dgecon dgecov dgels dgesv dlange dlansy dpocon dposv dsyev

dgesv() def dgesv ( n  , a  , ipiv  , b  , nrhs  = 1  ) Solution to system of linear equations AX = B for a general matrix Purpose dgesv computes the solution to a real system of linear equations A * X = B where A is an n x n matrix and X and B are n x nrhs matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B. Returns info (int) = 0: Successful exit. = -1: The argument n had an illegal value. (n < 0) = -2: The argument a is invalid. = -3: The argument ipiv is invalid. = -4: The argument b is invalid. = -5: The argument nrhs had an illegal value. (nrhs < 0) = i > 0: The i-th diagonal element of the factor U is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed. Parameters [in] n Number of linear equations, i.e., order of the matrix A. (n >= 0) (If n = 0, returns without computation) [in,out] a Numpy ndarray (2-dimensional, float, n x n) [in] n x n coefficient matrix A. [out] Factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. [out] ipiv Numpy ndarray (1-dimensional, int, n) Pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row ipiv[i - 1]. [in,out] b Numpy ndarray (1 or 2-dimensional, float, n or n x nrhs) [in] n x nrhs matrix of right hand side matrix B. [out] If info = 0, the n x nrhs solution matrix X. [in] nrhs (Optional) Number of right hand sides, i.e., number of columns of the matrix B. (nrhs >= 0) (If nrhs = 0, returns without computation) (default = 1) Reference LAPACK Example Program Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where ( 0.2 -0.11 -0.93 ) ( -0.3727 ) A = ( -0.32 0.81 0.37 ), B = ( 0.4319 ) ( -0.8 -0.92 -0.29 ) ( -1.4247 ) def TestDgesv(): n = 3 a = np.array([ [0.2, -0.32, -0.8], [-0.11, 0.81, -0.92], [-0.93, 0.37, -0.29]]) b = np.array([-0.3727, 0.4319, -1.4247]) ipiv = np.empty(n, dtype=int) anorm, info = dlange('1', n, n, a) info = dgesv(n, a, ipiv, b) print(b, info) rcond, info = dgecon('1', n, a, anorm) print(rcond, info) Example Results >>> TestDgesv() [0.86 0.64 0.51] 0 0.23270847318607646 0