TESTING/EIG/dlatm4.f(3)    Library Functions Manual    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 'type' 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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/EIG/dlatm4.f(3)