#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__0 = 0;

static real c_b7 = 1.f;

static integer c__1 = 1;

static integer c_n1 = -1;

/* > \brief \b SLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller o

nes by appending a row. Used by sbdsdc. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SLASD6 + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasd6.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasd6.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasd6.

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, */

/*                          IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, */

/*                          LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, */

/*                          IWORK, INFO ) */

/*       INTEGER            GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */

/*      $                   NR, SQRE */

/*       REAL               ALPHA, BETA, C, S */

/*       INTEGER            GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */

/*      $                   PERM( * ) */

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

/*      $                   GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */

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

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > SLASD6 computes the SVD of an updated upper bidiagonal matrix B */

/* > obtained by merging two smaller ones by appending a row. This */

/* > routine is used only for the problem which requires all singular */

/* > values and optionally singular vector matrices in factored form. */

/* > B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */

/* > A related subroutine, SLASD1, handles the case in which all singular */

/* > values and singular vectors of the bidiagonal matrix are desired. */

/* > */

/* > SLASD6 computes the SVD as follows: */

/* > */

/* >               ( D1(in)    0    0       0 ) */

/* >   B = U(in) * (   Z1**T   a   Z2**T    b ) * VT(in) */

/* >               (   0       0   D2(in)   0 ) */

/* > */

/* >     = U(out) * ( D(out) 0) * VT(out) */

/* > */

/* > where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M */

/* > with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */

/* > elsewhere; and the entry b is empty if SQRE = 0. */

/* > */

/* > The singular values of B can be computed using D1, D2, the first */

/* > components of all the right singular vectors of the lower block, and */

/* > the last components of all the right singular vectors of the upper */

/* > block. These components are stored and updated in VF and VL, */

/* > respectively, in SLASD6. Hence U and VT are not explicitly */

/* > referenced. */

/* > */

/* > The singular values are stored in D. The algorithm consists of two */

/* > stages: */

/* > */

/* >       The first stage consists of deflating the size of the problem */

/* >       when there are multiple singular values or if there is a zero */

/* >       in the Z vector. For each such occurrence the dimension of the */

/* >       secular equation problem is reduced by one. This stage is */

/* >       performed by the routine SLASD7. */

/* > */

/* >       The second stage consists of calculating the updated */

/* >       singular values. This is done by finding the roots of the */

/* >       secular equation via the routine SLASD4 (as called by SLASD8). */

/* >       This routine also updates VF and VL and computes the distances */

/* >       between the updated singular values and the old singular */

/* >       values. */

/* > */

/* > SLASD6 is called from SLASDA. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] ICOMPQ */

/* > \verbatim */

/* >          ICOMPQ is INTEGER */

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

/* >         factored form: */

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

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

/* > \endverbatim */

/* > */

/* > \param[in] NL */

/* > \verbatim */

/* >          NL is INTEGER */

/* >         The row dimension of the upper block.  NL >= 1. */

/* > \endverbatim */

/* > */

/* > \param[in] NR */

/* > \verbatim */

/* >          NR is INTEGER */

/* >         The row dimension of the lower block.  NR >= 1. */

/* > \endverbatim */

/* > */

/* > \param[in] SQRE */

/* > \verbatim */

/* >          SQRE is INTEGER */

/* >         = 0: the lower block is an NR-by-NR square matrix. */

/* >         = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */

/* > */

/* >         The bidiagonal matrix has row dimension N = NL + NR + 1, */

/* >         and column dimension M = N + SQRE. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          D is REAL array, dimension (NL+NR+1). */

/* >         On entry D(1:NL,1:NL) contains the singular values of the */

/* >         upper block, and D(NL+2:N) contains the singular values */

/* >         of the lower block. On exit D(1:N) contains the singular */

/* >         values of the modified matrix. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >         On entry, VF(1:NL+1) contains the first components of all */

/* >         right singular vectors of the upper block; and VF(NL+2:M) */

/* >         contains the first components of all right singular vectors */

/* >         of the lower block. On exit, VF contains the first components */

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

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >         On entry, VL(1:NL+1) contains the  last components of all */

