#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 real c_b7 = 1.f;

static real c_b8 = 0.f;

static integer c__2 = 2;

/* > \brief \b SLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. */

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

/* Online html documentation available at */

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

/* > \htmlonly */

/* > Download SLALSA + dependencies */

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

f"> */

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

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

f"> */

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

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

f"> */

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

/* > \endhtmlonly */

/*  Definition: */

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

/*       SUBROUTINE SLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, */

/*                          LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, */

/*                          GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, */

/*                          IWORK, INFO ) */

/*       INTEGER            ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, */

/*      $                   SMLSIZ */

/*       INTEGER            GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */

/*      $                   K( * ), PERM( LDGCOL, * ) */

/*       REAL               B( LDB, * ), BX( LDBX, * ), C( * ), */

/*      $                   DIFL( LDU, * ), DIFR( LDU, * ), */

/*      $                   GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), */

/*      $                   U( LDU, * ), VT( LDU, * ), WORK( * ), */

/*      $                   Z( LDU, * ) */

/* > \par Purpose: */

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

/* > */

/* > \verbatim */

/* > */

/* > SLALSA is an itermediate step in solving the least squares problem */

/* > by computing the SVD of the coefficient matrix in compact form (The */

/* > singular vectors are computed as products of simple orthorgonal */

/* > matrices.). */

/* > */

/* > If ICOMPQ = 0, SLALSA applies the inverse of the left singular vector */

/* > matrix of an upper bidiagonal matrix to the right hand side; and if */

/* > ICOMPQ = 1, SLALSA applies the right singular vector matrix to the */

/* > right hand side. The singular vector matrices were generated in */

/* > compact form by SLALSA. */

/* > \endverbatim */

/*  Arguments: */

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

/* > \param[in] ICOMPQ */

/* > \verbatim */

/* >          ICOMPQ is INTEGER */

/* >         Specifies whether the left or the right singular vector */

/* >         matrix is involved. */

/* >         = 0: Left singular vector matrix */

/* >         = 1: Right singular vector matrix */

/* > \endverbatim */

/* > */

/* > \param[in] SMLSIZ */

/* > \verbatim */

/* >          SMLSIZ is INTEGER */

/* >         The maximum size of the subproblems at the bottom of the */

/* >         computation tree. */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* >          N is INTEGER */

