/home/abui...N/dlatm5.f(3)

🦋 DLATM5 — the matrix maker 💅

okay so this little icon is straight out of the Library Functions Manual, and her whole gov job is generating matrices for the generalized Sylvester equation. no cap, she's a builder. ✨

The full path of this file is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/dlatm5.f

it's giving ✨deeply nested✨ but that's just how the LAPACK build tree rolls, bestie. 🎀

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🌸 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

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👑 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: text A * R - L * B = C D * R - L * E = F They also satisfy (the diagonalization condition) text [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] )

like, she doesn't just make matrices, she makes matrices that behave. main character energy fr fr. 🔥

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🌈 Parameters 🌈

• PRTYPE — PRTYPE is INTEGER, and it points to a certain type of the matrices to generate (see further details, bestie, there's a whole section for this 👀).
• 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. ⚠️

side note bestie: those last two are NOT referenced unless PRTYPE = 3, so don't come for me if they do nothing. 💀

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🧚 Author 🧚

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

the whole squad showed up for this one 🫶👑

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⭐ Further Details: ⭐

PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices text 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. text 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). (and yes, the E block literally says D(i, j) — I'm just the messenger, I don't write the source code, I only vibe with it 😭)

PRTYPE = 4 Full text 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 dlatm5.f. 📍

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (not me writing a heartfelt paragraph, a robot did this, and honestly? she ate. 🤖✨)

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and that's the whole page bestie — LAPACK, Version 3.12.0, closing out at /home/abui...N/dlatm5.f(3). slay, go generate some matrices, ily 💅💖🎀