SRC/sla_porcond.f(3)

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🦋 SRC/sla_porcond.f(3) — Library Functions Manual

okay so bestie, this is the page for SRC/sla_porcond.f(3) from the Library Functions Manual, and it’s lowkey iconic because it’s all about estimating the Skeel condition number for a symmetric positive-definite matrix. Let’s get into it 💅

💖 NAME

SRC/sla_porcond.f

✨ SYNOPSIS

🫶 Functions/Subroutines

real function sla_porcond (uplo, n, a, lda, af, ldaf, cmode, c, info,
           work, iwork)
           SLA_PORCOND estimates the Skeel condition number for a symmetric
           positive-definite matrix.

🧚 Function/Subroutine Documentation

real function sla_porcond (character uplo, integer n, real, dimension( lda,
    * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, integer
    cmode, real, dimension( * ) c, integer info, real, dimension( * ) work,
    integer, dimension( * ) iwork)

SLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.

🌸 Purpose

No cap, here’s the exact purpose vibe:

SLA_PORCOND Estimates the Skeel condition number of  op(A) * op2(C)
where op2 is determined by CMODE as follows
CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)
The Skeel condition number  cond(A) = norminf( |inv(A)||A| )
is computed by computing scaling factors R such that
diag(R)*A*op2(C) is row equilibrated and computing the standard
infinity-norm condition number.

🎀 Parameters

💜 UPLO

UPLO is CHARACTER*1.

  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

💜 N

N is INTEGER.

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

💜 A

A is REAL 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 REAL array, dimension (LDAF,N).

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF.

💜 LDAF

LDAF is INTEGER.

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

💜 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 REAL array, dimension (N).

The vector C in the formula op(A) * op2(C).

💜 INFO

INFO is INTEGER.

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

💜 WORK

WORK is REAL 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 138 of file sla_porcond.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

💖 That’s the whole page, bestie — footer vibes are LAPACK Version 3.12.0, source SRC/sla_porcond.f(3), and the original footer doesn’t print a date, so I’m not inventing one fr fr. 🎀

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