SRC/spbtf2.f(3)

💖 NAME 💖

Bestie, this page is for SRC/spbtf2.f, and it's hanging out in the LAPACK Library Functions Manual. That's the manual name folded in near the top, so we're oriented. ✨

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🫶 SYNOPSIS 🫶

🌟 Functions/Subroutines 🌟

subroutine spbtf2 (uplo, n, kd, ab, ldab, info)

Okay so SPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm). 💅

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🎀 Function/Subroutine Documentation 🎀

subroutine spbtf2 (character uplo, integer n, integer kd, real, dimension(
    ldab, * ) ab, integer ldab, integer info)

SPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm). No cap, it's literally right there. 🌈

💅 Purpose: 💅

Okay so here's the tea: SPBTF2 computes the Cholesky factorization of a real symmetric positive definite band matrix A. 💖

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. 🔥

🌸 Parameters 🌸

• UPLO — UPLO is CHARACTER*1. 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 REAL 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. 🙈

Definition at line 141 of file spbtf2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off time: this iconic page comes from LAPACK Version 3.12.0, source SRC/spbtf2.f(3). Slay, bestie. 💖✨