void matrix_demean(gsl_matrix *input){
gsl_vector *mean = gsl_vector_alloc(input->size2);
matrix_mean(mean, input);
size_t NCOL = input->size2;
size_t i;
gsl_vector_view column;
#pragma omp parallel for private(column)
for (i = 0; i < NCOL; i++) {
column = gsl_matrix_column(input, i);
gsl_vector_add_constant( &column.vector,
-gsl_vector_get(mean, i));
}
}
/** \brief Principal Components analysis.
\ingroup grplinalg
This implementation uses SVD to calculate the PCA.
Example:
\code
Array *X = get_data_from_somewhere();
Array *var, *X_pca;
matrix_pca( X, &var, FALSE ); // overwrite X
X_pca = matrix_pca( X, &var, TRUE ); // do not touch X
\endcode
\param X a 2D array observations x variables containing the data
\param var output: vector of eigenvalues of XX^T in decreasing order; if you
pass NULL, it is ignored;
\param alloc if true, new memory is allocated and returned. Else
X is overwritten.
\return pointer to the PCA'd matrix
*/
Array* matrix_pca( Array *X, Array **var, bool alloc ){
Array *out=NULL;
int i,j;
bool ismatrix;
matrix_CHECK( ismatrix, X );
if( !ismatrix ) return NULL;
int N,K; /* N observations, K variables */
N = X->size[0];
K = X->size[1];
Array *tmp = array_copy( X, TRUE );
/* subtract mean from observations */
Array *mean=matrix_mean( X, 0 );
for( i=0; i<N; i++ ){
for( j=0; j<K; j++ ){
array_INDEX2( tmp, double, i, j ) -=
array_INDEX1( mean, double, j );
}
}
array_scale( tmp, 1.0/sqrt((double) N-1 ) );
gsl_matrix *A=matrix_to_gsl( tmp, TRUE ); /* copy */
gsl_matrix *V=gsl_matrix_alloc( K, K );
gsl_vector *S=gsl_vector_alloc( K );
gsl_vector *workspace=gsl_vector_alloc( K );
/* A->U, V->V, S->S */
gsl_linalg_SV_decomp( A, V, S, workspace);
gsl_matrix_transpose( V );
if( var ){
(*var)=array_fromptr2( DOUBLE, 1, S->data, S->size );
S->owner=0; /* transfer ownership to array */
(*var)->free_data=1;
for( i=0; i<array_NUMEL( *var ); i++ ){
array_INDEX1( *var, double, i ) = SQR( array_INDEX1( *var, double, i ) );
}
}
Array *Vp=array_fromptr2( DOUBLE, 2, V->data, V->size1, V->size2 );
matrix_transpose( tmp, FALSE );
out=matrix_mult( Vp, tmp ); /* PCA'd data */
matrix_transpose( out, FALSE );
if( out->size[0]!=X->size[0] || out->size[1]!=X->size[1] ){
errprintf("Input/Output dimension mismatch: (%i,%i) vs. (%i,%i)\n",
X->size[0], X->size[1], out->size[0], out->size[1] );
}
if( !alloc ){ /* write back out->X */
memcpy( X->data, out->data, out->nbytes );
array_free( out );
out = X;
}
/* clean up */
gsl_matrix_free( A );
gsl_matrix_free( V );
gsl_vector_free( S );
gsl_vector_free( workspace );
array_free( mean );
array_free( Vp );
array_free( tmp );
return out;
}
