source: prextra/mexlasso.c @ 98

/* Copyright (C) 1998
   Berwin A Turlach <bturlach@stats.adelaide.edu.au> */

/* This library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Library General Public License
   as published by the Free Software Foundation; either version 2 of
   the License, or (at your option) any later version. */

/* This library is distributed in the hope that it will be useful, but
   WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Library General Public License for more details. */

/* You should have received a copy of the GNU Library General Public
   License along with this library; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston,
   MA 02111-1307, USA. */

#include "lasso.h"
//#include "fortify.h"

#define PRECISION FLT_EPSILON

static void lasso_alloc(long n, long m);
static void lasso_free(void);
static void qr_init(int n);
static void qr_incr(void);
static void qr_free(void);
static void qr_del(int l, int aug);
static void qr_add(double *x, int swap);
#if defined (S_Plus)
static void errmsg(char* string);
#else
static void errmsg(char* where, char* string);
#endif

  static int QR_CHUNK = 10;

  static double *xtr=NULL, *btmp=NULL, *qtr=NULL,
                *rinvt_theta=NULL, *step=NULL, ytyd2=0.0;
  static int *theta=NULL, *nz_x=NULL, num_nz_x=0;
  static double *qmat=NULL, *rmat=NULL;
  static int qr_max_size=0, r_ncol=0, q_nrow=0, q_use_row=0;
  static char *no_dyn_mem_message="Cannot allocate dynamic memory";

void lasso(double *x,           /* input: data */
           long *pn,            /* input: rows */
           long *pm,            /* input: columns */
           double *pt,          /* input: threshold */
           double *beta,        /* input/ouput: intial/final beta */
           double *y,           /* input: labels */

           double *yhat1,       /* output */
           double *r,           /* output */
           double *lagrangian,  /* output */
           long *psuc,          /* output: succeed: 0/-1 */
           long *pverb,         /* input: verbose: yes/no */
           long *pas_sub)       /* input: no!? */
{

  double t = *pt, prec;
  long n = *pn, m = *pm, verb = *pverb, as_sub = *pas_sub;
  int not_solved;
  double *x_elem=NULL, tmp, max_val, b_1norm;
  int i, j, max_ind;
  double p_obj, d_obj;
  int num_iter=0, max_num;
  double b_1norm_old, mu;
  double rho_up, rho_low, rho;
  int to_del;
  double *q_elem, wtc, wtw;
  double *r_elem;
  int k;
  int add;
  if( !as_sub)
    lasso_alloc(n,m);

  prec = sqrt(PRECISION);

  if( as_sub ){

  b_1norm = 0.0;
  for(j=0;j<num_nz_x;j++)
    b_1norm += fabs(beta[nz_x[j]]);
  }else{

  b_1norm = 0.0;
  num_nz_x = 0;
  for(j=0; j<m; j++){
    if(fabs(beta[j]) > prec){
      b_1norm += fabs(beta[j]);
      nz_x[num_nz_x] = j;
      num_nz_x++;
    }else
      beta[j] = 0.0;
  }
  }

  if( b_1norm > t){
    if(verb){
      mexPrintf("******************************\n");
      mexPrintf("Rescaling beta from L1-norm %f to %f\n",b_1norm,t);
      mexEvalString("drawnow;");

    }
    for(j=0; j<num_nz_x; j++)
      beta[nz_x[j]] = beta[nz_x[j]] * t/b_1norm;
    b_1norm = t;
  }

  for(i=0; i< n; i++)
    yhat1[i] = 0.0;
  for(j=0; j < num_nz_x; j++){
    /* x_elem points to the first element in the column of X to which
       the j-th entry in nz_x points  */
    x_elem = x + nz_x[j]*n;
    tmp = beta[nz_x[j]];
    for(i=0; i < n; i++){
      yhat1[i] += *x_elem*tmp;
      x_elem++;           /* now we point to the next element in X */
    }
  }

  /* calculate the residual vector */
  for(i=0; i< n; i++)
    r[i] = y[i]-yhat1[i];

