ZPBTRF(3)

💅 zpbtrf.f(3) — Library Functions Manual 🎀

okay bestie, so this is a page from the LAPACK Library Functions Manual ✨ — it's all about zpbtrf.f, and ngl it's kind of a whole vibe once you get past the Fortran of it all.

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💖 NAME 💖

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

like, that's the whole name. it's a path. she's a file. slay 🌸

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

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

ZPBTRF — that's her name, that's her whole thing, no notes 💅

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🦋 Function/Subroutine Documentation 🦋

subroutine ZPBTRF (character uplo, integer n, integer kd, complex*16,
    dimension( ldab, * ) ab, integer ldab, integer info)

ZPBTRF 🔥

👑 Purpose 👑

!> !> ZPBTRF computes the Cholesky factorization of a complex Hermitian !> positive definite band matrix A. !> !> The factorization has the form !> A = U**H * U, if UPLO = 'U', or !> A = L * L**H, if UPLO = 'L', !> where U is an upper triangular matrix and L is lower triangular. !>

so basically: she takes your complex Hermitian positive definite band matrix A and factorizes it into A = U**H * U (if UPLO = 'U') or A = L * L**H (if UPLO = 'L'), where U is upper triangular and L is lower triangular. main character math fr fr 💖

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

pick your fighter bestie 💅

• 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 COMPLEX*16 array, dimension (LDAB,N)
  • On entry, the upper or lower triangle of the Hermitian 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**H*U or A = L*L**H of the band matrix A, in the same storage format as A.

she comes in with A, she leaves with U or L. glow-up moment 🌟

• 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.

💀 heads up: a positive INFO legit means the factorization could not be completed — the leading principal minor of order i isn't positive. that's not a vibe, that's a "your matrix is not positive definite" moment. 😭

🌸 Author 🌸

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

the whole squad contributed, we love a collab 🫶

⭐ 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. !>

so the * lil stars are just... decorative. the routine does not touch them. they're there for the aesthetic and the aesthetic only 💅✨

🧚 Contributors: 🧚

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

icons. legends. writing Cholesky band factorization before it was cool. 👑

📌 Definition 📌

Definition at line 141 of file zpbtrf.f.

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🍓 Author 🍓

Generated automatically by Doxygen for LAPACK from the source code. no thoughts, just autogenerated, and honestly? respect. 🤖💖

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aaaand that's the page bestie 🎀 — LAPACK, Version 3.12.0, zpbtrf.f(3) from the Library Functions Manual. go forth and factorize your band matrices, ily, bye 💜🦋✨