SRC/zgbtf2.f(3)

🌸 NAME

Okay bestie, you're on the SRC/zgbtf2.f(3) page from the Library Functions Manual, and the name on the tin is literally SRC/zgbtf2.f. This is the tea: ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm. No cap, that's the whole plot. 💅

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✨ SYNOPSIS

🎀 Functions/Subroutines

• subroutine zgbtf2 (m, n, kl, ku, ab, ldab, ipiv, info) — ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm. Periodt.

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🧚 Function/Subroutine Documentation

Full signature, bestie — types and all:

subroutine zgbtf2 (integer m, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)

ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

💖 Purpose

ZGBTF2 computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.

This is the unblocked version of the algorithm, calling Level 2 BLAS.

🌈 Parameters

Vibe check on the args, because every single one matters:

• M — M is INTEGER; the number of rows of the matrix A. M >= 0.
• N — N is INTEGER; the number of columns of the matrix A. N >= 0.
• KL — KL is INTEGER; the number of subdiagonals within the band of A. KL >= 0.
• KU — KU is INTEGER; the number of superdiagonals within the band of A. KU >= 0.
• AB — AB is COMPLEX*16 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; the leading dimension of the array AB. 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 144 of file zgbtf2.f.

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💅 Author

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Later, bestie! The footer energy is LAPACK, Version 3.12.0, and the page is SRC/zgbtf2.f(3). Stay iconic, hydrate, and may your pivots be partial in the most correct way possible. 💖🦋✨