#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 DHSEIN */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DHSEIN + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, */ /* VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL, */ /* IFAILR, INFO ) */ /* CHARACTER EIGSRC, INITV, SIDE */ /* INTEGER INFO, LDH, LDVL, LDVR, M, MM, N */ /* LOGICAL SELECT( * ) */ /* INTEGER IFAILL( * ), IFAILR( * ) */ /* DOUBLE PRECISION H( LDH, * ), VL( LDVL, * ), VR( LDVR, * ), */ /* $ WI( * ), WORK( * ), WR( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DHSEIN uses inverse iteration to find specified right and/or left */ /* > eigenvectors of a real upper Hessenberg matrix H. */ /* > */ /* > The right eigenvector x and the left eigenvector y of the matrix H */ /* > corresponding to an eigenvalue w are defined by: */ /* > */ /* > H * x = w * x, y**h * H = w * y**h */ /* > */ /* > where y**h denotes the conjugate transpose of the vector y. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] SIDE */ /* > \verbatim */ /* > SIDE is CHARACTER*1 */ /* > = 'R': compute right eigenvectors only; */ /* > = 'L': compute left eigenvectors only; */ /* > = 'B': compute both right and left eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in] EIGSRC */ /* > \verbatim */ /* > EIGSRC is CHARACTER*1 */ /* > Specifies the source of eigenvalues supplied in (WR,WI): */ /* > = 'Q': the eigenvalues were found using DHSEQR; thus, if */ /* > H has zero subdiagonal elements, and so is */ /* > block-triangular, then the j-th eigenvalue can be */ /* > assumed to be an eigenvalue of the block containing */ /* > the j-th row/column. This property allows DHSEIN to */ /* > perform inverse iteration on just one diagonal block. */ /* > = 'N': no assumptions are made on the correspondence */ /* > between eigenvalues and diagonal blocks. In this */ /* > case, DHSEIN must always perform inverse iteration */ /* > using the whole matrix H. */ /* > \endverbatim */ /* > */ /* > \param[in] INITV */ /* > \verbatim */ /* > INITV is CHARACTER*1 */ /* > = 'N': no initial vectors are supplied; */ /* > = 'U': user-supplied initial vectors are stored in the arrays */ /* > VL and/or VR. */ /* > \endverbatim */ /* > */ /* > \param[in,out] SELECT */ /* > \verbatim */ /* > SELECT is LOGICAL array, dimension (N) */ /* > Specifies the eigenvectors to be computed. To select the */ /* > real eigenvector corresponding to a real eigenvalue WR(j), */ /* > SELECT(j) must be set to .TRUE.. To select the complex */ /* > eigenvector corresponding to a complex eigenvalue */ /* > (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)), */ /* > either SELECT(j) or SELECT(j+1) or both must be set to */ /* > .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is */ /* > .FALSE.. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix H. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] H */ /* > \verbatim */ /* > H is DOUBLE PRECISION array, dimension (LDH,N) */ /* > The upper Hessenberg matrix H. */ /* > If a NaN is detected in H, the routine will return with INFO=-6. */ /* > \endverbatim */ /* > */ /* > \param[in] LDH */ /* > \verbatim */ /* > LDH is INTEGER */ /* > The leading dimension of the array H. LDH >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] WR */ /* > \verbatim */ /* > WR is DOUBLE PRECISION array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[in] WI */ /* > \verbatim */ /* > WI is DOUBLE PRECISION array, dimension (N) */ /* > */ /* > On entry, the real and imaginary parts of the eigenvalues of */ /* > H; a complex conjugate pair of eigenvalues must be stored in */ /* > consecutive elements of WR and WI. */ /* > On exit, WR may have been altered since close eigenvalues */ /* > are perturbed slightly in searching for independent */ /* > eigenvectors. */ /* > \endverbatim */ /* > */ /* > \param[in,out] VL */ /* > \verbatim */ /* > VL is DOUBLE PRECISION array, dimension (LDVL,MM) */ /* > On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must */ /* > contain starting vectors for the inverse iteration for the */ /* > left eigenvectors; the starting vector for each eigenvector */ /* > must be in the same column(s) in which the eigenvector will */ /* > be stored. */ /* > On exit, if SIDE = 'L' or 'B', the left eigenvectors */ /* > specified by SELECT will be stored consecutively in the */ /* > columns of VL, in the same order as their eigenvalues. A */ /* > complex eigenvector corresponding to a complex eigenvalue is */ /* > stored in two consecutive columns, the first holding the real */ /* > part and the second the