#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__6 = 6;

static integer c__0 = 0;

static integer c__2 = 2;

static integer c_n1 = -1;

static doublereal c_b57 = 0.;

static integer c__1 = 1;

static doublereal c_b79 = 1.;

/* > \brief <b> DGESVD computes the singular value decomposition (SVD) for GE matrices</b> */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download DGESVD + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, */

/*                          WORK, LWORK, INFO ) */

/*       CHARACTER          JOBU, JOBVT */

/*       INTEGER            INFO, LDA, LDU, LDVT, LWORK, M, N */

/*       DOUBLE PRECISION   A( LDA, * ), S( * ), U( LDU, * ), */

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

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

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

/* > M-by-N matrix A, optionally computing the left and/or right singular */

/* > vectors. The SVD is written */

/* > */

/* >      A = U * SIGMA * transpose(V) */

/* > */

/* > where SIGMA is an M-by-N matrix which is zero except for its */

/* > f2cmin(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */

/* > V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA */

/* > are the singular values of A; they are real and non-negative, and */

/* > are returned in descending order.  The first f2cmin(m,n) columns of */

/* > U and V are the left and right singular vectors of A. */

/* > */

/* > Note that the routine returns V**T, not V. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] JOBU */

/* > \verbatim */

/* >          JOBU is CHARACTER*1 */

/* >          Specifies options for computing all or part of the matrix U: */

/* >          = 'A':  all M columns of U are returned in array U: */

/* >          = 'S':  the first f2cmin(m,n) columns of U (the left singular */

/* >                  vectors) are returned in the array U; */

/* >          = 'O':  the first f2cmin(m,n) columns of U (the left singular */

/* >                  vectors) are overwritten on the array A; */

/* >          = 'N':  no columns of U (no left singular vectors) are */

/* >                  computed. */

/* > \endverbatim */

/* > */

/* > \param[in] JOBVT */

/* > \verbatim */

/* >          JOBVT is CHARACTER*1 */

/* >          Specifies options for computing all or part of the matrix */

/* >          V**T: */

/* >          = 'A':  all N rows of V**T are returned in the array VT; */

/* >          = 'S':  the first f2cmin(m,n) rows of V**T (the right singular */

/* >                  vectors) are returned in the array VT; */

/* >          = 'O':  the first f2cmin(m,n) rows of V**T (the right singular */

/* >                  vectors) are overwritten on the array A; */

/* >          = 'N':  no rows of V**T (no right singular vectors) are */

/* >                  computed. */

/* > */

/* >          JOBVT and JOBU cannot both be 'O'. */

/* > \endverbatim */

/* > */

/* > \param[in] M */

/* > \verbatim */

/* >          M is INTEGER */

/* >          The number of rows of the input matrix A.  M >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >          The number of columns of the input matrix A.  N >= 0. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          On entry, the M-by-N matrix A. */

/* >          On exit, */

/* >          if JOBU = 'O',  A is overwritten with the first f2cmin(m,n) */

/* >                          columns of U (the left singular vectors, */

/* >                          stored columnwise); */

/* >          if JOBVT = 'O', A is overwritten with the first f2cmin(m,n) */

/* >                          rows of V**T (the right singular vectors, */

/* >                          stored rowwise); */

/* >          if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A */

/* >                          are destroyed. */

/* > \endverbatim */

/* > */

/* > \param[in] LDA */

/* > \verbatim */

/* >          LDA is INTEGER */

/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */

/* > \endverbatim */

/* > */

/* > \param[out] S */

/* > \verbatim */

/* >          S is DOUBLE PRECISION array, dimension (f2cmin(M,N)) */

/* >          The singular values of A, sorted so that S(i) >= S(i+1). */

/* > \endverbatim */

/* > */

/* > \param[out] U */

/* > \verbatim */

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

/* >          (LDU,M) if JOBU = 'A' or (LDU,f2cmin(M,N)) if JOBU = 'S'. */

/* >          If JOBU = 'A', U contains the M-by-M orthogonal matrix U; */

/* >          if JOBU = 'S', U contains the first f2cmin(m,n) columns of U */

/* >          (the left singular vectors, stored columnwise); */

/* >          if JOBU = 'N' or 'O', U is not referenced. */

/* > \endverbatim */

/* > */

/* > \param[in] LDU */

/* > \verbatim */

/* >          LDU is INTEGER */

/* >          The leading dimension of the array U.  LDU >= 1; if */

/* >          JOBU = 'S' or 'A', LDU >= M. */

/* > \endverbatim */

/* > */

/* > \param[out] VT */

/* > \verbatim */

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

/* >          If JOBVT = 'A', VT contains the N-by-N orthogonal matrix */

/* >          V**T; */

/* >          if JOBVT = 'S', VT contains the first f2cmin(m,n) rows of */

/* >          V**T (the right singular vectors, stored rowwise); */

/* >          if JOBVT = 'N' or 'O', VT is not referenced. */

/* > \endverbatim */

/* > */

/* > \param[in] LDVT */

/* > \verbatim */

/* >          LDVT is INTEGER */

/* >          The leading dimension of the array VT.  LDVT >= 1; if */

/* >          JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= f2cmin(M,N). */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* >          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */

