DPBTRF(3)

💖 NAME 💖

dpbtrf — okay bestie, this is the LAPACK routine that does the Cholesky factorization of a real symmetric positive definite band matrix. It lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dpbtrf.f, and this little doc page comes to you from the Library Functions Manual 📖✨

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

DPBTRF 💅

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🦋 Function/Subroutine Documentation 🦋

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

DPBTRF 👑

🌸 Purpose 🌸

Okay so, DPBTRF computes the Cholesky factorization of a real symmetric positive definite band matrix A. No cap. 💯

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 and L is lower triangular. That's it, that's the whole vibe. 🫶

🍓 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 order of the matrix A. N >= 0. (Yes, zero is allowed, she's flexible. 🧚)

💜 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 — that's a hard requirement, don't try it. 🙈

💜 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. She leaves the place looking exactly like she found it, just ✨better✨.

💜 LDAB

LDAB is INTEGER

The leading dimension of the array AB. LDAB >= KD+1. Periodt. 💅

💜 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 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':

 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 literally just there for the aesthetic. 🎀

🌈 Contributors: 🌈

Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989. Icons. Legends. The main characters of banded Cholesky. 👑👑

Definition at line 141 of file dpbtrf.f.

🌟 Author (the doc one) 🌟

Generated automatically by Doxygen for LAPACK from the source code. Not me, not you — the robot did it. 🤖💖

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And that's the whole page, bestie! This cutie pie of a doc came from LAPACK Version 3.12.0, serving you /home/abui...RC/dpbtrf.f(3) realness. Go factor some bands, ily, bye! 💅✨🦋💖