Classes | |
class | auxlib |
wrapper for accessing external functions defined in ATLAS, LAPACK or BLAS libraries More... | |
Functions | |
template<typename eT > | |
static void | auxlib::inv_noalias (Mat< eT > &out, const Mat< eT > &X) |
immediate matrix inverse | |
template<typename eT > | |
static void | 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::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. |
void auxlib::inv_noalias | ( | Mat< eT > & | out, | |
const Mat< eT > & | X | |||
) | [inline, static, inherited] |
immediate matrix inverse
Definition at line 25 of file auxlib_meat.hpp.
References arma_check(), arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), atlas::clapack_getri(), Mat< eT >::colptr(), det(), lapack::getrf_(), lapack::getri_(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, podarray< T1 >::set_size(), Mat< eT >::set_size(), and tmp_real().
Referenced by op_inv::apply().
00026 { 00027 arma_extra_debug_sigprint(); 00028 00029 switch(X.n_rows) 00030 { 00031 case 1: 00032 { 00033 out.set_size(1,1); 00034 out[0] = eT(1) / X[0]; 00035 }; 00036 break; 00037 00038 case 2: 00039 { 00040 out.set_size(2,2); 00041 00042 const eT a = X.at(0,0); 00043 const eT b = X.at(0,1); 00044 const eT c = X.at(1,0); 00045 const eT d = X.at(1,1); 00046 00047 const eT k = eT(1) / (a*d - b*c); 00048 00049 out.at(0,0) = d*k; 00050 out.at(0,1) = -b*k; 00051 out.at(1,0) = -c*k; 00052 out.at(1,1) = a*k; 00053 }; 00054 break; 00055 00056 case 3: 00057 { 00058 out.set_size(3,3); 00059 00060 const eT* X_col0 = X.colptr(0); 00061 const eT a11 = X_col0[0]; 00062 const eT a21 = X_col0[1]; 00063 const eT a31 = X_col0[2]; 00064 00065 const eT* X_col1 = X.colptr(1); 00066 const eT a12 = X_col1[0]; 00067 const eT a22 = X_col1[1]; 00068 const eT a32 = X_col1[2]; 00069 00070 const eT* X_col2 = X.colptr(2); 00071 const eT a13 = X_col2[0]; 00072 const eT a23 = X_col2[1]; 00073 const eT a33 = X_col2[2]; 00074 00075 const eT k = eT(1) / ( a11*(a33*a22 - a32*a23) - a21*(a33*a12-a32*a13) + a31*(a23*a12 - a22*a13) ); 00076 00077 00078 eT* out_col0 = out.colptr(0); 00079 out_col0[0] = (a33*a22 - a32*a23) * k; 00080 out_col0[1] = -(a33*a21 - a31*a23) * k; 00081 out_col0[2] = (a32*a21 - a31*a22) * k; 00082 00083 eT* out_col1 = out.colptr(1); 00084 out_col1[0] = -(a33*a12 - a32*a13) * k; 00085 out_col1[1] = (a33*a11 - a31*a13) * k; 00086 out_col1[2] = -(a32*a11 - a31*a12) * k; 00087 00088 eT* out_col2 = out.colptr(2); 00089 out_col2[0] = (a23*a12 - a22*a13) * k; 00090 out_col2[1] = -(a23*a11 - a21*a13) * k; 00091 out_col2[2] = (a22*a11 - a21*a12) * k; 00092 }; 00093 break; 00094 00095 case 4: 00096 { 00097 out.set_size(4,4); 00098 00099 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); 00100 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); 00101 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); 00102 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); 00103 00104 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); 00105 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); 00106 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); 00107 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); 00108 00109 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); 00110 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); 00111 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); 00112 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); 00113 00114 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); 00115 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); 00116 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); 00117 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); 00118 00119 out /= det(X); 00120 }; 00121 break; 00122 00123 default: 00124 { 00125 #if defined(ARMA_USE_ATLAS) 00126 { 00127 out = X; 00128 podarray<int> ipiv(out.n_rows); 00129 00130 int info = atlas::clapack_getrf(atlas::CblasColMajor, out.n_rows, out.n_cols, out.memptr(), out.n_rows, ipiv.memptr()); 00131 00132 if(info == 0) 00133 { 00134 info = atlas::clapack_getri(atlas::CblasColMajor, out.n_rows, out.memptr(), out.n_rows, ipiv.memptr()); 00135 } 00136 00137 arma_check( (info > 0), "auxlib::inv_noalias(): matrix appears to be singular" ); 00138 } 00139 #elif defined(ARMA_USE_LAPACK) 00140 { 00141 out = X; 00142 00143 int n_rows = out.n_rows; 00144 int n_cols = out.n_cols; 00145 int info = 0; 00146 00147 podarray<int> ipiv(out.n_rows); 00148 00149 // 84 was empirically found -- it is the maximum value suggested by LAPACK (as provided by ATLAS v3.6) 00150 // based on tests with various matrix types on 32-bit and 64-bit machines 00151 // 00152 // the "work" array is deliberately long so that a secondary (time-consuming) 00153 // memory allocation is avoided, if possible 00154 00155 int work_len = (std::max)(1, n_rows*84); 00156 podarray<eT> work(work_len); 00157 00158 lapack::getrf_(&n_rows, &n_cols, out.memptr(), &n_rows, ipiv.memptr(), &info); 00159 00160 if(info == 0) 00161 { 00162 // query for optimum size of work_len 00163 00164 int work_len_tmp = -1; 00165 lapack::getri_(&n_rows, out.memptr(), &n_rows, ipiv.memptr(), work.memptr(), &work_len_tmp, &info); 00166 00167 if(info == 0) 00168 { 00169 int proposed_work_len = static_cast<int>(auxlib::tmp_real(work[0])); 00170 00171 // if necessary, allocate more memory 00172 if(work_len < proposed_work_len) 00173 { 00174 work_len = proposed_work_len; 00175 work.set_size(work_len); 00176 } 00177 } 00178 00179 lapack::getri_(&n_rows, out.memptr(), &n_rows, ipiv.memptr(), work.memptr(), &work_len, &info); 00180 } 00181 00182 arma_check( (info > 0), "auxlib::inv_noalias(): matrix appears to be singular" ); 00183 } 00184 #else 00185 { 00186 arma_stop("auxlib::inv_noalias(): need ATLAS or LAPACK library"); 00187 } 00188 #endif 00189 }; 00190 } 00191 }
void auxlib::inv_inplace | ( | Mat< eT > & | X | ) | [inline, static, inherited] |
immediate inplace matrix inverse
Definition at line 199 of file auxlib_meat.hpp.
References arma_check(), arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), atlas::clapack_getri(), Mat< eT >::colptr(), det(), lapack::getrf_(), lapack::getri_(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, podarray< T1 >::set_size(), and tmp_real().
