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

🦋 NAME 🦋

okay so this is the Library Functions Manual page, and the header points at /home/abui.../dgetsls.f(3). The NAME section is literally this file path:

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

slay, that’s the whole NAME vibe 💅

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

👑 Function/Subroutine Documentation 👑

subroutine DGETSLS (character trans, integer m, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DGETSLS is the main character here, no cap 👑

💖 Purpose 💖

DGETSLS 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.

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 ||.

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 — 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 DOUBLE PRECISION 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 DGEQR or DGELQ.
• LDA — LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,M).
• B — B is DOUBLE PRECISION 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) DOUBLE PRECISION 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.

🌸 Author 🌸

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

Definition at line 160 of file dgetsls.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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