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Functions | Variables
lu.cc File Reference
#include "lu.h"
#include "sparse-lu.h"
#include "defun.h"
#include "error.h"
#include "errwarn.h"
#include "ovl.h"
#include "ov-re-sparse.h"
#include "ov-cx-sparse.h"
Include dependency graph for lu.cc:

Go to the source code of this file.

Functions

OCTAVE_EXPORT octave_value_list Flu (const octave_value_list &args, int nargout) ar
 
template<typename MT >
static octave_value get_lu_l (const octave::math::lu< MT > &fact)
 
template<typename MT >
static octave_value get_lu_u (const octave::math::lu< MT > &fact)
 

Variables

end example noindent then a
factorization of which is but
less stable The second form
uses a slower pivoted 
algorithm
 
the sparsity preserving column
transformation 
ar {Q} is returned
 
the sparsity preserving column
transformation such that that
defines the pivoting threshold
can be given in which case it
defines the 
c {umfpack} pivoting tolerance for both symmetric and unsymmetric cases. If ar{thres} is a 2-element vector
 
in that case
 
end example noindent then a
factorization of which is 
faster
 
for large enough k
 
the sparsity preserving column
transformation such that that
defines the pivoting threshold
can be given in which case it
defines the then the first
element defines the pivoting
tolerance for the unsymmetric
the values defined such that
for full and returns the
permuted forms of the upper
and lower triangular 
matrices
 
the sparsity preserving column
transformation such that that
defines the pivoting threshold
can be given in which case it
defines the then the first
element defines the pivoting
tolerance for the unsymmetric
the values defined such that
for full 
matrix
 
 ode {lu} does not attempt to perform sparsity preserving column permutations. Called with a fourth output argument
 
 p = lu (ar{a}) nd example oindent returns xample roup l = 1.00000 0.00000 0.33333 1.00000 u = 3.00000 4.00000 0.00000 0.66667 p = 0 1 1 0 nd group nd example The matrix is not required to be square. When called with two or three output arguments and a sparse input matrix
 
end example noindent then a
factorization of 
tcode {@var{A}+@var{x}*@var{y}.'} can be obtained either as xample [ar{L1}, ar{U1}] = lu (ar{L}, ar{U}, ar{P}*ar{x}, ar{y}) nd example oindent or xample [ar{L1}, ar{U1}, ar{P1}] = lu (ar{L}, ar{U}, ar{P}, ar{x}, ar{y}) nd example The first form uses the unpivoted algorithm
 
 thus
 
 u
 
end example noindent then a
factorization of which is but
less stable The second form
uses a slower pivoted which is
more stable The matrix case is
done as a sequence of rank 
updates
 
in that an updated permutation
matrix is returned Note that
if 
var {L}
 

Function Documentation

OCTAVE_EXPORT octave_value_list Flu ( const octave_value_list args,
int  nargout 
)

Definition at line 138 of file lu.cc.

Referenced by install_lu_fcns().

template<typename MT >
static octave_value get_lu_l ( const octave::math::lu< MT > &  fact)
static

Definition at line 39 of file lu.cc.

References octave::math::lu< T >::L(), and MatrixType::Lower.

template<typename MT >
static octave_value get_lu_u ( const octave::math::lu< MT > &  fact)
static

Variable Documentation

end example noindent then a factorization of which is but less stable The second form uses a slower pivoted algorithm

Definition at line 606 of file lu.cc.

the sparsity preserving column transformation such that that defines the pivoting threshold can be given ar {Q} is returned

Definition at line 138 of file lu.cc.

the sparsity preserving column transformation such that that defines the pivoting threshold can be given in which case it defines the then the first element defines the pivoting tolerance for the unsymmetric the values defined such that for full and returns the permuted forms of the upper and lower triangular such that then the matrix returned by the c {umfpack} pivoting tolerance for both symmetric and unsymmetric cases. If ar{thres} is a 2-element vector

Definition at line 138 of file lu.cc.

