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 );
}
static void dgemm_debug(const matrix_type *C , const matrix_type *A , const matrix_type * B , bool transA, bool transB) {
printf("\nC = [%d , %d]\n",matrix_get_rows( C ) , matrix_get_columns(C));
printf("A: [%d , %d]", matrix_get_rows( A ) , matrix_get_columns(A));
if (transA)
printf("^T");
printf("\nB: [%d , %d]", matrix_get_rows( B ) , matrix_get_columns(B));
if (transB)
printf("^T");
printf("\n\n");
printf("[%d ,%d] = ",matrix_get_rows( C ) , matrix_get_columns(C));
if (transA)
printf("[%d ,%d] x ",matrix_get_rows( A ) , matrix_get_columns(A));
else
printf("[%d ,%d] x ",matrix_get_columns( A ) , matrix_get_rows(A));
if (transB)
printf("[%d ,%d]\n",matrix_get_rows( B ) , matrix_get_columns(B));
else
printf("[%d ,%d]\n",matrix_get_columns( B ) , matrix_get_rows(B));
}
/* Updates matrix A by subtracting matrix B - elementwise. */
void matrix_inplace_sub(matrix_type * A , const matrix_type * B) {
if ((A->rows == B->rows) && (A->columns == B->columns)) {
int i,j;
for (j = 0; j < A->columns; j++)
for (i=0; i < A->rows; i++)
A->data[ GET_INDEX(A,i,j) ] -= B->data[ GET_INDEX(B,i,j) ];
} else
util_abort("%s: size mismatch A:[%d,%d] B:[%d,%d]\n",__func__ ,
matrix_get_rows(A),
matrix_get_columns(A),
matrix_get_rows(B),
matrix_get_columns(B));
}
/* Currently only used as 'support' function for the matrix_det function. */
static void matrix_dgetrf__( matrix_type * A, int * ipiv, int * info) {
int lda = matrix_get_column_stride( A );
int m = matrix_get_rows( A );
int n = matrix_get_columns( A );
dgetrf_( &m , &n , matrix_get_data( A ) , &lda , ipiv , info);
}
int matrix_inv( matrix_type * A ) {
matrix_lapack_assert_square( A );
{
int dgetrf_info;
int info;
int n = matrix_get_columns( A );
int * ipiv = util_malloc( n * sizeof * ipiv );
matrix_dgetrf__( A , ipiv , &dgetrf_info );
{
int lda = matrix_get_column_stride( A );
double * work = util_malloc( sizeof * work );
int work_size;
/* First call: determine optimal worksize: */
work_size = -1;
dgetri_( &n , matrix_get_data( A ), &lda , ipiv , work , &work_size , &info);
if (info == 0) {
work_size = (int) work[0];
work = util_realloc( work , sizeof * work * work_size );
dgetri_( &n , matrix_get_data( A ), &lda , ipiv , work , &work_size , &info);
} else
util_abort("%s: dgetri_ returned info:%d \n",__func__ , info);
free( work );
}
free( ipiv );
return info;
}
}
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 matrix_dorgqr(matrix_type * A , double * tau, int num_reflectors) { /* num_reflectors == length of tau. */
int lda = matrix_get_column_stride( A );
int m = matrix_get_rows( A );
int n = matrix_get_columns( A );
double * work = util_malloc(sizeof * work );
int worksize;
int info;
/* Determine optimal worksize. */
worksize = -1;
dorgqr_(&m , &n , &num_reflectors , matrix_get_data( A ), &lda , tau , work , &worksize , &info);
if (info != 0)
util_abort("%s: dorgqf routine failed with info:%d \n",__func__ , info);
worksize = ( int ) work[0];
{
double * tmp = realloc(work , sizeof * work * worksize );
if (tmp == NULL) {
/*
OK - we could not get the optimal worksize,
try again with the minimum.
