//! More...
Classes | |
| class | auxlib |
| wrapper for accessing external functions defined in ATLAS, LAPACK or BLAS libraries More... | |
Functions | |
| template<typename eT > | |
| static bool | auxlib::inv_noalias (Mat< eT > &out, const Mat< eT > &X) |
| immediate matrix inverse | |
| template<typename eT > | |
| static bool | auxlib::inv_inplace (Mat< eT > &X) |
| immediate inplace matrix inverse | |
| template<typename eT > | |
| static eT | auxlib::det (const Mat< eT > &X) |
| immediate determinant of a matrix using ATLAS or LAPACK | |
| template<typename eT > | |
| static void | auxlib::log_det (eT &out_val, typename get_pod_type< eT >::result &out_sign, const Mat< eT > &X) |
| immediate log determinant of a matrix using ATLAS or LAPACK | |
| template<typename eT > | |
| static void | auxlib::lu (Mat< eT > &L, Mat< eT > &U, podarray< int > &ipiv, const Mat< eT > &X_orig) |
| immediate LU decomposition of a matrix using ATLAS or LAPACK | |
| template<typename eT > | |
| static void | auxlib::lu (Mat< eT > &L, Mat< eT > &U, Mat< eT > &P, const Mat< eT > &X) |
| template<typename eT > | |
| static void | auxlib::lu (Mat< eT > &L, Mat< eT > &U, const Mat< eT > &X) |
| template<typename eT > | |
| static void | auxlib::eig_sym (Col< eT > &eigval, const Mat< eT > &A) |
| immediate eigenvalues of a symmetric real matrix using LAPACK | |
| template<typename T > | |
| static void | auxlib::eig_sym (Col< T > &eigval, const Mat< std::complex< T > > &A) |
| immediate eigenvalues of a hermitian complex matrix using LAPACK | |
| template<typename eT > | |
| static void | auxlib::eig_sym (Col< eT > &eigval, Mat< eT > &eigvec, const Mat< eT > &A) |
| immediate eigenvalues and eigenvectors of a symmetric real matrix using LAPACK | |
| template<typename T > | |
| static void | auxlib::eig_sym (Col< T > &eigval, Mat< std::complex< T > > &eigvec, const Mat< std::complex< T > > &A) |
| immediate eigenvalues and eigenvectors of a hermitian complex matrix using LAPACK | |
| template<typename T > | |
| void | auxlib::eig_gen (Col< std::complex< T > > &eigval, Mat< T > &l_eigvec, Mat< T > &r_eigvec, const Mat< T > &A, const char side) |
| Eigenvalues and eigenvectors of a general square real matrix using LAPACK. //! The argument 'side' specifies which eigenvectors should be calculated //! (see code for mode details). | |
| template<typename T > | |
| static void | auxlib::eig_gen (Col< std::complex< T > > &eigval, Mat< std::complex< T > > &l_eigvec, Mat< std::complex< T > > &r_eigvec, const Mat< std::complex< T > > &A, const char side) |
| Eigenvalues and eigenvectors of a general square complex matrix using LAPACK //! The argument 'side' specifies which eigenvectors should be calculated //! (see code for mode details). | |
| template<typename eT > | |
| static bool | auxlib::chol (Mat< eT > &out, const Mat< eT > &X) |
| template<typename eT > | |
| static bool | auxlib::qr (Mat< eT > &Q, Mat< eT > &R, const Mat< eT > &X) |
| template<typename eT > | |
| static bool | auxlib::svd (Col< eT > &S, const Mat< eT > &X) |
| template<typename T > | |
| static bool | auxlib::svd (Col< T > &S, const Mat< std::complex< T > > &X) |
| template<typename eT > | |
| static bool | auxlib::svd (Mat< eT > &U, Col< eT > &S, Mat< eT > &V, const Mat< eT > &X) |
| template<typename T > | |
| static bool | auxlib::svd (Mat< std::complex< T > > &U, Col< T > &S, Mat< std::complex< T > > &V, const Mat< std::complex< T > > &X) |
| template<typename eT > | |
| static bool | auxlib::solve (Mat< eT > &out, const Mat< eT > &A, const Mat< eT > &B) |
| Solve a system of linear equations //! Assumes that A.n_rows = A.n_cols //! and B.n_rows = A.n_rows. | |
| template<typename eT > | |
| static bool | auxlib::solve_od (Mat< eT > &out, const Mat< eT > &A, const Mat< eT > &B) |
| Solve an over-determined system. //! Assumes that A.n_rows > A.n_cols //! and B.n_rows = A.n_rows. | |
| template<typename eT > | |
| static bool | auxlib::solve_ud (Mat< eT > &out, const Mat< eT > &A, const Mat< eT > &B) |
| Solve an under-determined system. //! Assumes that A.n_rows < A.n_cols //! and B.n_rows = A.n_rows. | |
//!
| bool auxlib::inv_noalias | ( | Mat< eT > & | out, | |
| const Mat< eT > & | X | |||
| ) | [inline, static, inherited] |
immediate matrix inverse
Definition at line 26 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), atlas::clapack_getri(), Mat< eT >::colptr(), det(), lapack::getrf_(), lapack::getri_(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, podarray< eT >::set_size(), Mat< eT >::set_size(), and atlas::tmp_real().
Referenced by op_inv::apply().
{
arma_extra_debug_sigprint();
switch(X.n_rows)
{
case 1:
{
out.set_size(1,1);
out[0] = eT(1) / X[0];
};
break;
case 2:
{
out.set_size(2,2);
const eT a = X.at(0,0);
const eT b = X.at(0,1);
const eT c = X.at(1,0);
const eT d = X.at(1,1);
const eT k = eT(1) / (a*d - b*c);
out.at(0,0) = d*k;
out.at(0,1) = -b*k;
out.at(1,0) = -c*k;
out.at(1,1) = a*k;
};
break;
case 3:
{
out.set_size(3,3);
const eT* X_col0 = X.colptr(0);
const eT a11 = X_col0[0];
const eT a21 = X_col0[1];
const eT a31 = X_col0[2];
const eT* X_col1 = X.colptr(1);
const eT a12 = X_col1[0];
const eT a22 = X_col1[1];
const eT a32 = X_col1[2];
const eT* X_col2 = X.colptr(2);
const eT a13 = X_col2[0];
const eT a23 = X_col2[1];
const eT a33 = X_col2[2];
const eT k = eT(1) / ( a11*(a33*a22 - a32*a23) - a21*(a33*a12-a32*a13) + a31*(a23*a12 - a22*a13) );
eT* out_col0 = out.colptr(0);
out_col0[0] = (a33*a22 - a32*a23) * k;
out_col0[1] = -(a33*a21 - a31*a23) * k;
out_col0[2] = (a32*a21 - a31*a22) * k;
