#include <math.h>

#include <stdlib.h>

#include <string.h>

#include <stdio.h>

#include <complex.h>

#ifdef complex

#undef complex

#endif

#ifdef I

#undef I

#endif

#if defined(_WIN64)

typedef long long BLASLONG;

typedef unsigned long long BLASULONG;

#else

typedef long BLASLONG;

typedef unsigned long BLASULONG;

#endif

#ifdef LAPACK_ILP64

typedef BLASLONG blasint;

#if defined(_WIN64)

#define blasabs(x) llabs(x)

#else

#define blasabs(x) labs(x)

#endif

#else

typedef int blasint;

#define blasabs(x) abs(x)

#endif

typedef blasint integer;

typedef unsigned int uinteger;

typedef char *address;

typedef short int shortint;

typedef float real;

typedef double doublereal;

typedef struct { real r, i; } complex;

typedef struct { doublereal r, i; } doublecomplex;

#ifdef _MSC_VER

static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}

static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}

static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}

static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}

#else

static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}

static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}

static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}

static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}

#endif

#define pCf(z) (*_pCf(z))

#define pCd(z) (*_pCd(z))

typedef blasint logical;

typedef char logical1;

typedef char integer1;

#define TRUE_ (1)

#define FALSE_ (0)

/* Extern is for use with -E */

#ifndef Extern

#define Extern extern

#endif

/* I/O stuff */

typedef int flag;

typedef int ftnlen;

typedef int ftnint;

/*external read, write*/

typedef struct

{ flag cierr;

  ftnint ciunit;

  flag ciend;

  char *cifmt;

  ftnint cirec;

} cilist;

/*internal read, write*/

typedef struct

{ flag icierr;

  char *iciunit;

  flag iciend;

  char *icifmt;

  ftnint icirlen;

  ftnint icirnum;

} icilist;

/*open*/

typedef struct

{ flag oerr;

  ftnint ounit;

  char *ofnm;

  ftnlen ofnmlen;

  char *osta;

  char *oacc;

  char *ofm;

  ftnint orl;

  char *oblnk;

} olist;

/*close*/

typedef struct

{ flag cerr;

  ftnint cunit;

  char *csta;

} cllist;

/*rewind, backspace, endfile*/

typedef struct

{ flag aerr;

  ftnint aunit;

} alist;

/* inquire */

typedef struct

{ flag inerr;

  ftnint inunit;

  char *infile;

  ftnlen infilen;

  ftnint  *inex;  /*parameters in standard's order*/

  ftnint  *inopen;

  ftnint  *innum;

  ftnint  *innamed;

  char  *inname;

  ftnlen  innamlen;

  char  *inacc;

  ftnlen  inacclen;

  char  *inseq;

  ftnlen  inseqlen;

  char  *indir;

  ftnlen  indirlen;

  char  *infmt;

  ftnlen  infmtlen;

  char  *inform;

  ftnint  informlen;

  char  *inunf;

  ftnlen  inunflen;

  ftnint  *inrecl;

  ftnint  *innrec;

  char  *inblank;

  ftnlen  inblanklen;

} inlist;

#define VOID void

union Multitype { /* for multiple entry points */

  integer1 g;

  shortint h;

  integer i;

  /* longint j; */

  real r;

  doublereal d;

  complex c;

  doublecomplex z;

  };

typedef union Multitype Multitype;

struct Vardesc {  /* for Namelist */

  char *name;

  char *addr;

  ftnlen *dims;

  int  type;

  };

typedef struct Vardesc Vardesc;

struct Namelist {

  char *name;

  Vardesc **vars;

  int nvars;

  };

typedef struct Namelist Namelist;

#define abs(x) ((x) >= 0 ? (x) : -(x))

#define dabs(x) (fabs(x))

#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))

#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))

#define dmin(a,b) (f2cmin(a,b))

#define dmax(a,b) (f2cmax(a,b))

#define bit_test(a,b) ((a) >> (b) & 1)

#define bit_clear(a,b)  ((a) & ~((uinteger)1 << (b)))

#define bit_set(a,b)  ((a) |  ((uinteger)1 << (b)))

#define abort_() { sig_die("Fortran abort routine called", 1); }

#define c_abs(z) (cabsf(Cf(z)))

#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }

#ifdef _MSC_VER

#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}

#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}

#else

#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}

#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}

#endif

#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}

#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}

#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}

//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}

#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}

#define d_abs(x) (fabs(*(x)))

#define d_acos(x) (acos(*(x)))