*/
worksize = n;
work = util_realloc(work , sizeof * work * worksize );
} else
work = tmp; /* The request for optimal worksize succeeded */
}
/* Second call - do the actual computation. */
dorgqr_(&m , &n , &num_reflectors , matrix_get_data( A ), &lda , tau , work , &worksize , &info);
if (info != 0)
util_abort("%s: dorqf routine failed with info:%d \n",__func__ , info);
free( work );
}
void matrix_column_compressed_memcpy(matrix_type * target, const matrix_type * src, const bool_vector_type * mask) {
if (bool_vector_count_equal( mask , true ) != matrix_get_columns( target ))
util_abort("%s: size mismatch. \n",__func__);
if (bool_vector_size( mask ) != matrix_get_columns( src))
util_abort("%s: size mismatch. \n",__func__);
{
int target_col = 0;
int src_col;
for (src_col = 0; src_col < bool_vector_size( mask ); src_col++) {
if (bool_vector_iget( mask , src_col)) {
matrix_copy_column( target , src , target_col , src_col);
target_col++;
}
}
}
}
int matrix_gram_schmidt_process(matrix_t *q, matrix_t *p)
{
int n;
matrix_t *tmp;
assert(q);
assert(p);
assert(matrix_get_columns(q) >= matrix_get_columns(p));
assert(matrix_get_rows(q) >= matrix_get_rows(p));
tmp = matrix_new_and_copy(p);
n = matrix_self_gram_schmidt_process(tmp, 0, 0, matrix_get_columns(tmp), matrix_get_rows(tmp));
matrix_copy_matrix(q, 0, 0, tmp, 0, 0, n, matrix_get_rows(tmp));
matrix_destroy(tmp);
return n;
}
void matrix_gram_set( const matrix_type * X , matrix_type * G, bool col) {
int G_rows = matrix_get_rows( G );
int G_cols = matrix_get_columns( G );
int X_rows = matrix_get_rows( X );
int X_cols = matrix_get_columns( X );
if (col) {
// Calculate X' · X
if ((G_rows == G_cols) && (X_cols == G_rows))
matrix_dgemm( G , X , X , true , false , 1 , 0);
else
util_abort("%s: dimension mismatch \n",__func__);
} else {
// Calculate X · X'
if ((G_rows == G_cols) && (X_rows == G_rows))
matrix_dgemm( G , X , X , false , true , 1 , 0);
else
util_abort("%s: dimension mismatch \n",__func__);
}
}
matrix_t *matrix_new_and_gram_schmidt_process(matrix_t *p)
{
int n;
matrix_t *tmp, *q;
assert(p);
tmp = matrix_new_and_copy(p);
n = matrix_self_gram_schmidt_process(tmp, 0, 0, matrix_get_columns(tmp), matrix_get_rows(tmp));
if (n == matrix_get_columns(tmp)) return tmp;
q = matrix_new(n, matrix_get_rows(tmp), false);
matrix_copy_matrix(q, 0, 0, tmp, 0, 0, n, matrix_get_rows(tmp));
matrix_destroy(tmp);
return q;
}
matrix_type * matrix_alloc_column_compressed_copy(const matrix_type * src, const bool_vector_type * mask) {
if (bool_vector_size( mask ) != matrix_get_columns( src ))
util_abort("%s: size mismatch. Src matrix has %d rows mask has:%d elements\n", __func__ , matrix_get_rows( src ) , bool_vector_size( mask ));
{
int target_columns = bool_vector_count_equal( mask , true );
matrix_type * target = matrix_alloc( matrix_get_rows( src ) , target_columns );
matrix_column_compressed_memcpy( target , src , mask );
return target;
}
}
matrix_t *cmatrix_new_and_gram_schmidt_process(matrix_t *p)
{
int n;
matrix_t *q, *tmp;
assert(p);
assert(matrix_is_imaginary(p));
tmp = matrix_new_and_copy(p);
n = cmatrix_self_gram_schmidt_process(tmp, 0, 0, matrix_get_columns(tmp), matrix_get_rows(tmp));
if (n == matrix_get_columns(tmp)) return tmp;
q = matrix_new(n, matrix_get_rows(tmp), true);
cmatrix_copy_cmatrix(q, 0, 0, tmp, 0, 0, n, matrix_get_rows(tmp));
matrix_destroy(tmp);
return q;
}
void test_readwrite() {
test_work_area_type * test_area = test_work_area_alloc("matrix-test");
{
rng_type * rng = rng_alloc(MZRAN , INIT_DEV_URANDOM );
matrix_type * m1 = matrix_alloc(3 , 3);
matrix_type * m2 = matrix_alloc(3 , 3);