eT* out_col1 = out.colptr(1);
out_col1[0] = -(a33*a12 - a32*a13) * k;
out_col1[1] = (a33*a11 - a31*a13) * k;
out_col1[2] = -(a32*a11 - a31*a12) * k;
eT* out_col2 = out.colptr(2);
out_col2[0] = (a23*a12 - a22*a13) * k;
out_col2[1] = -(a23*a11 - a21*a13) * k;
out_col2[2] = (a22*a11 - a21*a12) * k;
};
break;
case 4:
{
out.set_size(4,4);
out.at(0,0) = X.at(1,2)*X.at(2,3)*X.at(3,1) - X.at(1,3)*X.at(2,2)*X.at(3,1) + X.at(1,3)*X.at(2,1)*X.at(3,2) - X.at(1,1)*X.at(2,3)*X.at(3,2) - X.at(1,2)*X.at(2,1)*X.at(3,3) + X.at(1,1)*X.at(2,2)*X.at(3,3);
out.at(1,0) = X.at(1,3)*X.at(2,2)*X.at(3,0) - X.at(1,2)*X.at(2,3)*X.at(3,0) - X.at(1,3)*X.at(2,0)*X.at(3,2) + X.at(1,0)*X.at(2,3)*X.at(3,2) + X.at(1,2)*X.at(2,0)*X.at(3,3) - X.at(1,0)*X.at(2,2)*X.at(3,3);
out.at(2,0) = X.at(1,1)*X.at(2,3)*X.at(3,0) - X.at(1,3)*X.at(2,1)*X.at(3,0) + X.at(1,3)*X.at(2,0)*X.at(3,1) - X.at(1,0)*X.at(2,3)*X.at(3,1) - X.at(1,1)*X.at(2,0)*X.at(3,3) + X.at(1,0)*X.at(2,1)*X.at(3,3);
out.at(3,0) = X.at(1,2)*X.at(2,1)*X.at(3,0) - X.at(1,1)*X.at(2,2)*X.at(3,0) - X.at(1,2)*X.at(2,0)*X.at(3,1) + X.at(1,0)*X.at(2,2)*X.at(3,1) + X.at(1,1)*X.at(2,0)*X.at(3,2) - X.at(1,0)*X.at(2,1)*X.at(3,2);
out.at(0,1) = X.at(0,3)*X.at(2,2)*X.at(3,1) - X.at(0,2)*X.at(2,3)*X.at(3,1) - X.at(0,3)*X.at(2,1)*X.at(3,2) + X.at(0,1)*X.at(2,3)*X.at(3,2) + X.at(0,2)*X.at(2,1)*X.at(3,3) - X.at(0,1)*X.at(2,2)*X.at(3,3);
out.at(1,1) = X.at(0,2)*X.at(2,3)*X.at(3,0) - X.at(0,3)*X.at(2,2)*X.at(3,0) + X.at(0,3)*X.at(2,0)*X.at(3,2) - X.at(0,0)*X.at(2,3)*X.at(3,2) - X.at(0,2)*X.at(2,0)*X.at(3,3) + X.at(0,0)*X.at(2,2)*X.at(3,3);
out.at(2,1) = X.at(0,3)*X.at(2,1)*X.at(3,0) - X.at(0,1)*X.at(2,3)*X.at(3,0) - X.at(0,3)*X.at(2,0)*X.at(3,1) + X.at(0,0)*X.at(2,3)*X.at(3,1) + X.at(0,1)*X.at(2,0)*X.at(3,3) - X.at(0,0)*X.at(2,1)*X.at(3,3);
out.at(3,1) = X.at(0,1)*X.at(2,2)*X.at(3,0) - X.at(0,2)*X.at(2,1)*X.at(3,0) + X.at(0,2)*X.at(2,0)*X.at(3,1) - X.at(0,0)*X.at(2,2)*X.at(3,1) - X.at(0,1)*X.at(2,0)*X.at(3,2) + X.at(0,0)*X.at(2,1)*X.at(3,2);
out.at(0,2) = X.at(0,2)*X.at(1,3)*X.at(3,1) - X.at(0,3)*X.at(1,2)*X.at(3,1) + X.at(0,3)*X.at(1,1)*X.at(3,2) - X.at(0,1)*X.at(1,3)*X.at(3,2) - X.at(0,2)*X.at(1,1)*X.at(3,3) + X.at(0,1)*X.at(1,2)*X.at(3,3);
out.at(1,2) = X.at(0,3)*X.at(1,2)*X.at(3,0) - X.at(0,2)*X.at(1,3)*X.at(3,0) - X.at(0,3)*X.at(1,0)*X.at(3,2) + X.at(0,0)*X.at(1,3)*X.at(3,2) + X.at(0,2)*X.at(1,0)*X.at(3,3) - X.at(0,0)*X.at(1,2)*X.at(3,3);
out.at(2,2) = X.at(0,1)*X.at(1,3)*X.at(3,0) - X.at(0,3)*X.at(1,1)*X.at(3,0) + X.at(0,3)*X.at(1,0)*X.at(3,1) - X.at(0,0)*X.at(1,3)*X.at(3,1) - X.at(0,1)*X.at(1,0)*X.at(3,3) + X.at(0,0)*X.at(1,1)*X.at(3,3);
out.at(3,2) = X.at(0,2)*X.at(1,1)*X.at(3,0) - X.at(0,1)*X.at(1,2)*X.at(3,0) - X.at(0,2)*X.at(1,0)*X.at(3,1) + X.at(0,0)*X.at(1,2)*X.at(3,1) + X.at(0,1)*X.at(1,0)*X.at(3,2) - X.at(0,0)*X.at(1,1)*X.at(3,2);
out.at(0,3) = X.at(0,3)*X.at(1,2)*X.at(2,1) - X.at(0,2)*X.at(1,3)*X.at(2,1) - X.at(0,3)*X.at(1,1)*X.at(2,2) + X.at(0,1)*X.at(1,3)*X.at(2,2) + X.at(0,2)*X.at(1,1)*X.at(2,3) - X.at(0,1)*X.at(1,2)*X.at(2,3);
out.at(1,3) = X.at(0,2)*X.at(1,3)*X.at(2,0) - X.at(0,3)*X.at(1,2)*X.at(2,0) + X.at(0,3)*X.at(1,0)*X.at(2,2) - X.at(0,0)*X.at(1,3)*X.at(2,2) - X.at(0,2)*X.at(1,0)*X.at(2,3) + X.at(0,0)*X.at(1,2)*X.at(2,3);
out.at(2,3) = X.at(0,3)*X.at(1,1)*X.at(2,0) - X.at(0,1)*X.at(1,3)*X.at(2,0) - X.at(0,3)*X.at(1,0)*X.at(2,1) + X.at(0,0)*X.at(1,3)*X.at(2,1) + X.at(0,1)*X.at(1,0)*X.at(2,3) - X.at(0,0)*X.at(1,1)*X.at(2,3);
out.at(3,3) = X.at(0,1)*X.at(1,2)*X.at(2,0) - X.at(0,2)*X.at(1,1)*X.at(2,0) + X.at(0,2)*X.at(1,0)*X.at(2,1) - X.at(0,0)*X.at(1,2)*X.at(2,1) - X.at(0,1)*X.at(1,0)*X.at(2,2) + X.at(0,0)*X.at(1,1)*X.at(2,2);
out /= det(X);
};
break;
default:
{
#if defined(ARMA_USE_ATLAS)
{
out = X;
podarray<int> ipiv(out.n_rows);
int info = atlas::clapack_getrf(atlas::CblasColMajor, out.n_rows, out.n_cols, out.memptr(), out.n_rows, ipiv.memptr());
if(info == 0)
{
info = atlas::clapack_getri(atlas::CblasColMajor, out.n_rows, out.memptr(), out.n_rows, ipiv.memptr());
}
return (info == 0);
}
#elif defined(ARMA_USE_LAPACK)
{
out = X;
int n_rows = out.n_rows;
int n_cols = out.n_cols;
int info = 0;
podarray<int> ipiv(out.n_rows);
// 84 was empirically found -- it is the maximum value suggested by LAPACK (as provided by ATLAS v3.6)
// based on tests with various matrix types on 32-bit and 64-bit machines
//
// the "work" array is deliberately long so that a secondary (time-consuming)
// memory allocation is avoided, if possible
int work_len = (std::max)(1, n_rows*84);
podarray<eT> work(work_len);
lapack::getrf_(&n_rows, &n_cols, out.memptr(), &n_rows, ipiv.memptr(), &info);
if(info == 0)
{
// query for optimum size of work_len
int work_len_tmp = -1;
lapack::getri_(&n_rows, out.memptr(), &n_rows, ipiv.memptr(), work.memptr(), &work_len_tmp, &info);
if(info == 0)
{
int proposed_work_len = static_cast<int>(access::tmp_real(work[0]));
// if necessary, allocate more memory
if(work_len < proposed_work_len)
{
work_len = proposed_work_len;
work.set_size(work_len);
}
}
lapack::getri_(&n_rows, out.memptr(), &n_rows, ipiv.memptr(), work.memptr(), &work_len, &info);
}
return (info == 0);
}
#else
{
arma_stop("inv(): need ATLAS or LAPACK");
}
#endif
};
}
return true;
}
| bool auxlib::inv_inplace | ( | Mat< eT > & | X | ) | [inline, static, inherited] |
immediate inplace matrix inverse
Definition at line 202 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), atlas::clapack_getri(), Mat< eT >::colptr(), det(), lapack::getrf_(), lapack::getri_(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, podarray< eT >::set_size(), and atlas::tmp_real().
Referenced by op_inv::apply().
