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

💅 NAME 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/spbsv.f — okay so this is that LAPACK file, bestie, and yes the manual page literally just names the whole path. Iconic of it, honestly.

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SPBSV (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)

SPBSV computes the solution to system of linear equations A * X = B for OTHER matrices 🫶

🦋 Function/Subroutine Documentation 🦋

subroutine SPBSV (character uplo, integer n, integer kd, integer nrhs, real,
    dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * ) b,
    integer ldb, integer info)

SPBSV computes the solution to system of linear equations A * X = B for OTHER matrices. no cap.

🌸 Purpose: 🌸

!>
!> SPBSV computes the solution to a real system of linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric positive definite band matrix and X
!> and B are N-by-NRHS matrices.
!>
!> The Cholesky decomposition is used to factor A as
!>    A = U**T * U,  if UPLO = 'U', or
!>    A = L * L**T,  if UPLO = 'L',
!> where U is an upper triangular band matrix, and L is a lower
!> triangular band matrix, with the same number of superdiagonals or
!> subdiagonals as A.  The factored form of A is then used to solve the
!> system of equations A * X = B.
!>

So like — A is this N-by-N symmetric positive definite band matrix, and X and B are N-by-NRHS matrices. The routine hits it with the Cholesky decomposition, factors A into either U**T * U (when UPLO = 'U') or L * L**T (when UPLO = 'L') — where U is an upper triangular band matrix and L is a lower triangular band matrix, both rocking the same number of superdiagonals or subdiagonals as A — and then uses that factored form to solve A * X = B. slay. 💜

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. It's giving "which triangle, bestie": = 'U' means the upper triangle of A is stored; = 'L' means the lower triangle of A is stored. pick your fighter 💅
• N — N is INTEGER. The number of linear equations, i.e. the order of the matrix A. Constraint: N >= 0. respectful king.
• KD — KD is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. Constraint: KD >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e. the number of columns of the matrix B. Constraint: NRHS >= 0.
• AB — AB is REAL array, dimension (LDAB,N). On entry, this is the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
  • if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
  • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).

See below for further details (and there ARE further details, keep reading 🧚). On exit, if INFO = 0, it holds the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A.

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. Constraint: LDAB >= KD+1.
• B — B is REAL 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. glow up. ✨
• LDB — LDB is INTEGER. The leading dimension of the array B. Constraint: LDB >= max(1,N).
• INFO — INFO is INTEGER, the vibe check:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 😭
  • > 0: if INFO = i, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed. 💀 so like, no solution for you.

👑 Author 👑

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

the whole squad, fr fr.

🌈 Further Details: 🌈

The band storage scheme is illustrated by the following example, when N = 6, KD = 2, and UPLO = 'U':

!>
!>  On entry:                       On exit:
!>
!>      *    *   a13  a24  a35  a46      *    *   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
!>

Similarly, if UPLO = 'L' the format of A is as follows:

!>
!>  On entry:                       On exit:
!>
!>     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
!>     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
!>     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
!>

Array elements marked * are not used by the routine. they're just there for the aesthetic, honestly. 🙈

---

Definition at line 163 of file spbsv.f. noted. 💖

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a robot doing its little robot thing 🎀)

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k that's the whole page bestie — LAPACK, Version 3.12.0, and yeah the footer is literally /home/abui...RC/spbsv.f(3) with the version tag. mwah. 💅✨🫶