refactor: rename and expand namespace

This commit is contained in:
Max Lübke 2022-08-17 11:58:18 +02:00
parent 46185571c0
commit bdd56bec82
6 changed files with 128 additions and 115 deletions

View File

@ -13,7 +13,9 @@
#include <type_traits>
#include <vector>
namespace Diffusion {
namespace tug {
namespace diffusion {
/*!
* Class implementing a solution for a 1/2/3D diffusion equation using backward
* euler.
@ -97,7 +99,8 @@ public:
*
* \return Time in seconds [s] used to simulate one iteration.
*/
auto simulate(double *c, double *alpha, const BTCSBoundaryCondition &bc)
auto simulate(double *c, double *alpha,
const tug::boundary_condition::BTCSBoundaryCondition &bc)
-> double;
/*!
@ -113,42 +116,43 @@ private:
typedef Eigen::Matrix<double, 1, Eigen::Dynamic, Eigen::RowMajor>
DVectorRowMajor;
static void simulate_base(DVectorRowMajor &c, const bc_tuple &bc_ghosts,
const bc_vec &bc_inner,
static void simulate_base(DVectorRowMajor &c,
const tug::boundary_condition::bc_tuple &bc_ghosts,
const tug::boundary_condition::bc_vec &bc_inner,
const DVectorRowMajor &alpha, double dx,
double time_step, int size,
const DVectorRowMajor &d_ortho);
void simulate1D(Eigen::Map<DVectorRowMajor> &c,
Eigen::Map<const DVectorRowMajor> &alpha,
const BTCSBoundaryCondition &bc);
const tug::boundary_condition::BTCSBoundaryCondition &bc);
void simulate2D(Eigen::Map<DMatrixRowMajor> &c,
Eigen::Map<const DMatrixRowMajor> &alpha,
const BTCSBoundaryCondition &bc);
const tug::boundary_condition::BTCSBoundaryCondition &bc);
static auto calc_d_ortho(const DMatrixRowMajor &c,
const DMatrixRowMajor &alpha,
const BTCSBoundaryCondition &bc, bool transposed,
double time_step, double dx) -> DMatrixRowMajor;
static auto
calc_d_ortho(const DMatrixRowMajor &c, const DMatrixRowMajor &alpha,
const tug::boundary_condition::BTCSBoundaryCondition &bc,
bool transposed, double time_step, double dx) -> DMatrixRowMajor;
static void fillMatrixFromRow(Eigen::SparseMatrix<double> &A_matrix,
const DVectorRowMajor &alpha,
const bc_vec &bc_inner, int size, double dx,
double time_step);
const tug::boundary_condition::bc_vec &bc_inner,
int size, double dx, double time_step);
static void fillVectorFromRow(Eigen::VectorXd &b_vector,
const DVectorRowMajor &c,
static void
fillVectorFromRow(Eigen::VectorXd &b_vector, const DVectorRowMajor &c,
const DVectorRowMajor &alpha,
const bc_tuple &bc_ghosts,
const bc_vec &bc_inner,
const DVectorRowMajor &d_ortho, int size,
double dx, double time_step);
const tug::boundary_condition::bc_tuple &bc_ghosts,
const tug::boundary_condition::bc_vec &bc_inner,
const DVectorRowMajor &d_ortho, int size, double dx,
double time_step);
void simulate3D(std::vector<double> &c);
inline static auto getBCFromFlux(Diffusion::boundary_condition bc,
double neighbor_c, double neighbor_alpha)
-> double;
inline static auto
getBCFromFlux(tug::boundary_condition::boundary_condition bc,
double neighbor_c, double neighbor_alpha) -> double;
void updateInternals();
@ -159,5 +163,6 @@ private:
std::vector<double> domain_size;
std::vector<double> deltas;
};
} // namespace Diffusion
} // namespace diffusion
} // namespace tug
#endif // BTCSDIFFUSION_H_

View File

@ -9,7 +9,8 @@
typedef uint8_t bctype;
namespace Diffusion {
namespace tug {
namespace boundary_condition {
enum {
BC_TYPE_CLOSED, /**< Defines a closed/Neumann boundary condition. */
@ -259,6 +260,6 @@ public:
}
};
} // namespace Diffusion
} // namespace boundary_condition
} // namespace tug
#endif // BOUNDARYCONDITION_H_

