#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_b11 = 0.f;

static real c_b12 = 1.f;

static integer c__1 = 1;

static integer c__2 = 2;

/* > \brief \b SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with d

iagonal d and off-diagonal e. Used by sbdsdc. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SLASDA + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, */

/*                          DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, */

/*                          PERM, GIVNUM, C, S, WORK, IWORK, INFO ) */

/*       INTEGER            ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE */

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

/*      $                   K( * ), PERM( LDGCOL, * ) */

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

/*      $                   E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), */

/*      $                   S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), */

/*      $                   Z( LDU, * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > Using a divide and conquer approach, SLASDA computes the singular */

/* > value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */

/* > B with diagonal D and offdiagonal E, where M = N + SQRE. The */

/* > algorithm computes the singular values in the SVD B = U * S * VT. */

/* > The orthogonal matrices U and VT are optionally computed in */

/* > compact form. */

/* > */

/* > A related subroutine, SLASD0, computes the singular values and */

/* > the singular vectors in explicit form. */

/* > \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] SMLSIZ */

/* > \verbatim */

/* >          SMLSIZ is INTEGER */

/* >         The maximum size of the subproblems at the bottom of the */

/* >         computation tree. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >         The row dimension of the upper bidiagonal matrix. This is */

/* >         also the dimension of the main diagonal array D. */

/* > \endverbatim */

/* > */

/* > \param[in] SQRE */

/* > \verbatim */

/* >          SQRE is INTEGER */

/* >         Specifies the column dimension of the bidiagonal matrix. */

/* >         = 0: The bidiagonal matrix has column dimension M = N; */

/* >         = 1: The bidiagonal matrix has column dimension M = N + 1. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >         On entry D contains the main diagonal of the bidiagonal */

