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// File: math_ComputeKronrodPointsAndWeights.cxx
// Created: Wed Dec 21 18:11:52 2005
// Author: Julia GERASIMOVA
// <jgv@clubox>
#include <math_ComputeKronrodPointsAndWeights.ixx>
#include <math_EigenValuesSearcher.hxx>
#include <math_Array1OfValueAndWeight.hxx>
#include <math_CompareOfValueAndWeight.hxx>
#include <math_QuickSortOfValueAndWeight.hxx>
#include <Standard_ErrorHandler.hxx>
math_ComputeKronrodPointsAndWeights::math_ComputeKronrodPointsAndWeights(const Standard_Integer Number)
{
myIsDone = Standard_False;
try {
Standard_Integer i, j;
Standard_Integer a2NP1 = 2*Number + 1;
myPoints = new TColStd_HArray1OfReal(1, a2NP1);
myWeights = new TColStd_HArray1OfReal(1, a2NP1);
TColStd_Array1OfReal aDiag(1, a2NP1);
TColStd_Array1OfReal aSubDiag(1, a2NP1);
// Initialize symmetric tridiagonal matrix.
Standard_Integer n = Number;
Standard_Integer aKronrodN = 2*Number + 1;
Standard_Integer a3KN2p1 = Min(3*(Number + 1)/2 + 1, aKronrodN);
for (i = 1; i <= a3KN2p1; i++) {
aDiag(i) = 0.;
if (i == 1)
aSubDiag(i) = 0.;
else {
Standard_Integer sqrIm1 = (i-1)*(i-1);
aSubDiag(i) = sqrIm1/(4.*sqrIm1 - 1);
}
}
for (i = a3KN2p1 + 1; i <= aKronrodN; i++) {
aDiag(i) = 0.;
aSubDiag(i) = 0.;
}
// Initialization of temporary data structures.
Standard_Integer aNd2 = Number/2;
Standard_Real *s = new Standard_Real[aNd2 + 2];
Standard_Real *t = new Standard_Real[aNd2 + 2];
Standard_Real *ss = s++;
Standard_Real *tt = t++;
for (i = -1; i <= aNd2; i++) {
s[i] = 0.;
t[i] = 0.;
}
// Generation of Jacobi-Kronrod matrix.
Standard_Real *aa = new Standard_Real [a2NP1+1];
Standard_Real *bb = new Standard_Real [a2NP1+1];
for (i = 1; i <= a2NP1; i++) {
aa[i] = aDiag(i);
bb[i] = aSubDiag(i);
}
Standard_Real *ptrtmp;
Standard_Real u;
Standard_Integer m;
Standard_Integer k;
Standard_Integer l;
Standard_Real *a = aa+1;
Standard_Real *b = bb+1;
// Eastward phase.
t[0] = b[Number + 1];
for (m = 0; m <= n - 2; m++) {
u = 0;
for (k = (m + 1)/2; k >= 0; k--) {
l = m - k;
u += (a[k + n + 1] - a[l])*t[k] + b[k + n + 1]*s[k - 1] - b[l]*s[k];
s[k] = u;
}
ptrtmp = t;
t = s;
s = ptrtmp;
}
for (j = aNd2; j >= 0; j--)
s[j] = s[j - 1];
// Southward phase.
for (m = n - 1; m <= 2*n - 3; m++) {
u = 0;
for (k = m + 1 - n; k <= (m - 1)/2; k++) {
l = m - k;
j = n - 1 - l;
u += -(a[k + n + 1] - a[l])*t[j] - b[k + n + 1]*s[j] + b[l]*s[j + 1];
s[j] = u;
}
if (m % 2 == 0) {
k = m/2;
a[k + n + 1] = a[k] + (s[j] - b[k + n + 1]*s[j + 1])/ t[j + 1];
} else {
k = (m + 1)/2;
b[k + n + 1] = s[j]/s[j + 1];
}
ptrtmp = t;
t = s;
s = ptrtmp;
}
// Termination phase.
a[2*Number] = a[n - 1] - b[2*Number]*s[0]/t[0];
delete [] ss;
delete [] tt;
for (i = 1; i <= a2NP1; i++) {
aDiag(i) = aa[i];
aSubDiag(i) = bb[i];
}
delete [] aa;
delete [] bb;
for (i = 1; i <= a2NP1; i++)
aSubDiag(i) = Sqrt(aSubDiag(i));
// Compute eigen values.
math_EigenValuesSearcher EVsearch(aDiag, aSubDiag);
if (EVsearch.IsDone()) {
math_Array1OfValueAndWeight VWarray(1, a2NP1);
for (i = 1; i <= a2NP1; i++) {
math_Vector anEigenVector = EVsearch.EigenVector(i);
Standard_Real aWeight = anEigenVector(1);
aWeight = 2. * aWeight * aWeight;
math_ValueAndWeight EVW( EVsearch.EigenValue(i), aWeight );
VWarray(i) = EVW;
}
math_CompareOfValueAndWeight theComparator;
math_QuickSortOfValueAndWeight::Sort(VWarray, theComparator);
for (i = 1; i <= a2NP1; i++) {
myPoints->ChangeValue(i) = VWarray(i).Value();
myWeights->ChangeValue(i) = VWarray(i).Weight();
}
myIsDone = Standard_True;
}
} catch (Standard_Failure) {
}
}
Standard_Boolean math_ComputeKronrodPointsAndWeights::IsDone() const
{
return myIsDone;
}
math_Vector math_ComputeKronrodPointsAndWeights::Points() const
{
Standard_Integer Number = myPoints->Length();
math_Vector thePoints(1, Number);
for (Standard_Integer i = 1; i <= Number; i++)
thePoints(i) = myPoints->Value(i);
return thePoints;
}
math_Vector math_ComputeKronrodPointsAndWeights::Weights() const
{
Standard_Integer Number = myWeights->Length();
math_Vector theWeights(1, Number);
for (Standard_Integer i = 1; i <= Number; i++)
theWeights(i) = myWeights->Value(i);
return theWeights;
}
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