slatm4.f - Man Page

subroutine slatm4 (itype, n, nz1, nz2, isign, amagn, rcond, triang, idist, iseed, a, lda)
SLATM4

SLATM4

Purpose:

 SLATM4 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 SLARND.)

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 REAL
          The diagonal and subdiagonal entries will be multiplied by
          AMAGN.

RCOND

          RCOND is REAL
          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 REAL
          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 SLATM4 to continue the same
          random number sequence.
          Note: ISEED(4) should be odd, for the random number generator
          used at present.

A

          A is REAL 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 slatm4.f.