SRC/sla_syrpvgrw.f(3)

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version 3.12.1 · 7 versions
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SRC/sla_syrpvgrw.f 💅

okay so this page is from the Library Functions Manual, and it's giving “small Fortran routine, serious linear algebra business” energy. Let's go, bestie. 🫶

💖 NAME 💖

SRC/sla_syrpvgrw.f

✨ SYNOPSIS ✨

Functions/Subroutines

real function sla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)

SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix. slay. ✨

🎀 Function/Subroutine Documentation 🎀

Full signature, character for character, no cap:

real function sla_syrpvgrw (character*1 uplo, integer n, integer info, real,
    dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af,
    integer ldaf, integer, dimension( * ) ipiv, real, dimension( * ) work)

SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

Purpose

okay so the purpose block is basically a vibe check on your factorization. It says: SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The norm is used. (Yes, there are two spaces there in the source — I'm not fixing it, I'm respecting the lore. 😭) If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

Parameters

  • UPLO — CHARACTER*1:
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • INFO — INTEGER. The value of INFO returned from SSYTRF, .i.e., the pivot in column INFO is exactly 0.
  • A — REAL array, dimension (LDA,N). On entry, the N-by-N matrix A.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • AF — REAL array, dimension (LDAF,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF.
  • LDAF — INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by SSYTRF.
  • WORK — REAL array, dimension (2*N).

Author

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

Definition at line 120 of file sla_syrpvgrw.f.

Author

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