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SPQR documentation (issue #536) #584

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Dec 10, 2023
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SPQR documentation (issue #536) #584

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Binary file modified SPQR/Doc/spqr_user_guide.pdf
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13 changes: 8 additions & 5 deletions SPQR/Doc/spqr_user_guide.tex
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Expand Up @@ -533,11 +533,14 @@ \subsection{C++ Syntax}

\item \verb'SuiteSparseQR_qmult': provides the same function as
\verb'spqr_qmult' in the MATLAB interface, computing
\verb"Q'*x", \verb"Q*x", \verb"x*Q'", or \verb"x*Q".
It uses either a QR factorization
in MATLAB-style sparse matrix format, or the QR factorization object
returned by \newline \verb'SuiteSparseQR_factorize' or
\verb'SuiteSparseQR_numeric'.
\verb"y=Q'*x", \verb"y=Q*x", \verb"y=x*Q'", or \verb"y=x*Q".
It uses the efficient Householder reprensentation of \verb'Q', which
represents a square orthonormal matrix computed by
\verb'SuiteSparseQR_factorize' or \verb'SuiteSparseQR_numeric'. The
Householder representation always represents a square orthonormal matrix,
regardless of whether \verb'Q' is a full or economy factor.
\verb'SuiteSparseQR_qmult' applies this square matrix to compute its result
\verb'y'.

\item \verb'SuiteSparseQR_min2norm': finds the minimum 2-norm solution to
an underdetermined linear system.
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4 changes: 3 additions & 1 deletion SPQR/MATLAB/spqr.m
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Expand Up @@ -92,7 +92,9 @@
% [Q,R,P]=spqr(A) where spqr finds P and Q is discarded instead). 'matrix'
% returns Q as a sparse matrix where A=Q*R or A*P=Q*R. 'Householder' returns
% Q as a struct containing the Householder reflections applied to A to obtain
% R, resulting in a far sparser Q than the 'matrix' option.
% R, resulting in a far sparser Q than the 'matrix' option. When returned as
% a struct, Q always represents a square orthonormal matrix, regardless of
% opts.econ.
%
% opts.permutation: a string describing how P is to be returned. The default
% is 'matrix', so that A*P=Q*R. 'vector' gives A(:,P)=Q*R instead.
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5 changes: 5 additions & 0 deletions SPQR/MATLAB/spqr_qmult.m
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Expand Up @@ -7,6 +7,11 @@
% method = 2: Y = X*Q'
% method = 3: Y = X*Q
%
% where Q is the struct from [Q,R,E] = spqr (A,opts) with
% opts.Q = 'Householder'. The struct Q always represents a square
% orthonormal matrix, regardless of opts.econ. spqr_qmult applies this
% square matrix to compute Y.
%
% Example:
% These two examples both compute the min-norm solution to an
% under determined system, but the latter is much more efficient:
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