Referenced by op_inv::apply().
00200 { 00201 arma_extra_debug_sigprint(); 00202 00203 // for more info, see: 00204 // http://www.dr-lex.34sp.com/random/matrix_inv.html 00205 // http://www.cvl.iis.u-tokyo.ac.jp/~miyazaki/tech/teche23.html 00206 // http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm 00207 // http://www.geometrictools.com//LibFoundation/Mathematics/Wm4Matrix4.inl 00208 00209 switch(X.n_rows) 00210 { 00211 case 1: 00212 { 00213 X[0] = eT(1) / X[0]; 00214 }; 00215 break; 00216 00217 case 2: 00218 { 00219 const eT a = X.at(0,0); 00220 const eT b = X.at(0,1); 00221 const eT c = X.at(1,0); 00222 const eT d = X.at(1,1); 00223 00224 const eT k = eT(1) / (a*d - b*c); 00225 00226 X.at(0,0) = d*k; 00227 X.at(0,1) = -b*k; 00228 X.at(1,0) = -c*k; 00229 X.at(1,1) = a*k; 00230 }; 00231 break; 00232 00233 case 3: 00234 { 00235 eT* X_col0 = X.colptr(0); 00236 eT* X_col1 = X.colptr(1); 00237 eT* X_col2 = X.colptr(2); 00238 00239 const eT a11 = X_col0[0]; 00240 const eT a21 = X_col0[1]; 00241 const eT a31 = X_col0[2]; 00242 00243 const eT a12 = X_col1[0]; 00244 const eT a22 = X_col1[1]; 00245 const eT a32 = X_col1[2]; 00246 00247 const eT a13 = X_col2[0]; 00248 const eT a23 = X_col2[1]; 00249 const eT a33 = X_col2[2]; 00250 00251 const eT k = eT(1) / ( a11*(a33*a22 - a32*a23) - a21*(a33*a12-a32*a13) + a31*(a23*a12 - a22*a13) ); 00252 00253 X_col0[0] = (a33*a22 - a32*a23) * k; 00254 X_col0[1] = -(a33*a21 - a31*a23) * k; 00255 X_col0[2] = (a32*a21 - a31*a22) * k; 00256 00257 X_col1[0] = -(a33*a12 - a32*a13) * k; 00258 X_col1[1] = (a33*a11 - a31*a13) * k; 00259 X_col1[2] = -(a32*a11 - a31*a12) * k; 00260 00261 X_col2[0] = (a23*a12 - a22*a13) * k; 00262 X_col2[1] = -(a23*a11 - a21*a13) * k; 00263 X_col2[2] = (a22*a11 - a21*a12) * k; 00264 }; 00265 break; 00266 00267 case 4: 00268 { 00269 const Mat<eT> A(X); 00270 00271 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); 00272 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); 00273 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); 00274 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); 00275 00276 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); 00277 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); 00278 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); 00279 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); 00280 00281 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); 00282 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); 00283 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); 00284 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); 00285 00286 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); 00287 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); 00288 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); 00289 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); 00290 00291 X /= det(A); 00292 }; 00293 break; 00294 00295 default: 00296 { 00297 #if defined(ARMA_USE_ATLAS) 00298 { 00299 Mat<eT>& out = X; 00300 podarray<int> ipiv(out.n_rows); 00301 00302 int info = atlas::clapack_getrf(atlas::CblasColMajor, out.n_rows, out.n_cols, out.memptr(), out.n_rows, ipiv.memptr()); 00303 00304 if(info == 0) 00305 { 00306 info = atlas::clapack_getri(atlas::CblasColMajor, out.n_rows, out.memptr(), out.n_rows, ipiv.memptr()); 00307 } 00308 00309 arma_check( (info > 0), "auxlib::inv_inplace(): matrix appears to be singular" ); 00310 } 00311 #elif defined(ARMA_USE_LAPACK) 00312 { 00313 Mat<eT>& out = X; 00314 00315 int n_rows = out.n_rows; 00316 int n_cols = out.n_cols; 00317 int info = 0; 00318 00319 podarray<int> ipiv(out.n_rows); 00320 00321 // 84 was empirically found -- it is the maximum value suggested by LAPACK (as provided by ATLAS v3.6) 00322 // based on tests with various matrix types on 32-bit and 64-bit machines 00323 // 00324 // the "work" array is deliberately long so that a secondary (time-consuming) 00325 // memory allocation is avoided, if possible 00326 00327 int work_len = (std::max)(1, n_rows*84); 00328 podarray<eT> work(work_len); 00329 00330 lapack::getrf_(&n_rows, &n_cols, out.memptr(), &n_rows, ipiv.memptr(), &info); 00331 00332 if(info == 0) 00333 { 00334 // query for optimum size of work_len 00335 00336 int work_len_tmp = -1; 00337 lapack::getri_(&n_rows, out.memptr(), &n_rows, ipiv.memptr(), work.memptr(), &work_len_tmp, &info); 00338 00339 if(info == 0) 00340 { 00341 int proposed_work_len = static_cast<int>(auxlib::tmp_real(work[0])); 00342 00343 // if necessary, allocate more memory 00344 if(work_len < proposed_work_len) 00345 { 00346 work_len = proposed_work_len; 00347 work.set_size(work_len); 00348 } 00349 } 00350 00351 lapack::getri_(&n_rows, out.memptr(), &n_rows, ipiv.memptr(), work.memptr(), &work_len, &info); 00352 } 00353 00354 arma_check( (info > 0), "auxlib::inv_noalias(): matrix appears to be singular" ); 00355 } 00356 #else 00357 { 00358 arma_stop("auxlib::inv_inplace(): need ATLAS or LAPACK"); 00359 } 00360 #endif 00361 } 00362 00363 } 00364 00365 }
eT auxlib::det | ( | const Mat< eT > & | X | ) | [inline, static, inherited] |
immediate determinant of a matrix using ATLAS or LAPACK
Definition at line 372 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), Mat< eT >::colptr(), lapack::getrf_(), podarray< T1 >::mem, podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, and Mat< eT >::n_rows.
Referenced by det(), inv_inplace(), and inv_noalias().
