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Moved all the linear algebra code into the matrix_la.h file.
--HG-- extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402849
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Davis King
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@ -9,6 +9,186 @@
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namespace dlib
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{
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// ----------------------------------------------------------------------------------------
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// ----------------------------------------------------------------------------------------
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// Global linear algebra functions
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// ----------------------------------------------------------------------------------------
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// ----------------------------------------------------------------------------------------
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const matrix_exp::matrix_type inv (
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const matrix_exp& m
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);
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/*!
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requires
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- m is a square matrix
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ensures
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- returns the inverse of m
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(Note that if m is singular or so close to being singular that there
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is a lot of numerical error then the returned matrix will be bogus.
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You can check by seeing if m*inv(m) is an identity matrix)
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix pinv (
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const matrix_exp& m
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);
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/*!
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ensures
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- returns the Moore-Penrose pseudoinverse of m.
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- The returned matrix has m.nc() rows and m.nr() columns.
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!*/
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// ----------------------------------------------------------------------------------------
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void svd (
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const matrix_exp& m,
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matrix<matrix_exp::type>& u,
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matrix<matrix_exp::type>& w,
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matrix<matrix_exp::type>& v
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);
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/*!
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ensures
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- computes the singular value decomposition of m
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- m == #u*#w*trans(#v)
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- trans(#u)*#u == identity matrix
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- trans(#v)*#v == identity matrix
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- diag(#w) == the singular values of the matrix m in no
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particular order. All non-diagonal elements of #w are
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set to 0.
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- #u.nr() == m.nr()
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- #u.nc() == m.nc()
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- #w.nr() == m.nc()
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- #w.nc() == m.nc()
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- #v.nr() == m.nc()
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- #v.nc() == m.nc()
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!*/
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// ----------------------------------------------------------------------------------------
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long svd2 (
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bool withu,
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bool withv,
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const matrix_exp& m,
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matrix<matrix_exp::type>& u,
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matrix<matrix_exp::type>& w,
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matrix<matrix_exp::type>& v
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);
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/*!
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requires
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- m.nr() >= m.nc()
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ensures
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- computes the singular value decomposition of matrix m
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- m == subm(#u,get_rect(m))*diagm(#w)*trans(#v)
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- trans(#u)*#u == identity matrix
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- trans(#v)*#v == identity matrix
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- #w == the singular values of the matrix m in no
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particular order.
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- #u.nr() == m.nr()
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- #u.nc() == m.nr()
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- #w.nr() == m.nc()
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- #w.nc() == 1
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- #v.nr() == m.nc()
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- #v.nc() == m.nc()
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- if (widthu == false) then
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- ignore the above regarding #u, it isn't computed and its
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output state is undefined.
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- if (widthv == false) then
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- ignore the above regarding #v, it isn't computed and its
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output state is undefined.
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- returns an error code of 0, if no errors and 'k' if we fail to
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converge at the 'kth' singular value.
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!*/
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// ----------------------------------------------------------------------------------------
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void svd3 (
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const matrix_exp& m,
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matrix<matrix_exp::type>& u,
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matrix<matrix_exp::type>& w,
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matrix<matrix_exp::type>& v
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);
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/*!
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ensures
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- computes the singular value decomposition of m
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- m == #u*diagm(#w)*trans(#v)
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- trans(#u)*#u == identity matrix
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- trans(#v)*#v == identity matrix
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- #w == the singular values of the matrix m in no
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particular order.
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- #u.nr() == m.nr()
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- #u.nc() == m.nc()
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- #w.nr() == m.nc()
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- #w.nc() == 1
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- #v.nr() == m.nc()
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- #v.nc() == m.nc()
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix_exp::type det (
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const matrix_exp& m
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);
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/*!
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requires
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- m is a square matrix
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ensures
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- returns the determinant of m
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix_exp::matrix_type chol (
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const matrix_exp& A
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);
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/*!
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requires
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- A is a square matrix
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ensures
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- if (A has a Cholesky Decomposition) then
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- returns the decomposition of A. That is, returns a matrix L
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such that L*trans(L) == A. L will also be lower triangular.
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- else
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- returns a matrix with the same dimensions as A but it
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will have a bogus value. I.e. it won't be a decomposition.
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix_exp::matrix_type inv_lower_triangular (
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const matrix_exp& A
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);
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/*!
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requires
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- A is a square matrix
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ensures
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- if (A is lower triangular) then
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- returns the inverse of A.
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- else
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- returns a matrix with the same dimensions as A but it
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will have a bogus value. I.e. it won't be an inverse.
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix_exp::matrix_type inv_upper_triangular (
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const matrix_exp& A
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);
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/*!
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requires
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- A is a square matrix
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ensures
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- if (A is upper triangular) then
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- returns the inverse of A.
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- else
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- returns a matrix with the same dimensions as A but it
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will have a bogus value. I.e. it won't be an inverse.