View File

@ -8,7 +8,7 @@
constexpr uint8_t DIM_1D = 2;
constexpr uint8_t DIM_2D = 4;
Diffusion::BTCSBoundaryCondition::BTCSBoundaryCondition(int x) {
tug::boundary_condition::BTCSBoundaryCondition::BTCSBoundaryCondition(int x) {
this->bc_internal.resize(DIM_1D, {0, 0});
this->special_cells.resize(x, {BC_UNSET, 0});
this->dim = 1;
@ -21,7 +21,8 @@ Diffusion::BTCSBoundaryCondition::BTCSBoundaryCondition(int x) {
this->maxindex = x - 1;
}
Diffusion::BTCSBoundaryCondition::BTCSBoundaryCondition(int x, int y) {
tug::boundary_condition::BTCSBoundaryCondition::BTCSBoundaryCondition(int x,
int y) {
this->maxsize = (x >= y ? x : y);
this->bc_internal.resize(DIM_2D * maxsize, {0, 0});
this->special_cells.resize(x * y, {BC_UNSET, 0});
@ -33,8 +34,8 @@ Diffusion::BTCSBoundaryCondition::BTCSBoundaryCondition(int x, int y) {
this->maxindex = (x * y) - 1;
}
void Diffusion::BTCSBoundaryCondition::setSide(
uint8_t side, Diffusion::boundary_condition &input_bc) {
void tug::boundary_condition::BTCSBoundaryCondition::setSide(
uint8_t side, tug::boundary_condition::boundary_condition &input_bc) {
if (this->dim == 1) {
throw_invalid_argument("setSide requires at least a 2D grid");
}
@ -42,8 +43,8 @@ void Diffusion::BTCSBoundaryCondition::setSide(
throw_out_of_range("Invalid range for 2D grid");
}
uint32_t size =
(side == Diffusion::BC_SIDE_LEFT || side == Diffusion::BC_SIDE_RIGHT
uint32_t size = (side == tug::boundary_condition::BC_SIDE_LEFT ||
side == tug::boundary_condition::BC_SIDE_RIGHT
? this->sizes[X_DIM]
: this->sizes[Y_DIM]);
@ -52,8 +53,9 @@ void Diffusion::BTCSBoundaryCondition::setSide(
}
}
void Diffusion::BTCSBoundaryCondition::setSide(
uint8_t side, std::vector<Diffusion::boundary_condition> &input_bc) {
void tug::boundary_condition::BTCSBoundaryCondition::setSide(
uint8_t side,
std::vector<tug::boundary_condition::boundary_condition> &input_bc) {
if (this->dim == 1) {
throw_invalid_argument("setSide requires at least a 2D grid");
}
@ -61,8 +63,8 @@ void Diffusion::BTCSBoundaryCondition::setSide(
throw_out_of_range("Invalid range for 2D grid");
}
uint32_t size =
(side == Diffusion::BC_SIDE_LEFT || side == Diffusion::BC_SIDE_RIGHT
uint32_t size = (side == tug::boundary_condition::BC_SIDE_LEFT ||
side == tug::boundary_condition::BC_SIDE_RIGHT
? this->sizes[X_DIM]
: this->sizes[Y_DIM]);
@ -75,8 +77,8 @@ void Diffusion::BTCSBoundaryCondition::setSide(
}
}
auto Diffusion::BTCSBoundaryCondition::getSide(uint8_t side)