Referenced by QtHandles::accelSequence(), Vt102Emulation::applyCharset(), octave_struct::as_mxArray(), octave_scalar_struct::as_mxArray(), mxArray_struct::as_octave_value(), mxArray_cell::as_octave_value(), Array< T >::assign(), base_det< T >::base_det(), octave::base_parser::bison_error(), brace_expand(), brace_gobbler(), SparseMatrix::bsolve(), axes::properties::calc_ticklabels(), Sparse< T >::SparseRep::celem(), Sparse< T >::SparseRep::change_length(), charNDArray::charNDArray(), cntr(), tree::column(), DiagMatrix::column(), FloatDiagMatrix::column(), ComplexDiagMatrix::column(), FloatComplexDiagMatrix::column(), jit_cond_branch::cond_llvm(), convert_to_string(), convolve(), convolve_nd(), DEFUN(), Matrix::determinant(), FloatMatrix::determinant(), ComplexMatrix::determinant(), FloatComplexMatrix::determinant(), dim_vector::dim_vector(), display_character(), do_cleanup_waitfor_listener(), resource_manager::do_combo_encoding(), octave::command_editor::do_decode_prompt_string(), octave::math::do_erfcinv(), octave::math::do_erfinv(), gh_manager::do_execute_callback(), octave_base_stream::do_gets(), text_label_property::do_set(), octave_call_stack::do_set_column(), octave_call_stack::do_set_location(), octave::opengl_renderer::draw_patch(), octave::opengl_renderer::draw_surface(), TerminalView::drawContents(), edit_history_readline(), octave::math::ellipj(), tree_identifier::eval_undefined_error(), expand_amble(), expand_char_class(), extract_keyword(), extract_num(), Faddeeva_w(), octave_base_diag< DMT, MT >::fast_elem_extract(), octave_perm_matrix::fast_elem_extract(), QtHandles::Utils::figureCurrentPoint(), octave::base_parser::finish_classdef_external_method(), octave::base_parser::finish_if_command(), octave::base_parser::finish_switch_command(), Fisfield(), QtHandles::Utils::fromRgb(), SparseMatrix::fsolve(), G__glpk__(), get_line(), get_line_offsets(), get_mat_data_input_line(), cdef_class::cdef_class_rep::get_methods(), parser::get_next_node(), cdef_class::cdef_class_rep::get_properties(), QConsolePrivate::getSelection(), glob_pattern_p(), Gsymrcm(), Array< T >::index(), Sparse< T >::SparseRep::indices_ok(), octave::opengl_renderer::init_gl_context(), input(), ComplexNDArray::insert(), FloatComplexNDArray::insert(), DiagMatrix::inverse(), FloatDiagMatrix::inverse(), ComplexDiagMatrix::inverse(), FloatComplexDiagMatrix::inverse(), Array< T >::is_sorted_rows(), is_superclass(), Java_org_octave_Octave_doInvoke(), kpse_tilde_expand(), kron(), lin_interpn(), octave_base_diag< DMT, MT >::load_ascii(), octave_float_complex_diag_matrix::load_binary(), octave_complex_diag_matrix::load_binary(), octave_float_diag_matrix::load_binary(), octave_diag_matrix::load_binary(), lookup_classes(), octave::base_parser::make_anon_fcn_handle(), octave::base_parser::make_assign_op(), octave::base_parser::make_binary_op(), octave::base_parser::make_boolean_op(), octave::base_parser::make_break_command(), octave::base_parser::make_classdef(), octave::base_parser::make_classdef_enum_block(), octave::base_parser::make_classdef_events_block(), octave::base_parser::make_classdef_methods_block(), octave::base_parser::make_classdef_properties_block(), octave::base_parser::make_constant(), octave::base_parser::make_continue_command(), octave::base_parser::make_decl_command(), octave::base_parser::make_do_until_command(), octave::base_parser::make_elseif_clause(), octave::base_parser::make_fcn_handle(), octave::base_parser::make_for_command(), octave::base_parser::make_index_expression(), octave::base_parser::make_indirect_ref(), octave::opengl_renderer::make_marker_list(), octave::base_parser::make_postfix_op(), octave::base_parser::make_prefix_op(), octave::base_parser::make_return_command(), octave::base_parser::make_switch_case(), octave::base_parser::make_try_command(), octave::base_parser::make_unwind_command(), make_valid_identifier(), octave::base_parser::make_while_command(), mark_facets(), Sparse< T >::SparseRep::maybe_compress(), oct_fill_float_randg(), oct_fill_randg(), octave_class::octave_class(), octave_kbhit(), octave_lex(), octave_print_internal(), color_values::operator!=(), operator*(), ComplexDiagMatrix::operator+=(), FloatComplexDiagMatrix::operator+=(), gzfilebuf::overflow(), package_getAllPackages(), Array< T >::page(), octave::directory_path::static_members::path_sep_char(), pr_complex(), pr_plus_format(), tree_print_code::print_comment_elt(), tree_print_code::print_fcn_handle_body(), octave::ft_text_renderer::process_character(), scanf_format_list::process_conversion(), octave::textscan_format_list::process_conversion(), DiagMatrix::pseudo_inverse(), FloatDiagMatrix::pseudo_inverse(), ComplexDiagMatrix::pseudo_inverse(), FloatComplexDiagMatrix::pseudo_inverse(), raw_help_from_docstrings_file(), read_maps(), read_mat_ascii_data(), read_mat_binary_data(), read_until_newline(), DiagArray2< T >::resize(), Sparse< T >::resize(), DiagMatrix::row(), FloatDiagMatrix::row(), ComplexDiagMatrix::row(), FloatComplexDiagMatrix::row(), charMatrix::row_as_string(), octave::math::rsf2csf< ComplexMatrix, Matrix >(), octave::math::rsf2csf< FloatComplexMatrix, FloatMatrix >(), octave_float_complex::save_ascii(), octave_complex::save_ascii(), octave_float_complex_diag_matrix::save_binary(), octave_complex_diag_matrix::save_binary(), octave_float_diag_matrix::save_binary(), octave_diag_matrix::save_binary(), QConsolePrivate::sendConsoleText(), octave::text_renderer::string::set_code(), octave::text_renderer::string::set_color(), octave::ft_text_renderer::set_color(), tree_statement::set_command(), tree::set_location(), Screen::ShowCharacter(), single_num(), single_type_concat(), skip_comments(), skip_preceeding_newline(), skip_until_newline(), octave_base_stream::skipl(), Array< T >::sort_rows_idx(), Sparse< T >::Sparse(), octave::base_parser::start_classdef_external_method(), string_array_property::string_array_property(), cdef_object_array::subsref(), SparseBoolMatrix::sum(), octave::math::sparse_qr< SPARSE_T >::sparse_qr_rep< SPARSE_T >::tall_solve(), octave::ten_little_endians(), text_label_property::text_label_property(), token::token(), SparseMatrix::trisolve(), octave_float_complex_matrix::try_narrowing_conversion(), octave_complex_matrix::try_narrowing_conversion(), octave_sparse_complex_matrix::try_narrowing_conversion(), c_file_ptr_buf::underflow_common(), c_zfile_ptr_buf::underflow_common(), TerminalView::updateImage(), octave::math::sparse_qr< SPARSE_T >::sparse_qr_rep< SPARSE_T >::wide_solve(), xgemm(), and Sparse< T >::SparseRep::~SparseRep().

in that case

Definition at line 606 of file lu.cc.

end example noindent then a factorization of which is faster

Definition at line 606 of file lu.cc.

for large enough k

Definition at line 606 of file lu.cc.

