void ica(gsl_matrix *A, gsl_matrix *S, gsl_matrix *X, int verbose){
/* Checking the existance of the enviroment variable
for controlling the number of threads used by openblas*/
const size_t NCOMP = A->size2;
const size_t NSUB = X->size1;
const size_t NVOX = X->size2;
gsl_matrix *weights = gsl_matrix_alloc(NCOMP, NCOMP);
gsl_matrix *inv_weights = gsl_matrix_alloc(NCOMP, NCOMP);
gsl_matrix *white_X = gsl_matrix_alloc(NCOMP, NVOX);
gsl_matrix *white = gsl_matrix_alloc(NCOMP, NSUB);
gsl_matrix *dewhite = gsl_matrix_alloc(NSUB, NCOMP);
pca_whiten(X, NCOMP, white_X, white, dewhite, 1);
if (verbose) printf("Done.");
if (verbose) printf("\nINFOMAX ...");
if (verbose) printf("\nPCA decomposition ...");
infomax(white_X, weights, S, verbose);
if (verbose) printf("Done");
matrix_inv(weights, inv_weights);
matrix_mmul(dewhite, inv_weights, A);
gsl_matrix_free(weights);
gsl_matrix_free(white_X);
gsl_matrix_free(white);
gsl_matrix_free(dewhite);
}
void rotator::update(float elapsed_seconds)
{
glm::mat4 matrix(1.0f);
matrix = glm::translate(matrix, glm::vec3(0, 0, dist_));
matrix = glm::rotate(matrix, angle_x_, glm::vec3(1, 0, 0));
matrix = glm::rotate(matrix, angle_y_, glm::vec3(0, 1, 0));
scene_->update_modelview(matrix);
glm::mat4 matrix_inv(1.0f);
matrix_inv = glm::rotate(matrix_inv, -angle_y_, glm::vec3(0, 1, 0));
matrix_inv = glm::rotate(matrix_inv, -angle_x_, glm::vec3(1, 0, 0));
matrix_inv = glm::translate(matrix_inv, glm::vec3(0, 0, -dist_));
scene_->update_modelview_inv(matrix_inv);
scene_->update(elapsed_seconds);
}
int main( int argc, char ** argv) {
rng_type * rng = rng_alloc( MZRAN , INIT_DEV_RANDOM );
matrix_type * A = matrix_alloc( 12 , 12 );
matrix_type * B = matrix_alloc( 12 , 12 );
matrix_random_init( A , rng );
matrix_assign( B , A );
matrix_pretty_print( A , " A " , "%8.4f" );
#ifdef WITH_LAPACK
matrix_inv( B );
printf("\n");
matrix_pretty_print( B , "inv(A)" , "%8.4f" );
matrix_inplace_matmul( B , A );
printf("\n");
matrix_pretty_print( B , " I " , "%8.4f" );
{
matrix_type * A3 = matrix_alloc(3,3);
matrix_random_init( A3 , rng );
matrix_iset( A3 , 0 , 0 , sin(0.98));
printf("matrix_det3:%g ",matrix_det3( A3 ));
printf("matrix_det:%g \n",matrix_det( A3 ));
}
{
matrix_type * A4 = matrix_alloc(4,4);
matrix_random_init( A4 , rng );
matrix_iset( A4 , 0 , 0 , sin(0.98));
printf("matrix_det4:%g ",matrix_det4( A4 ));
printf("matrix_det:%g \n",matrix_det( A4 ));
}
#endif
matrix_free( A );
matrix_free( B );
rng_free( rng );
}
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 );
}
void cox_test(double** covariates, size_t num_features_in_covariate, size_t num_samples, double* time, double* censor, double* coefficients, double** variance) {
// declare variables, init values and allocate memory
// gsl matrices
matrix_t* coefficients_matrix_p = NULL;
matrix_t* information_matrix_p = NULL;
matrix_t* information_matrix_inverse_p = NULL;
matrix_t* score_matrix_p = NULL;
matrix_t* error_matrix_p = NULL;
matrix_t* variance_matrix_p = NULL;
// other variables
double denominator = 0, numerator = 0;
double error1 = 1, error2 = 1;
double* risk_factor = (double*) calloc(num_samples, sizeof(double));
double* score = (double*) calloc(num_features_in_covariate, sizeof(double));
double** expected_covariate = (double**) calloc(num_features_in_covariate, sizeof(double*));
double** information = (double**) calloc(num_features_in_covariate, sizeof(double*));
for (size_t i = 0; i < num_features_in_covariate; i++) {
coefficients[i] = 0.1;
