double mxm_invert(double *r, const double *a, const int N)
{
mxm_local_block(a2, double, N);
mxm_set(a2, a, N);
double det = internal_invert(a2, r, N);
mxm_free_local(a2);
return det;
}
real mxm_invert(real *r, const real *a, const int N)
{
mxm_local_block(a2, real, N);
mxm_set(a2, a, N);
real det = internal_invert(a2, r, N);
mxm_free_local(a2);
return det;
}
double mxm_solve(double *x, const double *A, const double *b, const int N)
{
mxm_local_block(a2, double, N);
mxm_set(a2, A, N);
mxv_set(x, b, N);
double det = internal_solve(a2, x, N);
mxm_free_local(a2);
return det;
}
real mxm_solve(real *x, const real *A, const real *b, const int N)
{
mxm_local_block(a2, real, N);
mxm_set(a2, A, N);
mxv_set(x, b, N);
real det = internal_solve(a2, x, N);
mxm_free_local(a2);
return det;
}
// Originally based on public domain code by <*****@*****.**>
// which can be found at http://lib.stat.cmu.edu/general/ajay
//
// The factorization is valid as long as the returned nullity == 0
// U contains the upper triangular factor itself.
//
int mxm_cholesky(double *U, const double *A, const int N)
{
double sum;
int nullity = 0;
mxm_set(U, 0.0, N);
for(int i=0; i<N; i++)
{
/* First compute U[i][i] */
sum = mxm_ref(A, i, i, N);
for(int j=0; j<=(i-1); j++)
sum -= mxm_ref(U, j, i, N) * mxm_ref(U, j, i, N);
if( sum > 0 )
{
mxm_ref(U, i, i, N) = _sqrt(sum);
/* Now find elements U[i][k], k > i. */
for(int k=(i+1); k<N; k++)
{
sum = mxm_ref(A, i, k, N);
for(int j=0; j<=(i-1); j++)
sum -= mxm_ref(U, j, i, N)*mxm_ref(U, j, k, N);
mxm_ref(U, i, k, N) = sum / mxm_ref(U, i, i, N);
}
}
else
{
for(int k=i; k<N; k++) mxm_ref(U, i, k, N) = 0.0;
nullity++;
}
}
return nullity;
}
