TESTING/EIG/dsyt21.f(3)

NAME
TESTING/EIG/dsyt21.f

SYNOPSIS

  Functions/Subroutines
subroutine dsyt21 (itype, uplo, n, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, result)
DSYT21

Function/Subroutine Documentation

  subroutine dsyt21 (integer itype, character uplo, integer n, integer kband, 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( ldv, * ) v, integer ldv, double precision, dimension( * ) tau, double precision, dimension( * ) work, double precision, dimension( 2 ) result)

DSYT21

Purpose:

     DSYT21 generally checks a decomposition of the form
        A = U S U**T
     where **T means transpose, A is symmetric, U is orthogonal, 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 U is
     expressed as a product of Householder transformations, whose vectors
     are stored in the array 'V' and whose scaling constants are in 'TAU'.
     We shall use the letter 'V' to refer to the product of Householder
     transformations (which should be equal to U).
     Specifically, if ITYPE=1, then:
        RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
        RESULT(2) = | I - U U**T | / ( n ulp )
     If ITYPE=2, then:
        RESULT(1) = | A - V S V**T | / ( |A| n ulp )
     If ITYPE=3, then:
        RESULT(1) = | I - V U**T | / ( n ulp )
     For ITYPE > 1, the transformation U is expressed as a product
     V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)**T and each
     vector v(j) has its first j elements 0 and the remaining n-j elements
     stored in V(j+1:n,j).

Parameters
    ITYPE

              ITYPE is 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 )
              2: U expressed as a product V of Housholder transformations:
                 RESULT(1) = | A - V S V**T | / ( |A| n ulp )
              3: U expressed both as a dense orthogonal matrix and
                 as a product of Housholder transformations:
                 RESULT(1) = | I - V 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, DSYT21 does nothing.
              It must be at least zero.

    KBAND

              KBAND is 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.

    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 N.

    D

              D is DOUBLE PRECISION array, dimension (N)
              The diagonal of the (symmetric tri-) diagonal matrix.

    E

              E is DOUBLE PRECISION array, dimension (N-1)
              The off-diagonal of the (symmetric tri-) diagonal matrix.
              E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
              (3,2) element, etc.
              Not referenced if KBAND=0.

    U

              U is DOUBLE PRECISION 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.

    LDU

              LDU is INTEGER
              The leading dimension of U.  LDU must be at least N and
              at least 1.

    V

              V is DOUBLE PRECISION array, dimension (LDV, N)
              If ITYPE=2 or 3, the columns of this array contain the
              Householder vectors used to describe the orthogonal matrix
              in the decomposition.  If UPLO='L', then the vectors are in
              the lower triangle, if UPLO='U', then in the upper
              triangle.
              *NOTE* If ITYPE=2 or 3, V is modified and restored.  The
              subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')
              is set to one, and later reset to its original value, during
              the course of the calculation.
              If ITYPE=1, then it is neither referenced nor modified.

    LDV

              LDV is INTEGER
              The leading dimension of V.  LDV must be at least N and
              at least 1.

    TAU

              TAU is DOUBLE PRECISION 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.

    WORK

              WORK is DOUBLE PRECISION array, dimension (2*N**2)

    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.
              RESULT(1) is always modified.  RESULT(2) is modified only
              if ITYPE=1.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 205 of file dsyt21.f.

Author

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