CGGLSE(3)

CGGLSE(3) — Library Functions Manual 🫶

NAME

bestie, this whole page is about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgglse.f — that's the source file, and it's giving main character energy 💅

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine CGGLSE

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

CGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose

okay so CGGLSE solves the linear equality-constrained least squares (LSE) problem, and yes this is as iconic as it sounds:

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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (P).

• On entry, D contains the right hand side vector for the constrained equation.
• On exit, D is destroyed.

X

X is COMPLEX array, dimension (N).

• On exit, X is the solution of the LSE problem.

WORK

WORK is COMPLEX 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 CGEQRF, CGERQF, CUNMQR and CUNMRQ.
• 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.

Author

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

Definition at line 178 of file cgglse.f.

Author

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