /* Eigenvectors requested -- work on whole matrix. */ cgghrd_(jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset], ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr); } else { cgghrd_("N", "N", &irows, &c__1, &irows, &a[*ilo + *ilo * a_dim1], lda, &b[*ilo + *ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[ vr_offset], ldvr, &ierr); } /* Perform QZ algorithm (Compute eigenvalues, and optionally, the */ /* Schur forms and Schur vectors) */ /* (Complex Workspace: need N) */ /* (Real Workspace: need N) */ iwrk = itau; if (ilv || ! wantsn) { *(unsigned char *)chtemp = 'S'; } else { *(unsigned char *)chtemp = 'E'; } i__1 = *lwork + 1 - iwrk; chgeqz_(chtemp, jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset] , ldb, &alpha[1], &beta[1], &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &work[iwrk], &i__1, &rwork[1], &ierr); if (ierr != 0) { if (ierr > 0 && ierr <= *n) { *info = ierr; } else if (ierr > *n && ierr <= *n << 1) { *info = ierr - *n; } else { *info = *n + 1; } goto L90; } /* Compute Eigenvectors and estimate condition numbers if desired */ /* CTGEVC: (Complex Workspace: need 2*N ) */ /* (Real Workspace: need 2*N ) */ /* CTGSNA: (Complex Workspace: need 2*N*N if SENSE='V' or 'B') */ /* (Integer Workspace: need N+2 ) */ if (ilv || ! wantsn) { if (ilv) { if (ilvl) { if (ilvr) { *(unsigned char *)chtemp = 'B'; } else { *(unsigned char *)chtemp = 'L'; } } else { *(unsigned char *)chtemp = 'R'; } ctgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, & work[iwrk], &rwork[1], &ierr); if (ierr != 0) { *info = *n + 2; goto L90; } } if (! wantsn) { /* compute eigenvectors (STGEVC) and estimate condition */ /* numbers (STGSNA). Note that the definition of the condition */ /* number is not invariant under transformation (u,v) to */ /* (Q*u, Z*v), where (u,v) are eigenvectors of the generalized */ /* Schur form (S,T), Q and Z are orthogonal matrices. In order */ /* to avoid using extra 2*N*N workspace, we have to */ /* re-calculate eigenvectors and estimate the condition numbers */ /* one at a time. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { bwork[j] = FALSE_; /* L10: */ } bwork[i__] = TRUE_; iwrk = *n + 1; iwrk1 = iwrk + *n; if (wantse || wantsb) { ctgevc_("B", "S", &bwork[1], n, &a[a_offset], lda, &b[ b_offset], ldb, &work[1], n, &work[iwrk], n, & c__1, &m, &work[iwrk1], &rwork[1], &ierr); if (ierr != 0) { *info = *n + 2; goto L90; } } i__2 = *lwork - iwrk1 + 1; ctgsna_(sense, "S", &bwork[1], n, &a[a_offset], lda, &b[ b_offset], ldb, &work[1], n, &work[iwrk], n, &rconde[ i__], &rcondv[i__], &c__1, &m, &work[iwrk1], &i__2, & iwork[1], &ierr); /* L20: */ } } } /* Undo balancing on VL and VR and normalization */ /* (Workspace: none needed) */ if (ilvl) { cggbak_(balanc, "L", n, ilo, ihi, &lscale[1], &rscale[1], n, &vl[ vl_offset], ldvl, &ierr); i__1 = *n; for (jc = 1; jc <= i__1; ++jc) { temp = 0.f; i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { /* Computing MAX */ i__3 = jr + jc * vl_dim1; r__3 = temp, r__4 = (r__1 = vl[i__3].r, abs(r__1)) + (r__2 = r_imag(&vl[jr + jc * vl_dim1]), abs(r__2)); temp = f2cmax(r__3,r__4); /* L30: */ } if (temp < smlnum) { goto L50; } temp = 1.f / temp; i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr + jc * vl_dim1; i__4 = jr + jc * vl_dim1; q__1.r = temp * vl[i__4].r, q__1.i = temp * vl[i__4].i; vl[i__3].r = q__1.r, vl[i__3].i = q__1.i; /* L40: */ } L50: ; } } if (ilvr) { cggbak_(balanc, "R", n, ilo, ihi, &lscale[1], &rscale[1], n, &vr[ vr_offset], ldvr, &ierr); i__1 = *n; for (jc = 1; jc <= i__1; ++jc) { temp = 0.f; i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { /* Computing MAX */ i__3 = jr + jc * vr_dim1; r__3 = temp, r__4 = (r__1 = vr[i__3].r, abs(r__1)) + (r__2 = r_imag(&vr[jr + jc * vr_dim1]), abs(r__2)); temp = f2cmax(r__3,r__4); /* L60: */ } if (temp < smlnum) { goto L80; } temp = 1.f / temp; i__2 = *n; for (jr = 1; jr <= i__2; ++jr) { i__3 = jr + jc * vr_dim1; i__4 = jr + jc * vr_dim1; q__1.r = temp * vr[i__4].r, q__1.i = temp * vr[i__4].i; vr[i__3].r = q__1.r, vr[i__3].i = q__1.i; /* L70: */ } L80: ; } } /* Undo scaling if necessary */ L90: if (ilascl) { clascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, & ierr); } if (ilbscl) { clascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, & ierr); } work[1].r = (real) maxwrk, work[1].i = 0.f; return 0; /* End of CGGEVX */ } /* cggevx_ */