Flow123d
release_3.0.0-863-g23f23ed
|
#include <balance.hh>
Classes | |
class | Quantity |
Public Types | |
enum | OutputFormat { legacy, txt, gnuplot } |
Public Member Functions | |
Balance (const std::string &file_prefix, const Mesh *mesh) | |
~Balance () | |
void | init_from_input (const Input::Record &in_rec, TimeGovernor &tg) |
void | units (const UnitSI &unit) |
Setter for units of conserved quantities. More... | |
bool | cumulative () const |
Getter for cumulative_. More... | |
unsigned int | add_quantity (const string &name) |
std::vector< unsigned int > | add_quantities (const std::vector< string > &names) |
void | allocate (unsigned int n_loc_dofs, unsigned int max_dofs_per_boundary) |
bool | is_current () |
Returns true if the current time step is marked for the balance output. More... | |
void | start_mass_assembly (unsigned int quantity_idx) |
void | start_mass_assembly (std::vector< unsigned int > q_idx_vec) |
Variant of the start_mass_assembly() method for a set of quantities. More... | |
void | start_flux_assembly (unsigned int quantity_idx) |
void | start_flux_assembly (std::vector< unsigned int > q_idx_vec) |
Variant of the start_flux_assembly() method for a set of quantities. More... | |
void | start_source_assembly (unsigned int quantity_idx) |
void | start_source_assembly (std::vector< unsigned int > q_idx_vec) |
Variant of the start_source_assembly() method for a set of quantities. More... | |
void | add_mass_matrix_values (unsigned int quantity_idx, unsigned int region_idx, const std::vector< LongIdx > &dof_indices, const std::vector< double > &values) |
void | add_flux_matrix_values (unsigned int quantity_idx, unsigned int boundary_idx, const std::vector< LongIdx > &dof_indices, const std::vector< double > &values) |
void | add_source_matrix_values (unsigned int quantity_idx, unsigned int region_idx, const std::vector< LongIdx > &dof_indices, const std::vector< double > &values) |
void | add_mass_vec_value (unsigned int quantity_idx, unsigned int region_idx, double value) |
void | add_flux_vec_value (unsigned int quantity_idx, unsigned int boundary_idx, double value) |
void | add_source_vec_values (unsigned int quantity_idx, unsigned int region_idx, const std::vector< LongIdx > &dof_values, const std::vector< double > &values) |
void | finish_mass_assembly (unsigned int quantity_idx) |
This method must be called after assembling the matrix for computing mass. More... | |
void | finish_mass_assembly (std::vector< unsigned int > q_idx_vec) |
Variant of the finish_mass_assembly() method for a set of quantities. More... | |
void | finish_flux_assembly (unsigned int quantity_idx) |
This method must be called after assembling the matrix and vector for computing flux. More... | |
void | finish_flux_assembly (std::vector< unsigned int > q_idx_vec) |
Variant of the finish_flux_assembly() method for a set of quantities. More... | |
void | finish_source_assembly (unsigned int quantity_idx) |
This method must be called after assembling the matrix and vectors for computing source. More... | |
void | finish_source_assembly (std::vector< unsigned int > q_idx_vec) |
Variant of the finish_source_assembly() method for a set of quantities. More... | |
void | calculate_cumulative (unsigned int quantity_idx, const Vec &solution) |
void | calculate_mass (unsigned int quantity_idx, const Vec &solution, vector< double > &output_array) |
void | calculate_instant (unsigned int quantity_idx, const Vec &solution) |
void | add_cumulative_source (unsigned int quantity_idx, double source) |
void | output () |
Perform output to file for given time instant. More... | |
Static Public Member Functions | |
static const Input::Type::Record & | get_input_type () |
Main balance input record type. More... | |
static const Input::Type::Selection & | get_format_selection_input_type () |
Input selection for file format. More... | |
static void | set_yaml_output () |
Set global variable to output balance files into YAML format (in addition to the table format). More... | |
Private Member Functions | |
void | lazy_initialize () |
void | output_legacy (double time) |
Perform output in old format (for compatibility) More... | |
void | output_csv (double time, char delimiter, const std::string &comment_string, unsigned int repeat=0) |
Perform output in csv format. More... | |
void | output_yaml (double time) |
Perform output in yaml format. More... | |
std::string | csv_zero_vals (unsigned int cnt, char delimiter) |
Return part of output represented by zero values. Count of zero values is given by cnt parameter. More... | |
