DGGLSE(3)

👑 DGGLSE — the one where LAPACK solves your constrained least squares problem 💅

okay bestie, so this page is for dgglse.f, and the manual name is basically just that: dgglse.f(3), living under /home/abui...RC/dgglse.f(3). yes it's a Fortran file. yes it's iconic. let's get into it ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines 🎀

subroutine DGGLSE (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info)

DGGLSE solves overdetermined or underdetermined systems for OTHER matrices. (yes, "OTHER" in all caps, that's literally what it says, and honestly? mystery. intrigue. iykyk 💅)

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⭐ Function/Subroutine Documentation ⭐

subroutine DGGLSE (integer m, integer n, integer p, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) c, double precision, dimension( * ) d, double precision, dimension( * ) x, double precision, dimension( * ) work, integer lwork, integer info)

DGGLSE solves overdetermined or underdetermined systems for OTHER matrices — that's the whole vibe, and it ate 🔥

🦋 Purpose 🦋

so like, hear me out. DGGLSE solves the linear equality-constrained least squares (LSE) problem:

minimize || c - A*x ||_2   subject to   B*x = d

where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vector, and d is a given P-vector. And the rules of the house are: it is assumed that

P <= N <= M+P

and

         rank(B) = P and  rank( (A) ) = N.
                              ( (B) )

these conditions ensure that the LSE problem has a unique solution — no cap, that's the whole point. you get one answer, singular, main character energy 👑

and how do we get it? using a generalized RQ factorization of the matrices (B, A) given by

   B = (0 R)*Q,   A = Z*T*Q.

slay. literally a factorization moment ✨

💖 Parameters 💖

• M — M is INTEGER. The number of rows of the matrix A. M >= 0. 🫶
• N — N is INTEGER. The number of columns of the matrices A and B. N >= 0. 🌸
• P — P is INTEGER. The number of rows of the matrix B. 0 <= P <= N <= M+P. (yes bestie, that sandwich of inequalities is load-bearing, do NOT mess with it 💀)
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix T. (it becomes a whole new matrix, growth era 🌱)
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — B is DOUBLE PRECISION array, dimension (LDB,N). On entry, the P-by-N matrix B. On exit, the upper triangle of the subarray B(1:P,N-P+1:N) contains the P-by-P upper triangular matrix R. 🎀
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,P).
• C — C is DOUBLE PRECISION array, dimension (M). On entry, C contains the right hand side vector for the least squares part of the LSE problem. On exit, the residual sum of squares for the solution is given by the sum of squares of elements N-P+1 to M of vector C. (so it tells you how wrong you were, affectionately 😭)
• D — D is DOUBLE PRECISION array, dimension (P). On entry, D contains the right hand side vector for the constrained equation. On exit, D is destroyed. 💀 yes, destroyed, that's the actual word in the manual, she did not survive and that's just how it is.
• X — X is DOUBLE PRECISION array, dimension (N). On exit, X is the solution of the LSE problem. the moment we've all been waiting for 👑
• 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,M+N+P). For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, where NB is an upper bound for the optimal blocksizes for DGEQRF, SGERQF, DORMQR and SORMRQ.

okay so also: 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. (honestly a queen move — ask for the size without committing, we love a low-stakes vibe check 🧚)

• INFO — INFO is INTEGER, and here's the whole tea:
  • = 0: successful exit. 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value. (you fed it something cursed, it's telling you which one 🙈)
  • = 1: the upper triangular factor R associated with B in the generalized RQ factorization of the pair (B, A) is singular, so that rank(B) < P; the least squares solution could not be computed. 💀
  • = 2: the (N-P) by (N-P) part of the upper trapezoidal factor T associated with A in the generalized RQ factorization of the pair (B, A) is singular, so that

rank( (A) ) < N; the least squares solution could not
    ( (B) )
be computed.

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🌈 Author 🌈

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

(the whole squad showed up for this one 🫶)

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📍 Where it lives

Definition at line 178 of file dgglse.f. ✨

Author (the other one, the meta one): Generated automatically by Doxygen for LAPACK from the source code. not a human, just a very diligent little robot 🧚

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anyway bestie, that's the whole page. this manual page came to you from LAPACK, Version 3.12.0, dated /home/abui...RC/dgglse.f(3) — mwah, drink water, go solve some constrained least squares 💜🌸🎀