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!*/
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// ----------------------------------------------------------------------------------------
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// ----------------------------------------------------------------------------------------
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// Matrix decomposition classes
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// ----------------------------------------------------------------------------------------
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// ----------------------------------------------------------------------------------------
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template <
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File diff suppressed because it is too large
Load Diff
@ -596,182 +596,6 @@ namespace dlib
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(i.e. returns the length of the vector m)
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!*/
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// ----------------------------------------------------------------------------------------
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// ----------------------------------------------------------------------------------------
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// Linear algebra functions
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// ----------------------------------------------------------------------------------------
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// ----------------------------------------------------------------------------------------
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const matrix_exp::matrix_type inv (
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const matrix_exp& m
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);
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/*!
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requires
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- m is a square matrix
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ensures
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- returns the inverse of m
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(Note that if m is singular or so close to being singular that there
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is a lot of numerical error then the returned matrix will be bogus.
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You can check by seeing if m*inv(m) is an identity matrix)
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix pinv (
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const matrix_exp& m
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);
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/*!
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ensures
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- returns the Moore-Penrose pseudoinverse of m.
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- The returned matrix has m.nc() rows and m.nr() columns.
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!*/
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// ----------------------------------------------------------------------------------------
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void svd (
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const matrix_exp& m,
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matrix<matrix_exp::type>& u,
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matrix<matrix_exp::type>& w,
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matrix<matrix_exp::type>& v
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);
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/*!
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ensures
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- computes the singular value decomposition of m
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- m == #u*#w*trans(#v)
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- trans(#u)*#u == identity matrix
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- trans(#v)*#v == identity matrix
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- diag(#w) == the singular values of the matrix m in no
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particular order. All non-diagonal elements of #w are
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set to 0.
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- #u.nr() == m.nr()
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- #u.nc() == m.nc()
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- #w.nr() == m.nc()
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- #w.nc() == m.nc()
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- #v.nr() == m.nc()
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- #v.nc() == m.nc()
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!*/
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// ----------------------------------------------------------------------------------------
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long svd2 (
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bool withu,
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bool withv,
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const matrix_exp& m,
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matrix<matrix_exp::type>& u,
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matrix<matrix_exp::type>& w,
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matrix<matrix_exp::type>& v
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);
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/*!
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requires
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- m.nr() >= m.nc()
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ensures
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- computes the singular value decomposition of matrix m
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- m == subm(#u,get_rect(m))*diagm(#w)*trans(#v)
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- trans(#u)*#u == identity matrix
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- trans(#v)*#v == identity matrix
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- #w == the singular values of the matrix m in no
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particular order.
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- #u.nr() == m.nr()
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- #u.nc() == m.nr()
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- #w.nr() == m.nc()
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- #w.nc() == 1
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- #v.nr() == m.nc()
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- #v.nc() == m.nc()
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- if (widthu == false) then
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- ignore the above regarding #u, it isn't computed and its
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output state is undefined.
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- if (widthv == false) then
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- ignore the above regarding #v, it isn't computed and its
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output state is undefined.
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- returns an error code of 0, if no errors and 'k' if we fail to
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converge at the 'kth' singular value.
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!*/
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// ----------------------------------------------------------------------------------------
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void svd3 (
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const matrix_exp& m,
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matrix<matrix_exp::type>& u,
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matrix<matrix_exp::type>& w,
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matrix<matrix_exp::type>& v
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);
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/*!
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ensures
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- computes the singular value decomposition of m
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- m == #u*diagm(#w)*trans(#v)
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- trans(#u)*#u == identity matrix
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- trans(#v)*#v == identity matrix
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- #w == the singular values of the matrix m in no
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particular order.
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- #u.nr() == m.nr()
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- #u.nc() == m.nc()
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- #w.nr() == m.nc()
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- #w.nc() == 1
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- #v.nr() == m.nc()
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- #v.nc() == m.nc()
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix_exp::type det (
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const matrix_exp& m
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);
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/*!
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requires
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- m is a square matrix
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ensures
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- returns the determinant of m
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix_exp::matrix_type chol (
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const matrix_exp& A
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);
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/*!
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requires
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- A is a square matrix
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ensures
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- if (A has a Cholesky Decomposition) then
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- returns the decomposition of A. That is, returns a matrix L
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such that L*trans(L) == A. L will also be lower triangular.
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- else
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- returns a matrix with the same dimensions as A but it
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will have a bogus value. I.e. it won't be a decomposition.
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix_exp::matrix_type inv_lower_triangular (
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const matrix_exp& A
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);
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/*!
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requires
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- A is a square matrix
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ensures
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- if (A is lower triangular) then
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- returns the inverse of A.
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- else
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- returns a matrix with the same dimensions as A but it
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will have a bogus value. I.e. it won't be an inverse.
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!*/
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// ----------------------------------------------------------------------------------------
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const matrix_exp::matrix_type inv_upper_triangular (
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const matrix_exp& A
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);
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/*!
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requires
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- A is a square matrix
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ensures
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- if (A is upper triangular) then
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- returns the inverse of A.
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- else
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- returns a matrix with the same dimensions as A but it
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will have a bogus value. I.e. it won't be an inverse.
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!*/
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// ----------------------------------------------------------------------------------------
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// ----------------------------------------------------------------------------------------
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// Statistics
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