zhbt21.f - Man Page

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

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.