#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 ZLAQR5 performs a single small-bulge multi-shift QR sweep. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZLAQR5 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, */ /* H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, */ /* WV, LDWV, NH, WH, LDWH ) */ /* INTEGER IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV, */ /* $ LDWH, LDWV, LDZ, N, NH, NSHFTS, NV */ /* LOGICAL WANTT, WANTZ */ /* COMPLEX*16 H( LDH, * ), S( * ), U( LDU, * ), V( LDV, * ), */ /* $ WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZLAQR5, called by ZLAQR0, performs a */ /* > single small-bulge multi-shift QR sweep. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] WANTT */ /* > \verbatim */ /* > WANTT is LOGICAL */ /* > WANTT = .true. if the triangular Schur factor */ /* > is being computed. WANTT is set to .false. otherwise. */ /* > \endverbatim */ /* > */ /* > \param[in] WANTZ */ /* > \verbatim */ /* > WANTZ is LOGICAL */ /* > WANTZ = .true. if the unitary Schur factor is being */ /* > computed. WANTZ is set to .false. otherwise. */ /* > \endverbatim */ /* > */ /* > \param[in] KACC22 */ /* > \verbatim */ /* > KACC22 is INTEGER with value 0, 1, or 2. */ /* > Specifies the computation mode of far-from-diagonal */ /* > orthogonal updates. */ /* > = 0: ZLAQR5 does not accumulate reflections and does not */ /* > use matrix-matrix multiply to update far-from-diagonal */ /* > matrix entries. */ /* > = 1: ZLAQR5 accumulates reflections and uses matrix-matrix */ /* > multiply to update the far-from-diagonal matrix entries. */ /* > = 2: Same as KACC22 = 1. This option used to enable exploiting */ /* > the 2-by-2 structure during matrix multiplications, but */ /* > this is no longer supported. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > N is the order of the Hessenberg matrix H upon which this */ /* > subroutine operates. */ /* > \endverbatim */ /* > */ /* > \param[in] KTOP */ /* > \verbatim */ /* > KTOP is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[in] KBOT */ /* > \verbatim */ /* > KBOT is INTEGER */ /* > These are the first and last rows and columns of an */ /* > isolated diagonal block upon which the QR sweep is to be */ /* > applied. It is assumed without a check that */ /* > either KTOP = 1 or H(KTOP,KTOP-1) = 0 */ /* > and */ /* > either KBOT = N or H(KBOT+1,KBOT) = 0. */ /* > \endverbatim */ /* > */ /* > \param[in] NSHFTS */ /* > \verbatim */ /* > NSHFTS is INTEGER */ /* > NSHFTS gives the number of simultaneous shifts. NSHFTS */ /* > must be positive and even. */ /* > \endverbatim */ /* > */ /* > \param[in,out] S */ /* > \verbatim */ /* > S is COMPLEX*16 array, dimension (NSHFTS) */ /* > S contains the shifts of origin that define the multi- */ /* > shift QR sweep. On output S may be reordered. */ /* > \endverbatim */ /* > */ /* > \param[in,out] H */ /* > \verbatim */ /* > H is COMPLEX*16 array, dimension (LDH,N) */ /* > On input H contains a Hessenberg matrix. On output a */ /* > multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied */ /* > to the isolated diagonal block in rows and columns KTOP */ /* > through KBOT. */ /* > \endverbatim */ /* > */ /* > \param[in] LDH */ /* > \verbatim */ /* > LDH is INTEGER */ /* > LDH is the leading dimension of H just as declared in the */ /* > calling procedure. LDH >= MAX(1,N). */ /* > \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,IHIZ) */ /* > If WANTZ = .TRUE., then the QR Sweep unitary */ /* > similarity transformation is accumulated into */ /* > Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. */ /* > If WANTZ = .FALSE., then Z is unreferenced. */ /* > \endverbatim */ /* > */ /* > \param[in] LDZ */ /* > \verbatim */ /* > LDZ is INTEGER */ /* > LDA is the leading dimension of Z just as declared in */ /* > the calling procedure. LDZ >= N. */ /* > \endverbatim */ /* > */ /* > \param[out] V */ /* > \verbatim */ /* > V is COMPLEX*16 array, dimension (LDV,NSHFTS/2) */ /* > \endverbatim */ /* > */ /* > \param[in] LDV */ /* > \verbatim */ /* > LDV is INTEGER */ /* > LDV is the leading dimension of V as declared in the */ /* > calling procedure. LDV >= 3. */ /* > \endverbatim */ /* > */ /* > \param[out] U */ /* > \verbatim */ /* > U is COMPLEX*16 array, dimension (LDU,2*NSHFTS) */ /* > \endverbatim */ /* > */ /* > \param[in] LDU */ /* > \verbatim */ /* > LDU is INTEGER */ /* > LDU is the leading dimension of U just as declared in the */ /* > in the calling subroutine. LDU >= 2*NSHFTS. */ /* > \endverbatim */ /* > */ /* > \param[in] NV */ /* > \verbatim */ /* > NV is INTEGER */ /* > NV is the number of rows in WV agailable for workspace. */ /* > NV >= 1. */ /* > \endverbatim */ /* > */ /* > \param[out] WV */ /* > \verbatim */ /* > WV is COMPLEX*16 array, dimension (LDWV,2*NSHFTS) */ /* > \endverbatim */ /* > */ /* > \param[in] LDWV */ /* > \verbatim */ /* > LDWV is INTEGER */ /* > LDWV is the leading dimension of WV as declared in the */ /* > in the calling subroutine. LDWV >= NV. */ /* > \endverbatim */ /* > \param[in] NH */ /* > \verbatim */ /* > NH is INTEGER */ /* > NH is the number of columns in array WH available for */ /* > workspace. NH >= 1. */ /* > \endverbatim */ /* > */ /* > \param[out] WH */ /* > \verbatim */ /* > WH is COMPLEX*16 array, dimension (LDWH,NH) */ /* > \endverbatim */ /* > */ /* > \param[in] LDWH */ /* > \verbatim */ /* > LDWH is INTEGER */ /* > Leading dimension of WH just as declared in the */ /* > calling procedure. LDWH >= 2*NSHFTS. */ /* > \endverbatim */ /* > */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date January 2021 */ /* > \ingroup complex16OTHERauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Karen Braman and Ralph Byers, Department of Mathematics, */ /* > University of Kansas, USA */ /* > */ /* > Lars Karlsson, Daniel Kressner, and Bruno Lang */ /* > */ /* > Thijs Steel, Department of Computer science, */ /* > KU Leuven, Belgium */ /* > \par References: */ /* ================ */ /* > */ /* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */ /* > Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */ /* > Performance, SIAM Journal of Matrix Analysis, volume 23, pages */ /* > 929--947, 2002. */ /* > */ /* > Lars Karlsson, Daniel Kressner, and Bruno Lang, Optimally packed */ /* > chains of bulges in multishift QR algorithms. */ /* > ACM Trans. Math. Softw. 40, 2, Article 12 (February 2014). */ /* > */ /* ===================================================================== */ /* Subroutine */ int zlaqr5_(logical *wantt, logical *wantz, integer *kacc22, integer *n, integer *ktop, integer *kbot, integer *nshfts, doublecomplex *s, doublecomplex *h__, integer *ldh, integer *iloz, integer *ihiz, doublecomplex *z__, integer *ldz, doublecomplex *v, integer *ldv, doublecomplex *u, integer *ldu, integer *nv, doublecomplex *wv, integer *ldwv, integer *nh, doublecomplex *wh, integer *ldwh) { /* System generated locals */ integer h_dim1, h_offset, u_dim1, u_offset, v_dim1, v_offset, wh_dim1, wh_offset, wv_dim1, wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9, i__10, i__11; doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10; doublecomplex z__1, z__2, z__3, z__4, z__5, z__6, z__7, z__8; /* Local variables */ doublecomplex beta; logical bmp22; integer jcol, jlen, jbot, mbot, jtop, jrow, mtop, j, k, m; doublecomplex alpha; logical accum; integer ndcol, incol, krcol, nbmps; extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); integer i2, k1, i4; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); doublereal h11, h12, h21, h22; extern /* Subroutine */ int zlaqr1_(integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, doublecomplex *); integer m22; extern doublereal dlamch_(char *); integer ns, nu; doublecomplex vt[3]; doublereal safmin, safmax; extern /* Subroutine */ int zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *); doublecomplex refsum; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); doublereal smlnum, scl; integer kdu, kms; doublereal ulp; doublereal tst1, tst2; /* -- 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 */ /* ================================================================ */ /* ==== If there are no shifts, then there is nothing to do. ==== */ /* Parameter adjustments */ --s; h_dim1 = *ldh; h_offset = 1 + h_dim1 * 1; h__ -= h_offset; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; v_dim1 = *ldv; v_offset = 1 + v_dim1 * 1; v -= v_offset; u_dim1 = *ldu; u_offset = 1 + u_dim1 * 1; u -= u_offset; wv_dim1 = *ldwv; wv_offset = 1 + wv_dim1 * 1; wv -= wv_offset; wh_dim1 = *ldwh; wh_offset = 1 + wh_dim1 * 1; wh -= wh_offset; /* Function Body */ if (*nshfts < 2) { return 0; } /* ==== If the active block is empty or 1-by-1, then there */ /* . is nothing to do. ==== */ if (*ktop >= *kbot) { return 0; } /* ==== NSHFTS is supposed to be even, but if it is odd, */ /* . then simply reduce it by one. ==== */ ns = *nshfts - *nshfts % 2; /* ==== Machine constants for deflation ==== */ safmin = dlamch_("SAFE MINIMUM"); safmax = 1. / safmin; dlabad_(&safmin, &safmax); ulp = dlamch_("PRECISION"); smlnum = safmin * ((doublereal) (*n) / ulp); /* ==== Use accumulated reflections to update far-from-diagonal */ /* . entries ? ==== */ accum = *kacc22 == 1 || *kacc22 == 2; /* ==== clear trash ==== */ if (*ktop + 2 <= *kbot) { i__1 = *ktop + 2 + *ktop * h_dim1; h__[i__1].r = 0., h__[i__1].i = 0.; } /* ==== NBMPS = number of 2-shift bulges in the chain ==== */ nbmps = ns / 2; /* ==== KDU = width of slab ==== */ kdu = nbmps << 2; /* ==== Create and chase chains of NBMPS bulges ==== */ i__1 = *kbot - 2; i__2 = nbmps << 1; for (incol = *ktop - (nbmps << 1) + 1; i__2 < 0 ? incol >= i__1 : incol <= i__1; incol += i__2) { /* JTOP = Index from