void moveToConstReferenceNegatives() {
// No warning when actual move takes place.
MoveSemantics move_semantics;
callByValue(std::move(move_semantics));
callByRValueRef(std::move(move_semantics));
MoveSemantics other(std::move(move_semantics));
other = std::move(move_semantics);
// No warning if std::move() not used.
NoMoveSemantics no_move_semantics;
callByConstRef(no_move_semantics);
// No warning if instantiating a template.
templateFunction(no_move_semantics);
// No warning inside of macro expansions.
M3(NoMoveSemantics, no_move_semantics);
// No warning inside of macro expansion, even if the macro expansion is inside
// a lambda that is, in turn, an argument to a macro.
CALL([no_move_semantics] { M3(NoMoveSemantics, no_move_semantics); });
auto lambda = [] {};
auto lambda2 = std::move(lambda);
}
/* Adds an orientation observation to the "attitude profile matrix" B
*
* This is done with
* B += a * W * V'
* where
* a is the weight of the current measurment (how good it is, how often...)
* W is the observed vector
* V' is the (transposed) reference direction, that belongs to W.
*
* See Davenport's solution for Wabha's problem for more information
*/
void add_orientation_measurement(struct DoubleMat33 *B, struct Orientation_Measurement a)
{
M3(*B, 0, 0) += a.weight_of_the_measurement * a.measured_direction.x * a.reference_direction.x;
M3(*B, 0, 1) += a.weight_of_the_measurement * a.measured_direction.x * a.reference_direction.y;
M3(*B, 0, 2) += a.weight_of_the_measurement * a.measured_direction.x * a.reference_direction.z;
M3(*B, 1, 0) += a.weight_of_the_measurement * a.measured_direction.y * a.reference_direction.x;
M3(*B, 1, 1) += a.weight_of_the_measurement * a.measured_direction.y * a.reference_direction.y;
M3(*B, 1, 2) += a.weight_of_the_measurement * a.measured_direction.y * a.reference_direction.z;
M3(*B, 2, 0) += a.weight_of_the_measurement * a.measured_direction.z * a.reference_direction.x;
M3(*B, 2, 1) += a.weight_of_the_measurement * a.measured_direction.z * a.reference_direction.y;
M3(*B, 2, 2) += a.weight_of_the_measurement * a.measured_direction.z * a.reference_direction.z;
}
// =================================================
void DenseSubMatrix::left_multiply (const DenseMatrixBase& M2) {
// (*this) <- M2 * M3 Where: (*this) = (m x n), M2= (m x p), M3= (p x n)
// M3 is a simply a copy of *this
DenseSubMatrix M3(*this);
// Call the multiply function in the base class
this->multiply(*this, M2, M3);
}
int main()
{
vpMatrix M ;
vpMatrix M1(2,3) ;
vpMatrix M2(3,3) ;
vpMatrix M3(2,2) ;
std::cout << "** test matrix exception during multiplication" << std::endl;
try {
M = M1*M3 ;
}
catch (vpException &e) {
std::cout << "Catch an exception: " << e << std::endl;
}
std::cout << "** test matrix exception during addition" << std::endl;
try {
M = M1+M3 ;
}
catch (vpException &e) {
std::cout << "Catch an exception: " << e << std::endl;
}
}
static double
strikeyH0 (MagComp component, const fault_params *fault, const magnetic_params *mag, double xi, double et, double qq, double y, double z)
{
double val;
double h = mag->dcurier;
double qd = y * sd + (fault->fdepth - h) * cd;
double K2_val = K2 (component, 1.0, xi, et, qq);
double log_re_val = log_re (component, 1.0, xi, et, qq);
double J2_val = J2 (component, 1.0, xi, et, qq);
// double L2_val = L2 (component, 1.0, xi, et, qq);
double L2_val = L2 (component, 1.0, xi, et, qq) * cd; // todo: check this!
double M2_val = M2 (component, 1.0, xi, et, qq);
double M3_val = M3 (component, 1.0, xi, et, qq);
double M2y_val = M2y (component, 1.0, xi, et, qq);
double M2z_val = M2z (component, 1.0, xi, et, qq);
val = - (2.0 - alpha4) * K2_val
+ alpha4 * log_re_val * sd + alpha3 * J2_val
- alpha3 * (qd * M2_val + (z - h) * L2_val * sd)
- 2.0 * alpha4 * h * (M2_val * cd - L2_val * sd)
- 4.0 * alpha1 * h * L2_val * sd
+ 2.0 * alpha2 * h * M3_val * sd
+ 2.0 * alpha2 * h * ((qd + h * cd) * M2z_val - (z - 2.0 * h) * M2y_val * sd);
return val;
}
int main(int argc, char** argv) {
Manoscritto M1(0, "aaa", "aaa", 10),
M2(1, "bbb", "bbb", 10),
M3(3, "bbb", "bbb", 10);
Lettera L1(4, "aaa", "aaa", 10, "aaa", "aaa"),
L2(5, "bbb", "bbb", 10, "bbb", "bbb"),
L3=L1;
cout <<"Stampa normale:\n";
cout << M1 <<'\n'<< M2 <<'\n' << M3 <<"\n\n";
cout << L1 <<'\n'<< L2 <<'\n' << L3 ;
cout <<"\n\nStampa polimorfismo:\n";
Manoscritto * v[2];
v[0] = &M1;
v[1] = &L2;
for(int i=0; i<2; i++) {
v[i] -> visualizzaDati();
cout<<'\n';
}
cout <<"\n\nElenco:\n";
Elenco E1, E2;
E1.push(&M1);
E1.push(&M2);
E1.push(&L1);
E1.push(&L2);
E1.push(&M3);
E1.pop(0);
E1.stampa();
ofstream file;
file.open("./test.txt", ios::out);
if(!file) {
cout << "Errore file";
} else {
E1.memorizzaDati(file);
}
file.close();
cout <<"\n\nEccezione:\n";
try {
E2.push(&M1);
E2.push(&M1);
} catch (Duplicato e) {
cout << e.what() << endl;
}
}
double TtbarHypothesis::M3() const {
JetCollection jets;
jets.clear();
jets.push_back(jet1FromW);
jets.push_back(jet2FromW);
jets.push_back(leptonicBjet);
jets.push_back(hadronicBJet);
return M3(jets);
}
///////////////////////////////////////////////////////////////////////////////
// Ditto above, but for doubles
void m3dRotationMatrix33(M3DMatrix33d m, double angle, double x, double y, double z)
{
double mag, s, c;
double xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c;
s = sin(angle);
c = cos(angle);
mag = sqrt( x*x + y*y + z*z );
// Identity matrix
if (mag == 0.0) {
m3dLoadIdentity33(m);
return;
}
// Rotation matrix is normalized
x /= mag;
y /= mag;
z /= mag;
#define M3(row,col) m[col*3+row]
xx = x * x;
yy = y * y;
zz = z * z;
xy = x * y;
yz = y * z;
zx = z * x;
xs = x * s;
ys = y * s;
zs = z * s;
one_c = 1.0 - c;
M3(0,0) = (one_c * xx) + c;
M3(0,1) = (one_c * xy) - zs;
M3(0,2) = (one_c * zx) + ys;
M3(1,0) = (one_c * xy) + zs;
M3(1,1) = (one_c * yy) + c;
M3(1,2) = (one_c * yz) - xs;
M3(2,0) = (one_c * zx) - ys;
M3(2,1) = (one_c * yz) + xs;
M3(2,2) = (one_c * zz) + c;
#undef M3
}
SCMatrix operator-(const SCMatrix& M1,const SCMatrix& M2){
if (M1.Rows() != M2.Rows() || M1.Columns() != M2.Columns()){
cerr<<"Incompatible dimensions for matrix addition."<<endl;
exit(1);
}
SCMatrix M3(M1.Rows(),M1.Columns());
for (int i=0;i<M1.Rows();i++){
for (int j=0;j<M1.Columns();j++){
M3.data[i][j]=M1.data[i][j]-M2.data[i][j];
}
}
return M3;
}
static void
ggcm_mhd_diag_item_v_run(struct ggcm_mhd_diag_item *item,
struct mrc_io *io, struct mrc_fld *fld,
int diag_type, float plane)
{
struct ggcm_mhd *mhd = item->diag->mhd;
int bnd = fld->_nr_ghosts;
struct mrc_fld *fld_r = mrc_domain_fld_create(mhd->domain, bnd, "vx:vy:vz");
mrc_fld_set_type(fld_r, FLD_TYPE);
mrc_fld_setup(fld_r);
struct mrc_fld *r = mrc_fld_get_as(fld_r, FLD_TYPE);
struct mrc_fld *f = mrc_fld_get_as(fld, FLD_TYPE);
for (int p = 0; p < mrc_fld_nr_patches(fld); p++) {
mrc_fld_foreach(f, ix,iy,iz, bnd, bnd) {
mrc_fld_data_t rri = 1.f / RR_(f, ix,iy,iz, p);
M3(r, 0, ix,iy,iz, p) = rri * RVX_(f, ix,iy,iz, p);
M3(r, 1, ix,iy,iz, p) = rri * RVY_(f, ix,iy,iz, p);
M3(r, 2, ix,iy,iz, p) = rri * RVZ_(f, ix,iy,iz, p);
} mrc_fld_foreach_end;
}
int main (int narg, const char** argv) {
typedef Range<false> R;
typedef Range<true> CR;
Matrix<double> M1(10, 1), M2, M3(M1), M4(3, 4), M6(4, 3), M5(3, 4, 2), M7(3, 4, 2), M8, M9, M10, M11;
M1 = 0.0;
M2 = M1;
for (size_t i = 1; i < M1.Size(); ++i)
M1[i] = i;
for (size_t i = 1; i < M4.Size(); ++i)
M4[i] = i;
for (size_t i = 1; i < M5.Size(); ++i)
M5[i] = i;
M3(R(7,-2,2)) = M1(CR(2,4));
M6(R(3,-2,0),R(0,1)) = M4(CR(0,1),CR(1,2));
M7(R(2,-2,0),R(0,1),R(0,0)) = M5(CR(0,1),CR(1,2),CR(0,0));
M8 = M6(CR(1,-1,0),CR(1,2));
M6(R(0,1),R(1,2)) = M8;
M9 = M6(CR("1:-1:0"),CR("1:2"));
M10 = M6(CR("1:-1:0,1"),CR("1:2"));
M11 = M6(CR(),CR()) * M6(CR(),CR());
M11 = M6 * M6(CR(),CR());
std::cout << M3 << std::endl<< std::endl;
std::cout << M4 << std::endl<< std::endl;
std::cout << M6 << std::endl<< std::endl;
std::cout << M5 << std::endl<< std::endl;
std::cout << M7 << std::endl<< std::endl;
std::cout << M8 << std::endl<< std::endl;
std::cout << M9 << std::endl<< std::endl;
std::cout << M10 << std::endl<< std::endl;
std::cout << M11 << std::endl<< std::endl;
return 0;
}
static double
strikezHIII (MagComp component, const fault_params *fault, const magnetic_params *mag, double xi, double et, double qq, double y, double z)
{
double val;
double h = mag->dcurier;
double qd = y * sd + (fault->fdepth - h) * cd;
double K3_val = K3 (component, 1.0, xi, et, qq);
double log_re_val = log_re (component, 1.0, xi, et, qq);
double M2_val = M2 (component, 1.0, xi, et, qq);
double M3_val = M3 (component, 1.0, xi, et, qq);
val = alpha5 * K3_val + fault->alpha * log_re_val * cd
+ alpha3 * (qd * M3_val - (z - h) * M2_val * sd);
return val;
}
static void
ggcm_mhd_bnd_open_x_fill_ghosts_fcons_cc(struct ggcm_mhd_bnd *bnd, struct mrc_fld *fld,
float bntim)
{
struct ggcm_mhd *mhd = bnd->mhd;
struct mrc_fld *f = mrc_fld_get_as(fld, FLD_TYPE);
int gdims[3];
mrc_domain_get_global_dims(mhd->domain, gdims);
int sw_y = gdims[1] > 1 ? SW_2 : 0;
int sw_z = gdims[2] > 1 ? SW_2 : 0;
assert(mrc_fld_nr_patches(f) == 1);
int p = 0;
const int *ldims = mrc_fld_spatial_dims(f);
int mx = ldims[0];
struct mrc_patch_info info;
mrc_domain_get_local_patch_info(mhd->domain, 0, &info);
int nr_comps = mrc_fld_nr_comps(f);
if (info.off[0] == 0) { // x lo FIXME, there is (?) a function for this
for (int k = -sw_z; k < ldims[2] + sw_z; k++) {
for (int j = -sw_y; j < ldims[1] + sw_y; j++) {
for (int m = 0; m < nr_comps; m++) {
M3(f, m, -1,j,k, p) = M3(f, m, 0,j,k, p);
M3(f, m, -2,j,k, p) = M3(f, m, 1,j,k, p);
}
}
}
}
if (info.off[0] + info.ldims[0] == gdims[0]) { // x hi
for (int k = -sw_z; k < ldims[2] + sw_z; k++) {
for (int j = -sw_y; j < ldims[1] + sw_y; j++) {
for (int m = 0; m < nr_comps; m++) {
M3(f, m, mx ,j,k, p) = M3(f, m, mx-1,j,k, p);
M3(f, m, mx+1,j,k, p) = M3(f, m, mx-2,j,k, p);
}
}
}
}
mrc_fld_put_as(f, fld);
}
TEST(ResMonoidDense, create)
{
ResMonoidDense M1(4,
std::vector<int>{1, 1, 1, 1},
std::vector<int>{},
MonomialOrderingType::GRevLex);
ResMonoidDense M2(4,
std::vector<int>{1, 2, 3, 4},
std::vector<int>{1, 1, 1, 1, 1, 1, 0, 0},
MonomialOrderingType::Weights);
ResMonoidDense M3(4,
std::vector<int>{1, 1, 1, 1},
std::vector<int>{},
MonomialOrderingType::Lex);
EXPECT_EQ(4, M1.n_vars());
std::vector<res_monomial_word> monomspace(100);
EXPECT_EQ(100, monomspace.size());
}
void DenseMatrix<T>::left_multiply (const DenseMatrixBase<T>& M2)
{
if (this->use_blas_lapack)
this->_multiply_blas(M2, LEFT_MULTIPLY);
else
{
// (*this) <- M2 * (*this)
// Where:
// (*this) = (m x n),
// M2 = (m x p),
// M3 = (p x n)
// M3 is a copy of *this before it gets resize()d
DenseMatrix<T> M3(*this);
// Resize *this so that the result can fit
this->resize (M2.m(), M3.n());
// Call the multiply function in the base class
this->multiply(*this, M2, M3);
}
}
static double
strikezH0 (MagComp component, const fault_params *fault, const magnetic_params *mag, double xi, double et, double qq, double y, double z)
{
double val;
double h = mag->dcurier;
double qd = y * sd + (fault->fdepth - h) * cd;
double K3_val = K3 (component, 1.0, xi, et, qq);
double log_re_val = log_re (component, 1.0, xi, et, qq);
double M2_val = M2 (component, 1.0, xi, et, qq);
double M3_val = M3 (component, 1.0, xi, et, qq);
double M3y_val = M3y (component, 1.0, xi, et, qq);
double M3z_val = M3z (component, 1.0, xi, et, qq);
val = - (2.0 + alpha5) * K3_val
- fault->alpha * log_re_val * cd
- alpha3 * (qd * M3_val - (z - h) * M2_val * sd)
+ 2.0 * fault->alpha * h * (M3_val * cd + M2_val * sd)
- 4.0 * alpha1 * h * M2_val * sd
- 2.0 * alpha2 * h * M2_val * sd
- 2.0 * alpha2 * h * ((qd + h * cd) * M3z_val - (z - 2.0 * h) * M3y_val * sd);
return val;
}
int main()
{
try {
vpMatrix M ;
vpMatrix M1(2,3) ;
vpMatrix M2(3,3) ;
vpMatrix M3(2,2) ;
vpTRACE("test matrix size in multiply") ;
try
{
M = M1*M3 ;
}
catch (vpMatrixException me)
{
std::cout << me << std::endl ;
}
vpTRACE("test matrix size in addition") ;
try
{
M = M1+M3 ;
}
catch (vpMatrixException me)
{
std::cout << me << std::endl ;
}
}
catch(vpException e) {
std::cout << "Catch an exception: " << e << std::endl;
return 1;
}
}
static void
ggcm_mhd_bnd_open_x_fill_ghosts_scons(struct ggcm_mhd_bnd *bnd, struct mrc_fld *fld,
float bntim)
{
struct ggcm_mhd *mhd = bnd->mhd;
struct mrc_fld *f3 = mrc_fld_get_as(fld, FLD_TYPE);
assert(mrc_fld_nr_patches(f3) == 1);
int p = 0;
int gdims[3];
mrc_domain_get_global_dims(mhd->domain, gdims);
int dy = (gdims[1] > 1), dz = (gdims[2] > 1);
int sw_y = gdims[1] > 1 ? SW_2 : 0;
int sw_z = gdims[2] > 1 ? SW_2 : 0;
const int *dims = mrc_fld_dims(f3);
int nx = dims[0], ny = dims[1], nz = dims[2];
struct mrc_patch_info info;
mrc_domain_get_local_patch_info(mhd->domain, 0, &info);
float *bd2x = ggcm_mhd_crds_get_crd(mhd->crds, 0, BD2);
float *bd2y = ggcm_mhd_crds_get_crd(mhd->crds, 1, BD2);
float *bd2z = ggcm_mhd_crds_get_crd(mhd->crds, 2, BD2);
// fill boundary values with closes non-zero value
// FIXME: should this be necessary?