void | format_csv_output_header (char delimiter, const std::string &comment_string) |
Print output header. More... | |
std::string | format_csv_val (std::string val, char delimiter, bool initial=false) |
Format string value of csv output. Wrap string into quotes and if delimiter is space, align text to column. More... | |
std::string | format_csv_val (double val, char delimiter, bool initial=false) |
Format double value of csv output. If delimiter is space, align text to column. More... | |
Private Attributes | |
unsigned int | n_loc_dofs_ |
Allocation parameters. Set by the allocate method used in the lazy_initialize. More... | |
unsigned int | max_dofs_per_boundary_ |
std::string | file_prefix_ |
Save prefix passed in in constructor. More... | |
FilePath | balance_output_file_ |
File path for output_ stream. More... | |
ofstream | output_ |
Handle for file for output in given OutputFormat of balance and total fluxes over individual regions and region sets. More... | |
ofstream | output_yaml_ |
OutputFormat | output_format_ |
Format of output file. More... | |
std::vector< Quantity > | quantities_ |
Names of conserved quantities. More... | |
const Mesh * | mesh_ |
UnitSI | units_ |
Units of conserved quantities. More... | |
Mat * | region_mass_matrix_ |
Matrices for calculation of mass (n_dofs x n_bulk_regions). More... | |
Mat * | be_flux_matrix_ |
Matrices for calculation of flux (n_boundary_edges x n_dofs). More... | |
Mat * | region_source_matrix_ |
Matrices for calculation of source (n_dofs x n_bulk_regions). More... | |
Mat * | region_source_rhs_ |
Matrices for calculation of signed source (n_dofs x n_bulk_regions). More... | |
Vec * | be_flux_vec_ |
Vectors for calculation of flux (n_boundary_edges). More... | |
Vec * | region_mass_vec_ |
Vectors for calculation of mass (n_bulk_regions). More... | |
Vec * | region_source_vec_ |
Vectors for calculation of source (n_bulk_regions). More... | |
Mat | region_be_matrix_ |
Vec | ones_ |
auxiliary vectors for summation of matrix columns More... | |
Vec | ones_be_ |
std::vector< unsigned int > | be_regions_ |
Number of boundary region for each local boundary edge. More... | |
int | be_offset_ |
Offset for local part of vector of boundary edges. More... | |
std::vector< std::vector< double > > | fluxes_ |
std::vector< std::vector< double > > | fluxes_in_ |
std::vector< std::vector< double > > | fluxes_out_ |
std::vector< std::vector< double > > | masses_ |
std::vector< std::vector< double > > | sources_ |
std::vector< std::vector< double > > | sources_in_ |
std::vector< std::vector< double > > | sources_out_ |
std::vector< double > | sum_fluxes_ |
std::vector< double > | sum_fluxes_in_ |
std::vector< double > | sum_fluxes_out_ |
std::vector< double > | sum_masses_ |
std::vector< double > | sum_sources_ |
std::vector< double > | sum_sources_in_ |
std::vector< double > | sum_sources_out_ |
std::vector< double > | initial_mass_ |
std::vector< double > | integrated_sources_ |
std::vector< double > | integrated_fluxes_ |
std::vector< double > | increment_fluxes_ |
std::vector< double > | increment_sources_ |
double | last_time_ |
time of last calculated balance More... | |
TimeMark::Type | balance_output_type_ |
TimeMark type for balance output of particular equation. More... | |
TimeMark::Type | output_mark_type_ |
TimeMark type for output of particular equation. More... | |
bool | initial_ |
true before calculating the mass at initial time, otherwise false More... | |
bool | cumulative_ |
if true then cumulative balance is computed More... | |
bool | allocation_done_ |
true before allocating necessary internal structures (Petsc matrices etc.) More... | |
bool | balance_on_ |
If the balance is on. Balance is off in the case of no balance output time marks. More... | |
bool | add_output_times_ |
Add output time marks to balance output time marks. More... | |
int | rank_ |
MPI rank. More... | |
unsigned int | output_line_counter_ |
hold count of line printed into output_ More... | |
bool | output_yaml_header_ |
marks whether YAML output has printed header More... | |
Input::Record | input_record_ |
Record for current balance. More... | |
const TimeGovernor * | time_ |
Static Private Attributes | |
static const unsigned int | output_column_width = 20 |
Size of column in output (used if delimiter is space) More... | |
static bool | do_yaml_output_ = true |
Design of balance class - serves as storage and writer. Equations themselves call methods of Balance that add/modify mass, source and flux of various quantities and generate output.
