void test_content() {
rng_type * rng = rng_alloc(MZRAN , INIT_DEFAULT);
matrix_type * PC = matrix_alloc( 3 , 10);
matrix_type * PC_obs = matrix_alloc( 3 , 1 );
double_vector_type * singular_values = double_vector_alloc(3 , 1);
matrix_random_init( PC , rng );
matrix_random_init( PC_obs , rng );
{
pca_plot_data_type * data = pca_plot_data_alloc("KEY" , PC , PC_obs, singular_values);
for (int i=0; i < matrix_get_rows( PC ); i++) {
const pca_plot_vector_type * vector = pca_plot_data_iget_vector( data , i );
test_assert_double_equal( matrix_iget( PC_obs , i , 0) ,
pca_plot_vector_get_obs_value( vector ) );
test_assert_double_equal( double_vector_iget( singular_values , i),
pca_plot_vector_get_singular_value( vector ) );
for (int j=0; j < matrix_get_columns( PC ); j++)
test_assert_double_equal( matrix_iget( PC , i , j ) , pca_plot_vector_iget_sim_value( vector , j ));
test_assert_int_equal( matrix_get_columns( PC ) , pca_plot_vector_get_size( vector ));
}
pca_plot_data_free( data );
}
double_vector_free( singular_values );
matrix_free( PC );
matrix_free( PC_obs );
}
void matrix_fprintf( const matrix_type * matrix , const char * fmt , FILE * stream ) {
int i,j;
for (i=0; i < matrix->rows; i++) {
for (j=0; j < matrix->columns; j++)
fprintf(stream , fmt , matrix_iget( matrix , i , j));
fprintf(stream , "\n");
}
}
void matrix_pretty_fprint_submat(const matrix_type * matrix , const char * name , const char * fmt , FILE * stream, int m, int M, int n, int N) {
int i,j;
if (m<0 || m>M || M >= matrix->rows || n<0 || n>N || N >= matrix->columns)
util_abort("%s: matrix:%s not compatible with print subdimensions. \n",__func__ , matrix->name);
fprintf(stream , "%s =" , name);
for (i=m; i < M; i++) {
fprintf(stream , " [");
for (j=n; j < N; j++)
fprintf(stream , fmt , matrix_iget(matrix , i,j));
fprintf(stream , "]\n");
}
}
void matrix_pretty_fprint(const matrix_type * matrix , const char * name , const char * fmt , FILE * stream) {
int i,j;
for (i=0; i < matrix->rows; i++) {
if (i == (matrix->rows / 2))
fprintf(stream , "%s =" , name);
else {
int l;
for (l = 0; l < strlen(name) + 2; l++)
fprintf(stream , " ");
}
fprintf(stream , " [");
for (j=0; j < matrix->columns; j++)
fprintf(stream , fmt , matrix_iget(matrix , i,j));
fprintf(stream , "]\n");
}
}
double matrix_det( matrix_type *A ) {
matrix_lapack_assert_square( A );
{
int dgetrf_info;
double det = 1;
double det_scale = 0;
int n = matrix_get_columns( A );
int * ipiv = util_malloc( n * sizeof * ipiv );
matrix_dgetrf__( A , ipiv , &dgetrf_info );
{
int i;
for (i=0; i < n; i++) {
det *= matrix_iget(A , i , i);
if (det == 0) return 0; /* Holy f**k - a float == comparison ?? */
if (ipiv[i] != (i + 1)) /* A permutation has taken place. */
det *= -1;
/* Try to avoid overflow/underflow by factoring out the order of magnitude. */
while (fabs(det) > 10.0) {
det /= 10;
det_scale += 1;
}
while (fabs(det) < 1.0) {
det *= 10;
det_scale -= 1;
}
}
}
free( ipiv );
return det * pow(10 , det_scale );
}
}
double matrix_iget_safe(const matrix_type * matrix , int i , int j) {
matrix_assert_ij( matrix , i , j );
return matrix_iget( matrix , i , j );
}
double stepwise_iget_beta(const stepwise_type * stepwise, const int index ) {
return matrix_iget( stepwise->beta, index, 0);
}
static double stepwise_estimate__( stepwise_type * stepwise , bool_vector_type * active_rows) {
matrix_type * X;
matrix_type * E;
matrix_type * Y;
double y_mean = 0;
int nvar = matrix_get_columns( stepwise->X0 );
int nsample = matrix_get_rows( stepwise->X0 );
nsample = bool_vector_count_equal( active_rows , true );
nvar = bool_vector_count_equal( stepwise->active_set , true );
matrix_set( stepwise->beta , 0 ); // It is essential to make sure that old finite values in the beta0 vector do not hang around.