00373 { 00374 arma_extra_debug_sigprint(); 00375 00376 switch(X.n_rows) 00377 { 00378 case 0: 00379 return 0.0; 00380 00381 case 1: 00382 return X[0]; 00383 00384 case 2: 00385 return (X.at(0,0)*X.at(1,1) - X.at(0,1)*X.at(1,0)); 00386 00387 case 3: 00388 { 00389 const eT* a_col0 = X.colptr(0); 00390 const eT a11 = a_col0[0]; 00391 const eT a21 = a_col0[1]; 00392 const eT a31 = a_col0[2]; 00393 00394 const eT* a_col1 = X.colptr(1); 00395 const eT a12 = a_col1[0]; 00396 const eT a22 = a_col1[1]; 00397 const eT a32 = a_col1[2]; 00398 00399 const eT* a_col2 = X.colptr(2); 00400 const eT a13 = a_col2[0]; 00401 const eT a23 = a_col2[1]; 00402 const eT a33 = a_col2[2]; 00403 00404 return ( a11*(a33*a22 - a32*a23) - a21*(a33*a12-a32*a13) + a31*(a23*a12 - a22*a13) ); 00405 00406 // const double tmp1 = X.at(0,0) * X.at(1,1) * X.at(2,2); 00407 // const double tmp2 = X.at(0,1) * X.at(1,2) * X.at(2,0); 00408 // const double tmp3 = X.at(0,2) * X.at(1,0) * X.at(2,1); 00409 // const double tmp4 = X.at(2,0) * X.at(1,1) * X.at(0,2); 00410 // const double tmp5 = X.at(2,1) * X.at(1,2) * X.at(0,0); 00411 // const double tmp6 = X.at(2,2) * X.at(1,0) * X.at(0,1); 00412 // return (tmp1+tmp2+tmp3) - (tmp4+tmp5+tmp6); 00413 } 00414 00415 case 4: 00416 { 00417 const eT val = \ 00418 X.at(0,3) * X.at(1,2) * X.at(2,1) * X.at(3,0) \ 00419 - X.at(0,2) * X.at(1,3) * X.at(2,1) * X.at(3,0) \ 00420 - X.at(0,3) * X.at(1,1) * X.at(2,2) * X.at(3,0) \ 00421 + X.at(0,1) * X.at(1,3) * X.at(2,2) * X.at(3,0) \ 00422 + X.at(0,2) * X.at(1,1) * X.at(2,3) * X.at(3,0) \ 00423 - X.at(0,1) * X.at(1,2) * X.at(2,3) * X.at(3,0) \ 00424 - X.at(0,3) * X.at(1,2) * X.at(2,0) * X.at(3,1) \ 00425 + X.at(0,2) * X.at(1,3) * X.at(2,0) * X.at(3,1) \ 00426 + X.at(0,3) * X.at(1,0) * X.at(2,2) * X.at(3,1) \ 00427 - X.at(0,0) * X.at(1,3) * X.at(2,2) * X.at(3,1) \ 00428 - X.at(0,2) * X.at(1,0) * X.at(2,3) * X.at(3,1) \ 00429 + X.at(0,0) * X.at(1,2) * X.at(2,3) * X.at(3,1) \ 00430 + X.at(0,3) * X.at(1,1) * X.at(2,0) * X.at(3,2) \ 00431 - X.at(0,1) * X.at(1,3) * X.at(2,0) * X.at(3,2) \ 00432 - X.at(0,3) * X.at(1,0) * X.at(2,1) * X.at(3,2) \ 00433 + X.at(0,0) * X.at(1,3) * X.at(2,1) * X.at(3,2) \ 00434 + X.at(0,1) * X.at(1,0) * X.at(2,3) * X.at(3,2) \ 00435 - X.at(0,0) * X.at(1,1) * X.at(2,3) * X.at(3,2) \ 00436 - X.at(0,2) * X.at(1,1) * X.at(2,0) * X.at(3,3) \ 00437 + X.at(0,1) * X.at(1,2) * X.at(2,0) * X.at(3,3) \ 00438 + X.at(0,2) * X.at(1,0) * X.at(2,1) * X.at(3,3) \ 00439 - X.at(0,0) * X.at(1,2) * X.at(2,1) * X.at(3,3) \ 00440 - X.at(0,1) * X.at(1,0) * X.at(2,2) * X.at(3,3) \ 00441 + X.at(0,0) * X.at(1,1) * X.at(2,2) * X.at(3,3) \ 00442 ; 00443 00444 return val; 00445 } 00446 00447 default: 00448 { 00449 #if defined(ARMA_USE_ATLAS) 00450 { 00451 Mat<eT> tmp = X; 00452 podarray<int> ipiv(tmp.n_rows); 00453 00454 atlas::clapack_getrf(atlas::CblasColMajor, tmp.n_rows, tmp.n_cols, tmp.memptr(), tmp.n_rows, ipiv.memptr()); 00455 00456 // on output tmp appears to be L+U_alt, where U_alt is U with the main diagonal set to zero 00457 eT val = tmp.at(0,0); 00458 for(u32 i=1; i < tmp.n_rows; ++i) 00459 { 00460 val *= tmp.at(i,i); 00461 } 00462 00463 int sign = +1; 00464 for(u32 i=0; i < tmp.n_rows; ++i) 00465 { 00466 if( int(i) != ipiv.mem[i] ) // NOTE: no adjustment required, as the clapack version of getrf() assumes counting from 0 00467 { 00468 sign *= -1; 00469 } 00470 } 00471 00472 return val * eT(sign); 00473 } 00474 #elif defined(ARMA_USE_LAPACK) 00475 { 00476 Mat<eT> tmp = X; 00477 podarray<int> ipiv(tmp.n_rows); 00478 00479 int info = 0; 00480 int n_rows = int(tmp.n_rows); 00481 int n_cols = int(tmp.n_cols); 00482 00483 lapack::getrf_(&n_rows, &n_cols, tmp.memptr(), &n_rows, ipiv.memptr(), &info); 00484 00485 // on output tmp appears to be L+U_alt, where U_alt is U with the main diagonal set to zero 00486 eT val = tmp.at(0,0); 00487 for(u32 i=1; i < tmp.n_rows; ++i) 00488 { 00489 val *= tmp.at(i,i); 00490 } 00491 00492 int sign = +1; 00493 for(u32 i=0; i < tmp.n_rows; ++i) 00494 { 00495 if( int(i) != (ipiv.mem[i] - 1) ) // NOTE: adjustment of -1 is required as Fortran counts from 1 00496 { 00497 sign *= -1; 00498 } 00499 } 00500 00501 return val * eT(sign); 00502 } 00503 #else 00504 { 00505 arma_stop("auxlib::det(): need ATLAS or LAPACK library"); 00506 return eT(0); 00507 } 00508 #endif 00509 } 00510 } 00511 }
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 519 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), atlas::clapack_getrf(), lapack::getrf_(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Mat< eT >::set_size(), and podarray< T1 >::set_size().
