.Modelica.Math.Matrices.LAPACK

Information

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.

See also http://en.wikipedia.org/wiki/Lapack.

This package contains a direct interface to the LAPACK subroutines

Contents

Name	Description
dgeev	Compute eigenvalues and (right) eigenvectors for real nonsymmetric matrix A
dgeev_eigenValues	Compute eigenvalues for real nonsymmetric matrix A
dgegv	Compute generalized eigenvalues for a (A,B) system
dgelsx	Computes the minimum-norm solution to a real linear least squares problem with rank deficient A
dgelsx_vec	Computes the minimum-norm solution to a real linear least squares problem with rank deficient A
dgelsy	Computes the minimum-norm solution to a real linear least squares problem with rank deficient A
dgelsy_vec	Computes the minimum-norm solution to a real linear least squares problem with rank deficient A
dgels_vec	Solves overdetermined or underdetermined real linear equations A*x=b with a b vector
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
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
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
dgesvd	Determine singular value decomposition
dgesvd_sigma	Determine singular values
dgetrf	Compute LU factorization of square or rectangular matrix A (A = P*L*U)
dgetrs	Solves a system of linear equations with the LU decomposition from dgetrf(..)
dgetrs_vec	Solves a system of linear equations with the LU decomposition from dgetrf(..)
dgetri	Computes the inverse of a matrix using the LU factorization from dgetrf(..)
dgeqpf	Compute QR factorization of square or rectangular matrix A with column pivoting (A(:,p) = Q*R)
dorgqr	Generates a Real orthogonal matrix Q which is defined as the product of elementary reflectors as returned from dgeqpf
dgees	Computes real Schur form T of real nonsymmetric matrix A, and, optionally, the matrix of Schur vectors Z as well as the eigenvalues
dtrsen	Reorder the real Schur factorization of a real matrix
dgesvx	Solve real system of linear equations op(A)*X=B, op(A) is A or A' according to the Boolean input transposed
dtrsyl	Solve the real Sylvester matrix equation op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C
dhseqr	Compute eigenvalues of a matrix H using lapack routine DHSEQR for Hessenberg form matrix
dlange	Norm of a matrix
dgecon	Estimates the reciprocal of the condition number of a general real matrix A
dgehrd	reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H
dgeqrf	computes a QR factorization without pivoting
dgeevx	Compute the eigenvalues and the (real) left and right eigenvectors of matrix A, using lapack routine dgeevx
dgesdd	Determine singular value decomposition
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
dhgeqz	Compute generalized eigenvalues for a (A,B) system
dormhr	overwrites 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	overwrites 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
dtrevc	Compute the right and/or left eigenvectors of a real upper quasi-triangular matrix T
dpotrf	Computes the Cholesky factorization of a real symmetric positive definite matrix A
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
dorghr	Generates a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD