TESTING/MATGEN/dlatm5.f(3)

NAME 💖

TESTING/MATGEN/dlatm5.f — this is the DLATM5 subroutine page, bestie. Manual name? Library Functions Manual. The whole icon situation is TESTING/MATGEN/dlatm5.f(3).

SYNOPSIS ✨

Functions/Subroutines 🦋

• DLATM5 — the one and only subroutine here. Signature, copied exact:

       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 🌈

Here’s the full dlatm5 signature, no cap:

       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 💖

okay so 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; it points to a certain type of the matrices to generate (see further details below 👀).
• 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.

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💖 that’s the whole vibe, bestie — LAPACK Version 3.12.0, straight from TESTING/MATGEN/dlatm5.f(3). byeee 🫶