bd2x[-2] = bd2x[0];
bd2x[-1] = bd2x[0];
bd2x[nx] = bd2x[nx-1];
bd2x[nx+1] = bd2x[nx-1];
bd2y[-2] = bd2y[0];
bd2y[-1] = bd2y[0];
bd2y[ny] = bd2y[ny-1];
bd2y[ny+1] = bd2y[ny-1];
bd2z[-2] = bd2z[0];
bd2z[-1] = bd2z[0];
bd2z[nz] = bd2z[nz-1];
bd2z[nz+1] = bd2z[nz-1];
//-----------------------------------------------------------------------------------//
// lower bound
//-----------------------------------------------------------------------------------//
if (info.off[0] == 0) { // x lo
// transverse magnetic extrapolated
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
// bd1y and bd2y indices offset by one
M3(f3,BY, -1,iy,iz, p) = M3(f3,BY, 0,iy,iz, p);
M3(f3,BZ, -1,iy,iz, p) = M3(f3,BZ, 0,iy,iz, p);
}
}
// set normal magnetic field component for divB=0
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
M3(f3,BX, -1,iy,iz, p) = M3(f3,BX, 0,iy,iz, p) + bd2x[0] *
((M3(f3,BY, 0,iy,iz, p) - M3(f3,BY, 0,iy-dy,iz, p) ) / bd2y[iy] +
(M3(f3,BZ, 0,iy,iz, p) - M3(f3,BZ, 0,iy,iz-dz, p) ) / bd2z[iz]);
}
}
// transverse magnetic field extrapolated
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
// bd1x and bd2y indices offset by one
M3(f3,BY, -2,iy,iz, p) = M3(f3,BY, 1,iy,iz, p);
M3(f3,BZ, -2,iy,iz, p) = M3(f3,BZ, 1,iy,iz, p);
}
}
// set normal magnetic field component for divB=0
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
M3(f3,BX, -2,iy,iz, p) = M3(f3,BX, -1,iy,iz, p) + bd2x[-1] *
((M3(f3,BY, -1,iy,iz, p) - M3(f3,BY, -1,iy-dy,iz, p) ) / bd2y[iy] +
(M3(f3,BZ, -1,iy,iz, p) - M3(f3,BZ, -1,iy,iz-dz, p) ) / bd2z[iz]);
}
}
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
M3(f3,RVX, -1,iy,iz, p) = M3(f3,RVX, 0,iy,iz, p);
M3(f3,RVX, -2,iy,iz, p) = M3(f3,RVX, 1,iy,iz, p);
M3(f3,RR, -1,iy,iz, p) = M3(f3,RR, 0,iy,iz, p);
M3(f3,RR, -2,iy,iz, p) = M3(f3,RR, 1,iy,iz, p);
M3(f3,RVY, -1,iy,iz, p) = M3(f3,RVY, 0,iy,iz, p);
M3(f3,RVY, -2,iy,iz, p) = M3(f3,RVY, 1,iy,iz, p);
M3(f3,RVZ, -1,iy,iz, p) = M3(f3,RVZ, 0,iy,iz, p);
M3(f3,RVZ, -2,iy,iz, p) = M3(f3,RVZ, 1,iy,iz, p);
M3(f3,UU, -1,iy,iz, p) = M3(f3,UU, 0,iy,iz, p);
M3(f3,UU, -2,iy,iz, p) = M3(f3,UU, 1,iy,iz, p);
}
}
}
//-----------------------------------------------------------------------------------//
// upper bound
//-----------------------------------------------------------------------------------//
if (info.off[0] + info.ldims[0] == gdims[0]) { // x hi
// transverse magnetic field extrapolated
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
M3(f3,BY, nx,iy,iz, p) = M3(f3, BY, nx-1,iy,iz, p);
M3(f3,BZ, nx,iy,iz, p) = M3(f3, BZ, nx-1,iy,iz, p);
}
}
// set normal magnetic field component for divB=0
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
M3(f3,BX, nx-1,iy,iz, p) = M3(f3,BX, nx-2,iy,iz, p) - bd2x[nx-1] *
((M3(f3,BY, nx-1,iy,iz, p) - M3(f3,BY, nx-1,iy-dy,iz, p) ) / bd2y[iy] +
(M3(f3,BZ, nx-1,iy,iz, p) - M3(f3,BZ, nx-1,iy,iz-dz, p) ) / bd2z[iz]);
}
}
// transverse magnetic field extrapolated
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
M3(f3,BY, nx+1,iy,iz, p) = M3(f3, BY, nx-2,iy,iz, p);
M3(f3,BZ, nx+1,iy,iz, p) = M3(f3, BZ, nx-2,iy,iz, p);
}
}
// set normal magnetic field component for divB=0
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
M3(f3,BX, nx,iy,iz, p) = M3(f3,BX, nx-1,iy,iz, p) - bd2x[nx] *
((M3(f3,BY, nx,iy,iz, p) - M3(f3,BY, nx,iy-dy,iz, p) ) / bd2y[iy] +
(M3(f3,BZ, nx,iy,iz, p) - M3(f3,BZ, nx,iy,iz-dz, p) ) / bd2z[iz]);
}
}
for (int iz = -sw_z; iz < nz + sw_z; iz++) {
for (int iy = -sw_y; iy < ny + sw_y; iy++) {
M3(f3,RVX, nx+1,iy,iz, p) = M3(f3,RVX, nx-2,iy,iz, p);
M3(f3,RVX, nx,iy,iz, p) = M3(f3,RVX, nx-1,iy,iz, p);
M3(f3,RR, nx+1,iy,iz, p) = M3(f3,RR, nx-2,iy,iz, p);
M3(f3,RR, nx,iy,iz, p) = M3(f3,RR, nx-1,iy,iz, p);
M3(f3,RVY, nx+1,iy,iz, p) = M3(f3,RVY, nx-2,iy,iz, p);
M3(f3,RVY, nx,iy,iz, p) = M3(f3,RVY, nx-1,iy,iz, p);
M3(f3,RVZ, nx+1,iy,iz, p) = M3(f3,RVZ, nx-2,iy,iz, p);
M3(f3,RVZ, nx,iy,iz, p) = M3(f3,RVZ, nx-1,iy,iz, p);
M3(f3,UU, nx+1,iy,iz, p) = M3(f3,UU, nx-2,iy,iz, p);
M3(f3,UU, nx,iy,iz, p) = M3(f3,UU, nx-1,iy,iz, p);
}
}
}
mrc_fld_put_as(f3, fld);
}
/* This function generates the "K"-matrix out of an attitude profile matrix
*
* I don't know the real name of the "K"-Matrix, but everybody (see References from the other functions)
* calls it "K", so I do it as well.
*/
struct DoubleMat44 generate_K_matrix(struct DoubleMat33 B)
{
struct DoubleMat44 K;
double traceB = RMAT_TRACE(B);
double z1 = M3(B, 1, 2) - M3(B, 2, 1);
double z2 = M3(B, 2, 0) - M3(B, 0, 2);
double z3 = M3(B, 0, 1) - M3(B, 1, 0);
/** The "K"-Matrix. See the references for it **/
/* Fill the upper triangle matrix */
M4(K, 0, 0) = traceB; M4(K, 0, 1) = z1; M4(K, 0, 2) = z2; M4(K, 0, 3) = z3;
M4(K, 1, 1) = 2 * M3(B, 0, 0) - traceB; M4(K, 1, 2) = M3(B, 0, 1) + M3(B, 1, 0);
M4(K, 1, 3) = M3(B, 0, 2) + M3(B, 2, 0);
M4(K, 2, 2) = 2 * M3(B, 1, 1) - traceB; M4(K, 2, 3) = M3(B, 1, 2) + M3(B, 2, 1);
M4(K, 3, 3) = 2 * M3(B, 2, 2) - traceB;
/* Copy to lower triangle matrix */
M4(K, 1, 0) = M4(K, 0, 1);
M4(K, 2, 0) = M4(K, 0, 2); M4(K, 2, 1) = M4(K, 1, 2);
M4(K, 3, 0) = M4(K, 0, 3); M4(K, 3, 1) = M4(K, 1, 3); M4(K, 3, 2) = M4(K, 2, 3);
return K;
}
//declared the function for rho4 from rho3
double rho4(double r, double m, double p)
{
double Fn = rho(r+h,m+h*M3(r,m,p),p+h*rho3(r,m,p));
return Fn;
}
inline V3 Contact::calculate_friction_impulse(M3* inv_inertia_tensor)
{
F inverse_mass = bodies[0]->get_inverse_mass();
auto o = relative_contact_position[0];
//Usually you get a torque from an impulse by a cross product with the relative distance.
//If we build a M3 from the relative distance in this way, we have a matrix
//that goes from impulse to torque
M3 impulse_to_torque = -M3(
0, -o.z, o.y,
o.z, 0, -o.x,
-o.y, o.x, 0
);
M3 delta_vel_world = impulse_to_torque;
delta_vel_world *= inv_inertia_tensor[0]; //Rotation generated by unit torque
delta_vel_world *= impulse_to_torque; //Same as crossing the relative contact pos. Gives linear vel generated by torque only
delta_vel_world *= -1; //M1 x M2 = - M2 x M1, thus the minus
// Check if we need to the second body's data
if (bodies[1])
{
auto o = relative_contact_position[1];
impulse_to_torque = -M3(
0, -o.z, o.y,
o.z, 0, -o.x,
-o.y, o.x, 0
);
M3 delta_vel_world_2 = impulse_to_torque;
delta_vel_world_2 *= inv_inertia_tensor[1]; //Rotation generated by unit torque
delta_vel_world_2 *= impulse_to_torque; //Same as crossing the relative contact pos. Gives linear vel generated by torque only
delta_vel_world_2 *= -1; //M1 x M2 = - M2 x M1, thus the minus
//combine velocities and masses
delta_vel_world += delta_vel_world_2;
inverse_mass += bodies[1]->get_inverse_mass();
}
//change base of matrix (B x M x B^-1) to get velocity in contact coords
M3 delta_velocity = transpose(contact_to_world) * delta_vel_world * contact_to_world;
//Add the linear velocity. Need to build a matrix like this:
//m,0,0
//0,m,0
//0,0,m
delta_velocity[0].x += inverse_mass;
delta_velocity[1].y += inverse_mass;
delta_velocity[2].z += inverse_mass;
//From:
//unit velocity generated by impulse
//To:
//Impulse requires to generate unit velocity
M3 impulse_matrix = inverse(delta_velocity);
//Velocities to kill. The x element is the same as the frictionless impulse
//and must be completely null out
V3 vel_kill(desired_delta_velocity, -contact_velocity.y, -contact_velocity.z);
//Get impulse necessary to kill the velocities
V3 impulse_contact = impulse_matrix * vel_kill;
//Get only the planar impulse
F planar_impulse = sqrt(impulse_contact.y*impulse_contact.y + impulse_contact.z * impulse_contact.z);
//The X of the impulse is the one along the normal.
//This impulse, multiplied by friction, is the amount to overcome.
//If the planar is greater, than there is enough force for dynamic friction
if (planar_impulse > impulse_contact.x * friction) {
impulse_contact.y /= planar_impulse;
impulse_contact.z /= planar_impulse;
//Recalculate delta_velocity (and store it in impulse_contact.X just for caching)
impulse_contact.x =
delta_velocity[0].x +
delta_velocity[1].x * impulse_contact.y * friction +
delta_velocity[2].x * impulse_contact.z * friction;
impulse_contact.x = desired_delta_velocity / impulse_contact.x;
impulse_contact.y *= friction * impulse_contact.x;
impulse_contact.z *= friction * impulse_contact.x;
}
return impulse_contact;
}
void lidarBoostEngine::build_superresolution(short coeff)
{
std::cout<< "Num of clouds : " << Y.size() << std::endl;
// std::cout << Y[0] << std::endl;
beta = coeff;
std::vector < MatrixXd > optflow = lk_optical_flow( Y[2], Y[4], 10 );
MatrixXd D( beta*n, beta*m ); //, X( beta*n, beta*m );
// SparseMatrix<double> W( beta*n, beta*m ), T( beta*n, beta*m );
D = apply_optical_flow(Y[2], optflow);
T = check_unreliable_samples(intensityMap[2], 0.0001);
MatrixXd up_D = nearest_neigh_upsampling(D);
//// Display and Debug
cv::Mat M(n, m, CV_32FC1);
// MatrixXd diff1(n, m);
// diff1 = MatrixXd::Ones(n, m) - Y[0];
cv::eigen2cv(Y[2], M);
cv::Mat M1(n, m, CV_32FC1);
cv::eigen2cv(Y[4], M1);
// MatrixXd diff(beta*n, beta*m);
// diff = MatrixXd::Ones(beta*n, beta*m) - up_D;
cv::Mat M2(beta*n, beta*m, CV_32FC1);
cv::eigen2cv(up_D, M2);
cv::namedWindow("check", cv::WINDOW_AUTOSIZE );
cv::imshow("check", M);
cv::namedWindow("check1", cv::WINDOW_AUTOSIZE );
cv::imshow("check1", M1);
cv::namedWindow("check2", cv::WINDOW_AUTOSIZE );
cv::imshow("check2", M2);
//// Solve example equation with eigen
// Eigen::VectorXd x(2);
// x(0) = 10.0;
// x(1) = 25.0;
// std::cout << "x: " << x << std::endl;
// my_functor functor;
// Eigen::NumericalDiff<my_functor> numDiff(functor);
// Eigen::LevenbergMarquardt<Eigen::NumericalDiff<my_functor>,double> lm(numDiff);
// lm.parameters.maxfev = 2000;
// lm.parameters.xtol = 1.0e-10;
// std::cout << lm.parameters.maxfev << std::endl;
// int ret = lm.minimize(x);
// std::cout << lm.iter << std::endl;
// std::cout << ret << std::endl;
// std::cout << "x that minimizes the function: " << x << std::endl;
////// Try to solve lidarboost with Eigen
// my_functor functor;
// Eigen::NumericalDiff<my_functor> numDiff(functor);
// Eigen::LevenbergMarquardt<Eigen::NumericalDiff<my_functor>,double> lm(numDiff);
// lm.parameters.maxfev = 2000;
// lm.parameters.xtol = 1.0e-10;
// std::cout << lm.parameters.maxfev << std::endl;
// VectorXd val(2);
// for(int i = 0; i < X.rows(); i++)
// {
// for(int j = 0; j < X.cols(); j++)
// {
// val = X(i, j);
// int ret = lm.minimize(val);
// }
// }
// std::cout << lm.iter << std::endl;
// std::cout << ret << std::endl;
// std::cout << "x that minimizes the function: " << X << std::endl;
//// Solve example using ceres
// The variable to solve for with its initial value.