{
arma_extra_debug_sigprint();
// for more info, see:
// http://www.dr-lex.34sp.com/random/matrix_inv.html
// http://www.cvl.iis.u-tokyo.ac.jp/~miyazaki/tech/teche23.html
// http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
// http://www.geometrictools.com//LibFoundation/Mathematics/Wm4Matrix4.inl
switch(X.n_rows)
{
case 1:
{
X[0] = eT(1) / X[0];
};
break;
case 2:
{
const eT a = X.at(0,0);
const eT b = X.at(0,1);
const eT c = X.at(1,0);
const eT d = X.at(1,1);
const eT k = eT(1) / (a*d - b*c);
X.at(0,0) = d*k;
X.at(0,1) = -b*k;
X.at(1,0) = -c*k;
X.at(1,1) = a*k;
};
break;
case 3:
{
eT* X_col0 = X.colptr(0);
eT* X_col1 = X.colptr(1);
eT* X_col2 = X.colptr(2);
const eT a11 = X_col0[0];
const eT a21 = X_col0[1];
const eT a31 = X_col0[2];
const eT a12 = X_col1[0];
const eT a22 = X_col1[1];
const eT a32 = X_col1[2];
const eT a13 = X_col2[0];
const eT a23 = X_col2[1];
const eT a33 = X_col2[2];
const eT k = eT(1) / ( a11*(a33*a22 - a32*a23) - a21*(a33*a12-a32*a13) + a31*(a23*a12 - a22*a13) );
X_col0[0] = (a33*a22 - a32*a23) * k;
X_col0[1] = -(a33*a21 - a31*a23) * k;
X_col0[2] = (a32*a21 - a31*a22) * k;
X_col1[0] = -(a33*a12 - a32*a13) * k;
X_col1[1] = (a33*a11 - a31*a13) * k;
X_col1[2] = -(a32*a11 - a31*a12) * k;
X_col2[0] = (a23*a12 - a22*a13) * k;
X_col2[1] = -(a23*a11 - a21*a13) * k;
X_col2[2] = (a22*a11 - a21*a12) * k;
};
break;
case 4:
{
const Mat<eT> A(X);
X.at(0,0) = A.at(1,2)*A.at(2,3)*A.at(3,1) - A.at(1,3)*A.at(2,2)*A.at(3,1) + A.at(1,3)*A.at(2,1)*A.at(3,2) - A.at(1,1)*A.at(2,3)*A.at(3,2) - A.at(1,2)*A.at(2,1)*A.at(3,3) + A.at(1,1)*A.at(2,2)*A.at(3,3);
X.at(1,0) = A.at(1,3)*A.at(2,2)*A.at(3,0) - A.at(1,2)*A.at(2,3)*A.at(3,0) - A.at(1,3)*A.at(2,0)*A.at(3,2) + A.at(1,0)*A.at(2,3)*A.at(3,2) + A.at(1,2)*A.at(2,0)*A.at(3,3) - A.at(1,0)*A.at(2,2)*A.at(3,3);
X.at(2,0) = A.at(1,1)*A.at(2,3)*A.at(3,0) - A.at(1,3)*A.at(2,1)*A.at(3,0) + A.at(1,3)*A.at(2,0)*A.at(3,1) - A.at(1,0)*A.at(2,3)*A.at(3,1) - A.at(1,1)*A.at(2,0)*A.at(3,3) + A.at(1,0)*A.at(2,1)*A.at(3,3);
X.at(3,0) = A.at(1,2)*A.at(2,1)*A.at(3,0) - A.at(1,1)*A.at(2,2)*A.at(3,0) - A.at(1,2)*A.at(2,0)*A.at(3,1) + A.at(1,0)*A.at(2,2)*A.at(3,1) + A.at(1,1)*A.at(2,0)*A.at(3,2) - A.at(1,0)*A.at(2,1)*A.at(3,2);
X.at(0,1) = A.at(0,3)*A.at(2,2)*A.at(3,1) - A.at(0,2)*A.at(2,3)*A.at(3,1) - A.at(0,3)*A.at(2,1)*A.at(3,2) + A.at(0,1)*A.at(2,3)*A.at(3,2) + A.at(0,2)*A.at(2,1)*A.at(3,3) - A.at(0,1)*A.at(2,2)*A.at(3,3);
X.at(1,1) = A.at(0,2)*A.at(2,3)*A.at(3,0) - A.at(0,3)*A.at(2,2)*A.at(3,0) + A.at(0,3)*A.at(2,0)*A.at(3,2) - A.at(0,0)*A.at(2,3)*A.at(3,2) - A.at(0,2)*A.at(2,0)*A.at(3,3) + A.at(0,0)*A.at(2,2)*A.at(3,3);
X.at(2,1) = A.at(0,3)*A.at(2,1)*A.at(3,0) - A.at(0,1)*A.at(2,3)*A.at(3,0) - A.at(0,3)*A.at(2,0)*A.at(3,1) + A.at(0,0)*A.at(2,3)*A.at(3,1) + A.at(0,1)*A.at(2,0)*A.at(3,3) - A.at(0,0)*A.at(2,1)*A.at(3,3);
X.at(3,1) = A.at(0,1)*A.at(2,2)*A.at(3,0) - A.at(0,2)*A.at(2,1)*A.at(3,0) + A.at(0,2)*A.at(2,0)*A.at(3,1) - A.at(0,0)*A.at(2,2)*A.at(3,1) - A.at(0,1)*A.at(2,0)*A.at(3,2) + A.at(0,0)*A.at(2,1)*A.at(3,2);
X.at(0,2) = A.at(0,2)*A.at(1,3)*A.at(3,1) - A.at(0,3)*A.at(1,2)*A.at(3,1) + A.at(0,3)*A.at(1,1)*A.at(3,2) - A.at(0,1)*A.at(1,3)*A.at(3,2) - A.at(0,2)*A.at(1,1)*A.at(3,3) + A.at(0,1)*A.at(1,2)*A.at(3,3);
X.at(1,2) = A.at(0,3)*A.at(1,2)*A.at(3,0) - A.at(0,2)*A.at(1,3)*A.at(3,0) - A.at(0,3)*A.at(1,0)*A.at(3,2) + A.at(0,0)*A.at(1,3)*A.at(3,2) + A.at(0,2)*A.at(1,0)*A.at(3,3) - A.at(0,0)*A.at(1,2)*A.at(3,3);
X.at(2,2) = A.at(0,1)*A.at(1,3)*A.at(3,0) - A.at(0,3)*A.at(1,1)*A.at(3,0) + A.at(0,3)*A.at(1,0)*A.at(3,1) - A.at(0,0)*A.at(1,3)*A.at(3,1) - A.at(0,1)*A.at(1,0)*A.at(3,3) + A.at(0,0)*A.at(1,1)*A.at(3,3);
X.at(3,2) = A.at(0,2)*A.at(1,1)*A.at(3,0) - A.at(0,1)*A.at(1,2)*A.at(3,0) - A.at(0,2)*A.at(1,0)*A.at(3,1) + A.at(0,0)*A.at(1,2)*A.at(3,1) + A.at(0,1)*A.at(1,0)*A.at(3,2) - A.at(0,0)*A.at(1,1)*A.at(3,2);
X.at(0,3) = A.at(0,3)*A.at(1,2)*A.at(2,1) - A.at(0,2)*A.at(1,3)*A.at(2,1) - A.at(0,3)*A.at(1,1)*A.at(2,2) + A.at(0,1)*A.at(1,3)*A.at(2,2) + A.at(0,2)*A.at(1,1)*A.at(2,3) - A.at(0,1)*A.at(1,2)*A.at(2,3);
X.at(1,3) = A.at(0,2)*A.at(1,3)*A.at(2,0) - A.at(0,3)*A.at(1,2)*A.at(2,0) + A.at(0,3)*A.at(1,0)*A.at(2,2) - A.at(0,0)*A.at(1,3)*A.at(2,2) - A.at(0,2)*A.at(1,0)*A.at(2,3) + A.at(0,0)*A.at(1,2)*A.at(2,3);
X.at(2,3) = A.at(0,3)*A.at(1,1)*A.at(2,0) - A.at(0,1)*A.at(1,3)*A.at(2,0) - A.at(0,3)*A.at(1,0)*A.at(2,1) + A.at(0,0)*A.at(1,3)*A.at(2,1) + A.at(0,1)*A.at(1,0)*A.at(2,3) - A.at(0,0)*A.at(1,1)*A.at(2,3);
X.at(3,3) = A.at(0,1)*A.at(1,2)*A.at(2,0) - A.at(0,2)*A.at(1,1)*A.at(2,0) + A.at(0,2)*A.at(1,0)*A.at(2,1) - A.at(0,0)*A.at(1,2)*A.at(2,1) - A.at(0,1)*A.at(1,0)*A.at(2,2) + A.at(0,0)*A.at(1,1)*A.at(2,2);
X /= det(A);
};
break;
default:
{
#if defined(ARMA_USE_ATLAS)
{
Mat<eT>& out = X;
podarray<int> ipiv(out.n_rows);
int info = atlas::clapack_getrf(atlas::CblasColMajor, out.n_rows, out.n_cols, out.memptr(), out.n_rows, ipiv.memptr());
if(info == 0)
{
info = atlas::clapack_getri(atlas::CblasColMajor, out.n_rows, out.memptr(), out.n_rows, ipiv.memptr());
}
return (info == 0);
}
#elif defined(ARMA_USE_LAPACK)
{
Mat<eT>& out = X;
int n_rows = out.n_rows;
int n_cols = out.n_cols;
int info = 0;
podarray<int> ipiv(out.n_rows);
// 84 was empirically found -- it is the maximum value suggested by LAPACK (as provided by ATLAS v3.6)
// based on tests with various matrix types on 32-bit and 64-bit machines
//
// the "work" array is deliberately long so that a secondary (time-consuming)
// memory allocation is avoided, if possible
int work_len = (std::max)(1, n_rows*84);
podarray<eT> work(work_len);
lapack::getrf_(&n_rows, &n_cols, out.memptr(), &n_rows, ipiv.memptr(), &info);
if(info == 0)
{
// query for optimum size of work_len
int work_len_tmp = -1;
lapack::getri_(&n_rows, out.memptr(), &n_rows, ipiv.memptr(), work.memptr(), &work_len_tmp, &info);
if(info == 0)
{
int proposed_work_len = static_cast<int>(access::tmp_real(work[0]));
// if necessary, allocate more memory
if(work_len < proposed_work_len)
{
work_len = proposed_work_len;
work.set_size(work_len);
}
}
lapack::getri_(&n_rows, out.memptr(), &n_rows, ipiv.memptr(), work.memptr(), &work_len, &info);
}
return (info == 0);
}
#else
{
arma_stop("inv(): need ATLAS or LAPACK");
}
#endif
}
}
return true;
}
| eT auxlib::det | ( | const Mat< eT > & | X | ) | [inline, static, inherited] |
immediate determinant of a matrix using ATLAS or LAPACK
Definition at line 376 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), Mat< eT >::colptr(), lapack::getrf_(), podarray< eT >::mem, podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, and Mat< eT >::n_rows.
