SRC/cpbtf2.f(3)

🌸 NAME 🌸

hiii bestie 💖 you're on the SRC/cpbtf2.f(3) page from the Library Functions Manual — yes, LAPACK is giving main character energy again. This whole page is about CPBTF2: the routine that computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm). ✨

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine cpbtf2 (uplo, n, kd, ab, ldab, info)

CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm). 💅

👑 Function/Subroutine Documentation 👑

🎀 subroutine cpbtf2 🎀

subroutine cpbtf2 (character uplo, integer n, integer kd, complex,
     dimension( ldab, * ) ab, integer ldab, integer info)

CPBTF2 computes the Cholesky factorization of a complex Hermitian positive definite band matrix A. 🫶

✨ Purpose ✨

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, U**H is the conjugate 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 says whether the upper or lower triangular part of the Hermitian 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 COMPLEX array, dimension (LDAB,N). On entry, it holds 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 = -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. 🎀

Definition at line 141 of file cpbtf2.f.

🌸 Author 🌸

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