CSTT22
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
CSTT22 checks a set of M eigenvalues and eigenvectors,
A U = U S
where A is Hermitian tridiagonal, the columns of U are unitary,
and S is diagonal (if KBAND=0) or Hermitian tridiagonal (if KBAND=1).
Two tests are performed:
RESULT(1) = | U* A U - S | / ( |A| m ulp )
RESULT(2) = | I - U*U | / ( m ulp )
A U = U S
where A is Hermitian tridiagonal, the columns of U are unitary,
and S is diagonal (if KBAND=0) or Hermitian tridiagonal (if KBAND=1).
Two tests are performed:
RESULT(1) = | U* A U - S | / ( |A| m ulp )
RESULT(2) = | I - U*U | / ( m ulp )
Arguments
| N |
(input) INTEGER
The size of the matrix. If it is zero, CSTT22 does nothing.
It must be at least zero. |
| M |
(input) INTEGER
The number of eigenpairs to check. If it is zero, CSTT22
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 Hermitian tri-diagonal. |
| AD |
(input) REAL array, dimension (N)
The diagonal of the original (unfactored) matrix A. A is
assumed to be Hermitian tridiagonal. |
| AE |
(input) REAL array, dimension (N)
The off-diagonal of the original (unfactored) matrix A. A
is assumed to be Hermitian tridiagonal. AE(1) is ignored, AE(2) is the (1,2) and (2,1) element, etc. |
| SD |
(input) REAL array, dimension (N)
The diagonal of the (Hermitian tri-) diagonal matrix S.
|
| SE |
(input) REAL array, dimension (N)
The off-diagonal of the (Hermitian tri-) diagonal matrix S.
Not referenced if KBSND=0. If KBAND=1, then AE(1) is ignored, SE(2) is the (1,2) and (2,1) element, etc. |
| U |
(input) REAL 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 array, dimension (LDWORK, M+1)
|
| LDWORK |
(input) INTEGER
The leading dimension of WORK. LDWORK must be at least
max(1,M). |
| RWORK |
(workspace) REAL array, dimension (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. |