From 12b02743de4c10766466135ea0a322dec9df4de2 Mon Sep 17 00:00:00 2001 From: Benjamin Brands Date: Tue, 6 Feb 2018 16:19:07 +0100 Subject: [PATCH] improve documentation of ScaLAPACKMatrix::least_squares() --- include/deal.II/lac/scalapack.h | 34 +++++++++++++++------------------ 1 file changed, 15 insertions(+), 19 deletions(-) diff --git a/include/deal.II/lac/scalapack.h b/include/deal.II/lac/scalapack.h index 42468c81fc..dc7051b82c 100644 --- a/include/deal.II/lac/scalapack.h +++ b/include/deal.II/lac/scalapack.h @@ -290,29 +290,25 @@ public: * It is assumed that $A$ has full rank: $rank(A) = \min(M,N)$. * * The following options are supported: - * - 1. If transpose==false and $M \geq N$: least squares solution of overdetermined system - * $\min \Vert B - A*X\Vert$. + * -# If(!transpose) and $M \geq N$: least squares solution of overdetermined system + * $\min \Vert B - A*X\Vert$.\n + * Upon exit the rows $0$ to $N-1$ of $B$ contain the least square solution vectors. The residual sum of squares + * for each column is given by the sum of squares of elements $N$ to $M-1$ in that column. * - * Upon exit the rows 0 to N-1 of $B$ contain the least square solution vectors. The residual sum of squares - * for each column is given by the sum of squares of elements N to M-1 in that column. + * -# If(!transpose) and $M < N$: find minimum norm solutions of underdetermined systems + * $A * X = B$.\n + * Upon exit the columns of $B$ contain the minimum norm solution vectors. * - * - 2. If transpose==false and $M < N$: find minimum norm solutions of underdetermined systems - * $A * X = B$. + * -# If(transpose) and $M \geq N$: find minimum norm solutions of underdetermined system + * $ A^\top X = B$.\n + * Upon exit the columns of $B$ contain the minimum norm solution vectors. * - * Upon exit the columns of $B$ contain the minimum norm solution vectors. + * -# If(transpose) and $M < N$: least squares solution of overdetermined system + * $\min \Vert B - A^\top X\Vert$.\n + * Upon exit the rows $0$ to $M-1$ contain the least square solution vectors. The residual sum of squares + * for each column is given by the sum of squares of elements $M$ to $N-1$ in that column. * - * - 3. If transpose==true and $M \geq N$: find minimum norm solutions of underdetermined system - * $ A^\top X = B$. - * - * Upon exit the columns of $B$ contain the minimum norm solution vectors. - * - * - 4. If transpose==true and $M < N$: least squares solution of overdetermined system - * $\min \Vert B - A^\top X\Vert$. - * - * Upon exit the rows 0 to M-1 contain the least square solution vectors. The residual sum of squares - * for each column is given by the sum of squares of elements M to N-1 in that column. - * - * If transpose==false then $B \in \mathbb{R}^{M \times N_{\rm RHS}}$, + * If(!tranpose) then $B \in \mathbb{R}^{M \times N_{\rm RHS}}$, * otherwise $B \in \mathbb{R}^{N \times N_{\rm RHS}}}$. * The matrices $A$ and $B$ must have an identical block cyclic distribution for rows and columns. */ -- 2.39.5