SRC/sgetsls.f(3)

okay bestie, welcome to the Library Functions Manual for SRC/sgetsls.f — yes, the whole manual vibe is right here, and this page is lowkey a baddie. Let's get into it 💅✨

💖 NAME 💖

SRC/sgetsls.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

Here's the subroutine energy:

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

🦋 Function/Subroutine Documentation 🦋

🌸 subroutine sgetsls 🌸

subroutine sgetsls (character trans, integer m, integer n, integer nrhs,
    real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,
    integer ldb, real, dimension( * ) work, integer lwork, integer info)
    SGETSLS

The subroutine's name is SGETSLS, and it is absolutely the main character 👑.

💅 Purpose 💅

okay so SGETSLS solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, using a tall skinny QR or short wide LQ factorization of A.

Bestie, it assumes that A has full rank, and only a rudimentary protection against rank-deficient matrices is provided. This subroutine only detects exact rank-deficiency, where a diagonal element of the triangular factor of A is exactly zero.

It is conceivable for one (or more) of the diagonal elements of the triangular factor of A to be subnormally tiny numbers without this subroutine signalling an error. The solutions computed for such almost-rank-deficient matrices may be less accurate due to a loss of numerical precision. 😭

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

Also, several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. slay 🫶

🍓 Parameters 🍓

• TRANS — TRANS is CHARACTER*1; = 'N': the linear system involves A; = 'T': the linear system involves A**T.
• 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 REAL 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 SGEQR or SGELQ.
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
• B — B is REAL 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 = 'T'. 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 = 'T' and m >= n, rows 1 to M of B contain the minimum norm solution vectors;
  • if TRANS = 'T' 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) REAL 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. LWORK >= 1. 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).
• 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 exactly zero, so that A does not have full rank; the least squares solution could not be computed.

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 169 of file sgetsls.f.

👑 Author 👑

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Cute sign-off: this precious page is LAPACK Version 3.12.0, source/page SRC/sgetsls.f(3) — and the footer doesn't give a separate date, so I'm not manifesting one. Byeee bestie 💖🎀