#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 \b STRSNA */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download STRSNA + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE STRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, */ /* LDVR, S, SEP, MM, M, WORK, LDWORK, IWORK, */ /* INFO ) */ /* CHARACTER HOWMNY, JOB */ /* INTEGER INFO, LDT, LDVL, LDVR, LDWORK, M, MM, N */ /* LOGICAL SELECT( * ) */ /* INTEGER IWORK( * ) */ /* REAL S( * ), SEP( * ), T( LDT, * ), VL( LDVL, * ), */ /* $ VR( LDVR, * ), WORK( LDWORK, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > STRSNA estimates reciprocal condition numbers for specified */ /* > eigenvalues and/or right eigenvectors of a real upper */ /* > quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q */ /* > orthogonal). */ /* > */ /* > T must be in Schur canonical form (as returned by SHSEQR), that is, */ /* > block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each */ /* > 2-by-2 diagonal block has its diagonal elements equal and its */ /* > off-diagonal elements of opposite sign. */ /* > \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 eigenpair corresponding to a real eigenvalue w(j), */ /* > SELECT(j) must be set to .TRUE.. To select condition numbers */ /* > corresponding to a complex conjugate pair of eigenvalues w(j) */ /* > and w(j+1), either SELECT(j) or SELECT(j+1) or both, 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 REAL array, dimension (LDT,N) */ /* > The upper quasi-triangular matrix T, in Schur canonical form. */ /* > \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 REAL array, dimension (LDVL,M) */ /* > If JOB = 'E' or 'B', VL must contain left eigenvectors of T */ /* > (or of any Q*T*Q**T with Q orthogonal), corresponding to the */ /* > eigenpairs specified by HOWMNY and SELECT. The eigenvectors */ /* > must be stored in consecutive columns of VL, as returned by */ /* > SHSEIN or STREVC. */ /* > 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 REAL array, dimension (LDVR,M) */ /* > If JOB = 'E' or 'B', VR must contain right eigenvectors of T */ /* > (or of any Q*T*Q**T with Q orthogonal), corresponding to the */ /* > eigenpairs specified by HOWMNY and SELECT. The eigenvectors */ /* > must be stored in consecutive columns of VR, as returned by */ /* > SHSEIN or STREVC. */ /* > 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 REAL array, dimension (MM) */ /* > If JOB = 'E' or 'B', the reciprocal condition numbers of the */ /* > selected eigenvalues, stored in consecutive elements of the */ /* > array. For a complex conjugate pair of eigenvalues two */ /* > consecutive elements of S are set to the same value. 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 REAL array, dimension (MM) */ /* > If JOB = 'V' or 'B', the estimated reciprocal condition */ /* > numbers of the selected eigenvectors, stored in consecutive */ /* > elements of the array. For a complex eigenvector two */ /* > consecutive elements of SEP are set to the same value. If */ /* > the eigenvalues cannot be reordered to compute SEP(j), SEP(j) */ /* > is set to 0; this can only occur when the true value would be */ /* > very small anyway. */ /* > 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 REAL 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] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (2*(N-1)) */ /* > If JOB = 'E', IWORK 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 December 2016 */ /* > \ingroup realOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The reciprocal of the condition number of an eigenvalue lambda is */ /* > defined as */ /* > */ /* > S(lambda) = |v**T*u| / (norm(u)*norm(v)) */ /* > */ /* > where u and v are the right and left eigenvectors of T corresponding */ /* > to lambda; v**T denotes the 