-> std::vector<Diffusion::boundary_condition> {
auto tug::boundary_condition::BTCSBoundaryCondition::getSide(uint8_t side)
-> std::vector<tug::boundary_condition::boundary_condition> {
if (this->dim == 1) {
throw_invalid_argument("getSide requires at least a 2D grid");
}
@ -84,12 +86,12 @@ auto Diffusion::BTCSBoundaryCondition::getSide(uint8_t side)
throw_out_of_range("Invalid range for 2D grid");
}
uint32_t size =
(side == Diffusion::BC_SIDE_LEFT || side == Diffusion::BC_SIDE_RIGHT
uint32_t size = (side == tug::boundary_condition::BC_SIDE_LEFT ||
side == tug::boundary_condition::BC_SIDE_RIGHT
? this->sizes[X_DIM]
: this->sizes[Y_DIM]);
std::vector<Diffusion::boundary_condition> out(size);
std::vector<tug::boundary_condition::boundary_condition> out(size);
for (int i = 0; i < size; i++) {
out[i] = this->bc_internal[this->maxsize * side + i];
@ -98,8 +100,8 @@ auto Diffusion::BTCSBoundaryCondition::getSide(uint8_t side)
return out;
}
auto Diffusion::BTCSBoundaryCondition::col_boundary(uint32_t i) const
-> Diffusion::bc_tuple {
auto tug::boundary_condition::BTCSBoundaryCondition::col_boundary(
uint32_t i) const -> tug::boundary_condition::bc_tuple {
if (this->dim == 1) {
throw_invalid_argument("Access of column requires at least 2D grid");
}
@ -111,8 +113,8 @@ auto Diffusion::BTCSBoundaryCondition::col_boundary(uint32_t i) const
this->bc_internal[BC_SIDE_BOTTOM * this->maxsize + i]};
}
auto Diffusion::BTCSBoundaryCondition::row_boundary(uint32_t i) const
-> Diffusion::bc_tuple {
auto tug::boundary_condition::BTCSBoundaryCondition::row_boundary(
uint32_t i) const -> tug::boundary_condition::bc_tuple {
if (i >= this->sizes[X_DIM]) {
throw_out_of_range("Index out of range");
}
@ -121,7 +123,8 @@ auto Diffusion::BTCSBoundaryCondition::row_boundary(uint32_t i) const
this->bc_internal[BC_SIDE_RIGHT * this->maxsize + i]};
}
auto Diffusion::BTCSBoundaryCondition::getInnerRow(uint32_t i) const -> bc_vec {
auto tug::boundary_condition::BTCSBoundaryCondition::getInnerRow(
uint32_t i) const -> bc_vec {
if (i >= this->sizes[X_DIM]) {
throw_out_of_range("Index is out of range");
}
@ -134,7 +137,8 @@ auto Diffusion::BTCSBoundaryCondition::getInnerRow(uint32_t i) const -> bc_vec {
return row;
}
auto Diffusion::BTCSBoundaryCondition::getInnerCol(uint32_t i) const -> bc_vec {
auto tug::boundary_condition::BTCSBoundaryCondition::getInnerCol(
uint32_t i) const -> bc_vec {
if (this->dim != 2) {
throw_invalid_argument("getInnerCol is only applicable for 2D grids");
}

