dgecon dgecov dgels dgesv dlange dlansy dpocon dposv dsyev

dposv() function dposv ( uplo::Char  , n::Integer  , a::Array{Float64}  , b::Array{Float64}  , nrhs::Integer  = 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 (Int32) = 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 2-dimensional array (Float64, 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 1 or 2-dimensional array (Float64, 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 ) function TestDposv() n = 3 a = [ 2.2 -0.11 -0.32; 0.0 2.93 0.81; 0.0 0.0 2.37 ] b = [ -1.566, -2.8425, -1.1765 ] anorm, info = dlansy('1', 'U', n, a) info = dposv('U', n, a, b) println("x = ", b, ", info = ", info) if info == 0 rcond, info = dpocon('U', n, a, anorm) println("rcond = ", rcond, ", info = ", info) end end Example Results > TestDposv() x = [-0.7999999999999999, -0.9199999999999999, -0.29000000000000004], info = 0 rcond = 0.4467910780689557, info = 0