_dggglm _dgglse

_dgglse() void _dgglse ( int  m, int  n, int  p, int  lda, double  a[], int  ldb, double  b[], double  c[], double  d[], double  x[], double  work[], int  lwork, int *  info  ) Linear equality-constrained least squares (LSE) problem Purpose This routine solves the linear equality-constrained least squares (LSE) problem: minimize || c - Ax ||_2 subject to B*x = d where A is an m x n matrix, B is a p x 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 Parameters [in] m Number of rows of the matrix A. (m >= 0) [in] n Number of columns of the matrices A and B. (n >= 0) (If n = 0, returns without computation) [in] p Number of rows of the matrix B. (0 <= p <= n <= m + p) [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, m)) [in,out] a[][] Array a[la][lda] (la >= n) [in] m x n matrix A. [out] The elements on and above the diagonal of the array contain the min(m, n) x n upper trapezoidal matrix T. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, p)) [in,out] b[][] Array b[lb][ldb] (lb >= n) [in] p x n matrix B. [out] The upper triangle of the subarray b[n-p to n-1][0 to p-1] contains the p x p upper triangular matrix R. [in,out] c[] Array c[lc] (lc >= m) [in] The right hand side vector for the least squares part of the LSE problem. [out] The residual sum of squares for the solution is given by the sum of squares of elements n-p to m-1 of the array c[]. [in,out] d[] Array d[ld] (ld >= p) [in] The right hand side vector for the constrained equation. [out] d[] is destroyed. [out] x[] Array x[lx] (lx >= n) Solution of the LSE problem. [out] work[] Array work[lwork] Work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The dimension of the array work[]. (lwork >= max(1, m+n+p)) For optimum performance, lwork >= max(1, p + min(m, n) + max(m, n)*nb), where nb is the upper bound for the optimal block sizes. If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[] array, and returns the value in work[0]. [out] info = 0: Successful exit = -1: The argument m had an illegal value (m < 0) = -2: The argument n had an illegal value (n < 0) = -3: The argument p had an illegal value (p < 0 or p > n or p < n - m) = -4: The argument lda had an illegal value (lda < max(1, m)) = -6: The argument ldb had an illegal value (ldb < max(1, p)) = -12: The argument lwork had an illegal value (lwork too small) = 1: The upper triangular factor R associated with B in the generalized RQ factorization of the pair (B, A) is singular, so that rank(B) < p. The least squares solution could not be computed. = 2: The n-p x n-p part of the upper trapezoidal factor T associated with A in the generalized RQ factorization of the pair (B, A) is singular, so that rank((A^T B^T)^T) < n. The least squares solution could not be computed. Reference LAPACK