matrix_random_init( m1 , rng );
matrix_assign(m2 , m1);
test_assert_true( matrix_equal( m1 , m2 ) );
{
FILE * stream = util_fopen("m1" , "w");
matrix_fwrite( m1 , stream );
fclose( stream );
}
matrix_random_init( m1 , rng );
test_assert_false( matrix_equal( m1 , m2 ) );
{
FILE * stream = util_fopen("m1" , "r");
matrix_free( m1 );
m1 = matrix_alloc(1,1);
printf("-----------------------------------------------------------------\n");
matrix_fread( m1 , stream );
test_assert_int_equal( matrix_get_rows(m1) , matrix_get_rows( m2));
test_assert_int_equal( matrix_get_columns(m1) , matrix_get_columns( m2));
util_fseek( stream , 0 , SEEK_SET);
{
matrix_type * m3 = matrix_fread_alloc( stream );
test_assert_true( matrix_equal( m2 , m3 ));
matrix_free( m3 );
}
fclose( stream );
}
test_assert_true( matrix_equal( m1 , m2 ) );
matrix_free( m2 );
matrix_free( m1 );
rng_free( rng );
}
test_work_area_free( test_area );
}
static void * matrix_inplace_matmul_mt__(void * arg) {
arg_pack_type * arg_pack = arg_pack_safe_cast( arg );
int row_offset = arg_pack_iget_int( arg_pack , 0 );
int rows = arg_pack_iget_int( arg_pack , 1 );
matrix_type * A = arg_pack_iget_ptr( arg_pack , 2 );
const matrix_type * B = arg_pack_iget_const_ptr( arg_pack , 3 );
matrix_type * A_view = matrix_alloc_shared( A , row_offset , 0 , rows , matrix_get_columns( A ));
matrix_inplace_matmul( A_view , B );
matrix_free( A_view );
return NULL;
}
void sqrt_enkf_init_update( void * arg ,
const matrix_type * S ,
const matrix_type * R ,
const matrix_type * dObs ,
const matrix_type * E ,
const matrix_type * D ) {
sqrt_enkf_data_type * sqrt_data = sqrt_enkf_data_safe_cast( arg );
{
int ens_size = matrix_get_columns( S );
sqrt_data->randrot = enkf_linalg_alloc_mp_randrot( ens_size , sqrt_data->rng );
}
}
matrix_type * matrix_alloc_gram( const matrix_type * X , bool col) {
int X_rows = matrix_get_rows( X );
int X_columns = matrix_get_columns( X );
matrix_type * G;
if (col)
G = matrix_alloc( X_columns , X_columns );
else
G = matrix_alloc( X_rows , X_rows );
matrix_gram_set( X , G , col);
return G;
}
void matrix_dgemv(const matrix_type * A , const double *x , double * y, bool transA , double alpha , double beta) {
int m = matrix_get_rows( A );
int n = matrix_get_columns( A );
int lda = matrix_get_column_stride( A );
int incx = 1;
int incy = 1;
char transA_c;
if (transA)
transA_c = 'T';
else
transA_c = 'N';
dgemv_(&transA_c , &m , &n , &alpha , matrix_get_data( A ) , &lda , x , &incx , &beta , y , &incy);
}
void matrix_dgesv(matrix_type * A , matrix_type * B) {
matrix_lapack_assert_square( A );
matrix_lapack_assert_fortran_layout( B );
{
int n = matrix_get_rows( A );
int lda = matrix_get_column_stride( A );
int ldb = matrix_get_column_stride( B );
int nrhs = matrix_get_columns( B );
long int * ipivot = util_calloc( n , sizeof * ipivot );
int info;
dgesv_(&n , &nrhs , matrix_get_data( A ) , &lda , ipivot , matrix_get_data( B ), &ldb , &info);
if (info != 0)
util_abort("%s: low level lapack routine: dgesv() failed with info:%d \n",__func__ , info);
free(ipivot);
}
}
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);
}
void test_state() {
rng_type * rng = rng_alloc( MZRAN , INIT_DEFAULT );
int ens_size = 10;
int active_size = 8;
int rows = 100;
matrix_type * state = matrix_alloc(1,1);
bool_vector_type * ens_mask = bool_vector_alloc(ens_size , false);
matrix_type * A = matrix_alloc( rows , active_size);
matrix_type * A2 = matrix_alloc( rows, active_size );
matrix_type * A3 = matrix_alloc( 1,1 );
for (int i=0; i < active_size; i++)
bool_vector_iset( ens_mask , i + 1 , true );
matrix_random_init(A , rng);
