SRC/cla_gercond_x.f(3)

💅 SRC/cla_gercond_x.f — the LAPACK manual, bestie edition 🎀

okay so this page is from the Library Functions Manual, and it's literally all about one little function. sit down, grab a strawberry 🍓, we're gonna get through it together.

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✨ NAME ✨

SRC/cla_gercond_x.f — that's the file, that's the name, no cap. 💖

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• real function cla_gercond_x (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) — bestie. this one computes the infinity norm condition number of op(A)*diag(x) for general matrices. iconic behavior honestly. 👑

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🦋 Function/Subroutine Documentation 🦋

real function cla_gercond_x (character trans, integer n, complex, dimension(
    lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
    integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info,
    complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. that's the whole vibe. 💫

🎯 Purpose:

!>
!>
!>    CLA_GERCOND_X computes the infinity norm condition number of
!>    op(A) * diag(X) where X is a COMPLEX vector.
!>

so yeah — the infinity norm condition number of op(A) * diag(X), and X is a COMPLEX vector. periodt. 💅

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🌈 Parameters 🌈

TRANS

!>          TRANS is CHARACTER*1
!>     Specifies the form of the system of equations:
!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
!>

TRANS is a CHARACTER*1 and it tells us which form of the system of equations we're dealing with, iykyk:

• = 'N': A * X = B — no transpose, keeping it simple 🫶
• = 'T': A**T * X = B — transpose era
• = 'C': A**H * X = B — conjugate transpose, which here equals transpose, noted in the original as (Conjugate Transpose = Transpose) ✨

N

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

N is an INTEGER, the number of linear equations — aka the order of the matrix A. and N >= 0, no negatives allowed bestie. 🚫

A

!>          A is COMPLEX array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>

A is a COMPLEX array, dimension (LDA,N). on entry it's the N-by-N matrix A. main character matrix energy. 👑

LDA

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

LDA is an INTEGER, the leading dimension of the array A, and LDA >= max(1,N). rules are rules. 💅

AF

!>          AF is COMPLEX array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by CGETRF.
!>

AF is a COMPLEX array, dimension (LDAF,N) — it holds the factors L and U from the factorization A = P*L*U as computed by CGETRF. love that for us. 🔥

LDAF

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

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

IPIV

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

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

X

!>          X is COMPLEX array, dimension (N)
!>     The vector X in the formula op(A) * diag(X).
!>

X is a COMPLEX array, dimension (N) — the vector X in the formula op(A) * diag(X). the moment. 🌟

INFO

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

INFO is an INTEGER:

• = 0: successful exit, we ate. ✅
• i > 0: the *i*th argument is invalid 😭

WORK

!>          WORK is COMPLEX array, dimension (2*N).
!>     Workspace.
!>

WORK is a COMPLEX array, dimension (2*N). it's workspace, it's doing its thing. 🧚

RWORK

!>          RWORK is REAL array, dimension (N).
!>     Workspace.
!>

RWORK is a REAL array, dimension (N). also workspace. also slaying. ✨

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👑 Author 👑

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

the whole squad, honestly. 🫶

Definition at line 133 of file cla_gercond_x.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated 💀

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🎀 cute little sign-off: this lil page is LAPACK, Version 3.12.0, and it's the manual page for SRC/cla_gercond_x.f. go forth and condition those numbers, bestie. 💖🌟