which updates from the right start. */ if (accum) { jtop = f2cmax(*ktop,incol); } else if (*wantt) { jtop = 1; } else { jtop = *ktop; } ndcol = incol + kdu; if (accum) { zlaset_("ALL", &kdu, &kdu, &c_b1, &c_b2, &u[u_offset], ldu); } /* ==== Near-the-diagonal bulge chase. The following loop */ /* . performs the near-the-diagonal part of a small bulge */ /* . multi-shift QR sweep. Each 4*NBMPS column diagonal */ /* . chunk extends from column INCOL to column NDCOL */ /* . (including both column INCOL and column NDCOL). The */ /* . following loop chases a 2*NBMPS+1 column long chain of */ /* . NBMPS bulges 2*NBMPS columns to the right. (INCOL */ /* . may be less than KTOP and and NDCOL may be greater than */ /* . KBOT indicating phantom columns from which to chase */ /* . bulges before they are actually introduced or to which */ /* . to chase bulges beyond column KBOT.) ==== */ /* Computing MIN */ i__4 = incol + (nbmps << 1) - 1, i__5 = *kbot - 2; i__3 = f2cmin(i__4,i__5); for (krcol = incol; krcol <= i__3; ++krcol) { /* ==== Bulges number MTOP to MBOT are active double implicit */ /* . shift bulges. There may or may not also be small */ /* . 2-by-2 bulge, if there is room. The inactive bulges */ /* . (if any) must wait until the active bulges have moved */ /* . down the diagonal to make room. The phantom matrix */ /* . paradigm described above helps keep track. ==== */ /* Computing MAX */ i__4 = 1, i__5 = (*ktop - krcol) / 2 + 1; mtop = f2cmax(i__4,i__5); /* Computing MIN */ i__4 = nbmps, i__5 = (*kbot - krcol - 1) / 2; mbot = f2cmin(i__4,i__5); m22 = mbot + 1; bmp22 = mbot < nbmps && krcol + (m22 - 1 << 1) == *kbot - 2; /* ==== Generate reflections to chase the chain right */ /* . one column. (The minimum value of K is KTOP-1.) ==== */ if (bmp22) { /* ==== Special case: 2-by-2 reflection at bottom treated */ /* . separately ==== */ k = krcol + (m22 - 1 << 1); if (k == *ktop - 1) { zlaqr1_(&c__2, &h__[k + 1 + (k + 1) * h_dim1], ldh, &s[( m22 << 1) - 1], &s[m22 * 2], &v[m22 * v_dim1 + 1]) ; i__4 = m22 * v_dim1 + 1; beta.r = v[i__4].r, beta.i = v[i__4].i; zlarfg_(&c__2, &beta, &v[m22 * v_dim1 + 2], &c__1, &v[m22 * v_dim1 + 1]); } else { i__4 = k + 1 + k * h_dim1; beta.r = h__[i__4].r, beta.i = h__[i__4].i; i__4 = m22 * v_dim1 + 2; i__5 = k + 2 + k * h_dim1; v[i__4].r = h__[i__5].r, v[i__4].i = h__[i__5].i; zlarfg_(&c__2, &beta, &v[m22 * v_dim1 + 2], &c__1, &v[m22 * v_dim1 + 1]); i__4 = k + 1 + k * h_dim1; h__[i__4].r = beta.r, h__[i__4].i = beta.i; i__4 = k + 2 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; } /* ==== Perform update from right within */ /* . computational window. ==== */ /* Computing MIN */ i__5 = *kbot, i__6 = k + 3; i__4 = f2cmin(i__5,i__6); for (j = jtop; j <= i__4; ++j) { i__5 = m22 * v_dim1 + 1; i__6 = j + (k + 1) * h_dim1; i__7 = m22 * v_dim1 + 2; i__8 = j + (k + 2) * h_dim1; z__3.r = v[i__7].r * h__[i__8].r - v[i__7].i * h__[i__8] .i, z__3.i = v[i__7].r * h__[i__8].i + v[i__7].i * h__[i__8].r; z__2.r = h__[i__6].r + z__3.r, z__2.i = h__[i__6].i + z__3.i; z__1.r = v[i__5].r * z__2.r - v[i__5].i * z__2.i, z__1.i = v[i__5].r * z__2.i + v[i__5].i * z__2.r; refsum.r = z__1.r, refsum.i = z__1.i; i__5 = j + (k + 1) * h_dim1; i__6 = j + (k + 1) * h_dim1; z__1.r = h__[i__6].r - refsum.r, z__1.i = h__[i__6].i - refsum.i; h__[i__5].r = z__1.r, h__[i__5].i = z__1.i; i__5 = j + (k + 2) * h_dim1; i__6 = j + (k + 2) * h_dim1; d_cnjg(&z__3, &v[m22 * v_dim1 + 2]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = h__[i__6].r - z__2.r, z__1.i = h__[i__6].i - z__2.i; h__[i__5].r = z__1.r, h__[i__5].i = z__1.i; /* L30: */ } /* ==== Perform update from left within */ /* . computational window. ==== */ if (accum) { jbot = f2cmin(ndcol,*kbot); } else if (*wantt) { jbot = *n; } else { jbot = *kbot; } i__4 = jbot; for (j = k + 1; j <= i__4; ++j) { d_cnjg(&z__2, &v[m22 * v_dim1 + 1]); i__5 = k + 1 + j * h_dim1; d_cnjg(&z__5, &v[m22 * v_dim1 + 2]); i__6 = k + 2 + j * h_dim1; z__4.r = z__5.r * h__[i__6].r - z__5.i * h__[i__6].i, z__4.i = z__5.r * h__[i__6].i + z__5.i * h__[i__6] .r; z__3.r = h__[i__5].r + z__4.r, z__3.i = h__[i__5].i + z__4.i; z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; refsum.r = z__1.r, refsum.i = z__1.i; i__5 = k + 1 + j * h_dim1; i__6 = k + 1 + j * h_dim1; z__1.r = h__[i__6].r - refsum.r, z__1.i = h__[i__6].i - refsum.i; h__[i__5].r = z__1.r, h__[i__5].i = z__1.i; i__5 = k + 2 + j * h_dim1; i__6 = k + 2 + j * h_dim1; i__7 = m22 * v_dim1 + 2; z__2.r = refsum.r * v[i__7].r - refsum.i * v[i__7].i, z__2.i = refsum.r * v[i__7].i + refsum.i * v[i__7] .r; z__1.r = h__[i__6].r - z__2.r, z__1.i = h__[i__6].i - z__2.i; h__[i__5].r = z__1.r, h__[i__5].i = z__1.i; /* L40: */ } /* ==== The following convergence test requires that */ /* . the tradition small-compared-to-nearby-diagonals */ /* . criterion and the Ahues & Tisseur (LAWN 122, 1997) */ /* . criteria both be satisfied. The latter improves */ /* . accuracy in some examples. Falling back on an */ /* . alternate convergence criterion when TST1 or TST2 */ /* . is zero (as done here) is traditional but probably */ /* . unnecessary. ==== */ if (k >= *ktop) { i__4 = k + 1 + k * h_dim1; if (h__[i__4].r != 0. || h__[i__4].i != 0.) { i__4 = k + k * h_dim1; i__5 = k + 1 + (k + 1) * h_dim1; tst1 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + k * h_dim1]), abs(d__2)) + (( d__3 = h__[i__5].r, abs(d__3)) + (d__4 = d_imag(&h__[k + 1 + (k + 1) * h_dim1]), abs( d__4))); if (tst1 == 0.) { if (k >= *ktop + 1) { i__4 = k + (k - 1) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + ( d__2 = d_imag(&h__[k + (k - 1) * h_dim1]), abs(d__2)); } if (k >= *ktop + 2) { i__4 = k + (k - 2) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + ( d__2 = d_imag(&h__[k + (k - 2) * h_dim1]), abs(d__2)); } if (k >= *ktop + 3) { i__4 = k + (k - 3) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + ( d__2 = d_imag(&h__[k + (k - 3) * h_dim1]), abs(d__2)); } if (k <= *kbot - 2) { i__4 = k + 2 + (k + 1) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + ( d__2 = d_imag(&h__[k + 2 + (k + 1) * h_dim1]), abs(d__2)); } if (k <= *kbot - 3) { i__4 = k + 3 + (k + 1) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + ( d__2 = d_imag(&h__[k + 3 + (k + 1) * h_dim1]), abs(d__2)); } if (k <= *kbot - 4) { i__4 = k + 4 + (k + 1) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + ( d__2 = d_imag(&h__[k + 4 + (k + 1) * h_dim1]), abs(d__2)); } } i__4 = k + 1 + k * h_dim1; /* Computing MAX */ d__3 = smlnum, d__4 = ulp * tst1; if ((d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(& h__[k + 1 + k * h_dim1]), abs(d__2)) <= f2cmax( d__3,d__4)) { /* Computing MAX */ i__4 = k + 1 + k * h_dim1; i__5 = k + (k + 1) * h_dim1; d__5 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 1 + k * h_dim1]), abs( d__2)), d__6 = (d__3 = h__[i__5].r, abs( d__3)) + (d__4 = d_imag(&h__[k + (k + 1) * h_dim1]), abs(d__4)); h12 = f2cmax(d__5,d__6); /* Computing MIN */ i__4 = k + 1 + k * h_dim1; i__5 = k + (k + 1) * h_dim1; d__5 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 1 + k * h_dim1]), abs( d__2)), d__6 = (d__3 = h__[i__5].r, abs( d__3)) + (d__4 = d_imag(&h__[k + (k + 1) * h_dim1]), abs(d__4)); h21 = f2cmin(d__5,d__6); i__4 = k + k * h_dim1; i__5 = k + 1 + (k + 1) * h_dim1; z__2.r = h__[i__4].r - h__[i__5].r, z__2.i = h__[ i__4].i - h__[i__5].i; z__1.r = z__2.r, z__1.i = z__2.i; /* Computing MAX */ i__6 = k + 1 + (k + 1) * h_dim1; d__5 = (d__1 = h__[i__6].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 1 + (k + 1) * h_dim1]), abs(d__2)), d__6 = (d__3 = z__1.r, abs( d__3)) + (d__4 = d_imag(&z__1), abs(d__4)) ; h11 = f2cmax(d__5,d__6); i__4 = k + k * h_dim1; i__5 = k + 1 + (k + 1) * h_dim1; z__2.r = h__[i__4].r - h__[i__5].r, z__2.i = h__[ i__4].i - h__[i__5].i; z__1.r = z__2.r, z__1.i = z__2.i; /* Computing MIN */ i__6 = k + 1 + (k + 1) * h_dim1; d__5 = (d__1 = h__[i__6].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 1 + (k + 1) * h_dim1]), abs(d__2)), d__6 = (d__3 = z__1.r, abs( d__3)) + (d__4 = d_imag(&z__1), abs(d__4)) ; h22 = f2cmin(d__5,d__6); scl = h11 + h12; tst2 = h22 * (h11 / scl); /* Computing MAX */ d__1 = smlnum, d__2 = ulp * tst2; if (tst2 == 0. || h21 * (h12 / scl) <= f2cmax(d__1, d__2)) { i__4 = k + 1 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; } } } } /* ==== Accumulate orthogonal transformations. ==== */ if (accum) { kms = k - incol; /* Computing MAX */ i__4 = 1, i__5 = *ktop - incol; i__6 = kdu; for (j = f2cmax(i__4,i__5); j <= i__6; ++j) { i__4 = m22 * v_dim1 + 1; i__5 = j + (kms + 1) * u_dim1; i__7 = m22 * v_dim1 + 2; i__8 = j + (kms + 2) * u_dim1; z__3.r = v[i__7].r * u[i__8].r - v[i__7].i * u[i__8] .i, z__3.i = v[i__7].r * u[i__8].i + v[i__7] .i * u[i__8].r; z__2.r = u[i__5].r + z__3.r, z__2.i = u[i__5].i + z__3.i; z__1.r = v[i__4].r * z__2.r - v[i__4].i * z__2.i, z__1.i = v[i__4].r * z__2.i + v[i__4].i * z__2.r; refsum.r = z__1.r, refsum.i = z__1.i; i__4 = j + (kms + 1) * u_dim1; i__5 = j + (kms + 1) * u_dim1; z__1.r = u[i__5].r - refsum.r, z__1.i = u[i__5].i - refsum.i; u[i__4].r = z__1.r, u[i__4].i = z__1.i; i__4 = j + (kms + 2) * u_dim1; i__5 = j + (kms + 2) * u_dim1; d_cnjg(&z__3, &v[m22 * v_dim1 + 2]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = u[i__5].r - z__2.r, z__1.i = u[i__5].i - z__2.i; u[i__4].r = z__1.r, u[i__4].i = z__1.i; /* L50: */ } } else if (*wantz) { i__6 = *ihiz; for (j = *iloz; j <= i__6; ++j) { i__4 = m22 * v_dim1 + 1; i__5 = j + (k + 1) * z_dim1; i__7 = m22 * v_dim1 + 2; i__8 = j + (k + 2) * z_dim1; z__3.r = v[i__7].r * z__[i__8].r - v[i__7].i * z__[ i__8].i, z__3.i = v[i__7].r * z__[i__8].i + v[ i__7].i * z__[i__8].r; z__2.r = z__[i__5].r + z__3.r, z__2.i = z__[i__5].i + z__3.i; z__1.r = v[i__4].r * z__2.r - v[i__4].i * z__2.i, z__1.i = v[i__4].r * z__2.i + v[i__4].i * z__2.r; refsum.r = z__1.r, refsum.i = z__1.i; i__4 = j + (k + 1) * z_dim1; i__5 = j + (k + 1) * z_dim1; z__1.r = z__[i__5].r - refsum.r, z__1.i = z__[i__5].i - refsum.i; z__[i__4].r = z__1.r, z__[i__4].i = z__1.i; i__4 = j + (k + 2) * z_dim1; i__5 = j + (k + 2) * z_dim1; d_cnjg(&z__3, &v[m22 * v_dim1 + 2]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = z__[i__5].r - z__2.r, z__1.i = z__[i__5].i - z__2.i; z__[i__4].r = z__1.r, z__[i__4].i = z__1.i; /* L60: */ } } } /* ==== Normal case: Chain of 3-by-3 reflections ==== */ i__6 = mtop; for (m = mbot; m >= i__6; --m) { k = krcol + (m - 1 << 1); if (k == *ktop - 1) { zlaqr1_(&c__3, &h__[*ktop + *ktop * h_dim1], ldh, &s[(m << 1) - 1], &s[m * 2], &v[m * v_dim1 + 1]); i__4 = m * v_dim1 + 1; alpha.r = v[i__4].r, alpha.i = v[i__4].i; zlarfg_(&c__3, &alpha, &v[m * v_dim1 + 2], &c__1, &v[m * v_dim1 + 1]); } else { /* ==== Perform delayed transformation of row below */ /* . Mth bulge. Exploit fact that first two elements */ /* . of row are actually zero. ==== */ i__4 = m * v_dim1 + 1; i__5 = m * v_dim1 + 3; z__2.r = v[i__4].r * v[i__5].r - v[i__4].i * v[i__5].i, z__2.i = v[i__4].r * v[i__5].i + v[i__4].i * v[ i__5].r; i__7 = k + 3 + (k + 2) * h_dim1; z__1.r = z__2.r * h__[i__7].r - z__2.i * h__[i__7].i, z__1.i = z__2.r * h__[i__7].i + z__2.i * h__[i__7] .r; refsum.r = z__1.r, refsum.i = z__1.i; i__4 = k + 3 + k * h_dim1; z__1.r = -refsum.r, z__1.i = -refsum.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = k + 3 + (k + 1) * h_dim1; z__2.r = -refsum.r, z__2.i = -refsum.i; d_cnjg(&z__3, &v[m * v_dim1 + 2]); z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = k + 3 + (k + 2) * h_dim1; i__5 = k + 3 + (k + 2) * h_dim1; d_cnjg(&z__3, &v[m * v_dim1 + 3]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = h__[i__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; /* ==== Calculate reflection to move */ /* . Mth bulge one step. ==== */ i__4 = k + 1 + k * h_dim1; beta.r = h__[i__4].r, beta.i = h__[i__4].i; i__4 = m * v_dim1 + 2; i__5 = k + 2 + k * h_dim1; v[i__4].r = h__[i__5].r, v[i__4].i = h__[i__5].i; i__4 = m * v_dim1 + 3; i__5 = k + 3 + k * h_dim1; v[i__4].r = h__[i__5].r, v[i__4].i = h__[i__5].i; zlarfg_(&c__3, &beta, &v[m * v_dim1 + 2], &c__1, &v[m * v_dim1 + 1]); /* ==== A Bulge may collapse because of vigilant */ /* . deflation or destructive underflow. In the */ /* . underflow case, try the two-small-subdiagonals */ /* . trick to try to reinflate the bulge. ==== */ i__4 = k + 3 + k * h_dim1; i__5 = k + 3 + (k + 1) * h_dim1; i__7 = k + 3 + (k + 2) * h_dim1; if (h__[i__4].r != 0. || h__[i__4].i != 0. || (h__[i__5] .r != 0. || h__[i__5].i != 0.) || h__[i__7].r == 0. && h__[i__7].i == 0.) { /* ==== Typical case: not collapsed (yet). ==== */ i__4 = k + 1 + k * h_dim1; h__[i__4].r = beta.r, h__[i__4].i = beta.i; i__4 = k + 2 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; i__4 = k + 3 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; } else { /* ==== Atypical case: collapsed. Attempt to */ /* . reintroduce ignoring H(K+1,K) and H(K+2,K). */ /* . If the fill resulting from the new */ /* . reflector is too large, then abandon it. */ /* . Otherwise, use the new one. ==== */ zlaqr1_(&c__3, &h__[k + 1 + (k + 1) * h_dim1], ldh, & s[(m << 1) - 1], &s[m * 2], vt); alpha.r = vt[0].r, alpha.i = vt[0].i; zlarfg_(&c__3, &alpha, &vt[1], &c__1, vt); d_cnjg(&z__2, vt); i__4 = k + 1 + k * h_dim1; d_cnjg(&z__5, &vt[1]); i__5 = k + 2 + k * h_dim1; z__4.r = z__5.r * h__[i__5].r - z__5.i * h__[i__5].i, z__4.i = z__5.r * h__[i__5].i + z__5.i * h__[ i__5].r; z__3.r = h__[i__4].r + z__4.r, z__3.i = h__[i__4].i + z__4.i; z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; refsum.r = z__1.r, refsum.i = z__1.i; i__4 = k + 2 + k * h_dim1; z__3.r = refsum.r * vt[1].r - refsum.i * vt[1].i, z__3.i = refsum.r * vt[1].i + refsum.i * vt[1] .r; z__2.r = h__[i__4].r - z__3.r, z__2.i = h__[i__4].i - z__3.i; z__1.r = z__2.r, z__1.i = z__2.i; z__5.r = refsum.r * vt[2].r - refsum.i * vt[2].i, z__5.i = refsum.r * vt[2].i + refsum.i * vt[2] .r; z__4.r = z__5.r, z__4.i = z__5.i; i__5 = k + k * h_dim1; i__7 = k + 1 + (k + 1) * h_dim1; i__8 = k + 2 + (k + 2) * h_dim1; if ((d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1) , abs(d__2)) + ((d__3 = z__4.r, abs(d__3)) + ( d__4 = d_imag(&z__4), abs(d__4))) > ulp * (( d__5 = h__[i__5].r, abs(d__5)) + (d__6 = d_imag(&h__[k + k * h_dim1]), abs(d__6)) + (( d__7 = h__[i__7].r, abs(d__7)) + (d__8 = d_imag(&h__[k + 1 + (k + 1) * h_dim1]), abs( d__8))) + ((d__9 = h__[i__8].r, abs(d__9)) + ( d__10 = d_imag(&h__[k + 2 + (k + 2) * h_dim1]) , abs(d__10))))) { /* ==== Starting a new bulge here would */ /* . create non-negligible fill. Use */ /* . the old one with trepidation. ==== */ i__4 = k + 1 + k * h_dim1; h__[i__4].r = beta.r, h__[i__4].i = beta.i; i__4 = k + 2 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; i__4 = k + 3 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; } else { /* ==== Starting a new bulge here would */ /* . create only negligible fill. */ /* . Replace the old reflector with */ /* . the new one. ==== */ i__4 = k + 1 + k * h_dim1; i__5 = k + 1 + k * h_dim1; z__1.r = h__[i__5].r - refsum.r, z__1.i = h__[ i__5].i - refsum.