/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */

/* >          if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged */

/* >          superdiagonal elements of an upper bidiagonal matrix B */

/* >          whose diagonal is in S (not necessarily sorted). B */

/* >          satisfies A = U * B * VT, so it has the same singular values */

/* >          as A, and singular vectors related by U and VT. */

/* > \endverbatim */

/* > */

/* > \param[in] LWORK */

/* > \verbatim */

/* >          LWORK is INTEGER */

/* >          The dimension of the array WORK. */

/* >          LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): */

/* >             - PATH 1  (M much larger than N, JOBU='N') */

/* >             - PATH 1t (N much larger than M, JOBVT='N') */

/* >          LWORK >= MAX(1,3*MIN(M,N) + MAX(M,N),5*MIN(M,N)) for the other paths */

/* >          For good performance, LWORK should generally be larger. */

/* > */

/* >          If LWORK = -1, then a workspace query is assumed; the routine */

/* >          only calculates the optimal size of the WORK array, returns */

/* >          this value as the first entry of the WORK array, and no error */

/* >          message related to LWORK is issued by XERBLA. */

/* > \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 DBDSQR did not converge, INFO specifies how many */

/* >                superdiagonals of an intermediate bidiagonal form B */

/* >                did not converge to zero. See the description of WORK */

/* >                above for details. */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date April 2012 */

/* > \ingroup doubleGEsing */

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

/* Subroutine */ void dgesvd_(char *jobu, char *jobvt, integer *m, integer *n, 

  doublereal *a, integer *lda, doublereal *s, doublereal *u, integer *

  ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, 

  integer *info)

{

    /* System generated locals */

    address a__1[2];

    integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2], 

      i__2, i__3, i__4;

    char ch__1[2];

    /* Local variables */

    integer iscl;

    doublereal anrm;

    integer ierr, itau, ncvt, nrvt, lwork_dgebrd__, lwork_dgelqf__, 

      lwork_dgeqrf__, i__;

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

      integer *, doublereal *, doublereal *, integer *, doublereal *, 

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

    extern logical lsame_(char *, char *);

    integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork;

    logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs;

    integer ie;

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

      integer *, doublereal *, doublereal *, doublereal *, doublereal *,

       doublereal *, integer *, integer *);

    extern doublereal dlamch_(char *), dlange_(char *, integer *, 

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

    integer ir, bdspac, iu;

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

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

      dlascl_(char *, integer *, integer *, doublereal *, doublereal *, 

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

       dgeqrf_(integer *, integer *, doublereal *, integer *, 

      doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,

       integer *, integer *, doublereal *, integer *, doublereal *, 

      integer *), dlaset_(char *, integer *, integer *, 

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

      dbdsqr_(char *, integer *, integer *, integer *, integer *, 

      doublereal *, doublereal *, doublereal *, integer *, doublereal *,

       integer *, doublereal *, integer *, doublereal *, integer *), dorgbr_(char *, integer *, integer *, integer *, 

      doublereal *, integer *, doublereal *, doublereal *, integer *, 

      integer *);

    doublereal bignum;

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

    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 

      integer *, integer *, ftnlen, ftnlen);

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

      integer *, integer *, doublereal *, integer *, doublereal *, 

      doublereal *, integer *, doublereal *, integer *, integer *), dorglq_(integer *, integer *, integer *, 

      doublereal *, integer *, doublereal *, doublereal *, integer *, 

      integer *), dorgqr_(integer *, integer *, integer *, doublereal *,

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

    integer ldwrkr, minwrk, ldwrku, maxwrk;

    doublereal smlnum;

    logical lquery, wntuas, wntvas;

    integer lwork_dorgbr_p__, lwork_dorgbr_q__, lwork_dorglq_m__, 

      lwork_dorglq_n__, lwork_dorgqr_m__, lwork_dorgqr_n__, blk, ncu;

    doublereal dum[1], eps;

    integer nru;

/*  -- LAPACK driver 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..-- */

/*     April 2012 */

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

/*     Test the input arguments */

    /* Parameter adjustments */

    a_dim1 = *lda;

    a_offset = 1 + a_dim1 * 1;

    a -= a_offset;

    --s;

    u_dim1 = *ldu;

    u_offset = 1 + u_dim1 * 1;

    u -= u_offset;

    vt_dim1 = *ldvt;

    vt_offset = 1 + vt_dim1 * 1;

    vt -= vt_offset;

    --work;

    /* Function Body */

    *info = 0;

    minmn = f2cmin(*m,*n);

    wntua = lsame_(jobu, "A");

    wntus = lsame_(jobu, "S");

    wntuas = wntua || wntus;

    wntuo = lsame_(jobu, "O");

    wntun = lsame_(jobu, "N");

    wntva = lsame_(jobvt, "A");

    wntvs = lsame_(jobvt, "S");

    wntvas = wntva || wntvs;

    wntvo = lsame_(jobvt, "O");

    wntvn = lsame_(jobvt, "N");

    lquery = *lwork == -1;

    if (! (wntua || wntus || wntuo || wntun)) {

  *info = -1;

