/home/abui...N/clatm5.f(3)

💅 clatm5.f(3) — Library Functions Manual ✨

Okay so this is the Library Functions Manual page for clatm5.f(3), bestie. It's giving very specific LAPACK matrix-generation energy, and we're gonna get into every single detail 🫶

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/clatm5.f

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine CLATM5 (prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde,
    f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb)
    CLATM5

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👑 Function/Subroutine Documentation 👑

subroutine CLATM5 (integer prtype, integer m, integer n, complex, dimension(
    lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb,
    complex, dimension( ldc, * ) c, integer ldc, complex, dimension( ldd, *
    ) d, integer ldd, complex, dimension( lde, * ) e, integer lde, complex,
    dimension( ldf, * ) f, integer ldf, complex, dimension( ldr, * ) r,
    integer ldr, complex, dimension( ldl, * ) l, integer ldl, real alpha,
    integer qblcka, integer qblckb)

CLATM5 — that's the whole subroutine name, periodt 💅

🎀 Purpose 🎀

CLATM5 generates matrices involved in the Generalized Sylvester equation, bestie:

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 ] )

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💖 Parameters 💖

• PRTYPE — PRTYPE is INTEGER; it tells CLATM5 which certain type of matrices to generate (see further details, iykyk).
• 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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.

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💜 Author 💜

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

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🌈 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.

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Definition at line 265 of file clatm5.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie 💖 This is LAPACK Version 3.12.0, and the path at the end is /home/abui...N/clatm5.f(3). Slay and stay matrix-y ✨🎀