00520 { 00521 arma_extra_debug_sigprint(); 00522 00523 U = X; 00524 00525 #if defined(ARMA_USE_ATLAS) || defined(ARMA_USE_LAPACK) 00526 { 00527 00528 #if defined(ARMA_USE_ATLAS) 00529 { 00530 ipiv.set_size(U.n_rows); 00531 00532 //int info = 00533 atlas::clapack_getrf(atlas::CblasColMajor, U.n_rows, U.n_cols, U.memptr(), U.n_rows, ipiv.memptr()); 00534 } 00535 #elif defined(ARMA_USE_LAPACK) 00536 { 00537 ipiv.set_size(U.n_rows); 00538 int info = 0; 00539 00540 int n_rows = U.n_rows; 00541 int n_cols = U.n_cols; 00542 00543 lapack::getrf_(&n_rows, &n_cols, U.memptr(), &n_rows, ipiv.memptr(), &info); 00544 00545 // take into account that Fortran counts from 1 00546 for(u32 i=0; i<U.n_rows; ++i) 00547 { 00548 ipiv[i] -= 1; 00549 } 00550 00551 } 00552 #endif 00553 00554 00555 L.set_size(U.n_rows, U.n_rows); 00556 00557 for(u32 col=0; col<L.n_cols; ++col) 00558 { 00559 00560 for(u32 row=0; row<col; ++row) 00561 { 00562 L.at(row,col) = eT(0); 00563 } 00564 00565 L.at(col,col) = eT(1); 00566 00567 for(u32 row=col+1; row<L.n_rows; ++row) 00568 { 00569 L.at(row,col) = U.at(row,col); 00570 U.at(row,col) = eT(0); 00571 } 00572 00573 } 00574 } 00575 #else 00576 { 00577 arma_stop("auxlib::lu(): need ATLAS or LAPACK library"); 00578 } 00579 #endif 00580 00581 }
void auxlib::lu | ( | Mat< eT > & | L, | |
Mat< eT > & | U, | |||
Mat< eT > & | P, | |||
const Mat< eT > & | X | |||
) | [inline, static, inherited] |
Definition at line 588 of file auxlib_meat.hpp.
References lu(), podarray< T1 >::n_elem, and Mat< eT >::swap_rows().
00589 { 00590 arma_extra_debug_sigprint(); 00591 00592 podarray<int> ipiv; 00593 auxlib::lu(L, U, ipiv, X); 00594 00595 const u32 n = ipiv.n_elem; 00596 00597 Mat<u32> P_tmp(n,n); 00598 Mat<u32> ident = eye< Mat<u32> >(n,n); 00599 00600 for(u32 i=n; i>0; --i) 00601 { 00602 const u32 j = i-1; 00603 const u32 k = ipiv[j]; 00604 00605 ident.swap_rows(j,k); 00606 00607 if(i == n) 00608 { 00609 P_tmp = ident; 00610 } 00611 else 00612 { 00613 P_tmp *= ident; 00614 } 00615 00616 ident.swap_rows(j,k); 00617 } 00618 00619 P = conv_to< Mat<eT> >::from(P_tmp); 00620 }
void auxlib::lu | ( | Mat< eT > & | L, | |
Mat< eT > & | U, | |||
const Mat< eT > & | X | |||
) | [inline, static, inherited] |
Definition at line 627 of file auxlib_meat.hpp.
References lu().
00628 { 00629 arma_extra_debug_sigprint(); 00630 00631 podarray<int> ipiv; 00632 auxlib::lu(L, U, ipiv, X); 00633 }
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 641 of file auxlib_meat.hpp.
References arma_stop(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Col< eT >::set_size(), and lapack::syev_().
Referenced by eig_sym().
00642 { 00643 arma_extra_debug_sigprint(); 00644 00645 #if defined(ARMA_USE_LAPACK) 00646 { 00647 const unwrap_check<Mat<eT> > tmp(A_orig, eigval); 00648 const Mat<eT>& A = tmp.M; 00649 00650 arma_debug_check( (A.n_rows != A.n_cols), "auxlib::eig_sym(): given matrix is not square"); 00651 00652 // rudimentary "better-than-nothing" test for symmetry 00653 //arma_debug_check( (A.at(A.n_rows-1, 0) != A.at(0, A.n_cols-1)), "auxlib::eig(): given matrix is not symmetric" ); 00654 00655 char jobz = 'N'; 00656 char uplo = 'U'; 00657 00658 int n_rows = A.n_rows; 00659 int lwork = (std::max)(1,3*n_rows-1); 00660 00661 eigval.set_size(n_rows); 00662 podarray<eT> work(lwork); 00663 00664 Mat<eT> A_copy = A; 00665 int info; 00666 00667 arma_extra_debug_print("lapack::syev_()"); 00668 lapack::syev_(&jobz, &uplo, &n_rows, A_copy.memptr(), &n_rows, eigval.memptr(), work.memptr(), &lwork, &info); 00669 } 00670 #else 00671 { 00672 arma_stop("auxlib::eig_sym(): need LAPACK library"); 00673 } 00674 #endif 00675 }
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 683 of file auxlib_meat.hpp.
References arma_stop(), lapack::heev_(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), and Col< eT >::set_size().
00684 { 00685 arma_extra_debug_sigprint(); 00686 00687 typedef typename std::complex<T> eT; 00688 00689 #if defined(ARMA_USE_LAPACK) 00690 { 00691 arma_debug_check( (A.n_rows != A.n_cols), "auxlib::eig_sym(): given matrix is not hermitian"); 00692 00693 char jobz = 'N'; 00694 char uplo = 'U'; 00695 00696 int n_rows = A.n_rows; 00697 int lda = A.n_rows; 00698 int lwork = (std::max)(1, 2*n_rows - 1); // TODO: automatically find best size of lwork 00699 00700 eigval.set_size(n_rows); 00701 00702 podarray<eT> work(lwork); 00703 podarray<T> rwork( (std::max)(1, 3*n_rows - 2) ); 00704 00705 Mat<eT> A_copy = A; 00706 int info; 00707 00708 arma_extra_debug_print("lapack::heev_()"); 00709 lapack::heev_(&jobz, &uplo, &n_rows, A_copy.memptr(), &lda, eigval.memptr(), work.memptr(), &lwork, rwork.memptr(), &info); 00710 } 00711 #else 00712 { 00713 arma_stop("auxlib::eig_sym(): need LAPACK library"); 00714 } 00715 #endif 00716 }
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 724 of file auxlib_meat.hpp.
References arma_stop(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Col< eT >::set_size(), and lapack::syev_().
