HP MLIB User's Guide Vol. 2 7th Ed.

666 HP MLIB LAPACK User’s Guide
SLANSB/DLANSB/CLANHB/CLANSB/ZLANHB/ZLANSB Compute norm of symmetric or Hermitian band matrix
Name SLANSB/DLANSB/CLANHB/CLANSB/ZLANHB/ZLANSB
Compute norm of symmetric or Hermitian band matrix
Purpose These subprograms compute a norm of a real or complex symmetric or complex
Hermitian band matrix A. A real matrix is symmetric if A = A
T
, its transpose;
a complex matrix is Hermitian if A = A*, its conjugate transpose.
Tridiagonal matrices are the special case kd = 1. They can be handled more
efficiently by the LAPACK subprograms SLANST, DLANST, CLANHT, and
ZLANHT.
The structure of A is indicated by the name of the subprogram used:
Matrix
Storage
Because it is not necessary to store or operate on the zeros outside the band of
A, and since either triangle of A may be obtained from the other, you need only
provide the band within one triangle of A. Compared to storing the entire
matrix, this can save memory in two ways: Only the elements within the band
are stored and, of them, only the upper or the lower triangle.
The following examples illustrate the storage of symmetric or Hermitian band
matrices. Consider the following matrix A of order n = 7 and half bandwidth
kd =2:
Upper triangular storage
The upper triangle of A is stored in an array ab with at least kd+1 = 3 rows
and 7 columns as follows:
SLANSB or DLANSB A is a real symmetric matrix.
CLANSB or ZLANSB A is a complex symmetric matrix.
CLANHB or ZLANHB A is a complex Hermitian matrix.
1112130000
12 22 23 24 0 0 0
13 23 33 34 35 0 0
02434444546 0
0 0 35 45 55 56 57
0 0 0 46 56 66 67
0 0 0 0576777
* * 13 24 35 46 57
*122334455667
11 22 33 44 55 66 77