imaginary part. */ /* > If SIDE = 'R', VL is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVL */ /* > \verbatim */ /* > LDVL is INTEGER */ /* > The leading dimension of the array VL. */ /* > LDVL >= f2cmax(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise. */ /* > \endverbatim */ /* > */ /* > \param[in,out] VR */ /* > \verbatim */ /* > VR is DOUBLE PRECISION array, dimension (LDVR,MM) */ /* > On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must */ /* > contain starting vectors for the inverse iteration for the */ /* > right eigenvectors; the starting vector for each eigenvector */ /* > must be in the same column(s) in which the eigenvector will */ /* > be stored. */ /* > On exit, if SIDE = 'R' or 'B', the right eigenvectors */ /* > specified by SELECT will be stored consecutively in the */ /* > columns of VR, in the same order as their eigenvalues. A */ /* > complex eigenvector corresponding to a complex eigenvalue is */ /* > stored in two consecutive columns, the first holding the real */ /* > part and the second the imaginary part. */ /* > If SIDE = 'L', VR is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDVR */ /* > \verbatim */ /* > LDVR is INTEGER */ /* > The leading dimension of the array VR. */ /* > LDVR >= f2cmax(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. */ /* > \endverbatim */ /* > */ /* > \param[in] MM */ /* > \verbatim */ /* > MM is INTEGER */ /* > The number of columns in the arrays VL and/or VR. MM >= M. */ /* > \endverbatim */ /* > */ /* > \param[out] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of columns in the arrays VL and/or VR required to */ /* > store the eigenvectors; each selected real eigenvector */ /* > occupies one column and each selected complex eigenvector */ /* > occupies two columns. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension ((N+2)*N) */ /* > \endverbatim */ /* > */ /* > \param[out] IFAILL */ /* > \verbatim */ /* > IFAILL is INTEGER array, dimension (MM) */ /* > If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left */ /* > eigenvector in the i-th column of VL (corresponding to the */ /* > eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the */ /* > eigenvector converged satisfactorily. If the i-th and (i+1)th */ /* > columns of VL hold a complex eigenvector, then IFAILL(i) and */ /* > IFAILL(i+1) are set to the same value. */ /* > If SIDE = 'R', IFAILL is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] IFAILR */ /* > \verbatim */ /* > IFAILR is INTEGER array, dimension (MM) */ /* > If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right */ /* > eigenvector in the i-th column of VR (corresponding to the */ /* > eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the */ /* > eigenvector converged satisfactorily. If the i-th and (i+1)th */ /* > columns of VR hold a complex eigenvector, then IFAILR(i) and */ /* > IFAILR(i+1) are set to the same value. */ /* > If SIDE = 'L', IFAILR 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 */ /* > > 0: if INFO = i, i is the number of eigenvectors which */ /* > failed to converge; see IFAILL and IFAILR for further */ /* > details. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup doubleOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > Each eigenvector is normalized so that the element of largest */ /* > magnitude has magnitude 1; here the magnitude of a complex number */ /* > (x,y) is taken to be |x|+|y|. */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int dhsein_(char *side, char *eigsrc, char *initv, logical * select, integer *n, doublereal *h__, integer *ldh, doublereal *wr, doublereal *wi, doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, integer *mm, integer *m, doublereal *work, integer * ifaill, integer *ifailr, integer *info) { /* System generated locals */ integer h_dim1, h_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2; doublereal d__1, d__2; /* Local variables */ logical pair; doublereal unfl; integer i__, k; extern logical lsame_(char *, char *); integer iinfo; logical leftv, bothv; doublereal hnorm; integer kl; extern doublereal dlamch_(char *); extern /* Subroutine */ int dlaein_(logical *, logical *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal * , doublereal *, doublereal *, integer *); integer kr; extern doublereal dlanhs_(char *, integer *, doublereal *, integer *, doublereal *); extern logical disnan_(doublereal *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; logical noinit; integer ldwork; logical rightv, fromqr; doublereal smlnum; integer kln, ksi; doublereal wki; integer