On-Line SLICOT Overview

# SLICOT LIBRARY INDEX

To go to the beginning of a chapter click on the appropriate letter below:

A ; B ; C ; D ; F ; I ; M ; N ; S ; T ; U ;
or Return to SLICOT homepage
or Go to SLICOT Supporting Routines Index

## A - Analysis Routines

### AB - State-Space Analysis

#### Canonical and Quasi Canonical Forms

    AB01MD   Orthogonal controllability form for single-input system

    AB01ND   Orthogonal controllability staircase form for multi-input system

    AB01OD   Staircase form for multi-input system using orthogonal transformations

#### Continuous/Discrete Time

    AB04MD   Discrete-time <-> continuous-time conversion by bilinear transformation

#### Interconnections of Subsystems

    AB05MD   Cascade inter-connection of two systems in state-space form

    AB05ND   Feedback inter-connection of two systems in state-space form

    AB05OD   Rowwise concatenation of two systems in state-space form

    AB05PD   Parallel inter-connection of two systems in state-space form

    AB05QD   Appending two systems in state-space form

    AB05RD   Closed-loop system for a mixed output and state feedback control law

    AB05SD   Closed-loop system for an output feedback control law

#### Inverse and Dual Systems

    AB07MD   Dual of a given state-space representation

    AB07ND   Inverse of a given state-space representation

#### Poles, Zeros, Gain

    AB08MD   Normal rank of the transfer-function matrix of a state space model

    AB08MZ   Normal rank of the transfer-function matrix of a state space model (complex case)

    AB08ND   System zeros and Kronecker structure of system pencil

    AB08NW   System zeros and singular and infinite Kronecker structure of system pencil

    AB08NZ   System zeros and Kronecker structure of system pencil (complex case)

#### Model Reduction

    AB09AD   Balance & Truncate model reduction

    AB09BD   Singular perturbation approximation based model reduction

    AB09CD   Hankel norm approximation based model reduction

    AB09DD   Singular perturbation approximation formulas

    AB09ED   Hankel norm approximation based model reduction of unstable systems

    AB09FD   Balance & Truncate model reduction of coprime factors

    AB09GD   Singular perturbation approximation of coprime factors

    AB09HD   Stochastic balancing based model reduction

    AB09ID   Frequency-weighted model reduction based on balancing techniques

    AB09JD   Frequency-weighted Hankel norm approximation with invertible weights

    AB09KD   Frequency-weighted Hankel-norm approximation

    AB09MD   Balance & Truncate model reduction for the stable part

    AB09ND   Singular perturbation approximation based model reduction for the
             stable part

#### System Norms

    AB13AD   Hankel-norm of the stable projection

    AB13BD   H2 or L2 norm of a system

    AB13CD   H-infinity norm of a continuous-time stable system
             (obsolete, replaced by AB13DD)

    AB13DD   L-infinity norm of a state space system

    AB13HD   L-infinity norm of a state space system in standard or
             in descriptor form

    AB13ED   Complex stability radius, using bisection

    AB13FD   Complex stability radius, using bisection and SVD

    AB13ID   Properness of the transfer function matrix of a descriptor system

    AB13MD   Upper bound on the structured singular value for a square
             complex matrix

### AG - Generalized State-Space Analysis

#### Inverse and Dual Systems

    AG07BD   Descriptor inverse of a state-space or descriptor representation

#### Poles, Zeros, Gain

    AG08BD   Zeros and Kronecker structure of a descriptor system pencil

    AG08BZ   Zeros and Kronecker structure of a descriptor system pencil (complex case)

## B - Benchmark and Test Problems

### BB - State-space Models

    BB01AD   Benchmark examples for continuous-time Riccati equations

    BB02AD   Benchmark examples for discrete-time Riccati equations

    BB03AD   Benchmark examples of (generalized) continuous-time Lyapunov equations

    BB04AD   Benchmark examples of (generalized) discrete-time Lyapunov equations

### BD - Generalized State-space Models

    BD01AD   Benchmark examples of continuous-time systems

    BD02AD   Benchmark examples of discrete-time systems

## C - Adaptive Control

## D - Data Analysis

### DE - Covariances

    DE01OD   Convolution or deconvolution of two signals

    DE01PD   Convolution or deconvolution of two real signals using Hartley transform