View File

@ -31,7 +31,7 @@ constexpr double DOUBLE_MACHINE_EPSILON = 1.93e-34;
constexpr int BTCS_MAX_DEP_PER_CELL = 3;
constexpr int BTCS_2D_DT_SIZE = 2;
Diffusion::BTCSDiffusion::BTCSDiffusion(unsigned int dim) : grid_dim(dim) {
tug::diffusion::BTCSDiffusion::BTCSDiffusion(unsigned int dim) : grid_dim(dim) {
grid_cells.resize(dim, 1);
domain_size.resize(dim, 1);
@ -40,7 +40,7 @@ Diffusion::BTCSDiffusion::BTCSDiffusion(unsigned int dim) : grid_dim(dim) {
this->time_step = 0;
}
void Diffusion::BTCSDiffusion::setXDimensions(double domain_size,
void tug::diffusion::BTCSDiffusion::setXDimensions(double domain_size,
unsigned int n_grid_cells) {
this->domain_size[0] = domain_size;
this->grid_cells[0] = n_grid_cells;
@ -48,7 +48,7 @@ void Diffusion::BTCSDiffusion::setXDimensions(double domain_size,
updateInternals();
}
void Diffusion::BTCSDiffusion::setYDimensions(double domain_size,
void tug::diffusion::BTCSDiffusion::setYDimensions(double domain_size,
unsigned int n_grid_cells) {
this->domain_size[1] = domain_size;
this->grid_cells[1] = n_grid_cells;
@ -56,7 +56,7 @@ void Diffusion::BTCSDiffusion::setYDimensions(double domain_size,
updateInternals();
}
void Diffusion::BTCSDiffusion::setZDimensions(double domain_size,
void tug::diffusion::BTCSDiffusion::setZDimensions(double domain_size,
unsigned int n_grid_cells) {
this->domain_size[2] = domain_size;
this->grid_cells[2] = n_grid_cells;
@ -64,34 +64,35 @@ void Diffusion::BTCSDiffusion::setZDimensions(double domain_size,
updateInternals();
}
auto Diffusion::BTCSDiffusion::getXGridCellsN() -> unsigned int {
auto tug::diffusion::BTCSDiffusion::getXGridCellsN() -> unsigned int {
return this->grid_cells[0];
}
auto Diffusion::BTCSDiffusion::getYGridCellsN() -> unsigned int {
auto tug::diffusion::BTCSDiffusion::getYGridCellsN() -> unsigned int {
return this->grid_cells[1];
}
auto Diffusion::BTCSDiffusion::getZGridCellsN() -> unsigned int {
auto tug::diffusion::BTCSDiffusion::getZGridCellsN() -> unsigned int {
return this->grid_cells[2];
}
auto Diffusion::BTCSDiffusion::getXDomainSize() -> double {
auto tug::diffusion::BTCSDiffusion::getXDomainSize() -> double {
return this->domain_size[0];
}
auto Diffusion::BTCSDiffusion::getYDomainSize() -> double {
auto tug::diffusion::BTCSDiffusion::getYDomainSize() -> double {
return this->domain_size[1];
}
auto Diffusion::BTCSDiffusion::getZDomainSize() -> double {
auto tug::diffusion::BTCSDiffusion::getZDomainSize() -> double {
return this->domain_size[2];
}
void Diffusion::BTCSDiffusion::updateInternals() {
void tug::diffusion::BTCSDiffusion::updateInternals() {
for (int i = 0; i < grid_dim; i++) {
deltas[i] = (double)domain_size[i] / grid_cells[i];
}
}
void Diffusion::BTCSDiffusion::simulate_base(
DVectorRowMajor &c, const Diffusion::bc_tuple &bc_ghosts,
const Diffusion::bc_vec &bc_inner, const DVectorRowMajor &alpha, double dx,
double time_step, int size, const DVectorRowMajor &d_ortho) {
void tug::diffusion::BTCSDiffusion::simulate_base(
DVectorRowMajor &c, const tug::boundary_condition::bc_tuple &bc_ghosts,
const tug::boundary_condition::bc_vec &bc_inner,
const DVectorRowMajor &alpha, double dx, double time_step, int size,
const DVectorRowMajor &d_ortho) {
Eigen::SparseMatrix<double> A_matrix;
Eigen::VectorXd b_vector;
@ -119,9 +120,9 @@ void Diffusion::BTCSDiffusion::simulate_base(
c = x_vector.segment(1, size);
}
void Diffusion::BTCSDiffusion::simulate1D(
void tug::diffusion::BTCSDiffusion::simulate1D(
Eigen::Map<DVectorRowMajor> &c, Eigen::Map<const DVectorRowMajor> &alpha,
const Diffusion::BTCSBoundaryCondition &bc) {
const tug::boundary_condition::BTCSBoundaryCondition &bc) {
int size = this->grid_cells[0];
double dx = this->deltas[0];
