la_porpvgrw(3)

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🎀 la_porpvgrw(3) — Library Functions Manual 🎀

okay bestie, welcome to the la_porpvgrw(3) page from the Library Functions Manual — it's literally all about reciprocal pivot growth, and we're gonna get through it together. 💅✨

💖 NAME 💖

la_porpvgrw — la_porpvgrw: reciprocal pivot growth. That's the whole name section, no cap. 🫶

✨ SYNOPSIS ✨

🦋 Functions 🦋

real function cla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)
double precision function dla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)
real function sla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)
double precision function zla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)
  • real function cla_porpvgrw — CLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. 💖
  • double precision function dla_porpvgrw — DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. ✨
  • real function sla_porpvgrw — SLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. 🎀
  • double precision function zla_porpvgrw — ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. 🦋

🌸 Detailed Description 🌸

This is the “Detailed Description” zone, and honestly it's giving “the actual function docs are right below, bestie.” No extra tea here — the real breakdown lives in Function Documentation. 🫶

💜 Function Documentation 💜

💅 cla_porpvgrw 💅

real function cla_porpvgrw (character*1 uplo, integer ncols, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) work)

CLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. ✨

Purpose:

CLA_PORPVGRW 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. 😭

Parameters:

  • UPLO — CHARACTER*1
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • NCOLS — INTEGER The number of columns of the matrix A. NCOLS >= 0.
  • A — COMPLEX 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 — COMPLEX 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 CPOTRF.
  • LDAF — INTEGER The leading dimension of the array AF. LDAF >= max(1,N).
  • WORK — REAL array, dimension (2*N)

Author:

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

Definition at line 104 of file cla_porpvgrw.f.

💅 dla_porpvgrw 💅

double precision function dla_porpvgrw (character*1 uplo, integer ncols, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, double precision, dimension( * ) work)

DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. 🌈

Purpose:

DLA_PORPVGRW 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. 💀

Parameters:

  • UPLO — CHARACTER*1
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • NCOLS — INTEGER The number of columns of the matrix A. NCOLS >= 0.
  • A — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 DPOTRF.
  • LDAF — INTEGER The leading dimension of the array AF. LDAF >= max(1,N).
  • WORK — DOUBLE PRECISION array, dimension (2*N)

Author:

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

Definition at line 104 of file dla_porpvgrw.f.

💅 sla_porpvgrw 💅

real function sla_porpvgrw (character*1 uplo, integer ncols, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) work)

SLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. 🍓

Purpose:

SLA_PORPVGRW 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. 🙈

Parameters:

  • UPLO — CHARACTER*1
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • NCOLS — INTEGER The number of columns of the matrix A. NCOLS >= 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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF.
  • LDAF — INTEGER The leading dimension of the array AF. LDAF >= max(1,N).
  • WORK — REAL array, dimension (2*N)

Author:

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

Definition at line 103 of file sla_porpvgrw.f.

💅 zla_porpvgrw 💅

double precision function zla_porpvgrw (character*1 uplo, integer ncols, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, double precision, dimension( * ) work)

ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. 🧚

Purpose:

ZLA_PORPVGRW 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. 🔥

Parameters:

  • UPLO — CHARACTER*1
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • NCOLS — INTEGER The number of columns of the matrix A. NCOLS >= 0.
  • A — COMPLEX*16 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 — COMPLEX*16 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 ZPOTRF.
  • LDAF — INTEGER The leading dimension of the array AF. LDAF >= max(1,N).
  • WORK — DOUBLE PRECISION array, dimension (2*N)

Author:

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

Definition at line 105 of file zla_porpvgrw.f.

👑 Author 👑

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

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