// double initial_x = 5.0;
// double x = initial_x;
MatrixXd X(beta*n, beta*m);// init_X(beta*n, beta*m);
// X = MatrixXd::Zero(beta*n,beta*m);
X = up_D;
// MatrixXd init_X( beta*n, beta*m );
// init_X = X;
// int M[2][2], M2[2][2];
// M[0][0] = 5;
// M[1][0] = 10;
// M[0][1] = 20;
// M[1][1] = 30;
// M2 = *M;
// Build the problem.
Problem problem;
// Set up the only cost function (also known as residual). This uses
// auto-differentiation to obtain the derivative (jacobian).
double val, w, t, d;
Solver::Options options;
options.linear_solver_type = ceres::DENSE_QR;
options.minimizer_progress_to_stdout = false;
Solver::Summary summary;
for(int i = 0; i < X.rows(); i++)
{
for(int j = 0; j < X.cols(); j++)
{
val = X(i, j);
w = W(i, j);
t = T(i, j);
d = up_D(i, j);
std::cout << "i = " << i << "; j = " << j << std::endl;
std::cout << "w = " << w << "; t = " << t << "; d = " << d << std::endl;
CostFunction* cost_function =
new AutoDiffCostFunction<CostFunctor, 1, 1>(new CostFunctor(w, t, d));
problem.AddResidualBlock(cost_function, NULL, &val);
// Run the solver
Solve(options, &problem, &summary);
X(i, j) = val;
}
}
std::cout << summary.BriefReport() << "\n";
// std::cout << "x : " << init_X
// << " -> " << X << "\n";
cv::Mat M3(beta*n, beta*m, CV_32FC1);
cv::eigen2cv(X, M3);
cv::namedWindow("check3", cv::WINDOW_AUTOSIZE );
cv::imshow("check3", M3);
}
void main() //main code
{
printf("\nRUNGE-KUTTA METHOD\n\nR M Rho\n"); //printing titles for values displayed
double c = 10.0; //the parameter rho(c)
int n; //the integer steps, n
//declare arrays
float x[N];
float y[N];
float z[N];
//r,m,p as the radius, mass and density
double r,m,p;
//declare initial conditons for arrays
x[0] = h; //first array is for r=h
y[0] = (h*h*h/3)*c; //initial conditon for scaled mass (m)
z[0] = c*(1-((h*h*c)/(6*gamma(c)))); //initial conditon for rho
//for loop for n=0,1,...,200
for(n=0;n<N;n++)
{
//declared how x(n+1) relates to x(n), y(n+1) relates to y(n), z(n+1) relates to z(n)
x[n+1] = x[n]+h;
y[n+1] = y[n]+(h/6)*(M(x[n],y[n],z[n])+2*M2(x[n],y[n],z[n])+2*M3(x[n],y[n],z[n])+M4(x[n],y[n],z[n]));
z[n+1] = z[n]+(h/6)*(rho(x[n],y[n],z[n])+2*rho2(x[n],y[n],z[n])+2*rho3(x[n],y[n],z[n])+rho4(x[n],y[n],z[n]));
if(isnan(z[n+1]))
{
break;
}
//r,m,p will be declared in pg-plot
r = x[n+1];
m = y[n+1];
p = z[n+1];
printf("%.2e %.2e %.2e\n",x[n+1],y[n+1],z[n+1]); //printed values for x and y respectively
}
//Use pg-plot to plot mass and density
// cpgbeg starts a plotting page, in this case with 2x1 panels
cpgbeg(0,"?",2,1);
// sets colour: 1-black, 2-red, 3-green, 4-blue
cpgsci(1);
// sets line style: 1-solid, 2-dashed, 3-dot-dashed, 4-dotted
cpgsls(1);
// sets charachter height, larger number = bigger
cpgsch(1.);
// cpgpage() moves to the next panel
cpgpage();
// sets the axes limits in the panel
cpgswin(0,r,0,m);
// draw the axes
cpgbox("BCNST", 0.0, 0, "BCNST", 0.0, 0);
// label the bottom axis
cpgmtxt("B",2.,.5,.5,"radius");
// label the left axis
cpgmtxt("L",2.5,.5,.5,"saclaed mass");
// connect N points in ax and ay with a line
cpgline(n,x,y);
// cpgpage() moves to the next panel
cpgpage();
// sets the axes limits in the panel
cpgswin(0,r,0,c);
// draw the axes
cpgbox("BCNST", 0.0, 0, "BCNST", 0.0, 0);
// label the bottom axis
cpgmtxt("B",2.,.5,.5,"radius");
// label the left axis
cpgmtxt("L",2.5,.5,.5,"density");
// connect N points in ax and ay with a line
cpgline(n,x,z);
// close all pgplot applications
cpgend();
// end program
return;
}
void FastMatmulRecursive(LockAndCounter& locker, MemoryManager<Scalar>& mem_mngr, Matrix<Scalar>& A, Matrix<Scalar>& B, Matrix<Scalar>& C, int total_steps, int steps_left, int start_index, double x, int num_threads, Scalar beta) {
// Update multipliers
C.UpdateMultiplier(A.multiplier());
C.UpdateMultiplier(B.multiplier());
A.set_multiplier(Scalar(1.0));
B.set_multiplier(Scalar(1.0));
// Base case for recursion
if (steps_left == 0) {
MatMul(A, B, C);
return;
}
Matrix<Scalar> A11 = A.Subblock(2, 2, 1, 1);
Matrix<Scalar> A12 = A.Subblock(2, 2, 1, 2);
Matrix<Scalar> A21 = A.Subblock(2, 2, 2, 1);
Matrix<Scalar> A22 = A.Subblock(2, 2, 2, 2);
Matrix<Scalar> B11 = B.Subblock(2, 2, 1, 1);
Matrix<Scalar> B12 = B.Subblock(2, 2, 1, 2);
Matrix<Scalar> B21 = B.Subblock(2, 2, 2, 1);
Matrix<Scalar> B22 = B.Subblock(2, 2, 2, 2);
Matrix<Scalar> C11 = C.Subblock(2, 2, 1, 1);
Matrix<Scalar> C12 = C.Subblock(2, 2, 1, 2);
Matrix<Scalar> C21 = C.Subblock(2, 2, 2, 1);
Matrix<Scalar> C22 = C.Subblock(2, 2, 2, 2);
// Matrices to store the results of multiplications.
#ifdef _PARALLEL_
Matrix<Scalar> M1(mem_mngr.GetMem(start_index, 1, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M2(mem_mngr.GetMem(start_index, 2, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M3(mem_mngr.GetMem(start_index, 3, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M4(mem_mngr.GetMem(start_index, 4, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M5(mem_mngr.GetMem(start_index, 5, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M6(mem_mngr.GetMem(start_index, 6, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M7(mem_mngr.GetMem(start_index, 7, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M8(mem_mngr.GetMem(start_index, 8, total_steps - steps_left, M), C11.m(), C11.m(), C11.n(), C.multiplier());
#else
Matrix<Scalar> M1(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M2(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M3(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M4(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M5(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M6(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M7(C11.m(), C11.n(), C.multiplier());
Matrix<Scalar> M8(C11.m(), C11.n(), C.multiplier());
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
bool sequential1 = should_launch_task(8, total_steps, steps_left, start_index, 1, num_threads);
bool sequential2 = should_launch_task(8, total_steps, steps_left, start_index, 2, num_threads);
bool sequential3 = should_launch_task(8, total_steps, steps_left, start_index, 3, num_threads);
bool sequential4 = should_launch_task(8, total_steps, steps_left, start_index, 4, num_threads);
bool sequential5 = should_launch_task(8, total_steps, steps_left, start_index, 5, num_threads);
bool sequential6 = should_launch_task(8, total_steps, steps_left, start_index, 6, num_threads);
bool sequential7 = should_launch_task(8, total_steps, steps_left, start_index, 7, num_threads);
bool sequential8 = should_launch_task(8, total_steps, steps_left, start_index, 8, num_threads);
#else
bool sequential1 = false;
bool sequential2 = false;
bool sequential3 = false;
bool sequential4 = false;
bool sequential5 = false;
bool sequential6 = false;
bool sequential7 = false;
bool sequential8 = false;
#endif
// M1 = (1 * A11) * (1 * B11)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential1) shared(mem_mngr, locker) untied
{
#endif
M1.UpdateMultiplier(Scalar(1));
M1.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A11, B11, M1, total_steps, steps_left - 1, (start_index + 1 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 1, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M2 = (1 * A12) * (1 * B21)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential2) shared(mem_mngr, locker) untied
{
#endif
M2.UpdateMultiplier(Scalar(1));
M2.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A12, B21, M2, total_steps, steps_left - 1, (start_index + 2 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 2, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M3 = (1 * A11) * (1 * B12)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential3) shared(mem_mngr, locker) untied
{
#endif
M3.UpdateMultiplier(Scalar(1));
M3.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A11, B12, M3, total_steps, steps_left - 1, (start_index + 3 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 3, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M4 = (1 * A12) * (1 * B22)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential4) shared(mem_mngr, locker) untied
{
#endif
M4.UpdateMultiplier(Scalar(1));
M4.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A12, B22, M4, total_steps, steps_left - 1, (start_index + 4 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 4, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M5 = (1 * A21) * (1 * B11)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential5) shared(mem_mngr, locker) untied
{
#endif
M5.UpdateMultiplier(Scalar(1));
M5.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A21, B11, M5, total_steps, steps_left - 1, (start_index + 5 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 5, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M6 = (1 * A22) * (1 * B21)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential6) shared(mem_mngr, locker) untied
{
#endif
M6.UpdateMultiplier(Scalar(1));
M6.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A22, B21, M6, total_steps, steps_left - 1, (start_index + 6 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 6, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M7 = (1 * A21) * (1 * B12)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential7) shared(mem_mngr, locker) untied
{
#endif
M7.UpdateMultiplier(Scalar(1));
M7.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A21, B12, M7, total_steps, steps_left - 1, (start_index + 7 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 7, num_threads)) {
# pragma omp taskwait
# if defined(_PARALLEL_) && (_PARALLEL_ == _HYBRID_PAR_)
SwitchToDFS(locker, num_threads);
# endif
}
#endif
// M8 = (1 * A22) * (1 * B22)
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
# pragma omp task if(sequential8) shared(mem_mngr, locker) untied
{
#endif
M8.UpdateMultiplier(Scalar(1));
M8.UpdateMultiplier(Scalar(1));
FastMatmulRecursive(locker, mem_mngr, A22, B22, M8, total_steps, steps_left - 1, (start_index + 8 - 1) * 8, x, num_threads, Scalar(0.0));
#ifndef _PARALLEL_
#endif
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
locker.Decrement();
}
if (should_task_wait(8, total_steps, steps_left, start_index, 8, num_threads)) {
# pragma omp taskwait
}
#endif
M_Add1(M1, M2, C11, x, false, beta);
M_Add2(M3, M4, C12, x, false, beta);
M_Add3(M5, M6, C21, x, false, beta);
M_Add4(M7, M8, C22, x, false, beta);
// Handle edge cases with dynamic peeling
#if defined(_PARALLEL_) && (_PARALLEL_ == _BFS_PAR_ || _PARALLEL_ == _HYBRID_PAR_)
if (total_steps == steps_left) {
mkl_set_num_threads_local(num_threads);
mkl_set_dynamic(0);
}
#endif
DynamicPeeling(A, B, C, 2, 2, 2, beta);
}
int multiple_detector_fit()
{
std::cout << "Beginning : ... " << std::endl;
Int_t npoints = 1000;
Double_t emin = 0.2;
Double_t emax = 3.0;
bool use100m = true;
bool use470m = true;
bool use600m = true;
std::vector<int> baselines;
std::vector<double> scales;
std::vector<std::string> names;
std::vector<double> volume;
if (use100m) baselines.push_back(100);
if (use470m) baselines.push_back(470);
if (use600m) baselines.push_back(600);
double NULLVec[2][20];
double OscVec[2][1001][7][20];
for(int i = 0; i < 20; i++){
NULLVec[0][i] = 0;
NULLVec[1][i] = 0;
}
for(int u = 0; u < 1000; u++){
for(int s = 0; s < 7; s++){
for(int i = 0; i < 20; i++){
OscVec[0][u][s][i] = 0;
OscVec[1][u][s][i] = 0;
}
}
}
int nbinsE = 0;
if (use100m){
std::string temp_name = /*"../MatrixFiles/combined_ntuple_100m_nu_processed_numu.root";*/"../MatrixFiles/combined_ntuple_100m_nu_processed_CoreyBins_numu.root";
TFile temp_file(temp_name.c_str());
TH1D *NULL_100;
NULL_100 = (TH1D*)(temp_file.Get("NumuCC"));
nbinsE = NULL_100->GetNbinsX();
std::cout << nbinsE << std::endl;
for(int i = 1; i <= nbinsE; i++){
NULLVec[0][i-1] = (NULL_100->GetBinContent(i));
}
for(int u = 0; u < npoints; u++){
for(int s = 0; s < 7; s++){
TH1D *OSC_100;
TString upoint = Form("%d",u);
TString name = "Universe_";
TString name2 = "_MultiSim_";
TString mul = Form("%d",s);
name += upoint;
name += name2;
name += mul;
OSC_100 = (TH1D*)(temp_file.Get(name));
for(int i = 1; i <= nbinsE; i++){
OscVec[0][u][s][i-1] = (OSC_100->GetBinContent(i));
// if(OscVec[0][u][s][i-1] != OscVec[0][u][s][i-1]) std::cout << "erm" <<std::endl;
}
delete OSC_100;
}
}
delete NULL_100;
temp_file.Close();
}
if (use470m){
std::string temp_name = /*"../MatrixFiles/combined_ntuple_600m_onaxis_nu_processed_numu.root";*/"../MatrixFiles/combined_ntuple_600m_onaxis_nu_processed_CoreyBins_numu.root";
TFile temp_file(temp_name.c_str());
TH1D *NULL_470;
NULL_470 = (TH1D*)(temp_file.Get("NumuCC"));
nbinsE = NULL_470->GetNbinsX();
std::cout << nbinsE<< std::endl;
for(int i = 1; i <= nbinsE; i++){
NULLVec[1][i-1] = (NULL_470->GetBinContent(i));
}
for(int u = 0; u < npoints; u++){
for(int s = 0; s < 7; s++){
TH1D *OSC_470;
TString upoint = Form("%d",u);//std::to_string(u);
TString name = "Universe_";
TString name2 = "_MultiSim_";
TString mul = Form("%d",s);// = std::to_string(s);
name += upoint;
name += name2;
name += mul;
OSC_470 = (TH1D*)(temp_file.Get(name));
for(int i = 1; i <= nbinsE; i++){
OscVec[1][u][s][i-1] = (OSC_470->GetBinContent(i));
