SRC/zpbtrf.f(3)

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💅 SRC/zpbtrf.f(3) — Library Functions Manual ✨

🎀 NAME 🎀

SRC/zpbtrf.f — that's the page, bestie, and it lives under the Library Functions Manual. We're talking about the zpbtrf routine, and yes it's giving very linear-algebra main character energy. 💖

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

ZPBTRF — iconic, no notes. 💅

💅 Function/Subroutine Documentation 💅

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

ZPBTRF

🌸 Purpose 🌸

Okay so 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. 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 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.

🎀 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.

👑 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 unemployed, periodt. 💀

🫶 Contributors 🫶

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

Definition at line 141 of file zpbtrf.f.

👑 Author 👑

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