  /* multiply X^T with the residual vector */
  x_elem = x;
  for(j=0; j < m; j++){
    tmp = 0.0;
    for(i=0; i<n; i++){
      tmp += *x_elem*r[i];
      x_elem++;
    }
    xtr[j] = tmp;
  }

  max_val = fabs(xtr[0]);
  max_ind = 0;
  for(j=1; j<m; j++)
    if( fabs(xtr[j]) > max_val ){
      max_val = fabs(xtr[j]);
      max_ind = j;
    }

  if( !as_sub ){

  qr_add(y,TRUE);
  ytyd2 = *rmat * *rmat/2.0;
  for(j=0;j<num_nz_x;j++){
    qr_add(x+nz_x[j]*n, TRUE);
    if(fabs(beta[nz_x[j]])<prec)
      theta[j] = xtr[nz_x[j]] < 0 ? -1 : 1;
    else
      theta[j] = beta[nz_x[j]] < 0 ? -1 : 1;

  }
  }
  if( num_nz_x==0 ){
    nz_x[0] = max_ind;
    num_nz_x = 1;
    if(verb){
      mexPrintf("******************************\n");
      mexPrintf("  -->\tAdding variable: %d\n",max_ind+1);
      mexEvalString("drawnow;");
    }
    qr_add(x+max_ind*n, TRUE);
    theta[0] = xtr[max_ind] < 0 ? -1 : 1;
  }
  *psuc=0;
  if(verb){


  /* Find out how many times [[max_val]] is attained */
  tmp = (1.0-prec)*max_val;
  if( tmp < prec ) tmp = 0.0;
  max_num = 1;
  for(j=0; j<m; j++){
    if( tmp <= fabs(xtr[j]) && j!=max_ind){
      /*we found another element equal to the (current)
        maximal absolute value */
      max_num++;
    }
  }

  /* for the value of the dual objective function we need
     to calculate the L2 norm of the vector of fitted values */
  p_obj = 0.0;
  d_obj = 0.0;
  for(i=0;i<n;i++){
    p_obj += r[i]*r[i];
    d_obj += yhat1[i]*yhat1[i];
  }
  p_obj /= 2.0;
  d_obj = ytyd2 - d_obj/2.0 - t*max_val ;
  mexPrintf("******************************\n");
  mexPrintf("\nIteration number: %d\n", num_iter);
  mexPrintf("Value of primal object function      : %f\n", p_obj);
  mexPrintf("Value of dual   object function      : %f\n", d_obj);
  mexPrintf("L1 norm of current beta              : %f", b_1norm);
  mexPrintf(" <= %f\n", t);
  mexPrintf("Maximal absolute value in t(X)%%*%%r   : %e", max_val);
  mexPrintf(" attained %d time(s)\n", max_num);
  mexPrintf("Number of parameters allowed to vary : %d\n", num_nz_x);
  mexEvalString("drawnow;");
  num_iter++;
  }
  while(1){
    do{

  q_elem = qmat;

  for(j=0;j<num_nz_x;j++){
    tmp = 0.0;
    for(i=0;i<n;i++,q_elem++) {
      tmp += *q_elem*r[i];
    }
    qtr[j] = tmp;
  }

  if( b_1norm < (1.0-prec)*t )
    mu = 0.0;
  else{

  /* z=R^{-T}\theta can be calculated by solving R^Tz=\theta */
  r_elem = rmat;
  for(j=0;j<num_nz_x;j++,r_elem++){
    tmp = theta[j];
    for(k=0;k<j;k++,r_elem++)
      tmp -= *r_elem * rinvt_theta[k];
    rinvt_theta[j] = tmp /  *r_elem;
  }

  wtc = 0.0;
  wtw = 0.0;
  for(j=0;j<num_nz_x;j++){
    wtc += rinvt_theta[j]*qtr[j];
    wtw += rinvt_theta[j]*rinvt_theta[j];
  }
  mu = (wtc-(t-b_1norm))/wtw;
  }

  if(mu<=0.0)
    for(j=0;j<num_nz_x;j++)
      step[j] = qtr[j];
  else
    for(j=0;j<num_nz_x;j++)
      step[j] = qtr[j] - mu*rinvt_theta[j];

