Mercurial > hg > octave-nkf
diff libinterp/dldfcn/qr.cc @ 20373:075a5e2e1ba5 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed build-aux, libinterp/dldfcn, libinterp/octave-value,
libinterp/parse-tree directories.
* build-aux/mk-opts.pl, libinterp/dldfcn/__magick_read__.cc,
libinterp/dldfcn/amd.cc, libinterp/dldfcn/audiodevinfo.cc,
libinterp/dldfcn/audioread.cc, libinterp/dldfcn/ccolamd.cc,
libinterp/dldfcn/chol.cc, libinterp/dldfcn/colamd.cc,
libinterp/dldfcn/convhulln.cc, libinterp/dldfcn/dmperm.cc,
libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc, libinterp/dldfcn/symbfact.cc,
libinterp/dldfcn/symrcm.cc, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-bool-mat.cc, libinterp/octave-value/ov-cell.cc,
libinterp/octave-value/ov-class.cc, libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-null-mat.cc, libinterp/octave-value/ov-oncleanup.cc,
libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-typeinfo.cc, libinterp/octave-value/ov-usr-fcn.cc,
libinterp/octave-value/ov.cc, libinterp/parse-tree/lex.ll,
libinterp/parse-tree/oct-parse.in.yy, libinterp/parse-tree/pt-binop.cc,
libinterp/parse-tree/pt-eval.cc, libinterp/parse-tree/pt-mat.cc:
doc: Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 03 May 2015 21:52:42 -0700 |
parents | 4197fc428c7d |
children |
line wrap: on
line diff
--- a/libinterp/dldfcn/qr.cc +++ b/libinterp/dldfcn/qr.cc @@ -80,7 +80,9 @@ @deftypefnx {Loadable Function} {[@var{C}, @var{R}] =} qr (@var{A}, @var{B}, '0')\n\ @cindex QR factorization\n\ Compute the QR@tie{}factorization of @var{A}, using standard @sc{lapack}\n\ -subroutines. For example, given the matrix @code{@var{A} = [1, 2; 3, 4]},\n\ +subroutines.\n\ +\n\ +For example, given the matrix @code{@var{A} = [1, 2; 3, 4]},\n\ \n\ @example\n\ [@var{Q}, @var{R}] = qr (@var{A})\n\ @@ -124,7 +126,7 @@ @ifnottex\n\ @var{A}\n\ @end ifnottex\n\ - is a tall, thin matrix). The QR@tie{}factorization is\n\ +is a tall, thin matrix). The QR@tie{}factorization is\n\ @tex\n\ $QR = A$ where $Q$ is an orthogonal matrix and $R$ is upper triangular.\n\ @end tex\n\ @@ -140,8 +142,8 @@ If the matrix @var{A} is full, the permuted QR@tie{}factorization\n\ @code{[@var{Q}, @var{R}, @var{P}] = qr (@var{A})} forms the\n\ QR@tie{}factorization such that the diagonal entries of @var{R} are\n\ -decreasing in magnitude order. For example, given the matrix @code{a = [1,\n\ -2; 3, 4]},\n\ +decreasing in magnitude order. For example, given the matrix\n\ +@code{a = [1, 2; 3, 4]},\n\ \n\ @example\n\ [@var{Q}, @var{R}, @var{P}] = qr (@var{A})\n\ @@ -169,15 +171,15 @@ @end group\n\ @end example\n\ \n\ -The permuted @code{qr} factorization @code{[@var{Q}, @var{R}, @var{P}] = qr\n\ -(@var{A})} factorization allows the construction of an orthogonal basis of\n\ -@code{span (A)}.\n\ +The permuted @code{qr} factorization\n\ +@code{[@var{Q}, @var{R}, @var{P}] = qr (@var{A})} factorization allows the\n\ +construction of an orthogonal basis of @code{span (A)}.\n\ \n\ If the matrix @var{A} is sparse, then compute the sparse\n\ QR@tie{}factorization of @var{A}, using @sc{CSparse}. As the matrix @var{Q}\n\ is in general a full matrix, this function returns the @var{Q}-less\n\ -factorization @var{R} of @var{A}, such that @code{@var{R} = chol (@var{A}' *\n\ -@var{A})}.\n\ +factorization @var{R} of @var{A}, such that\n\ +@code{@var{R} = chol (@var{A}' * @var{A})}.