/* >         right singular vectors of the upper block; and VL(NL+2:M) */

/* >         contains the last components of all right singular vectors of */

/* >         the lower block. On exit, VL contains the last components of */

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

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          ALPHA is REAL */

/* >         Contains the diagonal element associated with the added row. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          BETA is REAL */

/* >         Contains the off-diagonal element associated with the added */

/* >         row. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          IDXQ is INTEGER array, dimension (N) */

/* >         This contains the permutation which will reintegrate the */

/* >         subproblem just solved back into sorted order, i.e. */

/* >         D( IDXQ( I = 1, N ) ) will be in ascending order. */

/* > \endverbatim */

/* > */

/* > \param[out] PERM */

/* > \verbatim */

/* >          PERM is INTEGER array, dimension ( N ) */

/* >         The permutations (from deflation and sorting) to be applied */

/* >         to each block. Not referenced if ICOMPQ = 0. */

/* > \endverbatim */

/* > */

/* > \param[out] GIVPTR */

/* > \verbatim */

/* >          GIVPTR is INTEGER */

/* >         The number of Givens rotations which took place in this */

/* >         subproblem. Not referenced if ICOMPQ = 0. */

/* > \endverbatim */

/* > */

/* > \param[out] GIVCOL */

/* > \verbatim */

/* >          GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */

/* >         Each pair of numbers indicates a pair of columns to take place */

/* >         in a Givens rotation. Not referenced if ICOMPQ = 0. */

/* > \endverbatim */

/* > */

/* > \param[in] LDGCOL */

/* > \verbatim */

/* >          LDGCOL is INTEGER */

/* >         leading dimension of GIVCOL, must be at least N. */

/* > \endverbatim */

/* > */

/* > \param[out] GIVNUM */

/* > \verbatim */

/* >          GIVNUM is REAL array, dimension ( LDGNUM, 2 ) */

/* >         Each number indicates the C or S value to be used in the */

/* >         corresponding Givens rotation. Not referenced if ICOMPQ = 0. */

/* > \endverbatim */

/* > */

/* > \param[in] LDGNUM */

/* > \verbatim */

/* >          LDGNUM is INTEGER */

/* >         The leading dimension of GIVNUM and POLES, must be at least N. */

/* > \endverbatim */

/* > */

/* > \param[out] POLES */

/* > \verbatim */

/* >          POLES is REAL array, dimension ( LDGNUM, 2 ) */

/* >         On exit, POLES(1,*) is an array containing the new singular */

/* >         values obtained from solving the secular equation, and */

/* >         POLES(2,*) is an array containing the poles in the secular */

/* >         equation. Not referenced if ICOMPQ = 0. */

/* > \endverbatim */

/* > */

/* > \param[out] DIFL */

/* > \verbatim */

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

/* >         On exit, DIFL(I) is the distance between I-th updated */

/* >         (undeflated) singular value and the I-th (undeflated) old */

/* >         singular value. */

/* > \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. */

/* > */

/* >         See SLASD8 for details on DIFL and DIFR. */

/* > \endverbatim */

/* > */

/* > \param[out] Z */

/* > \verbatim */

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

/* >         The first elements of this array contain the components */

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

/* > \endverbatim */

/* > */

/* > \param[out] K */

/* > \verbatim */

/* >          K is INTEGER */

/* >         Contains the dimension of the non-deflated matrix, */

/* >         This is the order of the related secular equation. 1 <= K <=N. */

/* > \endverbatim */

/* > */

/* > \param[out] C */

/* > \verbatim */

/* >          C is REAL */

/* >         C contains garbage if SQRE =0 and the C-value of a Givens */

/* >         rotation related to the right null space if SQRE = 1. */

/* > \endverbatim */

/* > */

/* > \param[out] S */

/* > \verbatim */

/* >          S is REAL */

/* >         S contains garbage if SQRE =0 and the S-value of a Givens */

/* >         rotation related to the right null space if SQRE = 1. */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* >          WORK is REAL array, dimension ( 4 * M ) */

