#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)

*/

/* > \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download DLASR + dependencies */

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

"> */

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

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

"> */

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

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

"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) */

/*       CHARACTER          DIRECT, PIVOT, SIDE */

/*       INTEGER            LDA, M, N */

/*       DOUBLE PRECISION   A( LDA, * ), C( * ), S( * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > DLASR applies a sequence of plane rotations to a real matrix A, */

/* > from either the left or the right. */

/* > */

/* > When SIDE = 'L', the transformation takes the form */

/* > */

/* >    A := P*A */

/* > */

/* > and when SIDE = 'R', the transformation takes the form */

/* > */

/* >    A := A*P**T */

/* > */

/* > where P is an orthogonal matrix consisting of a sequence of z plane */

/* > rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', */

/* > and P**T is the transpose of P. */

/* > */

/* > When DIRECT = 'F' (Forward sequence), then */

/* > */

/* >    P = P(z-1) * ... * P(2) * P(1) */

/* > */

/* > and when DIRECT = 'B' (Backward sequence), then */

/* > */

/* >    P = P(1) * P(2) * ... * P(z-1) */

/* > */

/* > where P(k) is a plane rotation matrix defined by the 2-by-2 rotation */

/* > */

/* >    R(k) = (  c(k)  s(k) ) */

/* >         = ( -s(k)  c(k) ). */

/* > */

/* > When PIVOT = 'V' (Variable pivot), the rotation is performed */

/* > for the plane (k,k+1), i.e., P(k) has the form */

/* > */

/* >    P(k) = (  1                                            ) */

/* >           (       ...                                     ) */

/* >           (              1                                ) */

/* >           (                   c(k)  s(k)                  ) */

/* >           (                  -s(k)  c(k)                  ) */

/* >           (                                1              ) */

/* >           (                                     ...       ) */

/* >           (                                            1  ) */

/* > */

/* > where R(k) appears as a rank-2 modification to the identity matrix in */

/* > rows and columns k and k+1. */

/* > */

/* > When PIVOT = 'T' (Top pivot), the rotation is performed for the */

/* > plane (1,k+1), so P(k) has the form */

/* > */

/* >    P(k) = (  c(k)                    s(k)                 ) */

/* >           (         1                                     ) */

/* >           (              ...                              ) */

/* >           (                     1                         ) */

/* >           ( -s(k)                    c(k)                 ) */

/* >           (                                 1             ) */

/* >           (                                      ...      ) */

/* >           (                                             1 ) */

/* > */

/* > where R(k) appears in rows and columns 1 and k+1. */

/* > */

/* > Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is */

/* > performed for the plane (k,z), giving P(k) the form */

/* > */

/* >    P(k) = ( 1                                             ) */

/* >           (      ...                                      ) */

/* >           (             1                                 ) */

/* >           (                  c(k)                    s(k) ) */

/* >           (                         1                     ) */

/* >           (                              ...              ) */

/* >           (                                     1         ) */

/* >           (                 -s(k)                    c(k) ) */

/* > */

/* > where R(k) appears in rows and columns k and z.  The rotations are */

/* > performed without ever forming P(k) explicitly. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] SIDE */

/* > \verbatim */

/* >          SIDE is CHARACTER*1 */

/* >          Specifies whether the plane rotation matrix P is applied to */

/* >          A on the left or the right. */

/* >          = 'L':  Left, compute A := P*A */

/* >          = 'R':  Right, compute A:= A*P**T */

/* > \endverbatim */

/* > */

/* > \param[in] PIVOT */

/* > \verbatim */

/* >          PIVOT is CHARACTER*1 */

/* >          Specifies the plane for which P(k) is a plane rotation */

/* >          matrix. */

/* >          = 'V':  Variable pivot, the plane (k,k+1) */

/* >          = 'T':  Top pivot, the plane (1,k+1) */

/* >          = 'B':  Bottom pivot, the plane (k,z) */

/* > \endverbatim */

/* > */

/* > \param[in] DIRECT */

/* > \verbatim */

/* >          DIRECT is CHARACTER*1 */

/* >          Specifies whether P is a forward or backward sequence of */

/* >          plane rotations. */

/* >          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1) */

/* >          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1) */

/* > \endverbatim */

/* > */

/* > \param[in] M */

/* > \verbatim */

/* >          M is INTEGER */

/* >          The number of rows of the matrix A.  If m <= 1, an immediate */

/* >          return is effected. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >          The number of columns of the matrix A.  If n <= 1, an */

