ZLATM4 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, RSIGN, 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 RSIGN.


          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 ZLARND.)

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.

RSIGN

          RSIGN is LOGICAL


          = .TRUE.:  The diagonal and subdiagonal entries will be


                     multiplied by random numbers of magnitude 1.


          = .FALSE.: The diagonal and subdiagonal entries will be


                     left as they are (usually non-negative real.)

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


          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


          On entry, DIST specifies the type of distribution to be used


          to generate a random matrix .


          = 1: real and imaginary parts each UNIFORM( 0, 1 )


          = 2: real and imaginary parts each UNIFORM( -1, 1 )


          = 3: real and imaginary parts each NORMAL( 0, 1 )


          = 4: complex number uniform in DISK( 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 ZLATM4 to continue the same


          random number sequence.


          Note: ISEED(4) should be odd, for the random number generator


          used at present.

A

          A is COMPLEX*16 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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