#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 ZTRSNA */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZTRSNA + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZTRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, */ /* LDVR, S, SEP, MM, M, WORK, LDWORK, RWORK, */ /* INFO ) */ /* CHARACTER HOWMNY, JOB */ /* INTEGER INFO, LDT, LDVL, LDVR, LDWORK, M, MM, N */ /* LOGICAL SELECT( * ) */ /* DOUBLE PRECISION RWORK( * ), S( * ), SEP( * ) */ /* COMPLEX*16 T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), */ /* $ WORK( LDWORK, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZTRSNA estimates reciprocal condition numbers for specified */ /* > eigenvalues and/or right eigenvectors of a complex upper triangular */ /* > matrix T (or of any matrix Q*T*Q**H with Q unitary). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOB */ /* > \verbatim */ /* > JOB is CHARACTER*1 */ /* > Specifies whether condition numbers are required for */ /* > eigenvalues (S) or eigenvectors (SEP): */ /* > = 'E': for eigenvalues only (S); */ /* > = 'V': for eigenvectors only (SEP); */ /* > = 'B': for both eigenvalues and eigenvectors (S and SEP). */ /* > \endverbatim */ /* > */ /* > \param[in] HOWMNY */ /* > \verbatim */ /* > HOWMNY is CHARACTER*1 */ /* > = 'A': compute condition numbers for all eigenpairs; */ /* > = 'S': compute condition numbers for selected eigenpairs */ /* > specified by the array SELECT. */ /* > \endverbatim */ /* > */ /* > \param[in] SELECT */ /* > \verbatim */ /* > SELECT is LOGICAL array, dimension (N) */ /* > If HOWMNY = 'S', SELECT specifies the eigenpairs for which */ /* > condition numbers are required. To select condition numbers */ /* > for the j-th eigenpair, SELECT(j) must be set to .TRUE.. */ /* > If HOWMNY = 'A', SELECT is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix T. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] T */ /* > \verbatim */ /* > T is COMPLEX*16 array, dimension (LDT,N) */ /* > The upper triangular matrix T. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. LDT >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] VL */ /* > \verbatim */ /* > VL is COMPLEX*16 array, dimension (LDVL,M) */ /* > If JOB = 'E' or 'B', VL must contain left eigenvectors of T */ /* > (or of any Q*T*Q**H with Q unitary), corresponding to the */ /* > eigenpairs specified by HOWMNY and SELECT. The eigenvectors */ /* > must be stored in consecutive columns of VL, as returned by */ /* > ZHSEIN or ZTREVC. */ /* > If JOB = 'V', VL is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVL */ /* > \verbatim */ /* > LDVL is INTEGER */ /* > The leading dimension of the array VL. */ /* > LDVL >= 1; and if JOB = 'E' or 'B', LDVL >= N. */ /* > \endverbatim */ /* > */ /* > \param[in] VR */ /* > \verbatim */ /* > VR is COMPLEX*16 array, dimension (LDVR,M) */ /* > If JOB = 'E' or 'B', VR must contain right eigenvectors of T */ /* > (or of any Q*T*Q**H with Q unitary), corresponding to the */ /* > eigenpairs specified by HOWMNY and SELECT. The eigenvectors */ /* > must be stored in consecutive columns of VR, as returned by */ /* > ZHSEIN or ZTREVC. */ /* > If JOB = 'V', VR is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVR */ /* > \verbatim */ /* > LDVR is INTEGER */ /* > The leading dimension of the array VR. */ /* > LDVR >= 1; and if JOB = 'E' or 'B', LDVR >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] S */ /* > \verbatim */ /* > S is DOUBLE PRECISION array, dimension (MM) */ /* > If JOB = 'E' or 'B', the reciprocal condition numbers of the */ /* > selected eigenvalues, stored in consecutive elements of the */ /* > array. Thus S(j), SEP(j), and the j-th columns of VL and VR */ /* > all correspond to the same eigenpair (but not in general the */ /* > j-th eigenpair, unless all eigenpairs are selected). */ /* > If JOB = 'V', S is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] SEP */ /* > \verbatim */ /* > SEP is DOUBLE PRECISION array, dimension (MM) */ /* > If JOB = 'V' or 'B', the estimated reciprocal condition */ /* > numbers of the selected eigenvectors, stored in consecutive */ /* > elements of the array. */ /* > If JOB = 'E', SEP is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] MM */ /* > \verbatim */ /* > MM is INTEGER */ /* > The number of elements in the arrays S (if JOB = 'E' or 'B') */ /* > and/or SEP (if JOB = 'V' or 'B'). MM >= M. */ /* > \endverbatim */ /* > */ /* > \param[out] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of elements of the arrays S and/or SEP actually */ /* > used to store the estimated condition numbers. */ /* > If HOWMNY = 'A', M is set to N. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX*16 array, dimension (LDWORK,N+6) */ /* > If JOB = 'E', WORK is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDWORK */ /* > \verbatim */ /* > LDWORK is INTEGER */ /* > The leading dimension of the array WORK. */ /* > LDWORK >= 1; and if JOB = 'V' or 'B', LDWORK >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] RWORK */ /* > \verbatim */ /* > RWORK is DOUBLE PRECISION array, dimension (N) */ /* > If JOB = 'E', RWORK 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 */ /* > \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 reciprocal of the condition number of an eigenvalue lambda is */ /* > defined as */ /* > */ /* > S(lambda) = |v**H*u| / (norm(u)*norm(v)) */ /* > */ /* > where u and v are the right and left eigenvectors of T corresponding */ /* > to lambda; v**H denotes the conjugate transpose of v, and norm(u) */ /* > denotes the Euclidean norm. These reciprocal condition numbers always */ /* > lie between zero (very badly conditioned) and one (very well */ /* > conditioned). If n = 1, S(lambda) is defined to be 1. */ /* > */ /* > An approximate error bound for a computed eigenvalue W(i) is given by */ /* > */ /* > EPS * norm(T) / S(i) */ /* > */ /* > where EPS is the machine precision. */ /* > */ /* > The reciprocal of the condition number of the right eigenvector u */ /* > corresponding to lambda is defined as follows. Suppose */ /* > */ /* > T = ( lambda c ) */ /* > ( 0 T22 ) */ /* > */ /* > Then the reciprocal condition number is */ /* > */ /* > SEP( lambda, T22 ) = sigma-f2cmin( T22 - lambda*I ) */ /* > */ /* > where sigma-f2cmin denotes the smallest singular value. We approximate */ /* > the smallest singular value by the reciprocal of an estimate of the */ /* > one-norm of the inverse of T22 - lambda*I. If n = 1, SEP(1) is */ /* > defined to be abs(T(1,1)). */ /* > */ /* > An approximate error bound for a computed right eigenvector VR(i) */ /* > is given by */ /* > */ /* > EPS * norm(T) / SEP(i) */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int ztrsna_(char *job, char *howmny, logical *select, integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, doublereal *s, doublereal *sep, integer *mm, integer *m, doublecomplex *work, integer *ldwork, doublereal *rwork, integer *info) { /* System generated locals */ integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, work_dim1, work_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2; doublecomplex z__1; /* Local variables */ integer kase, ierr; doublecomplex prod; doublereal lnrm, rnrm; integer i__, j, k; doublereal scale; extern logical lsame_(char *, char *); integer isave[3]; extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); doublecomplex dummy[1]; logical wants; doublereal xnorm; extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, doublecomplex *, doublereal *, integer *, integer *), dlabad_( doublereal *, doublereal *); extern doublereal dznrm2_(integer *, doublecomplex *, integer *), dlamch_( char *); integer ks, ix; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; logical wantbh; extern integer izamax_(integer *, doublecomplex *, integer *); logical somcon; extern /* Subroutine */ int zdrscl_(integer *, doublereal *, doublecomplex *, integer *); char normin[1]; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal