WOLFRAM SYSTEM MODELER

# LAPACK

Interface to LAPACK library (should usually not directly be used but only indirectly via Modelica.Math.Matrices)

# Package Contents

 Compute eigenvalues and (right) eigenvectors for real nonsymmetric matrix A Compute eigenvalues for real nonsymmetric matrix A Compute the minimum-norm solution to a real linear least squares problem with rank deficient A Compute the minimum-norm solution to a real linear least squares problem with rank deficient A Solve overdetermined or underdetermined real linear equations A*x=b with a b vector Solve real system of linear equations A*X=B with a B matrix Solve real system of linear equations A*x=b with a b vector Solve a linear equality constrained least squares problem Solve real system of linear equations A*X=B with B matrix and tridiagonal A Solve real system of linear equations A*x=b with b vector and tridiagonal A Solve real system of linear equations A*X=B with a B matrix Solve real system of linear equations A*x=b with a b vector Determine singular value decomposition Determine singular values Compute LU factorization of square or rectangular matrix A (A = P*L*U) Solve a system of linear equations with the LU decomposition from dgetrf Solve a system of linear equations with the LU decomposition from dgetrf Compute the inverse of a matrix using the LU factorization from dgetrf Compute QR factorization with column pivoting of square or rectangular matrix A Generate a Real orthogonal matrix Q which is defined as the product of elementary reflectors as returned from dgeqrf Compute real Schur form T of real nonsymmetric matrix A, and, optionally, the matrix of Schur vectors Z as well as the eigenvalues Reorder the real Schur factorization of a real matrix Solve real system of linear equations op(A)*X=B, op(A) is A or A' according to the Boolean input transposed Solve the real Sylvester matrix equation op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C Compute eigenvalues of a matrix H using lapack routine DHSEQR for Hessenberg form matrix Norm of a matrix Estimate the reciprocal of the condition number of a general real matrix A Reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H Compute a QR factorization without pivoting Compute the eigenvalues and the (real) left and right eigenvectors of matrix A, using lapack routine dgeevx Determine singular value decomposition Compute generalized eigenvalues, as well as the left and right eigenvectors for a (A,B) system Compute generalized eigenvalues for a (A,B) system, using lapack routine dggevx Compute generalized eigenvalues for a (A,B) system 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 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 Compute the right and/or left eigenvectors of a real upper quasi-triangular matrix T Compute the Cholesky factorization of a real symmetric positive definite matrix A Solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where A is triangular matrix. BLAS routine Generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD

# Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

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:

Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., and Sorensen D.:
Lapack Users' Guide. Third Edition, SIAM, 1999.

`SystemModel["Modelica.Math.Matrices.LAPACK"]`