SRC/dpbstf.f(3)

💖 SRC/dpbstf.f 💖

okay so this is the SRC/dpbstf.f(3) page from the Library Functions Manual — yes bestie, we're in the LAPACK docs and this one is all about DPBSTF, a real split Cholesky factorization moment. 💅

✨ NAME ✨

SRC/dpbstf.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine dpbstf (uplo, n, kd, ab, ldab, info)
    DPBSTF

🫶 Function/Subroutine Documentation 🫶

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

🎀 Purpose 🎀

okay so DPBSTF computes a split Cholesky factorization of a real symmetric positive definite band matrix A. no cap. 🫶

This routine is designed to be used in conjunction with DSBGST. iykyk.

The factorization has the form A = S**T*S where S is a band matrix of the same bandwidth as A and the following structure:

S = ( U    )
    ( M  L )

where U is upper triangular of order m = (n+kd)/2, and L is lower triangular of order n-m. the math is mathing ✨

💅 Parameters 💅

• UPLO — UPLO is CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. pick your triangle, bestie.
• N — N is INTEGER. The order of the matrix A. N >= 0. zero is valid, we love a boundary case.
• 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. bandwidth tea.
• 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 factor S from the split Cholesky factorization A = S**T*S. See Further Details. so iconic

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1. respect the leading dimension, periodt.
• INFO — INFO is INTEGER.
  • = 0: successful exit. slay
  • < 0: if INFO = -i, the i-th argument had an illegal value. oops, bad arg bestie
  • > 0: if INFO = i, the factorization could not be completed, because the updated element a(i,i) was negative; the matrix A is not positive definite. not positive definite, no cap — that's a real problem

🌸 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 = 7, KD = 2:

S = ( s11  s12  s13                     )
    (      s22  s23  s24                )
    (           s33  s34                )
    (                s44                )
    (           s53  s54  s55           )
    (                s64  s65  s66      )
    (                     s75  s76  s77 )

If UPLO = 'U', the array AB holds:

on entry:                          on exit:

   *    *   a13  a24  a35  a46  a57   *    *   s13  s24  s53  s64  s75
   *   a12  a23  a34  a45  a56  a67   *   s12  s23  s34  s54  s65  s76
  a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77

If UPLO = 'L', the array AB holds:

on entry:                          on exit:

  a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77
  a21  a32  a43  a54  a65  a76   *   s12  s23  s34  s54  s65  s76   *
  a31  a42  a53  a64  a64   *    *   s13  s24  s53  s64  s75   *    *

Array elements marked * are not used by the routine. ignore them, they're not in the group chat 💀

Definition at line 151 of file dpbstf.f.

🧚 Author (the meta one) 🧚

Generated automatically by Doxygen for LAPACK from the source code. the docs wrote themselves, lowkey iconic ✨

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okay that's the whole page, bestie 💖 this came from SRC/dpbstf.f(3) and the footer says LAPACK Version 3.12.0 — no date is listed on this footer, so I'm not making one up, periodt 💅