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = k + 2 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; i__4 = k + 3 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; i__4 = m * v_dim1 + 1; v[i__4].r = vt[0].r, v[i__4].i = vt[0].i; i__4 = m * v_dim1 + 2; v[i__4].r = vt[1].r, v[i__4].i = vt[1].i; i__4 = m * v_dim1 + 3; v[i__4].r = vt[2].r, v[i__4].i = vt[2].i; } } } /* ==== Apply reflection from the right and */ /* . the first column of update from the left. */ /* . These updates are required for the vigilant */ /* . deflation check. We still delay most of the */ /* . updates from the left for efficiency. ==== */ /* Computing MIN */ i__5 = *kbot, i__7 = k + 3; i__4 = f2cmin(i__5,i__7); for (j = jtop; j <= i__4; ++j) { i__5 = m * v_dim1 + 1; i__7 = j + (k + 1) * h_dim1; i__8 = m * v_dim1 + 2; i__9 = j + (k + 2) * h_dim1; z__4.r = v[i__8].r * h__[i__9].r - v[i__8].i * h__[i__9] .i, z__4.i = v[i__8].r * h__[i__9].i + v[i__8].i * h__[i__9].r; z__3.r = h__[i__7].r + z__4.r, z__3.i = h__[i__7].i + z__4.i; i__10 = m * v_dim1 + 3; i__11 = j + (k + 3) * h_dim1; z__5.r = v[i__10].r * h__[i__11].r - v[i__10].i * h__[ i__11].i, z__5.i = v[i__10].r * h__[i__11].i + v[ i__10].i * h__[i__11].r; z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i; z__1.r = v[i__5].r * z__2.r - v[i__5].i * z__2.i, z__1.i = v[i__5].r * z__2.i + v[i__5].i * z__2.r; refsum.r = z__1.r, refsum.i = z__1.i; i__5 = j + (k + 1) * h_dim1; i__7 = j + (k + 1) * h_dim1; z__1.r = h__[i__7].r - refsum.r, z__1.i = h__[i__7].i - refsum.i; h__[i__5].r = z__1.r, h__[i__5].i = z__1.i; i__5 = j + (k + 2) * h_dim1; i__7 = j + (k + 2) * h_dim1; d_cnjg(&z__3, &v[m * v_dim1 + 2]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = h__[i__7].r - z__2.r, z__1.i = h__[i__7].i - z__2.i; h__[i__5].r = z__1.r, h__[i__5].i = z__1.i; i__5 = j + (k + 3) * h_dim1; i__7 = j + (k + 3) * h_dim1; d_cnjg(&z__3, &v[m * v_dim1 + 3]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = h__[i__7].r - z__2.r, z__1.i = h__[i__7].i - z__2.i; h__[i__5].r = z__1.r, h__[i__5].i = z__1.i; /* L70: */ } /* ==== Perform update from left for subsequent */ /* . column. ==== */ d_cnjg(&z__2, &v[m * v_dim1 + 1]); i__4 = k + 1 + (k + 1) * h_dim1; d_cnjg(&z__6, &v[m * v_dim1 + 2]); i__5 = k + 2 + (k + 1) * h_dim1; z__5.r = z__6.r * h__[i__5].r - z__6.i * h__[i__5].i, z__5.i = z__6.r * h__[i__5].i + z__6.i * h__[i__5].r; z__4.r = h__[i__4].r + z__5.r, z__4.i = h__[i__4].i + z__5.i; d_cnjg(&z__8, &v[m * v_dim1 + 3]); i__7 = k + 3 + (k + 1) * h_dim1; z__7.r = z__8.r * h__[i__7].r - z__8.i * h__[i__7].i, z__7.i = z__8.r * h__[i__7].i + z__8.i * h__[i__7].r; z__3.r = z__4.r + z__7.r, z__3.i = z__4.i + z__7.i; z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; refsum.r = z__1.r, refsum.i = z__1.i; i__4 = k + 1 + (k + 1) * h_dim1; i__5 = k + 1 + (k + 1) * h_dim1; z__1.r = h__[i__5].r - refsum.r, z__1.i = h__[i__5].i - refsum.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = k + 2 + (k + 1) * h_dim1; i__5 = k + 2 + (k + 1) * h_dim1; i__7 = m * v_dim1 + 2; z__2.r = refsum.r * v[i__7].r - refsum.i * v[i__7].i, z__2.i = refsum.r * v[i__7].i + refsum.i * v[i__7].r; z__1.r = h__[i__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = k + 3 + (k + 1) * h_dim1; i__5 = k + 3 + (k + 1) * h_dim1; i__7 = m * v_dim1 + 3; z__2.r = refsum.r * v[i__7].r - refsum.i * v[i__7].i, z__2.i = refsum.r * v[i__7].i + refsum.i * v[i__7].r; z__1.r = h__[i__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; /* ==== The following convergence test requires that */ /* . the tradition small-compared-to-nearby-diagonals */ /* . criterion and the Ahues & Tisseur (LAWN 122, 1997) */ /* . criteria both be satisfied. The latter improves */ /* . accuracy in some examples. Falling back on an */ /* . alternate convergence criterion when TST1 or TST2 */ /* . is zero (as done here) is traditional but probably */ /* . unnecessary. ==== */ if (k < *ktop) { mycycle_(); } i__4 = k + 1 + k * h_dim1; if (h__[i__4].r != 0. || h__[i__4].i != 0.) { i__4 = k + k * h_dim1; i__5 = k + 1 + (k + 1) * h_dim1; tst1 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(& h__[k + k * h_dim1]), abs(d__2)) + ((d__3 = h__[ i__5].r, abs(d__3)) + (d__4 = d_imag(&h__[k + 1 + (k + 1) * h_dim1]), abs(d__4))); if (tst1 == 0.) { if (k >= *ktop + 1) { i__4 = k + (k - 1) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + (k - 1) * h_dim1]), abs( d__2)); } if (k >= *ktop + 2) { i__4 = k + (k - 2) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + (k - 2) * h_dim1]), abs( d__2)); } if (k >= *ktop + 3) { i__4 = k + (k - 3) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + (k - 3) * h_dim1]), abs( d__2)); } if (k <= *kbot - 2) { i__4 = k + 2 + (k + 1) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 2 + (k + 1) * h_dim1]), abs(d__2)); } if (k <= *kbot - 3) { i__4 = k + 3 + (k + 1) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 3 + (k + 1) * h_dim1]), abs(d__2)); } if (k <= *kbot - 4) { i__4 = k + 4 + (k + 1) * h_dim1; tst1 += (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 4 + (k + 1) * h_dim1]), abs(d__2)); } } i__4 = k + 1 + k * h_dim1; /* Computing MAX */ d__3 = smlnum, d__4 = ulp * tst1; if ((d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[ k + 1 + k * h_dim1]), abs(d__2)) <= f2cmax(d__3,d__4) ) { /* Computing MAX */ i__4 = k + 1 + k * h_dim1; i__5 = k + (k + 1) * h_dim1; d__5 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 1 + k * h_dim1]), abs(d__2)), d__6 = (d__3 = h__[i__5].r, abs(d__3)) + ( d__4 = d_imag(&h__[k + (k + 1) * h_dim1]), abs(d__4)); h12 = f2cmax(d__5,d__6); /* Computing MIN */ i__4 = k + 1 + k * h_dim1; i__5 = k + (k + 1) * h_dim1; d__5 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 1 + k * h_dim1]), abs(d__2)), d__6 = (d__3 = h__[i__5].r, abs(d__3)) + ( d__4 = d_imag(&h__[k + (k + 1) * h_dim1]), abs(d__4)); h21 = f2cmin(d__5,d__6); i__4 = k + k * h_dim1; i__5 = k + 1 + (k + 1) * h_dim1; z__2.r = h__[i__4].r - h__[i__5].r, z__2.i = h__[i__4] .i - h__[i__5].i; z__1.r = z__2.r, z__1.i = z__2.i; /* Computing MAX */ i__7 = k + 1 + (k + 1) * h_dim1; d__5 = (d__1 = h__[i__7].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 1 + (k + 1) * h_dim1]), abs( d__2)), d__6 = (d__3 = z__1.r, abs(d__3)) + ( d__4 = d_imag(&z__1), abs(d__4)); h11 = f2cmax(d__5,d__6); i__4 = k + k * h_dim1; i__5 = k + 1 + (k + 1) * h_dim1; z__2.r = h__[i__4].r - h__[i__5].r, z__2.i = h__[i__4] .i - h__[i__5].i; z__1.r = z__2.r, z__1.i = z__2.i; /* Computing MIN */ i__7 = k + 1 + (k + 1) * h_dim1; d__5 = (d__1 = h__[i__7].r, abs(d__1)) + (d__2 = d_imag(&h__[k + 1 + (k + 1) * h_dim1]), abs( d__2)), d__6 = (d__3 = z__1.r, abs(d__3)) + ( d__4 = d_imag(&z__1), abs(d__4)); h22 = f2cmin(d__5,d__6); scl = h11 + h12; tst2 = h22 * (h11 / scl); /* Computing MAX */ d__1 = smlnum, d__2 = ulp * tst2; if (tst2 == 0. || h21 * (h12 / scl) <= f2cmax(d__1,d__2)) { i__4 = k + 1 + k * h_dim1; h__[i__4].r = 0., h__[i__4].i = 0.; } } } /* L80: */ } /* ==== Multiply H by reflections from the left ==== */ if (accum) { jbot = f2cmin(ndcol,*kbot); } else if (*wantt) { jbot = *n; } else { jbot = *kbot; } i__6 = mtop; for (m = mbot; m >= i__6; --m) { k = krcol + (m - 1 << 1); /* Computing MAX */ i__4 = *ktop, i__5 = krcol + (m << 1); i__7 = jbot; for (j = f2cmax(i__4,i__5); j <= i__7; ++j) { d_cnjg(&z__2, &v[m * v_dim1 + 1]); i__4 = k + 1 + j * h_dim1; d_cnjg(&z__6, &v[m * v_dim1 + 2]); i__5 = k + 2 + j * h_dim1; z__5.r = z__6.r * h__[i__5].r - z__6.i * h__[i__5].i, z__5.i = z__6.r * h__[i__5].i + z__6.i * h__[i__5] .r; z__4.r = h__[i__4].r + z__5.r, z__4.i = h__[i__4].i + z__5.i; d_cnjg(&z__8, &v[m * v_dim1 + 3]); i__8 = k + 3 + j * h_dim1; z__7.r = z__8.r * h__[i__8].r - z__8.i * h__[i__8].i, z__7.i = z__8.r * h__[i__8].i + z__8.i * h__[i__8] .r; z__3.r = z__4.r + z__7.r, z__3.i = z__4.i + z__7.i; z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; refsum.r = z__1.r, refsum.i = z__1.i; i__4 = k + 1 + j * h_dim1; i__5 = k + 1 + j * h_dim1; z__1.r = h__[i__5].r - refsum.r, z__1.i = h__[i__5].i - refsum.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = k + 2 + j * h_dim1; i__5 = k + 2 + j * h_dim1; i__8 = m * v_dim1 + 2; z__2.r = refsum.r * v[i__8].r - refsum.i * v[i__8].i, z__2.i = refsum.r * v[i__8].i + refsum.i * v[i__8] .r; z__1.r = h__[i__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; i__4 = k + 3 + j * h_dim1; i__5 = k + 3 + j * h_dim1; i__8 = m * v_dim1 + 3; z__2.r = refsum.r * v[i__8].r - refsum.i * v[i__8].i, z__2.i = refsum.r * v[i__8].i + refsum.i * v[i__8] .r; z__1.r = h__[i__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i; h__[i__4].r = z__1.r, h__[i__4].i = z__1.i; /* L90: */ } /* L100: */ } /* ==== Accumulate orthogonal transformations. ==== */ if (accum) { /* ==== Accumulate U. (If needed, update Z later */ /* . with an efficient matrix-matrix */ /* . multiply.) ==== */ i__6 = mtop; for (m = mbot; m >= i__6; --m) { k = krcol + (m - 1 << 1); kms = k - incol; /* Computing MAX */ i__7 = 1, i__4 = *ktop - incol; i2 = f2cmax(i__7,i__4); /* Computing MAX */ i__7 = i2, i__4 = kms - (krcol - incol) + 1; i2 = f2cmax(i__7,i__4); /* Computing MIN */ i__7 = kdu, i__4 = krcol + (mbot - 1 << 1) - incol + 5; i4 = f2cmin(i__7,i__4); i__7 = i4; for (j = i2; j <= i__7; ++j) { i__4 = m * v_dim1 + 1; i__5 = j + (kms + 1) * u_dim1; i__8 = m * v_dim1 + 2; i__9 = j + (kms + 2) * u_dim1; z__4.r = v[i__8].r * u[i__9].r - v[i__8].i * u[i__9] .i, z__4.i = v[i__8].r * u[i__9].i + v[i__8] .i * u[i__9].r; z__3.r = u[i__5].r + z__4.r, z__3.i = u[i__5].i + z__4.i; i__10 = m * v_dim1 + 3; i__11 = j + (kms + 3) * u_dim1; z__5.r = v[i__10].r * u[i__11].r - v[i__10].i * u[ i__11].i, z__5.i = v[i__10].r * u[i__11].i + v[i__10].i * u[i__11].r; z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i; z__1.r = v[i__4].r * z__2.r - v[i__4].i * z__2.i, z__1.i = v[i__4].r * z__2.i + v[i__4].i * z__2.r; refsum.r = z__1.r, refsum.i = z__1.i; i__4 = j + (kms + 1) * u_dim1; i__5 = j + (kms + 1) * u_dim1; z__1.r = u[i__5].r - refsum.r, z__1.i = u[i__5].i - refsum.i; u[i__4].r = z__1.r, u[i__4].i = z__1.i; i__4 = j + (kms + 2) * u_dim1; i__5 = j + (kms + 2) * u_dim1; d_cnjg(&z__3, &v[m * v_dim1 + 2]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = u[i__5].r - z__2.r, z__1.i = u[i__5].i - z__2.i; u[i__4].r = z__1.r, u[i__4].i = z__1.i; i__4 = j + (kms + 3) * u_dim1; i__5 = j + (kms + 3) * u_dim1; d_cnjg(&z__3, &v[m * v_dim1 + 3]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = u[i__5].r - z__2.r, z__1.i = u[i__5].i - z__2.i; u[i__4].r = z__1.r, u[i__4].i = z__1.i; /* L110: */ } /* L120: */ } } else if (*wantz) { /* ==== U is not accumulated, so update Z */ /* . now by multiplying by reflections */ /* . from the right. ==== */ i__6 = mtop; for (m = mbot; m >= i__6; --m) { k = krcol + (m - 1 << 1); i__7 = *ihiz; for (j = *iloz; j <= i__7; ++j) { i__4 = m * v_dim1 + 1; i__5 = j + (k + 1) * z_dim1; i__8 = m * v_dim1 + 2; i__9 = j + (k + 2) * z_dim1; z__4.r = v[i__8].r * z__[i__9].r - v[i__8].i * z__[ i__9].i, z__4.i = v[i__8].r * z__[i__9].i + v[ i__8].i * z__[i__9].r; z__3.r = z__[i__5].r + z__4.r, z__3.i = z__[i__5].i + z__4.i; i__10 = m * v_dim1 + 3; i__11 = j + (k + 3) * z_dim1; z__5.r = v[i__10].r * z__[i__11].r - v[i__10].i * z__[ i__11].i, z__5.i = v[i__10].r * z__[i__11].i + v[i__10].i * z__[i__11].r; z__2.r = z__3.r + z__5.r, z__2.i = z__3.i + z__5.i; z__1.r = v[i__4].r * z__2.r - v[i__4].i * z__2.i, z__1.i = v[i__4].r * z__2.i + v[i__4].i * z__2.r; refsum.r = z__1.r, refsum.i = z__1.i; i__4 = j + (k + 1) * z_dim1; i__5 = j + (k + 1) * z_dim1; z__1.r = z__[i__5].r - refsum.r, z__1.i = z__[i__5].i - refsum.i; z__[i__4].r = z__1.r, z__[i__4].i = z__1.i; i__4 = j + (k + 2) * z_dim1; i__5 = j + (k + 2) * z_dim1; d_cnjg(&z__3, &v[m * v_dim1 + 2]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = z__[i__5].r - z__2.r, z__1.i = z__[i__5].i - z__2.i; z__[i__4].r = z__1.r, z__[i__4].i = z__1.i; i__4 = j + (k + 3) * z_dim1; i__5 = j + (k + 3) * z_dim1; d_cnjg(&z__3, &v[m * v_dim1 + 3]); z__2.r = refsum.r * z__3.r - refsum.i * z__3.i, z__2.i = refsum.r * z__3.i + refsum.i * z__3.r; z__1.r = z__[i__5].r - z__2.r, z__1.i = z__[i__5].i - z__2.i; z__[i__4].r = z__1.r, z__[i__4].i = z__1.i; /* L130: */ } /* L140: */ } } /* ==== End of near-the-diagonal bulge chase. ==== */ /* L145: */ } /* ==== Use U (if accumulated) to update far-from-diagonal */ /* . entries in H. If required, use U to update Z as */ /* . well. ==== */ if (accum) { if (*wantt) { jtop = 1; jbot = *n; } else { jtop = *ktop; jbot = *kbot; } /* Computing MAX */ i__3 = 1, i__6 = *ktop - incol; k1 = f2cmax(i__3,i__6); /* Computing MAX */ i__3 = 0, i__6 = ndcol - *kbot; nu = kdu - f2cmax(i__3,i__6) - k1 + 1; /* ==== Horizontal Multiply ==== */ i__3 = jbot; i__6 = *nh; for (jcol = f2cmin(ndcol,*kbot) + 1; i__6 < 0 ? jcol >= i__3 : jcol <= i__3; jcol += i__6) { /* Computing MIN */ i__7 = *nh, i__4 = jbot - jcol + 1; jlen = f2cmin(i__7,i__4); zgemm_("C", "N", &nu, &jlen, &nu, &c_b2, &u[k1 + k1 * u_dim1], ldu, &h__[incol + k1 + jcol * h_dim1], ldh, &c_b1, & wh[wh_offset], ldwh); zlacpy_("ALL", &nu, &jlen, &wh[wh_offset], ldwh, &h__[incol + k1 + jcol * h_dim1], ldh); /* L150: */ } /* ==== Vertical multiply ==== */ i__6 = f2cmax(*ktop,incol) - 1; i__3 = *nv; for (jrow = jtop; i__3 < 0 ? jrow >= i__6 : jrow <= i__6; jrow += i__3) { /* Computing MIN */ i__7 = *nv, i__4 = f2cmax(*ktop,incol) - jrow; jlen = f2cmin(i__7,i__4); zgemm_("N", "N", &jlen, &nu, &nu, &c_b2, &h__[jrow + (incol + k1) * h_dim1], ldh, &u[k1 + k1 * u_dim1], ldu, &c_b1, &wv[wv_offset], ldwv); zlacpy_("ALL", &jlen, &nu, &wv[wv_offset], ldwv, &h__[jrow + ( incol + k1) * h_dim1], ldh); /* L160: */ } /* ==== Z multiply (also vertical) ==== */ if (*wantz) { i__3 = *ihiz; i__6 = *nv; for (jrow = *iloz; i__6 < 0 ? jrow >= i__3 : jrow <= i__3; jrow += i__6) { /* Computing MIN */ i__7 = *nv, i__4 = *ihiz - jrow + 1; jlen = f2cmin(i__7,i__4); zgemm_("N", "N", &jlen, &nu, &nu, &c_b2, &z__[jrow + ( incol + k1) * z_dim1], ldz, &u[k1 + k1 * u_dim1], ldu, &c_b1, &wv[wv_offset], ldwv); zlacpy_("ALL", &jlen, &nu, &wv[wv_offset], ldwv, &z__[ jrow + (incol + k1) * z_dim1], ldz); /* L170: */ } } } /* L180: */ } /* ==== End of ZLAQR5 ==== */ return 0; } /* zlaqr5_ */