One instance of Balance can handle several conservative quantities of the same type (e.g. mass of several substances or their phases).
The mass, flux and source are calculated as follows:
m(q,r) = ( M'(q) * solution + mv(q) )[r] f(q,r) = -( R' * ( F(q) * solution + fv(q) ) )[r] s(q,r) = ( S'(q) * solution + sv(q) )[r]
where M' stands for matrix transpose,
m(q,r)...mass of q-th substance in region r f(q,r)...incoming flux of q-th substance in region r s(q,r)...source of q-th substance in region r
and
M(q)...region_mass_matrix_ n_dofs x n_bulk_regions F(q)...be_flux_matrix_ n_boundary_edges x n_dofs S(q)...region_source_matrix_ n_dofs x n_bulk_regions SV(q)..region_source_rhs_ n_dofs x n_bulk_regions
mv(q)..region_mass_vec_ n_bulk_regions fv(q)..be_flux_vec_ n_boundary_edges sv(q)..region_source_vec_ n_bulk_regions R......region_be_matrix_ n_boundary_edges x n_boundary_regions
Remark: Matrix F and the vector fv are such that F*solution+fv produces outcoming fluxes per boundary edge. However we write to output incoming flux due to users' convention and consistently with input interface.
Note that it holds:
sv(q) = column sum of SV(q)
Except for that, we also provide information on positive/negative flux and source:
fp(q,r) = ( R' * EFP(q) )[r], EFP(q)[e] = max{ 0, ( F(q) * solution + fv(q) )[e] } fn(q,r) = ( R' * EFN(q) )[r], EFN(q)[e] = min{ 0, ( F(q) * solution + fv(q) )[e] } sp(q,r) = sum_{i in DOFS } max{ 0, ( S(q)[i,r] * solution[i] + SV(q)[i,r] ) } sn(q,r) = sum_{i in DOFS } min{ 0, ( S(q)[i,r] * solution[i] + SV(q)[i,r] ) }
where
fp(q,r)...positive (inward) flux of q-th quantity in region r fn(q,r)...negative (outward) flux of q-th quantity in region r sp(q,r)...positive source (spring) of q-th quantity in region r sn(q,r)...negative source (sink) of q-th quantity in region r
Remark: The matrix R is needed only for calculation of signed fluxes. The reason is that to determine sign, we decompose flux to sum of local contributions per each boundary element and check its sign. It is not possible to decompose flux using shape functions, since their normal derivatives may have any sign.
Output values (if not relevant, zero is supplied):
#time bulk_region quantity 0 0 0 mass source source_in source_out 0 0 0 #time boundary_region quantity flux flux_in flux_out 0 0 0 0 0 0 0 #time ALL quantity flux flux_in flux_out mass source source_in source_out integrated_flux integrated_source error
error = current_mass - (initial_mass + integrated_source - integrated_flux)
Definition at line 114 of file balance.hh.
Possible formats of output file.
Enumerator | |
---|---|
legacy |
legacy |
txt |
csv |
gnuplot |
gnuplot |
Definition at line 141 of file balance.hh.
Balance::Balance | ( | const std::string & | file_prefix, |
const Mesh * | mesh | ||
) |
Constructor.
file_prefix | Prefix of output file name. |
mesh | Mesh. |
Definition at line 84 of file balance.cc.
Balance::~Balance | ( | ) |
Destructor.
Definition at line 101 of file balance.cc.
void Balance::add_cumulative_source | ( | unsigned int | quantity_idx, |
double | source | ||
) |
Adds provided values to the cumulative sources.
quantity_idx | Index of quantity. |
sources | Sources per region. |
dt | Actual time step. |
Definition at line 587 of file balance.cc.
void Balance::add_flux_matrix_values | ( | unsigned int | quantity_idx, |
unsigned int | boundary_idx, | ||
const std::vector< LongIdx > & | dof_indices, | ||
const std::vector< double > & | values | ||
) |
Adds elements into matrix for computing (outgoing) flux.
quantity_idx | Index of quantity. |
boundary_idx | Local index of boundary edge. |
dof_indices | Dof indices to be added. |
values | Values to be added. |
The order of local boundary edges is given by traversing the local elements and their sides.
