#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 doublereal c_b15 = -.125;

static integer c__1 = 1;

static doublereal c_b49 = 1.;

static doublereal c_b72 = -1.;

/* > \brief \b DBDSQR */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download DBDSQR + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE DBDSQR( UPLO, 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 */

/*       DOUBLE PRECISION   C( LDC, * ), D( * ), E( * ), U( LDU, * ), */

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

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > DBDSQR computes the singular values and, optionally, the right and/or */

/* > left singular vectors from the singular value decomposition (SVD) of */

/* > a real N-by-N (upper or lower) bidiagonal matrix B using the implicit */

/* > zero-shift QR algorithm.  The SVD of B has the form */

/* > */

/* >    B = Q * S * P**T */

/* > */

/* > where S is the diagonal matrix of singular values, Q is an orthogonal */

/* > matrix of left singular vectors, and P is an orthogonal matrix of */

/* > right singular vectors.  If left singular vectors are requested, this */

/* > subroutine actually returns U*Q instead of Q, and, if right singular */

/* > vectors are requested, this subroutine returns P**T*VT instead of */

/* > P**T, for given real input matrices U and VT.  When U and VT are the */

/* > orthogonal matrices that reduce a general matrix A to bidiagonal */

/* > form:  A = U*B*VT, as computed by DGEBRD, then */

/* > */

/* >    A = (U*Q) * S * (P**T*VT) */

/* > */

/* > is the SVD of A.  Optionally, the subroutine may also compute Q**T*C */

/* > for a given real input matrix C. */

/* > */

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

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

/* > LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, */

/* > no. 5, pp. 873-912, Sept 1990) and */

/* > "Accurate singular values and differential qd algorithms," by */

/* > B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics */

/* > Department, University of California at Berkeley, July 1992 */

/* > for a detailed description of the algorithm. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] UPLO */

/* > \verbatim */

/* >          UPLO is CHARACTER*1 */

/* >          = 'U':  B is upper bidiagonal; */

/* >          = 'L':  B is lower bidiagonal. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >          The order of the matrix B.  N >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NCVT */

/* > \verbatim */

/* >          NCVT is INTEGER */

/* >          The number of columns of the matrix VT. NCVT >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NRU */

/* > \verbatim */

/* >          NRU is INTEGER */

/* >          The number of rows of the matrix U. NRU >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NCC */

/* > \verbatim */

/* >          NCC is INTEGER */

/* >          The number of columns of the matrix C. NCC >= 0. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

/* >          D is DOUBLE PRECISION array, dimension (N) */

/* >          On entry, the n diagonal elements of the bidiagonal matrix B. */

/* >          On exit, if INFO=0, the singular values of B in decreasing */

/* >          order. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, the N-1 offdiagonal elements of the bidiagonal */

/* >          matrix B. */

/* >          On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E */

/* >          will contain the diagonal and superdiagonal elements of a */

/* >          bidiagonal matrix orthogonally equivalent to the one given */

/* >          as input. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, an N-by-NCVT matrix VT. */

/* >          On exit, VT is overwritten by P**T * VT. */

/* >          Not referenced if NCVT = 0. */

/* > \endverbatim */

/* > */

/* > \param[in] LDVT */

/* > \verbatim */

/* >          LDVT is INTEGER */

/* >          The leading dimension of the array VT. */

/* >          LDVT >= f2cmax(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, an NRU-by-N matrix U. */

/* >          On exit, U is overwritten by U * Q. */

/* >          Not referenced if NRU = 0. */

/* > \endverbatim */

/* > */

/* > \param[in] LDU */

/* > \verbatim */

/* >          LDU is INTEGER */

/* >          The leading dimension of the array U.  LDU >= f2cmax(1,NRU). */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, an N-by-NCC matrix C. */

/* >          On exit, C is overwritten by Q**T * C. */

/* >          Not referenced if NCC = 0. */

/* > \endverbatim */

/* > */

/* > \param[in] LDC */

/* > \verbatim */

/* >          LDC is INTEGER */

/* >          The leading dimension of the array C. */

/* >          LDC >= f2cmax(1,N) if NCC > 0; LDC >=1 if NCC = 0. */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* >          WORK is DOUBLE PRECISION array, dimension (4*(N-1)) */

/* > \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 NCVT = NRU = NCC = 0, */