if(OscVec[1][u][s][i-1] != OscVec[1][u][s][i-1]) OscVec[1][u][s][i-1] = NULLVec[1][i-1];//std::cout << "erm, u :" << u << " s : " << s << " E : " << i <<std::endl;
}
delete OSC_470;
}
}
delete NULL_470;
temp_file.Close();
}
int nL = 2;
int mbins = (nbinsE*nL);
TMatrix M6 (mbins,mbins);
TMatrix M5 (mbins,mbins);
TMatrix M4 (mbins,mbins);
TMatrix M3 (mbins,mbins);
TMatrix M2 (mbins,mbins);
TMatrix M1 (mbins,mbins);
TMatrix M0 (mbins,mbins);
TMatrix C6 (mbins,mbins);
TMatrix C5 (mbins,mbins);
TMatrix C4 (mbins,mbins);
TMatrix C3 (mbins,mbins);
TMatrix C2 (mbins,mbins);
TMatrix C1 (mbins,mbins);
TMatrix C0 (mbins,mbins);
int N = 0;
TH1D *Fig6 = new TH1D("Fig6",";;",mbins,0,mbins);
TH1D *Fig5 = new TH1D("Fig5",";;",mbins,0,mbins);
TH1D *Fig4 = new TH1D("Fig4",";;",mbins,0,mbins);
TH1D *Fig3 = new TH1D("Fig3",";;",mbins,0,mbins);
TH1D *Fig2 = new TH1D("Fig2",";;",mbins,0,mbins);
TH1D *Fig1 = new TH1D("Fig1",";;",mbins,0,mbins);
TH1D *Fig0 = new TH1D("Fig0",";;",mbins,0,mbins);
int Erri = 0, Errj = 0;
std::cout << "Filling Error Matrix..." << std::endl;
for(int Lrow = 0; Lrow < 2; Lrow++){
for(int Erow = 0; Erow < nbinsE; Erow++){
Errj = 0;
for(int Lcol = 0; Lcol < 2; Lcol++){
for(int Ecol = 0; Ecol < nbinsE; Ecol++){
M6 (Erri,Errj) = 0;
M5 (Erri,Errj) = 0;
M4 (Erri,Errj) = 0;
M3 (Erri,Errj) = 0;
M2 (Erri,Errj) = 0;
M1 (Erri,Errj) = 0;
M0 (Erri,Errj) = 0;
N = 0;
for(int u = 0; u < npoints; u++){
M6 (Erri,Errj) += (NULLVec[Lrow][Erow]-OscVec[Lrow][u][6][Erow])*(NULLVec[Lcol][Ecol]-OscVec[Lcol][u][6][Ecol]);
M5 (Erri,Errj) += (NULLVec[Lrow][Erow]-OscVec[Lrow][u][5][Erow])*(NULLVec[Lcol][Ecol]-OscVec[Lcol][u][5][Ecol]);
M4 (Erri,Errj) += (NULLVec[Lrow][Erow]-OscVec[Lrow][u][4][Erow])*(NULLVec[Lcol][Ecol]-OscVec[Lcol][u][4][Ecol]);
M3 (Erri,Errj) += (NULLVec[Lrow][Erow]-OscVec[Lrow][u][3][Erow])*(NULLVec[Lcol][Ecol]-OscVec[Lcol][u][3][Ecol]);
M2 (Erri,Errj) += (NULLVec[Lrow][Erow]-OscVec[Lrow][u][2][Erow])*(NULLVec[Lcol][Ecol]-OscVec[Lcol][u][2][Ecol]);
M1 (Erri,Errj) += (NULLVec[Lrow][Erow]-OscVec[Lrow][u][1][Erow])*(NULLVec[Lcol][Ecol]-OscVec[Lcol][u][1][Ecol]);
M0 (Erri,Errj) += (NULLVec[Lrow][Erow]-OscVec[Lrow][u][0][Erow])*(NULLVec[Lcol][Ecol]-OscVec[Lcol][u][0][Ecol]);
N++;
}
M6 (Erri,Errj) /= N;
M5 (Erri,Errj) /= N;
M4 (Erri,Errj) /= N;
M3 (Erri,Errj) /= N;
M2 (Erri,Errj) /= N;
M1 (Erri,Errj) /= N;
M0 (Erri,Errj) /= N;
M6 (Erri,Errj) /= NULLVec[Lrow][Erow]*NULLVec[Lcol][Ecol];
M5 (Erri,Errj) /= NULLVec[Lrow][Erow]*NULLVec[Lcol][Ecol];
M4 (Erri,Errj) /= NULLVec[Lrow][Erow]*NULLVec[Lcol][Ecol];
M3 (Erri,Errj) /= NULLVec[Lrow][Erow]*NULLVec[Lcol][Ecol];
M2 (Erri,Errj) /= NULLVec[Lrow][Erow]*NULLVec[Lcol][Ecol];
M1 (Erri,Errj) /= NULLVec[Lrow][Erow]*NULLVec[Lcol][Ecol];
M0 (Erri,Errj) /= NULLVec[Lrow][Erow]*NULLVec[Lcol][Ecol];
if(Erri == Errj) Fig6->SetBinContent(Erri+1, sqrt(M6 (Erri,Errj)));
if(Erri == Errj) Fig5->SetBinContent(Erri+1, sqrt(M5 (Erri,Errj)));
if(Erri == Errj) Fig4->SetBinContent(Erri+1, sqrt(M4 (Erri,Errj)));
if(Erri == Errj) Fig3->SetBinContent(Erri+1, sqrt(M3 (Erri,Errj)));
if(Erri == Errj) Fig2->SetBinContent(Erri+1, sqrt(M2 (Erri,Errj)));
if(Erri == Errj) Fig1->SetBinContent(Erri+1, sqrt(M1 (Erri,Errj)));
if(Erri == Errj) Fig0->SetBinContent(Erri+1, sqrt(M0 (Erri,Errj)));
std::cout << M6 (Erri,Errj) << "\t";
Errj++;
}}
Erri++;
}}
for(int i = 0; i < Erri; i++){
for(int j = 0; j < Errj; j++){
C6 (i,j) = M6(i,j) / sqrt(M6 (i,i) * M6 (j,j));
C5 (i,j) = M5(i,j) / sqrt(M5 (i,i) * M5 (j,j));
C4 (i,j) = M4(i,j) / sqrt(M4 (i,i) * M4 (j,j));
C3 (i,j) = M3(i,j) / sqrt(M3 (i,i) * M3 (j,j));
C2 (i,j) = M2(i,j) / sqrt(M2 (i,i) * M2 (j,j));
C1 (i,j) = M1(i,j) / sqrt(M1 (i,i) * M1 (j,j));
C0 (i,j) = M0(i,j) / sqrt(M0 (i,i) * M0 (j,j));
}
}
std::cout << "...Error Matrix Filled" << std::endl;
TCanvas* c6 = new TCanvas("c6","",700,700);
c6->SetLeftMargin(.1);
c6->SetBottomMargin(.1);
c6->SetTopMargin(.075);
c6->SetRightMargin(.15);
c6->cd();
M6.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
// TMatrixFBase->GetZaxis()->SetRangeUser(-0.05,0.4);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
// TMatrixFBase->GetZaxis()->SetTitle("Fractional Error Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kBlue);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *ND = new TLatex(.15,.01,"LAr1-ND (100m) ");
ND->SetNDC();
ND->SetTextFont(62);
ND->SetTextSize(0.04);
ND->Draw();
TLatex *MD = new TLatex(.5,.01,"T600 (600m, on axis)");
MD->SetNDC();
MD->SetTextFont(62);
MD->SetTextSize(0.04);
MD->Draw();
TLatex *ND45 = new TLatex(.05,.15,"LAr1-ND (100m) ");
ND45->SetNDC();
ND45->SetTextAngle(90);
ND45->SetTextFont(62);
ND45->SetTextSize(0.04);
ND45->Draw();
TLatex *MD45 = new TLatex(.05,.54,"T600 (600m, on axis)");
MD45->SetNDC();
MD45->SetTextAngle(90);
MD45->SetTextFont(62);
MD45->SetTextSize(0.04);
MD45->Draw();
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} Flux Fractional Error Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
// c6->Print("total_matrix.pdf");
TCanvas* c61 = new TCanvas("c61","",700,700);
c61->SetLeftMargin(.1);
c61->SetBottomMargin(.1);
c61->SetTopMargin(.075);
c61->SetRightMargin(.15);
c61->cd();
C6.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kYellow);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} Flux Correlation Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
// c61->Print("total_correlation_matrix.pdf");
TCanvas* c5 = new TCanvas("c5","",700,700);
c5->SetLeftMargin(.1);
c5->SetBottomMargin(.1);
c5->SetTopMargin(.075);
c5->SetRightMargin(.15);
c5->cd();
M5.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-0.005,0.045);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
// TMatrixFBase->GetZaxis()->SetTitle("K^{+} Covariance Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kBlue);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} K#lower[-0.15]{+} Fractional Error Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c5->Print("mult5_matrix.pdf");
TCanvas* c51 = new TCanvas("c51","",700,700);
c51->SetLeftMargin(.1);
c51->SetBottomMargin(.1);
c51->SetTopMargin(.075);
c51->SetRightMargin(.15);
c51->cd();
C5.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-1,1);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
// TMatrixFBase->GetZaxis()->SetTitle("K#lower[-0.15]{+} Correlation Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kYellow);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} K#lower[-0.15]{+} Correlation Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c51->Print("mult5_correlation_matrix.pdf");
TCanvas* c4 = new TCanvas("c4","",700,700);
c4->SetLeftMargin(.1);
c4->SetBottomMargin(.1);
c4->SetTopMargin(.075);
c4->SetRightMargin(.15);
c4->cd();
M4.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-0.005,0.045);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
//TMatrixFBase->GetZaxis()->SetTitle("K#lower[-0.15]{-} Covariance Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kBlue);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} K#lower[-0.15]{-} Fractional Error Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c4->Print("mult4_matrix.pdf");
TCanvas* c41 = new TCanvas("c41","",700,700);
c41->SetLeftMargin(.1);
c41->SetBottomMargin(.1);
c41->SetTopMargin(.075);
c41->SetRightMargin(.15);
c41->cd();
C4.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-1,1);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
// TMatrixFBase->GetZaxis()->SetTitle("K#lower[-0.15]{-} Correlation Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kYellow);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} K#lower[-0.15]{-} Correlation Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c41->Print("mult4_correlation_matrix.pdf");
TCanvas* c3 = new TCanvas("c3","",700,700);
c3->SetLeftMargin(.1);
c3->SetBottomMargin(.1);
c3->SetTopMargin(.075);
c3->SetRightMargin(.15);
c3->cd();
M3.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-0.005,0.045);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
//TMatrixFBase->GetZaxis()->SetTitle("K#lower[-0.15]{0} Covariance Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kBlue);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} K#lower[-0.15]{0} Fractional Error Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c3->Print("mult3_matrix.pdf");
TCanvas* c31 = new TCanvas("c31","",700,700);
c31->SetLeftMargin(.1);
c31->SetBottomMargin(.1);
c31->SetTopMargin(.075);
c31->SetRightMargin(.15);
c31->cd();
C3.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-1,1);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
//TMatrixFBase->GetZaxis()->SetTitle("K#lower[-0.15]{0} Correlation Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kYellow);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} K#lower[-0.15]{0} Correlation Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c31->Print("mult3_correlation_matrix.pdf");
TCanvas* c2 = new TCanvas("c2","",700,700);
c2->SetLeftMargin(.1);
c2->SetBottomMargin(.1);
c2->SetTopMargin(.075);
c2->SetRightMargin(.15);
c2->cd();
M2.Draw("COLZ");
gStyle->SetPalette(56,0);
//TMatrixFBase->GetZaxis()->SetRangeUser(-0.005,0.045);
TMatrixFBase->SetContour(999);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
//TMatrixFBase->GetZaxis()->SetTitle("#pi#lower[-0.15]{+} Covariance Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kBlue);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} #pi#lower[-0.15]{+} Fractional Error Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c2->Print("mult2_matrix.pdf");
TCanvas* c21 = new TCanvas("c21","",700,700);
c21->SetLeftMargin(.1);
c21->SetBottomMargin(.1);
c21->SetTopMargin(.075);
c21->SetRightMargin(.15);
c21->cd();
C2.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-1,1);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
//TMatrixFBase->GetZaxis()->SetTitle("#pi#lower[-0.15]{+} Correlation Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kYellow);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} #pi#lower[-0.15]{+} Correlation Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c21->Print("mult2_correlation_matrix.pdf");
TCanvas* c1 = new TCanvas("c1","",700,700);
c1->SetLeftMargin(.1);
c1->SetBottomMargin(.1);
c1->SetTopMargin(.075);
c1->SetRightMargin(.15);
c1->cd();
M1.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-0.005,0.045);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
//TMatrixFBase->GetZaxis()->SetTitle("#pi#lower[-0.15]{-} Covariance Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kBlue);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} #pi#lower[-0.15]{-} Fractional Error Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c1->Print("mult1_matrix.pdf");
TCanvas* c11 = new TCanvas("c11","",700,700);
c11->SetLeftMargin(.1);
c11->SetBottomMargin(.1);
c11->SetTopMargin(.075);
c11->SetRightMargin(.15);
c11->cd();
C1.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-1,1);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
// TMatrixFBase->GetZaxis()->SetTitle("#pi#lower[-0.15]{-} Correlation Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kYellow);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} #pi#lower[-0.15]{-} Correlation Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c11->Print("mult1_correlation_matrix.pdf");
TCanvas* c0 = new TCanvas("c0","",700,700);
c0->SetLeftMargin(.1);
c0->SetBottomMargin(.1);
c0->SetTopMargin(.075);
c0->SetRightMargin(.15);
c0->cd();
M0.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-0.005,0.045);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
// TMatrixFBase->GetZaxis()->SetTitle("Beam UniSim Covariance Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kBlue);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} Beam Fractional Error Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c0->Print("mult0_matrix.pdf");
TCanvas* c01 = new TCanvas("c01","",700,700);
c01->SetLeftMargin(.1);
c01->SetBottomMargin(.1);
c01->SetTopMargin(.075);
c01->SetRightMargin(.15);
c01->cd();
C0.Draw("COLZ");
gStyle->SetPalette(56,0);
TMatrixFBase->SetContour(999);
//TMatrixFBase->GetZaxis()->SetRangeUser(-1,1);
TMatrixFBase->GetZaxis()->SetTitleFont(62);
TMatrixFBase->GetZaxis()->SetLabelFont(62);
TMatrixFBase->GetZaxis()->SetTitleSize(0.045);
// TMatrixFBase->GetZaxis()->SetTitle("Beam UniSim Correlation Matrix");
TMatrixFBase->GetZaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetXaxis()->SetTitle("");
TMatrixFBase->GetXaxis()->SetLabelSize(0);
TMatrixFBase->GetXaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetTitle("");
TMatrixFBase->GetYaxis()->SetTitleOffset(1.5);
TMatrixFBase->GetYaxis()->SetLabelSize(0);
TMatrixFBase->SetStats(0);
TLine *split = new TLine();
split->SetLineStyle(2);
split->SetLineWidth(5);
split->SetLineColor(kYellow);
split->DrawLineNDC(.1,.51,.849,.51);
split->DrawLineNDC(.475,.101,.475,.930);
add_plot_label("| 0.2 #minus 3.0 GeV | 0.2 #minus 3.0 GeV | ", 0.48,0.08,0.03);
TLatex *Total = new TLatex(.2,.96,"#nu#lower[0.3]{#mu} Beam Correlation Matrix");
Total->SetNDC();
Total->SetTextFont(62);
Total->SetTextSize(0.045);
Total->Draw();
ND->Draw();