  /* h=R^{-1}z can be calculated by solving Rh=z */
  for(j=num_nz_x-1;j>=0;j--){
    tmp = step[j];
    for(k=num_nz_x-1;k>j;k--)
      tmp -= RMAT(j,k) * step[k];
    step[j] = tmp /  RMAT(j,j);
  }
  for(j=0;j<num_nz_x;j++){
    btmp[j] = beta[nz_x[j]];
    beta[nz_x[j]] += step[j];
  }
  b_1norm_old=b_1norm;

  b_1norm = 0.0;
  for(j=0;j<num_nz_x;j++) {
    b_1norm += fabs(beta[nz_x[j]]);
  }

  not_solved=FALSE;
  if( b_1norm > (1+prec)*t){
    not_solved=TRUE;
    if(b_1norm_old < (1.0-prec)*t){

    if(verb) {
      mexPrintf("  -->\tStepping onto the border of the L1 ball.\n");
      mexEvalString("drawnow;");
    }
    rho_up  = rho = 1.0;
    rho_low = 0.0;
    while( fabs(t-b_1norm) > prec*t ){
      if( b_1norm > t){
        rho_up = rho;
        rho = (rho+rho_low)/2.0;
      }
      if( b_1norm < t){
        rho_low = rho;
        rho = (rho+rho_up)/2.0;
      }
      if(rho < prec) break;
      for(j=0; j<num_nz_x; j++) {
        beta[nz_x[j]] = btmp[j]+rho*step[j];
      }

  b_1norm = 0.0;
  for(j=0;j<num_nz_x;j++)
    b_1norm += fabs(beta[nz_x[j]]);
    }
    for(j=0;j<num_nz_x;j++){
      if(fabs(beta[nz_x[j]])<prec)
        theta[j] = btmp[j] > 0 ? -1 : 1;
      else
        theta[j] = beta[nz_x[j]] < 0 ? -1 : 1;
    }
    }else{


  rho = 1.0;
  to_del = -1;
  for(j=0; j<num_nz_x; j++){
    if(fabs(step[j]) > prec){
      tmp = -btmp[j]/(step[j]);
      if( 0.0 < tmp && tmp < rho ){
        rho = tmp;
        to_del = j;
      }
    }
  }
  if(to_del < 0 ){
    *psuc= -1;
    goto EXIT_HERE;
  }
  for(j=0; j<num_nz_x; j++) {
    beta[nz_x[j]] = btmp[j]+rho*step[j];
  }
  if(verb) {
    mexPrintf("  -->\tRemoving variable: %d",nz_x[to_del]+1);
    mexEvalString("drawnow;");
  }
  beta[nz_x[to_del]] = 0.0;
  qr_del(to_del,TRUE);
  for(j=to_del+1; j< num_nz_x; j++){
    nz_x[j-1] = nz_x[j];
    theta[j-1] = theta[j];
  }
  num_nz_x--;
  
  b_1norm = 0.0;
  for(j=0;j<num_nz_x;j++)
    b_1norm += fabs(beta[nz_x[j]]);
  if(verb)
    if(b_1norm < (1-prec)*t)
      mexPrintf(", and stepping into the interior of the L1 ball\n");
    else
      mexPrintf("\n");
    }
    mexEvalString("drawnow;");
  }

  for(i=0; i< n; i++)
    yhat1[i] = 0.0;
  for(j=0; j < num_nz_x; j++){
    /* x_elem points to the first element in the column of X to which
       the j-th entry in nz_x points  */
    x_elem = x + nz_x[j]*n;
    tmp = beta[nz_x[j]];
    for(i=0; i < n; i++){
      yhat1[i] += *x_elem*tmp;
      x_elem++;           /* now we point to the next element in X */
    }
  }

  /* calculate the residual vector */
  for(i=0; i< n; i++) {
    r[i] = y[i]-yhat1[i];
  }
    }while(not_solved);
    
  
  for(i=0; i< n; i++)
    yhat1[i] = 0.0;
  for(j=0; j < num_nz_x; j++){
    /* x_elem points to the first element in the column of X to which
       the j-th entry in nz_x points  */
    x_elem = x + nz_x[j]*n;
    tmp = beta[nz_x[j]];
    for(i=0; i < n; i++){
      yhat1[i] += *x_elem*tmp;
      x_elem++;           /* now we point to the next element in X */
    }
  }

  /* calculate the residual vector */
  for(i=0; i< n; i++)
    r[i] = y[i]-yhat1[i];