/* >         The row and column dimensions of the upper bidiagonal matrix. */

/* > \endverbatim */

/* > */

/* > \param[in] NRHS */

/* > \verbatim */

/* >          NRHS is INTEGER */

/* >         The number of columns of B and BX. NRHS must be at least 1. */

/* > \endverbatim */

/* > */

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

/* > \verbatim */

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

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

/* >         squares problem in rows 1 through M. */

/* >         On output, B contains the solution X in rows 1 through N. */

/* > \endverbatim */

/* > */

/* > \param[in] LDB */

/* > \verbatim */

/* >          LDB is INTEGER */

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

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

/* > \endverbatim */

/* > */

/* > \param[out] BX */

/* > \verbatim */

/* >          BX is REAL array, dimension ( LDBX, NRHS ) */

/* >         On exit, the result of applying the left or right singular */

/* >         vector matrix to B. */

/* > \endverbatim */

/* > */

/* > \param[in] LDBX */

/* > \verbatim */

/* >          LDBX is INTEGER */

/* >         The leading dimension of BX. */

/* > \endverbatim */

/* > */

/* > \param[in] U */

/* > \verbatim */

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

/* >         On entry, U contains the left singular vector matrices of all */

/* >         subproblems at the bottom level. */

/* > \endverbatim */

/* > */

/* > \param[in] LDU */

/* > \verbatim */

/* >          LDU is INTEGER, LDU = > N. */

/* >         The leading dimension of arrays U, VT, DIFL, DIFR, */

/* >         POLES, GIVNUM, and Z. */

/* > \endverbatim */

/* > */

/* > \param[in] VT */

/* > \verbatim */

/* >          VT is REAL array, dimension ( LDU, SMLSIZ+1 ). */

/* >         On entry, VT**T contains the right singular vector matrices of */

/* >         all subproblems at the bottom level. */

/* > \endverbatim */

/* > */

/* > \param[in] K */

/* > \verbatim */

/* >          K is INTEGER array, dimension ( N ). */

/* > \endverbatim */

/* > */

/* > \param[in] DIFL */

/* > \verbatim */

/* >          DIFL is REAL array, dimension ( LDU, NLVL ). */

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

/* > \endverbatim */

/* > */

/* > \param[in] DIFR */

/* > \verbatim */

/* >          DIFR is REAL array, dimension ( LDU, 2 * NLVL ). */

/* >         On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record */

/* >         distances between singular values on the I-th level and */

/* >         singular values on the (I -1)-th level, and DIFR(*, 2 * I) */

/* >         record the normalizing factors of the right singular vectors */

/* >         matrices of subproblems on I-th level. */

/* > \endverbatim */

/* > */

/* > \param[in] Z */

/* > \verbatim */

/* >          Z is REAL array, dimension ( LDU, NLVL ). */

/* >         On entry, Z(1, I) contains the components of the deflation- */

/* >         adjusted updating row vector for subproblems on the I-th */

/* >         level. */

/* > \endverbatim */

/* > */

/* > \param[in] POLES */

/* > \verbatim */

/* >          POLES is REAL array, dimension ( LDU, 2 * NLVL ). */

/* >         On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old */

/* >         singular values involved in the secular equations on the I-th */

/* >         level. */

/* > \endverbatim */

/* > */

/* > \param[in] GIVPTR */

/* > \verbatim */

/* >          GIVPTR is INTEGER array, dimension ( N ). */

/* >         On entry, GIVPTR( I ) records the number of Givens */

/* >         rotations performed on the I-th problem on the computation */

/* >         tree. */

/* > \endverbatim */

/* > */

/* > \param[in] GIVCOL */

/* > \verbatim */

/* >          GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ). */

/* >         On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the */

/* >         locations of Givens rotations performed on the I-th level on */

/* >         the computation tree. */

/* > \endverbatim */

/* > */

/* > \param[in] LDGCOL */

/* > \verbatim */

/* >          LDGCOL is INTEGER, LDGCOL = > N. */

/* >         The leading dimension of arrays GIVCOL and PERM. */

/* > \endverbatim */

/* > */

/* > \param[in] PERM */

/* > \verbatim */

/* >          PERM is INTEGER array, dimension ( LDGCOL, NLVL ). */

/* >         On entry, PERM(*, I) records permutations done on the I-th */

/* >         level of the computation tree. */

/* > \endverbatim */

/* > */

/* > \param[in] GIVNUM */

/* > \verbatim */

/* >          GIVNUM is REAL array, dimension ( LDU, 2 * NLVL ). */

/* >         On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- */

/* >         values of Givens rotations performed on the I-th level on the */

/* >         computation tree. */

/* > \endverbatim */

/* > */

/* > \param[in] C */

/* > \verbatim */

/* >          C is REAL array, dimension ( N ). */

/* >         On entry, if the I-th subproblem is not square, */

/* >         C( I ) contains the C-value of a Givens rotation related to */

/* >         the right null space of the I-th subproblem. */

/* > \endverbatim */

/* > */

/* > \param[in] S */

/* > \verbatim */

/* >          S is REAL array, dimension ( N ). */

/* >         On entry, if the I-th subproblem is not square, */

/* >         S( I ) contains the S-value of a Givens rotation related to */

/* >         the right null space of the I-th subproblem. */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

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

/* > \endverbatim */

/* > */

/* > \param[out] IWORK */

/* > \verbatim */

/* >          IWORK is INTEGER array, dimension (3*N) */

/* > \endverbatim */

/* > */

/* > \param[out] INFO */

/* > \verbatim */

/* >          INFO is INTEGER */

/* >          = 0:  successful exit. */

/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */

/* > \endverbatim */

/*  Authors: */

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

/* > \author Univ. of Tennessee */

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

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

/* > \author NAG Ltd. */

/* > \date June 2017 */

/* > \ingroup realOTHERcomputational */

/* > \par Contributors: */

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

/* > */

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

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

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

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

/* Subroutine */ void slalsa_(integer *icompq, integer *smlsiz, integer *n, 

  integer *nrhs, real *b, integer *ldb, real *bx, integer *ldbx, real *

  u, integer *ldu, real *vt, integer *k, real *difl, real *difr, real *

  z__, real *poles, integer *givptr, integer *givcol, integer *ldgcol, 

  integer *perm, real *givnum, real *c__, real *s, real *work, integer *

  iwork, integer *info)

{

    /* System generated locals */

    integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1, 

      b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1, 

      difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset,

       u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, 

      i__2;

    /* Local variables */

    integer nlvl, sqre, i__, j, inode, ndiml;

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

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

      real *, integer *);

    integer ndimr, i1;

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

      integer *), slals0_(integer *, integer *, integer *, integer *, 

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

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

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

    integer ic, lf, nd, ll, nl, nr;

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

    extern void slasdt_(

      integer *, integer *, integer *, integer *, integer *, integer *, 

      integer *);

    integer im1, nlf, nrf, lvl, ndb1, nlp1, lvl2, nrp1;

