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Made the svd_fast() code a little more readable and memory efficient. 

Also added the orthogonalize() function.
This commit is contained in:
Davis King 2013-01-19 00:15:29 -05:00
parent 246a60c249
commit b51d11484e
2 changed files with 62 additions and 21 deletions
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59
dlib/matrix/matrix_la.h
View File

@ -816,6 +816,22 @@ convergence:
#endif
}
// ----------------------------------------------------------------------------------------
template <
typename T,
long NR,
long NC,
typename MM,
typename L
>
void orthogonalize (
matrix<T,NR,NC,MM,L>& m
)
{
qr_decomposition<matrix<T,NR,NC,MM,L> >(m).get_q(m);
}
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
@ -845,23 +861,21 @@ convergence:
!*/
{
DLIB_ASSERT(A.nr() >= (long)l, "Invalid inputs were given to this function.");
matrix<T> G = matrix_cast<T>(gaussian_randm(A.nc(), l));
matrix<T> Y = A*G;
Q = A*matrix_cast<T>(gaussian_randm(A.nc(), l));
Q = qr_decomposition<matrix<T> >(Y).get_q();
orthogonalize(Q);
// Do some extra iterations of the power method to make sure we get Q into the
// span of the most important singular vectors of A.
if (q != 0)
{
matrix<T> Z;
for (unsigned long itr = 0; itr < q; ++itr)
{
Z = trans(A)*Q;
Z = qr_decomposition<matrix<T> >(Z).get_q();
Q = trans(A)*Q;
orthogonalize(Q);
Y = A*Z;
Q = qr_decomposition<matrix<T> >(Y).get_q();
Q = A*Q;
orthogonalize(Q);
}
}
}
@ -928,27 +942,27 @@ convergence:
!*/
{
DLIB_ASSERT(A.size() >= l, "Invalid inputs were given to this function.");
matrix<T> Y(A.size(), l);
Q.set_size(A.size(), l);
// Compute Y = A*gaussian_randm()
for (long r = 0; r < Y.nr(); ++r)
// Compute Q = A*gaussian_randm()
for (long r = 0; r < Q.nr(); ++r)
{
for (long c = 0; c < Y.nc(); ++c)
for (long c = 0; c < Q.nc(); ++c)
{
Y(r,c) = dot(A[r], gaussian_randm(std::numeric_limits<long>::max(), 1, c));
Q(r,c) = dot(A[r], gaussian_randm(std::numeric_limits<long>::max(), 1, c));
}
}
Q = qr_decomposition<matrix<T> >(Y).get_q();
orthogonalize(Q);
// Do some extra iterations of the power method to make sure we get Q into the
// span of the most important singular vectors of A.
if (q != 0)
{
const unsigned long n = max_index_plus_one(A);
matrix<T> Z(n, l);
for (unsigned long itr = 0; itr < q; ++itr)
{
matrix<T> Z(n, l);
// Compute Z = trans(A)*Q
Z = 0;
for (unsigned long m = 0; m < A.size(); ++m)
@ -966,18 +980,21 @@ convergence:
}
}
Z = qr_decomposition<matrix<T> >(Z).get_q();
Q.set_size(0,0); // free RAM
orthogonalize(Z);
// Compute Y = A*Z
for (long r = 0; r < Y.nr(); ++r)
// Compute Q = A*Z
Q.set_size(A.size(), l);
for (long r = 0; r < Q.nr(); ++r)
{
for (long c = 0; c < Y.nc(); ++c)
for (long c = 0; c < Q.nc(); ++c)
{
Y(r,c) = dot(A[r], colm(Z,c));
Q(r,c) = dot(A[r], colm(Z,c));
}
}
Q = qr_decomposition<matrix<T> >(Y).get_q();
Z.set_size(0,0); // free RAM
orthogonalize(Q);
}
}
}

24
dlib/matrix/matrix_la_abstract.h
View File

@ -235,6 +235,30 @@ namespace dlib
Therefore, it is very fast and suitable for use with very large matrices.
!*/
// ----------------------------------------------------------------------------------------
template <
typename T,
long NR,
long NC,
typename MM,
typename L
>
void orthogonalize (
matrix<T,NR,NC,MM,L>& m
);
/*!
requires
- m.nr() >= m.nc()
- m.size() > 0
ensures
- #m == an orthogonal matrix with the same dimensions as m. In particular,
the columns of #m have the same span as the columns of m.
- trans(#m)*#m == identity matrix
- This function is just shorthand for performing the QR decomposition of m
and then storing the Q factor into #m.
!*/
// ----------------------------------------------------------------------------------------
const matrix real_eigenvalues (