la_gbrpvgrw(3)

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💅 la_gbrpvgrw — Library Functions Manual 💅

okay so bestie, welcome to la_gbrpvgrw(3) from the Library Functions Manual. This is the page for four little sibling routines that all do the exact same iconic thing, just in different precisions. Pull up a chair, we're getting into it 🫶

🌸 NAME 🌸

la_gbrpvgrw — reciprocal pivot growth. that's it, that's the whole vibe ✨

🦋 SYNOPSIS 🦋

✨ Functions ✨

here's the whole squad, four functions, same job, different vibes:

real function cla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb)

CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

double precision function dla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb)

DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

real function sla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb)

SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

double precision function zla_gbrpvgrw (n, kl, ku, ncols, ab, ldab, afb, ldafb)

ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

🎀 Detailed Description 🎀

okay so like, this is where it gets real. below you'll find the full Function Documentation for each of the four routines — every parameter, every bound, every file and line number, all of it, no skimping 💖

👑 Function Documentation 👑

💜 real function cla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb)

CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. main character energy fr fr 💅

🔥 Purpose

!> !> CLA_GBRPVGRW 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. !>

Translation bestie: if that number comes back much less than 1, the LU factorization of the (equilibrated) matrix A could be poor — and that means the solution X, the estimated condition numbers, and the error bounds could all be unreliable. so like, don't trust them. periodt 🙈

🧚 Parameters

  • N — !> N is INTEGER / !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0.
  • KL — !> KL is INTEGER / !> The number of subdiagonals within the band of A. KL >= 0.
  • KU — !> KU is INTEGER / !> The number of superdiagonals within the band of A. KU >= 0.
  • NCOLS — !> NCOLS is INTEGER / !> The number of columns of the matrix A. NCOLS >= 0.
  • AB — !> AB is COMPLEX array, dimension (LDAB,N) / !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. / !> The j-th column of A is stored in the j-th column of the !> array AB as follows: / !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
  • LDAB — !> LDAB is INTEGER / !> The leading dimension of the array AB. LDAB >= KL+KU+1.
  • AFB — !> AFB is COMPLEX array, dimension (LDAFB,N) / !> Details of the LU factorization of the band matrix A, as !> computed by CGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1.
  • LDAFB — !> LDAFB is INTEGER / !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.

🌈 Author

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

⭐ Definition

Definition at line 115 of file cla_gbrpvgrw.f.

🌸 double precision function dla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb)

DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. same routine, double the precision, double the slay 💖

🔥 Purpose

!> !> DLA_GBRPVGRW 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. !>

yes it's the same cautionary tale, and yes it still means the solution X, estimated condition numbers, and error bounds could be unreliable when this comes back much less than 1. the drama is consistent 😭

🧚 Parameters

  • N — !> N is INTEGER / !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0.
  • KL — !> KL is INTEGER / !> The number of subdiagonals within the band of A. KL >= 0.
  • KU — !> KU is INTEGER / !> The number of superdiagonals within the band of A. KU >= 0.
  • NCOLS — !> NCOLS is INTEGER / !> The number of columns of the matrix A. NCOLS >= 0.
  • AB — !> AB is DOUBLE PRECISION array, dimension (LDAB,N) / !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. / !> The j-th column of A is stored in the j-th column of the !> array AB as follows: / !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
  • LDAB — !> LDAB is INTEGER / !> The leading dimension of the array AB. LDAB >= KL+KU+1.
  • AFB — !> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) / !> Details of the LU factorization of the band matrix A, as !> computed by DGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1.
  • LDAFB — !> LDAFB is INTEGER / !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.

🌈 Author

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

⭐ Definition

Definition at line 115 of file dla_gbrpvgrw.f.

okay bestie we're only halfway through the squad — sla_gbrpvgrw and zla_gbrpvgrw are literally right there waiting, and they brought the exact same parameter list with them 🦋💜

🌸 AUTHOR 🌸

Okay bestie, real talk — nobody hand-wrote this one. This page was literally generated automatically by Doxygen for LAPACK from the source code. So there's no mysterious human author to stan, just a doc generator doing its thing and spitting out the page you're reading right now. It's giving "the algorithm ate and left no crumbs" 💅✨

And that's a wrap, bestie!! 🎀 This little beauty came straight out of LAPACK, Version 3.12.0, auto-generated by Doxygen from the source code — so if you ever need to cite it, that's your vibe. Now go forth and gbrpvgrw something iconic 💖🦋⭐

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