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cholesky factorization with rounding to zero

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nojhan 2011-11-15 17:10:46 +01:00
commit 9decda0c6a
2 changed files with 61 additions and 3 deletions
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52
edo/src/edoSamplerNormalMulti.h
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@ -70,6 +70,8 @@ public:
standard,
//! use the algorithm using absolute value within the square root @see factorize_LLT_abs
absolute,
//! use the method that set negative square roots to zero @see factorize_LLT_zero
zeroing,
//! use the robust algorithm, without square root @see factorize_LDLT
robust
};
@ -157,6 +159,8 @@ public:
factorize_LLT( V );
} else if( _use == absolute ) {
factorize_LLT_abs( V );
} else if( _use == zeroing ) {
factorize_LLT_zero( V );
} else if( _use == robust ) {
factorize_LDLT( V );
}
@ -254,6 +258,54 @@ public:
}
/** This standard algorithm makes use of square root but do not fail
* if the covariance matrix is very ill-conditioned.
* Here, if the diagonal difference ir negative, we set it to zero.
*
* Be aware that this increase round-off errors, this is just a ugly
* hack to avoid crash.
*/
void factorize_LLT_zero( const CovarMat & V)
{
unsigned int N = assert_properties( V );
unsigned int i=0, j=0, k;
_L(0, 0) = sqrt( V(0, 0) );
// end of the column
for ( j = 1; j < N; ++j ) {
_L(j, 0) = V(0, j) / _L(0, 0);
}
// end of the matrix
for ( i = 1; i < N; ++i ) { // each column
// diagonal
double sum = 0.0;
for ( k = 0; k < i; ++k) {
sum += _L(i, k) * _L(i, k);
}
if( V(i,i) - sum >= 0 ) {
_L(i,i) = sqrt( V(i,i) - sum);
} else {
_L(i,i) = 0;
}
for ( j = i + 1; j < N; ++j ) { // rows
// one element
sum = 0.0;
for ( k = 0; k < i; ++k ) {
sum += _L(j, k) * _L(i, k);
}
_L(j, i) = (V(j, i) - sum) / _L(i, i);
} // for j in ]i,N[
} // for i in [1,N[
}
/** This alternative algorithm do not use square root in an inner loop,
* but only for some diagonal elements of the matrix D.
*

12
edo/test/t-cholesky.cpp
View file

@ -158,9 +158,10 @@ int main(int argc, char** argv)
edoSamplerNormalMulti<EOT,EOD>::Cholesky LLT( edoSamplerNormalMulti<EOT,EOD>::Cholesky::standard );
edoSamplerNormalMulti<EOT,EOD>::Cholesky LLTa( edoSamplerNormalMulti<EOT,EOD>::Cholesky::absolute );
edoSamplerNormalMulti<EOT,EOD>::Cholesky LLTz( edoSamplerNormalMulti<EOT,EOD>::Cholesky::zeroing );
edoSamplerNormalMulti<EOT,EOD>::Cholesky LDLT( edoSamplerNormalMulti<EOT,EOD>::Cholesky::robust );
std::vector<double> s0,s1,s2;
std::vector<double> s0,s1,s2,s3;
for( unsigned int n=0; n<R; ++n ) {
// a variance-covariance matrix of size N*N
@ -182,15 +183,20 @@ int main(int argc, char** argv)
CovarMat V1 = ublas::prod( L1, ublas::trans(L1) );
s1.push_back( trigsum(error(V,V1)) );
FactorMat L2 = LDLT(V);
FactorMat L2 = LLTz(V);
CovarMat V2 = ublas::prod( L2, ublas::trans(L2) );
s2.push_back( trigsum(error(V,V2)) );
FactorMat L3 = LDLT(V);
CovarMat V3 = ublas::prod( L3, ublas::trans(L3) );
s3.push_back( trigsum(error(V,V3)) );
}
std::cout << "Average error:" << std::endl;
std::cout << "\tLLT: " << sum(s0)/R << std::endl;
std::cout << "\tLLTa: " << sum(s1)/R << std::endl;
std::cout << "\tLDLT: " << sum(s2)/R << std::endl;
std::cout << "\tLLTz: " << sum(s2)/R << std::endl;
std::cout << "\tLDLT: " << sum(s3)/R << std::endl;
// double precision = 1e-15;
// if( argc >= 4 ) {