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 strsna_(char *job, char *howmny, logical *select, integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr, integer *ldvr, real *s, real *sep, integer *mm, integer *m, real * work, integer *ldwork, integer *iwork, 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; real r__1, r__2; /* Local variables */ integer kase; real cond; logical pair; integer ierr; real dumm, prod; integer ifst; real lnrm; extern real sdot_(integer *, real *, integer *, real *, integer *); integer ilst; real rnrm, prod1, prod2; extern real snrm2_(integer *, real *, integer *); integer i__, j, k; real scale, delta; extern logical lsame_(char *, char *); integer isave[3]; logical wants; real dummy[1]; integer n2; extern /* Subroutine */ int slacn2_(integer *, real *, real *, integer *, real *, integer *, integer *); extern real slapy2_(real *, real *); real cs; extern /* Subroutine */ int slabad_(real *, real *); integer nn, ks; real sn, mu; extern real slamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real bignum; logical wantbh; extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *); logical somcon; extern /* Subroutine */ int slaqtr_(logical *, logical *, integer *, real *, integer *, real *, real *, real *, real *, real *, integer *), strexc_(char *, integer *, real *, integer *, real *, integer *, integer *, integer *, real *, integer *); real smlnum; logical wantsp; real eps, est; /* -- LAPACK computational routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Decode and test the input parameters */ /* Parameter adjustments */ --select; 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; --iwork; /* Function Body */ wantbh = lsame_(job, "B"); wants = lsame_(job, "E") || wantbh; wantsp = lsame_(job, "V") || wantbh; somcon = lsame_(howmny, "S"); *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 { /* Set M to the number of eigenpairs for which condition numbers */ /* are required, and test MM. */ if (somcon) { *m = 0; pair = FALSE_; i__1 = *n; for (k = 1; k <= i__1; ++k) { if (pair) { pair = FALSE_; } else { if (k < *n) { if (t[k + 1 + k * t_dim1] == 0.f) { if (select[k]) { ++(*m); } } else { pair = TRUE_; if (select[k] || select[k + 1]) { *m += 2; } } } else { if (select[*n]) { ++(*m); } } } /* L10: */ } } else { *m = *n; } if (*mm < *m) { *info = -13; } else if (*ldwork < 1 || wantsp && *ldwork < *n) { *info = -16; } } if (*info != 0) { i__1 = -(*info); xerbla_("STRSNA", &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.f; } if (wantsp) { sep[1] = (r__1 = t[t_dim1 + 1], abs(r__1)); } return 0; } /* Get machine constants */ eps = slamch_("P"); smlnum = slamch_("S") / eps; bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); ks = 0; pair = FALSE_; i__1 = *n; for (k = 1; k <= i__1; ++k) { /* Determine whether T(k,k) begins a 1-by-1 or 2-by-2 block. */ if (pair) { pair = FALSE_; goto L60; } else { if (k < *n) { pair = t[k + 1 + k * t_dim1] != 0.f; } } /* Determine whether condition numbers are required for the k-th */ /* eigenpair. */ if (somcon) { if (pair) { if (! select[k] && ! select[k + 1]) { goto L60; } } else { if (! select[k]) { goto L60; } } } ++ks; if (wants) { /* Compute the reciprocal condition number of the k-th */ /* eigenvalue. */ if (! pair) { /* Real eigenvalue. */ prod = sdot_(n, &vr[ks * vr_dim1 + 1], &c__1, &vl[ks * vl_dim1 + 1], &c__1); rnrm = snrm2_(n, &vr[ks * vr_dim1 + 1], &c__1); lnrm = snrm2_(n, &vl[ks * vl_dim1 + 1], &c__1); s[ks] = abs(prod) / (rnrm * lnrm); } else { /* Complex eigenvalue. */ prod1 = sdot_(n, &vr[ks * vr_dim1 + 1], &c__1, &vl[ks * vl_dim1 + 1], &c__1); prod1 += sdot_(n, &vr[(ks + 1) * vr_dim1 + 1], &c__1, &vl[(ks + 1) * vl_dim1 + 1], &c__1); prod2 = sdot_(n, &vl[ks * vl_dim1 + 1], &c__1, &vr[(ks + 1) * vr_dim1 + 1], &c__1); prod2 -= sdot_(n, &vl[(ks + 