Referenced by det(), inv_inplace(), and inv_noalias().
{
arma_extra_debug_sigprint();
switch(X.n_rows)
{
case 0:
return eT(0);
case 1:
return X[0];
case 2:
return (X.at(0,0)*X.at(1,1) - X.at(0,1)*X.at(1,0));
case 3:
{
const eT* a_col0 = X.colptr(0);
const eT a11 = a_col0[0];
const eT a21 = a_col0[1];
const eT a31 = a_col0[2];
const eT* a_col1 = X.colptr(1);
const eT a12 = a_col1[0];
const eT a22 = a_col1[1];
const eT a32 = a_col1[2];
const eT* a_col2 = X.colptr(2);
const eT a13 = a_col2[0];
const eT a23 = a_col2[1];
const eT a33 = a_col2[2];
return ( a11*(a33*a22 - a32*a23) - a21*(a33*a12-a32*a13) + a31*(a23*a12 - a22*a13) );
// const double tmp1 = X.at(0,0) * X.at(1,1) * X.at(2,2);
// const double tmp2 = X.at(0,1) * X.at(1,2) * X.at(2,0);
// const double tmp3 = X.at(0,2) * X.at(1,0) * X.at(2,1);
// const double tmp4 = X.at(2,0) * X.at(1,1) * X.at(0,2);
// const double tmp5 = X.at(2,1) * X.at(1,2) * X.at(0,0);
// const double tmp6 = X.at(2,2) * X.at(1,0) * X.at(0,1);
// return (tmp1+tmp2+tmp3) - (tmp4+tmp5+tmp6);
}
case 4:
{
const eT val = \
X.at(0,3) * X.at(1,2) * X.at(2,1) * X.at(3,0) \
- X.at(0,2) * X.at(1,3) * X.at(2,1) * X.at(3,0) \
- X.at(0,3) * X.at(1,1) * X.at(2,2) * X.at(3,0) \
+ X.at(0,1) * X.at(1,3) * X.at(2,2) * X.at(3,0) \
+ X.at(0,2) * X.at(1,1) * X.at(2,3) * X.at(3,0) \
- X.at(0,1) * X.at(1,2) * X.at(2,3) * X.at(3,0) \
- X.at(0,3) * X.at(1,2) * X.at(2,0) * X.at(3,1) \
+ X.at(0,2) * X.at(1,3) * X.at(2,0) * X.at(3,1) \
+ X.at(0,3) * X.at(1,0) * X.at(2,2) * X.at(3,1) \
- X.at(0,0) * X.at(1,3) * X.at(2,2) * X.at(3,1) \
- X.at(0,2) * X.at(1,0) * X.at(2,3) * X.at(3,1) \
+ X.at(0,0) * X.at(1,2) * X.at(2,3) * X.at(3,1) \
+ X.at(0,3) * X.at(1,1) * X.at(2,0) * X.at(3,2) \
- X.at(0,1) * X.at(1,3) * X.at(2,0) * X.at(3,2) \
- X.at(0,3) * X.at(1,0) * X.at(2,1) * X.at(3,2) \
+ X.at(0,0) * X.at(1,3) * X.at(2,1) * X.at(3,2) \
+ X.at(0,1) * X.at(1,0) * X.at(2,3) * X.at(3,2) \
- X.at(0,0) * X.at(1,1) * X.at(2,3) * X.at(3,2) \
- X.at(0,2) * X.at(1,1) * X.at(2,0) * X.at(3,3) \
+ X.at(0,1) * X.at(1,2) * X.at(2,0) * X.at(3,3) \
+ X.at(0,2) * X.at(1,0) * X.at(2,1) * X.at(3,3) \
- X.at(0,0) * X.at(1,2) * X.at(2,1) * X.at(3,3) \
- X.at(0,1) * X.at(1,0) * X.at(2,2) * X.at(3,3) \
+ X.at(0,0) * X.at(1,1) * X.at(2,2) * X.at(3,3) \
;
return val;
}
default:
{
#if defined(ARMA_USE_ATLAS)
{
Mat<eT> tmp = X;
podarray<int> ipiv(tmp.n_rows);
atlas::clapack_getrf(atlas::CblasColMajor, tmp.n_rows, tmp.n_cols, tmp.memptr(), tmp.n_rows, ipiv.memptr());
// on output tmp appears to be L+U_alt, where U_alt is U with the main diagonal set to zero
eT val = tmp.at(0,0);
for(u32 i=1; i < tmp.n_rows; ++i)
{
val *= tmp.at(i,i);
}
int sign = +1;
for(u32 i=0; i < tmp.n_rows; ++i)
{
if( int(i) != ipiv.mem[i] ) // NOTE: no adjustment required, as the clapack version of getrf() assumes counting from 0
{
sign *= -1;
}
}
return ( (sign < 0) ? -val : val );
}
#elif defined(ARMA_USE_LAPACK)
{
Mat<eT> tmp = X;
podarray<int> ipiv(tmp.n_rows);
int info = 0;
int n_rows = int(tmp.n_rows);
int n_cols = int(tmp.n_cols);
lapack::getrf_(&n_rows, &n_cols, tmp.memptr(), &n_rows, ipiv.memptr(), &info);
// on output tmp appears to be L+U_alt, where U_alt is U with the main diagonal set to zero
eT val = tmp.at(0,0);
for(u32 i=1; i < tmp.n_rows; ++i)
{
val *= tmp.at(i,i);
}
int sign = +1;
for(u32 i=0; i < tmp.n_rows; ++i)
{
if( int(i) != (ipiv.mem[i] - 1) ) // NOTE: adjustment of -1 is required as Fortran counts from 1
{
sign *= -1;
}
}
return ( (sign < 0) ? -val : val );
}
#else
{
arma_stop("det(): need ATLAS or LAPACK");
return eT(0);
}
#endif
}
}
}
| void auxlib::log_det | ( | eT & | out_val, | |
| typename get_pod_type< eT >::result & | out_sign, | |||
| const Mat< eT > & | X | |||
| ) | [inline, static, inherited] |
immediate log determinant of a matrix using ATLAS or LAPACK
Definition at line 523 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), lapack::getrf_(), log(), podarray< eT >::mem, podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, and access::tmp_real().