ksr; doublereal ulp, wkr, eps3; /* -- 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; h_dim1 = *ldh; h_offset = 1 + h_dim1 * 1; h__ -= h_offset; --wr; --wi; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1 * 1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1 * 1; vr -= vr_offset; --work; --ifaill; --ifailr; /* Function Body */ bothv = lsame_(side, "B"); rightv = lsame_(side, "R") || bothv; leftv = lsame_(side, "L") || bothv; fromqr = lsame_(eigsrc, "Q"); noinit = lsame_(initv, "N"); /* Set M to the number of columns required to store the selected */ /* eigenvectors, and standardize the array SELECT. */ *m = 0; pair = FALSE_; i__1 = *n; for (k = 1; k <= i__1; ++k) { if (pair) { pair = FALSE_; select[k] = FALSE_; } else { if (wi[k] == 0.) { if (select[k]) { ++(*m); } } else { pair = TRUE_; if (select[k] || select[k + 1]) { select[k] = TRUE_; *m += 2; } } } /* L10: */ } *info = 0; if (! rightv && ! leftv) { *info = -1; } else if (! fromqr && ! lsame_(eigsrc, "N")) { *info = -2; } else if (! noinit && ! lsame_(initv, "U")) { *info = -3; } else if (*n < 0) { *info = -5; } else if (*ldh < f2cmax(1,*n)) { *info = -7; } else if (*ldvl < 1 || leftv && *ldvl < *n) { *info = -11; } else if (*ldvr < 1 || rightv && *ldvr < *n) { *info = -13; } else if (*mm < *m) { *info = -14; } if (*info != 0) { i__1 = -(*info); xerbla_("DHSEIN", &i__1, (ftnlen)6); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* Set machine-dependent constants. */ unfl = dlamch_("Safe minimum"); ulp = dlamch_("Precision"); smlnum = unfl * (*n / ulp); bignum = (1. - ulp) / smlnum; ldwork = *n + 1; kl = 1; kln = 0; if (fromqr) { kr = 0; } else { kr = *n; } ksr = 1; i__1 = *n; for (k = 1; k <= i__1; ++k) { if (select[k]) { /* Compute eigenvector(s) corresponding to W(K). */ if (fromqr) { /* If affiliation of eigenvalues is known, check whether */ /* the matrix splits. */ /* Determine KL and KR such that 1 <= KL <= K <= KR <= N */ /* and H(KL,KL-1) and H(KR+1,KR) are zero (or KL = 1 or */ /* KR = N). */ /* Then inverse iteration can be performed with the */ /* submatrix H(KL:N,KL:N) for a left eigenvector, and with */ /* the submatrix H(1:KR,1:KR) for a right eigenvector. */ i__2 = kl + 1; for (i__ = k; i__ >= i__2; --i__) { if (h__[i__ + (i__ - 1) * h_dim1] == 0.) { goto L30; } /* L20: */ } L30: kl = i__; if (k > kr) { i__2 = *n - 1; for (i__ = k; i__ <= i__2; ++i__) { if (h__[i__ + 1 + i__ * h_dim1] == 0.) { goto L50; } /* L40: */ } L50: kr = i__; } } if (kl != kln) { kln = kl; /* Compute infinity-norm of submatrix H(KL:KR,KL:KR) if it */ /* has not ben computed before. */ i__2 = kr - kl + 1; hnorm = dlanhs_("I", &i__2, &h__[kl + kl * h_dim1], ldh, & work[1]); if (disnan_(&hnorm)) { *info = -6; return 0; } else if (hnorm > 0.) { eps3 = hnorm * ulp; } else { eps3 = smlnum; } } /* Perturb eigenvalue if it is close to any previous */ /* selected eigenvalues affiliated to the submatrix */ /* H(KL:KR,KL:KR). Close roots are modified by EPS3. */ wkr = wr[k]; wki = wi[k]; L60: i__2 = kl; for (i__ = k - 1; i__ >= i__2; --i__) { if (select[i__] && (d__1 = wr[i__] - wkr, abs(d__1)) + (d__2 = wi[i__] - wki, abs(d__2)) < eps3) { wkr += eps3; goto L60; } /* L70: */ } wr[k] = wkr; pair = wki != 0.; if (pair) { ksi = ksr + 1; } else { ksi = ksr; } if (leftv) { /* Compute left eigenvector. */ i__2 = *n - kl + 1; dlaein_(&c_false, &noinit, &i__2, &h__[kl + kl * h_dim1], ldh, &wkr, &wki, &vl[kl + ksr * vl_dim1], &vl[kl + ksi * vl_dim1], &work[1], &ldwork, &work[*n * *n + *n + 1], &eps3, &smlnum, &bignum, &iinfo); if (iinfo > 0) { if (pair) { *info += 2; } else { ++(*info); } ifaill[ksr] = k; ifaill[ksi] = k; } else { ifaill[ksr] = 0; ifaill[ksi] = 0; } i__2 = kl - 1; for (i__ = 1; i__ <= i__2; ++i__) { vl[i__ + ksr * vl_dim1] = 0.; /* L80: */ } if (pair) { i__2 = kl - 1; for (i__ = 1; i__ <= i__2; ++i__) { vl[i__ + ksi * vl_dim1] = 0.; /* L90: */ } } } if (rightv) { /* Compute right eigenvector. */ dlaein_(&c_true, &noinit, &kr, &h__[h_offset], ldh, &wkr, & wki, &vr[ksr * vr_dim1 + 1], &vr[ksi * vr_dim1 + 1], & work[1], &ldwork, &work[*n * *n + *n + 1], &eps3, & smlnum, &bignum, &iinfo); if (iinfo > 0) { if (pair) { *info += 2; } else { ++(*info); } ifailr[ksr] = k; ifailr[ksi] = k; } else { ifailr[ksr] = 0; ifailr[ksi] = 0; } i__2 = *n; for (i__ = kr + 1; i__ <= i__2; ++i__) { vr[i__ + ksr * vr_dim1] = 0.; /* L100: */ } if (pair) { i__2 = *n; for (i__ = kr + 1; i__ <= i__2; ++i__) { vr[i__ + ksi * vr_dim1] = 0.; /* L110: */ } } } if (pair) { ksr += 2; } else { ++ksr; } } /* L120: */ } return 0; /* End of DHSEIN */ } /* dhsein_ */