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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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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
Download CGGLSE + dependencies [TGZ] [ZIP] [TXT]
CGGLSE 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. 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 RQ factorization of the pair (B, A) 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.
[in] | M | M is INTEGER The number of rows of the matrix A. M >= 0. |
[in] | N | N is INTEGER The number of columns of the matrices A and B. N >= 0. |
[in] | P | P is INTEGER The number of rows of the matrix B. 0 <= P <= N <= M+P. |
[in,out] | 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. |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[in,out] | 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. |
[in] | LDB | LDB is INTEGER The leading dimension of the array B. LDB >= max(1,P). |
[in,out] | 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. |
[in,out] | 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. |
[out] | X | X is COMPLEX array, dimension (N) On exit, X is the solution of the LSE problem. |
[out] | WORK | WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | 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. |
[out] | 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 exactly 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 exactly singular, so that rank( (A) ) < N; the least squares solution could not ( (B) ) be computed. |