TESTING/LIN/zqrt16.f(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

🎀 TESTING/LIN/zqrt16.f 🎀

okay bestie, buckle up — this one's a Fortran file living its best life in the LAPACK test suite (the manual name is literally TESTING/LIN/zqrt16.f, iykyk), and it's about to be your new fave 💅

✨ NAME ✨

TESTING/LIN/zqrt16.f — that's the whole vibe, that's the name, periodt.

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine zqrt16 (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid) — the one and only ZQRT16, our main character 👑

🦋 Function/Subroutine Documentation 🦋

subroutine zqrt16 (character trans, integer m, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) rwork, double precision resid)

ZQRT16

subroutine zqrt16 (character trans, integer m, integer n, integer nrhs,
     complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
     ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb,
     double precision, dimension( * ) rwork, double precision resid)

💖 Purpose: 💖

so here's the tea, bestie 🍵 — ZQRT16 computes the residual for a solution of a system of linear equations A*x = b or A'*x = b:

RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),

where EPS is the machine epsilon. literally that's it, that's the whole job ✨

🌈 Parameters 🌈

TRANS

  • TRANS is CHARACTER*1
  • Specifies the form of the system of equations, no cap:
    • = 'N': A *x = b
    • = 'T': A^T*x = b, where A^T is the transpose of A
    • = 'C': A^H*x = b, where A^H is the conjugate transpose of A

M

  • M is INTEGER
  • The number of rows of the matrix A. M >= 0. 🫶

N

  • N is INTEGER
  • The number of columns of the matrix A. N >= 0. 🫶

NRHS

  • NRHS is INTEGER
  • The number of columns of B, the matrix of right hand sides. NRHS >= 0. 😌

A

  • A is COMPLEX*16 array, dimension (LDA,N)
  • The original M x N matrix A. iconic behavior honestly 💜

LDA

  • LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,M). don't skip this, fr fr 🙈

X

  • X is COMPLEX*16 array, dimension (LDX,NRHS)
  • The computed solution vectors for the system of linear equations. the moment of truth ✨

LDX

  • LDX is INTEGER
  • The leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M). read it carefully bestie, it flips depending on TRANS 💀

B

  • B is COMPLEX*16 array, dimension (LDB,NRHS)
  • On entry, the right hand side vectors for the system of linear equations.
  • On exit, B is overwritten with the difference B - A*X. ⚠️ heads up — the original B does NOT survive, she gets replaced, no cap

LDB

  • LDB is INTEGER
  • The leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). same flip energy as LDX, keep up 🧚

RWORK

  • RWORK is DOUBLE PRECISION array, dimension (M)

RESID

  • RESID is DOUBLE PRECISION
  • The maximum over the number of right hand sides of
norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).

👑 Author 👑

the legends behind this:

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

🌟 Definition at line 131 of file zqrt16.f. 🌟

⭐ Author (again, yes really) ⭐

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a very diligent little doc generator doing its thing 🤖💫

ok that's the whole page bestie, you ate that reading session, genuinely obsessed 🫶

LAPACK 🌈 — Version 3.12.0 💖 — footer said TESTING/LIN/zqrt16.f(3) and honestly it deserved a cute lil sign-off: go forth and compute residuals, queen 👑✨

📦 where this page comes from