TODO: Think of less error-prone way of finding the local boundary index for a given Boundary object. It can be possibly done when we will have a boundary mesh.
Definition at line 503 of file balance.cc.
void Balance::add_flux_vec_value | ( | unsigned int | quantity_idx, |
unsigned int | boundary_idx, | ||
double | value | ||
) |
Adds element into vector for computing (outgoing) flux.
quantity_idx | Index of quantity. |
boundary_idx | Local index of boundary edge. |
value | Value to be added. |
For determining the local boundary index see add_flux_matrix_values.
Definition at line 553 of file balance.cc.
void Balance::add_mass_matrix_values | ( | unsigned int | quantity_idx, |
unsigned int | region_idx, | ||
const std::vector< LongIdx > & | dof_indices, | ||
const std::vector< double > & | values | ||
) |
Adds elements into matrix for computing mass.
quantity_idx | Index of quantity. |
region_idx | Index of bulk region. |
dof_indices | Dof indices to be added. |
values | Values to be added. |
Definition at line 483 of file balance.cc.
void Balance::add_mass_vec_value | ( | unsigned int | quantity_idx, |
unsigned int | region_idx, | ||
double | value | ||
) |
Adds element into vector for computing mass.
quantity_idx | Index of quantity. |
region_idx | Index of bulk region. |
value | Value to be added. |
Definition at line 542 of file balance.cc.
std::vector< unsigned int > Balance::add_quantities | ( | const std::vector< string > & | names | ) |
Define a set of conservative quantities.
names | List of quantities' names. |
Definition at line 177 of file balance.cc.
unsigned int Balance::add_quantity | ( | const string & | name | ) |
Define a single conservative quantity.
name | Name of the quantity. |
Definition at line 166 of file balance.cc.
void Balance::add_source_matrix_values | ( | unsigned int | quantity_idx, |
unsigned int | region_idx, | ||
const std::vector< LongIdx > & | dof_indices, | ||
const std::vector< double > & | values | ||
) |
Adds elements into matrix for computing source.
quantity_idx | Index of quantity. |
region_idx | Index of bulk region. |
dof_indices | Dof indices to be added. |
values | Values to be added. |
Definition at line 522 of file balance.cc.
void Balance::add_source_vec_values | ( | unsigned int | quantity_idx, |
unsigned int | region_idx, | ||
const std::vector< LongIdx > & | dof_values, | ||
const std::vector< double > & | values | ||
) |
Adds elements into vector for computing source.
quantity_idx | Index of quantity. |
region_idx | Index of bulk region. |
dof_indices | Dof indices to be added. |
values | Values to be added. |
Definition at line 567 of file balance.cc.
void Balance::allocate | ( | unsigned int | n_loc_dofs, |
unsigned int | max_dofs_per_boundary | ||
) |
Allocates matrices and vectors for balance.
n_loc_dofs | Number of solution dofs on the local process. |
max_dofs_per_boundary | Number of dofs contributing to one boundary edge. |
Definition at line 186 of file balance.cc.
void Balance::calculate_cumulative | ( | unsigned int | quantity_idx, |
const Vec & | solution | ||
) |
Updates cumulative quantities for balance. This method can be called in substeps even if no output is generated. It calculates the sum of source and sum of (incoming) flux over time interval.
quantity_idx | Index of quantity. |
solution | Solution vector. |
Definition at line 597 of file balance.cc.
void Balance::calculate_instant | ( | unsigned int | quantity_idx, |
const Vec & | solution | ||
) |
Calculates actual mass, incoming flux and source.
quantity_idx | Index of quantity. |
solution | Solution vector. |
Definition at line 684 of file balance.cc.
void Balance::calculate_mass | ( | unsigned int | quantity_idx, |
const Vec & | solution, | ||
vector< double > & | output_array | ||
) |
Calculates actual mass and save it to given vector.
quantity_idx | Index of quantity. |
solution | Solution vector. |
output_array | Vector of output masses per region. |
Definition at line 659 of file balance.cc.
|
private |
Return part of output represented by zero values. Count of zero values is given by cnt parameter.
