CSGT01
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
modified August 1997, a new parameter M is added to the calling
sequence.
November 2006
modified August 1997, a new parameter M is added to the calling
sequence.
Purpose
CSGT01 checks a decomposition of the form
A Z = B Z D or
A B Z = Z D or
B A Z = Z D
where A is a Hermitian matrix, B is Hermitian positive definite,
Z is unitary, and D is diagonal.
One of the following test ratios is computed:
ITYPE = 1: RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )
ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )
A Z = B Z D or
A B Z = Z D or
B A Z = Z D
where A is a Hermitian matrix, B is Hermitian positive definite,
Z is unitary, and D is diagonal.
One of the following test ratios is computed:
ITYPE = 1: RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )
ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )
Arguments
| ITYPE |
(input) INTEGER
The form of the Hermitian generalized eigenproblem.
= 1: A*z = (lambda)*B*z = 2: A*B*z = (lambda)*z = 3: B*A*z = (lambda)*z |
| UPLO |
(input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrices A and B is stored. = 'U': Upper triangular = 'L': Lower triangular |
| N |
(input) INTEGER
The order of the matrix A. N >= 0.
|
| M |
(input) INTEGER
The number of eigenvalues found. M >= 0.
|
| A |
(input) COMPLEX array, dimension (LDA, N)
The original Hermitian matrix A.
|
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
|
| B |
(input) COMPLEX array, dimension (LDB, N)
The original Hermitian positive definite matrix B.
|
| LDB |
(input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
|
| Z |
(input) COMPLEX array, dimension (LDZ, M)
The computed eigenvectors of the generalized eigenproblem.
|
| LDZ |
(input) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
|
| D |
(input) REAL array, dimension (M)
The computed eigenvalues of the generalized eigenproblem.
|
| WORK |
(workspace) COMPLEX array, dimension (N*N)
|
| RWORK |
(workspace) REAL array, dimension (N)
|
| RESULT |
(output) REAL array, dimension (1)
The test ratio as described above.
|