#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 DHSEQR */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DHSEQR + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z, */ /* LDZ, WORK, LWORK, INFO ) */ /* INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N */ /* CHARACTER COMPZ, JOB */ /* DOUBLE PRECISION H( LDH, * ), WI( * ), WORK( * ), WR( * ), */ /* $ Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DHSEQR computes the eigenvalues of a Hessenberg matrix H */ /* > and, optionally, the matrices T and Z from the Schur decomposition */ /* > H = Z T Z**T, where T is an upper quasi-triangular matrix (the */ /* > Schur form), and Z is the orthogonal matrix of Schur vectors. */ /* > */ /* > Optionally Z may be postmultiplied into an input orthogonal */ /* > matrix Q so that this routine can give the Schur factorization */ /* > of a matrix A which has been reduced to the Hessenberg form H */ /* > by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] JOB */ /* > \verbatim */ /* > JOB is CHARACTER*1 */ /* > = 'E': compute eigenvalues only; */ /* > = 'S': compute eigenvalues and the Schur form T. */ /* > \endverbatim */ /* > */ /* > \param[in] COMPZ */ /* > \verbatim */ /* > COMPZ is CHARACTER*1 */ /* > = 'N': no Schur vectors are computed; */ /* > = 'I': Z is initialized to the unit matrix and the matrix Z */ /* > of Schur vectors of H is returned; */ /* > = 'V': Z must contain an orthogonal matrix Q on entry, and */ /* > the product Q*Z is returned. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix H. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] ILO */ /* > \verbatim */ /* > ILO is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[in] IHI */ /* > \verbatim */ /* > IHI is INTEGER */ /* > */ /* > It is assumed that H is already upper triangular in rows */ /* > and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */ /* > set by a previous call to DGEBAL, and then passed to ZGEHRD */ /* > when the matrix output by DGEBAL is reduced to Hessenberg */ /* > form. Otherwise ILO and IHI should be set to 1 and N */ /* > respectively. If N > 0, then 1 <= ILO <= IHI <= N. */ /* > If N = 0, then ILO = 1 and IHI = 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] H */ /* > \verbatim */ /* > H is DOUBLE PRECISION array, dimension (LDH,N) */ /* > On entry, the upper Hessenberg matrix H. */ /* > On exit, if INFO = 0 and JOB = 'S', then H contains the */ /* > upper quasi-triangular matrix T from the Schur decomposition */ /* > (the Schur form); 2-by-2 diagonal blocks (corresponding to */ /* > complex conjugate pairs of eigenvalues) are returned in */ /* > standard form, with H(i,i) = H(i+1,i+1) and */ /* > H(i+1,i)*H(i,i+1) < 0. If INFO = 0 and JOB = 'E', the */ /* > contents of H are unspecified on exit. (The output value of */ /* > H when INFO > 0 is given under the description of INFO */ /* > below.) */ /* > */ /* > Unlike earlier versions of DHSEQR, this subroutine may */ /* > explicitly H(i,j) = 0 for i > j and j = 1, 2, ... ILO-1 */ /* > or j = IHI+1, IHI+2, ... N. */ /* > \endverbatim */ /* > */ /* > \param[in] LDH */ /* > \verbatim */ /* > LDH is INTEGER */ /* > The leading dimension of the array H. LDH >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] WR */ /* > \verbatim */ /* > WR is DOUBLE PRECISION array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] WI */ /* > \verbatim */ /* > WI is DOUBLE PRECISION array, dimension (N) */ /* > */ /* > The real and imaginary parts, respectively, of the computed */ /* > eigenvalues. If two eigenvalues are computed as a complex */ /* > conjugate pair, they are stored in consecutive elements of */ /* > WR and WI, say the i-th and (i+1)th, with WI(i) > 0 and */ /* > WI(i+1) < 0. If JOB = 'S', the eigenvalues are stored in */ /* > the same order as on the diagonal of the Schur form returned */ /* > in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 */ /* > diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and */ /* > WI(i+1) = -WI(i). */ /* > \endverbatim */ /* > */ /* > \param[in,out] Z */ /* > \verbatim */ /* > Z is DOUBLE PRECISION array, dimension (LDZ,N) */ /* > If COMPZ = 'N', Z is not referenced. */ /* > If COMPZ = 'I', on entry Z need not be set and on exit, */ /* > if INFO = 0, Z contains the orthogonal matrix Z of the Schur */ /* > vectors of H. If COMPZ = 'V', on entry Z must contain an */ /* > N-by-N matrix Q, which is assumed to be equal to the unit */ /* > matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, */ /* > if INFO = 0, Z contains Q*Z. */ /* > Normally Q is the orthogonal matrix generated by DORGHR */ /* > after the call to DGEHRD which formed the Hessenberg matrix */ /* > H. (The output value of Z when INFO > 0 is given under */ /* > the description of INFO below.) */ /* > \endverbatim */ /* > */ /* > \param[in] LDZ */ /* > \verbatim */ /* > LDZ is INTEGER */ /* > The leading dimension of the array Z. if COMPZ = 'I' or */ /* > COMPZ = 'V', then LDZ >= MAX(1,N). Otherwise, LDZ >= 1. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (LWORK) */ /* > On exit, if INFO = 0, WORK(1) returns an estimate of */ /* > the optimal value for LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. LWORK >= f2cmax(1,N) */ /* > is sufficient and delivers very good and sometimes */ /* > optimal performance. However, LWORK as large as 11*N */ /* > may be required for optimal performance. A workspace */ /* > query is recommended to determine the optimal workspace */ /* > size. */ /* > */ /* > If LWORK = -1, then DHSEQR does a workspace query. */ /* > In this case, DHSEQR checks the input parameters and */ /* > estimates the optimal workspace size for the given */ /* > values of N, ILO and IHI. The estimate is returned */ /* > in WORK(1). No error message related to LWORK is */ /* > issued by XERBLA. Neither H nor Z are accessed. */ /* > \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, DHSEQR failed to compute all of */ /* > the eigenvalues. Elements 1:ilo-1 and i+1:n of WR */ /* > and WI contain those eigenvalues which have been */ /* > successfully computed. (Failures are rare.) */ /* > */ /* > If INFO > 0 and JOB = 'E', then on exit, the */ /* > remaining unconverged eigenvalues are the eigen- */ /* > values of the upper Hessenberg matrix rows and */ /* > columns ILO through INFO of the final, output */ /* > value of H. */ /* > */ /* > If INFO > 0 and JOB = 'S', then on exit */ /* > */ /* > (*) (initial value of H)*U = U*(final value of H) */ /* > */ /* > where U is an orthogonal matrix. The final */ /* > value of H is upper Hessenberg and quasi-triangular */ /* > in rows and columns INFO+1 through IHI. */ /* > */ /* > If INFO > 0 and COMPZ = 'V', then on exit */ /* > */ /* > (final value of Z) = (initial value of Z)*U */ /* > */ /* > where U is the orthogonal matrix in (*) (regard- */ /* > less of the value of JOB.) */ /* > */ /* > If INFO > 0 and COMPZ = 'I', then on exit */ /* > (final value of Z) = U */ /* > where U is the orthogonal matrix in (*) (regard- */ /* > less of the value of JOB.) */ /* > */ /* > If INFO > 0 and COMPZ = 'N', then Z is not */ /* > accessed. */ /* > \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 Contributors: */ /* ================== */ /* > */ /* > Karen Braman and Ralph Byers, Department of Mathematics, */ /* > University of Kansas, USA */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > Default values supplied by */ /* > ILAENV(ISPEC,'DHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK). */ /* > It is suggested that these defaults be adjusted in order */ /* > to attain best performance in each particular */ /* > computational environment. */ /* > */ /* > ISPEC=12: The DLAHQR vs DLAQR0 crossover point. */ /* > Default: 75. (Must be at least 11.) */ /* > */ /* > ISPEC=13: Recommended deflation window size. */ /* > This depends on ILO, IHI and NS. NS is the */ /* > number of simultaneous shifts returned */ /* > by ILAENV(ISPEC=15). (See ISPEC=15 below.) */ /* > The default for (IHI-ILO+1) <= 500 is NS. */ /* > The default for (IHI-ILO+1) > 500 is 3*NS/2. */ /* > */ /* > ISPEC=14: Nibble crossover point. (See IPARMQ for */ /* > details.) Default: 14% of deflation window */ /* > size. */ /* > */ /* > ISPEC=15: Number of simultaneous shifts in a multishift */ /* > QR iteration. */ /* > */ /* > If IHI-ILO+1 is ... */ /* > */ /* > greater than ...but less ... the */ /* > or equal to ... than default is */ /* > */ /* > 1 30 NS = 2(+) */ /* > 30 60 NS = 4(+) */ /* > 60 150 NS = 10(+) */ /* > 150 590 NS = ** */ /* > 590 3000 NS = 64 */ /* > 3000 6000 NS = 128 */ /* > 6000 infinity NS = 256 */ /* > */ /* > (+) By default some or all matrices of this order */ /* > are passed to the implicit double shift routine */ /* > DLAHQR and this parameter is ignored. See */ /* > ISPEC=12 above and comments in IPARMQ for */ /* > details. */ /* > */ /* > (**) The asterisks (**) indicate an ad-hoc */ /* > function of N increasing from 10 to 64. */ /* > */ /* > ISPEC=16: Select structured matrix multiply. */ /* > If the number of simultaneous shifts (specified */ /* > by ISPEC=15) is less than 14, then the default */ /* > for ISPEC=16 is 0. Otherwise the default for */ /* > ISPEC=16 is 2. */ /* > \endverbatim */ /* > \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. */ /* > \n */ /* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */ /* > Algorithm Part II: Aggressive Early Deflation, SIAM Journal */ /* > of Matrix Analysis, volume 23, pages 948--973, 2002. */ /* ===================================================================== */ /* Subroutine */ int dhseqr_(char *job, char *compz, integer *n, integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal *wr, doublereal *wi, doublereal *z__, integer *ldz, doublereal *work, integer *lwork, integer *info) { /* System generated locals */ address a__1[2]; integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2[2], i__3; doublereal d__1; char ch__1[2]; /* Local variables */ integer kbot, nmin, i__; extern logical lsame_(char *, char *); logical initz; doublereal workl[49]; logical wantt, wantz; extern /* Subroutine */ int dlaqr0_(logical *, logical *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *); doublereal hl[2401] /* was [49][49] */; extern /* Subroutine */ int dlahqr_(logical *, logical *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); logical lquery; /* -- 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 */ /* ===================================================================== */ /* ==== Matrices of order NTINY or smaller must be processed by */ /* . DLAHQR because of insufficient subdiagonal scratch space. */ /* . (This is a hard limit.) ==== */ /* ==== NL allocates some local workspace to help small matrices */ /* . through a rare DLAHQR failure. NL > NTINY = 15 is */ /* . required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom- */ /* . mended. (The default value of NMIN is 75.) Using NL = 49 */ /* . allows up to six simultaneous shifts and a 16-by-16 */ /* . deflation window. ==== */ /* ==== Decode and check the input parameters. ==== */ /* Parameter adjustments */ h_dim1 = *ldh; h_offset = 1 + h_dim1 * 1; h__ -= h_offset; --wr; --wi; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --work; /* Function Body */ wantt = lsame_(job, "S"); initz = lsame_(compz, "I"); wantz = initz || lsame_(compz, "V"); work[1] = (doublereal) f2cmax(1,*n); lquery = *lwork == -1; *info = 0; if (! lsame_(job, "E") && ! wantt) { *info = -1; } else if (! lsame_(compz, "N") && ! wantz) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ilo < 1 || *ilo > f2cmax(1,*n)) { *info = -4; } else if (*ihi < f2cmin(*ilo,*n) || *ihi > *n) { *info = -5; } else if (*ldh < f2cmax(1,*n)) { *info = -7; } else if (*ldz < 1 || wantz && *ldz < f2cmax(1,*n)) { *info = -11; } else if (*lwork < f2cmax(1,*n) && ! lquery) { *info = -13; } if (*info != 0) { /* ==== Quick return in case of invalid argument. ==== */ i__1 = -(*info); xerbla_("DHSEQR", &i__1, (ftnlen)6); return 0; } else if (*n == 0) { /* ==== Quick return in case N = 0; nothing to do. ==== */ return 0; } else if (lquery) { /* ==== Quick return in case of a workspace query ==== */ dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[ 1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info); /* ==== Ensure reported workspace size is backward-compatible with */ /* . previous LAPACK versions. ==== */ /* Computing MAX */ d__1 = (doublereal) f2cmax(1,*n); work[1] = f2cmax(d__1,work[1]); return 0; } else { /* ==== copy eigenvalues isolated by DGEBAL ==== */ i__1 = *ilo - 1; for (i__ = 1; i__ <= i__1; ++i__) { wr[i__] = h__[i__ + i__ * h_dim1]; wi[i__] = 0.; /* L10: */ } i__1 = *n; for (i__ = *ihi + 1; i__ <= i__1; ++i__) { wr[i__] = h__[i__ + i__ * h_dim1]; wi[i__] = 0.; /* L20: */ } /* ==== Initialize Z, if requested ==== */ if (initz) { dlaset_("A", n, n, &c_b11, &c_b12, &z__[z_offset], ldz) ; } /* ==== Quick return if possible ==== */ if (*ilo == *ihi) { wr[*ilo] = h__[*ilo + *ilo * h_dim1]; wi[*ilo] = 0.; return 0; } /* ==== DLAHQR/DLAQR0 crossover point ==== */ /* Writing concatenation */ i__2[0] = 1, a__1[0] = job; i__2[1] = 1, a__1[1] = compz; s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2); nmin = ilaenv_(&c__12, "DHSEQR", ch__1, n, ilo, ihi, lwork, (ftnlen)6, (ftnlen)2); nmin = f2cmax(15,nmin); /* ==== DLAQR0 for big matrices; DLAHQR for small ones ==== */ if (*n > nmin) { dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info); } else { /* ==== Small matrix ==== */ dlahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, info); if (*info > 0) { /* ==== A rare DLAHQR failure! DLAQR0 sometimes succeeds */ /* . when DLAHQR fails. ==== */ kbot = *info; if (*n >= 49) { /* ==== Larger matrices have enough subdiagonal scratch */ /* . space to call DLAQR0 directly. ==== */ dlaqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info); } else { /* ==== Tiny matrices don't have enough subdiagonal */ /* . scratch space to benefit from DLAQR0. Hence, */ /* . tiny matrices must be copied into a larger */ /* . array before calling DLAQR0. ==== */ dlacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49); hl[*n + 1 + *n * 49 - 50] = 0.; i__1 = 49 - *n; dlaset_("A", &c__49, &i__1, &c_b11, &c_b11, &hl[(*n + 1) * 49 - 49], &c__49); dlaqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, & wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, workl, &c__49, info); if (wantt || *info != 0) { dlacpy_("A", n, n, hl, &c__49, &h__[h_offset], ldh); } } } } /* ==== Clear out the trash, if necessary. ==== */ if ((wantt || *info != 0) && *n > 2) { i__1 = *n - 2; i__3 = *n - 2; dlaset_("L", &i__1, &i__3, &c_b11, &c_b11, &h__[h_dim1 + 3], ldh); } /* ==== Ensure reported workspace size is backward-compatible with */ /* . previous LAPACK versions. ==== */ /* Computing MAX */ d__1 = (doublereal) f2cmax(1,*n); work[1] = f2cmax(d__1,work[1]); } /* ==== End of DHSEQR ==== */ return 0; } /* dhseqr_ */