ZSTT21
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZSTT21 checks a decomposition of the form
A = U S U*
where * means conjugate transpose, A is real symmetric tridiagonal,
U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
tridiagonal (if KBAND=1). Two tests are performed:
RESULT(1) = | A - U S U* | / ( |A| n ulp )
RESULT(2) = | I - UU* | / ( n ulp )
A = U S U*
where * means conjugate transpose, A is real symmetric tridiagonal,
U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
tridiagonal (if KBAND=1). Two tests are performed:
RESULT(1) = | A - U S U* | / ( |A| n ulp )
RESULT(2) = | I - UU* | / ( n ulp )
Arguments
| N |
(input) INTEGER
The size of the matrix. If it is zero, ZSTT21 does nothing.
It must be at least zero. |
| KBAND |
(input) INTEGER
The bandwidth of the matrix S. It may only be zero or one.
If zero, then S is diagonal, and SE is not referenced. If one, then S is symmetric tri-diagonal. |
| AD |
(input) DOUBLE PRECISION array, dimension (N)
The diagonal of the original (unfactored) matrix A. A is
assumed to be real symmetric tridiagonal. |
| AE |
(input) DOUBLE PRECISION array, dimension (N-1)
The off-diagonal of the original (unfactored) matrix A. A
is assumed to be symmetric tridiagonal. AE(1) is the (1,2) and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc. |
| SD |
(input) DOUBLE PRECISION array, dimension (N)
The diagonal of the real (symmetric tri-) diagonal matrix S.
|
| SE |
(input) DOUBLE PRECISION array, dimension (N-1)
The off-diagonal of the (symmetric tri-) diagonal matrix S.
Not referenced if KBSND=0. If KBAND=1, then AE(1) is the (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) element, etc. |
| U |
(input) COMPLEX*16 array, dimension (LDU, N)
The unitary matrix in the decomposition.
|
| LDU |
(input) INTEGER
The leading dimension of U. LDU must be at least N.
|
| WORK |
(workspace) COMPLEX*16 array, dimension (N**2)
|
| RWORK |
(workspace) DOUBLE PRECISION array, dimension (N)
|
| RESULT |
(output) DOUBLE PRECISION array, dimension (2)
The values computed by the two tests described above. The
values are currently limited to 1/ulp, to avoid overflow. RESULT(1) is always modified. |