SRC/dpbtrf.f(3)

🎀 dpbtrf.f(3) — okay bestie, let’s get into it 🎀

Hi hi! This is the manual page for SRC/dpbtrf.f, aka the dpbtrf.f(3) page — folding the manual name in right here at the top like a lil name tag. 💖

✨ NAME ✨

SRC/dpbtrf.f — that’s the page/file name, periodt. The subroutine living here is dpbtrf. 💅

🦋 SYNOPSIS 🦋

🌸 Functions/Subroutines 🌸

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

💖 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. Slay. 💅

🧚 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.

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.

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 = -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.

bestie, if INFO > 0, the factorization could not be completed — that’s a real mood killer, so check it. 💀

🌟 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. 💅

🎀 Contributors 🎀

Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989. 🎀

Definition at line 141 of file dpbtrf.f.

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🦋 Author 🦋

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