TESTING/EIG/dsyt22.f(3)

NAME
TESTING/EIG/dsyt22.f

SYNOPSIS

  Functions/Subroutines
subroutine dsyt22 (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, result)
DSYT22

Function/Subroutine Documentation

  subroutine dsyt22 (integer itype, character uplo, integer n, integer m, 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)

DSYT22

Purpose:

          DSYT22  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 '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) = | 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, DSYT22 does nothing.
              It must be at least zero.
              Not modified.
      M       INTEGER
              The number of columns of U.  If it is zero, DSYT22 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       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.
              Not modified.
      LDA     INTEGER
              The leading dimension of A.  It must be at least 1
              and at least N.
              Not modified.
      D       DOUBLE PRECISION array, dimension (N)
              The diagonal of the (symmetric tri-) diagonal matrix.
              Not modified.
      E       DOUBLE PRECISION 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       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.
              Not modified.
      LDU     INTEGER
              The leading dimension of U.  LDU must be at least N and
              at least 1.
              Not modified.
      V       DOUBLE PRECISION 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     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.
              Not modified.
      WORK    DOUBLE PRECISION array, dimension (2*N**2)
              Workspace.
              Modified.
      RESULT  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 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 dsyt22.f.

Author

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