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

💖 NAME 💖

hey bestie 💖 this is the sgetsls.f page from the LAPACK Library Functions Manual, and the header path is /home/abui.../sgetsls.f(3). The source file is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgetsls.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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🦋 Function/Subroutine Documentation 🦋

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

🌸 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. It is assumed that A has full rank. no cap, that assumption is doing a lot of heavy lifting 🫶

The following options are provided, bestie:

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 ||.

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. it’s giving “group project but everyone actually showed up” 💅

🎀 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. 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 zero, so that A does not have full rank; the least squares solution could not be computed.

bestie, that INFO > 0 situation is not a slay: A does not have full rank, so 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 160 of file sgetsls.f.

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🫶 Author 🫶

this next Author bit is the auto-generated one: Generated automatically by Doxygen for LAPACK from the source code.

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Later, bestie 🫶 this page is from LAPACK Version 3.12.0 and lives at /home/abui.../sgetsls.f(3) — muah 💋