#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 SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by

 sbdsdc. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SLASDQ + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, */

/*                          U, LDU, C, LDC, WORK, INFO ) */

/*       CHARACTER          UPLO */

/*       INTEGER            INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE */

/*       REAL               C( LDC, * ), D( * ), E( * ), U( LDU, * ), */

/*      $                   VT( LDVT, * ), WORK( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > SLASDQ computes the singular value decomposition (SVD) of a real */

/* > (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */

/* > E, accumulating the transformations if desired. Letting B denote */

/* > the input bidiagonal matrix, the algorithm computes orthogonal */

/* > matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose */

/* > of P). The singular values S are overwritten on D. */

/* > */

/* > The input matrix U  is changed to U  * Q  if desired. */

/* > The input matrix VT is changed to P**T * VT if desired. */

/* > The input matrix C  is changed to Q**T * C  if desired. */

/* > */

/* > See "Computing  Small Singular Values of Bidiagonal Matrices With */

/* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */

/* > LAPACK Working Note #3, for a detailed description of the algorithm. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] UPLO */

/* > \verbatim */

/* >          UPLO is CHARACTER*1 */

/* >        On entry, UPLO specifies whether the input bidiagonal matrix */

/* >        is upper or lower bidiagonal, and whether it is square are */

/* >        not. */

/* >           UPLO = 'U' or 'u'   B is upper bidiagonal. */

/* >           UPLO = 'L' or 'l'   B is lower bidiagonal. */

/* > \endverbatim */

/* > */

/* > \param[in] SQRE */

/* > \verbatim */

/* >          SQRE is INTEGER */

/* >        = 0: then the input matrix is N-by-N. */

/* >        = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */

/* >             (N+1)-by-N if UPLU = 'L'. */

/* > */

/* >        The bidiagonal matrix has */

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

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

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >        On entry, N specifies the number of rows and columns */

/* >        in the matrix. N must be at least 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NCVT */

/* > \verbatim */

/* >          NCVT is INTEGER */

/* >        On entry, NCVT specifies the number of columns of */

/* >        the matrix VT. NCVT must be at least 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NRU */

/* > \verbatim */

/* >          NRU is INTEGER */

/* >        On entry, NRU specifies the number of rows of */

/* >        the matrix U. NRU must be at least 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NCC */

/* > \verbatim */

/* >          NCC is INTEGER */

/* >        On entry, NCC specifies the number of columns of */

/* >        the matrix C. NCC must be at least 0. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >        On entry, D contains the diagonal entries of the */

/* >        bidiagonal matrix whose SVD is desired. On normal exit, */

/* >        D contains the singular values in ascending order. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          E is REAL array. */

/* >        dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */

/* >        On entry, the entries of E contain the offdiagonal entries */

/* >        of the bidiagonal matrix whose SVD is desired. On normal */

/* >        exit, E will contain 0. If the algorithm does not converge, */

/* >        D and E will contain the diagonal and superdiagonal entries */

/* >        of a bidiagonal matrix orthogonally equivalent to the one */

/* >        given as input. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          VT is REAL array, dimension (LDVT, NCVT) */

/* >        On entry, contains a matrix which on exit has been */

/* >        premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 */

/* >        and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */

/* > \endverbatim */

/* > */

/* > \param[in] LDVT */

/* > \verbatim */

/* >          LDVT is INTEGER */

/* >        On entry, LDVT specifies the leading dimension of VT as */

/* >        declared in the calling (sub) program. LDVT must be at */

/* >        least 1. If NCVT is nonzero LDVT must also be at least N. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          U is REAL array, dimension (LDU, N) */

/* >        On entry, contains a  matrix which on exit has been */

/* >        postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */

/* >        and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */

/* > \endverbatim */

/* > */

/* > \param[in] LDU */

/* > \verbatim */

/* >          LDU is INTEGER */

/* >        On entry, LDU  specifies the leading dimension of U as */

/* >        declared in the calling (sub) program. LDU must be at */

/* >        least f2cmax( 1, NRU ) . */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          C is REAL array, dimension (LDC, NCC) */

/* >        On entry, contains an N-by-NCC matrix which on exit */

/* >        has been premultiplied by Q**T  dimension N-by-NCC if SQRE = 0 */

/* >        and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */

/* > \endverbatim */

/* > */

/* > \param[in] LDC */

/* > \verbatim */

/* >          LDC is INTEGER */

/* >        On entry, LDC  specifies the leading dimension of C as */

/* >        declared in the calling (sub) program. LDC must be at */

/* >        least 1. If NCC is nonzero, LDC must also be at least N. */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

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

/* >        Workspace. Only referenced if one of NCVT, NRU, or NCC is */

/* >        nonzero, and if N is at least 2. */

/* > \endverbatim */

/* > */

/* > \param[out] INFO */

/* > \verbatim */

/* >          INFO is INTEGER */

/* >        On exit, a value of 0 indicates a successful exit. */

/* >        If INFO < 0, argument number -INFO is illegal. */

/* >        If INFO > 0, the algorithm did not converge, and INFO */

/* >        specifies how many superdiagonals did not converge. */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date June 2016 */

