#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 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++ */

#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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];

      zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];

      zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];

    }

  }

  pCf(z) = zdotc;

}

#else

  _Complex float zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);

    }

  }

  pCf(z) = zdotc;

}

#endif

static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Dcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];

      zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];

      zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];

    }

  }

  pCd(z) = zdotc;

}

#else

  _Complex double zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conj(Cd(&x[i])) * Cd(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);

    }

  }

  pCd(z) = zdotc;

}

#endif  

static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];

      zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];

      zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];

    }

  }

  pCf(z) = zdotc;

}

#else

  _Complex float zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cf(&x[i]) * Cf(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);

    }

  }

  pCf(z) = zdotc;

}

#endif

static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Dcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];

      zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];

      zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];

    }

  }

  pCd(z) = zdotc;

}

#else

  _Complex double zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cd(&x[i]) * Cd(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);

    }

  }

  pCd(z) = zdotc;

}

#endif

/*  -- translated by f2c (version 20000121).

   You must link the resulting object file with the libraries:

  -lf2c -lm   (in that order)

*/

/* > \brief \b IPARMQ */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */

/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */

/* > Download IPARMQ + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.

f"> */

/* > [TGZ]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.

f"> */

/* > [ZIP]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.

f"> */

/* > [TXT]</a> */

/* > \endhtmlonly */

/*  Definition: */

/*  =========== */

/*       INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) */

/*       INTEGER            IHI, ILO, ISPEC, LWORK, N */

/*       CHARACTER          NAME*( * ), OPTS*( * ) */

/* > \par Purpose: */

/*  ============= */

/* > */

/* > \verbatim */

/* > */

/* >      This program sets problem and machine dependent parameters */

/* >      useful for xHSEQR and related subroutines for eigenvalue */

/* >      problems. It is called whenever */

/* >      IPARMQ is called with 12 <= ISPEC <= 16 */

/* > \endverbatim */

/*  Arguments: */

/*  ========== */

/* > \param[in] ISPEC */

/* > \verbatim */

/* >          ISPEC is INTEGER */

/* >              ISPEC specifies which tunable parameter IPARMQ should */

/* >              return. */

/* > */

/* >              ISPEC=12: (INMIN)  Matrices of order nmin or less */

/* >                        are sent directly to xLAHQR, the implicit */

/* >                        double shift QR algorithm.  NMIN must be */

/* >                        at least 11. */

/* > */

/* >              ISPEC=13: (INWIN)  Size of the deflation window. */

/* >                        This is best set greater than or equal to */

/* >                        the number of simultaneous shifts NS. */

/* >                        Larger matrices benefit from larger deflation */

/* >                        windows. */

/* > */

/* >              ISPEC=14: (INIBL) Determines when to stop nibbling and */

/* >                        invest in an (expensive) multi-shift QR sweep. */

/* >                        If the aggressive early deflation subroutine */

/* >                        finds LD converged eigenvalues from an order */

/* >                        NW deflation window and LD > (NW*NIBBLE)/100, */

/* >                        then the next QR sweep is skipped and early */

/* >                        deflation is applied immediately to the */

/* >                        remaining active diagonal block.  Setting */

/* >                        IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a */

