DGGGLM(3)

💖 DGGGLM(3) 💖

This is the dggglm.f(3) page from the Library Functions Manual — yes, the header has that little truncated /home/abui...RC/dggglm.f(3) look, and the real full source path lives down in NAME.

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✨ NAME ✨

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

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🎀 SYNOPSIS 🎀

Functions/Subroutines

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

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🌸 Function/Subroutine Documentation 🌸

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

💅 DGGGLM 💅

🦋 Purpose 🦋

okay bestie, DGGGLM 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.

🌈 Parameters 🌈

• N — INTEGER: the number of rows of the matrices A and B. Constraint: N >= 0.
• M — INTEGER: the number of columns of the matrix A. Constraint: 0 <= M <= N.
• P — INTEGER: the number of columns of the matrix B. Constraint: P >= N-M.
• A — DOUBLE PRECISION array, dimension (LDA,M). On entry, 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 — INTEGER: the leading dimension of the array A. Constraint: LDA >= max(1,N).
• B — DOUBLE PRECISION array, dimension (LDB,P). On entry, 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 — INTEGER: the leading dimension of the array B. Constraint: LDB >= max(1,N).
• D — DOUBLE PRECISION array, dimension (N). On entry, D is the left hand side of the GLM equation. On exit, D is destroyed.
• X — DOUBLE PRECISION array, dimension (M).
• Y — DOUBLE PRECISION array, dimension (P). On exit, X and Y are the solutions of the GLM problem.
• WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER: the dimension of the array WORK. Constraint: 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 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 — 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 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 singular, so that rank( A B ) < N; the least squares solution could not be computed.

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👑 Author 👑

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

Definition at line 183 of file dggglm.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole DGGGLM tea 💅 — the footer says LAPACK Version 3.12.0 and points back at /home/abui...RC/dggglm.f(3), so that’s the source/version sign-off, bestie 🫶✨