jama_cholesky.h

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#ifndef JAMA_CHOLESKY_H
#define JAMA_CHOLESKY_H
 
#include "../tnt/tnt_array1d.h"
#include "../tnt/tnt_array2d.h"
 
#include <math.h>
/* needed for sqrt() below. */
 
namespace JAMA
{
 
using namespace TNT;
 
template <class Real>
class Cholesky
{
    Array2D<Real> L_;       // lower triangular factor
    int isspd;              // 1 if matrix to be factored was SPD
 
public:
 
    Cholesky();
    Cholesky(const Array2D<Real> &A);
    Array2D<Real> getL() const;
    Array1D<Real> solve(const Array1D<Real> &B);
    Array2D<Real> solve(const Array2D<Real> &B);
    int is_spd() const;
 
};
 
template <class Real>
Cholesky<Real>::Cholesky() : L_(0,0), isspd(0) {}
 
template <class Real>
int Cholesky<Real>::is_spd() const
{
    return isspd;
}
 
template <class Real>
Array2D<Real> Cholesky<Real>::getL() const
{
    return L_;
}
 
template <class Real>
Cholesky<Real>::Cholesky(const Array2D<Real> &A)
{
 
 
    int m = A.dim1();
    int n = A.dim2();
    
    isspd = (m == n);
 
    if (m != n)
    {
        L_ = Array2D<Real>(0,0);
        return;
    }
 
    L_ = Array2D<Real>(n,n);
 
 
      // Main loop.
     for (int j = 0; j < n; j++) 
     {
        double d = 0.0;
        for (int k = 0; k < j; k++) 
        {
            Real s = 0.0;
            for (int i = 0; i < k; i++) 
            {
               s += L_[k][i]*L_[j][i];
            }
            L_[j][k] = s = (A[j][k] - s)/L_[k][k];
            d = d + s*s;
            isspd = isspd && (A[k][j] == A[j][k]); 
         }
         d = A[j][j] - d;
         isspd = isspd && (d > 0.0);
         L_[j][j] = sqrt(d > 0.0 ? d : 0.0);
         for (int k = j+1; k < n; k++) 
         {
            L_[j][k] = 0.0;
         }
    }
}
 
template <class Real>
Array1D<Real> Cholesky<Real>::solve(const Array1D<Real> &b)
{
    int n = L_.dim1();
    if (b.dim1() != n)
        return Array1D<Real>();
 
 
    Array1D<Real> x = b.copy();
 
 
      // Solve L*y = b;
      for (int k = 0; k < n; k++) 
      {
         for (int i = 0; i < k; i++) 
               x[k] -= x[i]*L_[k][i];
         x[k] /= L_[k][k];
        
      }
 
      // Solve L'*X = Y;
      for (int k = n-1; k >= 0; k--) 
      {
         for (int i = k+1; i < n; i++) 
               x[k] -= x[i]*L_[i][k];
         x[k] /= L_[k][k];
      }
 
    return x;
}
 
 
template <class Real>
Array2D<Real> Cholesky<Real>::solve(const Array2D<Real> &B)
{
    int n = L_.dim1();
    if (B.dim1() != n)
        return Array2D<Real>();
 
 
    Array2D<Real> X = B.copy();
    int nx = B.dim2();
 
// Cleve's original code
#if 0
      // Solve L*Y = B;
      for (int k = 0; k < n; k++) {
         for (int i = k+1; i < n; i++) {
            for (int j = 0; j < nx; j++) {
               X[i][j] -= X[k][j]*L_[k][i];
            }
         }
         for (int j = 0; j < nx; j++) {
            X[k][j] /= L_[k][k];
         }
      }
 
      // Solve L'*X = Y;
      for (int k = n-1; k >= 0; k--) {
         for (int j = 0; j < nx; j++) {
            X[k][j] /= L_[k][k];
         }
         for (int i = 0; i < k; i++) {
            for (int j = 0; j < nx; j++) {
               X[i][j] -= X[k][j]*L_[k][i];
            }
         }
      }
#endif
 
 
      // Solve L*y = b;
      for (int j=0; j< nx; j++)
      {
        for (int k = 0; k < n; k++) 
        {
            for (int i = 0; i < k; i++) 
               X[k][j] -= X[i][j]*L_[k][i];
            X[k][j] /= L_[k][k];
         }
      }
 
      // Solve L'*X = Y;
     for (int j=0; j<nx; j++)
     {
        for (int k = n-1; k >= 0; k--) 
        {
            for (int i = k+1; i < n; i++) 
               X[k][j] -= X[i][j]*L_[i][k];
            X[k][j] /= L_[k][k];
        }
      }
 
 
 
    return X;
}
 
 
}
// namespace JAMA
 
#endif
// JAMA_CHOLESKY_H