1DGGLSE(1) LAPACK driver routine (version 3.1) DGGLSE(1)
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6 DGGLSE - the linear equality-constrained least squares (LSE) problem
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9 SUBROUTINE DGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO
10 )
11 INTEGER INFO, LDA, LDB, LWORK, M, N, P
13 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( * ), D( * ),
15 WORK( * ), X( * )
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18 DGGLSE solves the linear equality-constrained least squares (LSE) prob‐
19 lem:
20 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‐
24 tor, and d is a given P-vector. It is assumed that
25 P <= N <= M+P, and
26 rank(B) = P and rank( (A) ) = N.
28 ( (B) )
29 These conditions ensure that the LSE problem has a unique solution,
31 which is obtained using a generalized RQ factorization of the matrices
32 (B, A) given by
33 B = (0 R)*Q, A = Z*T*Q.
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38 M (input) INTEGER
39 The number of rows of the matrix A. M >= 0.
40 N (input) INTEGER
42 The number of columns of the matrices A and B. N >= 0.
43 P (input) INTEGER
45 The number of rows of the matrix B. 0 <= P <= N <= M+P.
46 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
48 On entry, the M-by-N matrix A. On exit, the elements on and
49 above the diagonal of the array contain the min(M,N)-by-N upper
50 trapezoidal matrix T.
51 LDA (input) INTEGER
53 The leading dimension of the array A. LDA >= max(1,M).
54 B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
56 On entry, the P-by-N matrix B. On exit, the upper triangle of
57 the subarray B(1:P,N-P+1:N) contains the P-by-P upper triangu‐
58 lar matrix R.
59 LDB (input) INTEGER
61 The leading dimension of the array B. LDB >= max(1,P).
62 C (input/output) DOUBLE PRECISION array, dimension (M)
64 On entry, C contains the right hand side vector for the least
65 squares part of the LSE problem. On exit, the residual sum of
66 squares for the solution is given by the sum of squares of ele‐
67 ments N-P+1 to M of vector C.
68 D (input/output) DOUBLE PRECISION array, dimension (P)
70 On entry, D contains the right hand side vector for the con‐
71 strained equation. On exit, D is destroyed.
72 X (output) DOUBLE PRECISION array, dimension (N)
74 On exit, X is the solution of the LSE problem.
75 WORK (workspace/output) DOUBLE PRECISION array, dimension
77 (MAX(1,LWORK))
78 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
79 LWORK (input) INTEGER
81 The dimension of the array WORK. LWORK >= max(1,M+N+P). For
82 optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, where NB
83 is an upper bound for the optimal blocksizes for DGEQRF,
84 SGERQF, DORMQR and SORMRQ.
85 If LWORK = -1, then a workspace query is assumed; the routine
87 only calculates the optimal size of the WORK array, returns
88 this value as the first entry of the WORK array, and no error
89 message related to LWORK is issued by XERBLA.
90 INFO (output) INTEGER
92 = 0: successful exit.
93 < 0: if INFO = -i, the i-th argument had an illegal value.
94 = 1: the upper triangular factor R associated with B in the
95 generalized RQ factorization of the pair (B, A) is singular, so
96 that rank(B) < P; the least squares solution could not be com‐
97 puted. = 2: the (N-P) by (N-P) part of the upper trapezoidal
98 factor T associated with A in the generalized RQ factorization
99 of the pair (B, A) is singular, so that rank( (A) ) < N; the
100 least squares solution could not ( (B) ) be computed.
101 LAPACK driver routine (version 3.N1o)vember 2006 DGGLSE(1)