/*  -- 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 */

    b_dim1 = *ldb;

    b_offset = 1 + b_dim1 * 1;

    b -= b_offset;

    bx_dim1 = *ldbx;

    bx_offset = 1 + bx_dim1 * 1;

    bx -= bx_offset;

    givnum_dim1 = *ldu;

    givnum_offset = 1 + givnum_dim1 * 1;

    givnum -= givnum_offset;

    poles_dim1 = *ldu;

    poles_offset = 1 + poles_dim1 * 1;

    poles -= poles_offset;

    z_dim1 = *ldu;

    z_offset = 1 + z_dim1 * 1;

    z__ -= z_offset;

    difr_dim1 = *ldu;

    difr_offset = 1 + difr_dim1 * 1;

    difr -= difr_offset;

    difl_dim1 = *ldu;

    difl_offset = 1 + difl_dim1 * 1;

    difl -= difl_offset;

    vt_dim1 = *ldu;

    vt_offset = 1 + vt_dim1 * 1;

    vt -= vt_offset;

    u_dim1 = *ldu;

    u_offset = 1 + u_dim1 * 1;

    u -= u_offset;

    --k; 

    --givptr;

    perm_dim1 = *ldgcol;

    perm_offset = 1 + perm_dim1 * 1;

    perm -= perm_offset;

    givcol_dim1 = *ldgcol;

    givcol_offset = 1 + givcol_dim1 * 1;

    givcol -= givcol_offset;

    --c__;

    --s;

    --work;

    --iwork;

    /* Function Body */

    *info = 0;

    if (*icompq < 0 || *icompq > 1) {

  *info = -1;

    } else if (*smlsiz < 3) {

  *info = -2;

    } else if (*n < *smlsiz) {

  *info = -3;

    } else if (*nrhs < 1) {

  *info = -4;

    } else if (*ldb < *n) {

  *info = -6;

    } else if (*ldbx < *n) {

  *info = -8;

    } else if (*ldu < *n) {

  *info = -10;

    } else if (*ldgcol < *n) {

  *info = -19;

    }

    if (*info != 0) {

  i__1 = -(*info);

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

  return;

    }

/*     Book-keeping and  setting up the computation tree. */

    inode = 1;

    ndiml = inode + *n;

    ndimr = ndiml + *n;

    slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], 

      smlsiz);

/*     The following code applies back the left singular vector factors. */

/*     For applying back the right singular vector factors, go to 50. */

    if (*icompq == 1) {

  goto L50;

    }

/*     The nodes on the bottom level of the tree were solved */

/*     by SLASDQ. The corresponding left and right singular vector */

/*     matrices are in explicit form. First apply back the left */

/*     singular vector matrices. */

    ndb1 = (nd + 1) / 2;

    i__1 = nd;

    for (i__ = ndb1; i__ <= i__1; ++i__) {

/*        IC : center row of each node */

/*        NL : number of rows of left  subproblem */

/*        NR : number of rows of right subproblem */

/*        NLF: starting row of the left   subproblem */

/*        NRF: starting row of the right  subproblem */

  i1 = i__ - 1;

  ic = iwork[inode + i1];

  nl = iwork[ndiml + i1];

  nr = iwork[ndimr + i1];

  nlf = ic - nl;

  nrf = ic + 1;

  sgemm_("T", "N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf 

    + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx);

  sgemm_("T", "N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf 

    + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx);

/* L10: */

    }

/*     Next copy the rows of B that correspond to unchanged rows */

/*     in the bidiagonal matrix to BX. */

    i__1 = nd;

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

  ic = iwork[inode + i__ - 1];

  scopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx);

/* L20: */

    }

/*     Finally go through the left singular vector matrices of all */

/*     the other subproblems bottom-up on the tree. */

    j = pow_ii(c__2, nlvl);

    sqre = 0;

    for (lvl = nlvl; lvl >= 1; --lvl) {

  lvl2 = (lvl << 1) - 1;

/*        find the first node LF and last node LL on */

/*        the current level LVL */

  if (lvl == 1) {

      lf = 1;

      ll = 1;

  } else {

      i__1 = lvl - 1;

      lf = pow_ii(c__2, i__1);

      ll = (lf << 1) - 1;

  }

  i__1 = ll;

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

      im1 = i__ - 1;

      ic = iwork[inode + im1];

      nl = iwork[ndiml + im1];

      nr = iwork[ndimr + im1];

      nlf = ic - nl;

      nrf = ic + 1;

      --j;

      slals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, &

        b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], &

        givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &

        givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *

         poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + 

        lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[

        j], &s[j], &work[1], info);

/* L30: */

  }

/* L40: */

    }

    goto L90;

/*     ICOMPQ = 1: applying back the right singular vector factors. */

L50:

/*     First now go through the right singular vector matrices of all */

/*     the tree nodes top-down. */

    j = 0;

    i__1 = nlvl;

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

  lvl2 = (lvl << 1) - 1;

/*        Find the first node LF and last node LL on */

/*        the current level LVL. */

  if (lvl == 1) {

      lf = 1;

      ll = 1;

  } else {

      i__2 = lvl - 1;

      lf = pow_ii(c__2, i__2);

      ll = (lf << 1) - 1;

  }

  i__2 = lf;

  for (i__ = ll; i__ >= i__2; --i__) {

      im1 = i__ - 1;

      ic = iwork[inode + im1];