@ -135,9 +136,9 @@ void Diffusion::BTCSDiffusion::simulate1D(
c.row(0) << input_field;
}
void Diffusion::BTCSDiffusion::simulate2D(
void tug::diffusion::BTCSDiffusion::simulate2D(
Eigen::Map<DMatrixRowMajor> &c, Eigen::Map<const DMatrixRowMajor> &alpha,
const Diffusion::BTCSBoundaryCondition &bc) {
const tug::boundary_condition::BTCSBoundaryCondition &bc) {
int n_rows = this->grid_cells[1];
int n_cols = this->grid_cells[0];
@ -169,15 +170,15 @@ void Diffusion::BTCSDiffusion::simulate2D(
}
}
auto Diffusion::BTCSDiffusion::calc_d_ortho(
auto tug::diffusion::BTCSDiffusion::calc_d_ortho(
const DMatrixRowMajor &c, const DMatrixRowMajor &alpha,
const Diffusion::BTCSBoundaryCondition &bc, bool transposed,
const tug::boundary_condition::BTCSBoundaryCondition &bc, bool transposed,
double time_step, double dx) -> DMatrixRowMajor {
uint8_t upper =
(transposed ? Diffusion::BC_SIDE_LEFT : Diffusion::BC_SIDE_TOP);
uint8_t lower =
(transposed ? Diffusion::BC_SIDE_RIGHT : Diffusion::BC_SIDE_BOTTOM);
uint8_t upper = (transposed ? tug::boundary_condition::BC_SIDE_LEFT
: tug::boundary_condition::BC_SIDE_TOP);
uint8_t lower = (transposed ? tug::boundary_condition::BC_SIDE_RIGHT
: tug::boundary_condition::BC_SIDE_BOTTOM);
int n_rows = c.rows();
int n_cols = c.cols();
@ -188,10 +189,10 @@ auto Diffusion::BTCSDiffusion::calc_d_ortho(
// first, iterate over first row
for (int j = 0; j < n_cols; j++) {
boundary_condition tmp_bc = bc(upper, j);
tug::boundary_condition::boundary_condition tmp_bc = bc(upper, j);
double sy = (time_step * alpha(0, j)) / (dx * dx);
y_values[0] = (tmp_bc.type == Diffusion::BC_TYPE_CONSTANT
y_values[0] = (tmp_bc.type == tug::boundary_condition::BC_TYPE_CONSTANT
? tmp_bc.value
: getBCFromFlux(tmp_bc, c(0, j), alpha(0, j)));
y_values[1] = c(0, j);
@ -218,12 +219,12 @@ auto Diffusion::BTCSDiffusion::calc_d_ortho(
// and finally over last row
for (int j = 0; j < n_cols; j++) {
boundary_condition tmp_bc = bc(lower, j);
tug::boundary_condition::boundary_condition tmp_bc = bc(lower, j);
double sy = (time_step * alpha(end, j)) / (dx * dx);
y_values[0] = c(end - 1, j);
y_values[1] = c(end, j);
y_values[2] = (tmp_bc.type == Diffusion::BC_TYPE_CONSTANT
y_values[2] = (tmp_bc.type == tug::boundary_condition::BC_TYPE_CONSTANT
? tmp_bc.value
: getBCFromFlux(tmp_bc, c(end, j), alpha(end, j)));
@ -233,9 +234,10 @@ auto Diffusion::BTCSDiffusion::calc_d_ortho(
return d_ortho;
}
void Diffusion::BTCSDiffusion::fillMatrixFromRow(
void tug::diffusion::BTCSDiffusion::fillMatrixFromRow(
Eigen::SparseMatrix<double> &A_matrix, const DVectorRowMajor &alpha,
const Diffusion::bc_vec &bc_inner, int size, double dx, double time_step) {
const tug::boundary_condition::bc_vec &bc_inner, int size, double dx,
double time_step) {
double sx = 0;
@ -243,8 +245,8 @@ void Diffusion::BTCSDiffusion::fillMatrixFromRow(
A_matrix.insert(0, 0) = 1;
if (bc_inner[0].type != BC_UNSET) {
if (bc_inner[0].type != BC_TYPE_CONSTANT) {
if (bc_inner[0].type != tug::boundary_condition::BC_UNSET) {
if (bc_inner[0].type != tug::boundary_condition::BC_TYPE_CONSTANT) {
throw_invalid_argument("Inner boundary conditions with other type than "
"BC_TYPE_CONSTANT are currently not supported.");
}
@ -257,8 +259,8 @@ void Diffusion::BTCSDiffusion::fillMatrixFromRow(
}
for (int j = 2, k = j - 1; k < size - 1; j++, k++) {
if (bc_inner[k].type != BC_UNSET) {
if (bc_inner[k].type != BC_TYPE_CONSTANT) {
if (bc_inner[k].type != tug::boundary_condition::BC_UNSET) {
if (bc_inner[k].type != tug::boundary_condition::BC_TYPE_CONSTANT) {
throw_invalid_argument("Inner boundary conditions with other type than "
"BC_TYPE_CONSTANT are currently not supported.");
}
@ -272,8 +274,8 @@ void Diffusion::BTCSDiffusion::fillMatrixFromRow(
