SRC/sla_gbrpvgrw.f(3)

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version 3.12.1 · 4 versions
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okay bestie, welcome to SRC/sla_gbrpvgrw.f(3) from the Library Functions Manual — manual-name folded in, no boring header copy, we move 💅✨

🎀 NAME

SRC/sla_gbrpvgrw.f — that’s the file, that’s the vibe, periodt 🫶

✨ SYNOPSIS

🌸 Functions/Subroutines

  • 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. iconic behavior honestly 💖

💖 Function/Subroutine Documentation

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

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

🦋 Purpose

SLA_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… bestie, pay attention to that number 🔥

🍓 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 REAL 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 REAL array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by SGBTRF. 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 at line 115 of file sla_gbrpvgrw.f. ⭐

🫶 Author

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mwah 💋 — this cutie signs off with LAPACK Version 3.12.0, page SRC/sla_gbrpvgrw.f(3). bye bestie, go compute responsibly 🎀🦋💅

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