Referenced by mxArray_struct::add_field(), octave_struct::as_mxArray(), octave_scalar_struct::as_mxArray(), mxArray_struct::as_octave_value(), octave_base_matrix< MT >::assign(), octave_base_sparse< T >::assign(), octave_map::assign(), Sparse< T >::assign(), Array< T >::assign(), octave_user_function::bind_automatic_vars(), bitopxx(), calc_degrees(), Sparse< T >::cat(), SparseComplexMatrix::column(), SparseMatrix::column(), column_norms(), caseless_str::compare(), dim_vector::compute_index(), radio_values::contains(), convert_packcomplex_Nd(), dim_vector::cum_compute_index(), dim_vector::cumulative(), decode_subscripts(), defun_isargout(), qr< T >::delete_col(), octave_base_sparse< T >::delete_elements(), octave_map::delete_elements(), Sparse< T >::delete_elements(), Array< T >::delete_elements(), PermMatrix::determinant(), octave_perm_matrix::diag(), MSparse< Complex >::diag(), MDiagArray2< Complex >::diag(), octave_char_matrix_str::diag(), octave_base_sparse< SparseComplexMatrix >::diag(), octave_base_matrix< boolNDArray >::diag(), octave_char_matrix_sq_str::diag(), Sparse< T >::diag(), Array< T >::diag(), octave_value::diag(), dmdm_div_impl(), dmdm_leftdiv_impl(), dmm_leftdiv_impl(), octave_call_stack::do_backtrace(), do_bool_partition(), load_path::do_dirs(), children_property::do_get_children(), octave_diag_matrix::do_index_op(), octave_perm_matrix::do_index_op(), octave_base_diag< DMT, MT >::do_index_op(), octave_base_matrix< MT >::do_index_op(), octave_base_sparse< T >::do_index_op(), octave_char_matrix_str::do_index_op_internal(), do_leftdiv_dm_sm(), do_mul_dm_sm(), do_mul_sm_dm(), octave_call_stack::do_num_user_code_frames(), do_regexp_ptn_string_escapes(), do_regexp_rep_string_escapes(), rec_resize_helper::do_resize_fill(), do_rightdiv_sm_dm(), do_tril(), do_trilu(), do_triu(), octave::opengl_renderer::draw_patch(), octave::opengl_renderer::draw_surface(), drawcn(), octave::math::sparse_chol< chol_type >::sparse_chol_rep< chol_type >::drop_zeros(), SparseMatrix::dsolve(), SparseComplexMatrix::dsolve(), EigsComplexNonSymmetricFunc(), EigsComplexNonSymmetricMatrix(), EigsComplexNonSymmetricMatrixShift(), EigsRealNonSymmetricFunc(), EigsRealNonSymmetricMatrix(), EigsRealNonSymmetricMatrixShift(), EigsRealSymmetricFunc(), EigsRealSymmetricMatrix(), EigsRealSymmetricMatrixShift(), QWinTerminalImpl::eventFilter(), DiagMatrix::extract_diag(), FloatDiagMatrix::extract_diag(), ComplexDiagMatrix::extract_diag(), FloatComplexDiagMatrix::extract_diag(), F__dump_symtab_info__(), F__pchip_deriv__(), finalize_r(), Array< T >::find(), find_nonzero_elem_idx(), parser::find_ref(), flogfak(), qr< T >::form(), ComplexNDArray::fourier(), FloatComplexNDArray::fourier(), FloatNDArray::fourier(), NDArray::fourier(), G__eigs__(), G__voronoi__(), octave_sort< T >::gallop_left(), octave_sort< T >::gallop_right(), axes::properties::get_extent(), octave::math::lu< T >::getp(), octave::sys::glob(), octave::sys::group::group(), Gsymbfact(), SparseComplexMatrix::hermitian(), Array< T >::hermitian(), higham(), ichol_0(), ichol_t(), MArray< T >::idx_add_nd(), idx_vector::idx_vector_rep::idx_vector_rep(), ComplexNDArray::ifourier(), FloatComplexNDArray::ifourier(), FloatNDArray::ifourier(), NDArray::ifourier(), ilu_0(), ind2sub(), Cell::index(), octave_map::index(), Sparse< T >::index(), Array< T >::index(), initialize_r(), tree_parameter_list::initialize_undefined_elements(), inner_do_add_sm_dm(), Array< T >::insert(), qr< T >::insert_col(), qr< T >::insert_row(), SparseComplexMatrix::is_hermitian(), idx_vector::is_permutation(), SparseMatrix::is_symmetric(), jcobi(), octave::math::lanczos_approximation_psi(), SparseMatrix::ltsolve(), SparseComplexMatrix::ltsolve(), main(), octave_value_list::make_argv(), make_java_index(), MatrixType::MatrixType(), Sparse< T >::SparseRep::maybe_compress(), idx_vector::maybe_reduce(), maybe_update_column(), octave_sort< T >::merge_at(), octave_sort< T >::merge_hi(), octave_sort< T >::merge_lo(), load_path::loader::move_fcn_map(), oct_init_by_array(), octave_print_internal(), octave_print_internal_template(), octave_value_list::octave_value_list(), octinternal_do_mul_sm_colpm(), octinternal_do_mul_sm_rowpm(), octregexp(), operator<<(), octave_map::page(), octave::textscan::parse_options(), poisson_cdf_lookup(), poisson_cdf_lookup_float(), print_nd_array(), qs_search(), rec_permute_helper::rec_permute_helper(), dim_vector::redim(), octave::math::lu< T >::regular(), octave::math::qr< T >::regular(), load_path::loader::remove_fcn_map(), mxArray_struct::remove_field(), octave::regexp::replace(), Sparse< T >::reshape(), Sparse< T >::resize(), Array< T >::resize2(), SparseComplexMatrix::row(), SparseMatrix::row(), row_norms(), tree_multi_assignment::rvalue(), safe_comparator(), graphics_object::set(), qr< T >::shift_cols(), Sparse< T >::sort(), idx_vector::idx_vector_rep::sort_idx(), idx_vector::idx_vector_rep::sort_uniq_clone(), sparse(), Sparse< T >::Sparse(), octave_value_list::splice(), sqrtm_utri_inplace(), dim_vector::squeeze(), Array< T >::squeeze(), octave_cell::string_vector_value(), strip_spaces(), strip_trailing_separators(), octave_base_diag< DMT, MT >::subsasgn(), octave_struct::subsasgn(), octave_cell::subsasgn(), SparseBoolMatrix::sum(), symetree(), SparseComplexMatrix::tinverse(), SparseMatrix::tinverse(), transpose(), Sparse< T >::transpose(), try_cellfun_internal_ops(), string_vector::uniq(), lu< T >::update(), qr< T >::update(), lu< T >::update_piv(), SparseComplexMatrix::utsolve(), SparseMatrix::utsolve(), octave::opengl_renderer::patch_tesselator::vertex(), octave::sys::windows_glob(), octave::math::xpsi(), and zero_dims_inquire().