/* > \ingroup OTHERauxiliary */

/* > \par Contributors: */

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

/* > */

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

/* >     California at Berkeley, USA */

/* > */

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

/* Subroutine */ void slasdq_(char *uplo, integer *sqre, integer *n, integer *

  ncvt, integer *nru, integer *ncc, real *d__, real *e, real *vt, 

  integer *ldvt, real *u, integer *ldu, real *c__, integer *ldc, real *

  work, integer *info)

{

    /* System generated locals */

    integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, 

      i__2;

    /* Local variables */

    integer isub;

    real smin;

    integer sqre1, i__, j;

    real r__;

    extern logical lsame_(char *, char *);

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

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

    integer iuplo;

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

      integer *);

    real cs, sn;

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

    extern void slartg_(

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

    logical rotate;

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

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

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

    integer np1;

/*  -- LAPACK auxiliary routine (version 3.7.0) -- */

/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */

/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/*     June 2016 */

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

/*     Test the input parameters. */

    /* Parameter adjustments */

    --d__;

    --e;

    vt_dim1 = *ldvt;

    vt_offset = 1 + vt_dim1 * 1;

    vt -= vt_offset;

    u_dim1 = *ldu;

    u_offset = 1 + u_dim1 * 1;

    u -= u_offset;

    c_dim1 = *ldc;

    c_offset = 1 + c_dim1 * 1;

    c__ -= c_offset;

    --work;

    /* Function Body */

    *info = 0;

    iuplo = 0;

    if (lsame_(uplo, "U")) {

  iuplo = 1;

    }

    if (lsame_(uplo, "L")) {

  iuplo = 2;

    }

    if (iuplo == 0) {

  *info = -1;

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

  *info = -2;

    } else if (*n < 0) {

  *info = -3;

    } else if (*ncvt < 0) {

  *info = -4;

    } else if (*nru < 0) {

  *info = -5;

    } else if (*ncc < 0) {

  *info = -6;

    } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < f2cmax(1,*n)) {

  *info = -10;

    } else if (*ldu < f2cmax(1,*nru)) {

  *info = -12;

    } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < f2cmax(1,*n)) {

  *info = -14;

    }

    if (*info != 0) {

  i__1 = -(*info);

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

  return;

    }

    if (*n == 0) {

  return;

    }

/*     ROTATE is true if any singular vectors desired, false otherwise */

    rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;

    np1 = *n + 1;

    sqre1 = *sqre;

/*     If matrix non-square upper bidiagonal, rotate to be lower */

/*     bidiagonal.  The rotations are on the right. */

    if (iuplo == 1 && sqre1 == 1) {

  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 (rotate) {

    work[i__] = cs;

    work[*n + i__] = sn;

      }

/* L10: */

  }

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

  d__[*n] = r__;

  e[*n] = 0.f;

  if (rotate) {

      work[*n] = cs;

      work[*n + *n] = sn;

  }

  iuplo = 2;

  sqre1 = 0;

/*        Update singular vectors if desired. */

  if (*ncvt > 0) {

      slasr_("L", "V", "F", &np1, ncvt, &work[1], &work[np1], &vt[

        vt_offset], ldvt);

  }

    }

/*     If matrix lower bidiagonal, rotate to be upper bidiagonal */

/*     by applying Givens rotations on the left. */

    if (iuplo == 2) {

  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 (rotate) {

    work[i__] = cs;

    work[*n + i__] = sn;

      }

/* L20: */

  }

/*        If matrix (N+1)-by-N lower bidiagonal, one additional */

/*        rotation is needed. */

  if (sqre1 == 1) {

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

      d__[*n] = r__;

      if (rotate) {

    work[*n] = cs;

    work[*n + *n] = sn;

      }

  }

/*        Update singular vectors if desired. */

  if (*nru > 0) {

      if (sqre1 == 0) {

    slasr_("R", "V", "F", nru, n, &work[1], &work[np1], &u[

      u_offset], ldu);

      } else {

    slasr_("R", "V", "F", nru, &np1, &work[1], &work[np1], &u[

      u_offset], ldu);

      }

  }

  if (*ncc > 0) {

      if (sqre1 == 0) {

    slasr_("L", "V", "F", n, ncc, &work[1], &work[np1], &c__[

      c_offset], ldc);

      } else {

    slasr_("L", "V", "F", &np1, ncc, &work[1], &work[np1], &c__[

      c_offset], ldc);

      }

  }

    }

/*     Call SBDSQR to compute the SVD of the reduced real */

/*     N-by-N upper bidiagonal matrix. */

    sbdsqr_("U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[

      u_offset], ldu, &c__[c_offset], ldc, &work[1], info);

/*     Sort the singular values into ascending order (insertion sort on */

/*     singular values, but only one transposition per singular vector) */

    i__1 = *n;

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

/*        Scan for smallest D(I). */

  isub = i__;

  smin = d__[i__];

  i__2 = *n;

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

      if (d__[j] < smin) {

    isub = j;

    smin = d__[j];

      }

/* L30: */

  }

  if (isub != i__) {

/*           Swap singular values and vectors. */

      d__[isub] = d__[i__];

      d__[i__] = smin;

      if (*ncvt > 0) {

    sswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1], 

      ldvt);

      }

      if (*nru > 0) {

    sswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1]

      , &c__1);

      }

      if (*ncc > 0) {

    sswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc)

      ;

      }

  }

/* L40: */

    }

    return;

/*     End of SLASDQ */

} /* slasdq_ */