SQRT16(3)

🌸 LAPACK Library Functions Manual — sqrt16.f(3) 🌸

okay so bestie, this is the page for sqrt16.f(3) in the LAPACK Library Functions Manual, and it’s literally about the subroutine SQRT16. no cap, we’re in linear-algebra residual-checking territory. 💅

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sqrt16.f

✨ SYNOPSIS ✨

🧸 Functions/Subroutines 🧸

subroutine SQRT16 (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork,
    resid)
    SQRT16

💖 Function/Subroutine Documentation 💖

Here’s the full signature, copied exactly, no edits, periodt:

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)

this icon is SQRT16.

🎀 Purpose 🎀

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. that’s the whole purpose, bestie. ✨

🧚 Parameters 🧚

Every param, every constraint, all of it:

💅 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.

🔥 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 📜

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off bestie: LAPACK Version 3.12.0, footer/page path /home/abui...IN/sqrt16.f(3) — that’s the source/version and footer date line, slay. 🫶💖