the sparsity preserving column transformation such that that defines the pivoting threshold can be given in which case it defines the then the first element defines the pivoting tolerance for the unsymmetric the values defined such that for full and returns the permuted forms of the upper and lower triangular matrices

Definition at line 138 of file lu.cc.

the sparsity preserving column transformation such that that defines the pivoting threshold can be given in which case it defines the then the first element defines the pivoting tolerance for the unsymmetric the values defined such that for full matrix

Definition at line 138 of file lu.cc.

Referenced by octave_base_diag< DiagMatrix, Matrix >::all(), octave_base_sparse< SparseComplexMatrix >::all(), octave_base_matrix< boolNDArray >::all(), octave_base_diag< DiagMatrix, Matrix >::any(), octave_base_sparse< SparseComplexMatrix >::any(), octave_base_matrix< boolNDArray >::any(), octave_char_matrix::array_value(), octave_bool_matrix::array_value(), octave_matrix::array_value(), OCTAVE_VALUE_INT_MATRIX_T::array_value(), octave_base_int_matrix< T >::as_double(), octave_base_int_matrix< T >::as_int16(), octave_base_int_matrix< T >::as_int32(), octave_base_int_matrix< T >::as_int64(), octave_base_int_matrix< T >::as_int8(), OCTAVE_VALUE_INT_MATRIX_T::as_mxArray(), octave_base_int_matrix< T >::as_single(), octave_base_int_matrix< T >::as_uint16(), octave_base_int_matrix< T >::as_uint32(), octave_base_int_matrix< T >::as_uint64(), octave_base_int_matrix< T >::as_uint8(), octave_base_matrix< MT >::assign(), octave_base_sparse< T >::assign(), octave_bool_matrix::bool_array_value(), OCTAVE_VALUE_INT_MATRIX_T::bool_array_value(), octave_bool_matrix::bool_matrix_value(), octave_perm_matrix::byte_size(), octave_base_diag< DiagMatrix, Matrix >::byte_size(), octave_base_matrix< boolNDArray >::byte_size(), octave_base_sparse< SparseComplexMatrix >::byte_size(), octave_cell::cell_value(), octave_float_complex_matrix::changesign(), octave_complex_matrix::changesign(), octave_char_matrix::char_array_value(), octave_bool_matrix::char_array_value(), octave_range::char_array_value(), OCTAVE_VALUE_INT_MATRIX_T::char_array_value(), octave_char_matrix::char_matrix_value(), octave_float_complex_matrix::complex_array_value(), octave_complex_matrix::complex_array_value(), octave_char_matrix::complex_array_value(), octave_bool_matrix::complex_array_value(), OCTAVE_VALUE_INT_MATRIX_T::complex_array_value(), octave_char_matrix::complex_matrix_value(), octave_bool_matrix::complex_matrix_value(), OCTAVE_VALUE_INT_MATRIX_T::complex_matrix_value(), octave_base_diag< DMT, MT >::complex_value(), octave_base_int_matrix< T >::convert_to_str_internal(), octave_char_matrix::convert_to_str_internal(), octave_float_complex_matrix::decrement(), octave_complex_matrix::decrement(), octave_base_matrix< MT >::delete_elements(), octave_base_sparse< T >::delete_elements(), octave_base_diag< DMT, MT >::diag(), octave_char_matrix_str::diag(), octave_base_sparse< SparseComplexMatrix >::diag(), octave_base_matrix< boolNDArray >::diag(), octave_char_matrix_sq_str::diag(), octave_perm_matrix::dims(), octave_base_diag< DiagMatrix, Matrix >::dims(), octave_base_matrix< boolNDArray >::dims(), octave_base_sparse< SparseComplexMatrix >::dims(), octave_base_diag< DMT, MT >::do_index_op(), octave_base_matrix< MT >::do_index_op(), octave_base_sparse< T >::do_index_op(), jit_paren_subsasgn::do_initialize(), OCTAVE_VALUE_INT_MATRIX_T::double_value(), octave_base_diag< DMT, MT >::double_value(), octave_base_sparse< T >::fast_elem_extract(), octave_base_matrix< MT >::fast_elem_extract(), octave_base_diag< DMT, MT >::fast_elem_extract(), octave_base_matrix< MT >::fast_elem_insert(), octave_char_matrix::float_array_value(), octave_bool_matrix::float_array_value(), octave_float_matrix::float_array_value(), octave_matrix::float_array_value(), OCTAVE_VALUE_INT_MATRIX_T::float_array_value(), octave_char_matrix::float_complex_array_value(), octave_bool_matrix::float_complex_array_value(), OCTAVE_VALUE_INT_MATRIX_T::float_complex_array_value(), octave_char_matrix::float_complex_matrix_value(), octave_bool_matrix::float_complex_matrix_value(), OCTAVE_VALUE_INT_MATRIX_T::float_complex_matrix_value(), octave_base_diag< DMT, MT >::float_complex_value(), octave_char_matrix::float_matrix_value(), octave_bool_matrix::float_matrix_value(), OCTAVE_VALUE_INT_MATRIX_T::float_matrix_value(), OCTAVE_VALUE_INT_MATRIX_T::float_value(), octave_base_diag< DMT, MT >::float_value(), octave_base_matrix< boolNDArray >::full_value(), octave_base_sparse< SparseComplexMatrix >::full_value(), jit_paren_subsasgn::generate_matrix(), octave_float_complex_matrix::increment(), octave_complex_matrix::increment(), octave_sparse_bool_matrix::index_vector(), octave_bool_matrix::index_vector(), octave_float_matrix::index_vector(), octave_matrix::index_vector(), OCTAVE_VALUE_INT_MATRIX_T::index_vector(), OCTAVE_VALUE_INT_MATRIX_T::int16_array_value(), octave_bool_matrix::int16_array_value(), octave_float_matrix::int16_array_value(), octave_matrix::int16_array_value(), OCTAVE_VALUE_INT_MATRIX_T::int32_array_value(), octave_bool_matrix::int32_array_value(), octave_float_matrix::int32_array_value(), octave_matrix::int32_array_value(), OCTAVE_VALUE_INT_MATRIX_T::int64_array_value(), octave_bool_matrix::int64_array_value(), octave_float_matrix::int64_array_value(), octave_matrix::int64_array_value(), OCTAVE_VALUE_INT_MATRIX_T::int8_array_value(), octave_bool_matrix::int8_array_value(), octave_float_matrix::int8_array_value(), octave_matrix::int8_array_value(), octave_base_matrix< boolNDArray >::is_sorted(), octave_base_matrix< boolNDArray >::is_sorted_rows(), octave_base_diag< DMT, MT >::is_true(), octave_base_sparse< T >::is_true(), octave_base_matrix< MT >::is_true(), octave_base_int_matrix< T >::load_ascii(), octave_base_sparse< T >::load_ascii(), octave_base_diag< DMT, MT >::load_ascii(), octave_base_int_matrix< T >::load_binary(), octave_base_int_matrix< T >::load_hdf5(), octave_base_sparse< T >::map(), OCTAVE_VALUE_INT_MATRIX_T::map(), octave_base_matrix< boolNDArray >::matrix_ref(), octave_char_matrix::matrix_value(), octave_bool_matrix::matrix_value(), OCTAVE_VALUE_INT_MATRIX_T::matrix_value(), octave_base_matrix< boolNDArray >::maybe_economize(), octave_char_matrix::mex_get_data(), octave_base_sparse< SparseComplexMatrix >::mex_get_data(), octave_float_matrix::mex_get_data(), octave_bool_matrix::mex_get_data(), octave_matrix::mex_get_data(), OCTAVE_VALUE_INT_MATRIX_T::mex_get_data(), octave_base_sparse< SparseComplexMatrix >::mex_get_ir(), octave_base_sparse< SparseComplexMatrix >::mex_get_jc(), octave_base_matrix< boolNDArray >::ndims(), octave_perm_matrix::nnz(), octave_base_sparse< SparseComplexMatrix >::nnz(), octave_base_matrix< boolNDArray >::nnz(), octave_base_matrix< boolNDArray >::numel(), octave_base_sparse< SparseComplexMatrix >::nzmax(), octave_base_matrix< boolNDArray >::octave_base_matrix(), octave_base_sparse< SparseComplexMatrix >::octave_base_sparse(), octave_perm_matrix::perm_matrix_value(), octave_base_diag< DiagMatrix, Matrix >::permute(), octave_char_matrix_str::permute(), octave_base_sparse< SparseComplexMatrix >::permute(), octave_base_matrix< boolNDArray >::permute(), octave_char_matrix_sq_str::permute(), octave_base_sparse< T >::print_info(), octave_base_matrix< MT >::print_info(), octave_base_diag< DMT, MT >::print_info(), octave_base_int_matrix< T >::print_raw(), octave_base_sparse< T >::print_raw(), octave_base_diag< DMT, MT >::print_raw(), octave_char_matrix_str::reshape(), octave_base_sparse< SparseComplexMatrix >::reshape(), octave_base_matrix< boolNDArray >::reshape(), octave_char_matrix_sq_str::reshape(), octave_base_diag< DMT, MT >::resize(), octave_base_sparse< T >::resize(), octave_base_matrix< MT >::resize(), octave_char_matrix_sq_str::resize(), octave_base_int_matrix< T >::save_ascii(), octave_base_sparse< T >::save_ascii(), octave_base_diag< DMT, MT >::save_ascii(), octave_base_int_matrix< T >::save_binary(), octave_base_int_matrix< T >::save_hdf5(), octave_base_matrix< MT >::short_disp(), octave_base_sparse< SparseComplexMatrix >::sort(), octave_base_matrix< boolNDArray >::sort(), octave_char_matrix_str::sort(), octave_char_matrix_sq_str::sort(), octave_base_matrix< boolNDArray >::sort_rows_idx(), octave_sparse_bool_matrix::sparse_bool_matrix_value(), octave_bool_matrix::sparse_bool_matrix_value(), octave_sparse_complex_matrix::sparse_complex_matrix_value(), octave_sparse_matrix::sparse_complex_matrix_value(), octave_bool_matrix::sparse_complex_matrix_value(), octave_sparse_matrix::sparse_matrix_value(), octave_bool_matrix::sparse_matrix_value(), octave_perm_matrix::squeeze(), octave_base_diag< DiagMatrix, Matrix >::squeeze(), octave_base_matrix< boolNDArray >::squeeze(), octave_base_sparse< SparseComplexMatrix >::squeeze(), octave_char_matrix_str::squeeze(), octave_char_matrix_sq_str::squeeze(), octave_base_diag< DMT, MT >::subsasgn(), octave_base_diag< DMT, MT >::to_dense(), octave_base_int_matrix< T >::try_narrowing_conversion(), OCTAVE_VALUE_INT_MATRIX_T::uint16_array_value(), octave_bool_matrix::uint16_array_value(), octave_float_matrix::uint16_array_value(), octave_matrix::uint16_array_value(), OCTAVE_VALUE_INT_MATRIX_T::uint32_array_value(), octave_bool_matrix::uint32_array_value(), octave_float_matrix::uint32_array_value(), octave_matrix::uint32_array_value(), OCTAVE_VALUE_INT_MATRIX_T::uint64_array_value(), octave_bool_matrix::uint64_array_value(), octave_float_matrix::uint64_array_value(), octave_matrix::uint64_array_value(), OCTAVE_VALUE_INT_MATRIX_T::uint8_array_value(), octave_bool_matrix::uint8_array_value(), octave_float_matrix::uint8_array_value(), octave_matrix::uint8_array_value(), octave_char_matrix_str::write(), octave_float_matrix::write(), octave_bool_matrix::write(), octave_matrix::write(), and OCTAVE_VALUE_INT_MATRIX_T::write().