00725 { 00726 arma_extra_debug_sigprint(); 00727 00728 // TODO: check for aliasing 00729 00730 #if defined(ARMA_USE_LAPACK) 00731 { 00732 const unwrap_check< Mat<eT> > tmp1(A_orig, eigval); 00733 const Mat<eT>& A_tmp = tmp1.M; 00734 00735 const unwrap_check< Mat<eT> > tmp2(A_tmp, eigvec); 00736 const Mat<eT>& A = tmp2.M; 00737 00738 arma_debug_check( (A.n_rows != A.n_cols), "auxlib::eig_sym(): given matrix is not square" ); 00739 00740 // rudimentary "better-than-nothing" test for symmetry 00741 //arma_debug_check( (A.at(A.n_rows-1, 0) != A.at(0, A.n_cols-1)), "auxlib::eig(): given matrix is not symmetric" ); 00742 00743 00744 char jobz = 'V'; 00745 char uplo = 'U'; 00746 00747 int n_rows = A.n_rows; 00748 int lwork = (std::max)(1, 3*n_rows-1); 00749 00750 eigval.set_size(n_rows); 00751 podarray<eT> work(lwork); 00752 00753 eigvec = A; 00754 int info; 00755 00756 arma_extra_debug_print("lapack::syev_()"); 00757 lapack::syev_(&jobz, &uplo, &n_rows, eigvec.memptr(), &n_rows, eigval.memptr(), work.memptr(), &lwork, &info); 00758 } 00759 #else 00760 { 00761 arma_stop("auxlib::eig_sym(): need LAPACK library"); 00762 } 00763 #endif 00764 00765 }
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 773 of file auxlib_meat.hpp.
References arma_stop(), lapack::heev_(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, and Col< eT >::set_size().
00774 { 00775 arma_extra_debug_sigprint(); 00776 00777 typedef typename std::complex<T> eT; 00778 00779 #if defined(ARMA_USE_LAPACK) 00780 { 00781 const unwrap_check< Mat<eT> > tmp(A_orig, eigvec); 00782 const Mat<eT>& A = tmp.M; 00783 00784 arma_debug_check( (A.n_rows != A.n_cols), "auxlib::eig_sym(): given matrix is not hermitian" ); 00785 00786 char jobz = 'V'; 00787 char uplo = 'U'; 00788 00789 int n_rows = A.n_rows; 00790 int lda = A.n_rows; 00791 int lwork = (std::max)(1, 2*n_rows - 1); // TODO: automatically find best size of lwork 00792 00793 eigval.set_size(n_rows); 00794 00795 podarray<eT> work(lwork); 00796 podarray<T> rwork( (std::max)(1, 3*n_rows - 2) ); 00797 00798 eigvec = A; 00799 int info; 00800 00801 arma_extra_debug_print("lapack::heev_()"); 00802 lapack::heev_(&jobz, &uplo, &n_rows, eigvec.memptr(), &lda, eigval.memptr(), work.memptr(), &lwork, rwork.memptr(), &info); 00803 } 00804 #else 00805 { 00806 arma_stop("auxlib::eig_sym(): need LAPACK library"); 00807 } 00808 #endif 00809 00810 }
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 821 of file auxlib_meat.hpp.
References arma_stop(), lapack::geev_(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, and Mat< eT >::set_size().
00828 { 00829 arma_extra_debug_sigprint(); 00830 00831 // TODO: check for aliasing 00832 00833 #if defined(ARMA_USE_LAPACK) 00834 { 00835 arma_debug_check( (A.n_rows != A.n_cols), "auxlib::eig_gen(): given matrix is not square" ); 00836 00837 char jobvl; 00838 char jobvr; 00839 00840 switch(side) 00841 { 00842 case 'l': // left 00843 jobvl = 'V'; 00844 jobvr = 'N'; 00845 break; 00846 00847 case 'r': // right 00848 jobvl = 'N'; 00849 jobvr = 'V'; 00850 break; 00851 00852 case 'b': // both 00853 jobvl = 'V'; 00854 jobvr = 'V'; 00855 break; 00856 00857 case 'n': // neither 00858 jobvl = 'N'; 00859 jobvr = 'N'; 00860 break; 00861 00862 default: 00863 arma_stop("auxlib::eig_gen(): parameter 'side' is invalid"); 00864 } 00865 00866 00867 int n_rows = A.n_rows; 00868 int lda = A.n_rows; 00869 int lwork = (std::max)(1, 4*n_rows); // TODO: automatically find best size of lwork 00870 00871 eigval.set_size(n_rows); 00872 l_eigvec.set_size(n_rows, n_rows); 00873 r_eigvec.set_size(n_rows, n_rows); 00874 00875 podarray<T> work(lwork); 00876 podarray<T> rwork( (std::max)(1, 3*n_rows) ); 00877 00878 podarray<T> wr(n_rows); 00879 podarray<T> wi(n_rows); 00880 00881 Mat<T> A_copy = A; 00882 int info; 00883 00884 arma_extra_debug_print("lapack::cx_geev_()"); 00885 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); 00886 00887 00888 eigval.set_size(n_rows); 00889 for(u32 i=0; i<u32(n_rows); ++i) 00890 { 00891 eigval[i] = std::complex<T>(wr[i], wi[i]); 00892 } 00893 00894 } 00895 #else 00896 { 00897 arma_stop("auxlib::eig_gen(): need LAPACK library"); 00898 } 00899 #endif 00900 00901 }
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 914 of file auxlib_meat.hpp.
References arma_stop(), lapack::cx_geev_(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, and Mat< eT >::set_size().
00921 { 00922 arma_extra_debug_sigprint(); 00923 00924 // TODO: check for aliasing 00925 00926 typedef typename std::complex<T> eT; 00927 00928 #if defined(ARMA_USE_LAPACK) 00929 { 00930 arma_debug_check( (A.n_rows != A.n_cols), "auxlib::eig_gen(): given matrix is not square" ); 00931 00932 char jobvl; 00933 char jobvr; 00934 00935 switch(side) 00936 { 00937 case 'l': // left 00938 jobvl = 'V'; 00939 jobvr = 'N'; 00940 break; 00941 00942 case 'r': // right 00943 jobvl = 'N'; 00944 jobvr = 'V'; 00945 break; 00946 00947 case 'b': // both 00948 jobvl = 'V'; 00949 jobvr = 'V'; 00950 break; 00951 00952 case 'n': // neither 00953 jobvl = 'N'; 00954 jobvr = 'N'; 00955 break; 00956 00957 default: 00958 arma_stop("auxlib::eig_gen(): parameter 'side' is invalid"); 00959 } 00960 00961 00962 int n_rows = A.n_rows; 00963 int lda = A.n_rows; 00964 int lwork = (std::max)(1, 4*n_rows); // TODO: automatically find best size of lwork 00965 00966 eigval.set_size(n_rows); 00967 l_eigvec.set_size(n_rows, n_rows); 00968 r_eigvec.set_size(n_rows, n_rows); 00969 00970 podarray<eT> work(lwork); 00971 podarray<T> rwork( (std::max)(1, 3*n_rows) ); // was 2,3 00972 00973 Mat<eT> A_copy = A; 00974 int info; 00975 00976 arma_extra_debug_print("lapack::cx_geev_()"); 00977 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); 00978 } 00979 #else 00980 { 00981 arma_stop("auxlib::eig_gen(): need LAPACK library"); 00982 } 00983 #endif 00984 00985 }
bool auxlib::chol | ( | Mat< eT > & | out, | |
const Mat< eT > & | X | |||
) | [inline, static, inherited] |
Definition at line 992 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::colptr(), Mat< eT >::memptr(), Mat< eT >::n_rows, and lapack::potrf_().