MD->Draw();
ND45->Draw();
MD45->Draw();
// c01->Print("mult0_correlation_matrix.pdf");
TCanvas* c86 = new TCanvas("c86","",800,400);
c86->SetLeftMargin(.1);
c86->SetBottomMargin(.1);
c86->SetTopMargin(.05);
c86->SetRightMargin(.05);
c86->cd();
Fig6->GetYaxis()->SetTitle("Fractional Error");
Fig6->GetYaxis()->SetTitleFont(62);
Fig6->GetXaxis()->SetTitleFont(62);
Fig6->GetYaxis()->SetLabelFont(62);
Fig6->GetXaxis()->SetLabelFont(62);
Fig6->GetYaxis()->CenterTitle();
Fig6->GetYaxis()->SetTitleSize(0.06);
Fig6->GetYaxis()->SetTitleOffset(0.8);
Fig6->GetXaxis()->SetLabelSize(0.06);
Fig6->GetYaxis()->SetLabelSize(0.06);
Fig6->GetXaxis()->SetTitleOffset(1.5);
Fig6->SetStats(0);
Fig6->SetMinimum(-0.01);
Fig6->SetMaximum(0.21);
Fig6->SetMarkerStyle(8);
Fig6->GetYaxis()->SetNdivisions(509);
Fig6->GetXaxis()->SetNdivisions(509);
Fig6->Draw("P");
split->SetLineColor(1);
split->SetLineWidth(2);
split->DrawLine(19,-0.01,19,0.21);
TLatex *ND = new TLatex(.23,.85,"LAr1-ND (100m) ");
ND->SetNDC();
ND->SetTextFont(62);
ND->SetTextSize(0.05);
ND->Draw();
TLatex *MD = new TLatex(.65,.85,"T600 (600m, on axis)");
MD->SetNDC();
MD->SetTextFont(62);
MD->SetTextSize(0.05);
MD->Draw();
// c86->Print("FractionalErrors_Total.pdf");
TCanvas* c85 = new TCanvas("c85","",800,400);
c85->SetLeftMargin(.1);
c85->SetBottomMargin(.1);
c85->SetTopMargin(.05);
c85->SetRightMargin(.05);
c85->cd();
Fig5->GetYaxis()->SetTitle("K#lower[-0.2]{+} Fractional Error");
Fig5->GetYaxis()->SetTitleFont(62);
Fig5->GetXaxis()->SetTitleFont(62);
Fig5->GetYaxis()->SetLabelFont(62);
Fig5->GetXaxis()->SetLabelFont(62);
Fig5->GetYaxis()->CenterTitle();
Fig5->GetYaxis()->SetTitleSize(0.06);
Fig5->GetYaxis()->SetTitleOffset(0.8);
Fig5->GetXaxis()->SetLabelSize(0.06);
Fig5->GetYaxis()->SetLabelSize(0.06);
Fig5->GetXaxis()->SetTitleOffset(1.5);
Fig5->SetStats(0);
Fig5->SetMinimum(-0.01);
Fig5->SetMaximum(0.21);
Fig5->SetMarkerStyle(8);
Fig5->GetYaxis()->SetNdivisions(509);
Fig5->GetXaxis()->SetNdivisions(509);
Fig5->Draw("P");
split->SetLineColor(1);
split->SetLineWidth(2);
split->DrawLine(19,-0.01,19,0.21);
ND->Draw();
MD->Draw();
// c85->Print("FractionalErrors_Kplus.pdf");
TCanvas* c84 = new TCanvas("c84","",800,400);
c84->SetLeftMargin(.1);
c84->SetBottomMargin(.1);
c84->SetTopMargin(.05);
c84->SetRightMargin(.05);
c84->cd();
Fig4->GetYaxis()->SetTitle("K#lower[-0.2]{-} Fractional Error");
Fig4->GetYaxis()->SetTitleFont(62);
Fig4->GetXaxis()->SetTitleFont(62);
Fig4->GetYaxis()->SetLabelFont(62);
Fig4->GetXaxis()->SetLabelFont(62);
Fig4->GetYaxis()->CenterTitle();
Fig4->GetYaxis()->SetTitleSize(0.06);
Fig4->GetYaxis()->SetTitleOffset(0.8);
Fig4->GetXaxis()->SetLabelSize(0.06);
Fig4->GetYaxis()->SetLabelSize(0.06);
Fig4->GetXaxis()->SetTitleOffset(1.5);
Fig4->SetStats(0);
Fig4->SetMinimum(-0.01);
Fig4->SetMaximum(0.21);
Fig4->SetMarkerStyle(8);
Fig4->GetYaxis()->SetNdivisions(509);
Fig4->GetXaxis()->SetNdivisions(509);
Fig4->Draw("P");
split->SetLineColor(1);
split->SetLineWidth(2);
split->DrawLine(19,-0.01,19,0.21);
ND->Draw();
MD->Draw();
// c84->Print("FractionalErrors_Kmin.pdf");
TCanvas* c83 = new TCanvas("c83","",800,400);
c83->SetLeftMargin(.1);
c83->SetBottomMargin(.1);
c83->SetTopMargin(.05);
c83->SetRightMargin(.05);
c83->cd();
Fig3->GetYaxis()->SetTitle("K#lower[-0.2]{0} Fractional Error");
Fig3->GetYaxis()->SetTitleFont(62);
Fig3->GetXaxis()->SetTitleFont(62);
Fig3->GetYaxis()->SetLabelFont(62);
Fig3->GetXaxis()->SetLabelFont(62);
Fig3->GetYaxis()->CenterTitle();
Fig3->GetYaxis()->SetTitleSize(0.06);
Fig3->GetYaxis()->SetTitleOffset(0.8);
Fig3->GetXaxis()->SetLabelSize(0.06);
Fig3->GetYaxis()->SetLabelSize(0.06);
Fig3->GetXaxis()->SetTitleOffset(1.5);
Fig3->SetStats(0);
Fig3->SetMinimum(-0.01);
Fig3->SetMaximum(0.21);
Fig3->SetMarkerStyle(8);
Fig3->GetYaxis()->SetNdivisions(509);
Fig3->GetXaxis()->SetNdivisions(509);
Fig3->Draw("P");
split->SetLineColor(1);
split->SetLineWidth(2);
split->DrawLine(19,-0.01,19,0.21);
ND->Draw();
MD->Draw();
// c83->Print("FractionalErrors_K0.pdf");
TCanvas* c82 = new TCanvas("c82","",800,400);
c82->SetLeftMargin(.1);
c82->SetBottomMargin(.1);
c82->SetTopMargin(.05);
c82->SetRightMargin(.05);
c82->cd();
Fig2->GetYaxis()->SetTitle("#pi#lower[-0.2]{+} Fractional Error");
Fig2->GetYaxis()->SetTitleFont(62);
Fig2->GetXaxis()->SetTitleFont(62);
Fig2->GetYaxis()->SetLabelFont(62);
Fig2->GetXaxis()->SetLabelFont(62);
Fig2->GetYaxis()->CenterTitle();
Fig2->GetYaxis()->SetTitleSize(0.06);
Fig2->GetYaxis()->SetTitleOffset(0.8);
Fig2->GetXaxis()->SetLabelSize(0.06);
Fig2->GetYaxis()->SetLabelSize(0.06);
Fig2->GetXaxis()->SetTitleOffset(1.5);
Fig2->SetStats(0);
Fig2->SetMinimum(-0.01);
Fig2->SetMaximum(0.21);
Fig2->SetMarkerStyle(8);
Fig2->GetYaxis()->SetNdivisions(509);
Fig2->GetXaxis()->SetNdivisions(509);
Fig2->Draw("P");
split->SetLineColor(1);
split->SetLineWidth(2);
split->DrawLine(19,-0.01,19,0.21);
ND->Draw();
MD->Draw();
// c82->Print("FractionalErrors_piplus.pdf");
TCanvas* c81 = new TCanvas("c81","",800,400);
c81->SetLeftMargin(.1);
c81->SetBottomMargin(.1);
c81->SetTopMargin(.05);
c81->SetRightMargin(.05);
c81->cd();
Fig1->GetYaxis()->SetTitle("#pi#lower[-0.2]{-} Fractional Error");
Fig1->GetYaxis()->SetTitleFont(62);
Fig1->GetXaxis()->SetTitleFont(62);
Fig1->GetYaxis()->SetLabelFont(62);
Fig1->GetXaxis()->SetLabelFont(62);
Fig1->GetYaxis()->CenterTitle();
Fig1->GetYaxis()->SetTitleSize(0.06);
Fig1->GetYaxis()->SetTitleOffset(0.8);
Fig1->GetXaxis()->SetLabelSize(0.06);
Fig1->GetYaxis()->SetLabelSize(0.06);
Fig1->GetXaxis()->SetTitleOffset(1.5);
Fig1->SetStats(0);
Fig1->SetMinimum(-0.01);
Fig1->SetMaximum(0.21);
Fig1->SetMarkerStyle(8);
Fig1->GetYaxis()->SetNdivisions(509);
Fig1->GetXaxis()->SetNdivisions(509);
Fig1->Draw("P");
split->SetLineColor(1);
split->SetLineWidth(2);
split->DrawLine(19,-0.01,19,0.21);
ND->Draw();
MD->Draw();
// c81->Print("FractionalErrors_pimin.pdf");
TCanvas* c80 = new TCanvas("c80","",800,400);
c80->SetLeftMargin(.1);
c80->SetBottomMargin(.1);
c80->SetTopMargin(.05);
c80->SetRightMargin(.05);
c80->cd();
Fig0->GetYaxis()->SetTitle("Beam Fractional Error");
Fig0->GetYaxis()->SetTitleFont(62);
Fig0->GetXaxis()->SetTitleFont(62);
Fig0->GetYaxis()->SetLabelFont(62);
Fig0->GetXaxis()->SetLabelFont(62);
Fig0->GetYaxis()->CenterTitle();
Fig0->GetYaxis()->SetTitleSize(0.06);
Fig0->GetYaxis()->SetTitleOffset(0.8);
Fig0->GetXaxis()->SetLabelSize(0.06);
Fig0->GetYaxis()->SetLabelSize(0.06);
Fig0->GetXaxis()->SetTitleOffset(1.5);
Fig0->SetStats(0);
Fig0->SetMinimum(-0.01);
Fig0->SetMaximum(0.21);
Fig0->SetMarkerStyle(8);
Fig0->GetYaxis()->SetNdivisions(509);
Fig0->GetXaxis()->SetNdivisions(509);
Fig0->Draw("P");
split->SetLineColor(1);
split->SetLineWidth(2);
split->DrawLine(19,-0.01,19,0.21);
ND->Draw();
MD->Draw();
// c80->Print("FractionalErrors_beam.pdf");
cout<<"\nEnd of routine.\n";
return 0;
}
void main() //main code
{ //printing titles for values displayed
printf("\nRUNGE-KUTTA METHOD\nstep size R M Last Rho iterations\n");
double i; //power order for rho(c)
double c = 10; //the parameter rho(c)
int n; //the integer steps, n
//declare arrays
float x[N];
float y[N];
float z[N];
float x2[N];
float y2[N];
float z2[N];
//r,m,p as the radius, mass and density
double r,m,p,r2,m2,p2;
for(i=-5;i<2;i++)
{
h = pow(10,i); //how h is varied by i
c = 10; //the parameter rho(c)
//declare initial conditons for arrays
x[0] = h; //first array is for r=h
y[0] = (h*h*h/3)*c; //initial conditon for scaled mass (m)
z[0] = c*(1-((h*h*c)/(6*gamma(c)))); //initial conditon for rho
//for loop for n=0,1,...,when z[n]>1
for(n=0;z[n]>1;n++)
{
//declared how x(n+1) relates to x(n), y(n+1) relates to y(n), z(n+1) relates to z(n)
x[n+1] = x[n]+h;
y[n+1] = y[n]+(h/6)*(M(x[n],y[n],z[n])+2*M2(x[n],y[n],z[n])+2*M3(x[n],y[n],z[n])+M4(x[n],y[n],z[n]));
z[n+1] = z[n]+(h/6)*(rho(x[n],y[n],z[n])+2*rho2(x[n],y[n],z[n])+2*rho3(x[n],y[n],z[n])+rho4(x[n],y[n],z[n]));
//r,m,p will be declared for printf statement
r = x[n];
m = y[n];
p = z[n];
}
//printed values for x and y respectively
printf("%.2e %.2e %.2e %.2e %i\n",h,r,m,p,n);
}
//printing titles for values displayed
printf("\nEULER METHOD\nstep size R M Last Rho iterations\n");
for(i=-5;i<2;i++)
{
h = pow(10,i); //how h is varied by i
c = 10; //the parameter rho(c)
//declare initial conditons for arrays
x2[0] = h; //first array is for r=h
y2[0] = (h*h*h/3)*c; //initial conditon for scaled mass (m)
z2[0] = fabs(c*(1-((h*h*c)/(6*gamma(c))))); //initial conditon for rho
//for loop for n=0,1,..., when z2[n]>1
for(n=0;z2[n]>1;n++)
{
//declared how x2(n+1) relates to x2(n), y2(n+1) relates to y2(n), z2(n+1) relates to z2(n)
x2[n+1] = x2[n]+h;
y2[n+1] = y2[n]+h*(M(x2[n],y2[n],z2[n]));
z2[n+1] = z2[n]+h*(rho(x2[n],y2[n],z2[n]));
//r2,m2,p2 will be declared in pg-plot
r2 = x2[n];
m2 = y2[n];
p2 = z2[n];
}
//printed values for x and y respectively
printf("%.2e %.2e %.2e %.2e %i\n",h,r2,m2,p2,n);
}
}
void InitSLState(
const dTensorBC4& q, const dTensorBC4& aux, SL_state& sl_state )
{
void ComputeElecField(double t, const dTensor2& node1d,
const dTensorBC4& qvals, dTensorBC3& Evals);
void ConvertQ2dToQ1d(const int &mopt, int istart, int iend,
const dTensorBC4& qin, dTensorBC3& qout);
void IntegrateQ1dMoment1(const dTensorBC4& q2d, dTensorBC3& q1d);
const int space_order = dogParams.get_space_order();
const int mx = q.getsize(1);
const int my = q.getsize(2);
const int meqn = q.getsize(3);
const int maux = aux.getsize(2);
const int kmax = q.getsize(4);
const int mbc = q.getmbc();
const int mpoints = space_order*space_order;
const int kmax1d = space_order;
const double tn = sl_state.tn;
//////////////////////// Compute Electric Field E(t) ////////////////////
// save 1d grid points ( this is used for poisson solve )
dTensorBC3 Enow(mx, meqn, kmax1d, mbc, 1);
ComputeElecField( tn, *sl_state.node1d, *sl_state.qnew, Enow);
//////////// Necessary terms for Et = -M1 + g(x,t) /////////////////////
dTensorBC3 M1(mx, meqn, kmax1d,mbc,1);
IntegrateQ1dMoment1(q, M1); // first moment
//////////// Necessary terms for Ett = 2*KE_x - rho*E + g_t - psi_u ///////
dTensorBC3 KE(mx, meqn, kmax1d,mbc,1);
void IntegrateQ1dMoment2(const dTensorBC4& q2d, dTensorBC3& q1d);
IntegrateQ1dMoment2(q, KE); // 1/2 * \int v^2 * f dv //
SetBndValues1D( KE );
SetBndValues1D( Enow );
SetBndValues1D( M1 );
// do something to compute KE_x ... //
dTensorBC3 gradKE(mx,2,kmax1d,mbc,1);
FiniteDiff( 1, 2, KE, gradKE ); // compute KE_x and KE_xx //
dTensorBC3 rho(mx,meqn,kmax1d,mbc,1);
dTensorBC3 prod(mx,meqn,kmax1d,mbc,1);
void IntegrateQ1d(const int mopt, const dTensorBC4& q2d, dTensorBC3& q1d);
void MultiplyFunctions(const dTensorBC3& Q1, const dTensorBC3& Q2,
dTensorBC3& qnew);
IntegrateQ1d( 1, q, rho );
MultiplyFunctions( rho, Enow, prod );
/////////////////////// Save E, Et, Ett, //////////////////////////////////
for( int i = 1; i <= mx; i++ )
for( int k = 1; k <= kmax1d; k ++ )
{
double E = Enow.get ( i, 1, k );
double Et = -M1.get ( i, 1, k ); // + g(x,t)
double Ett = -prod.get(i,1,k) + 2.0*gradKE.get(i,1,k); // + others //
sl_state.aux1d->set(i,2,1, k, E );
sl_state.aux1d->set(i,2,2, k, Et );
sl_state.aux1d->set(i,2,3, k, Ett );
}
///////////////////////////////////////////////////////////////////////////
// terms used for 4th order stuff ... //
// Ettt = -M3_xx + (2*E_x+rho)*M1 + 3*E*(M1)_x
dTensorBC3 tmp0(mx,2*meqn,kmax1d,mbc,1);
dTensorBC3 tmp1(mx,meqn,kmax1d,mbc,1);
// compute the third moment and its 2nd derivative
dTensorBC3 M3 (mx,meqn,kmax1d,mbc,1);
dTensorBC3 M3_x (mx,2*meqn,kmax1d,mbc,1);
void IntegrateQ1dMoment3(const dTensorBC4& q2d, dTensorBC3& q1d);
IntegrateQ1dMoment3(q, M3 );
SetBndValues1D( M3 );
FiniteDiff( 1, 2, M3, M3_x );
// Compute 2*Ex+rho //
FiniteDiff(1, 2*meqn, Enow, tmp0);
for( int i=1; i <= mx; i++ )
for( int k=1; k <= kmax1d; k++ )
{ tmp1.set(i,1,k, 2.0*tmp0.get(i,1,k) + rho.get(i,1,k) ); }
// compute (2Ex+rho) * M1
dTensorBC3 prod1(mx,meqn,kmax1d,mbc,1);
MultiplyFunctions( tmp1, M1, prod1 );
// compute M1_x and M1_xx
dTensorBC3 M1_x (mx,2*meqn,kmax1d,mbc,1);
FiniteDiff( 1, 2, M1, M1_x );
//compute 3*M1_x and E * (3*M1)_x
dTensorBC3 prod2(mx,meqn,kmax1d,mbc,1);
for( int i=1; i <= mx; i++ )
for( int k=1; k <= kmax1d; k++ )
{ tmp1.set(i, 1, k, 3.0*M1_x.get(i, 1, k) ); }
MultiplyFunctions( Enow, tmp1, prod2 );
/////////////////////// Save Ettt /////////////////////////////////////////
for( int i = 1; i <= mx; i++ )
for( int k = 1; k <= kmax1d; k ++ )
{
double Ettt = -M3_x.get(i,2,k) + prod1.get(i,1,k) + prod2.get(i,1,k);
sl_state.aux1d->set(i,2,4, k, Ettt );
}
///////////////////////////////////////////////////////////////////////////
if ( dogParams.get_source_term()>0 )
{
double* t_ptr = new double;
*t_ptr = tn;
// 2D Electric field, and 1D Electric Field
dTensorBC4* ExactE;
ExactE = new dTensorBC4(mx,1,4,kmax,mbc);
dTensorBC3* ExactE1d;
ExactE1d = new dTensorBC3(mx,4,kmax1d,mbc,1);
// Extra Source terms needed for the electric field
dTensorBC4* ExtraE;
ExtraE = new dTensorBC4(mx,1,4,kmax,mbc);
dTensorBC3* ExtraE1d;
ExtraE1d = new dTensorBC3(mx,4,kmax1d,mbc,1);
// Exact, electric field: (TODO - REMOVE THIS!)
