chbt21.f3

!>
!> CHBT21  generally checks a decomposition of the form
!>
!>         A = U S U**H
!>
!> where **H means conjugate transpose, A is hermitian banded, U is
!> unitary, and S is diagonal (if KS=0) or symmetric
!> tridiagonal (if KS=1).
!>
!> Specifically:
!>
!>         RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
!>         RESULT(2) = | I - U U**H | / ( n ulp )
!> 

UPLO

!>          UPLO is 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

!>          N is INTEGER
!>          The size of the matrix.  If it is zero, CHBT21 does nothing.
!>          It must be at least zero.
!> 

KA

!>          KA is 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

!>          KS is 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

!>          A is COMPLEX array, dimension (LDA, N)
!>          The original (unfactored) matrix.  It is assumed to be
!>          hermitian, and only the upper (UPLO='U') or only the lower
!>          (UPLO='L') will be referenced.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of A.  It must be at least 1
!>          and at least min( KA, N-1 ).
!> 

D

!>          D is REAL array, dimension (N)
!>          The diagonal of the (symmetric tri-) diagonal matrix S.
!> 

E

!>          E is 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

!>          U is COMPLEX array, dimension (LDU, N)
!>          The unitary matrix in the decomposition, expressed as a
!>          dense matrix (i.e., not as a product of Householder
!>          transformations, Givens transformations, etc.)
!> 

LDU

!>          LDU is INTEGER
!>          The leading dimension of U.  LDU must be at least N and
!>          at least 1.
!> 

WORK

!>          WORK is COMPLEX array, dimension (N**2)
!> 

RWORK

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

RESULT

!>          RESULT is REAL array, dimension (2)
!>          The values computed by the two tests described above.  The
!>          values are currently limited to 1/ulp, to avoid overflow.
!> 

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