#include <stdio.h>
#include <math.h>
#include <AR/matrix.h>

#define     VZERO           1e-16
#define     EPS             1e-6
#define     MAX_ITER        100
#define     xmalloc(V,T,S)  { if( ((V) = (T *)malloc( sizeof(T) * (S) ))\
                               == NULL ) {printf("malloc error\n"); exit(1);} }

static int EX( ARMat *input, ARVec *mean );
static int CENTER( ARMat *inout, ARVec *mean );
static int PCA( ARMat *input, ARMat *output, ARVec *ev );
static int x_by_xt( ARMat *input, ARMat *output );
static int xt_by_x( ARMat *input, ARMat *output );
static int EV_create( ARMat *input, ARMat *u, ARMat *output, ARVec *ev );
static int QRM( ARMat *u, ARVec *ev );


/* === matrix definition ===

Input:
  <---- clm (Data dimention)--->
  [ 10  20  30 ] ^
  [ 20  10  15 ] |
  [ 12  23  13 ] row
  [ 20  10  15 ] |(Sample number)
  [ 13  14  15 ] v

Evec:
  <---- clm (Eigen vector)--->
  [ 10  20  30 ] ^
  [ 20  10  15 ] |
  [ 12  23  13 ] row
  [ 20  10  15 ] |(Number of egen vec)
  [ 13  14  15 ] v

Ev:
  <---- clm (Number of eigen vector)--->
  [ 10  20  30 ] eigen value

Mean:
  <---- clm (Data dimention)--->
  [ 10  20  30 ] mean value

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


int arMatrixPCA( ARMat *input, ARMat *evec, ARVec *ev, ARVec *mean )
{
    ARMat     *work;
    double  srow, sum;
    int     row, clm;
    int     check, rval;
    int     i;

    row = input->row;
    clm = input->clm;
    check = (row < clm)? row: clm;
    if( row < 2 || clm < 2 ) return(-1);
    if( evec->clm != input->clm || evec->row != check ) return(-1);
    if( ev->clm   != check )      return(-1);
    if( mean->clm != input->clm ) return(-1);

    work = arMatrixAllocDup( input );
    if( work == NULL ) return -1;

    srow = sqrt((double)row);
    if( EX( work, mean ) < 0 ) {
        arMatrixFree( work );
        return(-1);
    }
    if( CENTER( work, mean ) < 0 ) {
        arMatrixFree( work );
        return(-1);
    }
    for(i=0; i<row*clm; i++) work->m[i] /= srow;

    rval = PCA( work, evec, ev );
    arMatrixFree( work );

    sum = 0.0;
    for( i = 0; i < ev->clm; i++ ) sum += ev->v[i];
    for( i = 0; i < ev->clm; i++ ) ev->v[i] /= sum;

    return( rval );
}

static int PCA( ARMat *input, ARMat *output, ARVec *ev )
{
    ARMat     *u;
    double  *m1, *m2;
    int     row, clm, min;
    int     i, j;

    row = input->row;
    clm = input->clm;
    min = (clm < row)? clm: row;
    if( row < 2 || clm < 2 )        return(-1);
    if( output->clm != input->clm ) return(-1);
    if( output->row != min )        return(-1);
    if( ev->clm != min )            return(-1);

    u = arMatrixAlloc( min, min );
    if( u->row != min || u->clm != min ) return(-1);
    if( row < clm ) {
        if( x_by_xt( input, u ) < 0 ) { arMatrixFree(u); return(-1); }
    }
    else {
        if( xt_by_x( input, u ) < 0 ) { arMatrixFree(u); return(-1); }
    }

    if( QRM( u, ev ) < 0 ) { arMatrixFree(u); return(-1); }

    if( row < clm ) {
        if( EV_create( input, u, output, ev ) < 0 ) {
            arMatrixFree(u);
            return(-1);
        }
    }
    else{
        m1 = u->m;
        m2 = output->m;
	for( i = 0; i < min; i++){
	    if( ev->v[i] < VZERO ) break;
            for( j = 0; j < min; j++ ) *(m2++) = *(m1++);
        }
	for( ; i < min; i++){
            ev->v[i] = 0.0;
            for( j = 0; j < min; j++ ) *(m2++) = 0.0;
        }
    }

    arMatrixFree(u);

    return( 0 );
}

static int EX( ARMat *input, ARVec *mean )
{
    double  *m, *v;
    int     row, clm;
    int     i, j;

    row = input->row;
    clm = input->clm;
    if( row <= 0 || clm <= 0 )  return(-1);
    if( mean->clm != clm )      return(-1);

    for( i = 0; i < clm; i++ ) mean->v[i] = 0.0;

    m = input->m;
    for( i = 0; i < row; i++ ) {
        v = mean->v;
        for( j = 0; j < clm; j++ ) *(v++) += *(m++);
    }

    for( i = 0; i < clm; i++ ) mean->v[i] /= row;

    return(0);
}

static int CENTER( ARMat *inout, ARVec *mean )
{
    double  *m, *v;
    int     row, clm;
    int     i, j;

    row = inout->row;
    clm = inout->clm;
    if( mean->clm != clm ) return(-1);

    m = inout->m;
    for( i = 0; i < row; i++ ) {
        v = mean->v;
        for( j = 0; j < clm; j++ ) *(m++) -= *(v++);
    }

    return(0);
}

static int x_by_xt( ARMat *input, ARMat *output )
{
    double  *in1, *in2, *out;
    int     row, clm;
    int     i, j, k;

    row = input->row;
    clm = input->clm;
    if( output->row != row || output->clm != row ) return(-1);