Referenced by log_det().
{
arma_extra_debug_sigprint();
typedef typename get_pod_type<eT>::result T;
#if defined(ARMA_USE_ATLAS)
{
Mat<eT> tmp = X;
podarray<int> ipiv(tmp.n_rows);
atlas::clapack_getrf(atlas::CblasColMajor, tmp.n_rows, tmp.n_cols, tmp.memptr(), tmp.n_rows, ipiv.memptr());
// on output tmp appears to be L+U_alt, where U_alt is U with the main diagonal set to zero
s32 sign = (is_complex<eT>::value == false) ? ( (access::tmp_real( tmp.at(0,0) ) < T(0)) ? -1 : +1 ) : +1;
eT val = (is_complex<eT>::value == false) ? std::log( (access::tmp_real( tmp.at(0,0) ) < T(0)) ? tmp.at(0,0)*T(-1) : tmp.at(0,0) ) : std::log( tmp.at(0,0) );
for(u32 i=1; i < tmp.n_rows; ++i)
{
const eT x = tmp.at(i,i);
sign *= (is_complex<eT>::value == false) ? ( (access::tmp_real(x) < T(0)) ? -1 : +1 ) : +1;
val += (is_complex<eT>::value == false) ? std::log( (access::tmp_real(x) < T(0)) ? x*T(-1) : x ) : std::log(x);
}
for(u32 i=0; i < tmp.n_rows; ++i)
{
if( int(i) != ipiv.mem[i] ) // NOTE: no adjustment required, as the clapack version of getrf() assumes counting from 0
{
sign *= -1;
}
}
out_val = val;
out_sign = T(sign);
}
#elif defined(ARMA_USE_LAPACK)
{
Mat<eT> tmp = X;
podarray<int> ipiv(tmp.n_rows);
int info = 0;
int n_rows = int(tmp.n_rows);
int n_cols = int(tmp.n_cols);
lapack::getrf_(&n_rows, &n_cols, tmp.memptr(), &n_rows, ipiv.memptr(), &info);
// on output tmp appears to be L+U_alt, where U_alt is U with the main diagonal set to zero
s32 sign = (is_complex<eT>::value == false) ? ( (access::tmp_real( tmp.at(0,0) ) < T(0)) ? -1 : +1 ) : +1;
eT val = (is_complex<eT>::value == false) ? std::log( (access::tmp_real( tmp.at(0,0) ) < T(0)) ? tmp.at(0,0)*T(-1) : tmp.at(0,0) ) : std::log( tmp.at(0,0) );
for(u32 i=1; i < tmp.n_rows; ++i)
{
const eT x = tmp.at(i,i);
sign *= (is_complex<eT>::value == false) ? ( (access::tmp_real(x) < T(0)) ? -1 : +1 ) : +1;
val += (is_complex<eT>::value == false) ? std::log( (access::tmp_real(x) < T(0)) ? x*T(-1) : x ) : std::log(x);
}
for(u32 i=0; i < tmp.n_rows; ++i)
{
if( int(i) != (ipiv.mem[i] - 1) ) // NOTE: adjustment of -1 is required as Fortran counts from 1
{
sign *= -1;
}
}
out_val = val;
out_sign = T(sign);
}
#else
{
arma_stop("log_det(): need ATLAS or LAPACK");
out_val = eT(0);
out_sign = T(0);
}
#endif
}
| void auxlib::lu | ( | Mat< eT > & | L, | |
| Mat< eT > & | U, | |||
| podarray< int > & | ipiv, | |||
| const Mat< eT > & | X_orig | |||
| ) | [inline, static, inherited] |
immediate LU decomposition of a matrix using ATLAS or LAPACK
Definition at line 611 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), lapack::getrf_(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Mat< eT >::set_size(), and podarray< eT >::set_size().
{
arma_extra_debug_sigprint();
U = X;
#if defined(ARMA_USE_ATLAS) || defined(ARMA_USE_LAPACK)
{
#if defined(ARMA_USE_ATLAS)
{
ipiv.set_size(U.n_rows);
//int info =
atlas::clapack_getrf(atlas::CblasColMajor, U.n_rows, U.n_cols, U.memptr(), U.n_rows, ipiv.memptr());
}
#elif defined(ARMA_USE_LAPACK)
{
ipiv.set_size(U.n_rows);
int info = 0;
int n_rows = U.n_rows;
int n_cols = U.n_cols;
lapack::getrf_(&n_rows, &n_cols, U.memptr(), &n_rows, ipiv.memptr(), &info);
// take into account that Fortran counts from 1
for(u32 i=0; i<U.n_rows; ++i)
{
ipiv[i] -= 1;
}
}
#endif
L.set_size(U.n_rows, U.n_rows);
for(u32 col=0; col<L.n_cols; ++col)
{
for(u32 row=0; row<col; ++row)
{
L.at(row,col) = eT(0);
}
L.at(col,col) = eT(1);
for(u32 row=col+1; row<L.n_rows; ++row)
{
L.at(row,col) = U.at(row,col);
U.at(row,col) = eT(0);
}
}
}
#else
{
arma_stop("lu(): need ATLAS or LAPACK");
}
#endif
}
| void auxlib::lu | ( | Mat< eT > & | L, | |
| Mat< eT > & | U, | |||
| Mat< eT > & | P, | |||
| const Mat< eT > & | X | |||
| ) | [inline, static, inherited] |
Definition at line 680 of file auxlib_meat.hpp.
References lu(), podarray< eT >::n_elem, and Mat< eT >::swap_rows().
{
arma_extra_debug_sigprint();
podarray<int> ipiv;
auxlib::lu(L, U, ipiv, X);
const u32 n = ipiv.n_elem;
Mat<u32> P_tmp(n,n);
Mat<u32> ident = eye< Mat<u32> >(n,n);
for(u32 i=n; i>0; --i)
{
const u32 j = i-1;
const u32 k = ipiv[j];
ident.swap_rows(j,k);
if(i == n)
{
P_tmp = ident;
}
else
{
P_tmp *= ident;
}
ident.swap_rows(j,k);
}
P = conv_to< Mat<eT> >::from(P_tmp);
}
| void auxlib::lu | ( | Mat< eT > & | L, | |
| Mat< eT > & | U, | |||
| const Mat< eT > & | X | |||
| ) | [inline, static, inherited] |
Definition at line 719 of file auxlib_meat.hpp.
References lu().
{
arma_extra_debug_sigprint();
podarray<int> ipiv;
auxlib::lu(L, U, ipiv, X);
}
| void auxlib::eig_sym | ( | Col< eT > & | eigval, | |
| const Mat< eT > & | A | |||
| ) | [inline, static, inherited] |
immediate eigenvalues of a symmetric real matrix using LAPACK
Definition at line 733 of file auxlib_meat.hpp.
References arma_stop(), unwrap_check< T1 >::M, podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Col< eT >::set_size(), and lapack::syev_().
Referenced by eig_sym().
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
const unwrap_check<Mat<eT> > tmp(A_orig, eigval);
const Mat<eT>& A = tmp.M;
arma_debug_check( (A.n_rows != A.n_cols), "eig_sym(): given matrix is not square");
// rudimentary "better-than-nothing" test for symmetry
//arma_debug_check( (A.at(A.n_rows-1, 0) != A.at(0, A.n_cols-1)), "auxlib::eig(): given matrix is not symmetric" );
char jobz = 'N';
char uplo = 'U';
int n_rows = A.n_rows;
int lwork = (std::max)(1,3*n_rows-1);
eigval.set_size(n_rows);
podarray<eT> work(lwork);
Mat<eT> A_copy = A;
int info;
arma_extra_debug_print("lapack::syev_()");
lapack::syev_(&jobz, &uplo, &n_rows, A_copy.memptr(), &n_rows, eigval.memptr(), work.memptr(), &lwork, &info);
}
#else
{
arma_stop("eig_sym(): need LAPACK");
}
#endif
}
| void auxlib::eig_sym | ( | Col< T > & | eigval, | |
| const Mat< std::complex< T > > & | A | |||
| ) | [inline, static, inherited] |
immediate eigenvalues of a hermitian complex matrix using LAPACK
Definition at line 775 of file auxlib_meat.hpp.
References arma_stop(), lapack::heev_(), max(), podarray< eT >::memptr(), Mat< eT >::memptr(), and Col< eT >::set_size().