/* >                = 1, a split was marked by a positive value in E */

/* >                = 2, current block of Z not diagonalized after 30*N */

/* >                     iterations (in inner while loop) */

/* >                = 3, termination criterion of outer while loop not met */

/* >                     (program created more than N unreduced blocks) */

/* >             else NCVT = NRU = NCC = 0, */

/* >                   the algorithm did not converge; D and E contain the */

/* >                   elements of a bidiagonal matrix which is orthogonally */

/* >                   similar to the input matrix B;  if INFO = i, i */

/* >                   elements of E have not converged to zero. */

/* > \endverbatim */

/* > \par Internal Parameters: */

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

/* > */

/* > \verbatim */

/* >  TOLMUL  DOUBLE PRECISION, default = f2cmax(10,f2cmin(100,EPS**(-1/8))) */

/* >          TOLMUL controls the convergence criterion of the QR loop. */

/* >          If it is positive, TOLMUL*EPS is the desired relative */

/* >             precision in the computed singular values. */

/* >          If it is negative, abs(TOLMUL*EPS*sigma_max) is the */

/* >             desired absolute accuracy in the computed singular */

/* >             values (corresponds to relative accuracy */

/* >             abs(TOLMUL*EPS) in the largest singular value. */

/* >          abs(TOLMUL) should be between 1 and 1/EPS, and preferably */

/* >             between 10 (for fast convergence) and .1/EPS */

/* >             (for there to be some accuracy in the results). */

/* >          Default is to lose at either one eighth or 2 of the */

/* >             available decimal digits in each computed singular value */

/* >             (whichever is smaller). */

/* > */

/* >  MAXITR  INTEGER, default = 6 */

/* >          MAXITR controls the maximum number of passes of the */

/* >          algorithm through its inner loop. The algorithms stops */

/* >          (and so fails to converge) if the number of passes */

/* >          through the inner loop exceeds MAXITR*N**2. */

/* > */

/* > \endverbatim */

/* > \par Note: */

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

/* > */

/* > \verbatim */

/* >  Bug report from Cezary Dendek. */

/* >  On March 23rd 2017, the INTEGER variable MAXIT = MAXITR*N**2 is */

/* >  removed since it can overflow pretty easily (for N larger or equal */

/* >  than 18,919). We instead use MAXITDIVN = MAXITR*N. */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date June 2017 */

/* > \ingroup auxOTHERcomputational */

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

/* Subroutine */ void dbdsqr_(char *uplo, integer *n, integer *ncvt, integer *

  nru, integer *ncc, doublereal *d__, doublereal *e, doublereal *vt, 

  integer *ldvt, doublereal *u, integer *ldu, doublereal *c__, integer *

  ldc, doublereal *work, integer *info)

{

    /* System generated locals */

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

      i__2;

    doublereal d__1, d__2, d__3, d__4;

    /* Local variables */

    doublereal abse;

    integer idir;

    doublereal abss;

    integer oldm;

    doublereal cosl;

    integer isub, iter;

    doublereal unfl, sinl, cosr, smin, smax, sinr;

    extern /* Subroutine */ void drot_(integer *, doublereal *, integer *, 

      doublereal *, integer *, doublereal *, doublereal *);

    integer iterdivn;

    extern /* Subroutine */ void dlas2_(doublereal *, doublereal *, doublereal 

      *, doublereal *, doublereal *);

    doublereal f, g, h__;

    integer i__, j, m;

    doublereal r__;

    extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *, 

      integer *);

    extern logical lsame_(char *, char *);

    doublereal oldcs;

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

      integer *, doublereal *, doublereal *, doublereal *, integer *);

    integer oldll;

    doublereal shift, sigmn, oldsn;

    extern /* Subroutine */ void dswap_(integer *, doublereal *, integer *, 

      doublereal *, integer *);

    doublereal sminl, sigmx;

    logical lower;

    integer maxitdivn;

    extern /* Subroutine */ void dlasq1_(integer *, doublereal *, doublereal *,

       doublereal *, integer *), dlasv2_(doublereal *, doublereal *, 

      doublereal *, doublereal *, doublereal *, doublereal *, 

      doublereal *, doublereal *, doublereal *);

    doublereal cs;

    integer ll;

    extern doublereal dlamch_(char *);

    doublereal sn, mu;

    extern /* Subroutine */ void dlartg_(doublereal *, doublereal *, 

      doublereal *, doublereal *, doublereal *);

