/home/abui...D/dgelsx.f(3)

okay bestie, welcome to the Library Functions Manual page for /home/abui...D/dgelsx.f(3) 💅 no cap, this one is a LAPACK routine with big deprecated energy, and we are going to read it together.

🌸 NAME 🌸

This page is about the file:

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

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• subroutine DGELSX (m, n, nrhs, a, lda, b, ldb, jpvt, rcond, rank, work, info) — DGELSX solves overdetermined or underdetermined systems for GE matrices</p> 💖

💖 Function/Subroutine Documentation 💖

Here is the whole signature, bestie, exactly as it appears:

subroutine DGELSX (integer m, integer n, integer nrhs, double precision,
     dimension( lda, * ) a, integer lda, double precision, dimension( ldb, *
     ) b, integer ldb, integer, dimension( * ) jpvt, double precision rcond,
     integer rank, double precision, dimension( * ) work, integer info)

DGELSX solves overdetermined or underdetermined systems for GE matrices ✨

🎀 Purpose 🎀

🚨 deprecated alert, bestie 🚨 This routine is deprecated and has been replaced by routine DGELSY. like, she served, but she is not the current main character anymore 💅

DGELSX computes the minimum-norm solution to a real linear least squares problem:

minimize || A * X - B ||

using a complete orthogonal factorization of A. A is an M-by-N matrix which may be rank-deficient. the way this routine handles rank deficiency is lowkey iconic 🦋

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. one call, many right-hand sides, we love a multitasker 🫶

The routine first computes a QR factorization with column pivoting:

A * P = Q * [ R11 R12 ]
            [  0  R22 ]

with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND. The order of R11, RANK, is the effective rank of A. okay math bestie, we see you ✨

Then, R22 is considered to be negligible, and R12 is annihilated by orthogonal transformations from the right, arriving at the complete orthogonal factorization:

A * P = Q * [ T11 0 ] * Z
            [  0  0 ]

The minimum-norm solution is then

X = P * Z**T [ inv(T11)*Q1**T*B ]
             [        0         ]

where Q1 consists of the first RANK columns of Q. that is the whole plot, and honestly the plot is plotting 💜

🧚 Parameters 🧚

M

M is INTEGER — the number of rows of the matrix A. M >= 0. no negative rows, bestie, we do not do that here 💅

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 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 has been overwritten by details of its complete orthogonal factorization. she gets a whole new look on the way out, periodt 💅

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 M-by-NRHS right hand side matrix B. On exit, the N-by-NRHS solution matrix X. If m >= n and RANK = n, the residual sum-of-squares for the solution in the i-th column is given by the sum of squares of elements N+1:M in that column. glow-up: right hand side goes in, solution matrix comes out ✨

LDB

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

JPVT

JPVT is INTEGER array, dimension (N). On entry, if JPVT(i) .ne. 0, the i-th column of A is an initial column, otherwise it is a free column. Before the QR factorization of A, all initial columns are permuted to the leading positions; only the remaining free columns are moved as a result of column pivoting during the factorization. On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A. so JPVT is basically the seating chart for the columns 🪑✨

RCOND

RCOND is DOUBLE PRECISION. RCOND is used to determine the effective rank of A, which is defined as the order of the largest leading triangular submatrix R11 in the QR factorization with pivoting of A, whose estimated condition number < 1/RCOND. rank decisions are happening and RCOND is holding the clipboard 💅

RANK

RANK is INTEGER — the effective rank of A, i.e., the order of the submatrix R11. This is the same as the order of the submatrix T11 in the complete orthogonal factorization of A.

WORK

WORK is DOUBLE PRECISION array, dimension (max( min(M,N)+3*N, 2*min(M,N)+NRHS )), yes there is a trailing comma in the original vibe, we are keeping it 🫶

INFO

INFO is INTEGER

= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

if INFO is negative, somebody passed an illegal argument and we are calling it out 💀

👑 Author 👑

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

Definition at line 176 of file dgelsx.f. noted for the lore, bestie 📝

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. the robots made this page and honestly they ate ✨

---

and that's the vibe 💖 — this page came from LAPACK Version 3.12.0, at /home/abui...D/dgelsx.f(3). bye bestie, go solve those least squares 🌸🦋💅