#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 ZTREVC */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZTREVC + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, */ /* LDVR, MM, M, WORK, RWORK, INFO ) */ /* CHARACTER HOWMNY, SIDE */ /* INTEGER INFO, LDT, LDVL, LDVR, M, MM, N */ /* LOGICAL SELECT( * ) */ /* DOUBLE PRECISION RWORK( * ) */ /* COMPLEX*16 T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), */ /* $ WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZTREVC computes some or all of the right and/or left eigenvectors of */ /* > a complex upper triangular matrix T. */ /* > Matrices of this type are produced by the Schur factorization of */ /* > a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. */ /* > */ /* > The right eigenvector x and the left eigenvector y of T corresponding */ /* > to an eigenvalue w are defined by: */ /* > */ /* > T*x = w*x, (y**H)*T = w*(y**H) */ /* > */ /* > where y**H denotes the conjugate transpose of the vector y. */ /* > The eigenvalues are not input to this routine, but are read directly */ /* > from the diagonal of T. */ /* > */ /* > This routine returns the matrices X and/or Y of right and left */ /* > eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an */ /* > input matrix. If Q is the unitary factor that reduces a matrix A to */ /* > Schur form T, then Q*X and Q*Y are the matrices of right and left */ /* > eigenvectors of A. */ /* > \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 using the matrices supplied in */ /* > VR and/or VL; */ /* > = 'S': compute selected right and/or left eigenvectors, */ /* > as indicated 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 matrix T. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] T */ /* > \verbatim */ /* > T is COMPLEX*16 array, dimension (LDT,N) */ /* > The upper triangular matrix T. T is modified, but restored */ /* > on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. LDT >= 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 */ /* > Schur vectors returned by ZHSEQR). */ /* > On exit, if SIDE = 'L' or 'B', VL contains: */ /* > if HOWMNY = 'A', the matrix Y of left eigenvectors of T; */ /* > if HOWMNY = 'B', the matrix Q*Y; */ /* > if HOWMNY = 'S', the left eigenvectors of T 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 the array VL. LDVL >= 1, and if */ /* > SIDE = 'L' 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 Q of */ /* > Schur vectors returned by ZHSEQR). */ /* > On exit, if SIDE = 'R' or 'B', VR contains: */ /* > if HOWMNY = 'A', the matrix X of right eigenvectors of T; */ /* > if HOWMNY = 'B', the matrix Q*X; */ /* > if HOWMNY = 'S', the right eigenvectors of T 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 (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 November 2017 */ /* > \ingroup complex16OTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The algorithm used in this program is basically backward (forward) */ /* > substitution, with scaling to make the the code robust against */ /* > possible overflow. */ /* > */ /* > Each eigenvector is normalized so that the element of largest */ /* > magnitude has magnitude 1; here the magnitude of a complex number */ /* > (x,y) is taken to be |x| + |y|. