#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;

/* > \brief \b SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries 

to deflate the size of the problem. Used by sbdsdc. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SLASD7 + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasd7.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasd7.

f"> */

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

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasd7.

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, */

/*                          VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, */

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

/*                          C, S, INFO ) */

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

/*      $                   NR, SQRE */

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

/*       INTEGER            GIVCOL( LDGCOL, * ), IDX( * ), IDXP( * ), */

/*      $                   IDXQ( * ), PERM( * ) */

/*       REAL               D( * ), DSIGMA( * ), GIVNUM( LDGNUM, * ), */

/*      $                   VF( * ), VFW( * ), VL( * ), VLW( * ), Z( * ), */

/*      $                   ZW( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > SLASD7 merges the two sets of singular values together into a single */

/* > sorted set. Then it tries to deflate the size of the problem. There */

/* > are two ways in which deflation can occur:  when two or more singular */

/* > values are close together or if there is a tiny entry in the Z */

/* > vector. For each such occurrence the order of the related */

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

/* > */

/* > SLASD7 is called from SLASD6. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] ICOMPQ */

/* > \verbatim */

/* >          ICOMPQ is INTEGER */

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

/* >          in compact form, as follows: */

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

/* >          = 1: Compute singular vectors of upper */

/* >               bidiagonal matrix in compact form. */

/* > \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 */

/* >         N = NL + NR + 1 rows and */

/* >         M = N + SQRE >= N columns. */

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

/* > \verbatim */

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

/* >         On entry D contains the singular values of the two submatrices */

/* >         to be combined. On exit D contains the trailing (N-K) updated */

/* >         singular values (those which were deflated) sorted into */

/* >         increasing order. */

/* > \endverbatim */

/* > */

/* > \param[out] Z */

/* > \verbatim */

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

/* >         On exit Z contains the updating row vector in the secular */

/* >         equation. */

/* > \endverbatim */

/* > */

/* > \param[out] ZW */

/* > \verbatim */

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

/* >         Workspace for Z. */

/* > \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[out] VFW */

/* > \verbatim */

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

/* >         Workspace for VF. */

/* > \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[out] VLW */

/* > \verbatim */

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

/* >         Workspace for VL. */

/* > \endverbatim */

/* > */

/* > \param[in] ALPHA */

/* > \verbatim */

/* >          ALPHA is REAL */

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

/* > \endverbatim */

/* > */

/* > \param[in] BETA */

/* > \verbatim */

/* >          BETA is REAL */

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

/* >         row. */

/* > \endverbatim */

/* > */

/* > \param[out] DSIGMA */

/* > \verbatim */

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

/* >         Contains a copy of the diagonal elements (K-1 singular values */

/* >         and one zero) in the secular equation. */

/* > \endverbatim */

/* > */

/* > \param[out] IDX */

/* > \verbatim */

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

/* >         This will contain the permutation used to sort the contents of */

/* >         D into ascending order. */

/* > \endverbatim */

/* > */

/* > \param[out] IDXP */

/* > \verbatim */

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

/* >         This will contain the permutation used to place deflated */

/* >         values of D at the end of the array. On output IDXP(2:K) */

/* >         points to the nondeflated D-values and IDXP(K+1:N) */

/* >         points to the deflated singular values. */

/* > \endverbatim */

/* > */

/* > \param[in] IDXQ */

/* > \verbatim */

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

/* >         This contains the permutation which separately sorts the two */

/* >         sub-problems in D into ascending order.  Note that entries in */

/* >         the first half of this permutation must first be moved one */

/* >         position backward; and entries in the second half */

/* >         must first have NL+1 added to their values. */

/* > \endverbatim */

/* > */

/* > \param[out] PERM */

/* > \verbatim */

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

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

/* >         to each singular 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 */

/* >         The 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, must be at least 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] INFO */

/* > \verbatim */

/* >          INFO is INTEGER */

/* >         = 0:  successful exit. */

/* >         < 0:  if INFO = -i, the i-th argument had an illegal value. */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup OTHERauxiliary */

/* > \par Contributors: */

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

/* > */

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

/* >     California at Berkeley, USA */

/* > */

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

/* Subroutine */ void slasd7_(integer *icompq, integer *nl, integer *nr, 

  integer *sqre, integer *k, real *d__, real *z__, real *zw, real *vf, 

  real *vfw, real *vl, real *vlw, real *alpha, real *beta, real *dsigma,

   integer *idx, integer *idxp, integer *idxq, integer *perm, integer *

  givptr, integer *givcol, integer *ldgcol, real *givnum, integer *

  ldgnum, real *c__, real *s, integer *info)

{

    /* System generated locals */

    integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, i__1;

    real r__1, r__2;

    /* Local variables */

    integer idxi, idxj;

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

      integer *, real *, real *);

    integer i__, j, m, n, idxjp, jprev, k2;

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

      integer *);

    real z1;

    extern real slapy2_(real *, real *);

    integer jp;

    extern real slamch_(char *);

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

    extern void slamrg_(

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

    real hlftol, eps, tau, tol;

    integer nlp1, nlp2;

