SGGGLM(3)

💅 SGGGLM(3) — sggglm.f(3) · Library Functions Manual 💅

🌸 NAME 🌸

The source-file main character is exactly this path — no edits, no cap:

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

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✨ SYNOPSIS ✨

Functions/Subroutines

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

And yes, bestie, the subroutine is literally called SGGGLM.

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🦋 Function/Subroutine Documentation 🦋

Here's the full typed signature, character for character:

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 is the name, and we're about to get into the plot 💖

🎀 Purpose 🎀

Okay so SGGGLM solves a general Gauss-Markov linear model (GLM) problem. Like, literally this:

         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

N is INTEGER. It's the number of rows of the matrices A and B. Condition: N >= 0.

M

M is INTEGER. The number of columns of the matrix A. Condition: 0 <= M <= N.

P

P is INTEGER. The number of columns of the matrix B. Condition: P >= N-M.

A

A is REAL 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

LDA is INTEGER. The leading dimension of the array A. Condition: LDA >= max(1,N).

B

B is REAL 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

LDB is INTEGER. The leading dimension of the array B. Condition: 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.

🚨 Heads up, bestie: D gets destroyed on exit. Protect your data vibes.

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. Condition: 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. Its mood ring says:

• = 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 sggglm.f.

👑 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Signed off with LAPACK Version 3.12.0 energy, straight from /home/abui...RC/sggglm.f(3) — that's the whole page, bestie! 💖