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OpenBLAS/lapack-netlib/SRC/shseqr.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#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 blasint logical;
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 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);}
#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)}
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static real c_b11 = 0.f;
static real c_b12 = 1.f;
static integer c__12 = 12;
static integer c__2 = 2;
static integer c__49 = 49;
/* > \brief \b SHSEQR */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SHSEQR + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/shseqr.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/shseqr.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/shseqr.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SHSEQR( 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 */
/* REAL H( LDH, * ), WI( * ), WORK( * ), WR( * ), */
/* $ Z( LDZ, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SHSEQR 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 SGEBAL, and then passed to ZGEHRD */
/* > when the matrix output by SGEBAL 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 REAL 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 SHSEQR, 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 REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] WI */
/* > \verbatim */
/* > WI is REAL 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 REAL 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 SORGHR */
/* > after the call to SGEHRD 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 REAL 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 SHSEQR does a workspace query. */
/* > In this case, SHSEQR 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, SHSEQR 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 realOTHERcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Karen Braman and Ralph Byers, Department of Mathematics, */
/* > University of Kansas, USA */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > Default values supplied by */
/* > ILAENV(ISPEC,'SHSEQR',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 SLAHQR vs SLAQR0 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 */
/* > SLAHQR 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 */ void shseqr_(char *job, char *compz, integer *n, integer *ilo,
integer *ihi, real *h__, integer *ldh, real *wr, real *wi, real *z__,
integer *ldz, real *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;
real r__1;
char ch__1[2];
/* Local variables */
integer kbot, nmin, i__;
extern logical lsame_(char *, char *);
logical initz;
real workl[49];
logical wantt, wantz;
extern /* Subroutine */ void slaqr0_(logical *, logical *, integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, integer *, real *, integer *, real *, integer *, integer *);
real hl[2401] /* was [49][49] */;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ void slahqr_(logical *, logical *, integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
, integer *, real *, integer *, integer *), slacpy_(char *,
integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *,
real *, integer *);
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 */
/* . SLAHQR because of insufficient subdiagonal scratch space. */
/* . (This is a hard limit.) ==== */
/* ==== NL allocates some local workspace to help small matrices */
/* . through a rare SLAHQR 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] = (real) 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_("SHSEQR", &i__1, (ftnlen)6);
return;
} else if (*n == 0) {
/* ==== Quick return in case N = 0; nothing to do. ==== */
return;
} else if (lquery) {
/* ==== Quick return in case of a workspace query ==== */
slaqr0_(&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 */
r__1 = (real) f2cmax(1,*n);
work[1] = f2cmax(r__1,work[1]);
return;
} else {
/* ==== copy eigenvalues isolated by SGEBAL ==== */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
wr[i__] = h__[i__ + i__ * h_dim1];
wi[i__] = 0.f;
/* L10: */
}
i__1 = *n;
for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
wr[i__] = h__[i__ + i__ * h_dim1];
wi[i__] = 0.f;
/* L20: */
}
/* ==== Initialize Z, if requested ==== */
if (initz) {
slaset_("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.f;
return;
}
/* ==== SLAHQR/SLAQR0 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, "SHSEQR", ch__1, n, ilo, ihi, lwork, (ftnlen)6,
(ftnlen)2);
nmin = f2cmax(15,nmin);
/* ==== SLAQR0 for big matrices; SLAHQR for small ones ==== */
if (*n > nmin) {
slaqr0_(&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 ==== */
slahqr_(&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 SLAHQR failure! SLAQR0 sometimes succeeds */
/* . when SLAHQR fails. ==== */
kbot = *info;
if (*n >= 49) {
/* ==== Larger matrices have enough subdiagonal scratch */
/* . space to call SLAQR0 directly. ==== */
slaqr0_(&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 SLAQR0. Hence, */
/* . tiny matrices must be copied into a larger */
/* . array before calling SLAQR0. ==== */
slacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49);
hl[*n + 1 + *n * 49 - 50] = 0.f;
i__1 = 49 - *n;
slaset_("A", &c__49, &i__1, &c_b11, &c_b11, &hl[(*n + 1) *
49 - 49], &c__49);
slaqr0_(&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) {
slacpy_("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;
slaset_("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 */
r__1 = (real) f2cmax(1,*n);
work[1] = f2cmax(r__1,work[1]);
}
/* ==== End of SHSEQR ==== */
return;
} /* shseqr_ */
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