dgecov dgecovs dgecovy dgels dgelsd dgelss dgelsy dgetsls

dgelss() void dgelss ( int  m, int  n, int  nrhs, int  lda, double  a[], int  ldb, double  b[], double  s[], double  rcond, int *  rank, double  work[], int  lwork, int *  info  ) Solution to overdetermined or underdetermined linear equations Ax = b using the singular value decomposition (SVD) Purpose This routine computes the minimum norm solution to a real linear least squares problem: minimize || A * X - B || using the singular value decomposition (SVD) of A. A is an m x n matrix which may be rank-deficient. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the m x nrhs right hand side matrix B and the n x nrhs solution matrix X. The effective rank of A is determined by treating as zero those singular values which are less than rcond times the largest singular value. Parameters [in] m Number of rows of the matrix A. (m >= 0) (If m = 0, returns with rank = 0) [in] n Number of columns of the matrix A. (n >= 0) (If n = 0, returns with rank = 0) [in] nrhs Number of right hand sides, i.e., number of columns of the matrices B and X. (nrhs >= 0) [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 first min(m, n) rows of a[][] are overwritten with its right singular vectors, stored rowwise. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, m, n)) [in,out] b[][] Array b[lb][ldb] (lb >= nrhs) [in] m x nrhs right hand side matrix B. [out] b[][] is overwritten by the n x nrhs solution matrix X. If m >= n and rank = n, the residual sum of squares for the solution in the i-th column is given by the sum of squares of elements n to m-1 in that column. [out] s[] Array s[ls] (ls >= min(m, n)) The singular values of A in decreasing order. The condition number of A in the 2-norm = s[0]/s[min(m, n)-1]. [in] rcond rcond is used to determine the effective rank of A. Singular values s[i] <= rcond*s[0] are treated as zero. If rcond < 0, machine precision is used instead. [out] rank The effective rank of A, i.e., the number of singular values which are greater than rcond*s[0]. [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, 3*min(m, n)+max(2*min(m, n), max(m, n), nrhs))) For good performance, lwork must generally be larger. 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 nrhs had an illegal value (nrhs < 0) = -4: The argument lda had an illegal value (lda < max(1, m)) = -6: The argument ldb had an illegal value (ldb < max(1, m, n)) = -12: The argument lwork had an illegal value (lwork too small) = i > 0: The algorithm for computing the SVD failed to converge; i off-diagonal elements of an intermediate bidiagonal form did not converge to zero. Reference LAPACK