  /* multiply X^T with the residual vector */
  x_elem = x;
  for(j=0; j < m; j++){
    tmp = 0.0;
    for(i=0; i<n; i++){
      tmp += *x_elem*r[i];
      x_elem++;
    }
    xtr[j] = tmp;
  }
  max_val = fabs(xtr[0]);
  max_ind = 0;
  for(j=1; j<m; j++)
    if( fabs(xtr[j]) > max_val ){
      max_val = fabs(xtr[j]);
      max_ind = j;
    }

    if(verb){


  /* Find out how many times [[max_val]] is attained */
  tmp = (1.0-prec)*max_val;
  if( tmp < prec ) tmp = 0.0;
  max_num = 1;
  for(j=0; j<m; j++){
    if( tmp <= fabs(xtr[j]) && j!=max_ind){
      /*we found another element equal to the (current)
        maximal absolute value */
      max_num++;
    }
  }

  /* for the value of the dual objective function we need
     to calculate the L2 norm of the vector of fitted values */
  p_obj = 0.0;
  d_obj = 0.0;
  for(i=0;i<n;i++){
    p_obj += r[i]*r[i];
    d_obj += yhat1[i]*yhat1[i];
  }
  p_obj /= 2.0;
  d_obj = ytyd2 - d_obj/2.0 - t*max_val ;
  mexPrintf("******************************\n");
  mexPrintf("\nIteration number: %d\n", num_iter);
  mexPrintf("Value of primal object function      : %f\n", p_obj);
  mexPrintf("Value of dual   object function      : %f\n", d_obj);
  mexPrintf("L1 norm of current beta              : %f", b_1norm);
  mexPrintf(" <= %f\n", t);
  mexPrintf("Maximal absolute value in t(X)%%*%%r   : %e", max_val);
  mexPrintf(" attained %d time(s)\n", max_num);
  mexPrintf("Number of parameters allowed to vary : %d\n", num_nz_x);
  mexEvalString("drawnow;");
  num_iter++;
    }
    
  add = TRUE;
  for(i=0; i<num_nz_x; i++)
    if(nz_x[i]==max_ind){
      add = FALSE;
      break;
    }
  if(add){
    qr_add(x+max_ind*n,TRUE);
    nz_x[num_nz_x] = max_ind;
    theta[num_nz_x] = xtr[max_ind]<0 ? -1 : 1;
    num_nz_x++;
  }else{
    *lagrangian = max_val;
    break;
  }

  b_1norm = 0.0;
  for(j=0;j<num_nz_x;j++)
    b_1norm += fabs(beta[nz_x[j]]);
  if(verb) {
    mexPrintf("  -->\tAdding variable: %d\n",max_ind+1);
    mexEvalString("drawnow;");
  }
  }
  EXIT_HERE:
  if( !as_sub)
    lasso_free();
}
void mult_lasso(double *x, long *pn, long *pm, double *pt, long *pl,
                double *beta, double *y, double *yhat1, double *r,
                double *lagrangian, long *psuc, long *pverb)
{

  double prec;
  long n = *pn, m = *pm, l = *pl, verb = *pverb, as_sub = TRUE, i, j;
  lasso_alloc(n,m);

qr_add(y,TRUE);
ytyd2 = *rmat * *rmat/2.0;
prec = sqrt(PRECISION);
num_nz_x = 0;
for(j=0; j<m; j++){
  if(fabs(beta[j]) > prec){
    qr_add(x+j*n, TRUE);
    nz_x[num_nz_x] = j;
    num_nz_x++;
  }else
    beta[j] = 0.0;
}
*psuc = 0;
  for(i=0; i<l; i++){

if(verb){
  mexPrintf("\n\n++++++++++++++++++++++++++++++\n");
  mexPrintf("Solving problem number %ld with bound %f\n", i+1, pt[i]);
  mexPrintf("++++++++++++++++++++++++++++++\n");
  mexEvalString("drawnow;");
}
if(i>0) Memcpy(beta,beta-m,m);
lasso(x, pn, pm, pt+i, beta, y, yhat1, r, lagrangian, psuc, pverb, &as_sub);
if( *psuc < 0 ){
  goto EXIT_HERE;
}

beta += m;
yhat1 += n;
r += n;
lagrangian++;
  }
  EXIT_HERE:
  lasso_free();
}
static void lasso_alloc(long n, long m){