/* >                        multi-shift QR sweep whenever early deflation */

/* >                        finds a converged eigenvalue.  Setting */

/* >                        IPARMQ(ISPEC=14) greater than or equal to 100 */

/* >                        prevents TTQRE from skipping a multi-shift */

/* >                        QR sweep. */

/* > */

/* >              ISPEC=15: (NSHFTS) The number of simultaneous shifts in */

/* >                        a multi-shift QR iteration. */

/* > */

/* >              ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the */

/* >                        following meanings. */

/* >                        0:  During the multi-shift QR/QZ sweep, */

/* >                            blocked eigenvalue reordering, blocked */

/* >                            Hessenberg-triangular reduction, */

/* >                            reflections and/or rotations are not */

/* >                            accumulated when updating the */

/* >                            far-from-diagonal matrix entries. */

/* >                        1:  During the multi-shift QR/QZ sweep, */

/* >                            blocked eigenvalue reordering, blocked */

/* >                            Hessenberg-triangular reduction, */

/* >                            reflections and/or rotations are */

/* >                            accumulated, and matrix-matrix */

/* >                            multiplication is used to update the */

/* >                            far-from-diagonal matrix entries. */

/* >                        2:  During the multi-shift QR/QZ sweep, */

/* >                            blocked eigenvalue reordering, blocked */

/* >                            Hessenberg-triangular reduction, */

/* >                            reflections and/or rotations are */

/* >                            accumulated, and 2-by-2 block structure */

/* >                            is exploited during matrix-matrix */

/* >                            multiplies. */

/* >                        (If xTRMM is slower than xGEMM, then */

/* >                        IPARMQ(ISPEC=16)=1 may be more efficient than */

/* >                        IPARMQ(ISPEC=16)=2 despite the greater level of */

/* >                        arithmetic work implied by the latter choice.) */

/* > \endverbatim */

/* > */

/* > \param[in] NAME */

/* > \verbatim */

/* >          NAME is CHARACTER string */

/* >               Name of the calling subroutine */

/* > \endverbatim */

/* > */

/* > \param[in] OPTS */

/* > \verbatim */

/* >          OPTS is CHARACTER string */

/* >               This is a concatenation of the string arguments to */

/* >               TTQRE. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >               N is the order of the Hessenberg matrix H. */

/* > \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. */

/* > \endverbatim */

/* > */

/* > \param[in] LWORK */

/* > \verbatim */

/* >          LWORK is INTEGER */

/* >               The amount of workspace available. */

/* > \endverbatim */

/*  Authors: */

/*  ======== */

/* > \author Univ. of Tennessee */

/* > \author Univ. of California Berkeley */

/* > \author Univ. of Colorado Denver */

/* > \author NAG Ltd. */

/* > \date June 2017 */

/* > \ingroup OTHERauxiliary */

/* > \par Further Details: */

/*  ===================== */

/* > */

/* > \verbatim */

/* > */

/* >       Little is known about how best to choose these parameters. */

/* >       It is possible to use different values of the parameters */

/* >       for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. */

/* > */

/* >       It is probably best to choose different parameters for */

/* >       different matrices and different parameters at different */

/* >       times during the iteration, but this has not been */

/* >       implemented --- yet. */

/* > */

/* > */

/* >       The best choices of most of the parameters depend */

/* >       in an ill-understood way on the relative execution */

/* >       rate of xLAQR3 and xLAQR5 and on the nature of each */

/* >       particular eigenvalue problem.  Experiment may be the */

/* >       only practical way to determine which choices are most */

/* >       effective. */

/* > */

/* >       Following is a list of default values supplied by IPARMQ. */

/* >       These defaults may be adjusted in order to attain better */

/* >       performance in any particular computational environment. */

/* > */

/* >       IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. */

/* >                        Default: 75. (Must be at least 11.) */

/* > */

/* >       IPARMQ(ISPEC=13) Recommended deflation window size. */

/* >                        This depends on ILO, IHI and NS, the */

/* >                        number of simultaneous shifts returned */

/* >                        by IPARMQ(ISPEC=15).  The default for */

/* >                        (IHI-ILO+1) <= 500 is NS.  The default */

/* >                        for (IHI-ILO+1) > 500 is 3*NS/2. */

/* > */

/* >       IPARMQ(ISPEC=14) Nibble crossover point.  Default: 14. */

/* > */

/* >       IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. */

/* >                        a multi-shift QR iteration. */

/* > */

/* >                        If IHI-ILO+1 is ... */

/* > */

/* >                        greater than      ...but less    ... the */

/* >                        or equal to ...      than        default is */

/* > */

/* >                                0               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 matrices of this order are */

/* >                         passed to the implicit double shift routine */

/* >                         xLAHQR.  See IPARMQ(ISPEC=12) above.   These */

/* >                         values of NS are used only in case of a rare */

/* >                         xLAHQR failure. */

/* > */

/* >                    (**) The asterisks (**) indicate an ad-hoc */

/* >                         function increasing from 10 to 64. */

/* > */

/* >       IPARMQ(ISPEC=16) Select structured matrix multiply. */

/* >                        (See ISPEC=16 above for details.) */

/* >                        Default: 3. */

/* > \endverbatim */

/* > */

/*  ===================================================================== */

integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer 

  *ilo, integer *ihi, integer *lwork)

{

    /* System generated locals */

    integer ret_val, i__1, i__2;

    real r__1;

    /* Local variables */

    integer i__, ic, nh, ns, iz;

    char subnam[6];

    integer name_len;

/*  -- 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 2017 */

/*  ================================================================ */

    if (*ispec == 15 || *ispec == 13 || *ispec == 16) {

/*        ==== Set the number simultaneous shifts ==== */

  nh = *ihi - *ilo + 1;

  ns = 2;

  if (nh >= 30) {

      ns = 4;