expected_covariate[i] = (double*) calloc(num_samples, sizeof(double));
information[i] = (double*) calloc(num_features_in_covariate, sizeof(double));
}
// create gsl matrices
coefficients_matrix_p = matrix_new(num_features_in_covariate, 1);
matrix_init(0.1, coefficients_matrix_p);
information_matrix_p = matrix_new(num_features_in_covariate, num_features_in_covariate);
score_matrix_p = matrix_new(num_features_in_covariate, 1);
error_matrix_p = matrix_new(num_features_in_covariate, 1);
information_matrix_inverse_p = matrix_new(num_features_in_covariate, num_features_in_covariate);
while((error1 > COX_ERROR_LIMIT) || (error2 > COX_ERROR_LIMIT)) {
for (size_t i = 0; i < num_samples; ++i) {
risk_factor[i] = 1.0;
for (size_t s = 0; s < num_features_in_covariate; ++s) {
risk_factor[i] *= exp(coefficients[s] * covariates[s][i]);
}
}
for (size_t j = 0; j < num_features_in_covariate; j++) {
score[j] = 0.0;
for (size_t i = 0; i < num_samples; i++) {
for (size_t k = 0; k < num_samples; k++) {
if (time[k] >= time[i]) {
denominator += risk_factor[k];
numerator += covariates[j][k] * risk_factor[k];
}
}
expected_covariate[j][i] = numerator / denominator;
score[j] += censor[i] * (covariates[j][i] - expected_covariate[j][i]);
numerator = 0.0;
denominator = 0.0;
}
}
for (size_t r = 0; r < num_features_in_covariate; r++) {
for (size_t s = 0; s < num_features_in_covariate; s++) {
information[r][s] = 0.0;
for (size_t i = 0; i < num_samples; i++) {
for (size_t k = 0; k < num_samples; k++) {
if (time[k] >= time[i]) {
denominator += risk_factor[k];
numerator += (covariates[r][k] * covariates[s][k] * risk_factor[k]);
}
}
information[r][s] += censor[i] * (expected_covariate[r][i] * expected_covariate[s][i] - (numerator / denominator));
numerator = 0.0;
denominator = 0.0;
}
}
}
// fill information_matrix
matrix_fill(information, num_features_in_covariate, num_features_in_covariate, information_matrix_p); // fill the matrix with data
// fill score_matrix from score array
for (size_t i = 0; i < num_features_in_covariate; i++) {
matrix_set(i, 0, score[i], score_matrix_p);
}
// calculate error matrix: inv(information_matrix) * score_matrix
matrix_inv(information_matrix_p, information_matrix_inverse_p);
matrix_mul(information_matrix_inverse_p, score_matrix_p, error_matrix_p);
// calculate coefficients matrix
coefficients_matrix_p = matrix_sub(coefficients_matrix_p, error_matrix_p);
// fill coefficientes
for (size_t i = 0; i < num_features_in_covariate; i++) {
coefficients[i] = matrix_get(i, 0, coefficients_matrix_p);
}
error1 = sqrt(matrix_Fnorm(error_matrix_p));
error2 = sqrt(matrix_Fnorm(score_matrix_p));
} // end of while
// calculate variance: (-1 * inv(information_matrix))
variance_matrix_p = matrix_scale(information_matrix_inverse_p, -1.0);
for (size_t i = 0; i < num_features_in_covariate; i++) {
for (size_t j = 0; j < num_features_in_covariate; j++) {
variance[i][j] = matrix_get(i, j, variance_matrix_p);
}
}
// free gsl matrices
matrix_free(coefficients_matrix_p);
matrix_free(information_matrix_p);
matrix_free(information_matrix_inverse_p);
matrix_free(score_matrix_p);
matrix_free(error_matrix_p);
variance_matrix_p = NULL; // points to information_matrix_inverse_p previously freed
matrix_free(variance_matrix_p);
// free other resources
free(risk_factor);
free(score);
for (size_t i = 0; i < num_features_in_covariate; i++) {
free(expected_covariate[i]);
free(information[i]);
}
free(expected_covariate);
free(information);
return;
}