TESTING/EIG/dlatm4.f(3)

NAME
TESTING/EIG/dlatm4.f

SYNOPSIS

  Functions/Subroutines
subroutine dlatm4 (itype, n, nz1, nz2, isign, amagn, rcond, triang, idist, iseed, a, lda)
DLATM4

Function/Subroutine Documentation

  subroutine dlatm4 (integer itype, integer n, integer nz1, integer nz2, integer isign, double precision amagn, double precision rcond, double precision triang, integer idist, integer, dimension( 4 ) iseed, double precision, dimension( lda, * ) a, integer lda)

DLATM4

Purpose:

    !>
    !> DLATM4 generates basic square matrices, which may later be
    !> multiplied by others in order to produce test matrices.  It is
    !> intended mainly to be used to test the generalized eigenvalue
    !> routines.
    !>
    !> It first generates the diagonal and (possibly) subdiagonal,
    !> according to the value of ITYPE, NZ1, NZ2, ISIGN, AMAGN, and RCOND.
    !> It then fills in the upper triangle with random numbers, if TRIANG is
    !> non-zero.
    !>

Parameters
    ITYPE

    !>          ITYPE is INTEGER
    !>          The  of matrix on the diagonal and sub-diagonal.
    !>          If ITYPE < 0, then type abs(ITYPE) is generated and then
    !>             swapped end for end (A(I,J) := A'(N-J,N-I).)  See also
    !>             the description of AMAGN and ISIGN.
    !>
    !>          Special types:
    !>          = 0:  the zero matrix.
    !>          = 1:  the identity.
    !>          = 2:  a transposed Jordan block.
    !>          = 3:  If N is odd, then a k+1 x k+1 transposed Jordan block
    !>                followed by a k x k identity block, where k=(N-1)/2.
    !>                If N is even, then k=(N-2)/2, and a zero diagonal entry
    !>                is tacked onto the end.
    !>
    !>          Diagonal types.  The diagonal consists of NZ1 zeros, then
    !>             k=N-NZ1-NZ2 nonzeros.  The subdiagonal is zero.  ITYPE
    !>             specifies the nonzero diagonal entries as follows:
    !>          = 4:  1, ..., k
    !>          = 5:  1, RCOND, ..., RCOND
    !>          = 6:  1, ..., 1, RCOND
    !>          = 7:  1, a, a^2, ..., a^(k-1)=RCOND
    !>          = 8:  1, 1-d, 1-2*d, ..., 1-(k-1)*d=RCOND
    !>          = 9:  random numbers chosen from (RCOND,1)
    !>          = 10: random numbers with distribution IDIST (see DLARND.)
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix.
    !>

    NZ1

    !>          NZ1 is INTEGER
    !>          If abs(ITYPE) > 3, then the first NZ1 diagonal entries will
    !>          be zero.
    !>

    NZ2

    !>          NZ2 is INTEGER
    !>          If abs(ITYPE) > 3, then the last NZ2 diagonal entries will
    !>          be zero.
    !>

    ISIGN

    !>          ISIGN is INTEGER
    !>          = 0: The sign of the diagonal and subdiagonal entries will
    !>               be left unchanged.
    !>          = 1: The diagonal and subdiagonal entries will have their
    !>               sign changed at random.
    !>          = 2: If ITYPE is 2 or 3, then the same as ISIGN=1.
    !>               Otherwise, with probability 0.5, odd-even pairs of
    !>               diagonal entries A(2*j-1,2*j-1), A(2*j,2*j) will be
    !>               converted to a 2x2 block by pre- and post-multiplying
    !>               by distinct random orthogonal rotations.  The remaining
    !>               diagonal entries will have their sign changed at random.
    !>

    AMAGN

    !>          AMAGN is DOUBLE PRECISION
    !>          The diagonal and subdiagonal entries will be multiplied by
    !>          AMAGN.
    !>

    RCOND

    !>          RCOND is DOUBLE PRECISION
    !>          If abs(ITYPE) > 4, then the smallest diagonal entry will be
    !>          entry will be RCOND.  RCOND must be between 0 and 1.
    !>

    TRIANG

    !>          TRIANG is DOUBLE PRECISION
    !>          The entries above the diagonal will be random numbers with
    !>          magnitude bounded by TRIANG (i.e., random numbers multiplied
    !>          by TRIANG.)
    !>

    IDIST

    !>          IDIST is INTEGER
    !>          Specifies the type of distribution to be used to generate a
    !>          random matrix.
    !>          = 1:  UNIFORM( 0, 1 )
    !>          = 2:  UNIFORM( -1, 1 )
    !>          = 3:  NORMAL ( 0, 1 )
    !>

    ISEED

    !>          ISEED is INTEGER array, dimension (4)
    !>          On entry ISEED specifies the seed of the random number
    !>          generator.  The values of ISEED are changed on exit, and can
    !>          be used in the next call to DLATM4 to continue the same
    !>          random number sequence.
    !>          Note: ISEED(4) should be odd, for the random number generator
    !>          used at present.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA, N)
    !>          Array to be computed.
    !>

    LDA

    !>          LDA is INTEGER
    !>          Leading dimension of A.  Must be at least 1 and at least N.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 173 of file dlatm4.f.

Author

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