SRC/cggglm.f(3) | Library Functions Manual | SRC/cggglm.f(3) |
NAME
SRC/cggglm.f
SYNOPSIS
Functions/Subroutines
subroutine cggglm (n, m, p, a, lda, b, ldb, d, x, y, work,
lwork, info)
CGGGLM
Function/Subroutine Documentation
subroutine cggglm (integer n, integer m, integer p, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) d, complex, dimension( * ) x, complex, dimension( * ) y, complex, dimension( * ) work, integer lwork, integer info)
CGGGLM
Purpose:
!> !> CGGGLM 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 CTRTRS 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 !> The number of rows of the matrices A and B. N >= 0. !>
M
!> M is INTEGER !> The number of columns of the matrix A. 0 <= M <= N. !>
P
!> P is INTEGER !> The number of columns of the matrix B. P >= N-M. !>
A
!> A is COMPLEX 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. LDA >= max(1,N). !>
B
!> B is COMPLEX 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. LDB >= max(1,N). !>
D
!> D is COMPLEX array, dimension (N) !> On entry, D is the left hand side of the GLM equation. !> On exit, D is destroyed. !>
X
!> X is COMPLEX array, dimension (M) !>
Y
!> Y is COMPLEX array, dimension (P) !> !> On exit, X and Y are the solutions of the GLM 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,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 !> 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 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 cggglm.f.
Author
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