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.

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.

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