/home/abui...RC/dgbsv.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME

So bestie, the star of the show is this file right here: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgbsv.f — and the whole page lives in the LAPACK Library Functions Manual, no cap. 🫶

✨ SYNOPSIS

🎀 Functions/Subroutines

  • subroutine DGBSV (n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) — okay so this is the one: DGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver). iconic behavior fr fr 💖

🌸 FUNCTION/SUBROUTINE DOCUMENTATION

🫶 subroutine DGBSV

here's the full signature, character for character, don't @ me:

subroutine DGBSV (integer n, integer kl, integer ku, integer nrhs, double
    precision, dimension( ldab, * ) ab, integer ldab, integer, dimension( *
    ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, integer
    info)

DGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver). slay. 👑

💜 Purpose:

!>
!> DGBSV computes the solution to a real system of linear equations
!> A * X = B, where A is a band matrix of order N with KL subdiagonals
!> and KU superdiagonals, and X and B are N-by-NRHS matrices.
!>
!> The LU decomposition with partial pivoting and row interchanges is
!> used to factor A as A = L * U, where L is a product of permutation
!> and unit lower triangular matrices with KL subdiagonals, and U is
!> upper triangular with KL+KU superdiagonals.  The factored form of A
!> is then used to solve the system of equations A * X = B.
!>

👑 Parameters

  • N — N is INTEGER. it's the number of linear equations, aka the order of the matrix A. and N >= 0, periodt. ✨
  • KL — KL is INTEGER. the number of subdiagonals within the band of A. KL >= 0, bestie. 🎀
  • KU — KU is INTEGER. the number of superdiagonals within the band of A. KU >= 0. 💫
  • NRHS — NRHS is INTEGER. the number of right hand sides, i.e. the number of columns of the matrix B. NRHS >= 0, don't forget. 🌸
  • AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). okay so on entry, this is the matrix A in band storage, in rows KL+1 to 2*KL+KU+1; rows 1 to KL of the array need not be set. the j-th column of A is stored in the j-th column of the array AB like this:
AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)

on exit, it's got the details of the factorization: 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. see below for further details, iykyk. 🔥

  • LDAB — LDAB is INTEGER. the leading dimension of the array AB. LDAB >= 2*KL+KU+1, non-negotiable. 💅
  • IPIV — IPIV is INTEGER array, dimension (N). the pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i). 🦋
  • B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). on entry, the N-by-NRHS right hand side matrix B. on exit, if INFO = 0, the N-by-NRHS solution matrix X. main character energy honestly. ✨
  • LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= max(1,N), okurrr. 🌈
  • INFO — INFO is INTEGER. the vibe check, and it goes:
    • = 0: successful exit 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value 😭
    • > 0: if INFO = i, U(i,i) is exactly zero. the factorization has been completed, but the factor U is exactly singular, and the solution has not been computed. not me crying 💀

🌟 Author

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

🔥 Further Details:

!>
!>  The band storage scheme is illustrated by the following example, when
!>  M = N = 6, KL = 2, KU = 1:
!>
!>  On entry:                       On exit:
!>
!>      *    *    *    +    +    +       *    *    *   u14  u25  u36
!>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
!>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
!>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
!>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
!>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
!>
!>  Array elements marked * are not used by the routine; elements marked
!>  + need not be set on entry, but are required by the routine to store
!>  elements of U because of fill-in resulting from the row interchanges.
!>

so * elements? not used by the routine, ignore them bestie. the + elements? they don't need to be set on entry but the routine needs them to store elements of U because of fill-in resulting from the row interchanges. important. 🫶

⭐ DEFINITION AT LINE 161

Definition at line 161 of file dgbsv.f. ✨

🦋 AUTHOR

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and that's the whole thing bestie!! this page is from LAPACK, Version 3.12.0, and it's the manual page at /home/abui...RC/dgbsv.f(3) — go forth and solve those band systems, you absolute icon 💅👑✨

📦 where this page comes from