TESTING/EIG/dsbt21.f(3)    Library Functions Manual    TESTING/EIG/dsbt21.f(3)

NAME
       TESTING/EIG/dsbt21.f

SYNOPSIS
   Functions/Subroutines
       subroutine dsbt21 (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, result)
           DSBT21

Function/Subroutine Documentation
   subroutine dsbt21 (character uplo, integer n, integer ka, integer ks,
       double precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( * ) d, double precision, dimension( * ) e, double precision,
       dimension( ldu, * ) u, integer ldu, double precision, dimension( * )
       work, double precision, dimension( 2 ) result)
       DSBT21

       Purpose:


            DSBT21  generally checks a decomposition of the form

                    A = U S U**T

            where **T means transpose, A is symmetric banded, U is
            orthogonal, and S is diagonal (if KS=0) or symmetric
            tridiagonal (if KS=1).

            Specifically:

                    RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
                    RESULT(2) = | I - U U**T | / ( 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, DSBT21 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 DOUBLE PRECISION array, dimension (LDA, N)
                     The original (unfactored) matrix.  It is assumed to be
                     symmetric, 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 DOUBLE PRECISION array, dimension (LDU, N)
                     The orthogonal 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 DOUBLE PRECISION array, dimension (N**2+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 145 of file dsbt21.f.

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

LAPACK                          Version 3.12.0         TESTING/EIG/dsbt21.f(3)