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Gave pinv() an optional tolerance option.

This commit is contained in:
Davis King 2014-02-01 16:19:11 -05:00
parent 271366096b
commit dd0dacb818
3 changed files with 75 additions and 7 deletions
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38
dlib/matrix/matrix_la.h
View File

@ -1290,6 +1290,25 @@ convergence:
return matrix_diag_op<op>(op(reciprocal(diag(m))));
}
// ----------------------------------------------------------------------------------------
template <
typename EXP
>
const matrix_diag_op<op_diag_inv<EXP> > pinv (
const matrix_diag_exp<EXP>& m,
double tol
)
{
DLIB_ASSERT(tol >= 0,
"\tconst matrix_exp::type pinv(const matrix_exp& m)"
<< "\n\t tol can't be negative"
<< "\n\t tol: "<<tol
);
typedef op_diag_inv<EXP> op;
return matrix_diag_op<op>(op(reciprocal(round_zeros(diag(m),tol))));
}
// ----------------------------------------------------------------------------------------
template <typename EXP>
@ -1519,7 +1538,8 @@ convergence:
typename EXP
>
const matrix<typename EXP::type,EXP::NC,EXP::NR,typename EXP::mem_manager_type> pinv_helper (
const matrix_exp<EXP>& m
const matrix_exp<EXP>& m,
double tol
)
/*!
ensures
@ -1541,8 +1561,8 @@ convergence:
const double machine_eps = std::numeric_limits<typename EXP::type>::epsilon();
// compute a reasonable epsilon below which we round to zero before doing the
// reciprocal
const double eps = machine_eps*std::max(m.nr(),m.nc())*max(w);
// reciprocal. Unless a non-zero tol is given then we just use tol.
const double eps = (tol!=0) ? tol : machine_eps*std::max(m.nr(),m.nc())*max(w);
// now compute the pseudoinverse
return tmp(scale_columns(v,reciprocal(round_zeros(w,eps))))*trans(u);
@ -1552,15 +1572,21 @@ convergence:
typename EXP
>
const matrix<typename EXP::type,EXP::NC,EXP::NR,typename EXP::mem_manager_type> pinv (
const matrix_exp<EXP>& m
const matrix_exp<EXP>& m,
double tol = 0
)
{
DLIB_ASSERT(tol >= 0,
"\tconst matrix_exp::type pinv(const matrix_exp& m)"
<< "\n\t tol can't be negative"
<< "\n\t tol: "<<tol
);
// if m has more columns then rows then it is more efficient to
// compute the pseudo-inverse of its transpose (given the way I'm doing it below).
if (m.nc() > m.nr())
return trans(pinv_helper(trans(m)));
return trans(pinv_helper(trans(m),tol));
else
return pinv_helper(m);
return pinv_helper(m,tol);
}
// ----------------------------------------------------------------------------------------

10
dlib/matrix/matrix_la_abstract.h
View File

@ -31,12 +31,20 @@ namespace dlib
// ----------------------------------------------------------------------------------------
const matrix pinv (
const matrix_exp& m
const matrix_exp& m,
double tol = 0
);
/*!
requires
- tol >= 0
ensures
- returns the Moore-Penrose pseudoinverse of m.
- The returned matrix has m.nc() rows and m.nr() columns.
- if (tol == 0) then
- singular values less than max(m.nr(),m.nc()) times the machine epsilon
times the largest singular value are ignored.
- else
- singular values less than tol are ignored.
!*/
// ----------------------------------------------------------------------------------------

34
dlib/test/matrix.cpp
View File

@ -67,6 +67,40 @@ namespace
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
mi = pinv(m,1e-12);
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
m = diagm(diag(m));
mi = pinv(diagm(diag(m)),1e-12);
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
mi = pinv(m,0);
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
m = diagm(diag(m));
mi = pinv(diagm(diag(m)),0);
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
}
{
matrix<double,5,0,MM> m(5,5);