// void ElectricField(const dTensor2& xpts, dTensor2& e, void* data);
// L2Project_extra(1-mbc, mx+mbc, 1, 1, space_order, -1, ExactE,
// &ElectricField, (void*)t_ptr );
// ConvertQ2dToQ1d(1, 1, mx, *ExactE, *ExactE1d);
// Extra Source terms:
void ExtraSourceWrap(const dTensor2& xpts,
const dTensor2& NOT_USED_1,
const dTensor2& NOT_USED_2,
dTensor2& e,
void* data);
L2Project_extra(1, mx, 1, 1, 20, space_order,
space_order, space_order,
&q, &aux, ExtraE, &ExtraSourceWrap, (void*)t_ptr );
ConvertQ2dToQ1d(1, 1, mx, *ExtraE, *ExtraE1d);
for( int i=1; i <= mx; i++ )
for( int k=1; k <= kmax1d; k++ )
{
// electric fields w/o source term parts added in //
double Et = sl_state.aux1d->get(i,2,2,k);
double Ett = sl_state.aux1d->get(i,2,3,k);
double Ettt = sl_state.aux1d->get(i,2,4,k);
// add in missing terms from previously set values //
sl_state.aux1d->set(i,2,2, k, Et + ExtraE1d->get(i,2,k) );
sl_state.aux1d->set(i,2,3, k, Ett + ExtraE1d->get(i,3,k) );
sl_state.aux1d->set(i,2,4, k, Ettt + ExtraE1d->get(i,4,k) );
// sl_state.aux1d->set(i,2,1, k, 0. );
// sl_state.aux1d->set(i,2,2, k, 0. );
// sl_state.aux1d->set(i,2,3, k, 0. );
// sl_state.aux1d->set(i,2,4, k, 0. );
// ADD IN EXACT ELECTRIC FIELD HERE:
// sl_state.aux1d->set(i,2,1, k, ExactE1d->get(i,1,k) );
// sl_state.aux1d->set(i,2,2, k, ExactE1d->get(i,2,k) );
// sl_state.aux1d->set(i,2,3, k, ExactE1d->get(i,3,k) );
// sl_state.aux1d->set(i,2,4, k, ExactE1d->get(i,4,k) );
}
delete ExactE;
delete ExactE1d;
delete t_ptr;
delete ExtraE;
delete ExtraE1d;
}
}
Func ColorMgather(Func stBasis, float angle, uint8_t * orders, Expr filterthreshold, Expr divisionthreshold, Expr divisionthreshold2) {
uint8_t x_order = orders[0];
uint8_t y_order = orders[1];
uint8_t t_order = orders[2];
uint8_t c_order = orders[3];
Func X("X"),Y("Y"),T("T"),Xrg("Xrg"),Yrg("Yrg"),Trg("Trg");
uint8_t max_order = x_order;
// std::vector<Expr>Xk_expr (max_order,cast<float>(0.0f));
// std::vector<Expr>Yk_expr (max_order,cast<float>(0.0f));
// std::vector<Expr>Tk_expr (max_order,cast<float>(0.0f));
uint8_t Xk_uI[max_order];
uint8_t Yk_uI[max_order];
uint8_t Tk_uI[max_order];
Func Xk[max_order]; Func Yk[max_order]; Func Tk[max_order];
// Expr Xk[max_order],Yk[max_order],Tk[max_order];
for (int iO=0; iO < x_order; iO++) {
Xk[iO](x,y,t) = Expr(0.0f);
Yk[iO](x,y,t) = Expr(0.0f);
Tk[iO](x,y,t) = Expr(0.0f);
Xk_uI[iO] = 0;
Yk_uI[iO] = 0;
Tk_uI[iO] = 0;
}
int k = 0;
for (int iXo = 0; iXo < x_order; iXo++) // x_order
for (int iYo = 0; iYo < y_order; iYo++) // y_oder
for (int iTo = 0; iTo < t_order; iTo++) // t_order
for (int iCo = 0; iCo < c_order; iCo ++ ) // c_order: index of color channel
{
if ((iYo+iTo+iCo == 0 || iYo+iTo+iCo == 1)
&& ((iXo+iYo+iTo+iCo+1) < (x_order + 1))) {
X = ColorMgetfilter(stBasis, angle, iXo+1, iYo, iTo, iCo);
Y = ColorMgetfilter(stBasis, angle, iXo, iYo+1, iTo, iCo);
T = ColorMgetfilter(stBasis, angle, iXo, iYo, iTo+1, iCo);
Xrg = ColorMgetfilter(stBasis, angle, iXo+1, iYo, iTo, iCo+1);
Yrg = ColorMgetfilter(stBasis, angle, iXo, iYo+1, iTo, iCo+1);
Trg = ColorMgetfilter(stBasis, angle, iXo, iYo, iTo+1, iCo+1);
k = iXo + iYo + iTo + iCo;
Xk[k](x,y,t) += X(x,y,t) + Xrg(x,y,t);
Yk[k](x,y,t) += Y(x,y,t) + Yrg(x,y,t);
Tk[k](x,y,t) += T(x,y,t) + Trg(x,y,t);
Xk[k].update(Xk_uI[k]); Xk_uI[k]++;
Yk[k].update(Yk_uI[k]); Yk_uI[k]++;
Tk[k].update(Tk_uI[k]); Tk_uI[k]++;
}
}
// Scheduling
for (int iO = 0; iO <= k; iO++) {
Xk[iO].compute_root();
Yk[iO].compute_root();
Tk[iO].compute_root();
}
std::vector<Expr> st_expr(6,cast<float>(0.0f));
for (int iK=0; iK <= k; iK++) {
st_expr[0] += Xk[iK](x,y,t)*Tk[iK](x,y,t);
st_expr[1] += Tk[iK](x,y,t)*Tk[iK](x,y,t);
st_expr[2] += Xk[iK](x,y,t)*Xk[iK](x,y,t);
st_expr[3] += Yk[iK](x,y,t)*Tk[iK](x,y,t);
st_expr[4] += Yk[iK](x,y,t)*Yk[iK](x,y,t);
st_expr[5] += Xk[iK](x,y,t)*Yk[iK](x,y,t);
}
Func st("st"); st(x,y,t) = Tuple(st_expr);
st.compute_root();
Expr x_clamped = clamp(x,0,width-1);
Expr y_clamped = clamp(y,0,height-1);
Func st_clamped("st_clamped"); st_clamped(x,y,t) = st(x_clamped,y_clamped,t);
// float win = 7.0;
// Image<float> meanfilter(7,7,"meanfilter_data");
// meanfilter(x,y) = Expr(1.0f/(win*win));
// RDom rMF(meanfilter);
uint8_t win = 7;
RDom rMF(0,win,0,win);
Func st_filtered[6];
for (uint8_t iPc=0; iPc<6; iPc++) {
// iPc: index of product component
// Apply average filter
st_filtered[iPc](x,y,t) = sum(rMF,st_clamped(x + rMF.x,y + rMF.y,t)[iPc]/Expr(float(win*win)),"mean_filter");
st_filtered[iPc].compute_root();
}
// Tuple st_tuple = Tuple(st_expr);
// 4 debug
// Func tmpOut("tmpOut"); tmpOut(x,y,t) = Tuple(st_filtered[0](x,y,t),st_filtered[1](x,y,t),st_filtered[2](x,y,t),st_filtered[3](x,y,t),st_filtered[4](x,y,t),st_filtered[5](x,y,t));
// return tmpOut;
Tuple pbx = Tuple(st_filtered[2](x,y,t),st_filtered[5](x,y,t),st_filtered[0](x,y,t));
Tuple pby = Tuple(st_filtered[5](x,y,t),st_filtered[4](x,y,t),st_filtered[3](x,y,t));
Tuple pbt = Tuple(st_filtered[0](x,y,t),st_filtered[3](x,y,t),st_filtered[1](x,y,t));
Func pbxy("pbxy"); pbxy = cross(pby,pbx); pbxy.compute_root();
Func pbxt("pbxt"); pbxt = cross(pbx,pbt); pbxt.compute_root();
Func pbyt("pbyt"); pbyt = cross(pby,pbt); pbyt.compute_root();
Func pbxyd("pbxyd"); pbxyd = dot(pby,pbx); pbxyd.compute_root();
Func pbxtd("pbxtd"); pbxtd = dot(pbx,pbt); pbxtd.compute_root();
Func pbytd("pbytd"); pbytd = dot(pby,pbt); pbytd.compute_root();
// 4 debug
// Func tmpOut("tmpOut"); tmpOut(x,y,t) = Tuple(pbxy(x,y,t)[0],pbxt(x,y,t)[0],pbyt(x,y,t)[0],pbxyd(x,y,t),pbxtd(x,y,t),pbytd(x,y,t));
// return tmpOut;
Func yt_xy("yt_xy"); yt_xy = dot(pbyt(x,y,t),pbxy(x,y,t)); yt_xy.compute_root();
Func xt_yt("xt_yt"); xt_yt = dot(pbxt(x,y,t),pbyt(x,y,t)); xt_yt.compute_root();
Func xt_xy("xt_xy"); xt_xy = dot(pbxt(x,y,t),pbxy(x,y,t)); xt_xy.compute_root();
Func yt_yt("yt_yt"); yt_yt = dot(pbyt(x,y,t),pbyt(x,y,t)); yt_yt.compute_root();
Func xt_xt("xt_xt"); xt_xt = dot(pbxt(x,y,t),pbxt(x,y,t)); xt_xt.compute_root();
Func xy_xy("xy_xy"); xy_xy = dot(pbxy(x,y,t),pbxy(x,y,t)); xy_xy.compute_root();
Tuple Tk_tuple = Tuple(Tk[0](x,y,t),Tk[1](x,y,t),Tk[2](x,y,t),
Tk[3](x,y,t),Tk[4](x,y,t));
Func Tkd("Tkd"); Tkd = dot(Tk_tuple,Tk_tuple); Tkd.compute_root();
// Expr Dimen = pbxyd/xy_xy;
Expr kill(1.0f);
Func Oxy; Oxy(x,y,t) = Mdefdiv(st_filtered[5](x,y,t) - Mdefdivang(yt_xy(x,y,t),yt_yt(x,y,t),pbxyd(x,y,t),divisionthreshold2)*st_filtered[3](x,y,t)*kill,st_filtered[4](x,y,t),divisionthreshold);
Oxy.compute_root();
Func Oyx; Oyx(x,y,t) = Mdefdiv(st_filtered[5](x,y,t) + Mdefdivang(xt_xy(x,y,t),xt_xt(x,y,t),pbxyd(x,y,t),divisionthreshold2)*st_filtered[0](x,y,t)*kill,st_filtered[2](x,y,t),divisionthreshold);
Oyx.compute_root();
Func C0; C0(x,y,t) = st_filtered[3](x,y,t) * Mdefdivang(Expr(-1.0f)*xt_yt(x,y,t),yt_yt(x,y,t),pbxyd(x,y,t),divisionthreshold2)*kill;
C0.compute_root();
Func M0; M0(x,y,t) = Mdefdiv(st_filtered[0](x,y,t) + C0(x,y,t), st_filtered[1](x,y,t)*pow(Mdefdivang(xt_yt(x,y,t),yt_yt(x,y,t),pbxyd(x,y,t),divisionthreshold2),Expr(2.0f)),divisionthreshold);
M0.compute_root();
Func C1; C1(x,y,t) = st_filtered[5](x,y,t) * Mdefdivang(Expr(-1.0f)*xt_xy(x,y,t),xy_xy(x,y,t),pbxyd(x,y,t),divisionthreshold2)*kill;
C1.compute_root();
Func P1; P1(x,y,t) = pow(Mdefdivang(xt_yt(x,y,t),xt_xt(x,y,t),pbxyd(x,y,t),divisionthreshold2),Expr(2.0f))*kill + 1.0f;
P1.compute_root();
// 4 debug
// Func tmpOut("tmpOut"); tmpOut(x,y,t) = Tuple(Oxy(x,y,t),Oyx(x,y,t),C0(x,y,t),M0(x,y,t),C1(x,y,t),P1(x,y,t));
// return tmpOut;
Func Q1; Q1(x,y,t) = st_filtered[2](x,y,t) * (pow(Oyx(x,y,t),Expr(2.0f))+Expr(1.0f));
Q1.compute_root();
Func M1; M1(x,y,t) = Mdefdiv(((st_filtered[0](x,y,t)-C1(x,y,t))*P1(x,y,t)),Q1(x,y,t),divisionthreshold);
M1.compute_root();
Func C2; C2(x,y,t) = st_filtered[0](x,y,t) * Mdefdivang(Expr(-1.0f)*xt_yt(x,y,t),xt_xt(x,y,t),pbxyd(x,y,t),divisionthreshold2)*kill;
C2.compute_root();
Func M2; M2(x,y,t) = Mdefdiv(st_filtered[3](x,y,t)+C2(x,y,t),st_filtered[1](x,y,t)*(pow(Mdefdivang(xt_yt(x,y,t),xt_xt(x,y,t),pbxyd(x,y,t),divisionthreshold2),Expr(2.0f))*kill+Expr(1.0f)),divisionthreshold);
M2.compute_root();
Func C3; C3(x,y,t) = st_filtered[5](x,y,t) * Mdefdivang(yt_xy(x,y,t),xy_xy(x,y,t),pbxyd(x,y,t),divisionthreshold2)*kill;
C3.compute_root();
Func P3; P3(x,y,t) = pow(Mdefdivang(xt_yt(x,y,t),yt_yt(x,y,t),pbxyd(x,y,t),divisionthreshold2),Expr(2.0f))*kill + Expr(1.0f);
P3.compute_root();
Func Q3; Q3(x,y,t) = st_filtered[4](x,y,t) * (pow(Oxy(x,y,t),Expr(2.0f))+Expr(1.0f));
Q3.compute_root();
Func M3; M3(x,y,t) = Mdefdiv(((st_filtered[3](x,y,t)-C3(x,y,t))*P3(x,y,t)),Q3(x,y,t),divisionthreshold);
M3.compute_root();
Func basisAtAngle;
basisAtAngle(x,y,t) = Tuple(M0(x,y,t),M1(x,y,t),M2(x,y,t),M3(x,y,t),Tkd(x,y,t));
return basisAtAngle;
// Func hsv2rgb(Func colorImage) { // Took this function
// Var x, y, c, t;
// Func output;
// output(x,y,c,t) = cast <float> (0.0f);
// Expr fR, fG, fB; // R,G & B values
// Expr fH = (colorImage(x,y,0,t)); //H value [0-360)
// Expr fS = (colorImage(x,y,1,t)); //S value
// Expr fV = (colorImage(x,y,2,t)); //V value
// //Conversion (I took the one on Wikipedia)
// // https://fr.wikipedia.org/wiki/Teinte_Saturation_Valeur#Conversion_de_TSV_vers_RVB
// Expr fHi = floor(fH / Expr(60.0f));
// Expr fF = fH / 60.0f - fHi;
// Expr fL = fV * (1 - fS);