/*
Extracting the data used for regression, and storing them in the
temporary local matrices X and Y. Selecting data is based both on
which varibles are active (stepwise->active_set) and which rows
should be used for regression, versus which should be used for
validation (@active_rows).
*/
if ((nsample < matrix_get_rows( stepwise->X0 )) || (nvar < matrix_get_columns( stepwise->X0 ))) {
X = matrix_alloc( nsample , nvar );
E = matrix_alloc( nsample , nvar );
Y = matrix_alloc( nsample , 1);
{
int icol,irow; // Running over all values.
int arow,acol; // Running over active values.
arow = 0;
for (irow = 0; irow < matrix_get_rows( stepwise->X0 ); irow++) {
if (bool_vector_iget( active_rows , irow )) {
acol = 0;
for (icol = 0; icol < matrix_get_columns( stepwise->X0 ); icol++) {
if (bool_vector_iget( stepwise->active_set , icol )) {
matrix_iset( X , arow , acol , matrix_iget( stepwise->X0 , irow , icol ));
matrix_iset( E , arow , acol , matrix_iget( stepwise->E0 , irow , icol ));
acol++;
}
}
matrix_iset( Y , arow , 0 , matrix_iget( stepwise->Y0 , irow , 0 ));
arow++;
}
}
}
} else {
X = matrix_alloc_copy( stepwise->X0 );
E = matrix_alloc_copy( stepwise->E0 );
Y = matrix_alloc_copy( stepwise->Y0 );
}
{
if (stepwise->X_mean != NULL)
matrix_free( stepwise->X_mean);
stepwise->X_mean = matrix_alloc( 1 , nvar );
if (stepwise->X_norm != NULL)
matrix_free( stepwise->X_norm);
stepwise->X_norm = matrix_alloc( 1 , nvar );
matrix_type * beta = matrix_alloc( nvar , 1); /* This is the beta vector as estimated from the OLS estimator. */
regression_augmented_OLS( X , Y , E, beta );
/*
In this code block the beta/tmp_beta vector which is dense with
fewer elements than the full model is scattered into the beta0
vector which has full size and @nvar elements.
*/
{
int ivar,avar;
avar = 0;
for (ivar = 0; ivar < matrix_get_columns( stepwise->X0 ); ivar++) {
if (bool_vector_iget( stepwise->active_set , ivar )) {
matrix_iset( stepwise->beta , ivar , 0 , matrix_iget( beta , avar , 0));
avar++;
}
}
}
matrix_free( beta );
}
matrix_free( X );
matrix_free( E );
matrix_free( Y );
return y_mean;
}
static double stepwise_test_var( stepwise_type * stepwise , int test_var , int blocks) {
double prediction_error = 0;
bool_vector_iset( stepwise->active_set , test_var , true ); // Temporarily activate this variable
{
int nvar = matrix_get_columns( stepwise->X0 );
int nsample = matrix_get_rows( stepwise->X0 );
int block_size = nsample / blocks;
bool_vector_type * active_rows = bool_vector_alloc( nsample, true );
/*True Cross-Validation: */
int * randperms = util_calloc( nsample , sizeof * randperms );
for (int i=0; i < nsample; i++)
randperms[i] = i;
/* Randomly perturb ensemble indices */
rng_shuffle_int( stepwise->rng , randperms , nsample );
for (int iblock = 0; iblock < blocks; iblock++) {
int validation_start = iblock * block_size;
int validation_end = validation_start + block_size - 1;
if (iblock == (blocks - 1))
validation_end = nsample - 1;
/*
Ensure that the active_rows vector has a block consisting of
the interval [validation_start : validation_end] which is set to
false, and the remaining part of the vector is set to true.
*/
{
bool_vector_set_all(active_rows, true);
/*
If blocks == 1 that means all datapoint are used in the
regression, and then subsequently reused in the R2
calculation.
*/
if (blocks > 1) {
for (int i = validation_start; i <= validation_end; i++) {
bool_vector_iset( active_rows , randperms[i] , false );
}
}
}
/*
Evaluate the prediction error on the validation part of the
dataset.
