TESTING/EIG/dbdt01.f(3)

💖 TESTING/EIG/dbdt01.f(3) 💖 — from the Library Functions Manual 🦋

okay bestie, this page is all about TESTING/EIG/dbdt01.f — yes, the file name is literally the whole NAME vibe. it's giving Fortran test-subroutine main character energy, and we're about to read the tea on DBDT01. no cap. 💅

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✨ NAME ✨

TESTING/EIG/dbdt01.f — the manual page for the DBDT01 bidiagonal-reconstruction test subroutine. lowkey iconic, fr fr. 🎀

💅 SYNOPSIS 💅

🌸 Functions/Subroutines 🌸

• subroutine dbdt01 (m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, resid) — DBDT01

🌈 Function/Subroutine Documentation 🌈

💖 subroutine dbdt01 💖

   subroutine dbdt01 (integer m, integer n, integer kd, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( ldq, *
       ) q, integer ldq, double precision, dimension( * ) d, double precision,
       dimension( * ) e, double precision, dimension( ldpt, * ) pt, integer
       ldpt, double precision, dimension( * ) work, double precision resid)

DBDT01

🎀 Purpose 🎀

okay so DBDT01 reconstructs a general matrix A from its bidiagonal form

A = Q * B * P**T

where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal matrices and B is bidiagonal. literally the whole glow-up from bidiagonal back to general, and we're obsessed. ✨

The test ratio to test the reduction is

RESID = norm(A - Q * B * P**T) / ( n * norm(A) * EPS )

where EPS is the machine precision. slay, that's the accuracy check. 💅

💖 Parameters 💖

• M — M is INTEGER; the number of rows of the matrices A and Q. 🫶
• N — N is INTEGER; the number of columns of the matrices A and P**T. 🌸
• KD — KD is INTEGER; if KD = 0, B is diagonal and the array E is not referenced. If KD = 1, the reduction was performed by xGEBRD; B is upper bidiagonal if M >= N, and lower bidiagonal if M < N. If KD = -1, the reduction was performed by xGBBRD; B is always upper bidiagonal. bestie, read that carefully, it's the whole vibe check. 👑
• A — A is DOUBLE PRECISION array, dimension (LDA,N); the m by n matrix A. 🦋
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M). ✨
• Q — Q is DOUBLE PRECISION array, dimension (LDQ,N); the m by min(m,n) orthogonal matrix Q in the reduction A = Q * B * P**T. 💜
• LDQ — LDQ is INTEGER; the leading dimension of the array Q. LDQ >= max(1,M). 🎀
• D — D is DOUBLE PRECISION array, dimension (min(M,N)); the diagonal elements of the bidiagonal matrix B. ⭐
• E — E is DOUBLE PRECISION array, dimension (min(M,N)-1); the superdiagonal elements of the bidiagonal matrix B if m >= n, or the subdiagonal elements of B if m < n. 🌈
• PT — PT is DOUBLE PRECISION array, dimension (LDPT,N); the min(m,n) by n orthogonal matrix P**T in the reduction A = Q * B * P**T. 🧚
• LDPT — LDPT is INTEGER; the leading dimension of the array PT. LDPT >= max(1,min(M,N)). 💖
• WORK — WORK is DOUBLE PRECISION array, dimension (M+N). 🔥
• RESID — RESID is DOUBLE PRECISION; the test ratio: norm(A - Q * B * P**T) / ( n * norm(A) * EPS ). 😭

👑 Author 👑

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

Definition at line 139 of file dbdt01.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie! source/version/date check: source is LAPACK, version Version 3.12.0, page TESTING/EIG/dbdt01.f(3) — and the footer didn't hand us a date, so we're not making one up. periodt. 🫶✨