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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine sgglse | ( | integer | m, |
| integer | n, | ||
| integer | p, | ||
| real, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| real, dimension( ldb, * ) | b, | ||
| integer | ldb, | ||
| real, dimension( * ) | c, | ||
| real, dimension( * ) | d, | ||
| real, dimension( * ) | x, | ||
| real, dimension( * ) | work, | ||
| integer | lwork, | ||
| integer | info | ||
| ) |
SGGLSE solves overdetermined or underdetermined systems for OTHER matrices
Download SGGLSE + dependencies [TGZ] [ZIP] [TXT]
SGGLSE 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 STRTRS 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
On exit, X is the solution of the LSE problem. |
| [out] | WORK | WORK is REAL 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
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. |
| [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. |
1.9.8