/*  -- 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..-- */

/*     December 2016 */

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

/*     Test the input parameters. */

    /* Parameter adjustments */

    --d__;

    --z__;

    --zw;

    --vf;

    --vfw;

    --vl;

    --vlw;

    --dsigma;

    --idx;

    --idxp;

    --idxq;

    --perm;

    givcol_dim1 = *ldgcol;

    givcol_offset = 1 + givcol_dim1 * 1;

    givcol -= givcol_offset;

    givnum_dim1 = *ldgnum;

    givnum_offset = 1 + givnum_dim1 * 1;

    givnum -= givnum_offset;

    /* 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 = -22;

    } else if (*ldgnum < n) {

  *info = -24;

    }

    if (*info != 0) {

  i__1 = -(*info);

  xerbla_("SLASD7", &i__1, (ftnlen)6);

  return;

    }

    nlp1 = *nl + 1;

    nlp2 = *nl + 2;

    if (*icompq == 1) {

  *givptr = 0;

    }

/*     Generate the first part of the vector Z and move the singular */

/*     values in the first part of D one position backward. */

    z1 = *alpha * vl[nlp1];

    vl[nlp1] = 0.f;

    tau = vf[nlp1];

    for (i__ = *nl; i__ >= 1; --i__) {

  z__[i__ + 1] = *alpha * vl[i__];

  vl[i__] = 0.f;

  vf[i__ + 1] = vf[i__];

  d__[i__ + 1] = d__[i__];

  idxq[i__ + 1] = idxq[i__] + 1;

/* L10: */

    }

    vf[1] = tau;

/*     Generate the second part of the vector Z. */

    i__1 = m;

    for (i__ = nlp2; i__ <= i__1; ++i__) {

  z__[i__] = *beta * vf[i__];

  vf[i__] = 0.f;

/* L20: */

    }

/*     Sort the singular values into increasing order */

    i__1 = n;

    for (i__ = nlp2; i__ <= i__1; ++i__) {

  idxq[i__] += nlp1;

/* L30: */

    }

/*     DSIGMA, IDXC, IDXC, and ZW are used as storage space. */

    i__1 = n;

    for (i__ = 2; i__ <= i__1; ++i__) {

  dsigma[i__] = d__[idxq[i__]];

  zw[i__] = z__[idxq[i__]];

  vfw[i__] = vf[idxq[i__]];

  vlw[i__] = vl[idxq[i__]];

/* L40: */

    }

    slamrg_(nl, nr, &dsigma[2], &c__1, &c__1, &idx[2]);

    i__1 = n;

    for (i__ = 2; i__ <= i__1; ++i__) {

  idxi = idx[i__] + 1;

  d__[i__] = dsigma[idxi];

  z__[i__] = zw[idxi];

  vf[i__] = vfw[idxi];

  vl[i__] = vlw[idxi];

/* L50: */

    }

/*     Calculate the allowable deflation tolerance */

    eps = slamch_("Epsilon");

/* Computing MAX */

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

    tol = f2cmax(r__1,r__2);

/* Computing MAX */

    r__2 = (r__1 = d__[n], abs(r__1));

    tol = eps * 64.f * f2cmax(r__2,tol);

/*     There are 2 kinds of deflation -- first a value in the z-vector */

/*     is small, second two (or more) singular values are very close */

/*     together (their difference is small). */

/*     If the value in the z-vector is small, we simply permute the */

/*     array so that the corresponding singular value is moved to the */

/*     end. */

/*     If two values in the D-vector are close, we perform a two-sided */

/*     rotation designed to make one of the corresponding z-vector */

/*     entries zero, and then permute the array so that the deflated */

/*     singular value is moved to the end. */

/*     If there are multiple singular values then the problem deflates. */

/*     Here the number of equal singular values are found.  As each equal */

/*     singular value is found, an elementary reflector is computed to */

/*     rotate the corresponding singular subspace so that the */

/*     corresponding components of Z are zero in this new basis. */

    *k = 1;

    k2 = n + 1;

    i__1 = n;

    for (j = 2; j <= i__1; ++j) {

  if ((r__1 = z__[j], abs(r__1)) <= tol) {

/*           Deflate due to small z component. */

      --k2;

      idxp[k2] = j;

      if (j == n) {

    goto L100;

      }

  } else {

      jprev = j;

      goto L70;

  }

/* L60: */

    }

L70:

    j = jprev;

L80:

    ++j;

    if (j > n) {

  goto L90;

    }

    if ((r__1 = z__[j], abs(r__1)) <= tol) {

/*        Deflate due to small z component. */

  --k2;

  idxp[k2] = j;

    } else {

/*        Check if singular values are close enough to allow deflation. */

  if ((r__1 = d__[j] - d__[jprev], abs(r__1)) <= tol) {

/*           Deflation is possible. */

      *s = z__[jprev];

      *c__ = z__[j];

/*           Find sqrt(a**2+b**2) without overflow or */

/*           destructive underflow. */

      tau = slapy2_(c__, s);

      z__[j] = tau;

      z__[jprev] = 0.f;

      *c__ /= tau;

      *s = -(*s) / tau;

/*           Record the appropriate Givens rotation */