ZGGLSE(3)

🌸 NAME 🌸

okay so bestie, this is the zgglse.f(3) page from the Library Functions Manual, and the actual file it's documenting is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgglse.f. 💅✨

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices. periodt. 👑

💖 Function/Subroutine Documentation 💖

subroutine ZGGLSE (integer m, integer n, integer p, complex*16, dimension(
       lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb,
       complex*16, dimension( * ) c, complex*16, dimension( * ) d, complex*16,
       dimension( * ) x, complex*16, dimension( * ) work, integer lwork,
       integer info)

Same energy, one more time: ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices. 🫶

🎀 Purpose 🎀

Literally the whole point: it 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.

iconic math behavior, honestly. 🦋

🌈 Parameters 🌈

M

M is INTEGER. It's the number of rows of the matrix A. M >= 0. 👑

N

N is INTEGER. It's the number of columns of the matrices A and B. N >= 0. 🌸

P

P is INTEGER. It's the number of rows of the matrix B. 0 <= P <= N <= M+P. 💅

A

A is a COMPLEX*16 array, dimension (LDA,N). On entry, it's 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. It's the leading dimension of the array A. LDA >= max(1,M). ✨

B

B is a COMPLEX*16 array, dimension (LDB,N). On entry, it's 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. It's the leading dimension of the array B. LDB >= max(1,P). 💜

C

C is a COMPLEX*16 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 a COMPLEX*16 array, dimension (P). On entry, D contains the right hand side vector for the constrained equation. On exit, D is destroyed. 💀 dramatic, but that's literally what it says.

X

X is a COMPLEX*16 array, dimension (N). On exit, X is the solution of the LSE problem. 👑

WORK

WORK is a COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🫶

LWORK

LWORK is INTEGER. It's 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 ZGEQRF, CGERQF, ZUNMQR and CUNMRQ. 🌈

Workspace-query alert, bestie: 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, and it reports the outcome:

• = 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 the following rank condition holds and the least squares solution could not be computed:

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

Not me reading the stacked matrix notation like it's a text from your crush. 😭

👑 Author 👑

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

Definition at line 178 of file zgglse.f. 📍

👑 Author 👑

This next bit is the auto-generated author note, and it's exactly this: Generated automatically by Doxygen for LAPACK from the source code. 🤖💖

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That's the whole page, bestie! This one is LAPACK Version 3.12.0, and its footer source path is /home/abui...RC/zgglse.f(3). 💖✨🫶