This effort is still a "work in progress". Please feel free to add comments. BRBut please make the context less visible. – Edward J. Yoon

Sparse Matrix

NOTE that Sparse matrix operations cannot be optimized.

Why sparse matrices?

Many classes of problems result in matrices with a large number of zeros
A sparse matrix is a special class of matrix that allows only the non-zero terms to be stored
Reduction in the storage requirements for sparse matrices
Significant speed improvement as many calculations involving zero elements are neglected

I choosed HBase(sparse matrix storage) to reduce storage and complexity.

Hama use column-oriented storage of matrices (HBase) , and so compressed column format is a natural choice of sparse storage
Hama forces the elements of each column to be stored in increasing order of their row index

  1  0  0       (1,1) = 1           
  0  3  1       (2,2) = 3
  0  0  0       (2,3) = 1

See also: \[http://labs.google.com/papers/bigtable-osdi06.pdf Bigtable\], A Distributed Storage System for Structured Data

Function	Explanation
nnz	returns number of non zero elements in SM
nonzeros	Returns a vector of the non-zero values of the sparse matrix S

Function	Explanation
spdetermin	Compute the determinant of sparse matrix A
spcholesky	Compute the Cholesky factor, R, of the symmetric positive definite
splcholesky	Compute the Cholesky factor, L, of the symmetric positive definite
splu	Compute the LU decomposition of the sparse matrix A