Definition at line 1060 of file balance.cc.
|
inline |
Getter for cumulative_.
Definition at line 185 of file balance.hh.
void Balance::finish_flux_assembly | ( | unsigned int | quantity_idx | ) |
This method must be called after assembling the matrix and vector for computing flux.
Definition at line 457 of file balance.cc.
|
inline |
Variant of the finish_flux_assembly() method for a set of quantities.
Definition at line 344 of file balance.hh.
void Balance::finish_mass_assembly | ( | unsigned int | quantity_idx | ) |
This method must be called after assembling the matrix for computing mass.
Definition at line 446 of file balance.cc.
|
inline |
Variant of the finish_mass_assembly() method for a set of quantities.
Definition at line 334 of file balance.hh.
void Balance::finish_source_assembly | ( | unsigned int | quantity_idx | ) |
This method must be called after assembling the matrix and vectors for computing source.
Definition at line 468 of file balance.cc.
|
inline |
Variant of the finish_source_assembly() method for a set of quantities.
Definition at line 354 of file balance.hh.
|
private |
Print output header.
Definition at line 1149 of file balance.cc.
|
private |
Format string value of csv output. Wrap string into quotes and if delimiter is space, align text to column.
Definition at line 1176 of file balance.cc.
|
private |
Format double value of csv output. If delimiter is space, align text to column.
Definition at line 1193 of file balance.cc.
|
static |
Input selection for file format.
Definition at line 40 of file balance.cc.
|
static |
Main balance input record type.
Definition at line 48 of file balance.cc.
void Balance::init_from_input | ( | const Input::Record & | in_rec, |
TimeGovernor & | tg | ||
) |
Initialize the balance object according to the input. The balance output time marks are set according to the already existing output time marks of the same equation. So, this method must be called after Output::
in_rec | Input record of balance. |
tg | TimeGovernor of the equation. We need just equation mark type. |
Definition at line 133 of file balance.cc.
bool Balance::is_current | ( | ) |
Returns true if the current time step is marked for the balance output.
Definition at line 407 of file balance.cc.
|
private |
Postponed allocation and initialization to allow calling setters in arbitrary order. In particular we need to perform adding of output times after the output time marks are set. On the other hand we need to read the input before we make the allocation.
The initialization is done during the first call of any start_*_assembly method.
Definition at line 194 of file balance.cc.
void Balance::output | ( | ) |
Perform output to file for given time instant.
Definition at line 781 of file balance.cc.
|
private |
Perform output in csv format.
Definition at line 1068 of file balance.cc.
|
private |
Perform output in old format (for compatibility)
Definition at line 915 of file balance.cc.
|
private |
Perform output in yaml format.
Definition at line 1206 of file balance.cc.
|
static |
Set global variable to output balance files into YAML format (in addition to the table format).
Definition at line 61 of file balance.cc.
void Balance::start_flux_assembly | ( | unsigned int | quantity_idx | ) |
This method must be called before assembling the matrix and vector for fluxes. It actually erases the matrix and vector.
Definition at line 427 of file balance.cc.
|
inline |
Variant of the start_flux_assembly() method for a set of quantities.
Definition at line 234 of file balance.hh.
void Balance::start_mass_assembly | ( | unsigned int | quantity_idx | ) |
This method must be called before assembling the matrix for computing mass. It actually erases the matrix.
Definition at line 418 of file balance.cc.
|
inline |
Variant of the start_mass_assembly() method for a set of quantities.
Definition at line 221 of file balance.hh.
void Balance::start_source_assembly | ( | unsigned int | quantity_idx | ) |
This method must be called before assembling the matrix and vectors for sources. It actually erases the matrix and vectors.
Definition at line 436 of file balance.cc.
|
inline |
Variant of the start_source_assembly() method for a set of quantities.
Definition at line 247 of file balance.hh.
void Balance::units | ( | const UnitSI & | unit | ) |
Setter for units of conserved quantities.
Definition at line 158 of file balance.cc.
|
private |
Add output time marks to balance output time marks.
Definition at line 551 of file balance.hh.
|
private |
true before allocating necessary internal structures (Petsc matrices etc.)
Definition at line 545 of file balance.hh.
|
private |
If the balance is on. Balance is off in the case of no balance output time marks.