Referenced by chol().
00993 { 00994 arma_extra_debug_sigprint(); 00995 00996 #if defined(ARMA_USE_LAPACK) 00997 { 00998 char uplo = 'U'; 00999 int n = X.n_rows; 01000 int lda = X.n_rows; 01001 int info; 01002 01003 out = X; 01004 lapack::potrf_(&uplo, &n, out.memptr(), &lda, &info); 01005 01006 for(u32 col=0; col<X.n_rows; ++col) 01007 { 01008 eT* colptr = out.colptr(col); 01009 for(u32 row=col+1; row<X.n_rows; ++row) 01010 { 01011 colptr[row] = eT(0); 01012 } 01013 } 01014 01015 return (info == 0); 01016 } 01017 #else 01018 { 01019 arma_stop("auxlib::chol(): need LAPACK library"); 01020 return false; 01021 } 01022 #endif 01023 }
bool auxlib::qr | ( | Mat< eT > & | Q, | |
Mat< eT > & | R, | |||
const Mat< eT > & | X | |||
) | [inline, static, inherited] |
Definition at line 1030 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::at(), lapack::geqrf_(), max(), Mat< eT >::mem, podarray< T1 >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_elem, Mat< eT >::n_rows, lapack::orgqr_(), Mat< eT >::set_size(), podarray< T1 >::set_size(), tmp_real(), and lapack::ungqr_().
Referenced by qr().
01031 { 01032 arma_extra_debug_sigprint(); 01033 01034 #if defined(ARMA_USE_LAPACK) 01035 { 01036 int m = static_cast<int>(X.n_rows); 01037 int n = static_cast<int>(X.n_cols); 01038 int work_len = (std::max)(1,n); 01039 int work_len_tmp; 01040 int k = (std::min)(m,n); 01041 int info; 01042 01043 podarray<eT> tau(k); 01044 podarray<eT> work(work_len); 01045 01046 R = X; 01047 01048 // query for the optimum value of work_len 01049 work_len_tmp = -1; 01050 lapack::geqrf_(&m, &n, R.memptr(), &m, tau.memptr(), work.memptr(), &work_len_tmp, &info); 01051 01052 if(info == 0) 01053 { 01054 work_len = static_cast<int>(auxlib::tmp_real(work[0])); 01055 work.set_size(work_len); 01056 } 01057 01058 lapack::geqrf_(&m, &n, R.memptr(), &m, tau.memptr(), work.memptr(), &work_len, &info); 01059 01060 Q.set_size(X.n_rows, X.n_rows); 01061 01062 eT* Q_mem = Q.memptr(); 01063 const eT* R_mem = R.mem; 01064 01065 const u32 n_elem_copy = (std::min)(Q.n_elem, R.n_elem); 01066 for(u32 i=0; i < n_elem_copy; ++i) 01067 { 01068 Q_mem[i] = R_mem[i]; 01069 } 01070 01071 01072 // construct R 01073 for(u32 row=0; row < R.n_rows; ++row) 01074 { 01075 const u32 n_elem_tmp = (std::min)(row, R.n_cols); 01076 for(u32 col=0; col < n_elem_tmp; ++col) 01077 { 01078 R.at(row,col) = eT(0); 01079 } 01080 } 01081 01082 01083 if( (is_float<eT>::value == true) || (is_double<eT>::value == true) ) 01084 { 01085 // query for the optimum value of work_len 01086 work_len_tmp = -1; 01087 lapack::orgqr_(&m, &m, &k, Q.memptr(), &m, tau.memptr(), work.memptr(), &work_len_tmp, &info); 01088 01089 if(info == 0) 01090 { 01091 work_len = static_cast<int>(auxlib::tmp_real(work[0])); 01092 work.set_size(work_len); 01093 } 01094 01095 lapack::orgqr_(&m, &m, &k, Q.memptr(), &m, tau.memptr(), work.memptr(), &work_len, &info); 01096 } 01097 else 01098 if( (is_supported_complex_float<eT>::value == true) || (is_supported_complex_double<eT>::value == true) ) 01099 { 01100 // query for the optimum value of work_len 01101 work_len_tmp = -1; 01102 lapack::ungqr_(&m, &m, &k, Q.memptr(), &m, tau.memptr(), work.memptr(), &work_len_tmp, &info); 01103 01104 if(info == 0) 01105 { 01106 work_len = static_cast<int>(auxlib::tmp_real(work[0])); 01107 work.set_size(work_len); 01108 } 01109 01110 lapack::ungqr_(&m, &m, &k, Q.memptr(), &m, tau.memptr(), work.memptr(), &work_len, &info); 01111 } 01112 01113 return (info == 0); 01114 } 01115 #else 01116 { 01117 arma_stop("auxlib::qr(): need LAPACK library"); 01118 return false; 01119 } 01120 #endif 01121 }
bool auxlib::svd | ( | Col< eT > & | S, | |
const Mat< eT > & | X | |||
) | [inline, static, inherited] |
Definition at line 1128 of file auxlib_meat.hpp.
References arma_stop(), podarray< T1 >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_rows, podarray< T1 >::set_size(), and Col< eT >::set_size().
Referenced by rank(), and svd().
01129 { 01130 arma_extra_debug_sigprint(); 01131 01132 #if defined(ARMA_USE_LAPACK) 01133 { 01134 Mat<eT> A = X; 01135 01136 char jobu = 'N'; 01137 char jobvt = 'N'; 01138 01139 int m = A.n_rows; 01140 int n = A.n_cols; 01141 int lda = A.n_rows; 01142 int ldu = A.n_rows; 01143 int ldvt = A.n_cols; 01144 int lwork = 2; 01145 int info; 01146 01147 Mat<eT> U(1,1); 01148 Mat<eT> V(1,1); 01149 01150 S.set_size( (std::min)(m, n) ); 01151 01152 podarray<eT> work(lwork); 01153 01154 01155 // let gesvd_() calculate the optimum size of the workspace 01156 int lwork_tmp = -1; 01157 01158 lapack::gesvd_<eT> 01159 ( 01160 &jobu, &jobvt, 01161 &m,&n, 01162 A.memptr(), &lda, 01163 S.memptr(), 01164 U.memptr(), &ldu, 01165 V.memptr(), &ldvt, 01166 work.memptr(), &lwork_tmp, 01167 &info 01168 ); 01169 01170 if(info == 0) 01171 { 01172 lwork = static_cast<int>(work[0]); 01173 work.set_size(lwork); 01174 01175 lapack::gesvd_<eT> 01176 ( 01177 &jobu, &jobvt, 01178 &m, &n, 01179 A.memptr(), &lda, 01180 S.memptr(), 01181 U.memptr(), &ldu, 01182 V.memptr(), &ldvt, 01183 work.memptr(), &lwork, 01184 &info 01185 ); 01186 01187 return (info == 0); 01188 } 01189 else 01190 { 01191 return false; 01192 } 01193 } 01194 #else 01195 { 01196 arma_stop("auxlib::svd(): need LAPACK library"); 01197 return false; 01198 } 01199 #endif 01200 }
bool auxlib::svd | ( | Col< T > & | S, | |
const Mat< std::complex< T > > & | X | |||
) | [inline, static, inherited] |
Definition at line 1207 of file auxlib_meat.hpp.
