#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 ZTRSEN */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZTRSEN + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZTRSEN( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, W, M, S, */ /* SEP, WORK, LWORK, INFO ) */ /* CHARACTER COMPQ, JOB */ /* INTEGER INFO, LDQ, LDT, LWORK, M, N */ /* DOUBLE PRECISION S, SEP */ /* LOGICAL SELECT( * ) */ /* COMPLEX*16 Q( LDQ, * ), T( LDT, * ), W( * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZTRSEN reorders the Schur factorization of a complex matrix */ /* > A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in */ /* > the leading positions on the diagonal of the upper triangular matrix */ /* > T, and the leading columns of Q form an orthonormal basis of the */ /* > corresponding right invariant subspace. */ /* > */ /* > Optionally the routine computes the reciprocal condition numbers of */ /* > the cluster of eigenvalues and/or the invariant subspace. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOB */ /* > \verbatim */ /* > JOB is CHARACTER*1 */ /* > Specifies whether condition numbers are required for the */ /* > cluster of eigenvalues (S) or the invariant subspace (SEP): */ /* > = 'N': none; */ /* > = 'E': for eigenvalues only (S); */ /* > = 'V': for invariant subspace only (SEP); */ /* > = 'B': for both eigenvalues and invariant subspace (S and */ /* > SEP). */ /* > \endverbatim */ /* > */ /* > \param[in] COMPQ */ /* > \verbatim */ /* > COMPQ is CHARACTER*1 */ /* > = 'V': update the matrix Q of Schur vectors; */ /* > = 'N': do not update Q. */ /* > \endverbatim */ /* > */ /* > \param[in] SELECT */ /* > \verbatim */ /* > SELECT is LOGICAL array, dimension (N) */ /* > SELECT specifies the eigenvalues in the selected cluster. To */ /* > select the j-th eigenvalue, SELECT(j) must be set to .TRUE.. */ /* > \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) */ /* > On entry, the upper triangular matrix T. */ /* > On exit, T is overwritten by the reordered matrix T, with the */ /* > selected eigenvalues as the leading diagonal elements. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. LDT >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] Q */ /* > \verbatim */ /* > Q is COMPLEX*16 array, dimension (LDQ,N) */ /* > On entry, if COMPQ = 'V', the matrix Q of Schur vectors. */ /* > On exit, if COMPQ = 'V', Q has been postmultiplied by the */ /* > unitary transformation matrix which reorders T; the leading M */ /* > columns of Q form an orthonormal basis for the specified */ /* > invariant subspace. */ /* > If COMPQ = 'N', Q is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQ */ /* > \verbatim */ /* > LDQ is INTEGER */ /* > The leading dimension of the array Q. */ /* > LDQ >= 1; and if COMPQ = 'V', LDQ >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] W */ /* > \verbatim */ /* > W is COMPLEX*16 array, dimension (N) */ /* > The reordered eigenvalues of T, in the same order as they */ /* > appear on the diagonal of T. */ /* > \endverbatim */ /* > */ /* > \param[out] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The dimension of the specified invariant subspace. */ /* > 0 <= M <= N. */ /* > \endverbatim */ /* > */ /* > \param[out] S */ /* > \verbatim */ /* > S is DOUBLE PRECISION */ /* > If JOB = 'E' or 'B', S is a lower bound on the reciprocal */ /* > condition number for the selected cluster of eigenvalues. */ /* > S cannot underestimate the true reciprocal condition number */ /* > by more than a factor of sqrt(N). If M = 0 or N, S = 1. */ /* > If JOB = 'N' or 'V', S is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] SEP */ /* > \verbatim */ /* > SEP is DOUBLE PRECISION */ /* > If