the sparsity preserving column transformation such that that defines the pivoting threshold can be given in which case it defines the then the first element defines the pivoting tolerance for the unsymmetric the values defined such that for full and returns the permuted forms of the upper and lower triangular such that then the matrix returned by the ode {lu} does not attempt to perform sparsity preserving column permutations. Called with a fourth output argument

Definition at line 138 of file lu.cc.

p = lu (ar{a}) nd example oindent returns xample roup l = 1.00000 0.00000 0.33333 1.00000 u = 3.00000 4.00000 0.00000 0.66667 p = 0 1 1 0 nd group nd example The matrix is not required to be square. When called with two or three output arguments and a sparse input matrix

Definition at line 138 of file lu.cc.

Referenced by QtHandles::__init__(), load_path::add(), tree_statement_list::add_breakpoint(), symbol_table::add_dispatch(), octave::dynamic_library::dynlib_rep::add_fcn_name(), base_properties::add_listener(), load_path::loader::add_to_fcn_map(), load_path::loader::add_to_method_map(), tree_array_list::all_elements_are_constant(), tree_argument_list::all_elements_are_constant(), base_properties::all_property_names(), mxArray_octave_value::array_to_string(), octave_struct::as_mxArray(), octave_char_matrix::as_mxArray(), octave_float_complex_matrix::as_mxArray(), octave_complex_matrix::as_mxArray(), octave_float_matrix::as_mxArray(), octave_bool_matrix::as_mxArray(), octave_matrix::as_mxArray(), octave_scalar_struct::as_mxArray(), octave_range::as_mxArray(), OCTAVE_VALUE_INT_MATRIX_T::as_mxArray(), mxArray_struct::as_octave_value(), mxArray_cell::as_octave_value(), property_list::as_struct(), octave_map::assign(), autoloaded_functions(), octave::math::betain(), octave::math::betaincinv(), octave_sort< T >::binarysort(), octave_user_function::bind_automatic_vars(), binmap(), bitop(), symbol_table::built_in_function_names(), octave_struct::byte_size(), octave_class::byte_size(), octave_scalar_struct::byte_size(), cbknu(), tm_row_const::tm_row_const_rep::cellify(), file_editor_tab::change_editor_state(), check_access(), file_editor::check_closing(), symbol_table::fcn_info::fcn_info_rep::clear_dispatch(), symbol_table::clear_dispatch(), symbol_table::clear_dld_function(), symbol_table::clear_function_pattern(), symbol_table::clear_functions(), symbol_table::fcn_info::fcn_info_rep::clear_map(), symbol_table::clear_mex_functions(), symbol_table::clear_user_function(), array_property::clone(), row_vector_property::clone(), symbol_table::cmdline_function_names(), coletree(), octave_class::exemplar_info::compare(), convert_label_position(), tree_parameter_list::convert_to_const_vector(), tree_array_list::copy_base(), tree_parameter_list::define_from_arg_vector(), defun_isargout(), string_vector::delete_c_str_vec(), base_properties::delete_listener(), PermMatrix::determinant(), load_path::loader::display(), symbol_info_list::display(), dmsolve(), dmsolve_extract(), dmsolve_insert(), octave_call_stack::do_all_scripts(), symbol_table::do_all_variables(), symbol_table::scope_id_cache::do_alloc(), symbol_table::do_assign(), octave_call_stack::do_backtrace(), octave_call_stack::do_backtrace_frames(), symbol_table::do_builtin_find(), octave_call_stack::do_caller_user_code(), octave_call_stack::do_caller_user_code_column(), octave_call_stack::do_caller_user_code_line(), do_class_concat(), symbol_table::do_clear_global(), symbol_table::do_clear_global_pattern(), symbol_table::do_clear_objects(), symbol_table::do_clear_variable(), symbol_table::do_clear_variable_pattern(), symbol_table::do_clear_variable_regexp(), symbol_table::do_clear_variables(), octave::tree_evaluator::do_decl_init_list(), octave_shlib_list::do_display(), load_path::do_display(), symbol_table::do_dump(), symbol_table::do_dup_scope(), symbol_table::do_erase_persistent(), load_path::do_files(), symbol_table::do_find(), load_path::do_find_all_first_of(), load_path::do_find_dir(), octave_shlib_list::do_find_file(), load_path::do_find_file(), load_path::do_find_first_of(), load_path::do_find_matching_dirs(), symbol_table::do_find_symbol(), gtk_manager::do_find_toolkit(), symbol_table::scope_id_cache::do_free(), ch_manager::do_free(), gh_manager::do_free(), octave_stream_list::do_get_file_number(), ch_manager::do_get_handle(), gh_manager::do_get_handle(), ch_manager::do_get_object(), symbol_table::do_glob(), ch_manager::do_handle_list(), octave_perm_matrix::do_index_op(), symbol_table::do_inherit(), symbol_table::do_insert(), symbol_table::do_is_global(), symbol_table::do_is_local_variable(), symbol_table::do_is_variable(), octave_errno::do_list(), octave_stream_list::do_list_open_files(), ch_manager::do_lookup(), octave_call_stack::do_num_user_code_frames(), octave_stream_list::do_open_file_numbers(), symbol_table::do_persistent_assign(), symbol_table::do_persistent_varref(), symbol_table::do_persistent_varval(), symbol_table::do_pop_context(), symbol_table::do_push_context(), symbol_table::do_regexp(), octave_shlib_list::do_remove(), bp_table::do_remove_breakpoint_1(), symbol_table::do_rename(), gh_manager::do_renumber_figure(), symbol_table::scope_id_cache::do_scopes(), gtk_manager::do_unload_all_toolkits(), load_path::do_update(), symbol_table::do_variable_names(), symbol_table::do_varref(), symbol_table::do_varval(), do_who(), symbol_table::do_workspace_info(), octave_struct::dotref(), octave_class::dotref(), TerminalView::drawContents(), octave::math::sparse_chol< chol_type >::sparse_chol_rep< chol_type >::drop_zeros(), symbol_table::fcn_info::fcn_info_rep::dump(), symbol_table::dump(), symbol_table::dump_functions(), symbol_table::dump_global(), dump_octave_core(), tree_parameter_list::dup(), tree_index_expression::dup(), octave_comment_list::dup(), tree_if_command_list::dup(), tree_return_list::dup(), tree_decl_init_list::dup(), tree_statement_list::dup(), tree_switch_case_list::dup(), EigsComplexNonSymmetricFunc(), EigsComplexNonSymmetricMatrix(), EigsComplexNonSymmetricMatrixShift(), EigsRealNonSymmetricFunc(), EigsRealNonSymmetricMatrix(), EigsRealNonSymmetricMatrixShift(), EigsRealSymmetricFunc(), EigsRealSymmetricMatrix(), EigsRealSymmetricMatrixShift(), octave_fields::equal_up_to_order(), symbol_table::erase_scope(), symbol_table::fcn_info::fcn_info_rep::erase_subfunction(), Screen::eraseChars(), set_event::execute(), F__dispatch__(), F__dump_symtab_info__(), load_path::loader::fcn_names(), Ffunctions(), octave_fields::fieldnames(), find(), file_editor_tab::find(), symbol_table::find_autoload(), symbol_table::find_built_in_function(), symbol_table::find_cmdline_function(), load_path::loader::find_fcn(), find_first_of(), load_path::loader::find_method(), symbol_table::find_method(), find_nonzero_elem_idx(), load_path::loader::find_private_fcn(), parser::find_ref(), file_editor::find_tab_widget(), symbol_table::find_user_function(), mex::free(), mex::free_value(), profile_data_accumulator::stats::function_set_value(), G__delaunayn__(), G__eigs__(), G__osmesa_print__(), Gccolamd(), Gcolamd(), symbol_table::get_dispatch(), axes::properties::get_extent(), text::properties::get_extent(), symbol_table::get_fcn_info(), get_file_list(), profile_data_accumulator::tree_node::get_hierarchical(), octave::dynamic_library::dynlib_rep::get_instance(), symbol_table::get_instance(), cdef_class::get_method_function(), mxArray_octave_value::get_string(), octave_fields::getfield(), symbol_table::glob_global_variables(), symbol_table::global_assign(), mex::global_unmark(), symbol_table::global_variable_names(), symbol_table::global_varref(), symbol_table::global_varval(), octave::sys::group::group(), Gsymbfact(), H_insert(), tree_array_list::has_magic_end(), tree_argument_list::has_magic_end(), tree_index_expression::has_magic_end(), symbol_table::fcn_info::fcn_info_rep::help_for_dispatch(), symbol_table::help_for_dispatch(), octave_char_matrix::index_vector(), jit_phi::infer(), qrp< T >::init(), tm_row_const::tm_row_const_rep::init(), octave::sys::base_tm::init(), octave::sys::strptime::init(), tm_const::init(), tree_parameter_list::initialize_undefined_elements(), base_properties::insert_property(), symbol_table::install_built_in_function(), symbol_table::install_cmdline_function(), symbol_table::install_subfunction(), symbol_table::install_user_function(), intmap_to_ov(), tree_parameter_list::is_defined(), load_path::is_package(), symbol_table::is_superiorto(), tree_argument_list::is_valid_lvalue_list(), kpse_tilde_expand(), octave::math::lanczos_approximation_psi(), local_functions(), symbol_table::fcn_info::fcn_info_rep::lock_subfunction(), symbol_table::lock_subfunctions(), symbol_table::look_nonlocal(), property_list::lookup(), lookup_autoload(), LuAminusSigmaB(), make_graphics_object_from_type(), make_idx_args(), make_octave_logo(), make_option_struct(), Cell::map(), Array< octave_value >::map(), symbol_info_list::map_value(), tree_parameter_list::mark_as_formal_parameters(), symbol_table::fcn_info::fcn_info_rep::mark_subfunction_in_scope_as_private(), octave_user_function::maybe_relocate_end(), octave_sort< T >::merge_collapse(), octave_sort< T >::merge_force_collapse(), load_path::loader::methods(), mexUnlock(), load_path::move(), load_path::loader::move_fcn_map(), load_path::loader::move_method_map(), next_state(), oct_randn(), octave_dock_widget::octave_dock_widget(), octave_value_list::octave_value_list(), octregexp(), KPty::open(), octave::math::qrp< T >::operator=(), octave::math::qrp< T >::P(), octave::math::lu< T >::P_vec(), Array< T >::page(), symbol_info_list::parse_whos_line_format(), octave::sys::password::password(), PermMatrix::pos_power(), pr_where(), float_format::precision(), tree_print_code::print_comment_list(), symbol_table::fcn_info::fcn_info_rep::print_dispatch(), symbol_table::print_dispatch(), print_fcn_list(), octave_fcn_handle::print_raw(), jit_phi::prune(), qrp< T >::Pvec(), octave::math::sparse_chol< chol_type >::sparse_chol_rep< chol_type >::Q(), qp(), randi53(), randi54(), read_mat5_binary_element(), mex::realloc(), octave::child_list::child_list_rep::reap(), Vt102Emulation::receiveChar(), octave_class::reconstruct_parents(), symbol_table::regexp_global_variables(), load_path::remove(), base_graphics_object::remove_all_listeners(), load_path::loader::remove_fcn_map(), octave::dynamic_library::dynlib_rep::remove_fcn_name(), tree_argument_list::remove_front(), load_path::loader::remove_method_map(), load_path::loader::remove_private_fcn_map(), octave::regexp::replace(), reverse_lookup_autoload(), octave_fields::rmfield(), hook_function_list::run(), tree_multi_assignment::rvalue(), tree_cell::rvalue1(), tree_matrix::rvalue1(), octave_fcn_handle::save_ascii(), octave_fcn_handle::save_binary(), save_fields(), octave_fcn_handle::save_hdf5(), save_vars(), search_path_for_all_files(), search_path_for_file(), QtHandles::Canvas::select_object(), property_list::set(), graphics_object::set(), octave::opengl_renderer::set_clipbox(), load_path::set_command_line_path(), octave_fcn_handle::set_fcn(), glob_match::set_pattern(), symbol_table::set_scope(), symbol_table::set_scope_and_context(), gzfilebuf::setbuf(), TerminalView::setColorTable(), single_type_concat(), Sparse< T >::Sparse(), octave::math::sparse_lu< lu_type >::sparse_lu(), symbol_table::stash_dir_name_for_subfunctions(), octave_user_function::stash_parent_fcn_name(), symbol_table::fcn_info::fcn_info_rep::subfunction_defined_in_scope(), symbol_table::subfunctions_defined_in_scope(), octave_struct::subsasgn(), octave_class::subsasgn_common(), octave_struct::subsref(), octave_class::subsref(), symetree(), octave::math::umfpack_get_numeric< Complex >(), octave::math::umfpack_get_numeric< double >(), tree_parameter_list::undefine(), symbol_table::fcn_info::fcn_info_rep::unlock_subfunction(), symbol_table::unlock_subfunctions(), mex::unmark(), mex::unmark_array(), mex::unmark_foreign(), load_path::dir_info::update(), color_picker::update_button(), axes::properties::update_title_position(), surface::properties::update_vertex_normals(), axes::properties::update_xlabel_position(), axes::properties::update_ylabel_position(), axes::properties::update_zlabel_position(), QtHandles::Canvas::updateCurrentPoint(), TerminalView::updateImage(), QtHandles::updatePalette(), symbol_table::user_function_names(), tree_parameter_list::validate(), base_graphics_object::value_as_string(), base_graphics_object::values_as_string(), base_graphics_object::values_as_struct(), tree_parameter_list::variable_names(), symbol_table::symbol_record::symbol_record_rep::varref(), QWinTerminalImpl::viewPaintEvent(), tree_checker::visit_argument_list(), tree_print_code::visit_argument_list(), tree_checker::visit_cell(), tree_print_code::visit_cell(), octave::tree_evaluator::visit_complex_for_command(), tree_checker::visit_decl_init_list(), tree_print_code::visit_decl_init_list(), tree_checker::visit_if_command_list(), tree_breakpoint::visit_if_command_list(), octave::tree_evaluator::visit_if_command_list(), tree_print_code::visit_if_command_list(), tree_checker::visit_index_expression(), tree_checker::visit_matrix(), tree_print_code::visit_matrix(), tree_checker::visit_parameter_list(), tree_print_code::visit_parameter_list(), tree_checker::visit_return_list(), tree_print_code::visit_return_list(), tree_checker::visit_statement_list(), tree_breakpoint::visit_statement_list(), octave::tree_evaluator::visit_statement_list(), tree_print_code::visit_statement_list(), tree_checker::visit_switch_case_list(), tree_breakpoint::visit_switch_case_list(), tree_print_code::visit_switch_case_list(), octave::tree_evaluator::visit_switch_command(), octave::child_list::child_list_rep::wait(), symbol_table::fcn_info::fcn_info_rep::xfind(), octave::math::xpsi(), xreset_default_properties(), mex::~mex(), tree_argument_list::~tree_argument_list(), tree_array_list::~tree_array_list(), tree_classdef_attribute_list::~tree_classdef_attribute_list(), tree_classdef_body::~tree_classdef_body(), tree_classdef_enum_list::~tree_classdef_enum_list(), tree_classdef_events_list::~tree_classdef_events_list(), tree_classdef_property_list::~tree_classdef_property_list(), tree_classdef_superclass_list::~tree_classdef_superclass_list(), tree_decl_init_list::~tree_decl_init_list(), tree_if_command_list::~tree_if_command_list(), tree_index_expression::~tree_index_expression(), tree_parameter_list::~tree_parameter_list(), tree_return_list::~tree_return_list(), tree_statement_list::~tree_statement_list(), and tree_switch_case_list::~tree_switch_case_list().

end example noindent then a factorization of tcode {@var{A}+@var{x}*@var{y}.'} can be obtained either as xample [ar{L1}, ar{U1}] = lu (ar{L}, ar{U}, ar{P}*ar{x}, ar{y}) nd example oindent or xample [ar{L1}, ar{U1}, ar{P1}] = lu (ar{L}, ar{U}, ar{P}, ar{x}, ar{y}) nd example The first form uses the unpivoted algorithm

Definition at line 606 of file lu.cc.

thus

Definition at line 606 of file lu.cc.

u
end example noindent then a factorization of which is but less stable The second form uses a slower pivoted which is more stable The matrix case is done as a sequence of rank updates

Definition at line 606 of file lu.cc.

in that an updated permutation matrix is returned Note that if var {L}