  }

  if (nh >= 60) {

      ns = 10;

  }

  if (nh >= 150) {

/* Computing MAX */

      r__1 = log((real) nh) / log(2.f);

      i__1 = 10, i__2 = nh / i_nint(&r__1);

      ns = f2cmax(i__1,i__2);

  }

  if (nh >= 590) {

      ns = 64;

  }

  if (nh >= 3000) {

      ns = 128;

  }

  if (nh >= 6000) {

      ns = 256;

  }

/* Computing MAX */

  i__1 = 2, i__2 = ns - ns % 2;

  ns = f2cmax(i__1,i__2);

    }

    if (*ispec == 12) {

/*        ===== Matrices of order smaller than NMIN get sent */

/*        .     to xLAHQR, the classic double shift algorithm. */

/*        .     This must be at least 11. ==== */

  ret_val = 75;

    } else if (*ispec == 14) {

/*        ==== INIBL: skip a multi-shift qr iteration and */

/*        .    whenever aggressive early deflation finds */

/*        .    at least (NIBBLE*(window size)/100) deflations. ==== */

  ret_val = 14;

    } else if (*ispec == 15) {

/*        ==== NSHFTS: The number of simultaneous shifts ===== */

  ret_val = ns;

    } else if (*ispec == 13) {

/*        ==== NW: deflation window size.  ==== */

  if (nh <= 500) {

      ret_val = ns;

  } else {

      ret_val = ns * 3 / 2;

  }

    } else if (*ispec == 16) {

/*        ==== IACC22: Whether to accumulate reflections */

/*        .     before updating the far-from-diagonal elements */

/*        .     and whether to use 2-by-2 block structure while */

/*        .     doing it.  A small amount of work could be saved */

/*        .     by making this choice dependent also upon the */

/*        .     NH=IHI-ILO+1. */

/*        Convert NAME to upper case if the first character is lower case. */

  ret_val = 0;

  s_copy(subnam, name__, (ftnlen)6, name_len);

  ic = *(unsigned char *)subnam;

  iz = 'Z';

  if (iz == 90 || iz == 122) {

/*           ASCII character set */

      if (ic >= 97 && ic <= 122) {

    *(unsigned char *)subnam = (char) (ic - 32);

    for (i__ = 2; i__ <= 6; ++i__) {

        ic = *(unsigned char *)&subnam[i__ - 1];

        if (ic >= 97 && ic <= 122) {

      *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32);

        }

    }

      }

  } else if (iz == 233 || iz == 169) {

/*           EBCDIC character set */

      if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 

        && ic <= 169) {

    *(unsigned char *)subnam = (char) (ic + 64);

    for (i__ = 2; i__ <= 6; ++i__) {

        ic = *(unsigned char *)&subnam[i__ - 1];

        if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || 

          ic >= 162 && ic <= 169) {

      *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64);

        }

    }

      }

  } else if (iz == 218 || iz == 250) {

/*           Prime machines:  ASCII+128 */

      if (ic >= 225 && ic <= 250) {

    *(unsigned char *)subnam = (char) (ic - 32);

    for (i__ = 2; i__ <= 6; ++i__) {

        ic = *(unsigned char *)&subnam[i__ - 1];

        if (ic >= 225 && ic <= 250) {

      *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32);

        }

    }

      }

  }

  if (s_cmp(subnam + 1, "GGHRD", (ftnlen)5, (ftnlen)5) == 0 || s_cmp(

    subnam + 1, "GGHD3", (ftnlen)5, (ftnlen)5) == 0) {

      ret_val = 1;

      if (nh >= 14) {

    ret_val = 2;

      }

  } else if (s_cmp(subnam + 3, "EXC", (ftnlen)3, (ftnlen)3) == 0) {

      if (nh >= 14) {

    ret_val = 1;

      }

      if (nh >= 14) {

    ret_val = 2;

      }

  } else if (s_cmp(subnam + 1, "HSEQR", (ftnlen)5, (ftnlen)5) == 0 || 

    s_cmp(subnam + 1, "LAQR", (ftnlen)4, (ftnlen)4) == 0) {

      if (ns >= 14) {

    ret_val = 1;

      }

      if (ns >= 14) {

    ret_val = 2;

      }

  }

    } else {

/*        ===== invalid value of ispec ===== */

  ret_val = -1;

    }

/*     ==== End of IPARMQ ==== */

    return ret_val;

} /* iparmq_ */