.Modelica_LinearSystems2.Math.Matrices.LAPACK.dposv

Information

Lapack documentation:

   Purpose
   =======

   DPOSV computes the solution to a real system of linear equations
      A * X = B,
   where A is an N-by-N symmetric positive definite matrix and X and B
   are N-by-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.

   Arguments
   =========

   UPLO    (input) CHARACTER*1
           = 'U':  Upper triangle of A is stored;
           = 'L':  Lower triangle of A is stored.

   N       (input) INTEGER
           The number of linear equations, i.e., the order of the
           matrix A.  N >= 0.

   NRHS    (input) INTEGER
           The number of right hand sides, i.e., the number of columns
           of the matrix B.  NRHS >= 0.

   A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
           On entry, the symmetric matrix A.  If UPLO = 'U', the leading
           N-by-N upper triangular part of A contains the upper
           triangular part of the matrix A, and the strictly lower
           triangular part of A is not referenced.  If UPLO = 'L', the
           leading N-by-N lower triangular part of A contains the lower
           triangular part of the matrix A, and the strictly upper
           triangular part of A is not referenced.

           On exit, if INFO = 0, the factor U or L from the Cholesky
           factorization A = U**T*U or A = L*L**T.

   LDA     (input) INTEGER
           The leading dimension of the array A.  LDA >= max(1,N).

   B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
           On entry, the N-by-NRHS right hand side matrix B.
           On exit, if INFO = 0, the N-by-NRHS solution matrix X.

   LDB     (input) INTEGER
           The leading dimension of the array B.  LDB >= max(1,N).

   INFO    (output) INTEGER
           = 0:  successful exit
           < 0:  if INFO = -i, the i-th argument had an illegal value
           > 0:  if INFO = i, 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.

   =====================================================================

Interface

function dposv
  extends Modelica.Icons.Function;
  input Real A[:, size(A, 1)] "Real symmetric positive definite matrix A";
  input Real B[size(A, 2), :] "Right hand side of A*X = B";
  input Boolean upper = true "True if the upper triangle of A is provided";
  output Real X[size(B, 1), size(B, 2)] = B "Solution of A*X = B";
  output Integer info;
end dposv;