CLA_SYRPVGRW(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 CLA_SYRPVGRW(3) — Library Functions Manual 🎀

okay so bestie, we're in the Library Functions Manual today and this one is a whole LAPACK vibe, so grab a strawberry drink 🍓 and let's get into it.

✨ NAME ✨

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

like, yes, the "name" is literally a file path. iconic of the build system honestly. 💀

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • real function CLA_SYRPVGRW (uplo, n, info, a, lda, af, ldaf, ipiv, work) — CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

👑 Function/Subroutine Documentation 👑

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

CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix. that's the whole assignment, no cap. 💖

🌸 Purpose 🌸

!> !> !> CLA_SYRPVGRW computes the reciprocal pivot growth factor !> norm(A)/norm(U). The norm is used. 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. !>

fr fr, lowkey important: if that factor comes back much less than 1, the LU factorization of the (equilibrated) matrix A could be unstable, and then your solution X, your estimated condition numbers, and your error bounds could all be unreliable. not me trusting a sketchy answer 😭

🧚 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.
  • INFO — INFO is INTEGER
    • The value of INFO returned from CSYTRF, .i.e., the pivot in column INFO is exactly 0.
  • A — A is COMPLEX 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 COMPLEX array, dimension (LDAF,N)
    • The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF.
  • LDAF — LDAF is INTEGER
    • The leading dimension of the array AF. LDAF >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N)
    • Details of the interchanges and the block structure of D as determined by CSYTRF.
  • WORK — WORK is REAL array, dimension (2*N)
    • that's it, that's the workspace, she's just vibing in there 🫶

⭐ Author ⭐

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

Definition at line 121 of file cla_syrpvgrw.f. 🔥

💜 Author 💜

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