vec cheb(int n, const vec &x)
{
it_assert_debug(x.size() > 0, "cheb(): empty vector");
vec out(x.size());
for (int i = 0; i < x.size(); ++i) {
out(i) = cheb(n, x(i));
}
return out;
}
/**-------------------------------------------------
* Make a quadrature given a Polynomial.
* @param P :: A polynomial to use to make the quadrature.
*/
void MakeQuadrature::makeQuadrature(const Polynomial& P)
{
auto& r = P.getRoots();
auto& w = P.getWeights();
const size_t n = r.size();
auto quad = new Quadrature;
quad->setRowCount( int(n) );
quad->addDoubleColumn("r", API::NumericColumn::X);
auto& rc = quad->getDoubleData("r");
rc = r;
quad->addDoubleColumn("w", API::NumericColumn::Y);
auto& wc = quad->getDoubleData("w");
wc = w;
FunctionDomain1DView domain( r );
FunctionValues values( domain );
std::vector<double> wgt;
std::vector<double> wgtDeriv;
P.weightFunction()->function( domain, values );
values.copyToStdVector( wgt );
P.weightDerivative()->function( domain, values );
values.copyToStdVector( wgtDeriv );
quad->addDoubleColumn("weight", API::NumericColumn::Y);
auto& wgtc = quad->getDoubleData("weight");
wgtc = wgt;
quad->addDoubleColumn("deriv", API::NumericColumn::Y);
auto& derc = quad->getDoubleData("deriv");
derc = wgtDeriv;
Quadrature::FuncVector fvec( n );
Quadrature::FuncVector dvec( n );
for(size_t i = 0; i < n; ++i)
{
std::string colInd = boost::lexical_cast<std::string>( i );
quad->addDoubleColumn("f"+colInd, API::NumericColumn::Y);
fvec[i] = &quad->getDoubleData("f"+colInd);
quad->addDoubleColumn("d"+colInd, API::NumericColumn::Y);
dvec[i] = &quad->getDoubleData("d"+colInd);
}
P.calcPolyValues( fvec, dvec );
quad->init();
setClassProperty( "Quadrature", API::TableWorkspace_ptr( quad ) );
{
const double startX = get("StartX");
const double endX = get("EndX");
ChebfunWorkspace_sptr cheb( new ChebfunWorkspace(chebfun( 100, startX, endX )) );
cheb->fun().fit( P );
setClassProperty("ChebWorkspace", cheb);
}
}
mat cheb(int n, const mat &x)
{
it_assert_debug((x.rows() > 0) && (x.cols() > 0), "cheb(): empty matrix");
mat out(x.rows(), x.cols());
for (int i = 0; i < x.rows(); ++i) {
for (int j = 0; j < x.cols(); ++j) {
out(i, j) = cheb(n, x(i, j));
}
}
return out;
}
void setup (int N, const Parameter ¶m, Array<double, 1> &WR, Array<double,2> &ev, Array<double,2> &evInv)
{
int Nm1 = N;
int i;
Array<double, 1> x;
Array<double, 2> D;
Array<double, 1> r;
Array<double, 2> Dsec;
Array<double, 1> XX;
Array<double, 1> YY;
Array<double, 2> A(N,N);
Array<double, 2> B(N,N);
Array<int, 1> IPIV(Nm1);
char BALANC[1];
char JOBVL[1];
char JOBVR[1];
char SENSE[1];
int LDA;
int LDVL;
int LDVR;
int NRHS;
int LDB;
int INFO;
//resize output arrays
WR.resize(N);
ev.resize(N, N);
evInv.resize(N, N);
// parameters for DGEEVX
Array<double, 1> WI(Nm1); // WR(Nm1),
// The real and imaginary part of the eig.values
Array<double, 2> VL(N, N);
Array<double, 2> VR(Nm1,Nm1); //VR(Nm1,Nm1);
// The left and rigth eigenvectors
int ILO, IHI; // Info on the balanced output matrix
Array<double, 1> SCALE(Nm1); // Scaling factors applied for balancing
double ABNRM; // 1-Norm of the balanced matrix
Array<double, 1> RCONDE(Nm1);
// the reciprocal cond. numb of the respective eig.val
Array<double, 1> RCONDV(Nm1);
// the reciprocal cond. numb of the respective eig.vec
int LWORK = (N+1)*(N+7); // Depending on SENSE
Array<double, 1> WORK(LWORK);
Array<int, 1> IWORK(2*(N+1)-2);
// Compute the Chebyshev differensiation matrix and D*D
// cheb(N, x, D);
cheb(N, x, D);
Dsec.resize(D.shape());
MatrixMatrixMultiply(D, D, Dsec);
// Compute the 1. and 2. derivatives of the transformations
XYmat(N, param, XX, YY, r);
// Set up the full timepropagation matrix A
// dy/dt = - i A y
Range range(1, N); //Dsec and D have range 0, N+1.