Definition at line 548 of file balance.hh.
|
private |
File path for output_ stream.
Definition at line 446 of file balance.hh.
|
private |
TimeMark type for balance output of particular equation.
Definition at line 533 of file balance.hh.
|
private |
Matrices for calculation of flux (n_boundary_edges x n_dofs).
Definition at line 470 of file balance.hh.
|
private |
Vectors for calculation of flux (n_boundary_edges).
Definition at line 479 of file balance.hh.
|
private |
Offset for local part of vector of boundary edges.
Definition at line 500 of file balance.hh.
|
private |
Number of boundary region for each local boundary edge.
Definition at line 497 of file balance.hh.
|
private |
if true then cumulative balance is computed
Definition at line 542 of file balance.hh.
|
staticprivate |
Definition at line 435 of file balance.hh.
|
private |
Save prefix passed in in constructor.
Definition at line 443 of file balance.hh.
|
private |
Definition at line 505 of file balance.hh.
|
private |
Definition at line 506 of file balance.hh.
|
private |
Definition at line 507 of file balance.hh.
|
private |
Definition at line 526 of file balance.hh.
|
private |
Definition at line 527 of file balance.hh.
|
private |
true before calculating the mass at initial time, otherwise false
Definition at line 539 of file balance.hh.
|
private |
Definition at line 521 of file balance.hh.
|
private |
Record for current balance.
Definition at line 564 of file balance.hh.
|
private |
Definition at line 525 of file balance.hh.
|
private |
Definition at line 524 of file balance.hh.
|
private |
time of last calculated balance
Definition at line 530 of file balance.hh.
|
private |
Definition at line 508 of file balance.hh.
|
private |
Definition at line 439 of file balance.hh.
|
private |
Definition at line 460 of file balance.hh.
|
private |
Allocation parameters. Set by the allocate method used in the lazy_initialize.
Definition at line 438 of file balance.hh.
|
private |
auxiliary vectors for summation of matrix columns
Definition at line 494 of file balance.hh.
|
private |
Definition at line 494 of file balance.hh.
|
private |
Handle for file for output in given OutputFormat of balance and total fluxes over individual regions and region sets.
Definition at line 449 of file balance.hh.
|
staticprivate |
Size of column in output (used if delimiter is space)
Definition at line 401 of file balance.hh.
|
private |
Format of output file.
Definition at line 455 of file balance.hh.
|
private |
hold count of line printed into output_
Definition at line 558 of file balance.hh.
|
private |
TimeMark type for output of particular equation.
Definition at line 536 of file balance.hh.
|
private |
Definition at line 452 of file balance.hh.
|
private |
marks whether YAML output has printed header
Definition at line 561 of file balance.hh.
|
private |
Names of conserved quantities.
Definition at line 458 of file balance.hh.
|
private |
MPI rank.
Definition at line 555 of file balance.hh.
|
private |
Auxiliary matrix for transfer of quantities between boundary edges and regions (n_boundary_edges x n_boundary_regions).
Definition at line 491 of file balance.hh.
|
private |
Matrices for calculation of mass (n_dofs x n_bulk_regions).
Definition at line 467 of file balance.hh.
|
private |
Vectors for calculation of mass (n_bulk_regions).
Definition at line 482 of file balance.hh.
|
private |
Matrices for calculation of source (n_dofs x n_bulk_regions).
Definition at line 473 of file balance.hh.
|
private |
Matrices for calculation of signed source (n_dofs x n_bulk_regions).
Definition at line 476 of file balance.hh.
|
private |
Vectors for calculation of source (n_bulk_regions).
Definition at line 485 of file balance.hh.
|
private |
Definition at line 509 of file balance.hh.
|
private |
Definition at line 510 of file balance.hh.
|
private |
Definition at line 511 of file balance.hh.
|
private |
Definition at line 514 of file balance.hh.
|
private |
Definition at line 515 of file balance.hh.
|
private |
Definition at line 516 of file balance.hh.
|
private |
Definition at line 517 of file balance.hh.
|
private |
Definition at line 518 of file balance.hh.
|
private |
Definition at line 519 of file balance.hh.
|
private |
Definition at line 520 of file balance.hh.
|
private |
Definition at line 566 of file balance.hh.
|
private |
Units of conserved quantities.
Definition at line 463 of file balance.hh.