#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)

*/

/* Table of constant values */

static integer c__1 = 1;

static integer c__0 = 0;

static real c_b8 = 1.f;

/* > \brief \b SLASD8 finds the square roots of the roots of the secular equation, and stores, for each elemen

t in D, the distance to its two nearest poles. Used by sbdsdc. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SLASD8 + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasd8.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasd8.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasd8.

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, */

/*                          DSIGMA, WORK, INFO ) */

/*       INTEGER            ICOMPQ, INFO, K, LDDIFR */

/*       REAL               D( * ), DIFL( * ), DIFR( LDDIFR, * ), */

/*      $                   DSIGMA( * ), VF( * ), VL( * ), WORK( * ), */

/*      $                   Z( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > SLASD8 finds the square roots of the roots of the secular equation, */

/* > as defined by the values in DSIGMA and Z. It makes the appropriate */

/* > calls to SLASD4, and stores, for each  element in D, the distance */

/* > to its two nearest poles (elements in DSIGMA). It also updates */

/* > the arrays VF and VL, the first and last components of all the */

/* > right singular vectors of the original bidiagonal matrix. */

/* > */

/* > SLASD8 is called from SLASD6. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] ICOMPQ */

/* > \verbatim */

/* >          ICOMPQ is INTEGER */

/* >          Specifies whether singular vectors are to be computed in */

/* >          factored form in the calling routine: */

/* >          = 0: Compute singular values only. */

/* >          = 1: Compute singular vectors in factored form as well. */

/* > \endverbatim */

/* > */

/* > \param[in] K */

/* > \verbatim */

/* >          K is INTEGER */

/* >          The number of terms in the rational function to be solved */

/* >          by SLASD4.  K >= 1. */

/* > \endverbatim */

/* > */

/* > \param[out] D */

/* > \verbatim */

/* >          D is REAL array, dimension ( K ) */

/* >          On output, D contains the updated singular values. */

/* > \endverbatim */

/* > */

/* > \param[in,out] Z */

/* > \verbatim */

/* >          Z is REAL array, dimension ( K ) */

/* >          On entry, the first K elements of this array contain the */

/* >          components of the deflation-adjusted updating row vector. */

/* >          On exit, Z is updated. */

/* > \endverbatim */

/* > */

/* > \param[in,out] VF */

/* > \verbatim */

/* >          VF is REAL array, dimension ( K ) */

/* >          On entry, VF contains  information passed through DBEDE8. */

/* >          On exit, VF contains the first K components of the first */

/* >          components of all right singular vectors of the bidiagonal */

/* >          matrix. */

/* > \endverbatim */

/* > */

/* > \param[in,out] VL */

/* > \verbatim */

/* >          VL is REAL array, dimension ( K ) */

/* >          On entry, VL contains  information passed through DBEDE8. */

/* >          On exit, VL contains the first K components of the last */

/* >          components of all right singular vectors of the bidiagonal */

/* >          matrix. */

/* > \endverbatim */

/* > */

/* > \param[out] DIFL */

/* > \verbatim */

/* >          DIFL is REAL array, dimension ( K ) */

/* >          On exit, DIFL(I) = D(I) - DSIGMA(I). */

/* > \endverbatim */

/* > */

/* > \param[out] DIFR */

/* > \verbatim */

/* >          DIFR is REAL array, */

/* >                   dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */

/* >                   dimension ( K ) if ICOMPQ = 0. */

/* >          On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */

/* >          defined and will not be referenced. */

/* > */

/* >          If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */

/* >          normalizing factors for the right singular vector matrix. */

/* > \endverbatim */

/* > */

/* > \param[in] LDDIFR */

/* > \verbatim */

/* >          LDDIFR is INTEGER */

/* >          The leading dimension of DIFR, must be at least K. */

/* > \endverbatim */

/* > */

/* > \param[in,out] DSIGMA */

/* > \verbatim */

/* >          DSIGMA is REAL array, dimension ( K ) */

/* >          On entry, the first K elements of this array contain the old */

/* >          roots of the deflated updating problem.  These are the poles */

/* >          of the secular equation. */

/* >          On exit, the elements of DSIGMA may be very slightly altered */

/* >          in value. */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* >          WORK is REAL array, dimension (3*K) */

/* > \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 = 1, a singular value did not converge */

/* > \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 Contributors: */

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

/* > */

/* >     Ming Gu and Huan Ren, Computer Science Division, University of */

/* >     California at Berkeley, USA */

/* > */

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

/* Subroutine */ void slasd8_(integer *icompq, integer *k, real *d__, real *

  z__, real *vf, real *vl, real *difl, real *difr, integer *lddifr, 

  real *dsigma, real *work, integer *info)

{

    /* System generated locals */

    integer difr_dim1, difr_offset, i__1, i__2;

    real r__1, r__2;

    /* Local variables */

    real temp;

    extern real sdot_(integer *, real *, integer *, real *, integer *);

    integer iwk2i, iwk3i;

    extern real snrm2_(integer *, real *, integer *);

    integer i__, j;

    real diflj, difrj, dsigj;

    extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *, 

      integer *);

    extern real slamc3_(real *, real *);

    extern /* Subroutine */ void slasd4_(integer *, integer *, real *, real *, 

      real *, real *, real *, real *, integer *);

    real dj;

    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);

    real dsigjp;

    extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *, 

      real *, integer *, integer *, real *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *, 

      real *, integer *);

    real rho;

    integer iwk1, iwk2, iwk3;

