SLATM5 generates matrices involved in the Generalized Sylvester


 equation:


     A * R - L * B = C


     D * R - L * E = F


 They also satisfy (the diagonalization condition)


  [ I -L ] ( [ A  -C ], [ D -F ] ) [ I  R ] = ( [ A    ], [ D    ] )


  [    I ] ( [     B ]  [    E ] ) [    I ]   ( [    B ]  [    E ] )

PRTYPE

          PRTYPE is INTEGER


          'Points' to a certain type of the matrices to generate


          (see further details).

M

          M is INTEGER


          Specifies the order of A and D and the number of rows in


          C, F,  R and L.

N

          N is INTEGER


          Specifies the order of B and E and the number of columns in


          C, F, R and L.

A

          A is REAL array, dimension (LDA, M).


          On exit A M-by-M is initialized according to PRTYPE.

LDA

          LDA is INTEGER


          The leading dimension of A.

B

          B is REAL array, dimension (LDB, N).


          On exit B N-by-N is initialized according to PRTYPE.

LDB

          LDB is INTEGER


          The leading dimension of B.

C

          C is REAL array, dimension (LDC, N).


          On exit C M-by-N is initialized according to PRTYPE.

LDC

          LDC is INTEGER


          The leading dimension of C.

D

          D is REAL array, dimension (LDD, M).


          On exit D M-by-M is initialized according to PRTYPE.

LDD

          LDD is INTEGER


          The leading dimension of D.

E

          E is REAL array, dimension (LDE, N).


          On exit E N-by-N is initialized according to PRTYPE.

LDE

          LDE is INTEGER


          The leading dimension of E.

F

          F is REAL array, dimension (LDF, N).


          On exit F M-by-N is initialized according to PRTYPE.

LDF

          LDF is INTEGER


          The leading dimension of F.

R

          R is REAL array, dimension (LDR, N).


          On exit R M-by-N is initialized according to PRTYPE.

LDR

          LDR is INTEGER


          The leading dimension of R.

L

          L is REAL array, dimension (LDL, N).


          On exit L M-by-N is initialized according to PRTYPE.

LDL

          LDL is INTEGER


          The leading dimension of L.

ALPHA

          ALPHA is REAL


          Parameter used in generating PRTYPE = 1 and 5 matrices.

QBLCKA

          QBLCKA is INTEGER


          When PRTYPE = 3, specifies the distance between 2-by-2


          blocks on the diagonal in A. Otherwise, QBLCKA is not


          referenced. QBLCKA > 1.

QBLCKB

          QBLCKB is INTEGER


          When PRTYPE = 3, specifies the distance between 2-by-2


          blocks on the diagonal in B. Otherwise, QBLCKB is not


          referenced. QBLCKB > 1.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices


             A : if (i == j) then A(i, j) = 1.0


                 if (j == i + 1) then A(i, j) = -1.0


                 else A(i, j) = 0.0,            i, j = 1...M


             B : if (i == j) then B(i, j) = 1.0 - ALPHA


                 if (j == i + 1) then B(i, j) = 1.0


                 else B(i, j) = 0.0,            i, j = 1...N


             D : if (i == j) then D(i, j) = 1.0


                 else D(i, j) = 0.0,            i, j = 1...M


             E : if (i == j) then E(i, j) = 1.0


                 else E(i, j) = 0.0,            i, j = 1...N


             L =  R are chosen from [-10...10],


                  which specifies the right hand sides (C, F).


  PRTYPE = 2 or 3: Triangular and/or quasi- triangular.


             A : if (i <= j) then A(i, j) = [-1...1]


                 else A(i, j) = 0.0,             i, j = 1...M


                 if (PRTYPE = 3) then


                    A(k + 1, k + 1) = A(k, k)


                    A(k + 1, k) = [-1...1]


                    sign(A(k, k + 1) = -(sin(A(k + 1, k))


                        k = 1, M - 1, QBLCKA


             B : if (i <= j) then B(i, j) = [-1...1]


                 else B(i, j) = 0.0,            i, j = 1...N


                 if (PRTYPE = 3) then


                    B(k + 1, k + 1) = B(k, k)


                    B(k + 1, k) = [-1...1]


                    sign(B(k, k + 1) = -(sign(B(k + 1, k))


                        k = 1, N - 1, QBLCKB


             D : if (i <= j) then D(i, j) = [-1...1].


                 else D(i, j) = 0.0,            i, j = 1...M


             E : if (i <= j) then D(i, j) = [-1...1]


                 else E(i, j) = 0.0,            i, j = 1...N


                 L, R are chosen from [-10...10],


                 which specifies the right hand sides (C, F).


  PRTYPE = 4 Full


             A(i, j) = [-10...10]


             D(i, j) = [-1...1]    i,j = 1...M


             B(i, j) = [-10...10]


             E(i, j) = [-1...1]    i,j = 1...N


             R(i, j) = [-10...10]


             L(i, j) = [-1...1]    i = 1..M ,j = 1...N


             L, R specifies the right hand sides (C, F).


  PRTYPE = 5 special case common and/or close eigs.