SGBT01(3)

okay so bestie, we are literally in sgbt01.f(3) from the Library Functions Manual, and this page is giving main-character LAPACK testing-file energy. 🦋💅

🌸 NAME 🌸

the official file path is, no cap, exactly this:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sgbt01.f

🌈 SYNOPSIS 🌈

💫 Functions/Subroutines 💫

   subroutine SGBT01 (m, n, kl, ku, a, lda, afac, ldafac, ipiv, work,
       resid)
           SGBT01

🛠️ Function/Subroutine Documentation 🛠️

   subroutine SGBT01 (integer m, integer n, integer kl, integer ku, real,
       dimension( lda, * ) a, integer lda, real, dimension( ldafac, * ) afac,
       integer ldafac, integer, dimension( * ) ipiv, real, dimension( * ) work,
       real resid)
       SGBT01

🎯 Purpose 🎯

SGBT01 reconstructs a band matrix A from its L*U factorization and computes the residual:

norm(L*U - A) / ( N * norm(A) * EPS ),

where EPS is the machine epsilon.

The expression L*U - A is computed one column at a time, so A and AFAC are not modified. obsessed with the no-mutation vibe ✨

🧾 Parameters 🧾

• 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.
• A — A is REAL array, dimension (LDA,N). The original matrix A in band storage, stored in rows 1 to KL+KU+1.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KL+KU+1).
• AFAC — AFAC is REAL array, dimension (LDAFAC,N). The factored form of the matrix A. AFAC contains the banded factors L and U from the L*U factorization, as computed by SGBTRF. 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 SGBTRF for further details.
• LDAFAC — LDAFAC is INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,2*KL*KU+1).
• IPIV — IPIV is INTEGER array, dimension (min(M,N)). The pivot indices from SGBTRF.
• WORK — WORK is REAL array, dimension (2*KL+KU+1)
• RESID — RESID is REAL. norm(L*U - A) / ( N * norm(A) * EPS )

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 124 of file sgbt01.f.

👑 Author 👑

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