References arma_stop(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_rows, real(), podarray< T1 >::set_size(), and Col< eT >::set_size().
01208 { 01209 arma_extra_debug_sigprint(); 01210 01211 typedef std::complex<T> eT; 01212 01213 #if defined(ARMA_USE_LAPACK) 01214 { 01215 Mat<eT> A = X; 01216 01217 char jobu = 'N'; 01218 char jobvt = 'N'; 01219 01220 int m = A.n_rows; 01221 int n = A.n_cols; 01222 int lda = A.n_rows; 01223 int ldu = A.n_rows; 01224 int ldvt = A.n_cols; 01225 int lwork = 2 * (std::min)(m,n) + (std::max)(m,n); 01226 int info; 01227 01228 Mat<eT> U(1,1); 01229 Mat<eT> V(1,1); 01230 01231 S.set_size( (std::min)(m,n) ); 01232 01233 podarray<eT> work(lwork); 01234 podarray<T> rwork( 5*(std::min)(m,n) ); 01235 01236 // let gesvd_() calculate the optimum size of the workspace 01237 int lwork_tmp = -1; 01238 01239 lapack::cx_gesvd_<T> 01240 ( 01241 &jobu, &jobvt, 01242 &m, &n, 01243 A.memptr(), &lda, 01244 S.memptr(), 01245 U.memptr(), &ldu, 01246 V.memptr(), &ldvt, 01247 work.memptr(), &lwork_tmp, 01248 rwork.memptr(), 01249 &info 01250 ); 01251 01252 if(info == 0) 01253 { 01254 int proposed_lwork = static_cast<int>(real(work[0])); 01255 if(proposed_lwork > lwork) 01256 { 01257 lwork = proposed_lwork; 01258 work.set_size(lwork); 01259 } 01260 01261 lapack::cx_gesvd_<T> 01262 ( 01263 &jobu, &jobvt, 01264 &m, &n, 01265 A.memptr(), &lda, 01266 S.memptr(), 01267 U.memptr(), &ldu, 01268 V.memptr(), &ldvt, 01269 work.memptr(), &lwork, 01270 rwork.memptr(), 01271 &info 01272 ); 01273 01274 return (info == 0); 01275 } 01276 else 01277 { 01278 return false; 01279 } 01280 } 01281 #else 01282 { 01283 arma_stop("auxlib::svd(): need LAPACK library"); 01284 return false; 01285 } 01286 #endif 01287 }
bool auxlib::svd | ( | Mat< eT > & | U, | |
Col< eT > & | S, | |||
Mat< eT > & | V, | |||
const Mat< eT > & | X | |||
) | [inline, static, inherited] |
Definition at line 1294 of file auxlib_meat.hpp.
References op_trans::apply(), arma_stop(), podarray< T1 >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_rows, podarray< T1 >::set_size(), Col< eT >::set_size(), and Mat< eT >::set_size().
01295 { 01296 arma_extra_debug_sigprint(); 01297 01298 #if defined(ARMA_USE_LAPACK) 01299 { 01300 Mat<eT> A = X; 01301 01302 char jobu = 'A'; 01303 char jobvt = 'A'; 01304 01305 int m = A.n_rows; 01306 int n = A.n_cols; 01307 int lda = A.n_rows; 01308 int ldu = A.n_rows; 01309 int ldvt = A.n_cols; 01310 int lwork = 2; 01311 int info; 01312 01313 U.set_size(m,m); 01314 V.set_size(n,n); 01315 01316 S.set_size( (std::min)(m,n) ); 01317 podarray<eT> work(lwork); 01318 01319 // let gesvd_() calculate the optimum size of the workspace 01320 int lwork_tmp = -1; 01321 01322 lapack::gesvd_<eT> 01323 ( 01324 &jobu, &jobvt, 01325 &m, &n, 01326 A.memptr(), &lda, 01327 S.memptr(), 01328 U.memptr(), &ldu, 01329 V.memptr(), &ldvt, 01330 work.memptr(), &lwork_tmp, 01331 &info 01332 ); 01333 01334 if(info == 0) 01335 { 01336 lwork = static_cast<int>(work[0]); 01337 work.set_size(lwork); 01338 01339 lapack::gesvd_<eT> 01340 ( 01341 &jobu, &jobvt, 01342 &m, &n, 01343 A.memptr(), &lda, 01344 S.memptr(), 01345 U.memptr(), &ldu, 01346 V.memptr(), &ldvt, 01347 work.memptr(), &lwork, 01348 &info 01349 ); 01350 01351 op_trans::apply(V,V); // op_trans will work out that an in-place transpose can be done 01352 01353 return (info == 0); 01354 } 01355 else 01356 { 01357 return false; 01358 } 01359 } 01360 #else 01361 { 01362 arma_stop("auxlib::svd(): need LAPACK library"); 01363 return false; 01364 } 01365 #endif 01366 }
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 1373 of file auxlib_meat.hpp.
References op_htrans::apply(), arma_stop(), conj(), podarray< T1 >::memptr(), Mat< eT >::memptr(), min(), Mat< eT >::n_cols, Mat< eT >::n_rows, real(), podarray< T1 >::set_size(), and Col< eT >::set_size().