    } else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) {

  *info = -2;

    } else if (*m < 0) {

  *info = -3;

    } else if (*n < 0) {

  *info = -4;

    } else if (*lda < f2cmax(1,*m)) {

  *info = -6;

    } else if (*ldu < 1 || wntuas && *ldu < *m) {

  *info = -9;

    } else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) {

  *info = -11;

    }

/*     Compute workspace */

/*      (Note: Comments in the code beginning "Workspace:" describe the */

/*       minimal amount of workspace needed at that point in the code, */

/*       as well as the preferred amount for good performance. */

/*       NB refers to the optimal block size for the immediately */

/*       following subroutine, as returned by ILAENV.) */

    if (*info == 0) {

  minwrk = 1;

  maxwrk = 1;

  if (*m >= *n && minmn > 0) {

/*           Compute space needed for DBDSQR */

/* Writing concatenation */

      i__1[0] = 1, a__1[0] = jobu;

      i__1[1] = 1, a__1[1] = jobvt;

      s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);

      mnthr = ilaenv_(&c__6, "DGESVD", ch__1, m, n, &c__0, &c__0, (

        ftnlen)6, (ftnlen)2);

      bdspac = *n * 5;

/*           Compute space needed for DGEQRF */

      dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);

      lwork_dgeqrf__ = (integer) dum[0];

/*           Compute space needed for DORGQR */

      dorgqr_(m, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);

      lwork_dorgqr_n__ = (integer) dum[0];

      dorgqr_(m, m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);

      lwork_dorgqr_m__ = (integer) dum[0];

/*           Compute space needed for DGEBRD */

      dgebrd_(n, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1,

         &ierr);

      lwork_dgebrd__ = (integer) dum[0];

/*           Compute space needed for DORGBR P */

      dorgbr_("P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);

      lwork_dorgbr_p__ = (integer) dum[0];

/*           Compute space needed for DORGBR Q */

      dorgbr_("Q", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);

      lwork_dorgbr_q__ = (integer) dum[0];

      if (*m >= mnthr) {

    if (wntun) {

/*                 Path 1 (M much larger than N, JOBU='N') */

        maxwrk = *n + lwork_dgeqrf__;

/* Computing MAX */

        i__2 = maxwrk, i__3 = *n * 3 + lwork_dgebrd__;

        maxwrk = f2cmax(i__2,i__3);

        if (wntvo || wntvas) {

/* Computing MAX */

      i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__;

      maxwrk = f2cmax(i__2,i__3);

        }

        maxwrk = f2cmax(maxwrk,bdspac);

/* Computing MAX */

        i__2 = *n << 2;

        minwrk = f2cmax(i__2,bdspac);

    } else if (wntuo && wntvn) {

/*                 Path 2 (M much larger than N, JOBU='O', JOBVT='N') */

        wrkbl = *n + lwork_dgeqrf__;

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;

        wrkbl = f2cmax(i__2,i__3);

        wrkbl = f2cmax(wrkbl,bdspac);

/* Computing MAX */

        i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n;

        maxwrk = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = *n * 3 + *m;

        minwrk = f2cmax(i__2,bdspac);

    } else if (wntuo && wntvas) {

/*                 Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */

/*                 'A') */

        wrkbl = *n + lwork_dgeqrf__;

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__;

        wrkbl = f2cmax(i__2,i__3);

        wrkbl = f2cmax(wrkbl,bdspac);

/* Computing MAX */

        i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n;

        maxwrk = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = *n * 3 + *m;

        minwrk = f2cmax(i__2,bdspac);

    } else if (wntus && wntvn) {

/*                 Path 4 (M much larger than N, JOBU='S', JOBVT='N') */

        wrkbl = *n + lwork_dgeqrf__;

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;

        wrkbl = f2cmax(i__2,i__3);

        wrkbl = f2cmax(wrkbl,bdspac);

        maxwrk = *n * *n + wrkbl;

/* Computing MAX */

        i__2 = *n * 3 + *m;

        minwrk = f2cmax(i__2,bdspac);

    } else if (wntus && wntvo) {

/*                 Path 5 (M much larger than N, JOBU='S', JOBVT='O') */

        wrkbl = *n + lwork_dgeqrf__;

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__;

        wrkbl = f2cmax(i__2,i__3);

/* Computing MAX */

        i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__;

        wrkbl = f2cmax(i__2,i__3);

        wrkbl = f2cmax(wrkbl,bdspac);

        maxwrk = (*n << 1) * *n + wrkbl;

/* Computing MAX */

        i__2 = *n * 3 + *m;

        minwrk = f2cmax(i__2,bdspac);

    } else if (wntus && wntvas) {