/home/abui.../cgetsls.f(3)

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgetsls.f — bestie, this is the manual page for that exact file, straight outta LAPACK 3.12.0, sitting pretty in section 3 (Library Functions Manual). Yes the path is a whole mouthful, no we are not shortening it, it's iconic as-is. 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine CGETSLS (trans, m, n, nrhs, a, lda, b, ldb, work, lwork,
    info)

CGETSLS

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🌸 Function/Subroutine Documentation 🌸

subroutine CGETSLS (character trans, integer m, integer n, integer nrhs,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *
    ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer
    info)

CGETSLS

🎀 Purpose 🎀

okay so, real talk: CGETSLS solves overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, using a tall skinny QR or short wide LQ factorization of A. And it just assumes A has full rank. Like, that's the vibe it's going with. ✨

The following options are provided:

1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem

             minimize || B - A*X ||.

2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B.
3. If TRANS = 'C' and m >= n: find the minimum norm solution of an undetermined system A**T * X = B.
4. If TRANS = 'C' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem

             minimize || B - A**T * X ||.

Several right hand side vectors b and solution vectors x can be handled in a single call — they're stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. Multi-tasking queen behavior, honestly. 👑

💖 Parameters 💖

• TRANS — TRANS is CHARACTER*1, and it's literally just picking which system you're solving:
  • = 'N': the linear system involves A;
  • = 'C': the linear system involves A**H.
• 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.
• NRHS — NRHS is INTEGER, the number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >=0.
• A — A is COMPLEX array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, A is overwritten by details of its QR or LQ factorization as returned by CGEQR or CGELQ. She gets a whole glow-up on the way out, bestie. 🔥
• LDA — LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,M).
• B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the matrix B of right hand side vectors, stored columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS if TRANS = 'C'. On exit, if INFO = 0, B is overwritten by the solution vectors, stored columnwise:
  • if TRANS = 'N' and m >= n, rows 1 to n of B contain the least squares solution vectors.
  • if TRANS = 'N' and m < n, rows 1 to N of B contain the minimum norm solution vectors;
  • if TRANS = 'C' and m >= n, rows 1 to M of B contain the minimum norm solution vectors;
  • if TRANS = 'C' and m < n, rows 1 to M of B contain the least squares solution vectors.
• LDB — LDB is INTEGER, the leading dimension of the array B. LDB >= MAX(1,M,N).
• WORK — (workspace) COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) contains optimal (or either minimal or optimal, if query was assumed) LWORK. See LWORK for details. 🫶
• LWORK — LWORK is INTEGER, the dimension of the array WORK. If LWORK = -1 or -2, then a workspace query is assumed. If LWORK = -1, the routine calculates optimal size of WORK for the optimal performance and returns this value in WORK(1). If LWORK = -2, the routine calculates minimal size of WORK and returns this value in WORK(1). So like, negative LWORK = asking a question, not making a demand. 🙈
• INFO — INFO is INTEGER:
  • = 0: successful exit ✨
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the i-th diagonal element of the triangular factor of A is zero, so that A does not have full rank; the least squares solution could not be computed. 😭 no full rank, no solution, that's just how it is.

👑 Author 👑

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

Definition at line 160 of file cgetsls.f.

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (Not a human, just a very diligent little documentation goblin. 🧚)

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slay, that's the whole page. LAPACK, Version 3.12.0, page /home/abui.../cgetsls.f(3) — mwah, bye bestie, go solve something complex. 💜🌸