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int ztrevc_(char *side, char *howmny, logical *select, integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork, integer *info) { /* System generated locals */ integer t_dim1, t_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; doublecomplex z__1, z__2; /* Local variables */ logical allv; doublereal unfl, ovfl, smin; logical over; integer i__, j, k; doublereal scale; extern logical lsame_(char *, char *); doublereal remax; logical leftv, bothv; extern /* Subroutine */ int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); logical somev; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), dlabad_(doublereal *, doublereal *); integer ii, ki; extern doublereal dlamch_(char *); integer is; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), zdscal_( integer *, doublereal *, doublecomplex *, integer *); extern integer izamax_(integer *, doublecomplex *, integer *); logical rightv; extern doublereal dzasum_(integer *, doublecomplex *, integer *); doublereal smlnum; extern /* Subroutine */ int zlatrs_(char *, char *, char *, char *, integer *, doublecomplex *, integer *, doublecomplex *, doublereal *, doublereal *, integer *); doublereal ulp; /* -- LAPACK computational routine (version 3.8.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2017 */ /* ===================================================================== */ /* Decode and test the input parameters */ /* Parameter adjustments */ --select; t_dim1 = *ldt; t_offset = 1 + t_dim1 * 1; t -= t_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 */ bothv = lsame_(side, "B"); rightv = lsame_(side, "R") || bothv; leftv = lsame_(side, "L") || bothv; allv = lsame_(howmny, "A"); over = lsame_(howmny, "B"); somev = lsame_(howmny, "S"); /* Set M to the number of columns required to store the selected */ /* eigenvectors. */ if (somev) { *m = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (select[j]) { ++(*m); } /* L10: */ } } else { *m = *n; } *info = 0; if (! rightv && ! leftv) { *info = -1; } else if (! allv && ! over && ! somev) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*ldt < f2cmax(1,*n)) { *info = -6; } else if (*ldvl < 1 || leftv && *ldvl < *n) { *info = -8; } else if (*ldvr < 1 || rightv && *ldvr < *n) { *info = -10; } else if (*mm < *m) { *info = -11; } if (*info != 0) { i__1 = -(*info); xerbla_("ZTREVC", &i__1, (ftnlen)6); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* Set the constants to control overflow. */ unfl = dlamch_("Safe minimum"); ovfl = 1. / unfl; dlabad_(&unfl, &ovfl); ulp = dlamch_("Precision"); smlnum = unfl * (*n / ulp); /* Store the diagonal elements of T in working array WORK. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + *n; i__3 = i__ + i__ * t_dim1; work[i__2].r = t[i__3].r, work[i__2].i = t[i__3].i; /* L20: */ } /* Compute 1-norm of each column of strictly upper triangular */ /* part of T to control overflow in triangular solver. */ rwork[1] = 0.; i__1 = *n; for (j = 2; j <= i__1; ++j) { i__2 = j - 1; rwork[j] = dzasum_(&i__2, &t[j * t_dim1 + 1], &c__1); /* L30: */ } if (rightv) { /* Compute right eigenvectors. */ is = *m; for (ki = *n; ki >= 1; --ki) { if (somev) { if (! select[ki]) { goto L80; } } /* Computing MAX */ i__1 = ki + ki * t_dim1; d__3 = ulp * ((d__1 = t[i__1].r, abs(d__1)) + (d__2 = d_imag(&t[ ki + ki * t_dim1]), abs(d__2))); smin = f2cmax(d__3,smlnum); work[1].r = 1., work[1].i = 0.; /* Form right-hand side. */ i__1 = ki - 1; for (k = 1; k <= i__1; ++k) { i__2 = k; i__3 = k + ki * t_dim1; z__1.r = -t[i__3].r, z__1.i = -t[i__3].i; work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L40: */ } /* Solve the triangular system: */ /* (T(1:KI-1,1:KI-1) - T(KI,KI))*X = SCALE*WORK. */ i__1 = ki - 1; for (k = 1; k <= i__1; ++k) { i__2 = k + k * t_dim1; i__3 = k + k * t_dim1; i__4 = ki + ki * t_dim1; z__1.r = t[i__3].r - t[i__4].r, z__1.i = t[i__3].i - t[i__4] .i; t[i__2].r = z__1.r, t[i__2].i = z__1.i; i__2 = k + k * t_dim1; if ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[k + k * t_dim1]), abs(d__2)) < smin) { i__3 = k + k * t_dim1; t[i__3].r = smin, t[i__3].i = 0.; } /* L50: */ } if (ki > 1) { i__1 = ki - 1; zlatrs_("Upper", "No transpose", "Non-unit", "Y", &i__1, &t[ t_offset], ldt, &work[1], &scale, &rwork[1], info); i__1 = ki; work[i__1].r = scale, work[i__1].i = 0.; } /* Copy the vector x or Q*x to VR and normalize. */ if (! over) { zcopy_(&ki, &work[1], &c__1, &vr[is * vr_dim1 + 1], &c__1); ii = izamax_(&ki, &vr[is * vr_dim1 + 1], &c__1); i__1 = ii + is * vr_dim1; remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag( &vr[ii + is * vr_dim1]), abs(d__2))); zdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1); i__1 = *n; for (k = ki + 1; k <= i__1; ++k) { i__2 = k + is * vr_dim1; vr[i__2].r = 0., vr[i__2].i = 0.; /* L60: */ } } else { if (ki > 1) { i__1 = ki - 1; z__1.r = scale, z__1.i = 0.; zgemv_("N", n, &i__1, &c_b2, &vr[vr_offset], ldvr, &work[ 1], &c__1, &z__1, &vr[ki * vr_dim1 + 1], &c__1); } ii = izamax_(n, &vr[ki * vr_dim1 + 1], &c__1); i__1 = ii + ki * vr_dim1; remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag( &vr[ii + ki * vr_dim1]), abs(d__2))); zdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1); } /* Set back the original diagonal elements of T. */ i__1 = ki - 1; for (k = 1; k <= i__1; ++k) { i__2 = k + k * t_dim1; i__3 = k + *n; t[i__2].r = work[i__3].r, t[i__2].i = work[i__3].i; /* L70: */ } --is; L80: ; } } if (leftv) { /* Compute left eigenvectors. */ is = 1; i__1 = *n; for (ki = 1; ki <= i__1; ++ki) { if (somev) { if (! select[ki]) { goto L130; } } /* Computing MAX */ i__2 = ki + ki * t_dim1; d__3 = ulp * ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[ ki + ki * t_dim1]), abs(d__2))); smin = f2cmax(d__3,smlnum); i__2 = *n; work[i__2].r = 1., work[i__2].i = 0.; /* Form right-hand side. */ i__2 = *n; for (k = ki + 1; k <= i__2; ++k) { i__3 = k; d_cnjg(&z__2, &t[ki + k * t_dim1]); z__1.r = -z__2.r, z__1.i = -z__2.i; work[i__3].r = z__1.r, work[i__3].i = z__1.i; /* L90: */ } /* Solve the triangular system: */ /* (T(KI+1:N,KI+1:N) - T(KI,KI))**H * X = SCALE*WORK. */ i__2 = *n; for (k = ki + 1; k <= i__2; ++k) { i__3 = k + k * t_dim1; i__4 = k + k * t_dim1; i__5 = ki + ki * t_dim1; z__1.r = t[i__4].r - t[i__5].r, z__1.i = t[i__4].i - t[i__5] .i; t[i__3].r = z__1.r, t[i__3].i = z__1.i; i__3 = k + k * t_dim1; if ((d__1 = t[i__3].r, abs(d__1)) + (d__2 = d_imag(&t[k + k * t_dim1]), abs(d__2)) < smin) { i__4 = k + k * t_dim1; t[i__4].r = smin, t[i__4].i = 0.; } /* L100: */ } if (ki < *n) { i__2 = *n - ki; zlatrs_("Upper", "Conjugate transpose", "Non-unit", "Y", & i__2, &t[ki + 1 + (ki + 1) * t_dim1], ldt, &work[ki + 1], &scale, &rwork[1], info); i__2 = ki; work[i__2].r = scale, work[i__2].i = 0.; } /* Copy the vector x or Q*x to VL and normalize. */ if (! over) { i__2 = *n - ki + 1; zcopy_(&i__2, &work[ki], &c__1, &vl[ki + is * vl_dim1], &c__1) ; i__2 = *n - ki + 1; ii = izamax_(&i__2, &vl[ki + is * vl_dim1], &c__1) + ki - 1; i__2 = ii + is * vl_dim1; remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag( &vl[ii + is * vl_dim1]), abs(d__2))); i__2 = *n - ki + 1; zdscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1); i__2 = ki - 1; for (k = 1; k <= i__2; ++k) { i__3 = k + is * vl_dim1; vl[i__3].r = 0., vl[i__3].i = 0.; /* L110: */ } } else { if (ki < *n) { i__2 = *n - ki; z__1.r = scale, z__1.i = 0.; zgemv_("N", n, &i__2, &c_b2, &vl[(ki + 1) * vl_dim1 + 1], ldvl, &work[ki + 1], &c__1, &z__1, &vl[ki * vl_dim1 + 1], &c__1); } ii = izamax_(n, &vl[ki * vl_dim1 + 1], &c__1); i__2 = ii + ki * vl_dim1; remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag( &vl[ii + ki * vl_dim1]), abs(d__2))); zdscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1); } /* Set back the original diagonal elements of T. */ i__2 = *n; for (k = ki + 1; k <= i__2; ++k) { i__3 = k + k * t_dim1; i__4 = k + *n; t[i__3].r = work[i__4].r, t[i__3].i = work[i__4].i; /* L120: */ } ++is; L130: ; } } return 0; /* End of ZTREVC */ } /* ztrevc_ */