CBDT02(3)

🎀 NAME 🎀

ok so bestie, buckle up — this page is from the Library Functions Manual, and the star of the show is this file:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cbdt02.f

like yes that's a whole mouthful of a path, we know. it's the cbdt02.f source file living in the LAPACK TESTING/EIG directory and it's iconic. 💅

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

ok here's the actual call, no cap:

subroutine CBDT02 (m, n, b, ldb, c, ldc, u, ldu, work, rwork, resid)
    CBDT02

that's it. that's the whole vibe. CBDT02 with eleven arguments and main character energy. 👑

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💖 Function/Subroutine Documentation 💖

🦋 the full signature, in all its glory

subroutine CBDT02 (integer m, integer n, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( ldc, * ) c, integer ldc, complex,
    dimension( ldu, * ) u, integer ldu, complex, dimension( * ) work, real,
    dimension( * ) rwork, real resid)
    CBDT02

look at her. so many arguments. so many dimensions. we love a thorough queen. 🫶

⭐ Purpose

ok so what does this actually do, you ask? CBDT02 tests the change of basis C = U**H * B by computing the residual — and here's the formula, exactly as written, because she's important:

RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),

where B and C are M by N matrices, U is an M by M orthogonal matrix, and EPS is the machine precision. literally that's the whole job. measure how badly the change of basis went. slay. ✨

🎀 Parameters

ok parameter time, bestie, and there's a LOT of them so stay with me:

• M — M is INTEGER, and it's The number of rows of the matrices B and C and the order of the matrix Q. (yes it really says Q in there — we did not make that up, that's canon, we're just reading it to you verbatim 💀)
• N — N is INTEGER, The number of columns of the matrices B and C.
• B — B is COMPLEX array, dimension (LDB,N), and it's The m by n matrix B.
• LDB — LDB is INTEGER, The leading dimension of the array B. LDB >= max(1,M). bestie, respect the >=, it's not a suggestion. 🙈
• C — C is COMPLEX array, dimension (LDC,N), and it's The m by n matrix C, assumed to contain U**H * B. assumed — meaning you better have put that there correctly or the whole test is giving nothing. 💀
• LDC — LDC is INTEGER, The leading dimension of the array C. LDC >= max(1,M).
• U — U is COMPLEX array, dimension (LDU,M), and it's The m by m orthogonal matrix U. the main character matrix, honestly. 👑
• LDU — LDU is INTEGER, The leading dimension of the array U. LDU >= max(1,M).
• WORK — WORK is COMPLEX array, dimension (M) — that's it, that's the whole description, no notes. 🫶
• RWORK — RWORK is REAL array, dimension (M) — same deal, short and sweet. 🌸
• RESID — RESID is REAL, and then the formula again for the people in the back:

RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),

that's your answer, that's your output, that's the whole point of the function. periodt. 💅

ngl, that RESID line is the payoff of the entire page — it's the residual the routine computes, so if you're comparing numbers later, that's the one. 🔥

👑 Author

the brains behind the operation, take a bow:

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

Definition at line 118 of file cbdt02.f. — line 118, bestie, go look, we'll wait. 🦋

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

yep, nobody hand-wrote this one, the robots did it, and honestly? they ate. 🤖✨

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and that's the whole page, bestie — go forth and test those bases 🧚💜

cute little sign-off: this gorgeousness is LAPACK, Version 3.12.0, and it lives at /home/abui...IG/cbdt02.f(3). mwah. 💋🍓