1) * vl_dim1 + 1], &c__1, &vr[ks * vr_dim1 + 1], &c__1); r__1 = snrm2_(n, &vr[ks * vr_dim1 + 1], &c__1); r__2 = snrm2_(n, &vr[(ks + 1) * vr_dim1 + 1], &c__1); rnrm = slapy2_(&r__1, &r__2); r__1 = snrm2_(n, &vl[ks * vl_dim1 + 1], &c__1); r__2 = snrm2_(n, &vl[(ks + 1) * vl_dim1 + 1], &c__1); lnrm = slapy2_(&r__1, &r__2); cond = slapy2_(&prod1, &prod2) / (rnrm * lnrm); s[ks] = cond; s[ks + 1] = cond; } } if (wantsp) { /* Estimate the reciprocal condition number of the k-th */ /* eigenvector. */ /* Copy the matrix T to the array WORK and swap the diagonal */ /* block beginning at T(k,k) to the (1,1) position. */ slacpy_("Full", n, n, &t[t_offset], ldt, &work[work_offset], ldwork); ifst = k; ilst = 1; strexc_("No Q", n, &work[work_offset], ldwork, dummy, &c__1, & ifst, &ilst, &work[(*n + 1) * work_dim1 + 1], &ierr); if (ierr == 1 || ierr == 2) { /* Could not swap because blocks not well separated */ scale = 1.f; est = bignum; } else { /* Reordering successful */ if (work[work_dim1 + 2] == 0.f) { /* Form C = T22 - lambda*I in WORK(2:N,2:N). */ i__2 = *n; for (i__ = 2; i__ <= i__2; ++i__) { work[i__ + i__ * work_dim1] -= work[work_dim1 + 1]; /* L20: */ } n2 = 1; nn = *n - 1; } else { /* Triangularize the 2 by 2 block by unitary */ /* transformation U = [ cs i*ss ] */ /* [ i*ss cs ]. */ /* such that the (1,1) position of WORK is complex */ /* eigenvalue lambda with positive imaginary part. (2,2) */ /* position of WORK is the complex eigenvalue lambda */ /* with negative imaginary part. */ mu = sqrt((r__1 = work[(work_dim1 << 1) + 1], abs(r__1))) * sqrt((r__2 = work[work_dim1 + 2], abs(r__2))); delta = slapy2_(&mu, &work[work_dim1 + 2]); cs = mu / delta; sn = -work[work_dim1 + 2] / delta; /* Form */ /* C**T = WORK(2:N,2:N) + i*[rwork(1) ..... rwork(n-1) ] */ /* [ mu ] */ /* [ .. ] */ /* [ .. ] */ /* [ mu ] */ /* where C**T is transpose of matrix C, */ /* and RWORK is stored starting in the N+1-st column of */ /* WORK. */ i__2 = *n; for (j = 3; j <= i__2; ++j) { work[j * work_dim1 + 2] = cs * work[j * work_dim1 + 2] ; work[j + j * work_dim1] -= work[work_dim1 + 1]; /* L30: */ } work[(work_dim1 << 1) + 2] = 0.f; work[(*n + 1) * work_dim1 + 1] = mu * 2.f; i__2 = *n - 1; for (i__ = 2; i__ <= i__2; ++i__) { work[i__ + (*n + 1) * work_dim1] = sn * work[(i__ + 1) * work_dim1 + 1]; /* L40: */ } n2 = 2; nn = *n - 1 << 1; } /* Estimate norm(inv(C**T)) */ est = 0.f; kase = 0; L50: slacn2_(&nn, &work[(*n + 2) * work_dim1 + 1], &work[(*n + 4) * work_dim1 + 1], &iwork[1], &est, &kase, isave); if (kase != 0) { if (kase == 1) { if (n2 == 1) { /* Real eigenvalue: solve C**T*x = scale*c. */ i__2 = *n - 1; slaqtr_(&c_true, &c_true, &i__2, &work[(work_dim1 << 1) + 2], ldwork, dummy, &dumm, &scale, &work[(*n + 4) * work_dim1 + 1], &work[(* n + 6) * work_dim1 + 1], &ierr); } else { /* Complex eigenvalue: solve */ /* C**T*(p+iq) = scale*(c+id) in real arithmetic. */ i__2 = *n - 1; slaqtr_(&c_true, &c_false, &i__2, &work[( work_dim1 << 1) + 2], ldwork, &work[(*n + 1) * work_dim1 + 1], &mu, &scale, &work[(* n + 4) * work_dim1 + 1], &work[(*n + 6) * work_dim1 + 1], &ierr); } } else { if (n2 == 1) { /* Real eigenvalue: solve C*x = scale*c. */ i__2 = *n - 1; slaqtr_(&c_false, &c_true, &i__2, &work[( work_dim1 << 1) + 2], ldwork, dummy, & dumm, &scale, &work[(*n + 4) * work_dim1 + 1], &work[(*n + 6) * work_dim1 + 1], & ierr); } else { /* Complex eigenvalue: solve */ /* C*(p+iq) = scale*(c+id) in real arithmetic. */ i__2 = *n - 1; slaqtr_(&c_false, &c_false, &i__2, &work[( work_dim1 << 1) + 2], ldwork, &work[(*n + 1) * work_dim1 + 1], &mu, &scale, &work[(* n + 4) * work_dim1 + 1], &work[(*n + 6) * work_dim1 + 1], &ierr); } } goto L50; } } sep[ks] = scale / f2cmax(est,smlnum); if (pair) { sep[ks + 1] = sep[ks]; } } if (pair) { ++ks; } L60: ; } return 0; /* End of STRSNA */ } /* strsna_ */