SSBT21  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 )

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, SSBT21 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 REAL 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 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 REAL 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 REAL array, dimension (N**2+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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