    out = output->m;
    for( i = 0; i < row; i++ ) {
        for( j = 0; j < row; j++ ) {
            if( j < i ) {
                *out = output->m[j*row+i];
            }
            else {
                in1 = &(input->m[clm*i]);
                in2 = &(input->m[clm*j]);
                *out = 0.0;
                for( k = 0; k < clm; k++ ) {
                    *out += *(in1++) * *(in2++);
                }
            }
            out++;
        }
    }

    return(0);
}

static int xt_by_x( ARMat *input, ARMat *output )
{
    double  *in1, *in2, *out;
    int     row, clm;
    int     i, j, k;

    row = input->row;
    clm = input->clm;
    if( output->row != clm || output->clm != clm ) return(-1);

    out = output->m;
    for( i = 0; i < clm; i++ ) {
        for( j = 0; j < clm; j++ ) {
            if( j < i ) {
                *out = output->m[j*clm+i];
            }
            else {
                in1 = &(input->m[i]);
                in2 = &(input->m[j]);
                *out = 0.0;
                for( k = 0; k < row; k++ ) {
                    *out += *in1 * *in2;
                    in1 += clm;
                    in2 += clm;
                }
            }
            out++;
        }
    }

    return(0);
}

static int EV_create( ARMat *input, ARMat *u, ARMat *output, ARVec *ev )
{
    double  *m, *m1, *m2;
    double  sum, work;
    int     row, clm;
    int     i, j, k;

    row = input->row;
    clm = input->clm;
    if( row <= 0 || clm <= 0 ) return(-1);
    if( u->row != row || u->clm != row ) return(-1);
    if( output->row != row || output->clm != clm ) return(-1);
    if( ev->clm != row ) return(-1);

    m = output->m;
    for( i = 0; i < row; i++ ) {
        if( ev->v[i] < VZERO ) break;
        work = 1 / sqrt(fabs(ev->v[i]));
        for( j = 0; j < clm; j++ ) {
            sum = 0.0;
            m1 = &(u->m[i*row]);
            m2 = &(input->m[j]);
            for( k = 0; k < row; k++ ) {
                sum += *m1 * *m2;
                m1++;
                m2 += clm;
            }
            *(m++) = sum * work;
        }
    }
    for( ; i < row; i++ ) {
        ev->v[i] = 0.0;
        for( j = 0; j < clm; j++ ) *(m++) = 0.0;
    }

    return(0);
}

static int QRM( ARMat *a, ARVec *dv )
{
    ARVec     *ev, ev1;
    double  w, t, s, x, y, c;
    double  *v1, *v2;
    int     dim, iter;
    int     i, j, k, h;

    dim = a->row;
    if( dim != a->clm || dim < 2 ) return(-1);
    if( dv->clm != dim ) return(-1);

    ev = arVecAlloc( dim );
    if( ev == NULL ) return(-1);

    ev1.clm = dim-1;
    ev1.v = &(ev->v[1]);
    if( arVecTridiagonalize( a, dv, &ev1 ) < 0 ) {
        arVecFree( ev );
        return(-1);
    }

    ev->v[0] = 0.0;
    for( h = dim-1; h > 0; h-- ) {
        j = h;
        while(j>0 && fabs(ev->v[j]) > EPS*(fabs(dv->v[j-1])+fabs(dv->v[j]))) j--;
        if( j == h ) continue;

        iter = 0;
        do{
            iter++;
            if( iter > MAX_ITER ) break;

            w = (dv->v[h-1] - dv->v[h]) / 2;
            t = ev->v[h] * ev->v[h];
            s = sqrt(w*w+t); 
            if( w < 0 ) s = -s;
            x = dv->v[j] - dv->v[h] + t/(w+s);
            y = ev->v[j+1];
            for( k = j; k < h; k++ ) {
                if( fabs(x) >= fabs(y) ) {
		    if( fabs(x) > VZERO ) {
			t = -y / x;
			c = 1 / sqrt(t*t+1);
			s = t * c;
		    }
		    else{
			c = 1.0;
			s = 0.0;
		    }
                }
                else{
		    t = -x / y;
		    s = 1.0 / sqrt(t*t+1);
		    c = t * s;
                }
                w = dv->v[k] - dv->v[k+1];
                t = (w * s + 2 * c * ev->v[k+1]) * s;
                dv->v[k]   -= t;
                dv->v[k+1] += t;
                if( k > j) ev->v[k] = c * ev->v[k] - s * y;
                ev->v[k+1] += s * (c * w - 2 * s * ev->v[k+1]);

                for( i = 0; i < dim; i++ ) {
                    x = a->m[k*dim+i];
                    y = a->m[(k+1)*dim+i];
                    a->m[k*dim+i]     = c * x - s * y;
                    a->m[(k+1)*dim+i] = s * x + c * y;
                }
                if( k < h-1 ) {
                    x = ev->v[k+1];
                    y = -s * ev->v[k+2];
                    ev->v[k+2] *= c;
                }
            }
        } while(fabs(ev->v[h]) > EPS*(fabs(dv->v[h-1])+fabs(dv->v[h])));
    }

    for( k = 0; k < dim-1; k++ ) {
        h = k;
        t = dv->v[h];
        for( i = k+1; i < dim; i++ ) {
            if( dv->v[i] > t ) {
                h = i;
                t = dv->v[h];
            }
        }
        dv->v[h] = dv->v[k];
        dv->v[k] = t;
        v1 = &(a->m[h*dim]);
        v2 = &(a->m[k*dim]);
        for( i = 0; i < dim; i++ ) {
            w = *v1;
            *v1 = *v2;
            *v2 = w;
            v1++;
            v2++;
        }
    }

    arVecFree( ev );
    return(0);
}
