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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.
*