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

This is the dpbsv.f(3) page from the Library Functions Manual, filed at /home/abui...RC/dpbsv.f(3). Bestie, it’s a LAPACK routine and the vibe is “trust me, I do band matrices.” 💅

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dpbsv.f

That’s literally the whole NAME section — no cute nickname, just the full path. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DPBSV (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
     DPBSV computes the solution to system of linear equations A * X = B
    for OTHER matrices

🧮 Function/Subroutine Documentation 🧮

subroutine DPBSV (character uplo, integer n, integer kd, integer nrhs,
    double precision, dimension( ldab, * ) ab, integer ldab, double
    precision, dimension( ldb, * ) b, integer ldb, integer info)

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

🌸 Purpose 🌸

Okay so here’s the tea: DPBSV 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.

🎀 Parameters 🎀

UPLO

UPLO is CHARACTER*1

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

N

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

KD

KD is INTEGER — the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.

NRHS

NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N).

On entry, 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.

On exit, if INFO = 0, 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. LDAB >= KD+1.

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.

LDB

LDB is INTEGER — the leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER

• = 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.

👑 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 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.

Definition at line 163 of file dpbsv.f.

Author 🫶

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okay bestie, that’s the whole page — LAPACK, Version 3.12.0, at /home/abui...RC/dpbsv.f(3). Slay and goodbye 💖✨