TESTING/LIN/sqrt16.f(3)

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TESTING/LIN/sqrt16.f(3) 💅

okay bestie, this page lives in the Library Functions Manual, and it's all about TESTING/LIN/sqrt16.f. lowkey iconic. ✨

NAME 🌸

TESTING/LIN/sqrt16.f — that's the file, bestie. The main character here is SQRT16, a subroutine, and this page is its whole lore. 💖

SYNOPSIS ✨

Functions/Subroutines 🫶

subroutine sqrt16 (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork,
           resid)

SQRT16 — yeah, that's the synopsis vibe. 🫶

Function/Subroutine Documentation 🦋

subroutine sqrt16 (character trans, integer m, integer n, integer nrhs,
    real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x,
    integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension(
    * ) rwork, real resid)

SQRT16

Purpose 🎀

okay so SQRT16 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 the math version of a vibe check. no cap. 💅

Parameters 💖

  • TRANS — TRANS is CHARACTER*1; it specifies the form of the system of equations:
    • = 'N': A *x = b
    • = 'T': A'*x = b, where A' is the transpose of A
    • = 'C': A'*x = b, where A' is the 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 REAL array, dimension (LDA,N): the original M x N matrix A. 💜
  • LDA — LDA is INTEGER: the leading dimension of the array A. LDA >= max(1,M). 🌸
  • X — X is REAL array, dimension (LDX,NRHS): the computed solution vectors for the system of linear equations. ✨
  • 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). 🦋
  • B — B is REAL 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. important, bestie! 💀
  • 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). 👑
  • RWORK — RWORK is REAL array, dimension (M). 🧚
  • RESID — RESID is REAL: the maximum over the number of right hand sides of norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ). 🔥

Author 👑

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

Definition at line 131 of file sqrt16.f.

Author 💜

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kisses bestie, this page is from LAPACK Version 3.12.0, source TESTING/LIN/sqrt16.f(3) 💋✨ 🎀

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