SRC/dpbtf2.f(3)

💖 NAME 💖

SRC/dpbtf2.f — okay bestie, this page is from the Library Functions Manual, and it’s all about the dpbtf2 subroutine. ✨

✨ 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).

🎀 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).

💜 Purpose

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

UPLO 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 a 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. 😭

👑 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. Not them being literally “we don’t participate” 💀✨

Definition at line 141 of file dpbtf2.f.

🌟 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie that’s the whole page 💅 kisses from LAPACK — Version 3.12.0 — SRC/dpbtf2.f(3) 🫶