SRC/dgbtrf.f(3)

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version 3.12.1 · 4 versions
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🌸 NAME 🌸

SRC/dgbtrf.f — okay bestie, this is a page from the Library Functions Manual, and it's serving Fortran linear algebra realness. 💖

✨ SYNOPSIS ✨

Under Functions/Subroutines, we have:

       subroutine dgbtrf (m, n, kl, ku, ab, ldab, ipiv, info)
           DGBTRF

💅 Function/Subroutine Documentation 💅

   subroutine dgbtrf (integer m, integer n, integer kl, integer ku, double
       precision, dimension( ldab, * ) ab, integer ldab, integer, dimension( *
       ) ipiv, integer info)

DGBTRF — main character energy, no cap. 💅

🎀 Purpose 🎀

DGBTRF computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges. ✨

This is the blocked version of the algorithm, calling Level 3 BLAS. 🔥

🍓 Parameters 🍓

M

M is INTEGER. It's the number of rows of the matrix A. Constraint: M >= 0. 👑

N

N is INTEGER. It's the number of columns of the matrix A. Constraint: N >= 0. 🌸

KL

KL is INTEGER. It's the number of subdiagonals within the band of A. Constraint: KL >= 0. 🦋

KU

KU is INTEGER. It's the number of superdiagonals within the band of A. Constraint: KU >= 0. 🎀

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N).

On entry, the matrix A in band storage, in rows KL+1 to 2*KL+KU+1; rows 1 to KL of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows: AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).

On exit, details of the factorization: U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. See below for further details. 💖

LDAB

LDAB is INTEGER. It's the leading dimension of the array AB. Constraint: LDAB >= 2*KL+KU+1. 🌈

IPIV

IPIV is INTEGER array, dimension (min(M,N)). The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). 🫶

INFO

INFO is INTEGER.

  • = 0: successful exit. ✅
  • < 0: if INFO = -i, the i-th argument had an illegal value. 😭
  • > 0: if INFO = +i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations. 💀

👑 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 M = N = 6, KL = 2, KU = 1:

On entry:                       On exit:

      *    *    *    +    +    +       *    *    *   u14  u25  u36
      *    *    +    +    +    +       *    *   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
     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *

Array elements marked * are not used by the routine; elements marked + need not be set on entry, but are required by the routine to store elements of U because of fill-in resulting from the row interchanges. 🦋

Definition at line 143 of file dgbtrf.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. 🤖

Okay bestie, final footer tea: this page is from LAPACK, Version 3.12.0, source/page SRC/dgbtrf.f(3) — and that's the sign-off. No separate date was listed on the footer, so we're not making one up. 💖✨

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