{
arma_extra_debug_sigprint();
typedef typename std::complex<T> eT;
#if defined(ARMA_USE_LAPACK)
{
arma_debug_check( (A.n_rows != A.n_cols), "eig_sym(): given matrix is not hermitian");
char jobz = 'N';
char uplo = 'U';
int n_rows = A.n_rows;
int lda = A.n_rows;
int lwork = (std::max)(1, 2*n_rows - 1); // TODO: automatically find best size of lwork
eigval.set_size(n_rows);
podarray<eT> work(lwork);
podarray<T> rwork( (std::max)(1, 3*n_rows - 2) );
Mat<eT> A_copy = A;
int info;
arma_extra_debug_print("lapack::heev_()");
lapack::heev_(&jobz, &uplo, &n_rows, A_copy.memptr(), &lda, eigval.memptr(), work.memptr(), &lwork, rwork.memptr(), &info);
}
#else
{
arma_stop("eig_sym(): need LAPACK");
}
#endif
}
| void auxlib::eig_sym | ( | Col< eT > & | eigval, | |
| Mat< eT > & | eigvec, | |||
| const Mat< eT > & | A | |||
| ) | [inline, static, inherited] |
immediate eigenvalues and eigenvectors of a symmetric real matrix using LAPACK
Definition at line 816 of file auxlib_meat.hpp.
References arma_stop(), unwrap_check< T1 >::M, podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Col< eT >::set_size(), and lapack::syev_().
{
arma_extra_debug_sigprint();
// TODO: check for aliasing
#if defined(ARMA_USE_LAPACK)
{
const unwrap_check< Mat<eT> > tmp1(A_orig, eigval);
const Mat<eT>& A_tmp = tmp1.M;
const unwrap_check< Mat<eT> > tmp2(A_tmp, eigvec);
const Mat<eT>& A = tmp2.M;
arma_debug_check( (A.n_rows != A.n_cols), "eig_sym(): given matrix is not square" );
// rudimentary "better-than-nothing" test for symmetry
//arma_debug_check( (A.at(A.n_rows-1, 0) != A.at(0, A.n_cols-1)), "auxlib::eig(): given matrix is not symmetric" );
char jobz = 'V';
char uplo = 'U';
int n_rows = A.n_rows;
int lwork = (std::max)(1, 3*n_rows-1);
eigval.set_size(n_rows);
podarray<eT> work(lwork);
eigvec = A;
int info;
arma_extra_debug_print("lapack::syev_()");
lapack::syev_(&jobz, &uplo, &n_rows, eigvec.memptr(), &n_rows, eigval.memptr(), work.memptr(), &lwork, &info);
}
#else
{
arma_stop("eig_sym(): need LAPACK");
}
#endif
}
| void auxlib::eig_sym | ( | Col< T > & | eigval, | |
| Mat< std::complex< T > > & | eigvec, | |||
| const Mat< std::complex< T > > & | A | |||
| ) | [inline, static, inherited] |
immediate eigenvalues and eigenvectors of a hermitian complex matrix using LAPACK
Definition at line 865 of file auxlib_meat.hpp.
References arma_stop(), lapack::heev_(), unwrap_check< T1 >::M, max(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, and Col< eT >::set_size().
{
arma_extra_debug_sigprint();
typedef typename std::complex<T> eT;
#if defined(ARMA_USE_LAPACK)
{
const unwrap_check< Mat<eT> > tmp(A_orig, eigvec);
const Mat<eT>& A = tmp.M;
arma_debug_check( (A.n_rows != A.n_cols), "eig_sym(): given matrix is not hermitian" );
char jobz = 'V';
char uplo = 'U';
int n_rows = A.n_rows;
int lda = A.n_rows;
int lwork = (std::max)(1, 2*n_rows - 1); // TODO: automatically find best size of lwork
eigval.set_size(n_rows);
podarray<eT> work(lwork);
podarray<T> rwork( (std::max)(1, 3*n_rows - 2) );
eigvec = A;
int info;
arma_extra_debug_print("lapack::heev_()");
lapack::heev_(&jobz, &uplo, &n_rows, eigvec.memptr(), &lda, eigval.memptr(), work.memptr(), &lwork, rwork.memptr(), &info);
}
#else
{
arma_stop("eig_sym(): need LAPACK");
}
#endif
}
| void auxlib::eig_gen | ( | Col< std::complex< T > > & | eigval, | |
| Mat< T > & | l_eigvec, | |||
| Mat< T > & | r_eigvec, | |||
| const Mat< T > & | A, | |||
| const char | side | |||
| ) | [inline, inherited] |
Eigenvalues and eigenvectors of a general square real matrix using LAPACK. //! The argument 'side' specifies which eigenvectors should be calculated //! (see code for mode details).
Definition at line 913 of file auxlib_meat.hpp.
References arma_stop(), lapack::geev_(), max(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, and Mat< eT >::set_size().
{
arma_extra_debug_sigprint();
// TODO: check for aliasing
#if defined(ARMA_USE_LAPACK)
{
arma_debug_check( (A.n_rows != A.n_cols), "eig_gen(): given matrix is not square" );
char jobvl;
char jobvr;
switch(side)
{
case 'l': // left
jobvl = 'V';
jobvr = 'N';
break;
case 'r': // right
jobvl = 'N';
jobvr = 'V';
break;
case 'b': // both
jobvl = 'V';
jobvr = 'V';
break;
case 'n': // neither
jobvl = 'N';
jobvr = 'N';
break;
default:
arma_stop("eig_gen(): parameter 'side' is invalid");
}
int n_rows = A.n_rows;
int lda = A.n_rows;
int lwork = (std::max)(1, 4*n_rows); // TODO: automatically find best size of lwork
eigval.set_size(n_rows);
l_eigvec.set_size(n_rows, n_rows);
r_eigvec.set_size(n_rows, n_rows);
podarray<T> work(lwork);
podarray<T> rwork( (std::max)(1, 3*n_rows) );
podarray<T> wr(n_rows);
podarray<T> wi(n_rows);
Mat<T> A_copy = A;
int info;
arma_extra_debug_print("lapack::cx_geev_()");
lapack::geev_(&jobvl, &jobvr, &n_rows, A_copy.memptr(), &lda, wr.memptr(), wi.memptr(), l_eigvec.memptr(), &n_rows, r_eigvec.memptr(), &n_rows, work.memptr(), &lwork, &info);
eigval.set_size(n_rows);
for(u32 i=0; i<u32(n_rows); ++i)
{
eigval[i] = std::complex<T>(wr[i], wi[i]);
}
}
#else
{
arma_stop("eig_gen(): need LAPACK");
}
#endif
}
| void auxlib::eig_gen | ( | Col< std::complex< T > > & | eigval, | |
| Mat< std::complex< T > > & | l_eigvec, | |||
| Mat< std::complex< T > > & | r_eigvec, | |||
| const Mat< std::complex< T > > & | A, | |||
| const char | side | |||
| ) | [inline, static, inherited] |
Eigenvalues and eigenvectors of a general square complex matrix using LAPACK //! The argument 'side' specifies which eigenvectors should be calculated //! (see code for mode details).
Definition at line 1006 of file auxlib_meat.hpp.
References arma_stop(), lapack::cx_geev_(), max(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, and Mat< eT >::set_size().
{
arma_extra_debug_sigprint();
// TODO: check for aliasing
typedef typename std::complex<T> eT;
#if defined(ARMA_USE_LAPACK)
{
arma_debug_check( (A.n_rows != A.n_cols), "eig_gen(): given matrix is not square" );
char jobvl;
char jobvr;
switch(side)
{
case 'l': // left
jobvl = 'V';
jobvr = 'N';
break;
case 'r': // right
jobvl = 'N';
jobvr = 'V';
break;
case 'b': // both
jobvl = 'V';
jobvr = 'V';
break;
case 'n': // neither
jobvl = 'N';
jobvr = 'N';
break;
default:
arma_stop("eig_gen(): parameter 'side' is invalid");
}
int n_rows = A.n_rows;
int lda = A.n_rows;
int lwork = (std::max)(1, 4*n_rows); // TODO: automatically find best size of lwork
eigval.set_size(n_rows);
l_eigvec.set_size(n_rows, n_rows);
r_eigvec.set_size(n_rows, n_rows);
podarray<eT> work(lwork);
podarray<T> rwork( (std::max)(1, 3*n_rows) ); // was 2,3
Mat<eT> A_copy = A;
int info;
arma_extra_debug_print("lapack::cx_geev_()");
lapack::cx_geev_(&jobvl, &jobvr, &n_rows, A_copy.memptr(), &lda, eigval.memptr(), l_eigvec.memptr(), &n_rows, r_eigvec.memptr(), &n_rows, work.memptr(), &lwork, rwork.memptr(), &info);
}
#else
{
arma_stop("eig_gen(): need LAPACK");
}
#endif
}
| bool auxlib::chol | ( | Mat< eT > & | out, | |
| const Mat< eT > & | X | |||
| ) | [inline, static, inherited] |
Definition at line 1084 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::colptr(), Mat< eT >::memptr(), Mat< eT >::n_rows, and lapack::potrf_().
