#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 ZLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and defl ate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZLAQR3 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, */ /* IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, */ /* NV, WV, LDWV, WORK, LWORK ) */ /* INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV, */ /* $ LDZ, LWORK, N, ND, NH, NS, NV, NW */ /* LOGICAL WANTT, WANTZ */ /* COMPLEX*16 H( LDH, * ), SH( * ), T( LDT, * ), V( LDV, * ), */ /* $ WORK( * ), WV( LDWV, * ), Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > Aggressive early deflation: */ /* > */ /* > ZLAQR3 accepts as input an upper Hessenberg matrix */ /* > H and performs an unitary similarity transformation */ /* > designed to detect and deflate fully converged eigenvalues from */ /* > a trailing principal submatrix. On output H has been over- */ /* > written by a new Hessenberg matrix that is a perturbation of */ /* > an unitary similarity transformation of H. It is to be */ /* > hoped that the final version of H has many zero subdiagonal */ /* > entries. */ /* > */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] WANTT */ /* > \verbatim */ /* > WANTT is LOGICAL */ /* > If .TRUE., then the Hessenberg matrix H is fully updated */ /* > so that the triangular Schur factor may be */ /* > computed (in cooperation with the calling subroutine). */ /* > If .FALSE., then only enough of H is updated to preserve */ /* > the eigenvalues. */ /* > \endverbatim */ /* > */ /* > \param[in] WANTZ */ /* > \verbatim */ /* > WANTZ is LOGICAL */ /* > If .TRUE., then the unitary matrix Z is updated so */ /* > so that the unitary Schur factor may be computed */ /* > (in cooperation with the calling subroutine). */ /* > If .FALSE., then Z is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix H and (if WANTZ is .TRUE.) the */ /* > order of the unitary matrix Z. */ /* > \endverbatim */ /* > */ /* > \param[in] KTOP */ /* > \verbatim */ /* > KTOP is INTEGER */ /* > It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. */ /* > KBOT and KTOP together determine an isolated block */ /* > along the diagonal of the Hessenberg matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] KBOT */ /* > \verbatim */ /* > KBOT is INTEGER */ /* > It is assumed without a check that either */ /* > KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together */ /* > determine an isolated block along the diagonal of the */ /* > Hessenberg matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] NW */ /* > \verbatim */ /* > NW is INTEGER */ /* > Deflation window size. 1 <= NW <= (KBOT-KTOP+1). */ /* > \endverbatim */ /* > */ /* > \param[in,out] H */ /* > \verbatim */ /* > H is COMPLEX*16 array, dimension (LDH,N) */ /* > On input the initial N-by-N section of H stores the */ /* > Hessenberg matrix undergoing aggressive early deflation. */ /* > On output H has been transformed by a unitary */ /* > similarity transformation, perturbed, and the returned */ /* > to Hessenberg form that (it is to be hoped) has some */ /* > zero subdiagonal entries. */ /* > \endverbatim */ /* > */ /* > \param[in] LDH */ /* > \verbatim */ /* > LDH is INTEGER */ /* > Leading dimension of H just as declared in the calling */ /* > subroutine. N <= LDH */ /* > \endverbatim */ /* > */ /* > \param[in] ILOZ */ /* > \verbatim */ /* > ILOZ is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[in] IHIZ */ /* > \verbatim */ /* > IHIZ is INTEGER */ /* > Specify the rows of Z to which transformations must be */ /* > applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N. */ /* > \endverbatim */ /* > */ /* > \param[in,out] Z */ /* > \verbatim */ /* > Z is COMPLEX*16 array, dimension (LDZ,N) */ /* > IF WANTZ is .TRUE., then on output, the unitary */ /* > similarity transformation mentioned above has been */ /* > accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. */ /* > If WANTZ is .FALSE., then Z is unreferenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDZ */ /* > \verbatim */ /* > LDZ is INTEGER */ /* > The leading dimension of Z just as declared in the */ /* > calling subroutine. 1 <= LDZ. */ /* > \endverbatim */ /* > */ /* > \param[out] NS */ /* > \verbatim */ /* > NS is INTEGER */ /* > The number of unconverged (ie approximate) eigenvalues */ /* > returned in SR and SI that may be used as shifts by the */ /* > calling subroutine. */ /* > \endverbatim */ /* > */ /* > \param[out] ND */ /* > \verbatim */ /* > ND is INTEGER */ /* > The number of converged eigenvalues uncovered by this */ /* > subroutine. */ /* > \endverbatim */ /* > */ /* > \param[out] SH */ /* > \verbatim */ /* > SH is COMPLEX*16 array, dimension (KBOT) */ /* > On output, approximate eigenvalues that may */ /* > be used for shifts are stored in SH(KBOT-ND-NS+1) */ /* > through SR(KBOT-ND). Converged eigenvalues are */ /* > stored in SH(KBOT-ND+1) through SH(KBOT). */ /* > \endverbatim */ /* > */ /* > \param[out] V */ /* > \verbatim */ /* > V is COMPLEX*16 array, dimension (LDV,NW) */ /* > An NW-by-NW work array. */ /* > \endverbatim */ /* > */ /* > \param[in] LDV */ /* > \verbatim */ /* > LDV is INTEGER */ /* > The leading dimension of V just as declared in the */ /* > calling subroutine. NW <= LDV */ /* > \endverbatim */ /* > */ /* > \param[in] NH */ /* > \verbatim */ /* > NH is INTEGER */ /* > The number of columns of T. NH >= NW. */ /* > \endverbatim */ /* > */ /* > \param[out] T */ /* > \verbatim */ /* > T is COMPLEX*16 array, dimension (LDT,NW) */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of T just as declared in the */ /* > calling subroutine. NW <= LDT */ /* > \endverbatim */ /* > */ /* > \param[in] NV */ /* > \verbatim */ /* > NV is INTEGER */ /* > The number of rows of work array WV available for */ /* > workspace. NV >= NW. */ /* > \endverbatim */ /* > */ /* > \param[out] WV */ /* > \verbatim */ /* > WV is COMPLEX*16 array, dimension (LDWV,NW) */ /* > \endverbatim */ /* > */ /* > \param[in] LDWV */ /* > \verbatim */ /* > LDWV is INTEGER */ /* > The leading dimension of W just as declared in the */ /* > calling subroutine. NW <= LDV */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX*16 array, dimension (LWORK) */ /* > On exit, WORK(1) is set to an estimate of the optimal value */ /* > of LWORK for the given values of N, NW, KTOP and KBOT. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the work array WORK. LWORK = 2*NW */ /* > suffices, but greater efficiency may result from larger */ /* > values of LWORK. */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; ZLAQR3 */ /* > only estimates the optimal workspace size for the given */ /* > values of N, NW, KTOP and KBOT. The estimate is returned */ /* > in WORK(1). No error message related to LWORK is issued */ /* > by XERBLA. Neither H nor Z are accessed. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup complex16OTHERauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Karen Braman and Ralph Byers, Department of Mathematics, */ /* > University of Kansas, USA */ /* > */ /* ===================================================================== */ /* Subroutine */ int zlaqr3_(logical *wantt, logical *wantz, integer *n, integer *ktop, integer *kbot, integer *nw, doublecomplex *h__, integer *ldh, integer *iloz, integer *ihiz, doublecomplex *z__, integer *ldz, integer *ns, integer *nd, doublecomplex *sh, doublecomplex *v, integer *ldv, integer *nh, doublecomplex *t, integer *ldt, integer *nv, doublecomplex *wv, integer *ldwv, doublecomplex *work, integer *lwork) { /* System generated locals */ integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1, wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2, d__3, d__4, d__5, d__6; doublecomplex z__1, z__2; /* Local variables */ doublecomplex beta; integer kcol, info, nmin, ifst, ilst, ltop, krow, i__, j; doublecomplex s; extern /* Subroutine */ int zlarf_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *); integer infqr; extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); integer kwtop; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), dlabad_(doublereal *, doublereal *), zlaqr4_(logical *, logical *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer * ); extern doublereal dlamch_(char *); integer jw; doublereal safmin, safmax; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *), zlahqr_(logical *, logical *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); doublereal smlnum; extern /* Subroutine */ int ztrexc_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *, integer *); integer lwkopt; extern /* Subroutine */ int zunmhr_(char *, char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer * ); doublereal foo; integer kln; doublecomplex tau; integer knt; doublereal ulp; integer lwk1, lwk2, lwk3; /* -- LAPACK auxiliary routine (version 3.7.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* June 2016 */ /* ================================================================ */ /* ==== Estimate optimal workspace. ==== */ /* Parameter adjustments */ h_dim1 = *ldh; h_offset = 1 + h_dim1 * 1; h__ -= h_offset; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --sh; v_dim1 = *ldv; v_offset = 1 + v_dim1 * 1; v -= v_offset; t_dim1 = *ldt; t_offset = 1 + t_dim1 * 1; t -= t_offset; wv_dim1 = *ldwv; wv_offset = 1 + wv_dim1 * 1; wv -= wv_offset; --work; /* Function Body */ /* Computing MIN */ i__1 = *nw, i__2 = *kbot - *ktop + 1; jw = f2cmin(i__1,i__2); if (jw <= 2) { lwkopt = 1; } else { /* ==== Workspace query call to ZGEHRD ==== */ i__1 = jw - 1; zgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], & c_n1, &info); lwk1 = (integer) work[1].r; /* ==== Workspace query call to ZUNMHR ==== */ i__1 = jw - 1; zunmhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &v[v_offset], ldv, &work[1], &c_n1, &info); lwk2 = (integer) work[1].r; /* ==== Workspace query call to ZLAQR4 ==== */ zlaqr4_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[1], &c__1, &jw, &v[v_offset], ldv, &work[1], &c_n1, &infqr); lwk3 = (integer) work[1].r; /* ==== Optimal workspace ==== */ /* Computing MAX */ i__1 = jw + f2cmax(lwk1,lwk2); lwkopt = f2cmax(i__1,lwk3); } /* ==== Quick return in case of workspace query. ==== */ if (*lwork == -1) { d__1 = (doublereal) lwkopt; z__1.r = d__1, z__1.i = 0.; work[1].r = z__1.r, work[1].i = z__1.i; return 0; } /* ==== Nothing to do ... */ /* ... for an empty active block ... ==== */ *ns = 0; *nd = 0; work[1].r = 1., work[1].i = 0.; if (*ktop > *kbot) { return 0; } /* ... nor for an empty deflation window. ==== */ if (*nw < 1) { return 0; } /* ==== Machine constants ==== */ safmin = dlamch_("SAFE MINIMUM"); safmax = 1. / safmin; dlabad_(&safmin, &safmax); ulp = dlamch_("PRECISION"); smlnum = safmin * ((doublereal) (*n) / ulp); /* ==== Setup deflation window ==== */ /* Computing MIN */ i__1 = *nw, i__2 = *kbot - *ktop + 1; jw = f2cmin(i__1,i__2); kwtop = *kbot - jw + 1; if (kwtop == *ktop) { s.r = 0., s.i = 0.; } else { i__1 = kwtop + (kwtop - 1) * h_dim1; s.r = h__[i__1].r, s.i = h__[i__1].i; } if (*kbot == kwtop) { /* ==== 1-by-1 deflation window: not much to do ==== */ i__1 = kwtop; i__2 = kwtop + kwtop * h_dim1; sh[i__1].r = h__[i__2].r, sh[i__1].i = h__[i__2].i; *ns = 1; *nd = 0; /* Computing MAX */ i__1 = kwtop + kwtop * h_dim1; d__5 = smlnum, d__6 = ulp * ((d__1 = h__[i__1].r, abs(d__1)) + (d__2 = d_imag(&h__[kwtop + kwtop * h_dim1]), abs(d__2))); if ((d__3 = s.r, abs(d__3)) + (d__4 = d_imag(&s), abs(d__4)) <= f2cmax( d__5,d__6)) { *ns = 0; *nd = 1; if (kwtop > *ktop) { i__1 = kwtop + (kwtop - 1) * h_dim1; h__[i__1].r = 0., h__[i__1].i = 0.; } } work[1].r = 1., work[1].i = 0.; return 0; } /* ==== Convert to spike-triangular form. (In case of a */ /* . rare QR failure, this routine continues to do */ /* . aggressive early deflation using that part of */ /* . the deflation window that converged using INFQR */ /* . here and there to keep track.) ==== */ zlacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset], ldt); i__1 = jw - 1; i__2 = *ldh + 1; i__3 = *ldt + 1; zcopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], & i__3); zlaset_("A", &jw, &jw, &c_b1, &c_b2, &v[v_offset], ldv); nmin = ilaenv_(&c__12, "ZLAQR3", "SV", &jw, &c__1, &jw, lwork, (ftnlen)6, (ftnlen)2); if (jw > nmin) { zlaqr4_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[ kwtop], &c__1, &jw, &v[v_offset], ldv, &work[1], lwork, & infqr); } else { zlahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[ kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr); } /* ==== Deflation detection loop ==== */ *ns = jw; ilst = infqr + 1; i__1 = jw; for (knt = infqr + 1; knt <= i__1; ++knt) { /* ==== Small spike tip deflation test ==== */ i__2 = *ns + *ns * t_dim1; foo = (d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[*ns + *ns * t_dim1]), abs(d__2)); if (foo == 0.) { foo = (d__1 = s.r, abs(d__1)) + (d__2 = d_imag(&s), abs(d__2)); } i__2 = *ns * v_dim1 + 1; /* Computing MAX */ d__5 = smlnum, d__6 = ulp * foo; if (((d__1 = s.r, abs(d__1)) + (d__2 = d_imag(&s), abs(d__2))) * (( d__3 = v[i__2].r, abs(d__3)) + (d__4 = d_imag(&v[*ns * v_dim1 + 1]), abs(d__4))) <= f2cmax(d__5,d__6)) { /* ==== One more converged eigenvalue ==== */ --(*ns); } else { /* ==== One undeflatable eigenvalue. Move it up out of the */ /* . way. (ZTREXC can not fail in this case.) ==== */ ifst = *ns; ztrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, & ilst, &info); ++ilst; } /* L10: */ } /* ==== Return to Hessenberg form ==== */ if (*ns == 0) { s.r = 0., s.i = 0.; } if (*ns < jw) { /* ==== sorting the diagonal of T improves accuracy for */ /* . graded matrices. ==== */ i__1 = *ns; for (i__ = infqr + 1; i__ <= i__1; ++i__) { ifst = i__; i__2 = *ns; for (j = i__ + 1; j <= i__2; ++j) { i__3 = j + j * t_dim1; i__4 = ifst + ifst * t_dim1; if ((d__1 = t[i__3].r, abs(d__1)) + (d__2 = d_imag(&t[j + j * t_dim1]), abs(d__2)) > (d__3 = t[i__4].r, abs(d__3)) + (d__4 = d_imag(&t[ifst + ifst * t_dim1]), abs(d__4)) ) { ifst = j; } /* L20: */ } ilst = i__; if (ifst != ilst) { ztrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, &ilst, &info); } /* L30: */ } } /* ==== Restore shift/eigenvalue array from T ==== */ i__1 = jw; for (i__ = infqr + 1; i__ <= i__1; ++i__) { i__2 = kwtop + i__ - 1; i__3 = i__ + i__ * t_dim1; sh[i__2].r = t[i__3].r, sh[i__2].i = t[i__3].i; /* L40: */ } if (*ns < jw || s.r == 0. && s.i == 0.) { if (*ns > 1 && (s.r != 0. || s.i != 0.)) { /* ==== Reflect spike back into lower triangle ==== */ zcopy_(ns, &v[v_offset], ldv, &work[1], &c__1); i__1 = *ns; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; d_cnjg(&z__1, &work[i__]); work[i__2].r = z__1.r, work[i__2].i = z__1.i; /* L50: */ } beta.r = work[1].r, beta.i = work[1].i; zlarfg_(ns, &beta, &work[2], &c__1, &tau); work[1].r = 1., work[1].i = 0.; i__1 = jw - 2; i__2 = jw - 2; zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &t[t_dim1 + 3], ldt); d_cnjg(&z__1, &tau); zlarf_("L", ns, &jw, &work[1], &c__1, &z__1, &t[t_offset], ldt, & work[jw + 1]); zlarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, & work[jw + 1]); zlarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, & work[jw + 1]); i__1 = *lwork - jw; zgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1] , &i__1, &info); } /* ==== Copy updated reduced window into place ==== */ if (kwtop > 1) { i__1 = kwtop + (kwtop - 1) * h_dim1; d_cnjg(&z__2, &v[v_dim1 + 1]); z__1.r = s.r * z__2.r - s.i * z__2.i, z__1.i = s.r * z__2.i + s.i * z__2.r; h__[i__1].r = z__1.r, h__[i__1].i = z__1.i; } zlacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1] , ldh); i__1 = jw - 1; i__2 = *ldt + 1; i__3 = *ldh + 1; zcopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1], &i__3); /* ==== Accumulate orthogonal matrix in order update */ /* . H and Z, if requested. ==== */ if (*ns > 1 && (s.r != 0. || s.i != 0.)) { i__1 = *lwork - jw; zunmhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1], &v[v_offset], ldv, &work[jw + 1], &i__1, &info); } /* ==== Update vertical slab in H ==== */ if (*wantt) { ltop = 1; } else { ltop = *ktop; } i__1 = kwtop - 1; i__2 = *nv; for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow += i__2) { /* Computing MIN */ i__3 = *nv, i__4 = kwtop - krow; kln = f2cmin(i__3,i__4); zgemm_("N", "N", &kln, &jw, &jw, &c_b2, &h__[krow + kwtop * h_dim1], ldh, &v[v_offset], ldv, &c_b1, &wv[wv_offset], ldwv); zlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop * h_dim1], ldh); /* L60: */ } /* ==== Update horizontal slab in H ==== */ if (*wantt) { i__2 = *n; i__1 = *nh; for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2; kcol += i__1) { /* Computing MIN */ i__3 = *nh, i__4 = *n - kcol + 1; kln = f2cmin(i__3,i__4); zgemm_("C", "N", &jw, &kln, &jw, &c_b2, &v[v_offset], ldv, & h__[kwtop + kcol * h_dim1], ldh, &c_b1, &t[t_offset], ldt); zlacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol * h_dim1], ldh); /* L70: */ } } /* ==== Update vertical slab in Z ==== */ if (*wantz) { i__1 = *ihiz; i__2 = *nv; for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow += i__2) { /* Computing MIN */ i__3 = *nv, i__4 = *ihiz - krow + 1; kln = f2cmin(i__3,i__4); zgemm_("N", "N", &kln, &jw, &jw, &c_b2, &z__[krow + kwtop * z_dim1], ldz, &v[v_offset], ldv, &c_b1, &wv[wv_offset] , ldwv); zlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow + kwtop * z_dim1], ldz); /* L80: */ } } } /* ==== Return the number of deflations ... ==== */ *nd = jw - *ns; /* ==== ... and the number of shifts. (Subtracting */ /* . INFQR from the spike length takes care */ /* . of the case of a rare QR failure while */ /* . calculating eigenvalues of the deflation */ /* . window.) ==== */ *ns -= infqr; /* ==== Return optimal workspace. ==== */ d__1 = (doublereal) lwkopt; z__1.r = d__1, z__1.i = 0.; work[1].r = z__1.r, work[1].i = z__1.i; /* ==== End of ZLAQR3 ==== */ return 0; } /* zlaqr3_ */