*/
{
stepwise_estimate__( stepwise , active_rows );
{
int irow;
matrix_type * x_vector = matrix_alloc( 1 , nvar );
//matrix_type * e_vector = matrix_alloc( 1 , nvar );
for (irow=validation_start; irow <= validation_end; irow++) {
matrix_copy_row( x_vector , stepwise->X0 , 0 , randperms[irow]);
//matrix_copy_row( e_vector , stepwise->E0 , 0 , randperms[irow]);
{
double true_value = matrix_iget( stepwise->Y0 , randperms[irow] , 0 );
double estimated_value = stepwise_eval__( stepwise , x_vector );
prediction_error += (true_value - estimated_value) * (true_value - estimated_value);
//double e_estimated_value = stepwise_eval__( stepwise , e_vector );
//prediction_error += e_estimated_value*e_estimated_value;
}
}
matrix_free( x_vector );
}
}
}
free( randperms );
bool_vector_free( active_rows );
}
/*inactivate the test_var-variable after completion*/
bool_vector_iset( stepwise->active_set , test_var , false );
return prediction_error;
}
void lars_estimate(lars_type * lars , int max_vars , double max_beta , bool verbose) {
int nvars = matrix_get_columns( lars->X );
int nsample = matrix_get_rows( lars->X );
matrix_type * X = matrix_alloc( nsample, nvars ); // Allocate local X and Y variables
matrix_type * Y = matrix_alloc( nsample, 1 ); // which will hold the normalized data
lars_estimate_init( lars , X , Y); // during the estimation process.
{
matrix_type * G = matrix_alloc_gram( X , true );
matrix_type * mu = matrix_alloc( nsample , 1 );
matrix_type * C = matrix_alloc( nvars , 1 );
matrix_type * Y_mu = matrix_alloc_copy( Y );
int_vector_type * active_set = int_vector_alloc(0,0);
int_vector_type * inactive_set = int_vector_alloc(0,0);
int active_size;
if ((max_vars <= 0) || (max_vars > nvars))
max_vars = nvars;
{
int i;
for (i=0; i < nvars; i++)
int_vector_iset( inactive_set , i , i );
}
matrix_set( mu , 0 );
while (true) {
double maxC = 0;
/*
The first step is to calculate the correlations between the
covariates, and the current residual. All the currently inactive
covariates are searched; the covariate with the greatest
correlation with (Y - mu) is selected and added to the active set.
*/
matrix_sub( Y_mu , Y , mu ); // Y_mu = Y - mu
matrix_dgemm( C , X , Y_mu , true , false , 1.0 , 0); // C = X' * Y_mu
{
int i;
int max_set_index = 0;
for (i=0; i < int_vector_size( inactive_set ); i++) {
int set_index = i;
int var_index = int_vector_iget( inactive_set , set_index );
double value = fabs( matrix_iget(C , var_index , 0) );
if (value > maxC) {
maxC = value;
max_set_index = set_index;
}
}
/*
Remove element corresponding to max_set_index from the
inactive set and add it to the active set:
*/
int_vector_append( active_set , int_vector_idel( inactive_set , max_set_index ));
}
active_size = int_vector_size( active_set );
/*
Now we have calculated the correlations between all the
covariates and the current residual @Y_mu. The correlations are
stored in the matrix @C. The value of the maximum correlation is
stored in @maxC.
Based on the value of @maxC we have added one new covariate to
the model, technically by moving the index from @inactive_set to
@active_set.
*/
/*****************************************************************/
{
matrix_type * weights = matrix_alloc( active_size , 1);
double scale;
/*****************************************************************/
/* This scope should compute and initialize the variables
@weights and @scale. */
{
matrix_type * subG = matrix_alloc( active_size , active_size );
matrix_type * STS = matrix_alloc( active_size , active_size );
matrix_type * sign_vector = matrix_alloc( active_size , 1);
int i , j;
/*
STS = S' o S where 'o' is the Schur product and S is given
by:
[ s1 s2 s3 s4 ]
S = [ s1 s2 s3 s4 ]
[ s1 s2 s3 s4 ]
[ s1 s2 s3 s4 ]
Where si is the sign of the correlation between (active)
variable 'i' and Y_mu.