//We don't want the edge points in A
A = XX(tensor::i) * Dsec(range, range) + YY(tensor::i) * D(range, range);
//Transpose A
for (int i=0; i<A.extent(0); i++)
{
for (int j=0; j<i; j++)
{
double t = A(i,j);
A(i,j) = A(j, i);
A(j,i) = t;
}
}
// Add radialpart of non-time dependent potential here
/* 2D radial
for (int i=0; i<A.extent(0); i++)
{
A(i, i) += 0.25 / (r(i)*r(i));
}
*/
// Compute eigen decomposition
BALANC[0] ='B';
JOBVL[0] ='V';
JOBVR[0] ='V';
SENSE[0] ='B';
LDA = Nm1;
LDVL = Nm1;
LDVR = Nm1;
FORTRAN_NAME(dgeevx)(BALANC, JOBVL, JOBVR, SENSE, &Nm1,
A.data(), &LDA, WR.data(), WI.data(),
VL.data(), &LDVL, VR.data(), &LDVR, &ILO, &IHI,
SCALE.data(), &ABNRM,
RCONDE.data(), RCONDV.data(), WORK.data(), &LWORK,
IWORK.data(), &INFO);
// Compute the inverse of the eigen vector matrix
NRHS = Nm1;
evInv = VR ;// VL;
LDB = LDA;
B = 0.0;
for (i=0; i<Nm1; i++) B(i,i) = 1.0;
FORTRAN_NAME(dgesv)(&Nm1, &NRHS, evInv.data(), &LDA, IPIV.data(), B.data(), &LDB, &INFO);
ev = VR(tensor::j, tensor::i); //Transpose
evInv = B(tensor::j, tensor::i); //Transpose
//cout << "Eigenvectors (right): " << ev << endl;
//cout << "Eigenvectors (inv): " << evInv << endl;
//printf(" Done inverse, INFO = %d \n", INFO);
} // done
/*----------------------------------------------------------------------------*/
bool DEreader::GetPlanetPoz(double jdate, int index, bool geleo, double poz[])
{
if (jdate != dJD) {
bool r = read(jdate);
if (!r){
qDebug() << "GetPlanetPoz";
return false;
}
dJD = jdate;
}
double tc[16];
double tcp[16];
for (int i = 0; i < 16; i++) {
tc[i] = 0;
tcp[i] = 0;
}
double d = buf[0];
double c = d - deHeader.raz[index];
int n1 = -3 * deHeader.pow[index];
do {
c += deHeader.raz[index];
d += deHeader.raz[index];
n1 += 3*deHeader.pow[index];
} while (jdate < c || jdate > d);
cheb(false, c, d, jdate, deHeader.pow[index], tc, tcp);
coor(false, index, n1, tc, tcp, poz);
if (index == 2 || index == 9) {
int idx = index == 2 ? 9 : 2;
n1 = 0;
d = buf[0];
c = d - deHeader.raz[idx];
n1 = -3*deHeader.pow[idx];
do {
c += deHeader.raz[idx];
d += deHeader.raz[idx];
n1 += 3*deHeader.pow[idx];
} while (jdate < c || jdate > d);
cheb(false, c, d, jdate, deHeader.pow[idx], tc, tcp);
double x[6];
coor(false, idx, n1, tc, tcp, x);
if (index == 2)
for (int k = 0; k < 6; k++)
poz[k] = poz[k] - x[k] / (deHeader.EarthDivMoon + 1); // земля
else if (index == 9) {
for (int k = 0; k < 6; k++)
x[k] = x[k] - poz[k] / (deHeader.EarthDivMoon + 1); // земля
for (int k = 0; k < 6; k++)
poz[k] += x[k]; // луна
}
}
if (geleo) {
n1 = 0;
d = buf[0];
c = d - deHeader.raz[10];
n1 = -3*deHeader.pow[10];
do {
c += deHeader.raz[10];
d += deHeader.raz[10];
n1 += 3*deHeader.pow[10];
} while (jdate < c || jdate > d);
cheb(false, c, d, jdate, deHeader.pow[10], tc, tcp);
double x[6];
coor(false, 10, n1, tc, tcp, x);
for (int k = 0; k < 6; k++)
poz[k] = (poz[k] - x[k]) / deConst.AE;
} else
for (int k = 0; k < 6; k++)
poz[k] /= deConst.AE;
return true;
// qDebug() << poz[0];
// qDebug() << poz[1];
// qDebug() << poz[2];
}