SSBT21
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SSBT21 generally checks a decomposition of the form
A = U S U'
where ' means transpose, A is symmetric banded, U is
orthogonal, and S is diagonal (if KS=0) or symmetric
tridiagonal (if KS=1).
Specifically:
RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and*
RESULT(2) = | I - UU' | / ( n ulp )
A = U S U'
where ' means transpose, A is symmetric banded, U is
orthogonal, and S is diagonal (if KS=0) or symmetric
tridiagonal (if KS=1).
Specifically:
RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and*
RESULT(2) = | I - UU' | / ( n ulp )
Arguments
| UPLO |
(input) CHARACTER
If UPLO='U', the upper triangle of A and V will be used and
the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A and V will be used and the (strictly) upper triangle will not be referenced. |
| N |
(input) INTEGER
The size of the matrix. If it is zero, SSBT21 does nothing.
It must be at least zero. |
| KA |
(input) INTEGER
The bandwidth of the matrix A. It must be at least zero. If
it is larger than N-1, then max( 0, N-1 ) will be used. |
| KS |
(input) INTEGER
The bandwidth of the matrix S. It may only be zero or one.
If zero, then S is diagonal, and E is not referenced. If one, then S is symmetric tri-diagonal. |
| A |
(input) REAL array, dimension (LDA, N)
The original (unfactored) matrix. It is assumed to be
symmetric, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced. |
| LDA |
(input) INTEGER
The leading dimension of A. It must be at least 1
and at least min( KA, N-1 ). |
| D |
(input) REAL array, dimension (N)
The diagonal of the (symmetric tri-) diagonal matrix S.
|
| E |
(input) REAL array, dimension (N-1)
The off-diagonal of the (symmetric tri-) diagonal matrix S.
E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and (3,2) element, etc. Not referenced if KS=0. |
| U |
(input) REAL array, dimension (LDU, N)
The orthogonal matrix in the decomposition, expressed as a
dense matrix (i.e., not as a product of Householder transformations, Givens transformations, etc.) |
| LDU |
(input) INTEGER
The leading dimension of U. LDU must be at least N and
at least 1. |
| WORK |
(workspace) REAL array, dimension (N**2+N)
|
| RESULT |
(output) REAL array, dimension (2)
The values computed by the two tests described above. The
values are currently limited to 1/ulp, to avoid overflow. |