TESTING/EIG/cbdt01.f(3)

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version 3.12.1 · 2 versions
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🦋 TESTING/EIG/cbdt01.f 🦋

okay bestie so this is TESTING/EIG/cbdt01.f — a whole page straight out of the `LAPACK test suite, and honestly it's giving "trust but verify" energy 💅. it's the manual name, it's the whole vibe, we move.

✨ NAME ✨

TESTING/EIG/cbdt01.f — literally just the file itself, no cap 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine cbdt01 (m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, rwork, resid) — the main character herself, CBDT01 👑

💜 Function/Subroutine Documentation 💜

subroutine cbdt01 (integer m, integer n, integer kd, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldq, * ) q, integer ldq, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldpt, * ) pt, integer ldpt, complex, dimension( * ) work, real, dimension( * ) rwork, real resid)

CBDT01 ⭐

Purpose 🎀

!>
!> CBDT01 reconstructs a general matrix A from its bidiagonal form
!>    A = Q * B * P**H
!> where Q (m by min(m,n)) and P**H (min(m,n) by n) are unitary
!> matrices and B is bidiagonal.
!>
!> The test ratio to test the reduction is
!>    RESID = norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
!> where EPS is the machine precision.
!>

so basically it takes your bidiagonal B and the unitary friends Q and P**H, glues A = Q * B * P**H back together, and then measures how badly that gluing missed 💀 — that's RESID. and EPS is the machine precision, iykyk.

🌈 Parameters 🌈

  • M — M is INTEGER, the number of rows of the matrices A and Q. row count, periodt.
  • N — N is INTEGER, the number of columns of the matrices A and P**H. column count, she's counting too 💅
  • KD — KD is INTEGER, and this one's the vibe check on how the reduction happened:
    • If KD = 0, B is diagonal and the array E is not referenced. (E gets to sit this one out 🙈)
    • 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.
  • A — A is COMPLEX array, dimension (LDA,N), the m by n matrix A. yes, the actual star of the show ✨
  • LDA — LDA is INTEGER, the leading dimension of the array A. Constraint: LDA >= max(1,M). respect the constraint fr fr 🫶
  • Q — Q is COMPLEX array, dimension (LDQ,N), the m by min(m,n) unitary matrix Q in the reduction A = Q * B * P**H. unitary icon behavior 👑
  • LDQ — LDQ is INTEGER, the leading dimension of the array Q. Constraint: LDQ >= max(1,M).
  • D — D is REAL array, dimension (min(M,N)), the diagonal elements of the bidiagonal matrix B. the main diagonal, the moment 🎀
  • E — E is REAL 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. she switches sides depending on the shape, we love a flexible queen 💜
  • PT — PT is COMPLEX array, dimension (LDPT,N), the min(m,n) by n unitary matrix P**H in the reduction A = Q * B * P**H.
  • LDPT — LDPT is INTEGER, the leading dimension of the array PT. Constraint: LDPT >= max(1,min(M,N)).
  • WORK — WORK is COMPLEX array, dimension (M+N). workspace, doing the invisible labor 😭
  • RWORK — RWORK is REAL array, dimension (M). more workspace, this time the real kind 🌸
  • RESID — RESID is REAL, the test ratio:
norm(A - Q * B * P**H) / ( n * norm(A) * EPS )

this is the moment of truth — small number = slay, big number = something's wrong bestie 💀🔥

🧚 Author 🧚

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

Definition at line 145 of file cbdt01.f. (yes, line 145, we cite our sources 💅)

🍓 Author (the meta one) 🍓

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a robot doing its little robot thing 🤖✨

heads up bestie: RESID is the whole point of this routine — it's not returning your matrix, it's returning a verdict. the ratio is normalized by n * norm(A) * EPS, so read it as "how many epsilons of wrongness per column, relative to the size of A" 🫶

and that's the page!! brought to you by LAPACK, Version 3.12.0, dated with all the love on TESTING/EIG/cbdt01.f(3) — mwah, go reconstruct something beautiful 💖🎀🦋

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