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Fixed decomposition. Add sample matrix.

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This commit is contained in:
Guilhem Lavaux 2011-12-14 17:40:10 -05:00
parent cf279bbb19
commit 196e17c242
3 changed files with 89 additions and 38 deletions
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7
sample/Hartmann_Matrix.txt Normal file
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@ -0,0 +1,7 @@
6
14.8253 -6.4243 7.8746 -1.2498 10.2733 10.2733
-6.4243 15.1024 -1.1155 -0.2761 -8.2117 -8.2117
7.8746 -1.1155 51.8519 -23.3482 12.5902 12.5902
-1.2498 -0.2761 -23.3482 22.7962 -9.8958 -9.8958
10.2733 -8.2117 12.5902 -9.8958 21.0656 21.0656
10.2733 -8.2117 12.5902 -9.8958 21.0656 21.0656

26
sample/testEskow.cpp
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@ -1,3 +1,4 @@
#include <fstream>
#include <cstring>
#include <iostream>
#include <iomanip>
@ -26,28 +27,39 @@ struct MatrixOp
}
};
int main()
int main(int argc, char **argv)
{
MatrixOp M;
double norm_E;
ifstream fi(argv[1]);
ofstream f("eskowed.txt");
CholeskyEskow<double,MatrixOp> chol;
M.N = 6;
fi >> M.N;
M.M.resize(M.N*M.N);
memcpy(&M.M[0], &Hartmann_Matrix[0][0], sizeof(double)*36);
for (int i = 0; i < M.N; i++)
{
for (int j = 0; j < M.N; j++)
{
fi >> M(i,j);
if (j > i)
M(i,j) =0;
}
}
CholeskyEskow::cholesky_eskow(M, M.N, norm_E);
chol.cholesky(M, M.N, norm_E);
for (int i = 0; i < M.N; i++)
{
for (int j = 0; j < M.N; j++)
{
if (j > i)
cout << "0 ";
f << "0 ";
else
cout << setprecision(25) << M(i,j) << " ";
f << setprecision(25) << M(i,j) << " ";
}
cout << endl;
f << endl;
}
return 0;
}

88
src/eskow.hpp
View File

@ -7,24 +7,49 @@
/* Implementation of Schnabel & Eskow, 1999, Vol. 9, No. 4, pp. 1135-148, SIAM J. OPTIM. */
namespace CholeskyEskow
template<typename T, typename A>
class CholeskyEskow
{
private:
static const bool verbose_eskow = true;
T tau, tau_bar, mu;
void print_matrix(A& m, int N)
{
using std::cout;
using std::endl;
using std::setprecision;
if (verbose_eskow)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
cout.width(6);
cout << setprecision(5) << m(i,j) << " ";
}
cout << endl;
}
cout << endl;
}
}
template<typename T, typename A>
T max_diag(A& m, int j, int N)
{
T maxval = m(j,j);
T maxval = std::abs(m(j,j));
for (int k = j+1; k < N; k++)
{
maxval = std::max(maxval, m(k,k));
maxval = std::max(maxval, std::abs(m(k,k)));
}
return maxval;
}
template<typename T, typename A>
void minmax_diag(A& m, int j, int N, T& minval, T& maxval, int& i_min, int& i_max)
{
i_min = i_max = j;
minval = maxval = m(j,j);
for (int k = j+1; k < N; k++)
@ -35,34 +60,30 @@ namespace CholeskyEskow
for (int k = j; k < N; k++)
{
if (m(k,k) == minval)
if (m(k,k) == minval && i_min < 0)
i_min = k;
if (m(k,k) == maxval)
if (m(k,k) == maxval && i_max < 0)
i_max = k;
}
}
template<typename T, typename A>
void swap_rows(A& m, int N, int i0, int i1)
{
for (int r = 0; r < N; r++)
std::swap(m(r,i0), m(r,i1));
}
template<typename T, typename A>
void swap_cols(A& m, int N, int i0, int i1)
{
for (int c = 0; c < N; c++)
std::swap(m(i0,c), m(i1,c));
}
template<typename T>
T square(T x)
{
return x*x;
}
template<typename T, typename A>
T min_row(A& m, int j, int N)
{
T a = 1/m(j,j);
@ -70,13 +91,12 @@ namespace CholeskyEskow
for (int i = j+2; i < N; i++)
{
v = std::max(v, m(i, i) - square(m(i,j))*a);
v = std::min(v, m(i, i) - square(m(i,j))*a);
}
return v;
}
template<typename T>
int g_max(const std::vector<T>& g, int j, int N)
{
T a = g[j];
@ -93,14 +113,18 @@ namespace CholeskyEskow
return k;
}
template<typename T, typename A>
void cholesky_eskow(A& m, int N, T& norm_E)
public:
CholeskyEskow()
{
tau = std::pow(mach_epsilon<T>(), 1./3);
tau_bar = std::pow(mach_epsilon<T>(), 2./3);
mu=0.1;
}
void cholesky(A& m, int N, T& norm_E)
{
T tau_bar = std::pow(mach_epsilon<T>(), 2./3);
T tau = std::pow(mach_epsilon<T>(), 1./3);
T mu = 0.1;
bool phaseone = true;
T gamma = max_diag<T,A>(m, 0, N);
T gamma = max_diag(m, 0, N);
int j;
norm_E = 0;
@ -110,7 +134,9 @@ namespace CholeskyEskow
T minval, maxval;
int i_min, i_max;
minmax_diag<T,A>(m, j, N, minval, maxval, i_min, i_max);
print_matrix(m, N);
minmax_diag(m, j, N, minval, maxval, i_min, i_max);
if (maxval < tau_bar*gamma || minval < -mu*maxval)
{
phaseone = false;
@ -119,11 +145,13 @@ namespace CholeskyEskow
if (i_max != j)
{
swap_cols<T,A>(m, N, i_max, j);
swap_rows<T,A>(m, N, i_max, j);
std::cout << "Have to swap i=" << i_max << " and j=" << j << std::endl;
swap_cols(m, N, i_max, j);
swap_rows(m, N, i_max, j);
}
if (min_row<T,A>(m, j, N) < -mu*gamma)
if (min_row(m, j, N) < -mu*gamma)
{
phaseone = false;
break;
@ -135,7 +163,7 @@ namespace CholeskyEskow
for (int i = j+1; i < N; i++)
{
m(i,j) /= L_jj;
for (int k = j+1; k < i; k++)
for (int k = j+1; k <= i; k++)
m(i,k) -= m(i,j)*m(k,j);
}
}
@ -151,9 +179,10 @@ namespace CholeskyEskow
if (!phaseone && j < (N-1))
{
std::cout << "Phase two ! (j=" << j << ")" << std::endl;
int k = j-1;
std::vector<T> g(N);
@ -173,12 +202,15 @@ namespace CholeskyEskow
int i = g_max(g, j, N);
T norm_j;
print_matrix(m, N);
if (i != j)
{
swap_cols<T,A>(m, N, i, j);
swap_rows<T,A>(m, N, i, j);
swap_cols(m, N, i, j);
swap_rows(m, N, i, j);
}
for (int i = j+1; j < N; j++)
{
norm_j += std::abs(m(i,j));
@ -208,7 +240,7 @@ namespace CholeskyEskow
for (int i = j+1; i < N; i++)
{
m(i,j) /= L_jj;
for (int k = j+1; k < i; k++)
for (int k = j+1; k <= i; k++)
m(i,k) -= m(i,j)*m(k,j);
}
}