/home/abui...RC/dgels.f(3)

🦋 NAME 🦋

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

okay so bestie, this page is from the Library Functions Manual and its manual name is /home/abui...RC/dgels.f(3). The NAME section is literally that giant path above — no cap, it's giving “I am the source file and I said what I said.” 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

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

DGELS solves overdetermined or underdetermined systems for GE matrices. periodt. 💖

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💖 Function/Subroutine Documentation 💖

subroutine DGELS (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)

DGELS solves overdetermined or underdetermined systems for GE matrices. slay.

💫 Purpose: 💫

okay so here's the tea: DGELS 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. 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 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

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,
  if M >= N, A is overwritten by details of its QR
             factorization as returned by DGEQRF;
  if M <  N, A is overwritten by details of its LQ
             factorization as returned by DGELQF.

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; 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

LDB is INTEGER
The leading dimension of the array B. LDB >= MAX(1,M,N).

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is 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

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 181 of file dgels.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole lore. the footer vibe is LAPACK Version 3.12.0 and /home/abui...RC/dgels.f(3) — kisses, stay full rank, and may your least squares always be least dramatic. 🫶💖🌸