JOB = 'V' or 'B', SEP is the estimated reciprocal */ /* > condition number of the specified invariant subspace. If */ /* > M = 0 or N, SEP = norm(T). */ /* > If JOB = 'N' or 'E', SEP is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX*16 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 JOB = 'N', LWORK >= 1; */ /* > if JOB = 'E', LWORK = f2cmax(1,M*(N-M)); */ /* > if JOB = 'V' or 'B', LWORK >= f2cmax(1,2*M*(N-M)). */ /* > */ /* > 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] 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 complex16OTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > ZTRSEN first collects the selected eigenvalues by computing a unitary */ /* > transformation Z to move them to the top left corner of T. In other */ /* > words, the selected eigenvalues are the eigenvalues of T11 in: */ /* > */ /* > Z**H * T * Z = ( T11 T12 ) n1 */ /* > ( 0 T22 ) n2 */ /* > n1 n2 */ /* > */ /* > where N = n1+n2. The first */ /* > n1 columns of Z span the specified invariant subspace of T. */ /* > */ /* > If T has been obtained from the Schur factorization of a matrix */ /* > A = Q*T*Q**H, then the reordered Schur factorization of A is given by */ /* > A = (Q*Z)*(Z**H*T*Z)*(Q*Z)**H, and the first n1 columns of Q*Z span the */ /* > corresponding invariant subspace of A. */ /* > */ /* > The reciprocal condition number of the average of the eigenvalues of */ /* > T11 may be returned in S. S lies between 0 (very badly conditioned) */ /* > and 1 (very well conditioned). It is computed as follows. First we */ /* > compute R so that */ /* > */ /* > P = ( I R ) n1 */ /* > ( 0 0 ) n2 */ /* > n1 n2 */ /* > */ /* > is the projector on the invariant subspace associated with T11. */ /* > R is the solution of the Sylvester equation: */ /* > */ /* > T11*R - R*T22 = T12. */ /* > */ /* > Let F-norm(M) denote the Frobenius-norm of M and 2-norm(M) denote */ /* > the two-norm of M. Then S is computed as the lower bound */ /* > */ /* > (1 + F-norm(R)**2)**(-1/2) */ /* > */ /* > on the reciprocal of 2-norm(P), the true reciprocal condition number. */ /* > S cannot underestimate 1 / 2-norm(P) by more than a factor of */ /* > sqrt(N). */ /* > */ /* > An approximate error bound for the computed average of the */ /* > eigenvalues of T11 is */ /* > */ /* > EPS * norm(T) / S */ /* > */ /* > where EPS is the machine precision. */ /* > */ /* > The reciprocal condition number of the right invariant subspace */ /* > spanned by the first n1 columns of Z (or of Q*Z) is returned in SEP. */ /* > SEP is defined as the separation of T11 and T22: */ /* > */ /* > sep( T11, T22 ) = sigma-f2cmin( C ) */ /* > */ /* > where sigma-f2cmin(C) is the smallest singular value of the */ /* > n1*n2-by-n1*n2 matrix */ /* > */ /* > C = kprod( I(n2), T11 ) - kprod( transpose(T22), I(n1) ) */ /* > */ /* > I(m) is an m by m identity matrix, and kprod denotes the Kronecker */ /* > product. We estimate sigma-f2cmin(C) by the reciprocal of an estimate of */ /* > the 1-norm of inverse(C). The true reciprocal 1-norm of inverse(C) */ /* > cannot differ from sigma-f2cmin(C) by more than a factor of sqrt(n1*n2). */ /* > */ /* > When SEP is small, small changes in T can cause large changes in */ /* > the invariant subspace. An approximate bound on the maximum angular */ /* > error in the computed right invariant subspace is */ /* > */ /* > EPS * norm(T) / SEP */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int ztrsen_(char *job, char *compq, logical *select, integer *n, doublecomplex *t, integer *ldt, doublecomplex *q, integer *ldq, doublecomplex *w, integer *m, doublereal *s, doublereal *sep, doublecomplex *work, integer *lwork, integer *info) { /* System generated