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

okay so bestie, this is the SGELS page from /home/abui...RC/sgels.f(3) — yes, it’s in the Library Functions Manual and we’re about to make linear systems make sense. 💅✨

🌸 NAME 🌸

The source file for this whole icon is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgels.f. That’s the path, bestie — no cap. 🫶

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

Here’s the subroutine entrance music, exactly as written:

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

SGELS solves overdetermined or underdetermined systems for GE matrices — that’s the whole tagline. 💖

🦋 Function/Subroutine Documentation 🦋

Full signature with all the types and dimensions, copy-paste sacred text:

subroutine SGELS (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)

SGELS solves overdetermined or underdetermined systems for GE matrices. 💅

✨ Purpose ✨

Lowkey the whole plot:

SGELS 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 🎀

Every parameter gets its moment. No skipping. 💖

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,

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

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; 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 REAL 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 💜

Take a bow, academic legends:

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

📌 Definition at line 181 of file sgels.f. 📌

Yep, that’s the exact line. 🫶

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie. Footer vibe check: LAPACK Version 3.12.0 and /home/abui...RC/sgels.f(3). Slay, periodt. 💖✨