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
char uplo = 'U';
int n = X.n_rows;
int lda = X.n_rows;
int info;
out = X;
lapack::potrf_(&uplo, &n, out.memptr(), &lda, &info);
for(u32 col=0; col<X.n_rows; ++col)
{
eT* colptr = out.colptr(col);
for(u32 row=col+1; row<X.n_rows; ++row)
{
colptr[row] = eT(0);
}
}
return (info == 0);
}
#else
{
arma_stop("chol(): need LAPACK");
return false;
}
#endif
}
| bool auxlib::qr | ( | Mat< eT > & | Q, | |
| Mat< eT > & | R, | |||
| const Mat< eT > & | X | |||
| ) | [inline, static, inherited] |
Definition at line 1122 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), lapack::geqrf_(), Mat< eT >::mem, podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_elem, Mat< eT >::n_rows, lapack::orgqr_(), Mat< eT >::set_size(), podarray< eT >::set_size(), atlas::tmp_real(), and lapack::ungqr_().
Referenced by qr().
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
int m = static_cast<int>(X.n_rows);
int n = static_cast<int>(X.n_cols);
int work_len = (std::max)(1,n);
int work_len_tmp;
int k = (std::min)(m,n);
int info;
podarray<eT> tau(k);
podarray<eT> work(work_len);
R = X;
// query for the optimum value of work_len
work_len_tmp = -1;
lapack::geqrf_(&m, &n, R.memptr(), &m, tau.memptr(), work.memptr(), &work_len_tmp, &info);
if(info == 0)
{
work_len = static_cast<int>(access::tmp_real(work[0]));
work.set_size(work_len);
}
lapack::geqrf_(&m, &n, R.memptr(), &m, tau.memptr(), work.memptr(), &work_len, &info);
Q.set_size(X.n_rows, X.n_rows);
eT* Q_mem = Q.memptr();
const eT* R_mem = R.mem;
const u32 n_elem_copy = (std::min)(Q.n_elem, R.n_elem);
for(u32 i=0; i < n_elem_copy; ++i)
{
Q_mem[i] = R_mem[i];
}
// construct R
for(u32 row=0; row < R.n_rows; ++row)
{
const u32 n_elem_tmp = (std::min)(row, R.n_cols);
for(u32 col=0; col < n_elem_tmp; ++col)
{
R.at(row,col) = eT(0);
}
}
if( (is_float<eT>::value == true) || (is_double<eT>::value == true) )
{
// query for the optimum value of work_len
work_len_tmp = -1;
lapack::orgqr_(&m, &m, &k, Q.memptr(), &m, tau.memptr(), work.memptr(), &work_len_tmp, &info);
if(info == 0)
{
work_len = static_cast<int>(access::tmp_real(work[0]));
work.set_size(work_len);
}
lapack::orgqr_(&m, &m, &k, Q.memptr(), &m, tau.memptr(), work.memptr(), &work_len, &info);
}
else
if( (is_supported_complex_float<eT>::value == true) || (is_supported_complex_double<eT>::value == true) )
{
// query for the optimum value of work_len
work_len_tmp = -1;
lapack::ungqr_(&m, &m, &k, Q.memptr(), &m, tau.memptr(), work.memptr(), &work_len_tmp, &info);
if(info == 0)
{
work_len = static_cast<int>(access::tmp_real(work[0]));
work.set_size(work_len);
}
lapack::ungqr_(&m, &m, &k, Q.memptr(), &m, tau.memptr(), work.memptr(), &work_len, &info);
}
return (info == 0);
}
#else
{
arma_stop("qr(): need LAPACK");
return false;
}
#endif
}
| bool auxlib::svd | ( | Col< eT > & | S, | |
| const Mat< eT > & | X | |||
| ) | [inline, static, inherited] |
Definition at line 1220 of file auxlib_meat.hpp.
References arma_stop(), max(), podarray< eT >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_rows, podarray< eT >::set_size(), and Col< eT >::set_size().
Referenced by rank(), and svd().
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
Mat<eT> A = X;
Mat<eT> U(1, 1);
Mat<eT> V(1, A.n_cols);
char jobu = 'N';
char jobvt = 'N';
int m = A.n_rows;
int n = A.n_cols;
int lda = A.n_rows;
int ldu = U.n_rows;
int ldvt = V.n_rows;
int lwork = 2 * (std::max)(1, (std::max)( (3*(std::min)(m,n) + (std::max)(m,n)), 5*(std::min)(m,n) ) );
int info;
S.set_size( (std::min)(m, n) );
podarray<eT> work(lwork);
// let gesvd_() calculate the optimum size of the workspace
int lwork_tmp = -1;
lapack::gesvd_<eT>
(
&jobu, &jobvt,
&m,&n,
A.memptr(), &lda,
S.memptr(),
U.memptr(), &ldu,
V.memptr(), &ldvt,
work.memptr(), &lwork_tmp,
&info
);
if(info == 0)
{
int proposed_lwork = static_cast<int>(work[0]);
if(proposed_lwork > lwork)
{
lwork = proposed_lwork;
work.set_size(lwork);
}
lapack::gesvd_<eT>
(
&jobu, &jobvt,
&m, &n,
A.memptr(), &lda,
S.memptr(),
U.memptr(), &ldu,
V.memptr(), &ldvt,
work.memptr(), &lwork,
&info
);
}
return (info == 0);
}
#else
{
arma_stop("svd(): need LAPACK");
return false;
}
#endif
}
| bool auxlib::svd | ( | Col< T > & | S, | |
| const Mat< std::complex< T > > & | X | |||
| ) | [inline, static, inherited] |
Definition at line 1300 of file auxlib_meat.hpp.
References arma_stop(), max(), podarray< eT >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_rows, real(), podarray< eT >::set_size(), and Col< eT >::set_size().
{
arma_extra_debug_sigprint();
typedef std::complex<T> eT;
#if defined(ARMA_USE_LAPACK)
{
Mat<eT> A = X;
Mat<eT> U(1, 1);
Mat<eT> V(1, A.n_cols);
char jobu = 'N';
char jobvt = 'N';
int m = A.n_rows;
int n = A.n_cols;
int lda = A.n_rows;
int ldu = U.n_rows;
int ldvt = V.n_rows;
int lwork = 2 * (std::max)(1, 2*(std::min)(m,n)+(std::max)(m,n) );
int info;
S.set_size( (std::min)(m,n) );
podarray<eT> work(lwork);
podarray<T> rwork( 5*(std::min)(m,n) );
// let gesvd_() calculate the optimum size of the workspace
int lwork_tmp = -1;
lapack::cx_gesvd_<T>
(
&jobu, &jobvt,
&m, &n,
A.memptr(), &lda,
S.memptr(),
U.memptr(), &ldu,
V.memptr(), &ldvt,
work.memptr(), &lwork_tmp,
rwork.memptr(),
&info
);
if(info == 0)
{
int proposed_lwork = static_cast<int>(real(work[0]));
if(proposed_lwork > lwork)
{
lwork = proposed_lwork;
work.set_size(lwork);
}
lapack::cx_gesvd_<T>
(
&jobu, &jobvt,
&m, &n,
A.memptr(), &lda,
S.memptr(),
U.memptr(), &ldu,
V.memptr(), &ldvt,
work.memptr(), &lwork,
rwork.memptr(),
&info
);
}
return (info == 0);
}
#else
{
arma_stop("svd(): need LAPACK");
return false;
}
#endif
}
| bool auxlib::svd | ( | Mat< eT > & | U, | |
| Col< eT > & | S, | |||
| Mat< eT > & | V, | |||
| const Mat< eT > & | X | |||
| ) | [inline, static, inherited] |
Definition at line 1383 of file auxlib_meat.hpp.
