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ResInsight/ThirdParty/Ert/lib/util/lars.c

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/*
Copyright (C) 2011 Statoil ASA, Norway.
The file 'lars.c' is part of ERT - Ensemble based Reservoir Tool.
ERT 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.
ERT 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 at <http://www.gnu.org/licenses/gpl.html>
for more details.
*/
#include <stdlib.h>
#include <stdbool.h>
#include <math.h>
#include <ert/util/util.h>
#include <ert/util/int_vector.h>
#include <ert/util/matrix.h>
#include <ert/util/matrix_blas.h>
#include <ert/util/matrix_lapack.h>
#include <ert/util/regression.h>
#include <ert/util/lars.h>
#define LARS_TYPE_ID 77125439
struct lars_struct {
UTIL_TYPE_ID_DECLARATION;
matrix_type * X;
matrix_type * Y;
bool data_owner;
double Y0;
matrix_type * beta0;
matrix_type * beta;
matrix_type * X_norm;
matrix_type * X_mean;
double Y_mean;
};
static lars_type * lars_alloc__() {
lars_type * lars = (lars_type*)util_malloc( sizeof * lars );
UTIL_TYPE_ID_INIT( lars , LARS_TYPE_ID );
lars->X = NULL;
lars->Y = NULL;
lars->X_norm = NULL;
lars->X_mean = NULL;
lars->beta = NULL;
lars->beta0 = NULL;
lars->Y = 0;
return lars;
}
lars_type * lars_alloc1( int nsample , int nvars) {
lars_type * lars = lars_alloc__();
lars->X = matrix_alloc( nsample , nvars );
lars->Y = matrix_alloc( nsample , 1 );
lars->data_owner = true;
return lars;
}
lars_type * lars_alloc2( matrix_type * X , matrix_type * Y , bool internal_copy ) {
lars_type * lars = lars_alloc__();
if (internal_copy) {
lars->X = matrix_alloc_copy( X );
lars->Y = matrix_alloc_copy( Y );
lars->data_owner = true;
} else {
lars->X = X;
lars->Y = Y;
lars->data_owner = false;
}
return lars;
}
int lars_get_sample( const lars_type * lars ) {
return matrix_get_rows( lars->X );
}
int lars_get_nvar( const lars_type * lars ) {
return matrix_get_columns( lars->X );
}
void lars_isetX( lars_type * lars, int sample, int var , double value) {
matrix_iset( lars->X , sample , var , value );
}
void lars_isetY( lars_type * lars, int sample, double value) {
matrix_iset( lars->Y , sample , 0 , value );
}
#define MATRIX_SAFE_FREE( m ) if (m != NULL) matrix_free( m )
void lars_free( lars_type * lars ) {
if (lars->data_owner) {
MATRIX_SAFE_FREE( lars->X );
MATRIX_SAFE_FREE( lars->Y );
}
MATRIX_SAFE_FREE( lars->X_norm );
MATRIX_SAFE_FREE( lars->X_mean );
MATRIX_SAFE_FREE( lars->beta );
MATRIX_SAFE_FREE( lars->beta0 );
free( lars );
}
#undef MATRIX_SAFE_FREE
/*****************************************************************/
static double sgn(double x) {
return copysign(1 , x); // C99
}
static void lars_estimate_init( lars_type * lars, matrix_type * X , matrix_type * Y) {
int nvar = matrix_get_columns( lars->X );
matrix_assign( X , lars->X );
matrix_assign( Y , lars->Y );
if (lars->X_norm != NULL)
matrix_free( lars->X_norm );
lars->X_norm = matrix_alloc(1 , nvar );
if (lars->X_mean != NULL)
matrix_free( lars->X_mean );
lars->X_mean = matrix_alloc(1 , nvar );
if (lars->beta != NULL)
matrix_free( lars->beta );
lars->beta = matrix_alloc( nvar , nvar );
lars->Y_mean = regression_scale( X , Y , lars->X_mean , lars->X_norm);
}
double lars_getY0( const lars_type * lars) {
return lars->Y0;
}
double lars_iget_beta( const lars_type * lars , int index) {
return matrix_iget( lars->beta0 , index , 0 );
}
void lars_select_beta( lars_type * lars , int beta_index) {
int nvars = matrix_get_rows( lars->beta );
if (lars->beta0 == NULL)
lars->beta0 = matrix_alloc( nvars , 1 );
{
matrix_type * beta_vector = matrix_alloc( nvars , 1 );
matrix_copy_column( beta_vector , lars->beta , 0 , beta_index );
lars->Y0 = regression_unscale( beta_vector , lars->X_norm , lars->X_mean , lars->Y_mean , lars->beta0 );
matrix_free( beta_vector );
}
}
/*
The algorithm can very briefly be summarized as:
1. Determine the covariate with greatest correlation to the data and
add this covariate to the model. In the current implementation the
correlations are stored in the matrix @C and the greatest
correlation is stored in the scalar variable @maxC.
2. Determine an update direction in the set of active covariates
which is equiangular to all covariates.
3. Determine the step length @gamma - which is the exact step length
before a new covariate will enter the active set at the current
correlation level.
4. Update the beta estimate and the current 'location' mu.
*/
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'<27>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_eval1( const lars_type * lars , const matrix_type * x) {
return lars->Y0 + matrix_row_column_dot_product( x , 0 , lars->beta0 , 0 );
}
double lars_eval2( const lars_type * lars , double * x) {
matrix_type * x_view = matrix_alloc_view( x , 1 , matrix_get_columns( lars->X_mean ));
double y = lars_eval1( lars , x_view );
matrix_free( x_view );
return y;
}
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