// Expr fM = fV * (1 - fF * fS) ;
// Expr fN = fV * (1 - (1 - fF) * fS);
// fR = select((0 == fHi),fV,
// (1 == fHi),fM,
// (2 == fHi),fL,
// (3 == fHi),fL,
// (4 == fHi),fN,
// (5 == fHi),fV,
// 0.0f);
// fG = select((0 == fHi),fN,
// (1 == fHi),fV,
// (2 == fHi),fV,
// (3 == fHi),fM,
// (4 == fHi),fL,
// (5 == fHi),fL,
// 0.0f);
// fB = select((0 == fHi),fL,
// (1 == fHi),fL,
// (2 == fHi),fN,
// (3 == fHi),fV,
// (4 == fHi),fV,
// (5 == fHi),fM,
// 0.0f);
// output(x,y,0,t) = fR;
// output(x,y,1,t) = fG;
// output(x,y,2,t) = fB;
// return output;
// }
// Func angle2rgb (Func v) {
// Var x, y, c, t;
// Func ov, a;
// ov(x,y,c,t) = cast <float> (0.0f);
// Expr pi2(2*M_PI);
// a(x,y,c,t) = v(x,y,c,t) / pi2;
// ov(x,y,0,t) = a(x,y,c,t);
// ov(x,y,1,t) = 1;
// ov(x,y,2,t) = 1;
// return ov;
// }
// Func outputvelocity(Func Blur, Func Speed, Func Angle, int border, Expr speedthreshold, Expr filterthreshold) {
// extern Expr width;
// extern Expr height;
// Func Blur3, Speed3;
// Blur3(x,y,c,t) = cast <float> (0.0f);
// Speed3(x,y,c,t) = cast <float> (0.0f);
// //Scale the grey level images
// Blur(x,y,0,t) = (Blur(x,y,0,t) - minimum(Blur(x,y,0,t))) / (maximum(Blur(x,y,0,t)) - minimum(Blur(x,y,0,t)));
// //Concatenation along the third dimension
// Blur3(x,y,0,t) = Blur(x,y,0,t);
// Blur3(x,y,1,t) = Blur(x,y,0,t);
// Blur3(x,y,2,t) = Blur(x,y,0,t);
// //Speed scaled to 1
// //Concatenation along the third dimension
// Speed3(x,y,1,t) = Speed(x,y,0,t);
// Speed3(x,y,2,t) = Speed(x,y,0,t);
// //Use the log speed to visualise speed
// Func LogSpeed;
// LogSpeed(x,y,c,t) = fast_log(Speed3(x,y,c,t) + Expr(0.0000001f))/fast_log(Expr(10.0f));
// LogSpeed(x,y,c,t) = (LogSpeed(x,y,c,t) - minimum(LogSpeed(x,y,c,t))) / (maximum(LogSpeed(x,y,c,t)) - minimum(LogSpeed(x,y,c,t)));
// //Make a colour image
// // uint16_t rows = height;
// // uint16_t cols = width;
// // int depth = Angle.channels();
// //Do it the HSV way
// Func colorImage;
// colorImage(x,y,0,t) = Angle(x,y,0,t);
// //Do hsv to rgb
// Func colorImage1;
// colorImage1 = hsv2rgb(colorImage);
// // Assume the border equals to the size of spatial filter
// //Make the border
// // int bir = rows + 2 * border;
// // int bic = cols + 2 * border;
// Expr orows = height / Expr(2);
// Expr ocols = width / Expr(2);
// //Rotation matrix
// int ph = 0;
// Func mb, sb;
// // if (rx < border - 1 || rx >= rows+border -1 || ry < border - 1 || ry >= cols+border - 1) {
// Expr co1 = x - orows;
// Expr co2 = - (y - ocols);
// Expr cosPh(cos(ph));
// Expr sinPh(sin(ph));
// Expr rco1 = cosPh * co1 - sinPh * co2; //Using rotation matrix
// Expr rco2 = sinPh * co1 + cosPh * co2;
// // Expr justPi (M_PI);
// mb(x,y,c,t) =
// select (((x < (border - 1)) ||
// (x >= (height+border -1)) ||
// (y < (border - 1)) ||
// (y >= (width+border - 1))),
// atan2(rco1,rco2) + Expr(M_PI),mb(x,y,c,t));
// sb(x,y,c,t) =
// select (((x < (border - 1)) ||
// (x >= (height+border -1)) ||
// (y < (border - 1) ) ||
// (y >= (width+border - 1))),
// 1, sb (x,y,c,t));
// Func cb;
// cb = angle2rgb(mb);
// //Get the old data
// // Expr pi2(2*M_PI);
// colorImage1(x,y,0,t)=colorImage(x,y,0,t) * Expr(2*M_PI);
// colorImage1=angle2rgb(colorImage1);
// colorImage1(x,y,c,t)=select(abs(Speed3(x,y,c,t))<speedthreshold,Expr(0.0f),colorImage1(x,y,c,t));
// Func colorImage2;
// colorImage2(x,y,c,t) = colorImage1(x,y,c,t) * Speed(x,y,c,t);
// //Put the data in the border
// RDom bordx (border,rows + border);
// RDom bordy (border,cols + border);
// Func ang1, ang2;
// ang1 (x,y,c,t) = cast <float> (0.0f);
// ang2 (x,y,c,t) = cast <float> (0.0f);
// cb(bordx, bordy,c,t) = colorImage1(x,y,c,t);
// ang1 = cb;
// cb(bordx, bordy,c,t) = colorImage2(x,y,c,t);
// ang2 = cb;
// sb(bordx, bordy,c,t) = Speed3(x,y,c,t);
// Speed3 = sb;
// sb(bordx, bordy,c,t) = Blur3(x,y,c,t);
// Blur3 = sb;
// // Func I;
// // I (x,y,c,t) = Blur3(x,y,c,t) + Speed3(x,y - height,c,t) + ang1(x - width,y,c,t) + ang2(x - width,y - height,c,t);
// //I = cat(2,cat(1,Blur,Speed),cat(1,ang1,ang2));
// return I;
// }
}
void main() //main code
{
double Rs = Y*((7.72*pow(10,8))/(6.95*pow(10,10)));
double Ms = Y*Y*((5.67*pow(10,33))/(1.98*pow(10,33)));
double c = 82; //the parameter rho(c)
printf("\nSIRIUS B\n");
printf("\nRunge-Kutta Method\nMs (solar masses) Rs (solar radii) Rho(c) (solar densities) Y(e)\n"); //printing titles for values displayed
int n; //the integer steps, n
//declare arrays
float x[N];
float y[N];
float z[N];
float x2[N];
float y2[N];
float z2[N];
//r,m,p as the radius, mass and density
double r,m,p,r2,m2,p2;
//declare initial conditons for arrays
x[0] = h; //first array is for r=h
y[0] = (h*h*h/3)*c; //initial conditon for scaled mass (m)
z[0] = c*(1-((h*h*c)/(6*gamma(c)))); //initial conditon for rho
//for loop for n=0,1,...,N
for(n=0;n<N;n++)
{
//declared how x(n+1) relates to x(n), y(n+1) relates to y(n), z(n+1) relates to z(n)
x[n+1] = x[n]+h;
y[n+1] = y[n]+(h/6)*(M(x[n],y[n],z[n])+2*M2(x[n],y[n],z[n])+2*M3(x[n],y[n],z[n])+M4(x[n],y[n],z[n]));
z[n+1] = z[n]+(h/6)*(rho(x[n],y[n],z[n])+2*rho2(x[n],y[n],z[n])+2*rho3(x[n],y[n],z[n])+rho4(x[n],y[n],z[n]));
if(isnan(z[n+1]))
{
break;
}
//r,m,p will be declared in pg-plot
r = x[n+1];
m = y[n+1];
p = z[n+1];
}
printf("%.3e %.3e %.2f %.3f\n",y[n]*Ms,x[n]*Rs,c,Y); //printed values for x and y respectively
printf("\nEuler Method\nMs (solar masses) Rs (solar radii) Rho(c) (solar densities) Y(e)\n"); //printing titles for values displayed
//declare initial conditons for arrays
x2[0] = h; //first array is for r=h
y2[0] = (h*h*h/3)*c; //initial conditon for scaled mass (m)
z2[0] = c*(1-((h*h*c)/(6*gamma(c)))); //initial conditon for rho
//for loop for n=0,1,...,200
for(n=0;n<N;n++)
{
//declared how x2(n+1) relates to x2(n), y2(n+1) relates to y2(n), z2(n+1) relates to z2(n)
x2[n+1] = x2[n]+h;
y2[n+1] = y2[n]+h*(M(x2[n],y2[n],z2[n]));
z2[n+1] = z2[n]+h*(rho(x2[n],y2[n],z2[n]));
if(z2[n+1]<0)
{
break;
}
//r2,m2,p2 will be declared in pg-plot
r2 = x2[n+1];
m2 = y2[n+1];
p2 = z2[n+1];
}
//printed values for x and y respectively
printf("%.3e %.3e %.2f %.3f\n",y2[n]*Ms,x2[n]*Rs,c,Y);
}
void TestMatrix(ostream& os)
{
// display a headline
os << "Matrix test\r\n===========\r\n";
Matrix<int> A(3,3), B(3,3), C(3,3), D(3,3);
A(0,0) = 1;
A(0,1) = 3;
A(0,2) = -4;
A(1,0) = 1;
A(1,1) = 1;
A(1,2) = -2;
A(2,0) = -1;
A(2,1) = -2;
A(2,2) = 5;
B(0,0) = 8;
B(0,1) = 3;
B(0,2) = 0;
B(1,0) = 3;
B(1,1) = 10;
B(1,2) = 2;
B(2,0) = 0;
B(2,1) = 2;
B(2,2) = 6;
D(0,0) = 1;
D(0,1) = 2;
D(0,2) = -1;
D(1,0) = 2;
D(1,1) = -1;
D(1,2) = -3;
D(2,0) = 0;
D(2,1) = -2;
D(2,2) = 4;
os << "\r\nMatrix A = \r\n";
ShowMatrix(os,A);
os << "\r\nMatrix B = \r\n";
ShowMatrix(os,B);
C = A % B;
os << "\r\nMatrix C (A % B) = \r\n";
ShowMatrix(os,C);
C = A + B;
os << "\r\nMatrix C (A + B) = \r\n";
ShowMatrix(os,C);
C = A;
C += B;
os << "\r\nMatrix C (= A, += B) =\r\n";
ShowMatrix(os,C);
C = A + 1;
os << "\r\nMatrix C (= A + 1) =\r\n";
ShowMatrix(os,C);
C += 1;
os << "\r\nMatrix C (+= 1) =\r\n";
ShowMatrix(os,C);
C = A - B;
os << "\r\nMatrix C (A - B) = \r\n";
ShowMatrix(os,C);
C = A;
C -= B;
os << "\r\nMatrix C (= A, -= B) =\r\n";
ShowMatrix(os,C);
C = A - 1;
os << "\r\nMatrix C (= A - 1) =\r\n";
ShowMatrix(os,C);
C -= 1;
os << "\r\nMatrix C (-= 1) =\r\n";
ShowMatrix(os,C);
C = A * B;
os << "\r\nMatrix C (A * B) = \r\n";
ShowMatrix(os,C);
C = A;
C *= B;
os << "\r\nMatrix C (= A, *= B) =\r\n";
ShowMatrix(os,C);
C = A * 2;
os << "\r\nMatrix C (= A * 2) =\r\n";
ShowMatrix(os,C);
C *= 2;
os << "\r\nMatrix C (*= 2) =\r\n";
ShowMatrix(os,C);
C = B / A;
os << "\r\nMatrix C (B / A) = \r\n";
ShowMatrix(os,C);
C = B;
C /= A;
os << "\r\nMatrix C (= B, /= A) =\r\n";
ShowMatrix(os,C);
C = A / 2;
os << "\r\nMatrix C (= A / 2) =\r\n";
ShowMatrix(os,C);
C /= 2;
os << "\r\nMatrix C (/= 2) =\r\n";
ShowMatrix(os,C);
C = -A;
os << "\r\nMatrix C (-A) = \r\n";
ShowMatrix(os,C);
// test comparisons
os << "\r\nMatrix A = \r\n";
ShowMatrix(os,A);
os << "\r\nMatrix D = \r\n";
ShowMatrix(os,D);
if (A.Equals(D))
os << "\r\nERROR: A should not equal D";
else
os << "\r\nOKAY: A not equal D";
C = A;
if (A.Equals(C))
os << "\r\nOKAY: A equals C\r\n";
else
os << "\r\nERROR: A should equal C\r\n";
Matrix<bool> I(3,3);
I = (A == D);
os << "\r\nMatrix I = (A == D)\r\n";
ShowMatrix(os,I);
I = (A != D);
os << "\r\nMatrix I = (A != D)\r\n";
ShowMatrix(os,I);
I = (A < D);
os << "\r\nMatrix I = (A < D)\r\n";
ShowMatrix(os,I);
I = (A <= D);
os << "\r\nMatrix I = (A <= D)\r\n";
ShowMatrix(os,I);
I = (A > D);
os << "\r\nMatrix I = (A > D)\r\n";
ShowMatrix(os,I);
I = (A >= D);
os << "\r\nMatrix I = (A >= D)\r\n";
ShowMatrix(os,I);
// check fill function
C.Fill(9);
os << "\r\nC filled with 9 =\r\n";
ShowMatrix(os,C);
// check Apply functions
C = Apply(A, Times2);
os << "\r\nC = A.Apply(Times2)\r\n";
ShowMatrix(os,C);
C.Apply(Times2);
os << "\r\nApply(C,Times2)\r\n";
ShowMatrix(os,C);
// check row and column vector functions
Matrix<int> S(1,1);
Matrix<int> r1A(3,1);
Matrix<int> c0B(1,3);
r1A = A.VectorRow(1);
c0B = B.VectorCol(0);
os << "\r\nMatrix S = \r\n";
ShowMatrix(os,S);
os << "\r\nMatrix R1A = \r\n";
ShowMatrix(os,r1A);
os << "\r\nMatrix C0B = \r\n";
ShowMatrix(os,c0B);
if (r1A.IsRowVector())