smlnum; logical wantsp; extern /* Subroutine */ int zlatrs_(char *, char *, char *, char *, integer *, doublecomplex *, integer *, doublecomplex *, doublereal *, doublereal *, integer *), ztrexc_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *, integer *); doublereal eps, est; /* -- 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; --s; --sep; work_dim1 = *ldwork; work_offset = 1 + work_dim1 * 1; work -= work_offset; --rwork; /* Function Body */ wantbh = lsame_(job, "B"); wants = lsame_(job, "E") || wantbh; wantsp = lsame_(job, "V") || wantbh; somcon = lsame_(howmny, "S"); /* Set M to the number of eigenpairs for which condition numbers are */ /* to be computed. */ if (somcon) { *m = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (select[j]) { ++(*m); } /* L10: */ } } else { *m = *n; } *info = 0; if (! wants && ! wantsp) { *info = -1; } else if (! lsame_(howmny, "A") && ! somcon) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*ldt < f2cmax(1,*n)) { *info = -6; } else if (*ldvl < 1 || wants && *ldvl < *n) { *info = -8; } else if (*ldvr < 1 || wants && *ldvr < *n) { *info = -10; } else if (*mm < *m) { *info = -13; } else if (*ldwork < 1 || wantsp && *ldwork < *n) { *info = -16; } if (*info != 0) { i__1 = -(*info); xerbla_("ZTRSNA", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { if (somcon) { if (! select[1]) { return 0; } } if (wants) { s[1] = 1.; } if (wantsp) { sep[1] = z_abs(&t[t_dim1 + 1]); } return 0; } /* Get machine constants */ eps = dlamch_("P"); smlnum = dlamch_("S") / eps; bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); ks = 1; i__1 = *n; for (k = 1; k <= i__1; ++k) { if (somcon) { if (! select[k]) { goto L50; } } if (wants) { /* Compute the reciprocal condition number of the k-th */ /* eigenvalue. */ zdotc_(&z__1, n, &vr[ks * vr_dim1 + 1], &c__1, &vl[ks * vl_dim1 + 1], &c__1); prod.r = z__1.r, prod.i = z__1.i; rnrm = dznrm2_(n, &vr[ks * vr_dim1 + 1], &c__1); lnrm = dznrm2_(n, &vl[ks * vl_dim1 + 1], &c__1); s[ks] = z_abs(&prod) / (rnrm * lnrm); } if (wantsp) { /* Estimate the reciprocal condition number of the k-th */ /* eigenvector. */ /* Copy the matrix T to the array WORK and swap the k-th */ /* diagonal element to the (1,1) position. */ zlacpy_("Full", n, n, &t[t_offset], ldt, &work[work_offset], ldwork); ztrexc_("No Q", n, &work[work_offset], ldwork, dummy, &c__1, &k, & c__1, &ierr); /* Form C = T22 - lambda*I in WORK(2:N,2:N). */ i__2 = *n; for (i__ = 2; i__ <= i__2; ++i__) { i__3 = i__ + i__ * work_dim1; i__4 = i__ + i__ * work_dim1; i__5 = work_dim1 + 1; z__1.r = work[i__4].r - work[i__5].r, z__1.i = work[i__4].i - work[i__5].i; work[i__3].r = z__1.r, work[i__3].i = z__1.i; /* L20: */ } /* Estimate a lower bound for the 1-norm of inv(C**H). The 1st */ /* and (N+1)th columns of WORK are used to store work vectors. */ sep[ks] = 0.; est = 0.; kase = 0; *(unsigned char *)normin = 'N'; L30: i__2 = *n - 1; zlacn2_(&i__2, &work[(*n + 1) * work_dim1 + 1], &work[work_offset] , &est, &kase, isave); if (kase != 0) { if (kase == 1) { /* Solve C**H*x = scale*b */ i__2 = *n - 1; zlatrs_("Upper", "Conjugate transpose", "Nonunit", normin, &i__2, &work[(work_dim1 << 1) + 2], ldwork, & work[work_offset], &scale, &rwork[1], &ierr); } else { /* Solve C*x = scale*b */ i__2 = *n - 1; zlatrs_("Upper", "No transpose", "Nonunit", normin, &i__2, &work[(work_dim1 << 1) + 2], ldwork, &work[ work_offset], &scale, &rwork[1], &ierr); } *(unsigned char *)normin = 'Y'; if (scale != 1.) { /* Multiply by 1/SCALE if doing so will not cause */ /* overflow. */ i__2 = *n - 1; ix = izamax_(&i__2, &work[work_offset], &c__1); i__2 = ix + work_dim1; xnorm = (d__1 = work[i__2].r, abs(d__1)) + (d__2 = d_imag( &work[ix + work_dim1]), abs(d__2)); if (scale < xnorm * smlnum || scale == 0.) { goto L40; } zdrscl_(n, &scale, &work[work_offset], &c__1); } goto L30; } sep[ks] = 1. / f2cmax(est,smlnum); } L40: ++ks; L50: ; } return 0; /* End of ZTRSNA */ } /* ztrsna_ */