Database Reference
In-Depth Information
speaking, it represents BLAS levels 2 and 3 (matrix operations) plus main
LAPACK functionality (especially decompositions). Thus, we included JAMA
into the
Algebra
package and extended the
Matrix
class for further requirements.
Example 12.10
We consider two matrices
A
and
Bw
hich are defined as follows:
,
B ¼
14
3
12
3
001
A ¼
:
5
Now we demonstrate the generation and operations on
A
and
B
.
// Create A and B:
Matrix A
¼
new
Matrix(
new doubl
[ ][] {{1.,4.},{3.,-5.}} );
Matrix B
¼
new
Matrix(
new doubl
[ ][] {{1.,2.,-3},{0.,0.,1.}} );
// Transpose B. BT
¼
B^T:
Matrix BT
¼
B.transpose();
// Scalar multiplication. A2
¼
2*A:
Matrix A2
¼
A.times(2);
// Matrix multiplication. C
¼
A*B:
Matrix C
¼
A.times(B);
// Matrix addition. D
¼
B+C:
Matrix D
¼
B.plus(C);
// Frobenius norm:
double nF
¼
A.normF();
// Concatination of operations. E
¼
(B + 2*A*B + C)^T:
Matrix E
¼
B.plus( A.times(B).times(2) ).plus(C).trans-
pose();
■
Since JAMA only supports dense matrices, it was extended for sparse matrices.
Therefore, the abstract class
SparseMatrix
was designed, and a number of
implementations of this class had been added. The corresponding class diagram is
depicted in Fig.
12.12
.
The different implementations of
SparseMatrix
use different storage techniques
and are optimized for different applications.
So the classes
SparseMatrixCompRow
and
SparseMatrixCompRowStatic
are
based on the format
Compressed Row Storage
(
CRS
). Here all nonzero elements
(NZE) are stored in one array, and a second array contains the corresponding
column indexes, while a third array contains the pointers to the rows. The CRS
format is especially suited for fast matrix-vector multiplications. At the same time,
it is relatively static because inserting and deleting of NZEs in general require all
arrays to be reordered.