01374 { 01375 arma_extra_debug_sigprint(); 01376 01377 typedef std::complex<T> eT; 01378 01379 #if defined(ARMA_USE_LAPACK) 01380 { 01381 Mat<eT> A = X; 01382 01383 char jobu = 'A'; 01384 char jobvt = 'A'; 01385 01386 int m = A.n_rows; 01387 int n = A.n_cols; 01388 int lda = A.n_rows; 01389 int ldu = A.n_rows; 01390 int ldvt = A.n_cols; 01391 int lwork = 2; 01392 int info; 01393 01394 U.set_size(m,m); 01395 V.set_size(n,n); 01396 01397 S.set_size( (std::min)(m,n) ); 01398 01399 podarray<eT> work(lwork); 01400 podarray<T> rwork( 5*(std::min)(m,n) ); 01401 01402 // let gesvd_() calculate the optimum size of the workspace 01403 int lwork_tmp = -1; 01404 lapack::cx_gesvd_<T> 01405 ( 01406 &jobu, &jobvt, 01407 &m, &n, 01408 A.memptr(), &lda, 01409 S.memptr(), 01410 U.memptr(), &ldu, 01411 V.memptr(), &ldvt, 01412 work.memptr(), &lwork_tmp, 01413 rwork.memptr(), 01414 &info 01415 ); 01416 01417 if(info == 0) 01418 { 01419 lwork = static_cast<int>(real(work[0])); 01420 work.set_size(lwork); 01421 01422 lapack::cx_gesvd_<T> 01423 ( 01424 &jobu, &jobvt, 01425 &m, &n, 01426 A.memptr(), &lda, 01427 S.memptr(), 01428 U.memptr(), &ldu, 01429 V.memptr(), &ldvt, 01430 work.memptr(), &lwork, 01431 rwork.memptr(), 01432 &info 01433 ); 01434 01435 op_htrans::apply(V,V); // op_htrans will work out that an in-place transpose can be done 01436 01437 for(u32 i=0; i<A.n_cols; ++i) 01438 { 01439 V.at(i,i) = std::conj( V.at(i,i) ); 01440 } 01441 01442 return (info == 0); 01443 } 01444 else 01445 { 01446 return false; 01447 } 01448 } 01449 #else 01450 { 01451 arma_stop("auxlib::svd(): need LAPACK library"); 01452 return false; 01453 } 01454 #endif 01455 01456 }
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 1465 of file auxlib_meat.hpp.
References arma_stop(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, and Mat< eT >::n_rows.
Referenced by solve().
01466 { 01467 arma_extra_debug_sigprint(); 01468 01469 #if defined(ARMA_USE_LAPACK) 01470 { 01471 int n = A.n_rows; 01472 int lda = A.n_rows; 01473 int ldb = A.n_rows; 01474 int nrhs = B.n_cols; 01475 int info; 01476 01477 podarray<int> ipiv(n); 01478 01479 out = B; 01480 Mat<eT> A_copy = A; 01481 01482 lapack::gesv_<eT>(&n, &nrhs, A_copy.memptr(), &lda, ipiv.memptr(), out.memptr(), &ldb, &info); 01483 01484 return (info == 0); 01485 } 01486 #else 01487 { 01488 arma_stop("auxlib::solve(): need LAPACK library"); 01489 return false; 01490 } 01491 #endif 01492 }
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 1502 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::colptr(), syslib::copy_elem(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Mat< eT >::set_size(), and trans().
Referenced by solve().
01503 { 01504 arma_extra_debug_sigprint(); 01505 01506 #if defined(ARMA_USE_LAPACK) 01507 { 01508 char trans = 'N'; 01509 01510 int m = A.n_rows; 01511 int n = A.n_cols; 01512 int lda = A.n_rows; 01513 int ldb = A.n_rows; 01514 int nrhs = B.n_cols; 01515 int lwork = n + (std::max)(n, nrhs); 01516 int info; 01517 01518 Mat<eT> A_copy = A; 01519 Mat<eT> tmp = B; 01520 01521 01522 podarray<eT> work(lwork); 01523 01524 arma_extra_debug_print("lapack::gels_()"); 01525 01526 // NOTE: 01527 // the dgels() function in the lapack library supplied by ATLAS 3.6 01528 // seems to have problems 01529 01530 lapack::gels_<eT> 01531 ( 01532 &trans, &m, &n, &nrhs, 01533 A_copy.memptr(), &lda, 01534 tmp.memptr(), &ldb, 01535 work.memptr(), &lwork, 01536 &info 01537 ); 01538 01539 arma_extra_debug_print("lapack::gels_() -- finished"); 01540 01541 out.set_size(A.n_cols, B.n_cols); 01542 01543 for(u32 col=0; col<B.n_cols; ++col) 01544 { 01545 syslib::copy_elem( out.colptr(col), tmp.colptr(col), A.n_cols ); 01546 } 01547 01548 return (info == 0); 01549 } 01550 #else 01551 { 01552 arma_stop("auxlib::solve_od(): need LAPACK library"); 01553 return false; 01554 } 01555 #endif 01556 }
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 1566 of file auxlib_meat.hpp.
References arma_stop(), Mat< eT >::colptr(), syslib::copy_elem(), max(), podarray< T1 >::memptr(), Mat< eT >::memptr(), Mat< eT >::n_cols, Mat< eT >::n_rows, Mat< eT >::set_size(), trans(), and Mat< eT >::zeros().
Referenced by solve().
01567 { 01568 arma_extra_debug_sigprint(); 01569 01570 #if defined(ARMA_USE_LAPACK) 01571 { 01572 char trans = 'N'; 01573 01574 int m = A.n_rows; 01575 int n = A.n_cols; 01576 int lda = A.n_rows; 01577 int ldb = A.n_cols; 01578 int nrhs = B.n_cols; 01579 int lwork = m + (std::max)(m,nrhs); 01580 int info; 01581 01582 01583 Mat<eT> A_copy = A; 01584 01585 Mat<eT> tmp; 01586 tmp.zeros(A.n_cols, B.n_cols); 01587 01588 for(u32 col=0; col<B.n_cols; ++col) 01589 { 01590 eT* tmp_colmem = tmp.colptr(col); 01591 01592 syslib::copy_elem( tmp_colmem, B.colptr(col), B.n_rows ); 01593 01594 for(u32 row=B.n_rows; row<A.n_cols; ++row) 01595 { 01596 tmp_colmem[row] = eT(0); 01597 } 01598 } 01599 01600 podarray<eT> work(lwork); 01601 01602 arma_extra_debug_print("lapack::gels_()"); 01603 01604 // NOTE: 01605 // the dgels() function in the lapack library supplied by ATLAS 3.6 01606 // seems to have problems 01607 01608 lapack::gels_<eT> 01609 ( 01610 &trans, &m, &n, &nrhs, 01611 A_copy.memptr(), &lda, 01612 tmp.memptr(), &ldb, 01613 work.memptr(), &lwork, 01614 &info 01615 ); 01616 01617 arma_extra_debug_print("lapack::gels_() -- finished"); 01618 01619 out.set_size(A.n_cols, B.n_cols); 01620 01621 for(u32 col=0; col<B.n_cols; ++col) 01622 { 01623 syslib::copy_elem( out.colptr(col), tmp.colptr(col), A.n_cols ); 01624 } 01625 01626 return (info == 0); 01627 } 01628 #else 01629 { 01630 arma_stop("auxlib::solve_ud(): need LAPACK library"); 01631 return false; 01632 } 01633 #endif 01634 }