A_matrix.insert(j, (j + 1)) = sx;
}
if (bc_inner[size - 1].type != BC_UNSET) {
if (bc_inner[size - 1].type != BC_TYPE_CONSTANT) {
if (bc_inner[size - 1].type != tug::boundary_condition::BC_UNSET) {
if (bc_inner[size - 1].type != tug::boundary_condition::BC_TYPE_CONSTANT) {
throw_invalid_argument("Inner boundary conditions with other type than "
"BC_TYPE_CONSTANT are currently not supported.");
}
@ -288,23 +290,24 @@ void Diffusion::BTCSDiffusion::fillMatrixFromRow(
A_matrix.insert(A_size - 1, A_size - 1) = 1;
}
void Diffusion::BTCSDiffusion::fillVectorFromRow(
void tug::diffusion::BTCSDiffusion::fillVectorFromRow(
Eigen::VectorXd &b_vector, const DVectorRowMajor &c,
const DVectorRowMajor &alpha, const bc_tuple &bc,
const Diffusion::bc_vec &bc_inner, const DVectorRowMajor &d_ortho, int size,
double dx, double time_step) {
const DVectorRowMajor &alpha, const tug::boundary_condition::bc_tuple &bc,
const tug::boundary_condition::bc_vec &bc_inner,
const DVectorRowMajor &d_ortho, int size, double dx, double time_step) {
Diffusion::boundary_condition left = bc[0];
Diffusion::boundary_condition right = bc[1];
tug::boundary_condition::boundary_condition left = bc[0];
tug::boundary_condition::boundary_condition right = bc[1];
bool left_constant = (left.type == Diffusion::BC_TYPE_CONSTANT);
bool right_constant = (right.type == Diffusion::BC_TYPE_CONSTANT);
bool left_constant = (left.type == tug::boundary_condition::BC_TYPE_CONSTANT);
bool right_constant =
(right.type == tug::boundary_condition::BC_TYPE_CONSTANT);
int b_size = b_vector.size();
for (int j = 0; j < size; j++) {
if (bc_inner[j].type != BC_UNSET) {
if (bc_inner[j].type != BC_TYPE_CONSTANT)
if (bc_inner[j].type != tug::boundary_condition::BC_UNSET) {
if (bc_inner[j].type != tug::boundary_condition::BC_TYPE_CONSTANT)
throw_invalid_argument("Inner boundary conditions with other type than "
"BC_TYPE_CONSTANT are currently not supported.");
b_vector[j + 1] = bc_inner[j].value;
@ -323,13 +326,13 @@ void Diffusion::BTCSDiffusion::fillVectorFromRow(
: getBCFromFlux(right, c[size - 1], alpha[size - 1]));
}
void Diffusion::BTCSDiffusion::setTimestep(double time_step) {
void tug::diffusion::BTCSDiffusion::setTimestep(double time_step) {
this->time_step = time_step;
}
auto Diffusion::BTCSDiffusion::simulate(
double *c, double *alpha, const Diffusion::BTCSBoundaryCondition &bc)
-> double {
auto tug::diffusion::BTCSDiffusion::simulate(
double *c, double *alpha,
const tug::boundary_condition::BTCSBoundaryCondition &bc) -> double {
std::chrono::high_resolution_clock::time_point start =
std::chrono::high_resolution_clock::now();
@ -359,16 +362,15 @@ auto Diffusion::BTCSDiffusion::simulate(
return duration.count();
}
inline auto Diffusion::BTCSDiffusion::getBCFromFlux(boundary_condition bc,
double neighbor_c,
double neighbor_alpha)
-> double {
inline auto tug::diffusion::BTCSDiffusion::getBCFromFlux(
tug::boundary_condition::boundary_condition bc, double neighbor_c,
double neighbor_alpha) -> double {
double val = 0;
if (bc.type == Diffusion::BC_TYPE_CLOSED) {
if (bc.type == tug::boundary_condition::BC_TYPE_CLOSED) {
val = neighbor_c;
} else if (bc.type == Diffusion::BC_TYPE_FLUX) {
} else if (bc.type == tug::boundary_condition::BC_TYPE_FLUX) {
// TODO
// val = bc[index].value;
} else {

View File

@ -1,7 +1,7 @@
#include <grid/BTCSBoundaryCondition.hpp>
#include <doctest/doctest.h>
using namespace Diffusion;
using namespace tug::boundary_condition;
#define BC_CONST_VALUE 1e-5

View File

@ -4,7 +4,8 @@
#include <grid/BTCSBoundaryCondition.hpp>
#include <vector>
using namespace Diffusion;
using namespace tug::boundary_condition;
using namespace tug::diffusion;
#define DIMENSION 2
#define N 51