slatm5.f - Man Page

subroutine slatm5 (prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb)
SLATM5

SLATM5

Purpose:

 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 ] )

Parameters

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  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.

Definition at line 265 of file slatm5.f.