la_gerpvgrw(3)

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version 3.12.1 · 9 versions
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💅 la_gerpvgrw(3) 💅

okay bestie, welcome to the Library Functions Manual page for la_gerpvgrw — title is right there, manual name is folded in near the top, we love a lowkey header moment 💖. This page is all about reciprocal pivot growth, and we’re keeping every function, every parameter, every author credit, and every Definition at line ... of file ... because we are thorough and iconic. periodt.

🎀 NAME 🎀

la_gerpvgrw — la_gerpvgrw: reciprocal pivot growth. That’s the name, that’s the vibe: reciprocal pivot growth, no cap 💅.

✨ SYNOPSIS ✨

🌈 Functions 🌈

here’s the whole lineup, bestie — signatures verbatim because we do not play with code:

real function cla_gerpvgrw (n, ncols, a, lda, af, ldaf)
    CLA_GERPVGRW multiplies a square real matrix by a complex matrix.
double precision function dla_gerpvgrw (n, ncols, a, lda, af, ldaf)
    DLA_GERPVGRW
real function sla_gerpvgrw (n, ncols, a, lda, af, ldaf)
    SLA_GERPVGRW
double precision function zla_gerpvgrw (n, ncols, a, lda, af, ldaf)
    ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.

🦋 Detailed Description 🦋

no extra lore here — the page goes straight into the function documentation. keep scrolling, bestie, the four function breakdowns are right below 🫶.

🌸 Function Documentation 🌸

💜 real function cla_gerpvgrw 💜

real function cla_gerpvgrw (integer n, integer ncols, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf)

CLA_GERPVGRW multiplies a square real matrix by a complex matrix. yes, that’s the one-liner, and yes, we’re keeping it exactly as the page says.

Purpose:

okay so CLA_GERPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The page literally says The norm is used. with a double space and no norm type named, so I’m not guessing a norm — I’m just holding the source’s hand and keeping it as-is 💀. 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. that’s the important caveat, bestie — don’t ignore it.

Parameters:

  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NCOLS — NCOLS is INTEGER. The number of columns of the matrix A. NCOLS >= 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 factors L and U from the factorization A = P*L*U as computed by CGETRF.
  • LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).

Author:

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

Definition: Definition at line 97 of file cla_gerpvgrw.f.

💙 double precision function dla_gerpvgrw 💙

double precision function dla_gerpvgrw (integer n, integer ncols, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf)

DLA_GERPVGRW — that’s the entire one-liner description, and we respect the minimalism.

Purpose:

DLA_GERPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The source says The norm is used. — same double-space situation, same refusal to invent a norm type 🙈. 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. technical caveat, still loud and clear.

Parameters:

  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NCOLS — NCOLS is INTEGER. The number of columns of the matrix A. NCOLS >= 0.
  • A — A is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by DGETRF.
  • LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).

Author:

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

Definition: Definition at line 98 of file dla_gerpvgrw.f.

💖 real function sla_gerpvgrw 💖

real function sla_gerpvgrw (integer n, integer ncols, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf)

SLA_GERPVGRW — again, the one-liner is just the name, and honestly? iconic minimalism.

Purpose:

SLA_GERPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The page’s exact text is The norm is used. — double space, missing norm name, not my business to fill in 🫠. 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. same warning, same energy: this matters.

Parameters:

  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NCOLS — NCOLS is INTEGER. The number of columns of the matrix A. NCOLS >= 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 factors L and U from the factorization A = P*L*U as computed by SGETRF.
  • LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).

Author:

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

Definition: Definition at line 96 of file sla_gerpvgrw.f.

💛 double precision function zla_gerpvgrw 💛

double precision function zla_gerpvgrw (integer n, integer ncols, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf)

ZLA_GERPVGRW multiplies a square real matrix by a complex matrix. yes bestie, that’s the exact description, and we are not editing it.

Purpose:

ZLA_GERPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The source text says The norm is used. — double space and all — so no invented norm type from me 💅. 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. that’s the caveat, and it’s staying.

Parameters:

  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NCOLS — NCOLS is INTEGER. The number of columns of the matrix A. NCOLS >= 0.
  • A — A is COMPLEX*16 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*16 array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by ZGETRF.
  • LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).

Author:

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

Definition: Definition at line 98 of file zla_gerpvgrw.f.

👑 Author 👑

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k love u bye bestie 💖 — this page is from LAPACK, Version 3.12.0, and its page name is la_gerpvgrw(3). the footer didn’t give a date, so no fake date from me 💀🫶.

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