#if defined(S_Plus)
  if( nz_x != NULL || theta != NULL || xtr != NULL || btmp != NULL ||
      qtr != NULL || rinvt_theta != NULL || step != NULL ||
      num_nz_x != 0 || ytyd2 != 0.0){
    MESSAGE "Possible memory corruption or memory leak.\n  We"
      "advise to restart your S+ session"  WARNING(NULL_ENTRY);
     lasso_free();
  }
#endif

  QR_CHUNK = m;  // Added: CJV

  nz_x = Calloc(m,int);
  if( nz_x == NULL )
    ERRMSG("lasso_alloc", no_dyn_mem_message);
  theta = Calloc(m,int);
  if( theta==NULL )
    ERRMSG("lasso_alloc", no_dyn_mem_message);
  xtr = Calloc(m,double);
  if( xtr==NULL )
    ERRMSG("lasso_alloc", no_dyn_mem_message);
  btmp = Calloc(m,double);
  if( btmp==NULL )
    ERRMSG("lasso_alloc", no_dyn_mem_message);
  qtr = Calloc(m,double);
  if( qtr==NULL )
    ERRMSG("lasso_alloc", no_dyn_mem_message);
  rinvt_theta = Calloc(m,double);
  if( rinvt_theta==NULL )
    ERRMSG("lasso_alloc", no_dyn_mem_message);
  step = Calloc(m,double);
  if( step==NULL )
    ERRMSG("lasso_alloc", no_dyn_mem_message);
  qr_init(n);
}
static void lasso_free(void){
  num_nz_x=0;
  ytyd2 = 0.0;
  Free(nz_x);
  Free(theta);
  Free(xtr);
  Free(btmp);
  Free(qtr);
  Free(rinvt_theta);
  Free(step);
  qr_free();
}
static void qr_init(int n) {
#if defined (S_Plus)
  if(qr_max_size!=0 || r_ncol!=0 || q_nrow!=0 || q_use_row!=0 ||
     qmat!=NULL || rmat!=NULL){
    MESSAGE "Possible memory corruption or memory leak.\n  We"
      "advise to restart your S+ session"  WARNING(NULL_ENTRY);
    qr_free();
  }
#endif
  qr_max_size = QR_CHUNK;
  r_ncol = 0;
  q_nrow = n;
  qmat = Calloc(n*qr_max_size,double);
  if(qmat==NULL)
    ERRMSG("qr_init", no_dyn_mem_message);
  rmat = Calloc(qr_max_size*(qr_max_size+1)/2,double);
  if(rmat==NULL)
    ERRMSG("qr_init", no_dyn_mem_message);
}
static void qr_incr(void) {
  qr_max_size += QR_CHUNK;

  /* reallocate R always */
  rmat = Realloc(rmat,qr_max_size*(qr_max_size+1)/2,double);
  if(rmat==NULL)
    ERRMSG("qr_incr", no_dyn_mem_message);

  /* reallocate Q only if necessary and only to maximal necessary size */
  if( qr_max_size >= q_nrow){
    if( qr_max_size-QR_CHUNK < q_nrow){
      qmat = Realloc(qmat,q_nrow*q_nrow,double);
      if(qmat==NULL)
        ERRMSG("qr_incr", no_dyn_mem_message);
    }
  }else{
    qmat = Realloc(qmat,q_nrow*qr_max_size,double);
    if(qmat==NULL)
      ERRMSG("qr_incr", no_dyn_mem_message);
  }
}
static void qr_free(void)
{
  qr_max_size = 0;
  r_ncol = 0;
  q_nrow = 0;
  q_use_row = 0;
  Free(qmat);
  Free(rmat);
}
static void qr_del(int l, int aug) {

  double c, s, tau, nu, *col_k, *col_kp1, *a, *b, tmp;
  int i, j, k, l0;

  if( l<0 || l>=r_ncol )
    ERRMSG("qr_del", "Invalid column number");
  r_ncol--;
  if( l==r_ncol)
    if( aug )
      ERRMSG("qr_del", "Trying to delete last column of augmented matrix");
    else
      return;

