SRC/sgesv.f(3)

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💖 SRC/sgesv.f — Library Functions Manual 💖

okay bestie, welcome to the Library Functions Manual page for SRC/sgesv.f(3). This is the SGESV tea: solving a real linear system with LU energy. Let’s go ✨

🌸 NAME 🌸

SRC/sgesv.f

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

  • subroutine sgesv (n, nrhs, a, lda, ipiv, b, ldb, info)

👑 Function/Subroutine Documentation 👑

subroutine sgesv (integer n, integer nrhs, real, dimension( lda, * ) a,
    integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b,
    integer ldb, integer info)

🎯 Purpose

SGESV computes the solution to a real system of linear equations

A * X = B

where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as

A = P * L * U

where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B. Literally the whole plot. 💅

🍓 Parameters

  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry, the N-by-N coefficient matrix A. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).
  • B — B is REAL array, dimension (LDB,NRHS). On entry, the N-by-NRHS matrix of right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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
    • > 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.
bestie, the INFO > 0 case is the “math said no 💀” moment: the factorization finished, but U is exactly singular, so the solution could not be computed.

👑 Author 👑

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

Definition at line 123 of file sgesv.f.

👑 Author 👑

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and that’s the page, bestie 🫶. source/version corner: SRC/sgesv.f(3) and LAPACK Version 3.12.0 — no date on this footer, so we’re not inventing one 💖

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