/* > \endverbatim */

/* > */

/* > \param[out] IWORK */

/* > \verbatim */

/* >          IWORK is INTEGER array, dimension ( 3 * N ) */

/* > \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 2016 */

/* > \ingroup OTHERauxiliary */

/* > \par Contributors: */

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

/* > */

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

/* >     California at Berkeley, USA */

/* > */

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

/* Subroutine */ void slasd6_(integer *icompq, integer *nl, integer *nr, 

  integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta,

   integer *idxq, integer *perm, integer *givptr, integer *givcol, 

  integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *

  difl, real *difr, real *z__, integer *k, real *c__, real *s, real *

  work, integer *iwork, integer *info)

{

    /* System generated locals */

    integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, 

      poles_dim1, poles_offset, i__1;

    real r__1, r__2;

    /* Local variables */

    integer idxc, idxp, ivfw, ivlw, i__, m, n;

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

      integer *);

    integer n1, n2;

    extern /* Subroutine */ void slasd7_(integer *, integer *, integer *, 

      integer *, integer *, real *, real *, real *, real *, real *, 

      real *, real *, real *, real *, real *, integer *, integer *, 

      integer *, integer *, integer *, integer *, integer *, real *, 

      integer *, real *, real *, integer *), slasd8_(integer *, integer 

      *, real *, real *, real *, real *, real *, real *, integer *, 

      real *, real *, integer *);

    integer iw, isigma;

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

    extern void slascl_(

      char *, integer *, integer *, real *, real *, integer *, integer *

      , real *, integer *, integer *), slamrg_(integer *, 

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

    real orgnrm;

    integer idx;

/*  -- LAPACK auxiliary 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..-- */

/*     June 2016 */

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

/*     Test the input parameters. */

    /* Parameter adjustments */

    --d__;

    --vf;

    --vl;

    --idxq;

    --perm;

    givcol_dim1 = *ldgcol;

    givcol_offset = 1 + givcol_dim1 * 1;

    givcol -= givcol_offset;

    poles_dim1 = *ldgnum;

    poles_offset = 1 + poles_dim1 * 1;

    poles -= poles_offset;

    givnum_dim1 = *ldgnum;

    givnum_offset = 1 + givnum_dim1 * 1;

    givnum -= givnum_offset;

    --difl;

    --difr;

    --z__;

    --work;

    --iwork;

    /* Function Body */

    *info = 0;

    n = *nl + *nr + 1;

    m = n + *sqre;

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

  *info = -1;

    } else if (*nl < 1) {

  *info = -2;

    } else if (*nr < 1) {

  *info = -3;

    } else if (*sqre < 0 || *sqre > 1) {

  *info = -4;

    } else if (*ldgcol < n) {

  *info = -14;

    } else if (*ldgnum < n) {

  *info = -16;

    }

    if (*info != 0) {

  i__1 = -(*info);

  xerbla_("SLASD6", &i__1, (ftnlen)6);

  return;

    }

/*     The following values are for bookkeeping purposes only.  They are */

/*     integer pointers which indicate the portion of the workspace */

/*     used by a particular array in SLASD7 and SLASD8. */

    isigma = 1;

    iw = isigma + n;

    ivfw = iw + m;

    ivlw = ivfw + m;

    idx = 1;

    idxc = idx + n;

    idxp = idxc + n;

/*     Scale. */

/* Computing MAX */

    r__1 = abs(*alpha), r__2 = abs(*beta);

    orgnrm = f2cmax(r__1,r__2);

    d__[*nl + 1] = 0.f;

    i__1 = n;

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

  if ((r__1 = d__[i__], abs(r__1)) > orgnrm) {

      orgnrm = (r__1 = d__[i__], abs(r__1));

  }

/* L10: */

    }

    slascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);

    *alpha /= orgnrm;

    *beta /= orgnrm;

/*     Sort and Deflate singular values. */

    slasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &

      work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &

      iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[

      givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, 

      info);

/*     Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */

    slasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], 

      ldgnum, &work[isigma], &work[iw], info);

/*     Report the possible convergence failure. */

    if (*info != 0) {

  return;

    }

/*     Save the poles if ICOMPQ = 1. */

    if (*icompq == 1) {

  scopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);

  scopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);

    }

/*     Unscale. */

    slascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info);

/*     Prepare the IDXQ sorting permutation. */

    n1 = *k;

    n2 = n - *k;

    slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);

    return;

/*     End of SLASD6 */

} /* slasd6_ */