#define d_asin(x) (asin(*(x)))

#define d_atan(x) (atan(*(x)))

#define d_atn2(x, y) (atan2(*(x),*(y)))

#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }

#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }

#define d_cos(x) (cos(*(x)))

#define d_cosh(x) (cosh(*(x)))

#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )

#define d_exp(x) (exp(*(x)))

#define d_imag(z) (cimag(Cd(z)))

#define r_imag(z) (cimagf(Cf(z)))

#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))

#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))

#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )

#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )

#define d_log(x) (log(*(x)))

#define d_mod(x, y) (fmod(*(x), *(y)))

#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))

#define d_nint(x) u_nint(*(x))

#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))

#define d_sign(a,b) u_sign(*(a),*(b))

#define r_sign(a,b) u_sign(*(a),*(b))

#define d_sin(x) (sin(*(x)))

#define d_sinh(x) (sinh(*(x)))

#define d_sqrt(x) (sqrt(*(x)))

#define d_tan(x) (tan(*(x)))

#define d_tanh(x) (tanh(*(x)))

#define i_abs(x) abs(*(x))

#define i_dnnt(x) ((integer)u_nint(*(x)))

#define i_len(s, n) (n)

#define i_nint(x) ((integer)u_nint(*(x)))

#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))

#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))

#define pow_si(B,E) spow_ui(*(B),*(E))

#define pow_ri(B,E) spow_ui(*(B),*(E))

#define pow_di(B,E) dpow_ui(*(B),*(E))

#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}

#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}

#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}

#define s_cat(lpp, rpp, rnp, np, llp) {   ftnlen i, nc, ll; char *f__rp, *lp;   ll = (llp); lp = (lpp);   for(i=0; i < (int)*(np); ++i) {           nc = ll;          if((rnp)[i] < nc) nc = (rnp)[i];          ll -= nc;           f__rp = (rpp)[i];           while(--nc >= 0) *lp++ = *(f__rp)++;         }  while(--ll >= 0) *lp++ = ' '; }

#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))

#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }

#define sig_die(s, kill) { exit(1); }

#define s_stop(s, n) {exit(0);}

static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";

#define z_abs(z) (cabs(Cd(z)))

#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}

#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}

#define myexit_() break;

#define mycycle() continue;

#define myceiling(w) {ceil(w)}

#define myhuge(w) {HUGE_VAL}

//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}

#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/* procedure parameter types for -A and -C++ */

#ifdef __cplusplus

typedef logical (*L_fp)(...);

#else

typedef logical (*L_fp)();

#endif

static float spow_ui(float x, integer n) {

  float pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

static double dpow_ui(double x, integer n) {

  double pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#ifdef _MSC_VER

static _Fcomplex cpow_ui(complex x, integer n) {

  complex pow={1.0,0.0}; unsigned long int u;

    if(n != 0) {

    if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;

    for(u = n; ; ) {

      if(u & 01) pow.r *= x.r, pow.i *= x.i;

      if(u >>= 1) x.r *= x.r, x.i *= x.i;

      else break;

    }

  }

  _Fcomplex p={pow.r, pow.i};

  return p;

}

#else

static _Complex float cpow_ui(_Complex float x, integer n) {

  _Complex float pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#endif

#ifdef _MSC_VER

static _Dcomplex zpow_ui(_Dcomplex x, integer n) {

  _Dcomplex pow={1.0,0.0}; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];

    for(u = n; ; ) {

      if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];

      if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];

      else break;

    }

  }

  _Dcomplex p = {pow._Val[0], pow._Val[1]};

  return p;

}

#else

static _Complex double zpow_ui(_Complex double x, integer n) {

  _Complex double pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#endif

static integer pow_ii(integer x, integer n) {

  integer pow; unsigned long int u;

  if (n <= 0) {

    if (n == 0 || x == 1) pow = 1;

    else if (x != -1) pow = x == 0 ? 1/x : 0;

    else n = -n;

  }

  if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {

    u = n;

    for(pow = 1; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

static integer dmaxloc_(double *w, integer s, integer e, integer *n)

{

  double m; integer i, mi;

  for(m=w[s-1], mi=s, i=s+1; i<=e; i++)

    if (w[i-1]>m) mi=i ,m=w[i-1];

  return mi-s+1;

}

static integer smaxloc_(float *w, integer s, integer e, integer *n)

{

  float m; integer i, mi;

  for(m=w[s-1], mi=s, i=s+1; i<=e; i++)

    if (w[i-1]>m) mi=i ,m=w[i-1];

  return mi-s+1;

