SGGLSE(3)

okay so bestie, welcome to SGGLSE(3) — a Library Functions Manual page — and it's giving sgglse.f main character energy. ✨

🎀 NAME 🎀

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

that's the source file this page is serving, periodt. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine SGGLSE (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info) — SGGLSE solves overdetermined or underdetermined systems for OTHER matrices

💖 Function/Subroutine Documentation 💖

the full signature is:

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

SGGLSE solves overdetermined or underdetermined systems for OTHER matrices.

🌸 Purpose 🌸

okay so SGGLSE 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.

🦋 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (P). On entry, D contains the right hand side vector for the constrained equation. On exit, D is destroyed. 💀
• X — X is REAL array, dimension (N). On exit, X is the solution of the LSE problem. slay.
• 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,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 SGEQRF, SGERQF, SORMQR 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 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.

bestie, if INFO is 1 or 2, the solution is not being computed — that's a hard stop, not a vibe. 🫶

👑 Author 👑

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

Definition at line 178 of file sgglse.f.

💅 Author 💅

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mwah 💋 that's the whole page, bestie — LAPACK Version 3.12.0, footer path /home/abui...RC/sgglse.f(3). no cap, you got this. 🫶