  /* this is TRUE if $m\le n$ ($m-1\le n$ if the matrix is augmented) */
  if (r_ncol < q_nrow ){
    for(k=l; k<r_ncol; k++) /* Update the factorisation and be done */
    {

col_k = RCOL(k);  /* first element in column $k$ in R */
Memcpy(col_k,col_k+k+1,k+1);
a = col_k+k;
b = a+k+2;
tau = fabs(*a)+fabs(*b);
if( tau == 0.0 ) continue; /* both elements are zero
                              nothing to update */
nu = tau*sqrt((*a/tau)*(*a/tau)+(*b/tau)*(*b/tau));
c = *a/nu;
s = *b/nu;
*a = nu;
  b += k+2;
  a = b-1;
  for(j=k+2;j<=r_ncol;j++, a+=j, b+=j){
    tmp = c * *a + s * *b;
    *b  = c * *b - s * *a;
    *a  = tmp;
  }
  col_k = QCOL(k);
  col_kp1 = col_k+q_nrow;
  for(j=0;j<q_nrow;j++){
    tmp = c*col_k[j]+s*col_kp1[j];
    col_kp1[j] = c*col_kp1[j]-s*col_k[j];
    col_k[j] = tmp;
  }
    }
  }else
    if( l < q_nrow ){
    /* Update columns upto $m$ and than shift remaining columns */
      for(k=l; k<q_nrow-1; k++){

col_k = RCOL(k);  /* first element in column $k$ in R */
Memcpy(col_k,col_k+k+1,k+1);
a = col_k+k;
b = a+k+2;
tau = fabs(*a)+fabs(*b);
if( tau == 0.0 ) continue; /* both elements are zero
                              nothing to update */
nu = tau*sqrt((*a/tau)*(*a/tau)+(*b/tau)*(*b/tau));
c = *a/nu;
s = *b/nu;
*a = nu;
  b += k+2;
  a = b-1;
  for(j=k+2;j<=r_ncol;j++, a+=j, b+=j){
    tmp = c * *a + s * *b;
    *b  = c * *b - s * *a;
    *a  = tmp;
  }
  col_k = QCOL(k);
  col_kp1 = col_k+q_nrow;
  for(j=0;j<q_nrow;j++){
    tmp = c*col_k[j]+s*col_kp1[j];
    col_kp1[j] = c*col_kp1[j]-s*col_k[j];
    col_k[j] = tmp;
  }
      }
      l0 = q_nrow-1;
      
  col_k   = RCOL(l0); /* first element in column $l_0$ in R */
  for(i=l0; i<r_ncol; i++, col_k +=i)
     Memcpy(col_k,col_k+i+1,q_nrow);

  /* [[rmat + (q_nrow-1)*q_nrow/2+q_nrow-1]] is last element in column
     [[q_nrow]] in R */
  a = rmat + (q_nrow-1)*(q_nrow+2)/2;
  if( *a < 0 ){
    /* [[j<r_ncol]] sufficient since we shifted the columns already */
    for(j=l0;j<r_ncol;j++,a+=j) 
      *a = - *a;
    col_k = qmat+(q_nrow-1)*q_nrow;
    for(i=0;i<q_nrow;i++,col_k++)
      *col_k = -*col_k;
  }
    }else{ /* just shift last columns to the left */
      l0 = l;
      
  col_k   = RCOL(l0); /* first element in column $l_0$ in R */
  for(i=l0; i<r_ncol; i++, col_k +=i)
     Memcpy(col_k,col_k+i+1,q_nrow);
  
  /* [[rmat + (q_nrow-1)*q_nrow/2+q_nrow-1]] is last element in column
     [[q_nrow]] in R */
  a = rmat + (q_nrow-1)*(q_nrow+2)/2;
  if( *a < 0 ){
    /* [[j<r_ncol]] sufficient since we shifted the columns already */
    for(j=l0;j<r_ncol;j++,a+=j)
      *a = - *a;
    col_k = qmat+(q_nrow-1)*q_nrow;
    for(i=0;i<q_nrow;i++,col_k++)
      *col_k = -*col_k;
  }
    }
}
static void qr_add(double *x, int swap){

  double tmp, norm_orig, norm_init, norm_last, *q_new_col;
  int i;
  double *col_l, *col_lm1, *q_elem, *r_new_col;
  double norm_new;
  int j;
  double c, s, tau, nu, *a, *b;

  if( r_ncol == qr_max_size )
    qr_incr();

