#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 CGEEVX 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 CGEEVX + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL, */ /* LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, */ /* RCONDV, WORK, LWORK, RWORK, INFO ) */ /* CHARACTER BALANC, JOBVL, JOBVR, SENSE */ /* INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N */ /* REAL ABNRM */ /* REAL RCONDE( * ), RCONDV( * ), RWORK( * ), */ /* $ SCALE( * ) */ /* COMPLEX A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), */ /* $ W( * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the */ /* > eigenvalues and, optionally, the left and/or right eigenvectors. */ /* > */ /* > Optionally also, it computes a balancing transformation to improve */ /* > the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */ /* > SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues */ /* > (RCONDE), and reciprocal condition numbers for the right */ /* > eigenvectors (RCONDV). */ /* > */ /* > The right eigenvector v(j) of A satisfies */ /* > A * v(j) = lambda(j) * v(j) */ /* > where lambda(j) is its eigenvalue. */ /* > The left eigenvector u(j) of A satisfies */ /* > u(j)**H * A = lambda(j) * u(j)**H */ /* > where u(j)**H denotes the conjugate transpose of u(j). */ /* > */ /* > The computed eigenvectors are normalized to have Euclidean norm */ /* > equal to 1 and largest component real. */ /* > */ /* > Balancing a matrix means permuting the rows and columns to make it */ /* > more nearly upper triangular, and applying a diagonal similarity */ /* > transformation D * A * D**(-1), where D is a diagonal matrix, to */ /* > make its rows and columns closer in norm and the condition numbers */ /* > of its eigenvalues and eigenvectors smaller. 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 4.10.2 of the LAPACK */ /* > Users' Guide. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] BALANC */ /* > \verbatim */ /* > BALANC is CHARACTER*1 */ /* > Indicates how the input matrix should be diagonally scaled */ /* > and/or permuted to improve the conditioning of its */ /* > eigenvalues. */ /* > = 'N': Do not diagonally scale or permute; */ /* > = 'P': Perform permutations to make the matrix more nearly */ /* > upper triangular. Do not diagonally scale; */ /* > = 'S': Diagonally scale the matrix, ie. replace A by */ /* > D*A*D**(-1), where D is a diagonal matrix chosen */ /* > to make the rows and columns of A more equal in */ /* > norm. Do not permute; */ /* > = 'B': Both diagonally scale and permute A. */ /* > */ /* > Computed reciprocal condition numbers will be for the matrix */ /* > after balancing and/or permuting. Permuting does not change */ /* > condition numbers (in exact arithmetic), but balancing does. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBVL */ /* > \verbatim */ /* > JOBVL is CHARACTER*1 */ /* > = 'N': left eigenvectors of A are not computed; */ /* > = 'V': left eigenvectors of A are computed. */ /* > If SENSE = 'E' or 'B', JOBVL must = 'V'. */ /* > \endverbatim */ /* > */ /* > \param[in] JOBVR */ /* > \verbatim */ /* > JOBVR is CHARACTER*1 */ /* > = 'N': right eigenvectors of A are not computed; */ /* > = 'V': right eigenvectors of A are computed. */ /* > If SENSE = 'E' or 'B', JOBVR must = 'V'. */ /* > \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 right eigenvectors only; */ /* > = 'B': Computed for eigenvalues and right eigenvectors. */ /* > */ /* > If SENSE = 'E' or 'B', both left and right eigenvectors */ /* > must also be computed (JOBVL = 'V' and JOBVR = 'V'). */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA,N) */ /* > On entry, the N-by-N matrix A. */ /* > On exit, A has been overwritten. If JOBVL = 'V' or */ /* > JOBVR = 'V', A contains the Schur form of the balanced */ /* > version of the matrix A. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] W */ /* > \verbatim */ /* > W is COMPLEX array, dimension (N) */ /* > W contains the computed eigenvalues. */ /* > \endverbatim */ /* > */ /* > \param[out] VL */ /* > \verbatim */ /* > VL is COMPLEX array, dimension (LDVL,N) */ /* > If JOBVL = 'V', the left eigenvectors u(j) are stored one */ /* > after another in the columns of VL, in the same order */ /* > as their eigenvalues. */ /* > If JOBVL = 'N', VL is not referenced. */ /* > u(j) = VL(:,j), the j-th column of VL. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVL */ /* > \verbatim */ /* > LDVL is INTEGER */ /* > The leading dimension of the array VL. LDVL >= 1; if */ /* > JOBVL = 'V', LDVL >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] VR */ /* > \verbatim */ /* > VR is COMPLEX array, dimension (LDVR,N) */ /* > If JOBVR = 'V', the right eigenvectors v(j) are stored one */ /* > after another in the columns of VR, in the same order */ /* > as their eigenvalues. */ /* > If JOBVR = 'N', VR is not referenced. */ /* > v(j) = VR(:,j), the j-th column of VR. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVR */ /* > \verbatim */ /* > LDVR is INTEGER */ /* > The leading dimension of the array VR. LDVR >= 1; 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 determined when A was */ /* > balanced. The balanced A(i,j) = 0 if I > J and */ /* > J = 1,...,ILO-1 or I = IHI+1,...,N. */ /* > \endverbatim */ /* > */ /* > \param[out] SCALE */ /* > \verbatim */ /* > SCALE is REAL array, dimension (N) */ /* > Details of the permutations and scaling factors applied */ /* > when balancing A. If P(j) is the index of the row and column */ /* > interchanged with row and column j, and D(j) is the scaling */ /* > factor applied to row and column j, then */ /* > SCALE(J) = P(J), for J = 1,...,ILO-1 */ /* > = D(J), for J = ILO,...,IHI */ /* > = P(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 (the maximum */ /* > of the sum of absolute values of elements of any column). */ /* > \endverbatim */ /* > */ /* > \param[out] RCONDE */ /* > \verbatim */ /* > RCONDE is REAL array, dimension (N) */ /* > RCONDE(j) is the reciprocal condition number of the j-th */ /* > eigenvalue. */ /* > \endverbatim */ /* > */ /* > \param[out] RCONDV */ /* > \verbatim */ /* > RCONDV is REAL array, dimension (N) */ /* > RCONDV(j) is the reciprocal condition number of the j-th */ /* > right eigenvector. */ /* > \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. If SENSE = 'N' or 'E', */ /* > LWORK >= f2cmax(1,2*N), and if SENSE = 'V' or 'B', */ /* > LWORK >= N*N+2*N. */ /* > For good performance, LWORK must generally be larger. */ /* > */ /* > 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 (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. */ /* > > 0: if INFO = i, the QR algorithm failed to compute all the */ /* > eigenvalues, and no eigenvectors or condition numbers */ /* > have been computed; elements 1:ILO-1 and i+1:N of W */ /* > contain eigenvalues which have converged. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* @generated from zgeevx.f, fortran z -> c, Tue Apr 19 01:47:44 2016 */ /* > \ingroup complexGEeigen */ /* ===================================================================== */ /* Subroutine */ int cgeevx_(char *balanc, char *jobvl, char *jobvr, char * sense, integer *n, complex *a, integer *lda, complex *w, complex *vl, integer *ldvl, complex *vr, integer *ldvr, integer *ilo, integer *ihi, real *scale, real *abnrm, real *rconde, real *rcondv, complex *work, integer *lwork, real *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3; real r__1, r__2; complex q__1, q__2; /* Local variables */ char side[1]; real anrm; integer ierr, itau, iwrk, nout, i__, k; extern /* Subroutine */ int cscal_(integer *, complex *, complex *, integer *); integer icond; extern logical lsame_(char *, char *); extern real scnrm2_(integer *, complex *, integer *); extern /* Subroutine */ int cgebak_(char *, char *, integer *, integer *, integer *, real *, integer *, complex *, integer *, integer *), cgebal_(char *, integer *, complex *, integer *, integer *, integer *, real *, integer *), slabad_(real *, real *); logical scalea; extern real clange_(char *, integer *, integer *, complex *, integer *, real *); real cscale; extern /* Subroutine */ int cgehrd_(integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *); extern real slamch_(char *); extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); logical select[1]; real bignum; extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); extern integer isamax_(integer *, real *, integer *); extern /* Subroutine */ int chseqr_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *), cunghr_(integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), ctrsna_(char *, char *, logical *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, integer *, integer *, complex *, integer *, real *, integer *); integer minwrk, maxwrk; logical wantvl, wntsnb; integer hswork; logical wntsne; real smlnum; logical lquery, wantvr, wntsnn, wntsnv; extern /* Subroutine */ int ctrevc3_(char *, char *, logical *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, integer *, integer *, complex *, integer *, real *, integer *, integer *); char job[1]; real scl, dum[1], eps; complex tmp; integer lwork_trevc__; /* -- LAPACK driver routine (version 3.7.