This package contains external Modelica functions as interface to the LAPACK library (http://www.netlib.org/lapack) that provides FORTRAN subroutines to solve linear algebra tasks. Usually, these functions are not directly called, but only via the much more convenient interface of Modelica.Math.Matrices. The documentation of the LAPACK functions is a copy of the original FORTRAN code. The details of LAPACK are described in:
See also http://en.wikipedia.org/wiki/Lapack.
This package contains a direct interface to the LAPACK subroutines
| Name | Description |
|---|---|
| dgbsv | Solve real system of linear equations A*X=B with a B matrix |
| dgbsv_vec | Solve real system of linear equations A*x=b with a b vector |
| dgecon | Estimate the reciprocal of the condition number of a general real matrix A |
| dgees | Compute real Schur form T of real nonsymmetric matrix A, and, optionally, the matrix of Schur vectors Z as well as the eigenvalues |
| dgeev | Compute eigenvalues and (right) eigenvectors for real nonsymmetric matrix A |
| dgeev_eigenValues | Compute eigenvalues for real nonsymmetric matrix A |
| dgeevx | Compute the eigenvalues and the (real) left and right eigenvectors of matrix A, using lapack routine dgeevx |
| dgehrd | Reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H |
| dgels_vec | Solve overdetermined or underdetermined real linear equations A*x=b with a b vector |
| dgelsy | Compute the minimum-norm solution to a real linear least squares problem with rank deficient A |
| dgelsy_vec | Compute the minimum-norm solution to a real linear least squares problem with rank deficient A |
| dgeqp3 | Compute QR factorization with column pivoting of square or rectangular matrix A |
| dgeqrf | Compute a QR factorization without pivoting |
| dgesdd | Determine singular value decomposition |
| dgesv | Solve real system of linear equations A*X=B with a B matrix |
| dgesv_vec | Solve real system of linear equations A*x=b with a b vector |
| dgesvd | Determine singular value decomposition |
| dgesvd_sigma | Determine singular values |
| dgesvx | Solve real system of linear equations op(A)*X=B, op(A) is A or A' according to the Boolean input transposed |
| dgetrf | Compute LU factorization of square or rectangular matrix A (A = P*L*U) |
| dgetri | Compute the inverse of a matrix using the LU factorization from dgetrf |
| dgetrs | Solve a system of linear equations with the LU decomposition from dgetrf |
| dgetrs_vec | Solve a system of linear equations with the LU decomposition from dgetrf |
| dggev | Compute generalized eigenvalues, as well as the left and right eigenvectors for a (A,B) system |
| dggevx | Compute generalized eigenvalues for a (A,B) system, using lapack routine dggevx |
| dgglse_vec | Solve a linear equality constrained least squares problem |
| dgtsv | Solve real system of linear equations A*X=B with B matrix and tridiagonal A |
| dgtsv_vec | Solve real system of linear equations A*x=b with b vector and tridiagonal A |
| dhgeqz | Compute generalized eigenvalues for a (A,B) system |
| dhseqr | Compute eigenvalues of a matrix H using lapack routine DHSEQR for Hessenberg form matrix |
| dlange | Norm of a matrix |
| dorghr | Generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD |
| dorgqr | Generate a Real orthogonal matrix Q which is defined as the product of elementary reflectors as returned from dgeqrf |
| dormhr | Overwrite the general real M-by-N matrix C with Q * C or C * Q or Q' * C or C * Q', where Q is an orthogonal matrix as returned by dgehrd |
| dormqr | Overwrite the general real M-by-N matrix C with Q * C or C * Q or Q' * C or C * Q', where Q is an orthogonal matrix of a QR factorization as returned by dgeqrf |
| dpotrf | Compute the Cholesky factorization of a real symmetric positive definite matrix A |
| dtrevc | Compute the right and/or left eigenvectors of a real upper quasi-triangular matrix T |
| dtrsen | Reorder the real Schur factorization of a real matrix |
| dtrsm | Solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where A is triangular matrix. BLAS routine |
| dtrsyl | Solve the real Sylvester matrix equation op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C |