.Modelica.Math.Matrices .Modelica.Math.MatricesThis library provides functions operating on matrices. Below, the functions are ordered according to categories and a typical call of the respective function is shown. Most functions are solely an interface to the external LAPACK library.
Note: A' is a short hand notation of transpose(A):
Basic Information
Linear Equations
Matrix Factorizations
Matrix Properties
Matrix Exponentials
Matrix Equations
Matrix Manipulation
| Name | Description |
|---|---|
 Examples | Examples demonstrating the usage of the Math.Matrices functions |
 toString | Convert a matrix into its string representation |
 isEqual | Compare whether two Real matrices are identical |
 solve | Solve real system of linear equations A*x=b with a b vector (Gaussian elimination with partial pivoting) |
 solve2 | Solve real system of linear equations A*X=B with a B matrix (Gaussian elimination with partial pivoting) |
 leastSquares | Solve linear equation A*x = b (exactly if possible, or otherwise in a least square sense; A may be non-square and may be rank deficient) |
 leastSquares2 | Solve linear equation A*X = B (exactly if possible, or otherwise in a least square sense; A may be non-square and may be rank deficient) |
 equalityLeastSquares | Solve a linear equality constrained least squares problem |
 LU | LU decomposition of square or rectangular matrix |
 LU_solve | Solve real system of linear equations P*L*U*x=b with a b vector and an LU decomposition (from LU(..)) |
 LU_solve2 | Solve real system of linear equations P*L*U*X=B with a B matrix and an LU decomposition (from LU(..)) |
 eigenValues | Return eigenvalues and eigenvectors for a real, nonsymmetric matrix in a Real representation |
 eigenValueMatrix | Return real valued block diagonal matrix J of eigenvalues of matrix A (A=V*J*Vinv) |
 singularValues | Return singular values and left and right singular vectors |
 QR | Return the QR decomposition of a square matrix with optional column pivoting (A(:,p) = Q*R) |
 hessenberg | Return upper Hessenberg form of a matrix |
 realSchur | Return the real Schur form (rsf) S of a square matrix A, A=QZ*S*QZ' |
 cholesky | Return the Cholesky factorization of a symmetric positive definite matrix |
 balance | Return a balanced form of matrix A to improve the condition of A |
 balanceABC | Return a balanced form of a system [A,B;C,0] to improve its condition by a state transformation |
 trace | Return the trace of matrix A, i.e., the sum of the diagonal elements |
 det | Return determinant of a matrix (computed by LU decomposition; try to avoid det(..)) |
 inv | Return inverse of a matrix (try to avoid inv(..)) |
 rank | Return rank of a rectangular matrix (computed with singular values) |
 conditionNumber | Return the condition number norm(A)*norm(inv(A)) of a matrix A |
 rcond | Return the reciprocal condition number of a matrix |
 norm | Return the p-norm of a matrix |
 frobeniusNorm | Return the Frobenius norm of a matrix |
 nullSpace | Return the orthonormal nullspace of a matrix |
 exp | Return the exponential of a matrix by adaptive Taylor series expansion with scaling and balancing |
 integralExp | Return the exponential and the integral of the exponential of a matrix |
 integralExpT | Return the exponential, the integral of the exponential, and time-weighted integral of the exponential of a matrix |
 continuousLyapunov | Return solution X of the continuous-time Lyapunov equation X*A + A'*X = C |
 continuousSylvester | Return solution X of the continuous-time Sylvester equation A*X + X*B = C |
 continuousRiccati | Return solution X of the continuous-time algebraic Riccati equation A'*X + X*A - X*B*inv(R)*B'*X + Q = 0 (care) |
 discreteLyapunov | Return solution X of the discrete-time Lyapunov equation A'*X*A + sgn*X = C |
 discreteSylvester | Return solution of the discrete-time Sylvester equation A*X*B + sgn*X = C |
 discreteRiccati | Return solution of discrete-time algebraic Riccati equation A'*X*A - X - A'*X*B*inv(R + B'*X*B)*B'*X*A + Q = 0 (dare) |
 sort | Sort the rows or columns of a matrix in ascending or descending order |
 flipLeftRight | Flip the columns of a matrix in left/right direction |
 flipUpDown | Flip the rows of a matrix in up/down direction |
 LAPACK | Interface to LAPACK library (should usually not directly be used but only indirectly via Modelica.Math.Matrices) |
 Utilities | Utility functions that should not be directly utilized by the user |