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* June 2016 */ /* ===================================================================== */ /* Test the input arguments */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --w; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1 * 1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1 * 1; vr -= vr_offset; --scale; --rconde; --rcondv; --work; --rwork; /* Function Body */ *info = 0; lquery = *lwork == -1; wantvl = lsame_(jobvl, "V"); wantvr = lsame_(jobvr, "V"); wntsnn = lsame_(sense, "N"); wntsne = lsame_(sense, "E"); wntsnv = lsame_(sense, "V"); wntsnb = lsame_(sense, "B"); if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P") || lsame_(balanc, "B"))) { *info = -1; } else if (! wantvl && ! lsame_(jobvl, "N")) { *info = -2; } else if (! wantvr && ! lsame_(jobvr, "N")) { *info = -3; } else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb) && ! (wantvl && wantvr)) { *info = -4; } else if (*n < 0) { *info = -5; } else if (*lda < f2cmax(1,*n)) { *info = -7; } else if (*ldvl < 1 || wantvl && *ldvl < *n) { *info = -10; } else if (*ldvr < 1 || wantvr && *ldvr < *n) { *info = -12; } /* 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. */ /* CWorkspace refers to complex workspace, and RWorkspace to real */ /* workspace. NB refers to the optimal block size for the */ /* immediately following subroutine, as returned by ILAENV. */ /* HSWORK refers to the workspace preferred by CHSEQR, as */ /* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */ /* the worst case.) */ if (*info == 0) { if (*n == 0) { minwrk = 1; maxwrk = 1; } else { maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, & c__0, (ftnlen)6, (ftnlen)1); if (wantvl) { ctrevc3_("L", "B", select, n, &a[a_offset], lda, &vl[ vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, & work[1], &c_n1, &rwork[1], &c_n1, &ierr); lwork_trevc__ = (integer) work[1].r; maxwrk = f2cmax(maxwrk,lwork_trevc__); chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[ vl_offset], ldvl, &work[1], &c_n1, info); } else if (wantvr) { ctrevc3_("R", "B", select, n, &a[a_offset], lda, &vl[ vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, & work[1], &c_n1, &rwork[1], &c_n1, &ierr); lwork_trevc__ = (integer) work[1].r; maxwrk = f2cmax(maxwrk,lwork_trevc__); chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[1], &c_n1, info); } else { if (wntsnn) { chseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], & vr[vr_offset], ldvr, &work[1], &c_n1, info); } else { chseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &w[1], & vr[vr_offset], ldvr, &work[1], &c_n1, info); } } hswork = (integer) work[1].r; if (! wantvl && ! wantvr) { minwrk = *n << 1; if (! (wntsnn || wntsne)) { /* Computing MAX */ i__1 = minwrk, i__2 = *n * *n + (*n << 1); minwrk = f2cmax(i__1,i__2); } maxwrk = f2cmax(maxwrk,hswork); if (! (wntsnn || wntsne)) { /* Computing MAX */ i__1 = maxwrk, i__2 = *n * *n + (*n << 1); maxwrk = f2cmax(i__1,i__2); } } else { minwrk = *n << 1; if (! (wntsnn || wntsne)) { /* Computing MAX */ i__1 = minwrk, i__2 = *n * *n + (*n << 1); minwrk = f2cmax(i__1,i__2); } maxwrk = f2cmax(maxwrk,hswork); /* Computing MAX */ i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR", " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1); maxwrk = f2cmax(i__1,i__2); if (! (wntsnn || wntsne)) { /* Computing MAX */ i__1 = maxwrk, i__2 = *n * *n + (*n << 1); maxwrk = f2cmax(i__1,i__2); } /* Computing MAX */ i__1 = maxwrk, i__2 = *n << 1; maxwrk = f2cmax(i__1,i__2); } maxwrk = f2cmax(maxwrk,minwrk); } work[1].r = (real) maxwrk, work[1].i = 0.f; if (*lwork < minwrk && ! lquery) { *info = -20; } } if (*info != 0) { i__1 = -(*info); xerbla_("CGEEVX", &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] */ icond = 0; anrm = clange_("M", n, n, &a[a_offset], lda, dum); scalea = FALSE_; if (anrm > 0.f && anrm < smlnum) { scalea = TRUE_; cscale = smlnum; } else if (anrm > bignum) { scalea = TRUE_; cscale = bignum; } if (scalea) { clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, & ierr); } /* Balance the matrix and compute ABNRM */ cgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr); *abnrm = clange_("1", n, n, &a[a_offset], lda, dum); if (scalea) { dum[0] = *abnrm; slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, & ierr); *abnrm = dum[0]; } /* Reduce to upper Hessenberg form */ /* (CWorkspace: need 2*N, prefer N+N*NB) */ /* (RWorkspace: none) */ itau = 1; iwrk = itau + *n; i__1 = *lwork - iwrk + 1; cgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, & ierr); if (wantvl) { /* Want left eigenvectors */ /* Copy Householder vectors to VL */ *(unsigned char *)side = 'L'; clacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl) ; /* Generate unitary matrix in VL */ /* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwrk + 1; cunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], & i__1, &ierr); /* Perform QR iteration, accumulating Schur vectors in VL */ /* (CWorkspace: need 1, prefer HSWORK (see comments) ) */ /* (RWorkspace: none) */ iwrk = itau; i__1 = *lwork - iwrk + 1; chseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vl[ vl_offset], ldvl, &work[iwrk], &i__1, info); if (wantvr) { /* Want left and right eigenvectors */ /* Copy Schur vectors to VR */ *(unsigned char *)side = 'B'; clacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr); } } else if (wantvr) { /* Want right eigenvectors */ /* Copy Householder vectors to VR */ *(unsigned char *)side = 'R'; clacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr) ; /* Generate unitary matrix in VR */ /* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */ /* (RWorkspace: none) */ i__1 = *lwork - iwrk + 1; cunghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], & i__1, &ierr); /* Perform QR iteration, accumulating Schur vectors in VR */ /* (CWorkspace: need 1, prefer HSWORK (see comments) ) */ /* (RWorkspace: none) */ iwrk = itau; i__1 = *lwork - iwrk + 1; chseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[iwrk], &i__1, info); } else { /* Compute eigenvalues only */ /* If condition numbers desired, compute Schur form */ if (wntsnn) { *(unsigned char *)job = 'E'; } else { *(unsigned char *)job = 'S'; } /* (CWorkspace: need 1, prefer HSWORK (see comments) ) */ /* (RWorkspace: none) */ iwrk = itau; i__1 = *lwork - iwrk + 1; chseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[iwrk], &i__1, info); } /* If INFO .NE. 0 from CHSEQR, then quit */ if (*info != 0) { goto L50; } if (wantvl || wantvr) { /* Compute left and/or right eigenvectors */ /* (CWorkspace: need 2*N, prefer N + 2*N*NB) */ /* (RWorkspace: need N) */ i__1 = *lwork - iwrk + 1; ctrevc3_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &work[iwrk], &i__1, & rwork[1], n, &ierr); } /* Compute condition numbers if desired */ /* (CWorkspace: need N*N+2*N unless SENSE = 'E') */ /* (RWorkspace: need 2*N unless SENSE = 'E') */ if (! wntsnn) { ctrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout, &work[iwrk], n, &rwork[1], &icond); } if (wantvl) { /* Undo balancing of left eigenvectors */ cgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl, &ierr); /* Normalize left eigenvectors and make largest component real */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { scl = 1.f / scnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1); csscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1); i__2 = *n; for (k = 1; k <= i__2; ++k) { i__3 = k + i__ * vl_dim1; /* Computing 2nd power */ r__1 = vl[i__3].r; /* Computing 2nd power */ r__2 = r_imag(&vl[k + i__ * vl_dim1]); rwork[k] = r__1 * r__1 + r__2 * r__2; /* L10: */ } k = isamax_(n, &rwork[1], &c__1); r_cnjg(&q__2, &vl[k + i__ * vl_dim1]); r__1 = sqrt(rwork[k]); q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1; tmp.r = q__1.r, tmp.i = q__1.i; cscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1); i__2 = k + i__ * vl_dim1; i__3 = k + i__ * vl_dim1; r__1 = vl[i__3].r; q__1.r = r__1, q__1.i = 0.f; vl[i__2].r = q__1.r, vl[i__2].i = q__1.i; /* L20: */ } } if (wantvr) { /* Undo balancing of right eigenvectors */ cgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr, &ierr); /* Normalize right eigenvectors and make largest component real */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { scl = 1.f / scnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1); csscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1); i__2 = *n; for (k = 1; k <= i__2; ++k) { i__3 = k + i__ * vr_dim1; /* Computing 2nd power */ r__1 = vr[i__3].r; /* Computing 2nd power */ r__2 = r_imag(&vr[k + i__ * vr_dim1]); rwork[k] = r__1 * r__1 + r__2 * r__2; /* L30: */ } k = isamax_(n, &rwork[1], &c__1); r_cnjg(&q__2, &vr[k + i__ * vr_dim1]); r__1 = sqrt(rwork[k]); q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1; tmp.r = q__1.r, tmp.i = q__1.i; cscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1); i__2 = k + i__ * vr_dim1; i__3 = k + i__ * vr_dim1; r__1 = vr[i__3].r; q__1.r = r__1, q__1.i = 0.f; vr[i__2].r = q__1.r, vr[i__2].i = q__1.i; /* L40: */ } } /* Undo scaling if necessary */ L50: if (scalea) { i__1 = *n - *info; /* Computing MAX */ i__3 = *n - *info; i__2 = f2cmax(i__3,1); clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1] , &i__2, &ierr); if (*info == 0) { if ((wntsnv || wntsnb) && icond == 0) { slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[ 1], n, &ierr); } } else { i__1 = *ilo - 1; clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n, &ierr); } } work[1].r = (real) maxwrk, work[1].i = 0.f; return 0; /* End of CGEEVX */ } /* cgeevx_ */