1DGGLSE(1) LAPACK driver routine (version 3.2) DGGLSE(1)
2
6 DGGLSE - solves the linear equality-constrained least squares (LSE)
7 problem
8
10 SUBROUTINE DGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO
11 )
12 INTEGER INFO, LDA, LDB, LWORK, M, N, P
14 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( * ), D( * ),
16 WORK( * ), X( * )
17
19 DGGLSE solves the linear equality-constrained least squares (LSE) prob‐
20 lem:
21 minimize || c - A*x ||_2 subject to B*x = d
22 where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vec‐
23 tor, and d is a given P-vector. It is assumed that
24 P <= N <= M+P, and
25 rank(B) = P and rank( (A) ) = N.
26 ( (B) )
27 These conditions ensure that the LSE problem has a unique solution,
28 which is obtained using a generalized RQ factorization of the matrices
29 (B, A) given by
30 B = (0 R)*Q, A = Z*T*Q.
31
33 M (input) INTEGER
34 The number of rows of the matrix A. M >= 0.
35 N (input) INTEGER
37 The number of columns of the matrices A and B. N >= 0.
38 P (input) INTEGER
40 The number of rows of the matrix B. 0 <= P <= N <= M+P.
41 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
43 On entry, the M-by-N matrix A. On exit, the elements on and
44 above the diagonal of the array contain the min(M,N)-by-N upper
45 trapezoidal matrix T.
46 LDA (input) INTEGER
48 The leading dimension of the array A. LDA >= max(1,M).
49 B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
51 On entry, the P-by-N matrix B. On exit, the upper triangle of
52 the subarray B(1:P,N-P+1:N) contains the P-by-P upper triangu‐
53 lar matrix R.
54 LDB (input) INTEGER
56 The leading dimension of the array B. LDB >= max(1,P).
57 C (input/output) DOUBLE PRECISION array, dimension (M)
59 On entry, C contains the right hand side vector for the least
60 squares part of the LSE problem. On exit, the residual sum of
61 squares for the solution is given by the sum of squares of ele‐
62 ments N-P+1 to M of vector C.
63 D (input/output) DOUBLE PRECISION array, dimension (P)
65 On entry, D contains the right hand side vector for the con‐
66 strained equation. On exit, D is destroyed.
67 X (output) DOUBLE PRECISION array, dimension (N)
69 On exit, X is the solution of the LSE problem.
70 WORK (workspace/output) DOUBLE PRECISION array, dimension
72 (MAX(1,LWORK))
73 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
74 LWORK (input) INTEGER
76 The dimension of the array WORK. LWORK >= max(1,M+N+P). For
77 optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, where NB
78 is an upper bound for the optimal blocksizes for DGEQRF,
79 SGERQF, DORMQR and SORMRQ. If LWORK = -1, then a workspace
80 query is assumed; the routine only calculates the optimal size
81 of the WORK array, returns this value as the first entry of the
82 WORK array, and no error message related to LWORK is issued by
83 XERBLA.
84 INFO (output) INTEGER
86 = 0: successful exit.
87 < 0: if INFO = -i, the i-th argument had an illegal value.
88 = 1: the upper triangular factor R associated with B in the
89 generalized RQ factorization of the pair (B, A) is singular, so
90 that rank(B) < P; the least squares solution could not be com‐
91 puted. = 2: the (N-P) by (N-P) part of the upper trapezoidal
92 factor T associated with A in the generalized RQ factorization
93 of the pair (B, A) is singular, so that rank( (A) ) < N; the
94 least squares solution could not ( (B) ) be computed.
95 LAPACK driver routine (version 3.N2o)vember 2008 DGGLSE(1)