/* >          immediate return is effected. */

/* > \endverbatim */

/* > */

/* > \param[in] C */

/* > \verbatim */

/* >          C is DOUBLE PRECISION array, dimension */

/* >                  (M-1) if SIDE = 'L' */

/* >                  (N-1) if SIDE = 'R' */

/* >          The cosines c(k) of the plane rotations. */

/* > \endverbatim */

/* > */

/* > \param[in] S */

/* > \verbatim */

/* >          S is DOUBLE PRECISION array, dimension */

/* >                  (M-1) if SIDE = 'L' */

/* >                  (N-1) if SIDE = 'R' */

/* >          The sines s(k) of the plane rotations.  The 2-by-2 plane */

/* >          rotation part of the matrix P(k), R(k), has the form */

/* >          R(k) = (  c(k)  s(k) ) */

/* >                 ( -s(k)  c(k) ). */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

/* >          The M-by-N matrix A.  On exit, A is overwritten by P*A if */

/* >          SIDE = 'L' or by A*P**T if SIDE = 'R'. */

/* > \endverbatim */

/* > */

/* > \param[in] LDA */

/* > \verbatim */

/* >          LDA is INTEGER */

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

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup OTHERauxiliary */

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

/* Subroutine */ void dlasr_(char *side, char *pivot, char *direct, integer *m,

   integer *n, doublereal *c__, doublereal *s, doublereal *a, integer *

  lda)

{

    /* System generated locals */

    integer a_dim1, a_offset, i__1, i__2;

    /* Local variables */

    integer info;

    doublereal temp;

    integer i__, j;

    extern logical lsame_(char *, char *);

    doublereal ctemp, stemp;

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

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

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

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

/*     December 2016 */

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

/*     Test the input parameters */

    /* Parameter adjustments */

    --c__;

    --s;

    a_dim1 = *lda;

    a_offset = 1 + a_dim1 * 1;

    a -= a_offset;

    /* Function Body */

    info = 0;

    if (! (lsame_(side, "L") || lsame_(side, "R"))) {

  info = 1;

    } else if (! (lsame_(pivot, "V") || lsame_(pivot, 

      "T") || lsame_(pivot, "B"))) {

  info = 2;

    } else if (! (lsame_(direct, "F") || lsame_(direct, 

      "B"))) {

  info = 3;

    } else if (*m < 0) {

  info = 4;

    } else if (*n < 0) {

  info = 5;

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

  info = 9;

    }

    if (info != 0) {

  xerbla_("DLASR ", &info, (ftnlen)6);

  return;

    }

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {

  return;

    }

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

/*        Form  P * A */

  if (lsame_(pivot, "V")) {

      if (lsame_(direct, "F")) {

    i__1 = *m - 1;

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

        ctemp = c__[j];

        stemp = s[j];

        if (ctemp != 1. || stemp != 0.) {

      i__2 = *n;

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

          temp = a[j + 1 + i__ * a_dim1];

          a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * 

            a[j + i__ * a_dim1];

          a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j 

            + i__ * a_dim1];

/* L10: */

      }

        }

/* L20: */

    }

      } else if (lsame_(direct, "B")) {

    for (j = *m - 1; j >= 1; --j) {

        ctemp = c__[j];

        stemp = s[j];

        if (ctemp != 1. || stemp != 0.) {

      i__1 = *n;

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

          temp = a[j + 1 + i__ * a_dim1];

          a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * 

            a[j + i__ * a_dim1];

          a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j 

            + i__ * a_dim1];

/* L30: */

      }

        }

/* L40: */

    }

      }

  } else if (lsame_(pivot, "T")) {

      if (lsame_(direct, "F")) {

    i__1 = *m;

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

        ctemp = c__[j - 1];

        stemp = s[j - 1];

        if (ctemp != 1. || stemp != 0.) {

      i__2 = *n;

