#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 CTGSNA */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CTGSNA + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CTGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, */ /* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, */ /* IWORK, INFO ) */ /* CHARACTER HOWMNY, JOB */ /* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, M, MM, N */ /* LOGICAL SELECT( * ) */ /* INTEGER IWORK( * ) */ /* REAL DIF( * ), S( * ) */ /* COMPLEX A( LDA, * ), B( LDB, * ), VL( LDVL, * ), */ /* $ VR( LDVR, * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CTGSNA estimates reciprocal condition numbers for specified */ /* > eigenvalues and/or eigenvectors of a matrix pair (A, B). */ /* > */ /* > (A, B) must be in generalized Schur canonical form, that is, A and */ /* > B are both upper triangular. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOB */ /* > \verbatim */ /* > JOB is CHARACTER*1 */ /* > Specifies whether condition numbers are required for */ /* > eigenvalues (S) or eigenvectors (DIF): */ /* > = 'E': for eigenvalues only (S); */ /* > = 'V': for eigenvectors only (DIF); */ /* > = 'B': for both eigenvalues and eigenvectors (S and DIF). */ /* > \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 corresponding j-th eigenvalue and/or eigenvector, */ /* > 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 square matrix pair (A, B). N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA,N) */ /* > The upper triangular matrix A in the pair (A,B). */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is COMPLEX array, dimension (LDB,N) */ /* > The upper triangular matrix B in the pair (A, B). */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in] VL */ /* > \verbatim */ /* > VL is COMPLEX array, dimension (LDVL,M) */ /* > IF JOB = 'E' or 'B', VL must contain left eigenvectors of */ /* > (A, B), corresponding to the eigenpairs specified by HOWMNY */ /* > and SELECT. The eigenvectors must be stored in consecutive */ /* > columns of VL, as returned by CTGEVC. */ /* > 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 array, dimension (LDVR,M) */ /* > IF JOB = 'E' or 'B', VR must contain right eigenvectors of */ /* > (A, B), corresponding to the eigenpairs specified by HOWMNY */ /* > and SELECT. The eigenvectors must be stored in consecutive */ /* > columns of VR, as returned by CTGEVC. */ /* > If JOB = 'V', VR is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVR */ /* > \verbatim */ /* > LDVR is INTEGER */ /* > The leading dimension of the array VR. LDVR >= 1; */ /* > 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. */ /* > If JOB = 'V', S is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] DIF */ /* > \verbatim */ /* > DIF 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. */ /* > If the eigenvalues cannot be reordered to compute DIF(j), */ /* > DIF(j) is set to 0; this can only occur when the true value */ /* > would be very small anyway. */ /* > For each eigenvalue/vector specified by SELECT, DIF stores */ /* > a Frobenius norm-based estimate of Difl. */ /* > If JOB = 'E', DIF is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] MM */ /* > \verbatim */ /* > MM is INTEGER */ /* > The number of elements in the arrays S and DIF. MM >= M. */ /* > \endverbatim */ /* > */ /* > \param[out] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of elements of the arrays S and DIF used to store */ /* > the specified condition numbers; for each selected eigenvalue */ /* > one element is used. If HOWMNY = 'A', M is set to N. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */ /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. LWORK >= f2cmax(1,N). */ /* > If JOB = 'V' or 'B', LWORK >= f2cmax(1,2*N*N). */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (N+2) */ /* > 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 complexOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The reciprocal of the condition number of the i-th generalized */ /* > eigenvalue w = (a, b) is defined as */ /* > */ /* > S(I) = (|v**HAu|**2 + |v**HBu|**2)**(1/2) / (norm(u)*norm(v)) */ /* > */ /* > where u and v are the right and left eigenvectors of (A, B) */ /* > corresponding to w; |z| denotes the absolute value of the complex */ /* > number, and norm(u) denotes the 2-norm of the vector u. The pair */ /* > (a, b) corresponds to an eigenvalue w = a/b (= v**HAu/v**HBu) of the */ /* > matrix pair (A, B). If both a and b equal zero, then (A,B) is */ /* > singular and S(I) = -1 is returned. */ /* > */ /* > An approximate error bound on the chordal distance between the i-th */ /* > computed generalized eigenvalue w and the corresponding exact */ /* > eigenvalue lambda is */ /* > */ /* > chord(w, lambda) <= EPS * norm(A, B) / S(I), */ /* > */ /* > where EPS is the machine precision. */ /* > */ /* > The reciprocal of the condition number of the right eigenvector u */ /* > and left eigenvector v corresponding to the generalized eigenvalue w */ /* > is defined as follows. Suppose */ /* > */ /* > (A, B) = ( a * ) ( b * ) 1 */ /* > ( 0 A22 ),( 0 B22 ) n-1 */ /* > 1 n-1 1 n-1 */ /* > */ /* > Then the reciprocal condition number DIF(I) is */ /* > */ /* > Difl[(a, b), (A22, B22)] = sigma-f2cmin( Zl ) */ /* > */ /* > where sigma-f2cmin(Zl) denotes the smallest singular value of */ /* > */ /* > Zl = [ kron(a, In-1) -kron(1, A22) ] */ /* > [ kron(b, In-1) -kron(1, B22) ]. */ /* > */ /* > Here In-1 is the identity matrix of size n-1 and X**H is the conjugate */ /* > transpose of X. kron(X, Y) is the Kronecker product between the */ /* > matrices X and Y. */ /* > */ /* > We approximate the smallest singular value of Zl with an upper */ /* > bound. This is done by CLATDF. */ /* > */ /* > An approximate error bound for a computed eigenvector VL(i) or */ /* > VR(i) is given by */ /* > */ /* > EPS * norm(A, B) / DIF(i). */ /* > */ /* > See ref. [2-3] for more details and further references. */ /* > \endverbatim */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */ /* > Umea University, S-901 87 Umea, Sweden. */ /* > \par References: */ /* ================ */ /* > */ /* > \verbatim */ /* > */ /* > [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */ /* > Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */ /* > M.S. Moonen et al (eds), Linear Algebra for Large Scale and */ /* > Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */ /* > */ /* > [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */ /* > Eigenvalues of a Regular Matrix Pair (A, B) and Condition */ /* > Estimation: Theory, Algorithms and Software, Report */ /* > UMINF - 94.04, Department of Computing Science, Umea University, */ /* > S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. */ /* > To appear in Numerical Algorithms, 1996. */ /* > */ /* > [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */ /* > for Solving the Generalized Sylvester Equation and Estimating the */ /* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */ /* > Department of Computing Science, Umea University, S-901 87 Umea, */ /* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */ /* > Note 75. */ /* > To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int ctgsna_(char *job, char *howmny, logical *select, integer *n, complex *a, integer *lda, complex *b, integer *ldb, complex *vl, integer *ldvl, complex *vr, integer *ldvr, real *s, real *dif, integer *mm, integer *m, complex *work, integer *lwork, integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1; real r__1, r__2; complex q__1; /* Local variables */ real cond; integer ierr, ifst; real lnrm; complex yhax, yhbx; integer ilst; real rnrm; integer i__, k; real scale; extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer *, complex *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *); integer lwmin; logical wants; complex dummy[1]; integer n1, n2; extern real scnrm2_(integer *, complex *, integer *), slapy2_(real *, real *); complex dummy1[1]; extern /* Subroutine */ int slabad_(real *, real *); integer ks; extern real slamch_(char *); extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), ctgexc_(logical *, logical *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, integer *, integer *, integer *), xerbla_(char *, integer *, ftnlen); real bignum; logical wantbh, wantdf, somcon; extern /* Subroutine */ int ctgsyl_(char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, complex *, integer *, integer *, integer *); real smlnum; logical lquery; real eps; /* -- 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; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_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; --dif; --work; --iwork; /* Function Body */ wantbh = lsame_(job, "B"); wants = lsame_(job, "E") || wantbh; wantdf = lsame_(job, "V") || wantbh; somcon = lsame_(howmny, "S"); *info = 0; lquery = *lwork == -1; if (! wants && ! wantdf) { *info = -1; } else if (! lsame_(howmny, "A") && ! somcon) { *info = -2; } else if (*n < 0) { *info = -4; } else if (*lda < f2cmax(1,*n)) { *info = -6; } else if (*ldb < f2cmax(1,*n)) { *info = -8; } else if (wants && *ldvl < *n) { *info = -10; } else if (wants && *ldvr < *n) { *info = -12; } else { /* Set M to the number of eigenpairs for which condition numbers */ /* are required, and test MM. */ if (somcon) { *m = 0; i__1 = *n; for (k = 1; k <= i__1; ++k) { if (select[k]) { ++(*m); } /* L10: */ } } else { *m = *n; } if (*n == 0) { lwmin = 1; } else if (lsame_(job, "V") || lsame_(job, "B")) { lwmin = (*n << 1) * *n; } else { lwmin = *n; } work[1].r = (real) lwmin, work[1].i = 0.f; if (*mm < *m) { *info = -15; } else if (*lwork < lwmin && ! lquery) { *info = -18; } } if (*info != 0) { i__1 = -(*info); xerbla_("CTGSNA", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Get machine constants */ eps = slamch_("P"); smlnum = slamch_("S") / eps; bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); ks = 0; i__1 = *n; for (k = 1; k <= i__1; ++k) { /* Determine whether condition numbers are required for the k-th */ /* eigenpair. */ if (somcon) { if (! select[k]) { goto L20; } } ++ks; if (wants) { /* Compute the reciprocal condition number of the k-th */ /* eigenvalue. */ rnrm = scnrm2_(n, &vr[ks * vr_dim1 + 1], &c__1); lnrm = scnrm2_(n, &vl[ks * vl_dim1 + 1], &c__1); cgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[ks * vr_dim1 + 1] , &c__1, &c_b20, &work[1], &c__1); cdotc_(&q__1, n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1); yhax.r = q__1.r, yhax.i = q__1.i; cgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[ks * vr_dim1 + 1] , &c__1, &c_b20, &work[1], &c__1); cdotc_(&q__1, n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1); yhbx.r = q__1.r, yhbx.i = q__1.i; r__1 = c_abs(&yhax); r__2 = c_abs(&yhbx); cond = slapy2_(&r__1, &r__2); if (cond == 0.f) { s[ks] = -1.f; } else { s[ks] = cond / (rnrm * lnrm); } } if (wantdf) { if (*n == 1) { r__1 = c_abs(&a[a_dim1 + 1]); r__2 = c_abs(&b[b_dim1 + 1]); dif[ks] = slapy2_(&r__1, &r__2); } else { /* Estimate the reciprocal condition number of the k-th */ /* eigenvectors. */ /* Copy the matrix (A, B) to the array WORK and move the */ /* (k,k)th pair to the (1,1) position. */ clacpy_("Full", n, n, &a[a_offset], lda, &work[1], n); clacpy_("Full", n, n, &b[b_offset], ldb, &work[*n * *n + 1], n); ifst = k; ilst = 1; ctgexc_(&c_false, &c_false, n, &work[1], n, &work[*n * *n + 1] , n, dummy, &c__1, dummy1, &c__1, &ifst, &ilst, &ierr) ; if (ierr > 0) { /* Ill-conditioned problem - swap rejected. */ dif[ks] = 0.f; } else { /* Reordering successful, solve generalized Sylvester */ /* equation for R and L, */ /* A22 * R - L * A11 = A12 */ /* B22 * R - L * B11 = B12, */ /* and compute estimate of Difl[(A11,B11), (A22, B22)]. */ n1 = 1; n2 = *n - n1; i__ = *n * *n + 1; ctgsyl_("N", &c__3, &n2, &n1, &work[*n * n1 + n1 + 1], n, &work[1], n, &work[n1 + 1], n, &work[*n * n1 + n1 + i__], n, &work[i__], n, &work[n1 + i__], n, & scale, &dif[ks], dummy, &c__1, &iwork[1], &ierr); } } } L20: ; } work[1].r = (real) lwmin, work[1].i = 0.f; return 0; /* End of CTGSNA */ } /* ctgsna_ */