SSL II USER'S GUIDE - Lahey Computer Systems

⎡a11
a12 a13 a14 a15
⎤
⎢
a a a a a
⎥
⎢ 21 22 23 24 25⎥
A = ⎢a
a a a a ⎥
31 32 33 34 35
⎢
⎥
⎢a41
a42 a43 a44 a45⎥
⎢
⎣a
a a a a ⎥
51 52 53 54 55 ⎦
NOTE: · Correspondence a ij → A (I,J)
· K is the adjustable dimension
Fig. 2.8 Storage of unsymmetric dense matrices
⎡ a11
⎤
⎢
⎥
⎢a21
+ i⋅b21 a22
⎥
⎢
⎥
A = ⎢a31
+ i⋅ b31 a32 + i⋅b32 a33
⎥
⎢
⎥
⎢a41
+ i⋅ b41 a42 + i⋅ b42 a43 + i⋅b43 a44
⎥
⎢
⎥
⎣a51
+ i⋅ b51 a52 + i⋅ b52 a53 + i⋅ b53 a54 + i⋅b54 a55⎦
Note: Correspondence a ij → A(I,J)(i ≥ j)
b ij → A(J,I)(i > j)
Fig. 2.10 Storage of Hermitian matrices
⎡a11
⎤
⎢
⎥
⎢a21
a22
⎥
A = ⎢
⎥
⎢a31
a32 a33
⎥
⎢
⎥
⎣a41
a42 a43 a44
⎦
Note : Correspondence
a ij
( I −1)
⎛ I ⎞
→ A⎜
+ J ⎟
⎝ 2 ⎠
The value of NT is
n
NT =
( n + 1)
2
Where n : order of matrix
Fig. 2.9 Storage of symmetric dense matrices
Two-demensional array A(K,L)
a 11 a 12 a 13 a 14 a 15
a 21 a 22 a 23 a 24 a 25
a 31 a 32 a 33 a 34 a 35
a 41 a 42 a 43 a 44 a 45
a 51 a 52 a 53 a 54 a 55
One-dimensinal array A
of size NT
a11 a21 a22 a31 a32 a33 a41 a42 • Compressed mode for symmetric band matrix
The elements of the diagonal and the lower band
portions of a symmetric band matrix A are stored row
by row in a one-dimensional array A as shown in Fig.
2.11.
• Compressed mode for band matrix
The elements of the diagonal and the upper and lower
band portions of an unsymmetric band matrix A are
stored row by row in a one-dimensional array A as
shown in Fig. 2.12.
a 43
a 44
NT
L
5
K
Two-demensional array A(K,L)
a 11 b 21 b 31 b 41 b 51
a 21 a 22 b 32 b 42 b 52
a 31 a 32 a 33 b 43 b 53
a 41 a 42 a 43 a 44 b 54
a 51 a 52 a 53 a 54 a 55
L
5
K
⎡a11
⎤
⎢
⎥
⎢a21
a22
⎥
⎢
⎥
A = ⎢a31
a32 a33
⎥
⎢
⎥
⎢ a42 a43 a44
⎥
⎢
⎥
⎣ 0 a53 a54 a55⎦
Note : Correspondence
For i ≤ h+ 1,
For j > h + 1,
a → A
→
The value of NT is
NT = n(
h + 1)
− h ( h + 1)
2
Where
n = orderof
matrix
h = bandwidth
a
( I ( I −1)
2 + J )
A(
hI + J − h(
h + 1)
2)
Fig. 2.11 Storage of symmetric band matrices
Vectors
Vector is stored as shown in Fig. 2.13.
ij
ij
GENERAL RULES
One dimensional
array A of size NT
a11 a21 a22 a31 a32 a33 a42 a43 a44 a53 a54 a55 NT
25