\n\ \n\ If the final argument is the scalar @code{0} and the number of rows is\n\ larger than the number of columns, then an economy factorization is\n\ @@ -763,15 +765,15 @@ @deftypefn {Loadable Function} {[@var{Q1}, @var{R1}] =} qrupdate (@var{Q}, @var{R}, @var{u}, @var{v})\n\ Given a QR@tie{}factorization of a real or complex matrix\n\ @w{@var{A} = @var{Q}*@var{R}}, @var{Q}@tie{}unitary and\n\ -@var{R}@tie{}upper trapezoidal, return the QR@tie{}factorization\n\ -of @w{@var{A} + @var{u}*@var{v}'}, where @var{u} and @var{v} are\n\ -column vectors (rank-1 update) or matrices with equal number of columns\n\ +@var{R}@tie{}upper trapezoidal, return the QR@tie{}factorization of\n\ +@w{@var{A} + @var{u}*@var{v}'}, where @var{u} and @var{v} are column vectors\n\ +(rank-1 update) or matrices with equal number of columns\n\ (rank-k update). Notice that the latter case is done as a sequence of rank-1\n\ updates; thus, for k large enough, it will be both faster and more accurate\n\ to recompute the factorization from scratch.\n\ \n\ -The QR@tie{}factorization supplied may be either full\n\ -(Q is square) or economized (R is square).\n\ +The QR@tie{}factorization supplied may be either full (Q is square) or\n\ +economized (R is square).\n\ \n\ @seealso{qr, qrinsert, qrdelete, qrshift}\n\ @end deftypefn") @@ -944,24 +946,21 @@ Given a QR@tie{}factorization of a real or complex matrix\n\ @w{@var{A} = @var{Q}*@var{R}}, @var{Q}@tie{}unitary and\n\ @var{R}@tie{}upper trapezoidal, return the QR@tie{}factorization of\n\ -@w{[A(:,1:j-1) x A(:,j:n)]}, where @var{u} is a column vector to be\n\ -inserted into @var{A} (if @var{orient} is @qcode{\"col\"}), or the\n\ -QR@tie{}factorization of @w{[A(1:j-1,:);x;A(:,j:n)]}, where @var{x}\n\ -is a row vector to be inserted into @var{A} (if @var{orient} is\n\ -@qcode{\"row\"}).\n\ +@w{[A(:,1:j-1) x A(:,j:n)]}, where @var{u} is a column vector to be inserted\n\ +into @var{A} (if @var{orient} is @qcode{\"col\"}), or the\n\ +QR@tie{}factorization of @w{[A(1:j-1,:);x;A(:,j:n)]}, where @var{x} is a row\n\ +vector to be inserted into @var{A} (if @var{orient} is @qcode{\"row\"}).\n\ \n\ -The default value of @var{orient} is @qcode{\"col\"}.\n\ -If @var{orient} is @qcode{\"col\"},\n\ -@var{u} may be a matrix and @var{j} an index vector\n\ +The default value of @var{orient} is @qcode{\"col\"}. If @var{orient} is\n\ +@qcode{\"col\"}, @var{u} may be a matrix and @var{j} an index vector\n\ resulting in the QR@tie{}factorization of a matrix @var{B} such that\n\ @w{B(:,@var{j})} gives @var{u} and @w{B(:,@var{j}) = []} gives @var{A}.\n\ Notice that the latter case is done as a sequence of k insertions;\n\ thus, for k large enough, it will be both faster and more accurate to\n\ recompute the factorization from scratch.\n\ \n\ -If @var{orient} is @qcode{\"col\"},\n\ -the QR@tie{}factorization supplied may be either full\n\ -(Q is square) or economized (R is square).\n\ +If @var{orient} is @qcode{\"col\"}, the QR@tie{}factorization supplied may\n\ +be either full (Q is square) or economized (R is square).\n\ \n\ If @var{orient} is @qcode{\"row\"}, full factorization is needed.\n\ @seealso{qr, qrupdate, qrdelete, qrshift}\n\ @@ -1173,17 +1172,14 @@ \n\ The default value of @var{orient} is @qcode{\"col\"}.\n\ \n\ -If @var{orient} is @qcode{\"col\"},\n\ -@var{j} may be an index vector\n\ +If @var{orient} is @qcode{\"col\"}, @var{j} may be an index vector\n\ resulting in the QR@tie{}factorization of a matrix @var{B} such that\n\ -@w{A(:,@var{j}) = []} gives @var{B}.\n\ -Notice that the latter case is done as a sequence of k deletions;\n\ -thus, for k large enough, it will be both faster and more accurate to\n\ -recompute the factorization from scratch.\n\ +@w{A(:,@var{j}) = []} gives @var{B}. Notice that the latter case is done as\n\ +a sequence of k deletions; thus, for k large enough, it will be both faster\n\ +and more accurate to recompute the factorization from scratch.\n\ \n\ -If @var{orient} is @qcode{\"col\"},\n\ -the QR@tie{}factorization supplied may be either full\n\ -(Q is square) or economized (R is square).\n\ +If @var{orient} is @qcode{\"col\"}, the QR@tie{}factorization supplied may\n\ +be either full (Q is square) or economized (R is square).\n\ \n\ If @var{orient} is @qcode{\"row\"}, full factorization is needed.\n\ @seealso{qr, qrupdate, qrinsert, qrshift}\n\