Mercurial > octave
diff libinterp/corefcn/qz.cc @ 32488:d7a3ed7f2fdc stable
doc: grammarcheck C++ files before 9.1 release.
* libinterp/corefcn/graphics.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/qz.cc,
libinterp/corefcn/sysdep.cc:
grammarcheck C++ files before 9.1 release.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 23 Nov 2023 19:42:27 -0800 |
parents | f5c0a0754da1 |
children | 2e484f9f1f18 |
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--- a/libinterp/corefcn/qz.cc Thu Nov 23 18:28:08 2023 -0800 +++ b/libinterp/corefcn/qz.cc Thu Nov 23 19:42:27 2023 -0800 @@ -61,7 +61,7 @@ DEFUN (qz, args, nargout, doc: /* -*- texinfo -*- -@deftypefn {} {[@var{AA}, @var{BB}, @var{Q}, @var{Z}, @var{V}, @var{W}] =} qz (@var{A}, @var{B}) +@deftypefn {} {[@var{AA}, @var{BB}, @var{Q}, @var{Z}, @var{V}, @var{W}] =} qz (@var{A}, @var{B}) @deftypefnx {} {[@var{AA}, @var{BB}, @var{Q}, @var{Z}, @var{V}, @var{W}] =} qz (@var{A}, @var{B}, @var{opt}) Compute the QZ@tie{}decomposition of a generalized eigenvalue problem. @@ -81,8 +81,8 @@ @enumerate @item @code{[@var{AA}, @var{BB}, @var{Q}, @var{Z}, @var{V}, @var{W}, @var{lambda}] = qz (@var{A}, @var{B})} -Compute the complex QZ@tie{}decomposition, generalized eigenvectors, and generalized -eigenvalues. +Compute the complex QZ@tie{}decomposition, generalized eigenvectors, and +generalized eigenvalues. @tex $$ AA = Q^T AZ, BB = Q^T BZ $$ $$ { \rm diag }(BB)AV = BV{ \rm diag }(AA) $$ @@ -102,20 +102,20 @@ @end ifnottex with @var{AA} and @var{BB} upper triangular, and @var{Q} and @var{Z} -unitary. The matrices @var{V} and @var{W} respectively contain the right +unitary. The matrices @var{V} and @var{W} respectively contain the right and left generalized eigenvectors. @item @code{[@var{AA}, @var{BB}, @var{Z} @{, @var{lambda}@}] = qz (@var{A}, @var{B}, @var{opt})} The @var{opt} argument must be equal to either @qcode{"real"} or -@qcode{"complex"}. If it is equal to @qcode{"complex"}, then this +@qcode{"complex"}. If it is equal to @qcode{"complex"}, then this calling form is equivalent to the first one with only two input arguments. If @var{opt} is equal to @qcode{"real"}, then the real QZ decomposition -is computed. In particular, @var{AA} is only guaranteed to be +is computed. In particular, @var{AA} is only guaranteed to be quasi-upper triangular with 1-by-1 and 2-by-2 blocks on the diagonal, -and @var{Q} and @var{Z} are orthogonal. The identities mentioned above +and @var{Q} and @var{Z} are orthogonal. The identities mentioned above for right and left generalized eigenvectors are only verified if @var{AA} is upper triangular (i.e., when all the generalized eigenvalues are real, in which case the real and complex QZ coincide).