csgt013

!>
!> 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 )
!> 

ITYPE

!>          ITYPE is 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

!>          UPLO is 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

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!> 

M

!>          M is INTEGER
!>          The number of eigenvalues found.  M >= 0.
!> 

A

!>          A is COMPLEX array, dimension (LDA, N)
!>          The original Hermitian matrix A.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!> 

B

!>          B is COMPLEX array, dimension (LDB, N)
!>          The original Hermitian positive definite matrix B.
!> 

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!> 

Z

!>          Z is COMPLEX array, dimension (LDZ, M)
!>          The computed eigenvectors of the generalized eigenproblem.
!> 

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z.  LDZ >= max(1,N).
!> 

D

!>          D is REAL array, dimension (M)
!>          The computed eigenvalues of the generalized eigenproblem.
!> 

WORK

!>          WORK is COMPLEX array, dimension (N*N)
!> 

RWORK

!>          RWORK is REAL array, dimension (N)
!> 

RESULT

!>          RESULT is REAL array, dimension (1)
!>          The test ratio as described above.
!> 

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