TESTING/EIG/zhbt21.f(3)    Library Functions Manual    TESTING/EIG/zhbt21.f(3)

NAME
       TESTING/EIG/zhbt21.f

SYNOPSIS
   Functions/Subroutines
       subroutine zhbt21 (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, rwork,
           result)
           ZHBT21

Function/Subroutine Documentation
   subroutine zhbt21 (character uplo, integer n, integer ka, integer ks,
       complex*16, dimension( lda, * ) a, integer lda, double precision,
       dimension( * ) d, double precision, dimension( * ) e, complex*16,
       dimension( ldu, * ) u, integer ldu, complex*16, dimension( * ) work,
       double precision, dimension( * ) rwork, double precision, dimension( 2
       ) result)
       ZHBT21

       Purpose:


           !>
           !> ZHBT21  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 )
           !>

       Parameters
           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, ZHBT21 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*16 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 DOUBLE PRECISION array, dimension (N)
           !>          The diagonal of the (symmetric tri-) diagonal matrix S.
           !>

           E

           !>          E is DOUBLE PRECISION 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*16 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*16 array, dimension (N**2)
           !>

           RWORK

           !>          RWORK is DOUBLE PRECISION array, dimension (N)
           !>

           RESULT

           !>          RESULT is 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.
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Definition at line 150 of file zhbt21.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/EIG/zhbt21.f(3)