rml_enkf_common_store_state( state , A , ens_mask );
test_assert_int_equal( matrix_get_rows( state ) , rows );
test_assert_int_equal( matrix_get_columns( state ) , ens_size );
{
int g;
int a = 0;
for (g=0; g < ens_size; g++) {
if (bool_vector_iget( ens_mask , g )) {
test_assert_true( matrix_columns_equal( state , g , A , a ));
a++;
}
}
}
rml_enkf_common_recover_state( state , A2 , ens_mask);
rml_enkf_common_recover_state( state , A3 , ens_mask);
test_assert_true( matrix_equal( A , A2 ));
test_assert_true( matrix_equal( A , A3 ));
bool_vector_free( ens_mask );
matrix_free( state );
matrix_free( A );
}
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 );
}
}
void matrix_dgemm(matrix_type *C , const matrix_type *A , const matrix_type * B , bool transA, bool transB , double alpha , double beta) {
int m = matrix_get_rows( C );
int n = matrix_get_columns( C );
int lda = matrix_get_column_stride( A );
int ldb = matrix_get_column_stride( B );
int ldc = matrix_get_column_stride( C );
char transA_c;
char transB_c;
int k , innerA, innerB , outerA , outerB;
if (transA)
k = matrix_get_rows( A );
else
k = matrix_get_columns( A );
if (transA) {
innerA = matrix_get_rows(A);
outerA = matrix_get_columns(A);
transA_c = 'T';
} else {
innerA = matrix_get_columns(A);
outerA = matrix_get_rows(A);
transA_c = 'N';
}
if (transB) {
innerB = matrix_get_columns( B );
outerB = matrix_get_rows( B );
transB_c = 'T';
} else {
transB_c = 'N';
innerB = matrix_get_rows( B );
outerB = matrix_get_columns( B );
}
/*
This is the dimension check which must pass:
--------------------------------------------------
A | B | Columns(A) = Rows(B)
Trans(A) | Trans(B) | Rows(A) = Columns(B)
A | Trans(B) | Columns(A) = Columns(B)
Trans(A) | B | Rows(A) = Rows(B)
--------------------------------------------------
--------------------------------------------------
A | Rows(A) = Rows(C)
Trans(A) | Columns(A) = Rows(C)
B | Columns(B) = Columns(C)
Trans(B) | Rows(B) = Columns(B)
--------------------------------------------------
*/
if (innerA != innerB) {
dgemm_debug(C,A,B,transA , transB);
util_abort("%s: matrix size mismatch between A and B \n", __func__);
}
if (outerA != matrix_get_rows( C )) {
dgemm_debug(C,A,B,transA , transB);
printf("outerA:%d rows(C):%d \n",outerA , matrix_get_rows( C ));
util_abort("%s: matrix size mismatch between A and C \n",__func__);
}
if (outerB != matrix_get_columns( C )) {
dgemm_debug(C,A,B,transA , transB);
util_abort("%s: matrix size mismatch between B and C \n",__func__);
}
if (!ldc >= util_int_max(1 , m)) {
dgemm_debug(C,A,B,transA , transB);
fprintf(stderr,"Tried to capture blas message: \"** On entry to DGEMM parameter 13 had an illegal value\"\n");
fprintf(stderr,"m:%d ldc:%d ldc should be >= max(1,%d) \n",m,ldc,m);
util_abort("%s: invalid value for ldc\n",__func__);
}
dgemm_(&transA_c , // 1
&transB_c , // 2
&m , // 3
&n , // 4
&k , // 5
&alpha , // 6
matrix_get_data( A ) , // 7
&lda , // 8
matrix_get_data( B ) , // 9
&ldb , // 10
&beta , // 11
matrix_get_data( C ) , // 12
&ldc); // 13
}
matrix_type * matrix_alloc_transpose( const matrix_type * A) {
matrix_type * B = matrix_alloc( matrix_get_columns( A ) , matrix_get_rows( A ));
matrix_transpose( A , B );
return B;
}
void matrix_inplace_matmul(matrix_type * A, const matrix_type * B) {
if ((A->columns == B->rows) && (B->rows == B->columns)) {
double * tmp = util_malloc( sizeof * A->data * A->columns );
int i,j,k;
for (i=0; i < A->rows; i++) {
/* Clearing the tmp vector */
for (k=0; k < B->rows; k++)
tmp[k] = 0;
for (j=0; j < B->rows; j++) {
double scalar_product = 0;
for (k=0; k < A->columns; k++)