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

    doublereal sminoa, thresh;

    logical rotate;

    integer nm1;

    doublereal tolmul;

    integer nm12, nm13, lll;

    doublereal eps, sll, tol;

/*  -- LAPACK computational routine (version 3.7.1) -- */

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

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

/*     June 2017 */

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

/*     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;

    lower = lsame_(uplo, "L");

    if (! lsame_(uplo, "U") && ! lower) {

  *info = -1;

    } else if (*n < 0) {

  *info = -2;

    } else if (*ncvt < 0) {

  *info = -3;

    } else if (*nru < 0) {

  *info = -4;

    } else if (*ncc < 0) {

  *info = -5;

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

  *info = -9;

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

  *info = -11;

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

  *info = -13;

    }

    if (*info != 0) {

  i__1 = -(*info);

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

  return;

    }

    if (*n == 0) {

  return;

    }

    if (*n == 1) {

  goto L160;

    }

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

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

/*     If no singular vectors desired, use qd algorithm */

    if (! rotate) {

  dlasq1_(n, &d__[1], &e[1], &work[1], info);

/*     If INFO equals 2, dqds didn't finish, try to finish */

  if (*info != 2) {

      return;

  }

  *info = 0;

    }

    nm1 = *n - 1;

    nm12 = nm1 + nm1;

    nm13 = nm12 + nm1;

    idir = 0;

/*     Get machine constants */

    eps = dlamch_("Epsilon");

    unfl = dlamch_("Safe minimum");

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

/*     by applying Givens rotations on the left */

    if (lower) {

  i__1 = *n - 1;

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

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

      d__[i__] = r__;

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

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

      work[i__] = cs;

      work[nm1 + i__] = sn;

/* L10: */

  }

/*        Update singular vectors if desired */

  if (*nru > 0) {

      dlasr_("R", "V", "F", nru, n, &work[1], &work[*n], &u[u_offset], 

        ldu);

  }

  if (*ncc > 0) {

      dlasr_("L", "V", "F", n, ncc, &work[1], &work[*n], &c__[c_offset],

         ldc);

  }

    }

/*     Compute singular values to relative accuracy TOL */

/*     (By setting TOL to be negative, algorithm will compute */

/*     singular values to absolute accuracy ABS(TOL)*norm(input matrix)) */

/* Computing MAX */

/* Computing MIN */

    d__3 = 100., d__4 = pow_dd(&eps, &c_b15);

    d__1 = 10., d__2 = f2cmin(d__3,d__4);

    tolmul = f2cmax(d__1,d__2);

    tol = tolmul * eps;

/*     Compute approximate maximum, minimum singular values */

    smax = 0.;

    i__1 = *n;

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

/* Computing MAX */

  d__2 = smax, d__3 = (d__1 = d__[i__], abs(d__1));

  smax = f2cmax(d__2,d__3);

/* L20: */

    }

    i__1 = *n - 1;

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

/* Computing MAX */

  d__2 = smax, d__3 = (d__1 = e[i__], abs(d__1));

  smax = f2cmax(d__2,d__3);

/* L30: */

    }

    sminl = 0.;

    if (tol >= 0.) {

/*        Relative accuracy desired */

  sminoa = abs(d__[1]);

  if (sminoa == 0.) {

      goto L50;

  }

  mu = sminoa;

  i__1 = *n;

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

      mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1]

        , abs(d__1))));

      sminoa = f2cmin(sminoa,mu);

      if (sminoa == 0.) {

    goto L50;

      }

/* L40: */

  }

L50:

  sminoa /= sqrt((doublereal) (*n));

/* Computing MAX */

  d__1 = tol * sminoa, d__2 = *n * (*n * unfl) * 6;

  thresh = f2cmax(d__1,d__2);

    } else {

/*        Absolute accuracy desired */

/* Computing MAX */

  d__1 = abs(tol) * smax, d__2 = *n * (*n * unfl) * 6;

  thresh = f2cmax(d__1,d__2);

    }

/*     Prepare for main iteration loop for the singular values */

/*     (MAXIT is the maximum number of passes through the inner */

/*     loop permitted before nonconvergence signalled.) */

    maxitdivn = *n * 6;

    iterdivn = 0;

    iter = -1;

    oldll = -1;

    oldm = -1;

/*     M points to last element of unconverged part of matrix */

    m = *n;