/home/abui..._gercond.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 /home/abui..._gercond.f(3) 💅

okay bestie, welcome to the Library Functions Manual page for this LAPACK source file. it's giving “deep math but make it group chat” ✨ no cap, we're gonna walk through every single parameter so you don't get lost.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dla_gercond.f

That's the file we're talking about, periodt. 💖

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

       double precision function DLA_GERCOND (trans, n, a, lda, af, ldaf, ipiv,
           cmode, c, info, work, iwork)

DLA_GERCOND estimates the Skeel condition number for a general matrix. cute little summary, exactly what it says 😌

🦋 Function/Subroutine Documentation 🦋

   double precision function DLA_GERCOND (character trans, integer n, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
       integer cmode, double precision, dimension( * ) c, integer info, double
       precision, dimension( * ) work, integer, dimension( * ) iwork)

DLA_GERCOND estimates the Skeel condition number for a general matrix. again, that's the one-line tea ☕

🔥 Purpose 🔥

okay so here's the whole point 💅 DLA_GERCOND estimates the Skeel condition number of op(A) * op2(C), where op2 is picked by CMODE like this:

CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)

The Skeel condition number is cond(A) = norminf( |inv(A)||A| ), and it's computed by finding scaling factors R such that diag(R)*A*op2(C) is row equilibrated, then computing the standard infinity-norm condition number. math girlies rise 🧚‍♀️✨

🌈 Parameters 🌈

🌟 TRANS 🌟

TRANS is CHARACTER*1 — this tells you what form the system of equations is in:

= 'N':  A * X = B     (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

🌟 N 🌟

N is INTEGER — the number of linear equations, i.e., the order of the matrix A. N >= 0. 🫶

🌟 A 🌟

A is DOUBLE PRECISION array, dimension (LDA,N) — on entry, the N-by-N matrix A.

🌟 LDA 🌟

LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,N).

🌟 AF 🌟

AF is DOUBLE PRECISION array, dimension (LDAF,N) — the factors L and U from the factorization A = P*L*U as computed by DGETRF.

🌟 LDAF 🌟

LDAF is INTEGER — the leading dimension of the array AF. LDAF >= max(1,N).

🌟 IPIV 🌟

IPIV is INTEGER array, dimension (N) — the pivot indices from the factorization A = P*L*U as computed by DGETRF; row i of the matrix was interchanged with row IPIV(i). iykyk 🔥

🌟 CMODE 🌟

CMODE is INTEGER — determines op2(C) in the formula op(A) * op2(C) as follows:

CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)

🌟 C 🌟

C is DOUBLE PRECISION array, dimension (N) — the vector C in the formula op(A) * op2(C).

🌟 INFO 🌟

INFO is INTEGER — here's the status tea:

= 0:  Successful exit.
i > 0:  The ith argument is invalid.

🌟 WORK 🌟

WORK is DOUBLE PRECISION array, dimension (3*N) — workspace. 🛠️

🌟 IWORK 🌟

IWORK is INTEGER array, dimension (N) — workspace. 🛠️

💖 Author 💖

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

Definition at line 149 of file dla_gercond.f. — that's exactly where it lives, iykyk ✨

🎀 Author 🎀

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okay bestie, that's the whole page 💖 — LAPACK Version 3.12.0, from the page file /home/abui..._gercond.f(3). No date is listed in the footer, so I'm not gonna invent one, periodt. 🦋💜

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