SRC/cla_gbrpvgrw.f(3)

💅 SRC/cla_gbrpvgrw.f — LAPACK Library Functions Manual 🎀

okay so bestie, welcome to the group chat. this is a page from the LAPACK manual (that's the Library Functions Manual, mwah) and it's all about one very specific little function. buckle up, it's actually kinda cute. 🦋

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✨ SYNOPSIS ✨

Functions/Subroutines

• 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.

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🌸 Function/Subroutine 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. that's the whole vibe. 💖

👑 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.
!>

so like, literally: if that number comes back way less than 1, the LU factorization of the (equilibrated) matrix A could be shaky, and that means your solution X, your estimated condition numbers, and your error bounds could all be unreliable. not me warning you about that. 🫶

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✨ Parameters ✨

• N

!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>

it's the number of linear equations, aka the order of the matrix A. and N >= 0, no cap. 💅

• KL

!>          KL is INTEGER
!>     The number of subdiagonals within the band of A.  KL >= 0.
!>

the number of subdiagonals within the band of A. KL >= 0. slay. ✨

• KU

!>          KU is INTEGER
!>     The number of superdiagonals within the band of A.  KU >= 0.
!>

the number of superdiagonals within the band of A. KU >= 0. iconic. 🎀

• NCOLS

!>          NCOLS is INTEGER
!>     The number of columns of the matrix A.  NCOLS >= 0.
!>

the number of columns of the matrix A. NCOLS >= 0. so many numbers bestie 😭

• 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)
!>

it's a COMPLEX array, dimension (LDAB,N). on entry it holds the matrix A in band storage, in rows 1 to KL+KU+1. and the j-th column of A lives in the j-th column of the array AB like this: AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl). copy that exactly, bestie, i'm not kidding 🙈

• LDAB

!>          LDAB is INTEGER
!>     The leading dimension of the array AB.  LDAB >= KL+KU+1.
!>

the leading dimension of the array AB. and it better be LDAB >= KL+KU+1 or we're gonna have a problem. 💀

• 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.
!>

a COMPLEX array, dimension (LDAFB,N). it's giving 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. obsessed with this storage scheme honestly 🌈

• LDAFB

!>          LDAFB is INTEGER
!>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
!>

the leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. periodt. 💜

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👑 Author 👑

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

absolute legends, all of them 🫶

Definition at line 115 of file cla_gbrpvgrw.f. go look, iykyk ⭐

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. so like, not a human wrote this one, the robot did, and honestly? it ate. 💅

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LAPACK · Version 3.12.0 · SRC/cla_gbrpvgrw.f(3)

kk that's the whole page bestie, go forth and compute your reciprocal pivot growth factor responsibly. mwah 💖🎀🦋✨