SGELST(3)

🌸 NAME 🌸

okay bestie, this is the sgelst.f page from the LAPACK manual — a Library Functions Manual moment, fr fr. The actual file path is:

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

✨ SYNOPSIS ✨

Functions/Subroutines

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

the whole vibe: SGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q. 🫶

🦋 Function/Subroutine Documentation 🦋

subroutine SGELST (...)

   subroutine SGELST (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)

SGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q. iconic behavior, honestly 💅

💖 Purpose 💖

• SGELST solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A with compact WY representation of Q.
• it is assumed that A has full rank. no cap.
• 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 underdetermined 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.

🎀 Parameters 🎀

• TRANS — CHARACTER*1
  • = 'N': the linear system involves A;
  • = 'T': the linear system involves A**T.
• M — INTEGER
  • The number of rows of the matrix A. M >= 0.
• N — INTEGER
  • The number of columns of the matrix A. N >= 0.
• NRHS — INTEGER
  • The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >=0.
• A — REAL array, dimension (LDA,N)
  • On entry, the M-by-N matrix A.
  • On exit,
    • if M >= N, A is overwritten by details of its QR factorization as returned by SGEQRT;
    • if M < N, A is overwritten by details of its LQ factorization as returned by SGELQT.
• LDA — INTEGER
  • The leading dimension of the array A. LDA >= max(1,M).
• B — 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; the residual sum of squares for the solution in each column is given by the sum of squares of elements N+1 to M in that column;
    • 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; the residual sum of squares for the solution in each column is given by the sum of squares of elements M+1 to N in that column.
• LDB — INTEGER
  • The leading dimension of the array B. LDB >= MAX(1,M,N).
• WORK — REAL array, dimension (MAX(1,LWORK))
  • On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER
  • The dimension of the array WORK.
  • LWORK >= max( 1, MN + max( MN, NRHS ) ).
  • For optimal performance, LWORK >= max( 1, (MN + max( MN, NRHS ))*NB ).
  • where MN = min(M,N) and NB is the optimum block size.
  • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• INFO — 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.

🌈 Author 🌈

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

💜 Contributors 💜

• November 2022, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 192 of file sgelst.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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✨ okay bye bestie — this page is from LAPACK, Version 3.12.0, and the footer points at /home/abui...RC/sgelst.f(3). slay. 💅🎀