altra.cpp

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/*   This program is free software: you can redistribute it and/or modify
 *   it under the terms of the GNU General Public License as published by
 *   the Free Software Foundation, either version 3 of the License, or
 *   (at your option) any later version.
 *
 *   This program 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 General Public License for more details.
 *
 *   You should have received a copy of the GNU General Public License
 *   along with this program.  If not, see <http://www.gnu.org/licenses/>.
 *
 *   Copyright (C) 2009 - 2012 Jun Liu and Jieping Ye
 */

#include <shogun/lib/slep/tree/altra.h>
#include <shogun/mathematics/Math.h>
#include <stdlib.h>
#include <string.h>

void altra(double *x, double *v, int n, double *ind, int nodes, double mult)
{
    int i, j;
    double lambda,twoNorm, ratio;

    /*
     * test whether the first node is special
     */
    if ((int) ind[0]==-1){

        /*
         *Recheck whether ind[1] equals to zero
         */
        if ((int) ind[1]!=-1){
            printf("\n Error! \n Check ind");
            exit(1);
        }

        lambda=mult*ind[2];

        for(j=0;j<n;j++){
            if (v[j]>lambda)
                x[j]=v[j]-lambda;
            else
                if (v[j]<-lambda)
                    x[j]=v[j]+lambda;
                else
                    x[j]=0;
        }

        i=1;
    }
    else{
        memcpy(x, v, sizeof(double) * n);
        i=0;
    }

    /*
     * sequentially process each node
     *
     */
    for(;i < nodes; i++){
        /*
         * compute the L2 norm of this group
         */
        twoNorm=0;
        for(j=(int) ind[3*i]-1;j< (int) ind[3*i+1];j++)
            twoNorm += x[j] * x[j];
        twoNorm=sqrt(twoNorm);

        lambda=mult*ind[3*i+2];
        if (twoNorm>lambda){
            ratio=(twoNorm-lambda)/twoNorm;

            /*
             * shrinkage this group by ratio
             */
            for(j=(int) ind[3*i]-1;j<(int) ind[3*i+1];j++)
                x[j]*=ratio;
        }
        else{
            /*
             * threshold this group to zero
             */
            for(j=(int) ind[3*i]-1;j<(int) ind[3*i+1];j++)
                x[j]=0;
        }
    }
}

void altra_mt(double *X, double *V, int n, int k, double *ind, int nodes, double mult)
{
    int i, j;

    double *x=(double *)malloc(sizeof(double)*k);
    double *v=(double *)malloc(sizeof(double)*k);

    for (i=0;i<n;i++){
        /*
         * copy a row of V to v
         *
         */
        for(j=0;j<k;j++)
            v[j]=V[j*n + i];

        altra(x, v, k, ind, nodes, mult);

        /*
         * copy the solution to X
         */
        for(j=0;j<k;j++)
            X[j*n+i]=x[j];
    }

    free(x);
    free(v);
}

void computeLambda2Max(double *lambda2_max, double *x, int n, double *ind, int nodes)
{
    int i, j;
    double twoNorm;

    *lambda2_max=0;

    for(i=0;i < nodes; i++){
        /*
         * compute the L2 norm of this group
         */
        twoNorm=0;
        for(j=(int) ind[3*i]-1;j< (int) ind[3*i+1];j++)
            twoNorm += x[j] * x[j];
        twoNorm=sqrt(twoNorm);

        twoNorm=twoNorm/ind[3*i+2];

        if (twoNorm >*lambda2_max )
            *lambda2_max=twoNorm;
    }
}

double treeNorm(double *x, int ldx, int n, double *ind, int nodes){

    int i, j;
    double twoNorm, lambda;

    double tree_norm = 0;

    /*
     * test whether the first node is special
     */
    if ((int) ind[0]==-1){

        /*
         *Recheck whether ind[1] equals to zero
         */
        if ((int) ind[1]!=-1){
            printf("\n Error! \n Check ind");
            exit(1);
        }

        lambda=ind[2];

        for(j=0;j<n*ldx;j+=ldx){
            tree_norm+=fabs(x[j]);
        }

        tree_norm = tree_norm * lambda;

        i=1;
    }
    else{
        i=0;
    }

    /*
     * sequentially process each node
     *
     */
    for(;i < nodes; i++){
        /*
         * compute the L2 norm of this group
         */
        twoNorm=0;

        int n_in_node = (int) ind[3*i+1] - (int) ind[3*i]-1;
        for(j=(int) ind[3*i]-1;j< (int) ind[3*i]-1 + n_in_node*ldx;j+=ldx)
            twoNorm += x[j] * x[j];
        twoNorm=sqrt(twoNorm);

