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b/include/deal.II/lac/scalapack.h index 693f1b4217..02d267a729 100644 --- a/include/deal.II/lac/scalapack.h +++ b/include/deal.II/lac/scalapack.h @@ -40,57 +40,26 @@ DEAL_II_NAMESPACE_OPEN * * ScaLAPACK assumes that matrices are distributed according to the * block-cyclic decomposition scheme. An $M$ by $N$ matrix is first decomposed - * into $MB$ by $NB$ blocks which are then uniformly distributed across - * the 2D process grid $p*q \le Np$, where $p,q$ are grid dimensions and - * $Np$ is the total number of processes. + * into $\lceil M / MB \rceil$ by $\lceil N / NB \rceil$ blocks which are then + * uniformly distributed across the 2D process grid with $p q \le Np$ processes, + * where $p,q$ are grid dimensions and $Np$ is the total number of processes. + * The parameters MB and NB are referred to as row and column block size and + * determine the granularity of the block-cyclic distribution. * - * For example, a global real symmetric matrix of size $9\times 9$ is stored in - * upper storage mode with block sizes 4 × 4: - * @code - * 0 1 2 - * ┌ ┐ - * | -6.0 0.0 0.0 0.0 | 0.0 -2.0 -2.0 0.0 | -2.0 | - * | . -6.0 -2.0 0.0 | -2.0 -4.0 0.0 -4.0 | -2.0 | - * 0 | . . -6.0 -2.0 | -2.0 0.0 2.0 0.0 | 6.0 | - * | . . . -6.0 | 2.0 0.0 2.0 0.0 | 2.0 | - * | ---------------------|-----------------------|------- | - * | . . . . | -8.0 -4.0 0.0 -2.0 | 0.0 | - * | . . . . | . -6.0 0.0 -4.0 | -6.0 | - * 1 | . . . . | . . -4.0 0.0 | 0.0 | - * | . . . . | . . . -4.0 | -4.0 | - * | ---------------------|-----------------------|------- | - * 2 | . . . . | . . . . | -16.0 | - * └ ┘ - * @endcode - * may be distributed using the 2x2 process grid: - * @code - * | 0 2 | 1 - * -----| ------- |----- - * 0 | P00 | P01 - * 2 | | - * -----| ------- |----- - * 1 | P10 | P11 - * @endcode - * with the following local arrays: - * @code - * p,q | 0 | 1 - * -----|----------------------------|---------------------- - * | -6.0 0.0 0.0 0.0 -2.0 | 0.0 -2.0 -2.0 0.0 - * | . -6.0 -2.0 0.0 -2.0 | -2.0 -4.0 0.0 -4.0 - * 0 | . . -6.0 -2.0 6.0 | -2.0 0.0 2.0 0.0 - * | . . . -6.0 2.0 | 2.0 0.0 2.0 0.0 - * | . . . . -16.0 | . . . . - * -----|----------------------------|---------------------- - * | . . . . 0.0 | -8.0 -4.0 0.0 -2.0 - * | . . . . -6.0 | . -6.0 0.0 -4.0 - * 1 | . . . . 0.0 | . . -4.0 0.0 - * | . . . . -4.0 | . . . -4.0 - * @endcode - * Note how processes $(0,0)$ and $(1,0)$ of the process grid store an - * extra column to represent the last column of the original matrix that - * did not fit the decomposition into $4\times 4$ sub-blocks. + * In the following the block-cyclic distribution of a $10 \times 9$ matrix + * onto a $3\times 3$ Cartesian process grid with block sizes + * $\text{MB}=\text{NB}=2$ is displayed. * - * The choice of the block size is a compromise between a sufficiently large + * \htmlonly + * \endhtmlonly + * @image html scalapack_block_cycling.png "Block-Cyclic Distribution" + * + * Note that the odd number of columns of the local matrices owned by the + * processes P2, P5 and P8 accounts for $N=9$ not being an integral multiple of + * $\text{NB}=2$. + * + * The choice of the block sizes is a compromise between a sufficiently large * size for efficient local/serial BLAS, but one that is also small enough to * achieve good parallel load balance. * @@ -116,6 +85,10 @@ public: /** * Constructor for a rectangular matrix with @p n_rows and @p n_cols * and distributed using the grid @p process_grid. + * + * The parameters @p row_block_size and @p column_block_size are the block sizes used + * for the block-cyclic distribution of the matrix. + * In general, it is recommended to use powers of $2$, e.g. $16,32,64, \dots$. */ ScaLAPACKMatrix( const size_type n_rows, @@ -128,6 +101,11 @@ public: /** * Constructor for a square matrix of size @p size, and distributed * using the process grid in @p process_grid. + * + * The parameter @p block_size is used for the block-cyclic distribution of the matrix. + * An identical block size is used for the rows and columns of the matrix. + * In general, it is recommended to use powers of $2$, e.g. $16,32,64, \dots$. + * */ ScaLAPACKMatrix( const size_type size, @@ -143,6 +121,10 @@ public: * Loads the matrix from file @p filename using HDF5. * In case that deal.II was built without HDF5 * a call to this function will cause an exception to be thrown. + * + * The parameters @p row_block_size and @p column_block_size are the block sizes used + * for the block-cyclic distribution of the matrix. + * In general, it is recommended to use powers of $2$, e.g. $16,32,64, \dots$. */ ScaLAPACKMatrix( const std::string & filename, @@ -158,6 +140,10 @@ public: /** * Initialize the rectangular matrix with @p n_rows and @p n_cols * and distributed using the grid @p process_grid. + * + * The parameters @p row_block_size and @p column_block_size are the block sizes used + * for the block-cyclic distribution of the matrix. + * In general, it is recommended to use powers of $2$, e.g. $16,32,64, \dots$. */ void reinit( @@ -170,6 +156,10 @@ public: /** * Initialize the square matrix of size @p size and distributed using the grid @p process_grid. + * + * The parameter @p block_size is used for the block-cyclic distribution of the matrix. + * An identical block size is used for the rows and columns of the matrix. + * In general, it is recommended to use powers of $2$, e.g. $16,32,64, \dots$. */ void reinit(const size_type size, -- 2.39.5

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