稀疏矩阵压缩格式（Sparse Matrix Compression Formats）

BCCS	Block Compressed Column Storage format
BCRS	Block Compressed Row Storage format
BND	Linpack Banded format
BSR	Block Sparse Row format
CCS	Compressed Column Storage format
COO	Coordinate format
CRS	Compressed Row Storage format
CSC	Compressed Sparse Column format
CSR	Compressed Sparse Row format
DIA	Diagonal format
DNS	Dense format
ELL	Ellpack-Itpack generalized diagonal format
JAD	Jagged Diagonal format
LNK	Linked list storage format
MSR	Modified Compressed Sparse Row format
NSK	Nonsymmetric Skyline format
SSK	Symmetric Skyline format
SSS	Symmetric Sparse Skyline format
USS	Unsymmetric Sparse Skyline format
VBR	Variable Block Row format

Example

Uncompressed Matrix

 

	Nj
A=	11 12 13 14 0 0 0 22 23 0 0 0 0 0 33 34 35 36 0 0 0 44 45 0 0 0 0 0 0 56 0 0 0 0 0 66	Ni

 

Variables
i	Row index
j	Column index
k	Element index in compressed data vector
a(i,j)	Element at matrix row i, column j
Abbreviations
N	Number of elements per side of the matrix
NB	Number of elements per side of the Block
NDZ	Number of Diagonal Zeros
NNZ	Number of Non-Zeros
NNZB	Number of Non-Zero Blocks
NR	Number of blocks per side of the matrix
O	Order of magnitude

Compressed Row Storage / Compressed Sparse Row

	i	1				2		3				4		5	6	7	O
Row Start Index	k	1				5		7				11		13	14	15	Ni+1
	k	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Column Index	j	1	2	3	4	2	3	3	4	5	6	4	5	6	6		NNZ
Data	a(i,j)	11	12	13	14	22	23	33	34	35	36	44	45	56	66		NNZ

Row Start Index :	1 ≤ i ≤ Ni	:	if Data(k) = a(i,j) then RowStartIndex(i) ≤ k < RowStartIndex(i+1)
	i = Ni+1	:	k = NNZ+1

Order is 2*NNZ + Ni + 1 (=35)

Compressed Column Storage / Compressed Sparse Column / Harwell-Boeing Sparse Matrix

	j	1	2		3			4			5		6			7	O
Column Start Index	k	1	2		4			7			10		12			15	Nj+1
	k	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Row Index	i	1	1	2	1	2	3	1	3	4	3	4	3	5	6		NNZ
Data	a(i,j)	11	12	22	13	23	33	14	34	44	35	45	36	56	66		NNZ

Column Start Index :	1 ≤ j ≤ Nj	:	if Data(k) = a(i,j) then ColumnStartIndex(j) ≤ k < ColumnStartIndex(j+1)
	j = Nj+1	:	k = NNZ+1

Order is 2*NNZ + Nj + 1 (=35)

Modified Compressed Sparse Row

	k	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	O
Index	k;j	8	11	12	15	16	17	17	2	3	4	3	4	5	6	5	6	NNZ+NDZ+1
Data	a(i,j)	11	22	33	44	0	66		12	13	14	23	34	35	36	45	56	NNZ+NDZ+1

k	Index	Data
1 ≤ k ≤ Ni	Row Start Index	a(k,k)
Ni+1	NNZ+NDZ+1
Ni+2 ≤ k ≤ NNZ+NDZ+1	Column Index	a(i,j), i<>j

Order is 2*NNZ + 2*NDZ + 2 (=32)

Modified Compressed Sparse Column

	k	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	O
Index	k;i	8	8	9	11	13	15	17	1	1	2	1	3	3	4	3	5	NNZ+NDZ+1
Data	a(i,j)	11	22	33	44	0	66		12	13	23	14	34	35	45	36	56	NNZ+NDZ+1

k	Index	Data
1 ≤ k ≤ Nj	Column Start Index	a(k,k)
Nj+1	NNZ+NDZ+1
Nj+2 ≤ k ≤ NNZ+NDZ+1	Row Index	a(i,j), i<>j

Order is 2*NNZ + 2*NDZ + 2 (=32)

Block Compressed Row Storage / Block Sparse Row

	i	1				2				3		4	O
Row Start Index	k	1				3				5		6	NRi+1
	k	1		2		3		4		5
Column Index	j	1		3		3		5		5			NNZB
Data	a(i,j)	11	12	13	14	33	34	35	36	0	56		NNZB*NBi*NBj
		0	22	23	0	0	44	45	0	0	66

NRi = Ni/NBi
Order is NNZB*NBi*NBj + NNZB + NRi + 1 (=29)

以上内内容来自传送门

更多参考1和参考2和cuSparse文档