SRC/cgesv.f(3)

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version 3.12.1 · 4 versions
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💅 SRC/cgesv.f(3) — LAPACK Library Functions Manual 🎀

ok so bestie, welcome to the cgesv page ✨ this is a real one from the LAPACK manual, and it's genuinely iconic — let's get into it 🫶

✨ NAME ✨

SRC/cgesv.f — like, that's literally the file, that's the whole name, no notes 💀

🌸 SYNOPSIS 🌸

Functions/Subroutines

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

👑 Function/Subroutine Documentation 👑

subroutine cgesv (integer n, integer nrhs, complex, dimension( lda, * ) a,
    integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * )
    b, integer ldb, integer info)

⭐ Purpose ⭐

!> !> CGESV computes the solution to a complex 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. !>

so, in bestie terms: you hand it a complex linear system A * X = B, and it goes off and does an LU decomposition with partial pivoting and row interchanges, factoring A as A = P * L * U — P is a permutation matrix, L is unit lower triangular, U is upper triangular — and then it uses that factored form to actually solve the system 💖 no cap, that's the whole vibe.

🎀 Parameters 🎀

ok this is the part where you actually pay attention, bestie, because every single one of these matters 🔥

  • N — N is INTEGER. it's the number of linear equations, i.e. the order of the matrix A. and N >= 0, always, no exceptions 💅
  • NRHS — NRHS is INTEGER. the number of right hand sides, i.e. the number of columns of the matrix B. also NRHS >= 0 🫶
  • A — A is COMPLEX array, dimension (LDA,N). on entry, it's the N-by-N coefficient matrix A. on exit, it holds the factors L and U from the factorization A = P*L*U — and heads up, the unit diagonal elements of L are not stored 🙈
  • LDA — LDA is INTEGER. the leading dimension of the array A, and it's gotta satisfy LDA >= max(1,N) ⭐
  • IPIV — IPIV is INTEGER array, dimension (N). the pivot indices that define the permutation matrix P — specifically, row i of the matrix was interchanged with row IPIV(i) 👑
  • B — B is COMPLEX array, dimension (LDB,NRHS). on entry, the N-by-NRHS matrix of right hand side matrix B. on exit, if INFO = 0, it's the N-by-NRHS solution matrix X ✨ slay.
  • LDB — LDB is INTEGER. the leading dimension of the array B, and it needs LDB >= max(1,N) 🦋
  • INFO — INFO is INTEGER, and this one's the vibe check at the end:
    • = 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 💀 — fr fr, that's a real "we did all that work and it still didn't solve" moment.

🌈 Author 🌈

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

Definition at line 123 of file cgesv.f. 📍

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (yes, a robot wrote this page, not me, i'm just the messenger 🧚)

🍓 that's the whole page bestie, every flag, every value, every default, every single !> line — nothing skipped, nothing invented 💅

signing off with love: LAPACK, Version 3.12.0 — SRC/cgesv.f(3) — go solve something iconic today, iykyk ✨💖🎀

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