norm_orig = 0.0;
tmp = 0.0;
for(i=0; i<q_nrow; i++) tmp += x[i]*x[i];
norm_orig = sqrt(tmp);
if(r_ncol<q_nrow){
  q_new_col = QCOL(r_ncol); /* points to the first element of new column */
  tmp = 0.0;
  for(i=0; i<q_nrow; i++){
    q_new_col[i] = x[i]/norm_orig;
    tmp += q_new_col[i]*q_new_col[i];
  }
  if(r_ncol==0){
    *rmat = norm_orig;
    r_ncol++;
    return;
  }
  norm_init = norm_last = sqrt(tmp);
}
r_new_col = RCOL(r_ncol);
for(i=0; i<=r_ncol; i++) r_new_col[i] = 0.0;
if( r_ncol >= q_nrow ){
  /* Multiply new column with Q-transpose in [[qr_add]] */
  q_elem = qmat;
  for(i=0;i<q_nrow;i++){
    tmp = 0.0;
    for(j=0;j<q_nrow;j++,q_elem++)
      tmp += *q_elem * x[j];
    r_new_col[i] = tmp;
  }
  if( swap ){ /* swap last two columns */
    col_l   = r_new_col;
    col_lm1 = r_new_col-r_ncol;
    for(i=0; i<q_nrow; i++,col_l++,col_lm1++){
      tmp = *col_l;
      *col_l = *col_lm1;
      *col_lm1 = tmp;
    }
    col_lm1--;
    col_l--;
    if(q_nrow==r_ncol && *col_lm1<0){
      /* if new R[$n$,$n$] is negative, than change signs */
      *col_lm1 = - *col_lm1;
      *col_l   = - *col_l;
      q_new_col = qmat+(q_nrow-1)*q_nrow;
      for(j=0;j<q_nrow;j++)
        q_new_col[j] = -q_new_col[j];
    }
  }
  r_ncol++;
  return;
}
  while(1){

q_elem = qmat;
for(j=0; j<r_ncol;j++){
  tmp = 0.0;
  for(i=0;i<q_nrow;i++,q_elem++)
    tmp += *q_elem * q_new_col[i];
  r_new_col[j] += tmp;
  q_elem -= q_nrow;
  for(i=0;i<q_nrow;i++,q_elem++)
    q_new_col[i] -= *q_elem*tmp;
}
tmp = 0.0;
for(i=0;i<q_nrow;i++) tmp += q_new_col[i]*q_new_col[i];
norm_new = sqrt(tmp);

  if( norm_new >= norm_last/2.0) break;
  if( norm_new > 0.1*norm_init*PRECISION )
    norm_last = norm_new;
  else{
    norm_init = norm_last = 0.1*norm_last*PRECISION;
    for(i=0;i<q_nrow;i++)
      q_new_col[i] = 0.0;
    if(q_use_row == q_nrow)
      ERRMSG("qr_add","Cannot orthogonalise new column\n");

    q_new_col[q_use_row] = norm_new = norm_last;
    q_use_row++;
   }
  }
  
  for(i=0;i<q_nrow;i++)
    q_new_col[i] /= norm_new;
  for(i=0;i<r_ncol;i++)
    r_new_col[i] *= norm_orig;
  r_new_col[r_ncol] = norm_new*norm_orig;
  if(swap){

col_l = r_new_col; /* first element in last column in R */
col_lm1 = r_new_col-r_ncol; /* first element in column before last in R */
for(j=0;j<r_ncol;j++,col_l++,col_lm1++){
  tmp = *col_l;
  *col_l = *col_lm1;
  *col_lm1 = tmp;
}
a = col_lm1-1;
b = col_l;
tau = fabs(*a)+fabs(*b);
if( tau > 0.0 ){
  /*Calculate Givens rotation*/
  nu = tau*sqrt((*a/tau)*(*a/tau)+(*b/tau)*(*b/tau));
  c = *a/nu;
  s = *b/nu;

  *a = nu;   /* Fix column before last in R */
  *b = -s* *(b-1);  /* Fix last element of last column in R */
  *(b-1) = c * *(b-1); /* Fix second last element of last column in R */
  if( *b < 0){
    *b = -*b;
    
  col_lm1 = QCOL(r_ncol-1);
  col_l   = col_lm1+q_nrow;
  for(j=0;j<q_nrow;j++){
    tmp = c*col_lm1[j]+s*col_l[j];
    col_l[j] = -c*col_l[j]+s*col_lm1[j];
    col_lm1[j] = tmp;
  }
  