/* >         matrix. On exit D, if INFO = 0, contains its singular values. */

/* > \endverbatim */

/* > */

/* > \param[in] E */

/* > \verbatim */

/* >          E is REAL array, dimension ( M-1 ) */

/* >         Contains the subdiagonal entries of the bidiagonal matrix. */

/* >         On exit, E has been destroyed. */

/* > \endverbatim */

/* > */

/* > \param[out] U */

/* > \verbatim */

/* >          U is REAL array, */

/* >         dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */

/* >         if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */

/* >         singular vector matrices of all subproblems at the bottom */

/* >         level. */

/* > \endverbatim */

/* > */

/* > \param[in] LDU */

/* > \verbatim */

/* >          LDU is INTEGER, LDU = > N. */

/* >         The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */

/* >         GIVNUM, and Z. */

/* > \endverbatim */

/* > */

/* > \param[out] VT */

/* > \verbatim */

/* >          VT is REAL array, */

/* >         dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */

/* >         if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right */

/* >         singular vector matrices of all subproblems at the bottom */

/* >         level. */

/* > \endverbatim */

/* > */

/* > \param[out] K */

/* > \verbatim */

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

/* >         if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */

/* >         If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */

/* >         secular equation on the computation tree. */

/* > \endverbatim */

/* > */

/* > \param[out] DIFL */

/* > \verbatim */

/* >          DIFL is REAL array, dimension ( LDU, NLVL ), */

/* >         where NLVL = floor(log_2 (N/SMLSIZ))). */

/* > \endverbatim */

/* > */

/* > \param[out] DIFR */

/* > \verbatim */

/* >          DIFR is REAL array, */

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

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

/* >         If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */

/* >         record distances between singular values on the I-th */

/* >         level and singular values on the (I -1)-th level, and */

/* >         DIFR(1:N, 2 * I ) contains the normalizing factors for */

/* >         the right singular vector matrix. See SLASD8 for details. */

/* > \endverbatim */

/* > */

/* > \param[out] Z */

/* > \verbatim */

/* >          Z is REAL array, */

/* >                  dimension ( LDU, NLVL ) if ICOMPQ = 1 and */

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

/* >         The first K elements of Z(1, I) contain the components of */

/* >         the deflation-adjusted updating row vector for subproblems */

/* >         on the I-th level. */

/* > \endverbatim */

/* > */

/* > \param[out] POLES */

/* > \verbatim */

/* >          POLES is REAL array, */

/* >         dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */

/* >         if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */

/* >         POLES(1, 2*I) contain  the new and old singular values */

/* >         involved in the secular equations on the I-th level. */

/* > \endverbatim */

/* > */

/* > \param[out] GIVPTR */

/* > \verbatim */

/* >          GIVPTR is INTEGER array, */

/* >         dimension ( N ) if ICOMPQ = 1, and not referenced if */

/* >         ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */

/* >         the number of Givens rotations performed on the I-th */

/* >         problem on the computation tree. */

/* > \endverbatim */

/* > */

/* > \param[out] GIVCOL */

/* > \verbatim */

/* >          GIVCOL is INTEGER array, */

/* >         dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */

/* >         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */

/* >         GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */

/* >         of Givens rotations performed on the I-th level on the */

/* >         computation tree. */

/* > \endverbatim */

/* > */

/* > \param[in] LDGCOL */

/* > \verbatim */

/* >          LDGCOL is INTEGER, LDGCOL = > N. */

/* >         The leading dimension of arrays GIVCOL and PERM. */

/* > \endverbatim */

/* > */

/* > \param[out] PERM */

/* > \verbatim */

/* >          PERM is INTEGER array, dimension ( LDGCOL, NLVL ) */

/* >         if ICOMPQ = 1, and not referenced */

/* >         if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */

/* >         permutations done on the I-th level of the computation tree. */

/* > \endverbatim */

/* > */

/* > \param[out] GIVNUM */

/* > \verbatim */

/* >          GIVNUM is REAL array, */

/* >         dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not */

/* >         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */

/* >         GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */

/* >         values of Givens rotations performed on the I-th level on */

/* >         the computation tree. */

/* > \endverbatim */

/* > */

/* > \param[out] C */

/* > \verbatim */

/* >          C is REAL array, */

/* >         dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */

/* >         If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */

/* >         C( I ) contains the C-value of a Givens rotation related to */

/* >         the right null space of the I-th subproblem. */

/* > \endverbatim */

/* > */

/* > \param[out] S */

/* > \verbatim */

/* >          S is REAL array, dimension ( N ) if */

/* >         ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */

/* >         and the I-th subproblem is not square, on exit, S( I ) */

/* >         contains the S-value of a Givens rotation related to */

/* >         the right null space of the I-th subproblem. */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* >          WORK is REAL array, dimension */

/* >         (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */

/* > \endverbatim */

/* > */

/* > \param[out] IWORK */

/* > \verbatim */

/* >          IWORK is INTEGER array, dimension (7*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 December 2016 */

/* > \ingroup OTHERauxiliary */

/* > \par Contributors: */

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

/* > */

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

/* >     California at Berkeley, USA */

/* > */

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

/* Subroutine */ void slasda_(integer *icompq, integer *smlsiz, integer *n, 

  integer *sqre, real *d__, real *e, real *u, integer *ldu, real *vt, 

  integer *k, real *difl, real *difr, real *z__, real *poles, integer *

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

   real *c__, real *s, real *work, integer *iwork, integer *info)

{

    /* System generated locals */

    integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, 

      difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, 

      poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, 

      z_dim1, z_offset, i__1, i__2;

    /* Local variables */

    real beta;

    integer idxq, nlvl, i__, j, m;

    real alpha;

    integer inode, ndiml, ndimr, idxqi, itemp, sqrei, i1;

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

      integer *), slasd6_(integer *, integer *, integer *, integer *, 

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

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

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

      integer *);

    integer ic, nwork1, lf, nd, nwork2, ll, nl, vf, nr, vl;

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

    extern void slasdq_(

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

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

      integer *, real *, integer *), slasdt_(integer *, integer 

      *, integer *, integer *, integer *, integer *, integer *), 

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

      integer *);

    integer im1, smlszp, ncc, nlf, nrf, vfi, iwk, vli, lvl, nru, ndb1, nlp1, 

      lvl2, nrp1;

/*  -- 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__;

