TESTING/EIG/ssyt22.f(3)

NAME
TESTING/EIG/ssyt22.f

SYNOPSIS

  Functions/Subroutines
subroutine ssyt22 (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, result)
SSYT22

Function/Subroutine Documentation

  subroutine ssyt22 (integer itype, character uplo, integer n, integer m, integer kband, real, dimension( lda, * ) a, integer lda, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( * ) tau, real, dimension( * ) work, real, dimension( 2 ) result)

SSYT22

Purpose:

    !>
    !>      SSYT22  generally checks a decomposition of the form
    !>
    !>              A U = U S
    !>
    !>      where A is symmetric, the columns of U are orthonormal, and S
    !>      is diagonal (if KBAND=0) or symmetric tridiagonal (if
    !>      KBAND=1).  If ITYPE=1, then U is represented as a dense matrix,
    !>      otherwise the U is expressed as a product of Householder
    !>      transformations, whose vectors are stored in the array  and
    !>      whose scaling constants are in
     we shall use the letter
    !>       to refer to the product of Householder transformations
    !>      (which should be equal to U).
    !>
    !>      Specifically, if ITYPE=1, then:
    !>
    !>              RESULT(1) = | U**T A U - S | / ( |A| m ulp ) and
    !>              RESULT(2) = | I - U**T U | / ( m ulp )
    !>

    !>  ITYPE   INTEGER
    !>          Specifies the type of tests to be performed.
    !>          1: U expressed as a dense orthogonal matrix:
    !>             RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
    !>             RESULT(2) = | I - U U**T | / ( n ulp )
    !>
    !>  UPLO    CHARACTER
    !>          If UPLO='U', the upper triangle of A will be used and the
    !>          (strictly) lower triangle will not be referenced.  If
    !>          UPLO='L', the lower triangle of A will be used and the
    !>          (strictly) upper triangle will not be referenced.
    !>          Not modified.
    !>
    !>  N       INTEGER
    !>          The size of the matrix.  If it is zero, SSYT22 does nothing.
    !>          It must be at least zero.
    !>          Not modified.
    !>
    !>  M       INTEGER
    !>          The number of columns of U.  If it is zero, SSYT22 does
    !>          nothing.  It must be at least zero.
    !>          Not modified.
    !>
    !>  KBAND   INTEGER
    !>          The bandwidth of the matrix.  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.
    !>          Not modified.
    !>
    !>  A       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.
    !>          Not modified.
    !>
    !>  LDA     INTEGER
    !>          The leading dimension of A.  It must be at least 1
    !>          and at least N.
    !>          Not modified.
    !>
    !>  D       REAL array, dimension (N)
    !>          The diagonal of the (symmetric tri-) diagonal matrix.
    !>          Not modified.
    !>
    !>  E       REAL array, dimension (N)
    !>          The off-diagonal of the (symmetric tri-) diagonal matrix.
    !>          E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc.
    !>          Not referenced if KBAND=0.
    !>          Not modified.
    !>
    !>  U       REAL array, dimension (LDU, N)
    !>          If ITYPE=1 or 3, this contains the orthogonal matrix in
    !>          the decomposition, expressed as a dense matrix.  If ITYPE=2,
    !>          then it is not referenced.
    !>          Not modified.
    !>
    !>  LDU     INTEGER
    !>          The leading dimension of U.  LDU must be at least N and
    !>          at least 1.
    !>          Not modified.
    !>
    !>  V       REAL array, dimension (LDV, N)
    !>          If ITYPE=2 or 3, the lower triangle of this array contains
    !>          the Householder vectors used to describe the orthogonal
    !>          matrix in the decomposition.  If ITYPE=1, then it is not
    !>          referenced.
    !>          Not modified.
    !>
    !>  LDV     INTEGER
    !>          The leading dimension of V.  LDV must be at least N and
    !>          at least 1.
    !>          Not modified.
    !>
    !>  TAU     REAL array, dimension (N)
    !>          If ITYPE >= 2, then TAU(j) is the scalar factor of
    !>          v(j) v(j)**T in the Householder transformation H(j) of
    !>          the product  U = H(1)...H(n-2)
    !>          If ITYPE < 2, then TAU is not referenced.
    !>          Not modified.
    !>
    !>  WORK    REAL array, dimension (2*N**2)
    !>          Workspace.
    !>          Modified.
    !>
    !>  RESULT  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.  RESULT(2) is modified only
    !>          if LDU is at least N.
    !>          Modified.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 155 of file ssyt22.f.

Author

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