}

static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {

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

#ifdef _MSC_VER

  _Fcomplex zdotc = {0.0, 0.0};

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

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

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

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

    }

  } else {

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

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

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

    }

  }

  pCf(z) = zdotc;

}

#else

  _Complex float zdotc = 0.0;

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

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

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

    }

  } else {

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

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

    }

  }

  pCf(z) = zdotc;

}

#endif

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

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

#ifdef _MSC_VER

  _Dcomplex zdotc = {0.0, 0.0};

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

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

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

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

    }

  } else {

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

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

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

    }

  }

  pCd(z) = zdotc;

}

#else

  _Complex double zdotc = 0.0;

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

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

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

    }

  } else {

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

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

    }

  }

  pCd(z) = zdotc;

}

#endif  

static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {

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

#ifdef _MSC_VER

  _Fcomplex zdotc = {0.0, 0.0};

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

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

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

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

    }

  } else {

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

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

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

    }

  }

  pCf(z) = zdotc;

}

#else

  _Complex float zdotc = 0.0;

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

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

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

    }

  } else {

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

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

    }

  }

  pCf(z) = zdotc;

}

#endif

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

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

#ifdef _MSC_VER

  _Dcomplex zdotc = {0.0, 0.0};

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

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

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

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

    }

  } else {

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

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

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

    }

  }

  pCd(z) = zdotc;

}

#else

  _Complex double zdotc = 0.0;

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

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

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

    }

  } else {

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

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

    }

  }

  pCd(z) = zdotc;

}

#endif

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

   You must link the resulting object file with the libraries:

  -lf2c -lm   (in that order)

*/

/* Table of constant values */

static integer c__1 = 1;

static real c_b6 = 0.f;

static integer c__0 = 0;

static real c_b11 = 1.f;

/* > \brief \b SLALSD uses the singular value decomposition of A to solve the least squares problem. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SLALSD + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, */

/*                          RANK, WORK, IWORK, INFO ) */

/*       CHARACTER          UPLO */

/*       INTEGER            INFO, LDB, N, NRHS, RANK, SMLSIZ */

/*       REAL               RCOND */

/*       INTEGER            IWORK( * ) */

/*       REAL               B( LDB, * ), D( * ), E( * ), WORK( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > SLALSD uses the singular value decomposition of A to solve the least */

/* > squares problem of finding X to minimize the Euclidean norm of each */

/* > column of A*X-B, where A is N-by-N upper bidiagonal, and X and B */

/* > are N-by-NRHS. The solution X overwrites B. */

/* > */

/* > The singular values of A smaller than RCOND times the largest */

/* > singular value are treated as zero in solving the least squares */

/* > problem; in this case a minimum norm solution is returned. */

/* > The actual singular values are returned in D in ascending order. */

/* > */

/* > This code makes very mild assumptions about floating point */

/* > arithmetic. It will work on machines with a guard digit in */

/* > add/subtract, or on those binary machines without guard digits */

/* > which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. */

/* > It could conceivably fail on hexadecimal or decimal machines */

/* > without guard digits, but we know of none. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] UPLO */

/* > \verbatim */

/* >          UPLO is CHARACTER*1 */

/* >         = 'U': D and E define an upper bidiagonal matrix. */

/* >         = 'L': D and E define a  lower bidiagonal matrix. */

/* > \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 dimension of the  bidiagonal matrix.  N >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NRHS */

/* > \verbatim */

/* >          NRHS is INTEGER */

/* >         The number of columns of B. NRHS must be at least 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, if INFO = 0, D contains its singular values. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >         Contains the super-diagonal entries of the bidiagonal matrix. */

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

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          B is REAL array, dimension (LDB,NRHS) */

/* >         On input, B contains the right hand sides of the least */

/* >         squares problem. On output, B contains the solution X. */

/* > \endverbatim */

/* > */

/* > \param[in] LDB */

/* > \verbatim */

/* >          LDB is INTEGER */

/* >         The leading dimension of B in the calling subprogram. */

/* >         LDB must be at least f2cmax(1,N). */

/* > \endverbatim */

/* > */

/* > \param[in] RCOND */

/* > \verbatim */

/* >          RCOND is REAL */

/* >         The singular values of A less than or equal to RCOND times */

/* >         the largest singular value are treated as zero in solving */

/* >         the least squares problem. If RCOND is negative, */

/* >         machine precision is used instead. */

/* >         For example, if diag(S)*X=B were the least squares problem, */

/* >         where diag(S) is a diagonal matrix of singular values, the */

/* >         solution would be X(i) = B(i) / S(i) if S(i) is greater than */

/* >         RCOND*f2cmax(S), and X(i) = 0 if S(i) is less than or equal to */

/* >         RCOND*f2cmax(S). */

/* > \endverbatim */

/* > */

/* > \param[out] RANK */

/* > \verbatim */

/* >          RANK is INTEGER */

/* >         The number of singular values of A greater than RCOND times */

/* >         the largest singular value. */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* >          WORK is REAL array, dimension at least */