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

          temp = a[j + i__ * a_dim1];

          a[j + i__ * a_dim1] = ctemp * temp - stemp * a[

            i__ * a_dim1 + 1];

          a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[

            i__ * a_dim1 + 1];

/* L50: */

      }

        }

/* L60: */

    }

      } else if (lsame_(direct, "B")) {

    for (j = *m; j >= 2; --j) {

        ctemp = c__[j - 1];

        stemp = s[j - 1];

        if (ctemp != 1. || stemp != 0.) {

      i__1 = *n;

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

          temp = a[j + i__ * a_dim1];

          a[j + i__ * a_dim1] = ctemp * temp - stemp * a[

            i__ * a_dim1 + 1];

          a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[

            i__ * a_dim1 + 1];

/* L70: */

      }

        }

/* L80: */

    }

      }

  } else if (lsame_(pivot, "B")) {

      if (lsame_(direct, "F")) {

    i__1 = *m - 1;

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

        ctemp = c__[j];

        stemp = s[j];

        if (ctemp != 1. || stemp != 0.) {

      i__2 = *n;

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

          temp = a[j + i__ * a_dim1];

          a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1]

             + ctemp * temp;

          a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * 

            a_dim1] - stemp * temp;

/* L90: */

      }

        }

/* L100: */

    }

      } else if (lsame_(direct, "B")) {

    for (j = *m - 1; j >= 1; --j) {

        ctemp = c__[j];

        stemp = s[j];

        if (ctemp != 1. || stemp != 0.) {

      i__1 = *n;

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

          temp = a[j + i__ * a_dim1];

          a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1]

             + ctemp * temp;

          a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * 

            a_dim1] - stemp * temp;

/* L110: */

      }

        }

/* L120: */

    }

      }

  }

    } else if (lsame_(side, "R")) {

/*        Form A * P**T */

  if (lsame_(pivot, "V")) {

      if (lsame_(direct, "F")) {

    i__1 = *n - 1;

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

        ctemp = c__[j];

        stemp = s[j];

        if (ctemp != 1. || stemp != 0.) {

      i__2 = *m;

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

          temp = a[i__ + (j + 1) * a_dim1];

          a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp *

             a[i__ + j * a_dim1];

          a[i__ + j * a_dim1] = stemp * temp + ctemp * a[

            i__ + j * a_dim1];

/* L130: */

      }

        }

/* L140: */

    }

      } else if (lsame_(direct, "B")) {

    for (j = *n - 1; j >= 1; --j) {

        ctemp = c__[j];

        stemp = s[j];

        if (ctemp != 1. || stemp != 0.) {

      i__1 = *m;

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

          temp = a[i__ + (j + 1) * a_dim1];

          a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp *

             a[i__ + j * a_dim1];

          a[i__ + j * a_dim1] = stemp * temp + ctemp * a[

            i__ + j * a_dim1];

/* L150: */

      }

        }

/* L160: */

    }

      }

  } else if (lsame_(pivot, "T")) {

      if (lsame_(direct, "F")) {

    i__1 = *n;

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

        ctemp = c__[j - 1];

        stemp = s[j - 1];

        if (ctemp != 1. || stemp != 0.) {

      i__2 = *m;

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

          temp = a[i__ + j * a_dim1];

          a[i__ + j * a_dim1] = ctemp * temp - stemp * a[

            i__ + a_dim1];

          a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + 

            a_dim1];

/* L170: */

      }

        }

/* L180: */

    }

      } else if (lsame_(direct, "B")) {

    for (j = *n; j >= 2; --j) {

        ctemp = c__[j - 1];

        stemp = s[j - 1];

        if (ctemp != 1. || stemp != 0.) {

      i__1 = *m;

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

          temp = a[i__ + j * a_dim1];

          a[i__ + j * a_dim1] = ctemp * temp - stemp * a[

            i__ + a_dim1];

          a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + 

            a_dim1];

/* L190: */

      }

        }

/* L200: */

    }

      }

  } else if (lsame_(pivot, "B")) {

      if (lsame_(direct, "F")) {

    i__1 = *n - 1;

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

        ctemp = c__[j];

        stemp = s[j];

        if (ctemp != 1. || stemp != 0.) {

      i__2 = *m;

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

          temp = a[i__ + j * a_dim1];

          a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1]