SRC/spbtrf.f(3)

🎀 SRC/spbtrf.f(3) 🎀

okay so bestie, this is the Library Functions Manual page for SRC/spbtrf.f(3), and it's literally giving “I know my LAPACK routines” main character energy. No cap. 💅

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✨ NAME ✨

SRC/spbtrf.f — yep, that's the name, and it's just the source file name. Iconic minimalism, honestly. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine spbtrf (uplo, n, kd, ab, ldab, info) — SPBTRF

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💫 Function/Subroutine Documentation 💫

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

SPBTRF — that's the routine, and she's the whole moment of this page. 🫶

🎀 Purpose: 🎀

Okay so SPBTRF 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 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 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 = -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':

!>
!>  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 spbtrf.f.

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🎀 Author 🎀

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