void sqrt_enkf_initX(void * module_data ,
matrix_type * X ,
matrix_type * A ,
matrix_type * S ,
matrix_type * R ,
matrix_type * dObs ,
matrix_type * E ,
matrix_type *D ) {
sqrt_enkf_data_type * data = sqrt_enkf_data_safe_cast( module_data );
{
int ncomp = std_enkf_get_subspace_dimension( data->std_data );
double truncation = std_enkf_get_truncation( data->std_data );
int nrobs = matrix_get_rows( S );
int ens_size = matrix_get_columns( S );
int nrmin = util_int_min( ens_size , nrobs);
matrix_type * W = matrix_alloc(nrobs , nrmin);
double * eig = util_calloc( nrmin , sizeof * eig );
matrix_subtract_row_mean( S ); /* Shift away the mean */
enkf_linalg_lowrankCinv( S , R , W , eig , truncation , ncomp);
enkf_linalg_init_sqrtX( X , S , data->randrot , dObs , W , eig , false);
matrix_free( W );
free( eig );
enkf_linalg_checkX( X , false );
}
}
void rml_enkf_common_initA__( matrix_type * A ,
matrix_type * S ,
matrix_type * Cd ,
matrix_type * E ,
matrix_type * D ,
double truncation,
double lamda,
matrix_type * Udr,
double * Wdr,
matrix_type * VdTr) {
int nrobs = matrix_get_rows( S );
int ens_size = matrix_get_columns( S );
double a = lamda + 1;
matrix_type *tmp = matrix_alloc (nrobs, ens_size);
double nsc = 1/sqrt(ens_size-1);
printf("The lamda Value is %5.5f\n",lamda);
printf("The Value of Truncation is %4.2f \n",truncation);
matrix_subtract_row_mean( S ); /* Shift away the mean in the ensemble predictions*/
matrix_inplace_diag_sqrt(Cd);
matrix_dgemm(tmp, Cd, S,false, false, 1.0, 0.0);
matrix_scale(tmp, nsc);
printf("The Scaling of data matrix completed !\n ");
// SVD(S) = Ud * Wd * Vd(T)
int nsign = enkf_linalg_svd_truncation(tmp , truncation , -1 , DGESVD_MIN_RETURN , Wdr , Udr , VdTr);
/* After this we only work with the reduced dimension matrices */
printf("The number of siginificant ensembles are %d \n ",nsign);
matrix_type * X1 = matrix_alloc( nsign, ens_size);
matrix_type * X2 = matrix_alloc (nsign, ens_size );
matrix_type * X3 = matrix_alloc (ens_size, ens_size );
// Compute the matrices X1,X2,X3 and dA
enkf_linalg_rml_enkfX1(X1, Udr ,D ,Cd ); //X1 = Ud(T)*Cd(-1/2)*D -- D= -(dk-d0)
enkf_linalg_rml_enkfX2(X2, Wdr ,X1 ,a, nsign); //X2 = ((a*Ipd)+Wd^2)^-1 * X1
matrix_free(X1);
enkf_linalg_rml_enkfX3(X3, VdTr ,Wdr,X2, nsign); //X3 = Vd *Wd*X2
printf("The X3 matrix is computed !\n ");
matrix_type *dA1= matrix_alloc (matrix_get_rows(A), ens_size);
matrix_type * Dm = matrix_alloc_copy( A );
matrix_subtract_row_mean( Dm ); /* Remove the mean from the ensemble of model parameters*/
matrix_scale(Dm, nsc);
enkf_linalg_rml_enkfdA(dA1, Dm, X3); //dA = Dm * X3
matrix_inplace_add(A,dA1); //dA
matrix_free(X3);
matrix_free(Dm);
matrix_free(dA1);
}