/* >         (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2), */

/* >         where NLVL = f2cmax(0, INT(log_2 (N/(SMLSIZ+1))) + 1). */

/* > \endverbatim */

/* > */

/* > \param[out] IWORK */

/* > \verbatim */

/* >          IWORK is INTEGER array, dimension at least */

/* >         (3*N*NLVL + 11*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:  The algorithm failed to compute a singular value while */

/* >               working on the submatrix lying in rows and columns */

/* >               INFO/(N+1) through MOD(INFO,N+1). */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup realOTHERcomputational */

/* > \par Contributors: */

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

/* > */

/* >     Ming Gu and Ren-Cang Li, Computer Science Division, University of */

/* >       California at Berkeley, USA \n */

/* >     Osni Marques, LBNL/NERSC, USA \n */

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

/* Subroutine */ void slalsd_(char *uplo, integer *smlsiz, integer *n, integer 

  *nrhs, real *d__, real *e, real *b, integer *ldb, real *rcond, 

  integer *rank, real *work, integer *iwork, integer *info)

{

    /* System generated locals */

    integer b_dim1, b_offset, i__1, i__2;

    real r__1;

    /* Local variables */

    integer difl, difr;

    real rcnd;

    integer perm, nsub, nlvl, sqre, bxst;

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

      integer *, real *, real *);

    integer c__, i__, j, k;

    real r__;

    integer s, u, z__;

    extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *, 

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

      real *, integer *);

    integer poles, sizei, nsize;

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

      integer *);

    integer nwork, icmpq1, icmpq2;

    real cs;

    integer bx;

    real sn;

    integer st;

    extern real slamch_(char *);

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

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

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

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

    integer vt;

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

    extern void slalsa_(

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

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

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

      , real *, real *, real *, real *, integer *, integer *), slascl_(

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

      , real *, integer *, integer *);

    integer givcol;

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

    extern /* Subroutine */ void slasdq_(char *, integer *, integer *, integer 

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

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

      slacpy_(char *, integer *, integer *, real *, integer *, real *, 

      integer *), slartg_(real *, real *, real *, real *, real *

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

      integer *);

    real orgnrm;

    integer givnum;

    extern real slanst_(char *, integer *, real *, real *);

    extern /* Subroutine */ void slasrt_(char *, integer *, real *, integer *);

    integer givptr, nm1, smlszp, st1;

    real eps;

    integer iwk;

    real tol;

/*  -- LAPACK computational 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;

    b_dim1 = *ldb;

    b_offset = 1 + b_dim1 * 1;

    b -= b_offset;

    --work;

    --iwork;

    /* Function Body */

    *info = 0;

    if (*n < 0) {

  *info = -3;

    } else if (*nrhs < 1) {

  *info = -4;

    } else if (*ldb < 1 || *ldb < *n) {

  *info = -8;

    }

    if (*info != 0) {

  i__1 = -(*info);

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

  return;

    }

    eps = slamch_("Epsilon");

/*     Set up the tolerance. */

    if (*rcond <= 0.f || *rcond >= 1.f) {

  rcnd = eps;

    } else {

  rcnd = *rcond;

    }

    *rank = 0;

/*     Quick return if possible. */

    if (*n == 0) {

  return;

    } else if (*n == 1) {

  if (d__[1] == 0.f) {

      slaset_("A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb);

  } else {

      *rank = 1;

      slascl_("G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[

        b_offset], ldb, info);

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

  }

  return;

    }

/*     Rotate the matrix if it is lower bidiagonal. */

    if (*(unsigned char *)uplo == 'L') {

  i__1 = *n - 1;

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

      slartg_(&d__[i__], &e[i__], &cs, &sn, &r__);

      d__[i__] = r__;

      e[i__] = sn * d__[i__ + 1];

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

      if (*nrhs == 1) {

    srot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], &

      c__1, &cs, &sn);

