format.h File Reference

Detailed Description

Block compressed sparse row data structure.

For an overview, see Block Compressed Sparse Row (BCSR) Format.

#include <oski/common.h>
#include <oski/matrix.h>

Go to the source code of this file.

Data Structures

struct  tagBebop_matBCSR_t
 Block compressed sparse row (BCSR) format. More...
#define INC_OSKI_BCSR_FORMAT_H
 BCSR/format.h included.

Name mangling.

#define oski_matBCSR_t   MANGLE_(oski_matBCSR_t)
 BCSR matrix representation.

Typedefs

typedef tagBebop_matBCSR_t oski_matBCSR_t
 Block compressed sparse row (BCSR) format.

Typedef Documentation

typedef struct tagBebop_matBCSR_t oski_matBCSR_t
 

Block compressed sparse row (BCSR) format.

An $m\times n$ matrix $A$ is stored in $r\times c$ BCSR format using six arrays, $(P, J, V, \hat{P}, \hat{J}, \hat{V})$. The triplet $(P, J, V)$ stores rows 1 through $M = \lfloor\frac{m}{r}\rfloor$ using uniformly aligned $r\times c$ blocks, and the triplet $(\hat{P}, \hat{J}, \hat{V})$ stores any remaining $r' = m\bmod r$ rows using uniformly aligned $r'\times c$ blocks.

  1. $P$ is an integer array of block-row pointers, of length at least $M+1$.
  2. $J$ is an integer array of block column indices, of length at least $P[M]$.
  3. $V$ is an array of non-zero block values, of length at least $P[M]\cdot r\cdot c$.

Define block-row $I$ to be rows $1 + (I-1)\cdot r$ through $I\cdot r$ of $A$, where $1 \leq I \leq M$. For each $k$ such that $P[I-1] \leq k \leq P[I]$, $j_0=J[k]+1$ is the column index $(1,1)$ entry of an explicitly stored non-zero block whose values are laid out in row-major order in the subarray $V[krc : (k+1)rc-1]$.

These blocks are uniformly aligned, meaning that $(j_0-1)\bmod c = 0$. However, there is one exception: if $c$ does not divide $n$, then each block row may contain one block with $j_0 = n - c + 1$. If such a block overlaps with another block starting at column index $j_0'$, then the initial columns of the block at $j_0$ are set to zero.

If $r$ does not divide $m$, then the remaining rows are stored in $(\hat{P},\hat{J},\hat{V})$ as a single block row with $r'\times c$ blocks. These arrays follow the same conventions as $(P,J,V)$.

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