/*  -- 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 */

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

/*     Test the input parameters. */

    /* Parameter adjustments */

    --d__;

    --z__;

    --vf;

    --vl;

    --difl;

    difr_dim1 = *lddifr;

    difr_offset = 1 + difr_dim1 * 1;

    difr -= difr_offset;

    --dsigma;

    --work;

    /* Function Body */

    *info = 0;

    if (*icompq < 0 || *icompq > 1) {

  *info = -1;

    } else if (*k < 1) {

  *info = -2;

    } else if (*lddifr < *k) {

  *info = -9;

    }

    if (*info != 0) {

  i__1 = -(*info);

  xerbla_("SLASD8", &i__1, (ftnlen)6);

  return;

    }

/*     Quick return if possible */

    if (*k == 1) {

  d__[1] = abs(z__[1]);

  difl[1] = d__[1];

  if (*icompq == 1) {

      difl[2] = 1.f;

      difr[(difr_dim1 << 1) + 1] = 1.f;

  }

  return;

    }

/*     Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can */

/*     be computed with high relative accuracy (barring over/underflow). */

/*     This is a problem on machines without a guard digit in */

/*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */

/*     The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I), */

/*     which on any of these machines zeros out the bottommost */

/*     bit of DSIGMA(I) if it is 1; this makes the subsequent */

/*     subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation */

/*     occurs. On binary machines with a guard digit (almost all */

/*     machines) it does not change DSIGMA(I) at all. On hexadecimal */

/*     and decimal machines with a guard digit, it slightly */

/*     changes the bottommost bits of DSIGMA(I). It does not account */

/*     for hexadecimal or decimal machines without guard digits */

/*     (we know of none). We use a subroutine call to compute */

/*     2*DLAMBDA(I) to prevent optimizing compilers from eliminating */

/*     this code. */

    i__1 = *k;

    for (i__ = 1; i__ <= i__1; ++i__) {

  dsigma[i__] = slamc3_(&dsigma[i__], &dsigma[i__]) - dsigma[i__];

/* L10: */

    }

/*     Book keeping. */

    iwk1 = 1;

    iwk2 = iwk1 + *k;

    iwk3 = iwk2 + *k;

    iwk2i = iwk2 - 1;

    iwk3i = iwk3 - 1;

/*     Normalize Z. */

    rho = snrm2_(k, &z__[1], &c__1);

    slascl_("G", &c__0, &c__0, &rho, &c_b8, k, &c__1, &z__[1], k, info);

    rho *= rho;

/*     Initialize WORK(IWK3). */

    slaset_("A", k, &c__1, &c_b8, &c_b8, &work[iwk3], k);

/*     Compute the updated singular values, the arrays DIFL, DIFR, */

/*     and the updated Z. */

    i__1 = *k;

    for (j = 1; j <= i__1; ++j) {

  slasd4_(k, &j, &dsigma[1], &z__[1], &work[iwk1], &rho, &d__[j], &work[

    iwk2], info);

/*        If the root finder fails, report the convergence failure. */

  if (*info != 0) {

      return;

  }

  work[iwk3i + j] = work[iwk3i + j] * work[j] * work[iwk2i + j];

  difl[j] = -work[j];

  difr[j + difr_dim1] = -work[j + 1];

  i__2 = j - 1;

  for (i__ = 1; i__ <= i__2; ++i__) {

      work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + 

        i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[

        j]);

/* L20: */

  }

  i__2 = *k;

  for (i__ = j + 1; i__ <= i__2; ++i__) {

      work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + 

        i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[

        j]);

/* L30: */

  }

/* L40: */

    }

/*     Compute updated Z. */

    i__1 = *k;

    for (i__ = 1; i__ <= i__1; ++i__) {

  r__2 = sqrt((r__1 = work[iwk3i + i__], abs(r__1)));

  z__[i__] = r_sign(&r__2, &z__[i__]);

/* L50: */

    }

/*     Update VF and VL. */

    i__1 = *k;

    for (j = 1; j <= i__1; ++j) {

  diflj = difl[j];

  dj = d__[j];

  dsigj = -dsigma[j];

  if (j < *k) {

      difrj = -difr[j + difr_dim1];

      dsigjp = -dsigma[j + 1];

  }

  work[j] = -z__[j] / diflj / (dsigma[j] + dj);

  i__2 = j - 1;

  for (i__ = 1; i__ <= i__2; ++i__) {

      work[i__] = z__[i__] / (slamc3_(&dsigma[i__], &dsigj) - diflj) / (

        dsigma[i__] + dj);

/* L60: */

  }

  i__2 = *k;

  for (i__ = j + 1; i__ <= i__2; ++i__) {

      work[i__] = z__[i__] / (slamc3_(&dsigma[i__], &dsigjp) + difrj) / 

        (dsigma[i__] + dj);

/* L70: */

  }

  temp = snrm2_(k, &work[1], &c__1);

  work[iwk2i + j] = sdot_(k, &work[1], &c__1, &vf[1], &c__1) / temp;

  work[iwk3i + j] = sdot_(k, &work[1], &c__1, &vl[1], &c__1) / temp;

  if (*icompq == 1) {

      difr[j + (difr_dim1 << 1)] = temp;

  }

/* L80: */

    }

    scopy_(k, &work[iwk2], &c__1, &vf[1], &c__1);

    scopy_(k, &work[iwk3], &c__1, &vl[1], &c__1);

    return;

/*     End of SLASD8 */

} /* slasd8_ */