SRC/sggglm.f(3)

🌸 SRC/sggglm.f(3) 🌸

okay bestie, welcome to the Library Functions Manual page for SRC/sggglm.f. We're gonna get you comfy with SGGGLM without dropping a single deet. 🫶

🌟 NAME 🌟

SRC/sggglm.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

SGGGLM

🦋 Function/Subroutine Documentation 🦋

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

SGGGLM

🎯 Purpose 🎯

okay so SGGGLM solves a general Gauss-Markov linear model (GLM) problem:

minimize || y ||_2   subject to   d = A*x + B*y
    x

where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-vector. It is assumed that M <= N <= M+P, and

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

Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of the matrices (A, B) given by

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

In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem

minimize || inv(B)*(d-A*x) ||_2
    x

where inv(B) denotes the inverse of B.

⚠️ Callers of this subroutine should note that the singularity/rank-deficiency checks implemented in this subroutine are rudimentary. The STRTRS 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 QR factorization of the pair (A, B) 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. 💀

🍓 Parameters 🍓

• N — N is INTEGER. It's the number of rows of the matrices A and B. N >= 0. ✨
• M — M is INTEGER. It's the number of columns of the matrix A. 0 <= M <= N. 🌸
• P — P is INTEGER. It's the number of columns of the matrix B. P >= N-M. 🦋
• A — A is REAL array, dimension (LDA,M). On entry, it's the N-by-M matrix A. On exit, the upper triangular part of the array A contains the M-by-M upper triangular matrix R. 🔥
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💅
• B — B is REAL array, dimension (LDB,P). On entry, it's the N-by-P matrix B. On exit, if N <= P, the upper triangle of the subarray B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; if N > P, the elements on and above the (N-P)th subdiagonal contain the N-by-P upper trapezoidal matrix T. 👑
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🎀
• D — D is REAL array, dimension (N). On entry, D is the left hand side of the GLM equation. On exit, D is destroyed. 😭
• X — X is REAL array, dimension (M). 🌈
• Y — Y is REAL array, dimension (P). On exit, X and Y are the solutions of the GLM problem. ⭐
• 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,N+M+P). For optimum performance, LWORK >= M+min(N,P)+max(N,P)*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 A in the generalized QR factorization of the pair (A, B) is exactly singular, so that rank(A) < M; the least squares solution could not be computed. 💀
  • = 2: the bottom (N-M) by (N-M) part of the upper trapezoidal factor T associated with B in the generalized QR factorization of the pair (A, B) is exactly singular, so that rank( A B ) < N; 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 193 of file sggglm.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole SGGGLM page. Signing off with the footer deets: LAPACK Version 3.12.0 and SRC/sggglm.f(3). Stay slay, stay accurate. 💅✨