DPBTF2(3)

💖 DPBTF2(3) — Library Functions Manual 💖

okay so bestie, we’re in the DPBTF2(3) page of the Library Functions Manual, and the source file is giving main-character LAPACK energy:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dpbtf2.f

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dpbtf2.f

✨ SYNOPSIS ✨

💕 Functions/Subroutines 💕

subroutine DPBTF2 (uplo, n, kd, ab, ldab, info)

DPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm). No cap, that’s the whole synopsis vibe. 💅

🦋 Function/Subroutine Documentation 🦋

subroutine DPBTF2 (character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, integer info)

DPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm). Yes bestie, it said it twice — the original page does that, and we’re keeping every detail. 🫶

🎀 Purpose 🎀

DPBTF2 computes the Cholesky factorization of a real symmetric positive definite band matrix A.

The factorization has the form

A = U**T * U ,  if UPLO = 'U', or
A = L  * L**T,  if UPLO = 'L',

where U is an upper triangular matrix, U**T is the transpose of U, and L is lower triangular.

This is the unblocked version of the algorithm, calling Level 2 BLAS. Periodt. ✨

🌈 Parameters 🌈

• UPLO — this one is CHARACTER*1. It specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The order of the matrix A. N >= 0.
• KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 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).

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.
• INFO — INFO is INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -k, the k-th argument had an illegal value
  • > 0: if INFO = k, the leading principal minor of order k is not positive, and the factorization could not be completed.

bestie, that last one is the “vibe check failed” branch: if INFO > 0, the leading principal minor of order k is not positive and the factorization could not be completed. 😭

👑 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':

!>
!>  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 141 of file dpbtf2.f.

🌟 Author 🌟

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