scalar_product += A->data[ GET_INDEX(A,i,k) ] * B->data[ GET_INDEX(B,k,j) ];
/* Assign first to tmp[j] */
tmp[j] = scalar_product;
}
for (j=0; j < A->columns; j++)
A->data[ GET_INDEX(A , i, j) ] = tmp[j];
}
free(tmp);
} else
util_abort("%s: size mismatch: A:[%d,%d] B:[%d,%d]\n",__func__ , matrix_get_rows(A) , matrix_get_columns(A) , matrix_get_rows(B) , matrix_get_columns(B));
}
void bootstrap_enkf_updateA(void * module_data ,
matrix_type * A ,
matrix_type * S ,
matrix_type * R ,
matrix_type * dObs ,
matrix_type * E ,
matrix_type * D ) {
bootstrap_enkf_data_type * bootstrap_data = bootstrap_enkf_data_safe_cast( module_data );
{
const int num_cpu_threads = 4;
int ens_size = matrix_get_columns( A );
matrix_type * X = matrix_alloc( ens_size , ens_size );
matrix_type * A0 = matrix_alloc_copy( A );
matrix_type * S_resampled = matrix_alloc_copy( S );
matrix_type * A_resampled = matrix_alloc( matrix_get_rows(A0) , matrix_get_columns( A0 ));
int ** iens_resample = alloc_iens_resample( bootstrap_data->rng , ens_size );
{
int ensemble_members_loop;
for ( ensemble_members_loop = 0; ensemble_members_loop < ens_size; ensemble_members_loop++) {
int unique_bootstrap_components;
int ensemble_counter;
/* Resample A and meas_data. Here we are careful to resample the working copy.*/
{
{
int_vector_type * bootstrap_components = int_vector_alloc( ens_size , 0);
for (ensemble_counter = 0; ensemble_counter < ens_size; ensemble_counter++) {
int random_column = iens_resample[ ensemble_members_loop][ensemble_counter];
int_vector_iset( bootstrap_components , ensemble_counter , random_column );
matrix_copy_column( A_resampled , A0 , ensemble_counter , random_column );
matrix_copy_column( S_resampled , S , ensemble_counter , random_column );
}
int_vector_select_unique( bootstrap_components );
unique_bootstrap_components = int_vector_size( bootstrap_components );
int_vector_free( bootstrap_components );
}
if (bootstrap_data->doCV) {
const bool_vector_type * ens_mask = NULL;
cv_enkf_init_update( bootstrap_data->cv_enkf_data , ens_mask , S_resampled , R , dObs , E , D);
cv_enkf_initX( bootstrap_data->cv_enkf_data , X , A_resampled , S_resampled , R , dObs , E , D);
} else
std_enkf_initX(bootstrap_data->std_enkf_data , X , NULL , S_resampled,R, dObs, E,D );
matrix_inplace_matmul_mt1( A_resampled , X , num_cpu_threads );
matrix_inplace_add( A_resampled , A0 );
matrix_copy_column( A , A_resampled, ensemble_members_loop, ensemble_members_loop);
}
}
}
free_iens_resample( iens_resample , ens_size);
matrix_free( X );
matrix_free( S_resampled );
matrix_free( A_resampled );
matrix_free( A0 );
}
}
/**
Will not respect strides - that is considered low level data
layout.
*/
static matrix_type * matrix_alloc_copy__( const matrix_type * src , bool safe_mode) {
matrix_type * copy = matrix_alloc__( matrix_get_rows( src ), matrix_get_columns( src ) , safe_mode);
if (copy != NULL)
matrix_assign(copy , src);
return copy;
}
double matrix_row_column_dot_product(const matrix_type * m1 , int row1 , const matrix_type * m2 , int col2) {
if (m1->columns != m2->rows)
util_abort("%s: size mismatch: m1:[%d,%d] m2:[%d,%d] \n",__func__ , matrix_get_rows( m1 ) , matrix_get_columns( m1 ) , matrix_get_rows( m2 ) , matrix_get_columns( m2 ));
{
int k;
double sum = 0;
for( k = 0; k < m1->columns; k++)
sum += m1->data[ GET_INDEX(m1 , row1 , k) ] * m2->data[ GET_INDEX(m2, k , col2) ];
return sum;
}
}
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);
}
matrix_type * matrix_alloc_matmul(const matrix_type * A, const matrix_type * B) {
matrix_type * C = matrix_alloc( matrix_get_rows( A ) , matrix_get_columns( B ));
matrix_matmul( C , A , B );
return C;
}
