TESTING/MATGEN/dlatm5.f(3)                            Library Functions Manual

NAME
       TESTING/MATGEN/dlatm5.f

SYNOPSIS
   Functions/Subroutines
       subroutine dlatm5 (prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e,
           lde, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb)
           DLATM5

Function/Subroutine Documentation
   subroutine dlatm5 (integer prtype, integer m, integer n, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( ldb, *
       ) b, integer ldb, double precision, dimension( ldc, * ) c, integer ldc,
       double precision, dimension( ldd, * ) d, integer ldd, double precision,
       dimension( lde, * ) e, integer lde, double precision, dimension( ldf, *
       ) f, integer ldf, double precision, dimension( ldr, * ) r, integer ldr,
       double precision, dimension( ldl, * ) l, integer ldl, double precision
       alpha, integer qblcka, integer qblckb)
       DLATM5

       Purpose:


            DLATM5 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
                     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 dlatm5.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0      TESTING/MATGEN/dlatm5.f(3)