        lambda=ind[3*i+2];

        tree_norm = tree_norm + lambda*twoNorm;
    }

    return tree_norm;
}

double findLambdaMax(double *v, int n, double *ind, int nodes){

    int i;
    double lambda=0,squaredWeight=0, lambda1,lambda2;
    double *x=(double *)malloc(sizeof(double)*n);
    double *ind2=(double *)malloc(sizeof(double)*nodes*3);
    int num=0;

    for(i=0;i<n;i++){
        lambda+=v[i]*v[i];
    }

    if ( (int)ind[0]==-1 )
        squaredWeight=n*ind[2]*ind[2];
    else
        squaredWeight=ind[2]*ind[2];

    for (i=1;i<nodes;i++){
        squaredWeight+=ind[3*i+2]*ind[3*i+2];
    }

    /* set lambda to an initial guess
    */
    lambda=sqrt(lambda/squaredWeight);

    /*
       printf("\n\n   lambda=%2.5f",lambda);
       */

    /*
     *copy ind to ind2,
     *and scale the weight 3*i+2
     */
    for(i=0;i<nodes;i++){
        ind2[3*i]=ind[3*i];
        ind2[3*i+1]=ind[3*i+1];
        ind2[3*i+2]=ind[3*i+2]*lambda;
    }

    /* test whether the solution is zero or not
    */
    altra(x, v, n, ind2, nodes);
    for(i=0;i<n;i++){
        if (x[i]!=0)
            break;
    }

    if (i>=n) {
        /*x is a zero vector*/
        lambda2=lambda;
        lambda1=lambda;

        num=0;

        while(1){
            num++;

            lambda2=lambda;
            lambda1=lambda1/2;
            /* update ind2
            */
            for(i=0;i<nodes;i++){
                ind2[3*i+2]=ind[3*i+2]*lambda1;
            }

            /* compute and test whether x is zero
            */
            altra(x, v, n, ind2, nodes);
            for(i=0;i<n;i++){
                if (x[i]!=0)
                    break;
            }

            if (i<n){
                break;
                /*x is not zero
                 *we have found lambda1
                 */
            }
        }

    }
    else{
        /*x is a non-zero vector*/
        lambda2=lambda;
        lambda1=lambda;

        num=0;
        while(1){
            num++;

            lambda1=lambda2;
            lambda2=lambda2*2;
            /* update ind2
            */
            for(i=0;i<nodes;i++){
                ind2[3*i+2]=ind[3*i+2]*lambda2;
            }

            /* compute and test whether x is zero
            */
            altra(x, v, n, ind2, nodes);
            for(i=0;i<n;i++){
                if (x[i]!=0)
                    break;
            }

            if (i>=n){
                break;
                /*x is a zero vector
                 *we have found lambda2
                 */
            }
        }
    }

    /*
       printf("\n num=%d, lambda1=%2.5f, lambda2=%2.5f",num, lambda1,lambda2);
       */

    while ( fabs(lambda2-lambda1) > lambda2 * 1e-10 ){

        num++;

        lambda=(lambda1+lambda2)/2;

        /* update ind2
        */
        for(i=0;i<nodes;i++){
            ind2[3*i+2]=ind[3*i+2]*lambda;
        }

        /* compute and test whether x is zero
        */
        altra(x, v, n, ind2, nodes);
        for(i=0;i<n;i++){
            if (x[i]!=0)
                break;
        }

        if (i>=n){
            lambda2=lambda;
        }
        else{
            lambda1=lambda;
        }

        /*
           printf("\n lambda1=%2.5f, lambda2=%2.5f",lambda1,lambda2);
           */
    }

    /*
       printf("\n num=%d",num);

       printf("   lambda1=%2.5f, lambda2=%2.5f",lambda1,lambda2);

*/

    free(x);
    free(ind2);

    return lambda2;
}

double findLambdaMax_mt(double *V, int n, int k, double *ind, int nodes)
{
    int i, j;

    double *v=(double *)malloc(sizeof(double)*k);
    double lambda;

    double lambdaMax=0;

    for (i=0;i<n;i++){
        /*
         * copy a row of V to v
         *
         */
        for(j=0;j<k;j++)
            v[j]=V[j*n + i];

        lambda = findLambdaMax(v, k, ind, nodes);

        /*
           printf("\n   lambda=%5.2f",lambda);
           */

        if (lambda>lambdaMax)
            lambdaMax=lambda;
    }

    /*
       printf("\n *lambdaMax=%5.2f",*lambdaMax);
       */

    free(v);
    return lambdaMax;
}