SRC/dgglse.f(3)

🧚 SRC/dgglse.f 🧚

okay bestie, welcome to the Library Functions Manual page for SRC/dgglse.f — yes it's a .f file, yes it's iconic, and yes we're getting into it 💅. This is the dgglse subroutine documentation, and I promise we're keeping every single detail. No cap.

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🌸 NAME 🌸

SRC/dgglse.f

✨ 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 🫶

🦋 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 — yes, "OTHER" is doing a lot of work here, but it's exactly what the page says, so we're keeping it.

🌟 Purpose 🌟

ok so 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. 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, which is obtained using a generalized RQ factorization of the matrices (B, A) given by

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

Callers of this subroutine should note that the singularity/rank-deficiency checks implemented in this subroutine are rudimentary. The DTRTRS subroutine called by this subroutine only signals a failure due to singularity if the problem is exactly singular.

It is conceivable for one (or more) of the factors involved in the generalized RQ factorization of the pair (B, A) to be subnormally close to singularity without this subroutine signalling an error. The solutions computed for such almost-rank-deficient problems may be less accurate due to a loss of numerical precision. 😭 this is important, bestie.

🎀 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.
• 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.
• 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.
• 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. 💀
• X — X is DOUBLE PRECISION array, dimension (N). On exit, X is the solution of the LSE problem. slay.
• 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. 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.
  • = 1: the upper triangular factor R associated with B in the generalized RQ factorization of the pair (B, A) is exactly 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 exactly singular, so that

rank( (A) ) < N
      ( (B) )

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 188 of file dgglse.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie 🫶 no details left behind, periodt. kisses from your Unix group chat 💖 — LAPACK, Version 3.12.0, SRC/dgglse.f(3).