dgecon dgecov dgels dgesv dlange dlansy dpocon dposv dsyev

dposv() def dposv ( uplo  , n  , a  , b  , nrhs  = 1  ) Solution to system of linear equations AX = B for a symmetric positive definite matrix Purpose dposv computes the solution to a real system of linear equations A * X = B, where A is an n x n symmetric positive definite matrix and X and B are n x nrhs matrices. The Cholesky decomposition is used to factor A as A = U^T*U, if uplo = 'U', or A = L*L^T, if uplo = 'L', where U is an upper triangular matrix and L is a lower triangular matrix. 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 uplo had an illegal value (uplo != 'U' nor 'L') = -2: The argument n had an illegal value (n < 0) = -3: The argument a is invalid. = -4: The argument b is invalid. = -5: The argument nrhs had an illegal value (nrhs < 0) = i > 0: The leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed. Parameters [in] uplo = 'U': Upper triangle of A is stored. = 'L': Lower triangle of A is stored. [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 symmetric positove definite matrix A. The upper or lower triangular part is to be referenced in accordance with uplo. [out] If info = 0, the factor U or L from the Cholesky factorization A = U^T*U or A = L*L^T. [in,out] b Numpy ndarray (1 or 2-dimensional, float, n or n x nrhs) [in] n x nrhs 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 A is symmetric positive definite and ( 2.2 -0.11 -0.32 ) ( -1.566 ) A = ( -0.11 2.93 0.81 ), B = ( -2.8425 ) ( -0.32 0.81 2.37 ) ( -1.1765 ) def TestDposv(): n = 3 a = np.array([ [2.2, 0.0, 0.0], [-0.11, 2.93, 0.0], [-0.32, 0.81, 2.37]]) b = np.array([-1.566, -2.8425, -1.1765]) anorm, info = dlansy('1', 'U', n, a) info = dposv('U', n, a, b) print(b, info) rcond, info = dpocon('U', n, a, anorm) print(rcond, info) Example Results >>> TestDposv() [-0.8 -0.92 -0.29] 0 0.4467910780689557 0