zggglm zgglse

zggglm() void zggglm ( int  n, int  m, int  p, int  lda, doublecomplex  a[], int  ldb, doublecomplex  b[], doublecomplex  d[], doublecomplex  x[], doublecomplex  y[], doublecomplex  work[], int  lwork, int *  info  ) General Gauss-Markov linear model (GLM) problem of complex matrices Purpose This routine solves a general Gauss-Markov linear model (GLM) problem: minimize || y ||_2 subject to d = A*x + B*y x where A is an n x m matrix, B is an n x p matrix, and d is a given n-vector. It is assumed that m <= n <= m+p, and rank(A) = m and rank(A B) = n Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of the matrices (A, B) given by A = Q*(R), B = Q*T*Z (0) In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem minimize || inv(B)*(d - A*x) ||_2 x Parameters [in] n Number of rows of the matrices A and B. (n >= 0) (If n = 0, returns without computation) [in] m Number of columns of the matrix A. (0 <= m <= n) [in] p Number of columns of the matrix B. (p >= n - m) [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, n)) [in,out] a[][] Array a[la][lda] (la >= m) [in] n x m matrix A. [out] The upper triangular part of the array a[][] contains the m x m upper triangular matrix R. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, n)) [in,out] b[][] Array b[lb][ldb] (lb >= p) [in] n x p matrix B. [out] n <= p: The upper triangle of the subarray b[p-n to p-1][0 to n-1] contains the n x n upper triangular matrix T.   n > p: The elements on and above the (n-p)th sub-diagonal contain the n x p upper trapezoidal matrix T. [in,out] d[] Array d[ld] (ld >= n) [in] d[] is the left hand side of the GLM equation. [out] d[] is destroyed. [out] x[] Array x[lx] (lx >= m) [out] y[] Array y[ly] (ly >= p) x[] and y[] are the solutions of the GLM 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, n+m+p)) For optimum performance, lwork >= max(1, m + min(n, p) + max(n, p)*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 n had an illegal value (n < 0) = -2: The argument m had an illegal value (m < 0 or m > n) = -3: The argument p had an illegal value (p < 0 or p < n - m) = -4: The argument lda had an illegal value (lda < max(1, n)) = -6: The argument ldb had an illegal value (ldb < max(1, n)) = -12: The argument lwork had an illegal value (lwork too small) = 1: The upper triangular factor R associated with A in the generalized QR factorization of the pair (A, B) is singular, so that rank(A) < m. The least squares solution could not be computed. = 2: The bottom n-m x n-m part of the upper trapezoidal factor T associated with B in the generalized QR factorization of the pair (A, B) is singular, so that rank(A B) < n. The least squares solution could not be computed. Reference LAPACK