      } else {

    work[(i__ << 1) - 1] = cs;

    work[i__ * 2] = sn;

      }

/* L10: */

  }

  if (*nrhs > 1) {

      i__1 = *nrhs;

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

    i__2 = *n - 1;

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

        cs = work[(j << 1) - 1];

        sn = work[j * 2];

        srot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ *

           b_dim1], &c__1, &cs, &sn);

/* L20: */

    }

/* L30: */

      }

  }

    }

/*     Scale. */

    nm1 = *n - 1;

    orgnrm = slanst_("M", n, &d__[1], &e[1]);

    if (orgnrm == 0.f) {

  slaset_("A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb);

  return;

    }

    slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info);

    slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, 

      info);

/*     If N is smaller than the minimum divide size SMLSIZ, then solve */

/*     the problem with another solver. */

    if (*n <= *smlsiz) {

  nwork = *n * *n + 1;

  slaset_("A", n, n, &c_b6, &c_b11, &work[1], n);

  slasdq_("U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, &

    work[1], n, &b[b_offset], ldb, &work[nwork], info);

  if (*info != 0) {

      return;

  }

  tol = rcnd * (r__1 = d__[isamax_(n, &d__[1], &c__1)], abs(r__1));

  i__1 = *n;

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

      if (d__[i__] <= tol) {

    slaset_("A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb);

      } else {

    slascl_("G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[

      i__ + b_dim1], ldb, info);

    ++(*rank);

      }

/* L40: */

  }

  sgemm_("T", "N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, &

    c_b6, &work[nwork], n);

  slacpy_("A", n, nrhs, &work[nwork], n, &b[b_offset], ldb);

/*        Unscale. */

  slascl_("G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, 

    info);

  slasrt_("D", n, &d__[1], info);

  slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], 

    ldb, info);

  return;

    }

/*     Book-keeping and setting up some constants. */

    nlvl = (integer) (log((real) (*n) / (real) (*smlsiz + 1)) / log(2.f)) + 1;

    smlszp = *smlsiz + 1;

    u = 1;

    vt = *smlsiz * *n + 1;

    difl = vt + smlszp * *n;

    difr = difl + nlvl * *n;

    z__ = difr + (nlvl * *n << 1);

    c__ = z__ + nlvl * *n;

    s = c__ + *n;

    poles = s + *n;

    givnum = poles + (nlvl << 1) * *n;

    bx = givnum + (nlvl << 1) * *n;

    nwork = bx + *n * *nrhs;

    sizei = *n + 1;

    k = sizei + *n;

    givptr = k + *n;

    perm = givptr + *n;

    givcol = perm + nlvl * *n;

    iwk = givcol + (nlvl * *n << 1);

    st = 1;

    sqre = 0;

    icmpq1 = 1;

    icmpq2 = 0;

    nsub = 0;

    i__1 = *n;

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

  if ((r__1 = d__[i__], abs(r__1)) < eps) {

      d__[i__] = r_sign(&eps, &d__[i__]);

  }

/* L50: */

    }

    i__1 = nm1;

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

  if ((r__1 = e[i__], abs(r__1)) < eps || i__ == nm1) {

      ++nsub;

      iwork[nsub] = st;

/*           Subproblem found. First determine its size and then */

/*           apply divide and conquer on it. */

      if (i__ < nm1) {

/*              A subproblem with E(I) small for I < NM1. */

    nsize = i__ - st + 1;

    iwork[sizei + nsub - 1] = nsize;

      } else if ((r__1 = e[i__], abs(r__1)) >= eps) {

/*              A subproblem with E(NM1) not too small but I = NM1. */

    nsize = *n - st + 1;

    iwork[sizei + nsub - 1] = nsize;

      } else {

/*              A subproblem with E(NM1) small. This implies an */

/*              1-by-1 subproblem at D(N), which is not solved */

/*              explicitly. */

    nsize = i__ - st + 1;

    iwork[sizei + nsub - 1] = nsize;

    ++nsub;

    iwork[nsub] = *n;

    iwork[sizei + nsub - 1] = 1;

    scopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n);

      }

      st1 = st - 1;

      if (nsize == 1) {

/*              This is a 1-by-1 subproblem and is not solved */

/*              explicitly. */

    scopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n);

      } else if (nsize <= *smlsiz) {

/*              This is a small subproblem and is solved by SLASDQ. */

    slaset_("A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], 

      n);

    slasdq_("U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[

      st], &work[vt + st1], n, &work[nwork], n, &b[st +