  }else{
    
  col_lm1 = QCOL(r_ncol-1);
  col_l   = col_lm1+q_nrow;
  for(j=0;j<q_nrow;j++){
    tmp = c*col_lm1[j]+s*col_l[j];
    col_l[j] = c*col_l[j]-s*col_lm1[j];
    col_lm1[j] = tmp;
  }
  }
}

  }
  r_ncol++;

}
#if defined (S_Plus)
static void errmsg(char *string){
  PROBLEM "%s\n", string RECOVER(NULL_ENTRY);
}
#elif defined(Matlab)
static void errmsg(char *where, char *string){
  char str[1024];
  sprintf(str, "Error in %s: %s\n", where, string);
  mexErrMsgTxt(str);
}
#else
static void errmsg(char *where, char *string){
  fprintf(stderr, "Error in %s: %s\n", where, string);
  exit(EXIT_FAILURE);
}
#endif

int assertFail(const char *ex, const char *file, const char *func, const int line)
{
static bool ignore = false;

    if (!ignore) {
        char str[1024];
        sprintf(str, "%s:%u: %s(): failed assertion `%s'\n",
                     file, line, func, ex);
        mexErrMsgTxt(str);
    } /* if */
    return(1);
}

static void fortifyPrintf(const char *s)
{
   mexPrintf(s);
}

void
mexFunction(int nlhs,mxArray *plhs[],int nrhs,const mxArray *prhs[])
{
   mxArray *array_ptr;
   int i;
   long dataSize;
   long dimensions;
   long succeed;
   long verbose = 0;
   long as_sub = 0;
   double lagrangian;
   double threshold;
   double *mx;
   double *y;
   double *yhat1;
   double *r;
   double *beta;
   int arg;

#ifdef FORTIFY
   Fortify_SetOutputFunc(fortifyPrintf);
   Fortify_EnterScope();
#endif

   if (nrhs > 3) {
      mexErrMsgTxt("Syntax error: too many arguments\n");
      return;
   } /* if */

   if (nrhs < 3) {
      mexErrMsgTxt("Syntax error: arguments missing\n");
      return;
   } /* if */

   if (nlhs > 1) {
      mexErrMsgTxt("Syntax error: too many return arguments\n");
      return;
   } /* if */

   arg = 2;
   array_ptr = (mxArray *) prhs[arg];
   if (mxGetClassID(array_ptr) != mxDOUBLE_CLASS) {
      mexErrMsgTxt("Threshold argument is not a number\n");
      return;
   } /* if */

   threshold = mxGetScalar(array_ptr);

   arg = 1;
   array_ptr = (mxArray *) prhs[arg];
   if (mxGetClassID(array_ptr) != mxDOUBLE_CLASS) {
      mexErrMsgTxt("Label argument is not a number\n");
      return;
   } /* if */

   y = mxGetPr(array_ptr);

   arg = 0;
   array_ptr = (mxArray *) prhs[arg];
   if (mxGetClassID(array_ptr) != mxDOUBLE_CLASS) {
      mexErrMsgTxt("Data set argument is not a double matrix\n");
      return;
   } /* if */

   dataSize = mxGetM(array_ptr);
   dimensions = mxGetN(array_ptr);

   mx = mxGetPr(array_ptr);

   arg = 0;
   plhs[arg] = mxCreateDoubleMatrix(dimensions, 1, mxREAL);

   yhat1 = new double[dataSize];
   r = new double[dataSize];
   beta = mxGetPr(plhs[arg]);

   for (i=0; i<dimensions; i++) {
       beta[i] = 0.0;
   } /* for */

   if (dimensions > 0) {
       lasso(mx, &dataSize, &dimensions, &threshold, beta, y,
             yhat1, r, &lagrangian, &succeed, &verbose, &as_sub);
   } else {
       mexPrintf("Dataset with 0 dimensions\n");
   } /* if */

   delete [] yhat1;
   delete [] r;

#ifdef  FORTIFY
   Fortify_LeaveScope();
#endif

}