locals */ integer q_dim1, q_offset, t_dim1, t_offset, i__1, i__2, i__3; /* Local variables */ integer kase, ierr, k; doublereal scale; extern logical lsame_(char *, char *); integer isave[3], lwmin; logical wantq, wants; doublereal rnorm; integer n1, n2; doublereal rwork[1]; extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, doublecomplex *, doublereal *, integer *, integer *); integer nn, ks; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); logical wantbh; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); logical wantsp; extern /* Subroutine */ int ztrexc_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *, integer *); logical lquery; extern /* Subroutine */ int ztrsyl_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *); doublereal 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; q_dim1 = *ldq; q_offset = 1 + q_dim1 * 1; q -= q_offset; --w; --work; /* Function Body */ wantbh = lsame_(job, "B"); wants = lsame_(job, "E") || wantbh; wantsp = lsame_(job, "V") || wantbh; wantq = lsame_(compq, "V"); /* Set M to the number of selected eigenvalues. */ *m = 0; i__1 = *n; for (k = 1; k <= i__1; ++k) { if (select[k]) { ++(*m); } /* L10: */ } n1 = *m; n2 = *n - *m; nn = n1 * n2; *info = 0; lquery = *lwork == -1; if (wantsp) { /* Computing MAX */ i__1 = 1, i__2 = nn << 1; lwmin = f2cmax(i__1,i__2); } else if (lsame_(job, "N")) { lwmin = 1; } else if (lsame_(job, "E")) { lwmin = f2cmax(1,nn); } if (! lsame_(job, "N") && ! wants && ! wantsp) { *info = -1; } else if (! lsame_(compq, "N") && ! wantq) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*ldt < f2cmax(1,*n)) { *info = -6; } else if (*ldq < 1 || wantq && *ldq < *n) { *info = -8; } else if (*lwork < lwmin && ! lquery) { *info = -14; } if (*info == 0) { work[1].r = (doublereal) lwmin, work[1].i = 0.; } if (*info != 0) { i__1 = -(*info); xerbla_("ZTRSEN", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*m == *n || *m == 0) { if (wants) { *s = 1.; } if (wantsp) { *sep = zlange_("1", n, n, &t[t_offset], ldt, rwork); } goto L40; } /* Collect the selected eigenvalues at the top left corner of T. */ ks = 0; i__1 = *n; for (k = 1; k <= i__1; ++k) { if (select[k]) { ++ks; /* Swap the K-th eigenvalue to position KS. */ if (k != ks) { ztrexc_(compq, n, &t[t_offset], ldt, &q[q_offset], ldq, &k, & ks, &ierr); } } /* L20: */ } if (wants) { /* Solve the Sylvester equation for R: */ /* T11*R - R*T22 = scale*T12 */ zlacpy_("F", &n1, &n2, &t[(n1 + 1) * t_dim1 + 1], ldt, &work[1], &n1); ztrsyl_("N", "N", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 + 1 + (n1 + 1) * t_dim1], ldt, &work[1], &n1, &scale, &ierr); /* Estimate the reciprocal of the condition number of the cluster */ /* of eigenvalues. */ rnorm = zlange_("F", &n1, &n2, &work[1], &n1, rwork); if (rnorm == 0.) { *s = 1.; } else { *s = scale / (sqrt(scale * scale / rnorm + rnorm) * sqrt(rnorm)); } } if (wantsp) { /* Estimate sep(T11,T22). */ est = 0.; kase = 0; L30: zlacn2_(&nn, &work[nn + 1], &work[1], &est, &kase, isave); if (kase != 0) { if (kase == 1) { /* Solve T11*R - R*T22 = scale*X. */ ztrsyl_("N", "N", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 + 1 + (n1 + 1) * t_dim1], ldt, &work[1], &n1, &scale, & ierr); } else { /* Solve T11**H*R - R*T22**H = scale*X. */ ztrsyl_("C", "C", &c_n1, &n1, &n2, &t[t_offset], ldt, &t[n1 + 1 + (n1 + 1) * t_dim1], ldt, &work[1], &n1, &scale, & ierr); } goto L30; } *sep = scale / est; } L40: /* Copy reordered eigenvalues to W. */ i__1 = *n; for (k = 1; k <= i__1; ++k) { i__2 = k; i__3 = k + k * t_dim1; w[i__2].r = t[i__3].r, w[i__2].i = t[i__3].i; /* L50: */ } work[1].r = (doublereal) lwmin, work[1].i = 0.; return 0; /* End of ZTRSEN */ } /* ztrsen_ */