    --e;

    givnum_dim1 = *ldu;

    givnum_offset = 1 + givnum_dim1 * 1;

    givnum -= givnum_offset;

    poles_dim1 = *ldu;

    poles_offset = 1 + poles_dim1 * 1;

    poles -= poles_offset;

    z_dim1 = *ldu;

    z_offset = 1 + z_dim1 * 1;

    z__ -= z_offset;

    difr_dim1 = *ldu;

    difr_offset = 1 + difr_dim1 * 1;

    difr -= difr_offset;

    difl_dim1 = *ldu;

    difl_offset = 1 + difl_dim1 * 1;

    difl -= difl_offset;

    vt_dim1 = *ldu;

    vt_offset = 1 + vt_dim1 * 1;

    vt -= vt_offset;

    u_dim1 = *ldu;

    u_offset = 1 + u_dim1 * 1;

    u -= u_offset;

    --k;

    --givptr;

    perm_dim1 = *ldgcol;

    perm_offset = 1 + perm_dim1 * 1;

    perm -= perm_offset;

    givcol_dim1 = *ldgcol;

    givcol_offset = 1 + givcol_dim1 * 1;

    givcol -= givcol_offset;

    --c__;

    --s;

    --work;

    --iwork;

    /* Function Body */

    *info = 0;

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

  *info = -1;

    } else if (*smlsiz < 3) {

  *info = -2;

    } else if (*n < 0) {

  *info = -3;

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

  *info = -4;

    } else if (*ldu < *n + *sqre) {

  *info = -8;

    } else if (*ldgcol < *n) {

  *info = -17;

    }

    if (*info != 0) {

  i__1 = -(*info);

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

  return;

    }

    m = *n + *sqre;

/*     If the input matrix is too small, call SLASDQ to find the SVD. */

    if (*n <= *smlsiz) {

  if (*icompq == 0) {

      slasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[

        vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, &

        work[1], info);

  } else {

      slasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset]

        , ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], 

        info);

  }

  return;

    }

/*     Book-keeping and  set up the computation tree. */

    inode = 1;

    ndiml = inode + *n;

    ndimr = ndiml + *n;

    idxq = ndimr + *n;

    iwk = idxq + *n;

    ncc = 0;

    nru = 0;

    smlszp = *smlsiz + 1;

    vf = 1;

    vl = vf + m;

    nwork1 = vl + m;

    nwork2 = nwork1 + smlszp * smlszp;

    slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], 

      smlsiz);

/*     for the nodes on bottom level of the tree, solve */

/*     their subproblems by SLASDQ. */

    ndb1 = (nd + 1) / 2;

    i__1 = nd;

    for (i__ = ndb1; i__ <= i__1; ++i__) {

/*        IC : center row of each node */

/*        NL : number of rows of left  subproblem */

/*        NR : number of rows of right subproblem */

/*        NLF: starting row of the left   subproblem */

/*        NRF: starting row of the right  subproblem */

  i1 = i__ - 1;

  ic = iwork[inode + i1];

  nl = iwork[ndiml + i1];

  nlp1 = nl + 1;

  nr = iwork[ndimr + i1];

  nlf = ic - nl;

  nrf = ic + 1;

  idxqi = idxq + nlf - 2;

  vfi = vf + nlf - 1;

  vli = vl + nlf - 1;

  sqrei = 1;

  if (*icompq == 0) {

      slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp);

      slasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], &

        work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2], 

        &nl, &work[nwork2], info);

      itemp = nwork1 + nl * smlszp;

      scopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1);

      scopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1);

  } else {

      slaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu);

      slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], 

        ldu);

      slasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &

        vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf + 

        u_dim1], ldu, &work[nwork1], info);

      scopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1);

      scopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1)

        ;

  }

  if (*info != 0) {

      return;

  }

  i__2 = nl;

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

      iwork[idxqi + j] = j;

/* L10: */

  }

  if (i__ == nd && *sqre == 0) {

      sqrei = 0;

  } else {

      sqrei = 1;

  }

  idxqi += nlp1;

  vfi += nlp1;

  vli += nlp1;

  nrp1 = nr + sqrei;

  if (*icompq == 0) {

      slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp);

      slasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], &

        work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2], 

        &nr, &work[nwork2], info);

      itemp = nwork1 + (nrp1 - 1) * smlszp;

      scopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1);

      scopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1);

  } else {

      slaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu);

      slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], 

        ldu);

      slasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &

        vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf + 

        u_dim1], ldu, &work[nwork1], info);

      scopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1);

      scopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1)

        ;

  }