TESTING/MATGEN/slatm5.f(3)

💖 TESTING/MATGEN/slatm5.f(3) 💖

okay so this is the Library Functions Manual page for TESTING/MATGEN/slatm5.f(3), and it's giving very serious matrix-generator business bestie. Like, we are in TESTING/MATGEN, and this page is about one subroutine that makes test matrices for the generalized Sylvester equation. No cap, it's a whole vibe. ✨

🌸 NAME 🌸

TESTING/MATGEN/slatm5.f

🎀 SYNOPSIS 🎀

✨ Functions/Subroutines ✨

       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

The routine is SLATM5, and yes, that's the whole synopsis tea. 💅

🛠️ Function/Subroutine Documentation 🛠️

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

SLATM5

🌼 Purpose: 🌼

okay so here's the main character moment: 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; 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 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.

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.

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

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.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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