SRC/sgbtrs.f(3)

okay bestie, this page is SRC/sgbtrs.f(3) from the Library Functions Manual, and it's giving one very specific Fortran subroutine. Buckle up, we're reading it together 💅

💖 NAME

SRC/sgbtrs.f — that's the file, and she's the main character of this whole page.

✨ SYNOPSIS

🧚 Functions/Subroutines

   subroutine sgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
       SGBTRS

🫶 Function/Subroutine Documentation

🌟 subroutine sgbtrs

   subroutine sgbtrs (character trans, integer n, integer kl, integer ku,
       integer nrhs, real, dimension( ldab, * ) ab, integer ldab, integer,
       dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integer
       info)

SGBTRS — yes, that's the name, and no, she did not come to play.

🌈 Purpose

SGBTRS solves a system of linear equations

A * X = B  or  A**T * X = B

with a general band matrix A using the LU factorization computed by SGBTRF.

🌸 Parameters

💅 TRANS

TRANS is CHARACTER*1. Specifies the form of the system of equations.

• = 'N': A * X = B (No transpose)
• = 'T': A**T* X = B (Transpose)
• = 'C': A**T* X = B (Conjugate transpose = Transpose)

🐚 N

N is INTEGER. The order 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.

🐚 NRHS

NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

🐚 AB

AB is REAL array, dimension (LDAB,N). Details of the LU factorization of the band matrix A, 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.

🐚 LDAB

LDAB is INTEGER. The leading dimension of the array AB. LDAB >= 2*KL+KU+1.

🐚 IPIV

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

🐚 B

B is REAL array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.

🐚 LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

🐚 INFO

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author

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

Definition at line 136 of file sgbtrs.f.

🎀 Author

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the whole vibe check, bestie: LAPACK, Version 3.12.0, source stamp SRC/sgbtrs.f(3), and the footer doesn't list a date — just that source/version flex. Bye! 💖✨