*/
for (i=0; i < active_size ; i++) {
int vari = int_vector_iget( active_set , i );
double signi = sgn( matrix_iget( C , vari , 0));
matrix_iset( sign_vector , i , 0 , signi );
for (j=0; j < active_size; j++) {
int varj = int_vector_iget( active_set , j );
double signj = sgn( matrix_iget( C , varj , 0));
matrix_iset( STS , i , j , signi * signj );
}
}
// Extract the elements from G corresponding to active indices and
// copy to the matrix subG:
for (i=0; i < active_size ; i++) {
int ii = int_vector_iget( active_set , i );
for (j=0; j < active_size; j++) {
int jj = int_vector_iget( active_set , j );
matrix_iset( subG , i , j , matrix_iget(G , ii , jj));
}
}
// Weights
matrix_inplace_mul( subG , STS );
matrix_inv( subG );
{
matrix_type * ones = matrix_alloc( active_size , 1 );
matrix_type * GA1 = matrix_alloc( active_size , 1 );
matrix_set( ones , 1.0 );
matrix_matmul( GA1 , subG , ones );
scale = 1.0 / sqrt( matrix_get_column_sum( GA1 , 0 ));
matrix_mul( weights , GA1 , sign_vector );
matrix_scale( weights , scale );
matrix_free( GA1 );
matrix_free( ones );
}
matrix_free( sign_vector );
matrix_free( subG );
matrix_free( STS );
}
/******************************************************************/
/* The variables weight and scale have been calculated, proceed
to calculate the step length @gamma. */
{
int i;
double gamma;
{
matrix_type * u = matrix_alloc( nsample , 1 );
int j;
for (i=0; i < nsample; i++) {
double row_sum = 0;
for (j =0; j < active_size; j++)
row_sum += matrix_iget( X , i , int_vector_iget( active_set , j)) * matrix_iget(weights , j , 0 );
matrix_iset( u , i , 0 , row_sum );
}
gamma = maxC / scale;
if (active_size < matrix_get_columns( X )) {
matrix_type * equi_corr = matrix_alloc( nvars , 1 );
matrix_dgemm( equi_corr , X , u , true , false , 1.0 , 0); // equi_corr = X'·u
for (i=0; i < (nvars - active_size); i++) {
int var_index = int_vector_iget( inactive_set , i );
double gamma1 = (maxC - matrix_iget(C , var_index , 0 )) / ( scale - matrix_iget( equi_corr , var_index , 0));
double gamma2 = (maxC + matrix_iget(C , var_index , 0 )) / ( scale + matrix_iget( equi_corr , var_index , 0));
if ((gamma1 > 0) && (gamma1 < gamma))
gamma = gamma1;
if ((gamma2 > 0) && (gamma2 < gamma))
gamma = gamma2;
}
matrix_free( equi_corr );
}
/* Update the current estimated 'location' mu. */
matrix_scale( u , gamma );
matrix_inplace_add( mu , u );
matrix_free( u );
}
/*
We have calculated the step length @gamma, and the @weights. Update the @beta matrix.
*/
for (i=0; i < active_size; i++)
matrix_iset( lars->beta , int_vector_iget( active_set , i ) , active_size - 1 , gamma * matrix_iget( weights , i , 0));
if (active_size > 1)
for (i=0; i < nvars; i++)
matrix_iadd( lars->beta , i , active_size - 1 , matrix_iget( lars->beta , i , active_size - 2));
matrix_free( weights );
}
}
if (active_size == max_vars)
break;
if (max_beta > 0) {
double beta_norm2 = matrix_get_column_abssum( lars->beta , active_size - 1 );
if (beta_norm2 > max_beta) {
// We stop - we will use an interpolation between this beta estimate and
// the previous, to ensure that the |beta| = max_beta criteria is satisfied.
if (active_size >= 2) {
double beta_norm1 = matrix_get_column_abssum( lars->beta , active_size - 2 );
double s = (max_beta - beta_norm1)/(beta_norm2 - beta_norm1);
{
int j;
for (j=0; j < nvars; j++) {
double beta1 = matrix_iget( lars->beta , j , active_size - 2 );
double beta2 = matrix_iget( lars->beta , j , active_size - 1 );
matrix_iset( lars->beta , j , active_size - 1 , beta1 + s*(beta2 - beta1));
}
}
}
break;
}
}
}
matrix_free( G );
matrix_free( mu );
matrix_free( C );
matrix_free( Y_mu );
int_vector_free( active_set );
int_vector_free( inactive_set );
matrix_resize( lars->beta , nvars , active_size , true );
if (verbose)
matrix_pretty_fprint( lars->beta , "beta" , "%12.5f" , stdout );
lars_select_beta( lars , active_size - 1);
}
matrix_free( X );
matrix_free( Y );
}
double lars_iget_beta( const lars_type * lars , int index) {
return matrix_iget( lars->beta0 , index , 0 );
}
