TESTING/EIG/sstt21.f(3)

NAME
TESTING/EIG/sstt21.f

SYNOPSIS

  Functions/Subroutines
subroutine sstt21 (n, kband, ad, ae, sd, se, u, ldu, work, result)
SSTT21

Function/Subroutine Documentation

  subroutine sstt21 (integer n, integer kband, real, dimension( * ) ad, real, dimension( * ) ae, real, dimension( * ) sd, real, dimension( * ) se, real, dimension( ldu, * ) u, integer ldu, real, dimension( * ) work, real, dimension( 2 ) result)

SSTT21

Purpose:

    !>
    !> SSTT21 checks a decomposition of the form
    !>
    !>    A = U S U'
    !>
    !> where ' means transpose, A is symmetric tridiagonal, U is orthogonal,
    !> and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
    !> Two tests are performed:
    !>
    !>    RESULT(1) = | A - U S U' | / ( |A| n ulp )
    !>
    !>    RESULT(2) = | I - UU' | / ( n ulp )
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The size of the matrix.  If it is zero, SSTT21 does nothing.
    !>          It must be at least zero.
    !>

    KBAND

    !>          KBAND is INTEGER
    !>          The bandwidth of the matrix S.  It may only be zero or one.
    !>          If zero, then S is diagonal, and SE is not referenced.  If
    !>          one, then S is symmetric tri-diagonal.
    !>

    AD

    !>          AD is REAL array, dimension (N)
    !>          The diagonal of the original (unfactored) matrix A.  A is
    !>          assumed to be symmetric tridiagonal.
    !>

    AE

    !>          AE is REAL array, dimension (N-1)
    !>          The off-diagonal of the original (unfactored) matrix A.  A
    !>          is assumed to be symmetric tridiagonal.  AE(1) is the (1,2)
    !>          and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.
    !>

    SD

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

    SE

    !>          SE is REAL array, dimension (N-1)
    !>          The off-diagonal of the (symmetric tri-) diagonal matrix S.
    !>          Not referenced if KBSND=0.  If KBAND=1, then AE(1) is the
    !>          (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2)
    !>          element, etc.
    !>

    U

    !>          U is REAL array, dimension (LDU, N)
    !>          The orthogonal matrix in the decomposition.
    !>

    LDU

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

    WORK

    !>          WORK is REAL array, dimension (N*(N+1))
    !>

    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.
    !>          RESULT(1) is always modified.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 125 of file sstt21.f.

Author

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