os << "\r\nOKAY: R1A is row vector";
else
os << "\r\nERROR: R1A should be a row vector";
if (!r1A.IsColVector())
os << "\r\nOKAY: R1A is not a column vector";
else
os << "\r\nERROR: R1A should not be a column vector";
if (!c0B.IsRowVector())
os << "\r\nOKAY: C0B is not a row vector";
else
os << "\r\nERROR: C0B should not be a row vector";
if (c0B.IsColVector())
os << "\r\nOKAY: C0B is column vector";
else
os << "\r\nERROR: C0B should be a column vector";
if (c0B.IsVector())
os << "\r\nOKAY: C0B is a vector";
else
os << "\r\nERROR: C0B should be a vector";
if (!A.IsVector())
os << "\r\nOKAY: A is not a vector";
else
os << "\r\nERROR: A should not be a vector";
if (!c0B.IsSquare())
os << "\r\nOKAY: C0B is not square";
else
os << "\r\nERROR: C0B should not be square";
if (A.IsSquare())
os << "\r\nOKAY: A is square";
else
os << "\r\nERROR: A should be square";
B.Fill(0);
if (B.IsZero())
os << "\r\nOKAY: B is zero";
else
os << "\r\nERROR: B should be zero";
if (!A.IsZero())
os << "\r\nOKAY: A is not zero";
else
os << "\r\nERROR: A should not be zero";
// test inner product
int ip = r1A.InnerProduct(c0B);
os << "\r\n\r\ninner product of R1A and C0B = " << ip << "\r\n";
// make some bigger matrices
Matrix<int> M1(5,5), M2(5,5,3), M3(5,5), M4(5,5);
const int junk[] = { 1, 5, 3, 0, 1,
0, 2, 0, 4, 5,
1, 0, 0, 2, 3,
7, 1, 3, 0, 0,
2, 1, 0, 4, 6 };
const int ident[] = { 1, 0, 0, 0, 0,
0, 1, 0, 0, 0,
0, 0, 1, 0, 0,
0, 0, 0, 1, 0,
0, 0, 0, 0, 1 };
const int tridi[] = { 1, 1, 0, 0, 0,
1, 1, 1, 0, 0,
0, 1, 1, 1, 0,
0, 0, 1, 1, 1,
0, 0, 0, 1, 1 };
const int utri[] = { 1, 1, 1, 1, 1,
0, 1, 1, 1, 1,
0, 0, 1, 1, 1,
0, 0, 0, 1, 1,
0, 0, 0, 0, 1 };
const int ltri[] = { 1, 0, 0, 0, 0,
1, 1, 0, 0, 0,
1, 1, 1, 0, 0,
1, 1, 1, 1, 0,
1, 1, 1, 1, 1 };
const int perm[] = { 0, 1, 0, 0, 0,
1, 0, 0, 0, 0,
0, 0, 0, 1, 0,
0, 0, 0, 0, 1,
0, 0, 1, 0, 0 };
const int det[] = { 3, 5, 3, 8, 1,
2, 6, 3, 4, 5,
1, 4, 5, 2, 3,
7, 1, 3, 6, 8,
2, 4, 1, 4, 9 };
M1 = ident;
M3 = M1 * 2;
M4 = junk;
os << "\r\nmatrix M1 = \r\n";
ShowMatrix(os,M1);
os << "\r\nmatrix M2 = \r\n";
ShowMatrix(os,M2);
os << "\r\nmatrix M3 = \r\n";
ShowMatrix(os,M3);
os << "\r\nmatrix M4 = \r\n";
ShowMatrix(os,M4);
if (M1.IsDiagonal())
os << "\r\nOKAY: M1 is diagonal";
else
os << "\r\nERROR: M1 should be diagonal";
if (M1.IsIdentity())
os << "\r\nOKAY: M1 is an identity matrix";
else
os << "\r\nERROR: M1 should be an identity matrix";
if (!M2.IsDiagonal())
os << "\r\nOKAY: M2 is not diagonal";
else
os << "\r\nERROR: M2 should not be diagonal";
if (!M2.IsIdentity())
os << "\r\nOKAY: M2 is not an identity matrix";
else
os << "\r\nERROR: M2 should not be an identity matrix";
if (M3.IsDiagonal())
os << "\r\nOKAY: M3 is diagonal";
else
os << "\r\nERROR: M3 should be diagonal";
if (!M3.IsIdentity())
os << "\r\nOKAY: M3 is not an identity matrix";
else
os << "\r\nERROR: M3 should not be an identity matrix";
if (!M4.IsDiagonal())
os << "\r\nOKAY: M4 is not diagonal";
else
os << "\r\nERROR: M4 should not be diagonal";
if (!M4.IsIdentity())
os << "\r\nOKAY: M4 is not an identity matrix";
else
os << "\r\nERROR: M4 should not be an identity matrix";
// tridiagonal tests
M1 = tridi;
os << "\r\n\r\nmatrix M1 = \r\n";
ShowMatrix(os,M1);
if (M1.IsTridiagonal())
os << "\r\nOKAY: M1 is tridiagonal";
else
os << "\r\nERROR: M1 should be tridiagonal";
if (!M4.IsTridiagonal())
os << "\r\nOKAY: M4 is not tridiagonal";
else
os << "\r\nERROR: M1 should not be tridiagonal";
// upper triangular tests
M1 = utri;
os << "\r\n\r\nmatrix M1 = \r\n";
ShowMatrix(os,M1);
if (M1.IsUpperTriangular())
os << "\r\nOKAY: M1 is upper-triangular";
else
os << "\r\nERROR: M1 should be upper-triangular";
if (!M4.IsUpperTriangular())
os << "\r\nOKAY: M4 is not upper-triangular";
else
os << "\r\nERROR: M4 should not be upper-triangular";
// lower triangular tests
M1 = ltri;
os << "\r\n\r\nmatrix M1 = \r\n";
ShowMatrix(os,M1);
if (M1.IsLowerTriangular())
os << "\r\nOKAY: M1 is lower-triangular";
else
os << "\r\nERROR: M1 should be lower-triangular";
if (!M4.IsLowerTriangular())
os << "\r\nOKAY: M4 is not lower-triangular";
else
os << "\r\nERROR: M4 should not be lower-triangular";
// permutation tests
M1 = perm;
os << "\r\n\r\nmatrix M1 = \r\n";
ShowMatrix(os,M1);
M2 = ident;
os << "\r\n\r\nmatrix M2 = \r\n";
ShowMatrix(os,M2);
if (M1.IsPermutation())
os << "\r\nOKAY: M1 is permutation matrix";
else
os << "\r\nERROR: M1 should be permutation";
if (M2.IsPermutation())
os << "\r\nOKAY: M2 is permutation matrix";
else
os << "\r\nERROR: M2 should be permutation";
if (!M4.IsPermutation())
os << "\r\nOKAY: M4 is not permutation";
else
os << "\r\nERROR: M4 should not be permutation";
// check singularity function
M1(0,1) = 0;
os << "\r\n\r\nmatrix M1 = \r\n";
ShowMatrix(os,M1);
if (M1.IsSingular())
os << "\r\nOKAY: M1 is singular";
else
os << "\r\nERROR: M1 should be singular";
if (!M2.IsSingular())
os << "\r\nOKAY: M2 is not singular";
else
os << "\r\nERROR: M2 should not be singular";
if (!M4.IsSingular())
os << "\r\nOKAY: M4 is not singular";
else
os << "\r\nERROR: M4 should not be singular";
// change main window heading
os <<endl
<<"Matrix Tests (manipulations)" <<endl
<<"============================" <<endl;
// test minors and determinants
os << "\r\n\r\nmatrix M4 = \r\n";
ShowMatrix(os,M4);
os << "\r\nminor M4(1,1) = \r\n";
ShowMatrix(os,M4.Minor(1,1));
os << "\r\nminor M4(0,4) = \r\n";
ShowMatrix(os,M4.Minor(0,4));
Matrix<int> M5(2,2), M6(3,3);
M5(0,0) = 1;
M5(0,1) = 2;
M5(1,0) = 3;
M5(1,1) = 4;
M6(0,0) = 1;
M6(0,1) = 3;
M6(0,2) = 2;
M6(1,0) = 5;
M6(1,1) = 4;
M6(1,2) = 7;
M6(2,0) = 6;
M6(2,1) = 9;
M6(2,2) = 8;
M4 = det;
Matrix<int> T4(5,5), T5(2,2), T6(3,3);
T4 = M4.Transpose();
T5 = M5.Transpose();
T6 = M6.Transpose();
os << "\r\nmatrix M5 = \r\n";
ShowMatrix(os,M5);
os << "\r\ndeterminant of M5 = "
<< M5.Determinant() << "\r\n";
os << "\r\nmatrix T5 = \r\n";
ShowMatrix(os,T5);
os << "\r\ndeterminant of T5 = "
<< T5.Determinant() << "\r\n";
os << "\r\nmatrix M6 = \r\n";
ShowMatrix(os,M6);
os << "\r\ndeterminant of M6 = "
<< M6.Determinant() << "\r\n";
os << "\r\nmatrix T6 = \r\n";
ShowMatrix(os,T6);
os << "\r\ndeterminant of T6 = "
<< T6.Determinant() << "\r\n";
os << "\r\nmatrix M4 = \r\n";
ShowMatrix(os,M4);
os << "\r\ndeterminant of M4 = "
<< M4.Determinant() << "\r\n";
os << "\r\nmatrix T4 = \r\n";
ShowMatrix(os,T4);
os << "\r\ndeterminant of T4 = "
<< T4.Determinant() << "\r\n";
Matrix<int> R;
os << "\r\nMatrix R (def. constr.) = \r\n";
ShowMatrix(os,R);
R.Resize(10,10);
os << "\r\nMatrix R (now 10x10) = \r\n";
ShowMatrix(os,R);
// change main window heading
os <<endl
<<"Matrix Tests (double)" <<endl
<<"=====================" <<endl;
// check <double> Matrix
os << "\r\nFLOATING POINT!";
Matrix<double> X(3,4), Y(4,3), Z(3,3);
X(0,0) = 1.0; X(1,0) = 5.0; X(2,0) = 2.0;
X(0,1) = 2.0; X(1,1) = 2.0; X(2,1) = 4.0;
X(0,2) = 0.0; X(1,2) = 3.0; X(2,2) = 3.0;
X(0,3) = 1.0; X(1,3) = 2.0; X(2,3) = 1.0;
Y(0,0) = 0.0; Y(2,0) = 1.0;
Y(0,1) = 1.0; Y(2,1) = 0.0;
Y(0,2) = 2.0; Y(2,2) = 5.0;
Y(1,0) = 1.0; Y(3,0) = 3.0;
Y(1,1) = 3.0; Y(3,1) = 1.0;
Y(1,2) = 2.0; Y(3,2) = 2.0;
os << "\r\nMatrix X = \r\n";
ShowMatrix(os,X);
os << "\r\nMatrix Y = \r\n";
ShowMatrix(os,Y);
Z = X % Y;
os << "\r\nMatrix Z (X % Y) = \r\n";
ShowMatrix(os,Z);
// check transposition
Matrix<double> tX;
tX = X.Transpose();
os << "\r\nOriginal X =\r\n";
ShowMatrix(os,X);
os << "\r\nTranspose X =\r\n";
ShowMatrix(os,tX);
X(0,0) = 1; X(0,1) = 3; X(0,2) = -4; X(0,3) = 8;
X(1,0) = 1; X(1,1) = 1; X(1,2) = -2; X(1,3) = 2;
X(2,0) = -1; X(2,1) = -2; X(2,2) = 5; X(2,3) = -1;
os << "\r\nOriginal X =\r\n";
ShowMatrix(os,X);
Matrix<double> lX(X.LinSolve());
os << "\r\nX after elimination =\r\n";
ShowMatrix(os,X);
os << "\r\nlinear equation solution =\r\n";
ShowMatrix(os,lX);
X(0,0) = 1.0; X(1,0) = 3.0; X(2,0) = 5.0;
X(0,1) = 2.0; X(1,1) = 5.0; X(2,1) = 6.0;
X(0,2) = 0.0; X(1,2) = 4.0; X(2,2) = 3.0;
X(0,3) = 0.1; X(1,3) = 12.5; X(2,3) = 10.3;
os << "\r\nOriginal X =\r\n";
ShowMatrix(os,X);
lX = X.LinSolve();
os << "\r\nX after elimination =\r\n";
ShowMatrix(os,X);
os << "\r\nlinear equation solution =\r\n";
ShowMatrix(os,lX);
Matrix<double> Adbl(3,3), Bdbl(3,1);
Adbl(0,0) = 1.0; Adbl(0,1) = 2.0; Adbl(0,2) = 0.0;
Adbl(1,0) = 3.0; Adbl(1,1) = 5.0; Adbl(1,2) = 4.0;
Adbl(2,0) = 5.0; Adbl(2,1) = 6.0; Adbl(2,2) = 3.0;
Bdbl(0,0) = 0.1;
Bdbl(1,0) = 12.5;
Bdbl(2,0) = 10.3;
os << "\r\n\r\nmatrix Adbl = \r\n";
ShowMatrix(os,Adbl);
os << "\r\nmatrix Bdbl = \r\n";
ShowMatrix(os,Bdbl);
Matrix<double> alup(Adbl); // copy Adbl before LUP decomp
os << "\r\nLU decomp of Adbl (before) = \r\n";
ShowMatrix(os,alup);
Matrix<size_t> aperm = alup.LUPDecompose();
os << "\r\nLU decomp of Adbl (after) = \r\n";
ShowMatrix(os,alup);
os << "\r\nPermutation of Adbl = \r\n";
ShowMatrix(os,aperm);
Matrix<double> asol = alup.LUPSolve(aperm,Bdbl);
os << "\r\nlinear solution of Adbl and Bdbl = \r\n";
ShowMatrix(os,asol);
Matrix<double> ainv = alup.LUPInvert(aperm);
os << "\r\ninverse of Adbl and Bdbl = \r\n";
ShowMatrix(os,ainv);
Matrix<double> aid = Adbl % ainv;
os << "\r\ninverse dot Adbl = \r\n";
ShowMatrix(os,aid);
Grid<size_t> iperm = ainv.LUPDecompose();
Matrix<double> invinv = ainv.LUPInvert(iperm);
os << "\r\ninverse of inverse =\r\n";
ShowMatrix(os,invinv);
}