References op_trans::apply(), arma_stop(), max(), podarray< eT >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_rows, podarray< eT >::set_size(), Col< eT >::set_size(), and Mat< eT >::set_size().
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
Mat<eT> A = X;
U.set_size(A.n_rows, A.n_rows);
V.set_size(A.n_cols, A.n_cols);
char jobu = 'A';
char jobvt = 'A';
int m = A.n_rows;
int n = A.n_cols;
int lda = A.n_rows;
int ldu = U.n_rows;
int ldvt = V.n_rows;
int lwork = 2 * (std::max)(1, (std::max)( (3*(std::min)(m,n) + (std::max)(m,n)), 5*(std::min)(m,n) ) );
int info;
S.set_size( (std::min)(m,n) );
podarray<eT> work(lwork);
// let gesvd_() calculate the optimum size of the workspace
int lwork_tmp = -1;
lapack::gesvd_<eT>
(
&jobu, &jobvt,
&m, &n,
A.memptr(), &lda,
S.memptr(),
U.memptr(), &ldu,
V.memptr(), &ldvt,
work.memptr(), &lwork_tmp,
&info
);
if(info == 0)
{
int proposed_lwork = static_cast<int>(work[0]);
if(proposed_lwork > lwork)
{
lwork = proposed_lwork;
work.set_size(lwork);
}
lapack::gesvd_<eT>
(
&jobu, &jobvt,
&m, &n,
A.memptr(), &lda,
S.memptr(),
U.memptr(), &ldu,
V.memptr(), &ldvt,
work.memptr(), &lwork,
&info
);
op_trans::apply(V,V); // op_trans will work out that an in-place transpose can be done
}
return (info == 0);
}
#else
{
arma_stop("svd(): need LAPACK");
return false;
}
#endif
}
| bool auxlib::svd | ( | Mat< std::complex< T > > & | U, | |
| Col< T > & | S, | |||
| Mat< std::complex< T > > & | V, | |||
| const Mat< std::complex< T > > & | X | |||
| ) | [inline, static, inherited] |
Definition at line 1463 of file auxlib_meat.hpp.
References op_htrans::apply(), arma_stop(), max(), podarray< eT >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_rows, real(), podarray< eT >::set_size(), Col< eT >::set_size(), and Mat< eT >::set_size().
{
arma_extra_debug_sigprint();
typedef std::complex<T> eT;
#if defined(ARMA_USE_LAPACK)
{
Mat<eT> A = X;
U.set_size(A.n_rows, A.n_rows);
V.set_size(A.n_cols, A.n_cols);
char jobu = 'A';
char jobvt = 'A';
int m = A.n_rows;
int n = A.n_cols;
int lda = A.n_rows;
int ldu = U.n_rows;
int ldvt = V.n_rows;
int lwork = 2 * (std::max)(1, 2*(std::min)(m,n)+(std::max)(m,n) );
int info;
S.set_size( (std::min)(m,n) );
podarray<eT> work(lwork);
podarray<T> rwork( 5*(std::min)(m,n) );
// let gesvd_() calculate the optimum size of the workspace
int lwork_tmp = -1;
lapack::cx_gesvd_<T>
(
&jobu, &jobvt,
&m, &n,
A.memptr(), &lda,
S.memptr(),
U.memptr(), &ldu,
V.memptr(), &ldvt,
work.memptr(), &lwork_tmp,
rwork.memptr(),
&info
);
if(info == 0)
{
int proposed_lwork = static_cast<int>(real(work[0]));
if(proposed_lwork > lwork)
{
lwork = proposed_lwork;
work.set_size(lwork);
}
lapack::cx_gesvd_<T>
(
&jobu, &jobvt,
&m, &n,
A.memptr(), &lda,
S.memptr(),
U.memptr(), &ldu,
V.memptr(), &ldvt,
work.memptr(), &lwork,
rwork.memptr(),
&info
);
op_htrans::apply(V,V); // op_htrans will work out that an in-place transpose can be done
}
return (info == 0);
}
#else
{
arma_stop("svd(): need LAPACK");
return false;
}
#endif
}
| bool auxlib::solve | ( | Mat< eT > & | out, | |
| const Mat< eT > & | A, | |||
| const Mat< eT > & | B | |||
| ) | [inline, static, inherited] |
Solve a system of linear equations //! Assumes that A.n_rows = A.n_cols //! and B.n_rows = A.n_rows.
Definition at line 1550 of file auxlib_meat.hpp.
References arma_stop(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, and Mat< eT >::n_rows.
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
int n = A.n_rows;
int lda = A.n_rows;
int ldb = A.n_rows;
int nrhs = B.n_cols;
int info;
podarray<int> ipiv(n);
out = B;
Mat<eT> A_copy = A;
lapack::gesv_<eT>(&n, &nrhs, A_copy.memptr(), &lda, ipiv.memptr(), out.memptr(), &ldb, &info);
return (info == 0);
}
#else
{
arma_stop("solve(): need LAPACK");
return false;
}
#endif
}
| bool auxlib::solve_od | ( | Mat< eT > & | out, | |
| const Mat< eT > & | A, | |||
| const Mat< eT > & | B | |||
| ) | [inline, static, inherited] |
Solve an over-determined system. //! Assumes that A.n_rows > A.n_cols //! and B.n_rows = A.n_rows.
Definition at line 1587 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::colptr(), syslib::copy_elem(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Mat< eT >::set_size(), and trans().
Referenced by glue_solve::apply().
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
char trans = 'N';
int m = A.n_rows;
int n = A.n_cols;
int lda = A.n_rows;
int ldb = A.n_rows;
int nrhs = B.n_cols;
int lwork = n + (std::max)(n, nrhs);
int info;
Mat<eT> A_copy = A;
Mat<eT> tmp = B;
podarray<eT> work(lwork);
arma_extra_debug_print("lapack::gels_()");
// NOTE:
// the dgels() function in the lapack library supplied by ATLAS 3.6
// seems to have problems
lapack::gels_<eT>
(
&trans, &m, &n, &nrhs,
A_copy.memptr(), &lda,
tmp.memptr(), &ldb,
work.memptr(), &lwork,
&info
);
arma_extra_debug_print("lapack::gels_() -- finished");
out.set_size(A.n_cols, B.n_cols);
for(u32 col=0; col<B.n_cols; ++col)
{
syslib::copy_elem( out.colptr(col), tmp.colptr(col), A.n_cols );
}
return (info == 0);
}
#else
{
arma_stop("auxlib::solve_od(): need LAPACK");
return false;
}
#endif
}
| bool auxlib::solve_ud | ( | Mat< eT > & | out, | |
| const Mat< eT > & | A, | |||
| const Mat< eT > & | B | |||
| ) | [inline, static, inherited] |
Solve an under-determined system. //! Assumes that A.n_rows < A.n_cols //! and B.n_rows = A.n_rows.
Definition at line 1651 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::colptr(), syslib::copy_elem(), podarray< eT >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Mat< eT >::set_size(), trans(), and Mat< eT >::zeros().
Referenced by glue_solve::apply().
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
char trans = 'N';
int m = A.n_rows;
int n = A.n_cols;
int lda = A.n_rows;
int ldb = A.n_cols;
int nrhs = B.n_cols;
int lwork = m + (std::max)(m,nrhs);
int info;
Mat<eT> A_copy = A;
Mat<eT> tmp;
tmp.zeros(A.n_cols, B.n_cols);
for(u32 col=0; col<B.n_cols; ++col)
{
eT* tmp_colmem = tmp.colptr(col);
syslib::copy_elem( tmp_colmem, B.colptr(col), B.n_rows );
for(u32 row=B.n_rows; row<A.n_cols; ++row)
{
tmp_colmem[row] = eT(0);
}
}
podarray<eT> work(lwork);
arma_extra_debug_print("lapack::gels_()");
// NOTE:
// the dgels() function in the lapack library supplied by ATLAS 3.6
// seems to have problems
lapack::gels_<eT>
(
&trans, &m, &n, &nrhs,
A_copy.memptr(), &lda,
tmp.memptr(), &ldb,
work.memptr(), &lwork,
&info
);
arma_extra_debug_print("lapack::gels_() -- finished");
out.set_size(A.n_cols, B.n_cols);
for(u32 col=0; col<B.n_cols; ++col)
{
syslib::copy_elem( out.colptr(col), tmp.colptr(col), A.n_cols );
}
return (info == 0);
}
#else
{
arma_stop("auxlib::solve_ud(): need LAPACK");
return false;
}
#endif
}