### DF - Spectra

    DF01MD   Sine transform or cosine transform of a real signal

### DG - Discrete Fourier and Hartley Transforms

    DG01MD   Discrete Fourier transform of a complex signal

    DG01ND   Discrete Fourier transform of a real signal

    DG01OD   Scrambled discrete Hartley transform of a real signal

### DK - Windowing

    DK01MD   Anti-aliasing window applied to a real signal

## F - Filtering

### FB - Kalman Filters

    FB01QD   Time-varying square root covariance filter (dense matrices)

    FB01RD   Time-invariant square root covariance filter (Hessenberg form)

    FB01SD   Time-varying square root information filter (dense matrices)

    FB01TD   Time-invariant square root information filter (Hessenberg form)

    FB01VD   One recursion of the conventional Kalman filter

### FD - Fast Recursive Least Squares Filters

    FD01AD   Fast recursive least-squares filter

## I - Identification

### IB - Subspace Identification

#### Time Invariant State-space Systems

    IB01AD   Input-output data preprocessing and finding the system order

    IB01BD   Estimating the system matrices, covariances, and Kalman gain

    IB01CD   Estimating the initial state and the system matrices B and D

#### Wiener Systems

    IB03AD   Estimating a Wiener system by a Levenberg-Marquardt algorithm
             (Cholesky-based or conjugate gradients solver)

    IB03BD   Estimating a Wiener system by a MINPACK-like Levenberg-Marquardt
             algorithm

## M - Mathematical Routines

### MB - Linear Algebra

#### Basic Linear Algebra Manipulations

    MB01PD   Matrix scaling (higher level routine)

    MB01QD   Matrix scaling (lower level routine)

    MB01RB   Computation of a triangle of matrix expression alpha*R + beta*A*B
             or alpha*R + beta*B*A ( BLAS 3 version)

    MB01RD   Computation of matrix expression alpha*R + beta*A*X*trans(A)

    MB01TD   Product of two upper quasi-triangular matrices

    MB01UD   Computation of matrix expressions alpha*H*A or alpha*A*H,
             with H an upper Hessenberg matrix

    MB01UX   Computation of matrix expressions alpha*T*A or alpha*A*T, T quasi-triangular

    MB01UY   Computation of matrix expressions alpha*T*A or alpha*A*T, over T, T triangular

    MB01UZ   Computation of matrix expressions alpha*T*A or alpha*A*T, over T, T triangular
             (complex version)

    MB01WD   Residuals of Lyapunov or Stein equations for Cholesky factored
             solutions

    MB01XD   Computation of the product U'*U or L*L', with U and L upper and
             lower triangular matrices (block algorithm)

    MB01YD   Symmetric rank k operation C := alpha*A*A' + beta*C, C symmetric

    MB01ZD   Computation of matrix expressions H := alpha*T*H, or H := alpha*H*T,
             with H Hessenberg-like, T triangular

#### Linear Equations and Least Squares

    MB02CD   Cholesky factorization of a positive definite block Toeplitz matrix

    MB02DD   Updating Cholesky factorization of a positive definite block
             Toeplitz matrix

    MB02ED   Solution of T*X = B or X*T = B, with T a positive definite
             block Toeplitz matrix

    MB02FD   Incomplete Cholesky factor of a positive definite block Toeplitz matrix

    MB02GD   Cholesky factorization of a banded symmetric positive definite
             block Toeplitz matrix

    MB02HD   Cholesky factorization of the matrix T'*T, with T a banded
             block Toeplitz matrix of full rank

    MB02ID   Solution of over- or underdetermined linear systems with a full rank
             block Toeplitz matrix

    MB02JD   Full QR factorization of a block Toeplitz matrix of full rank

    MB02JX   Low rank QR factorization with column pivoting of a block Toeplitz matrix

    MB02KD   Computation of the product C = alpha*op( T )*B + beta*C, with T
             a block Toeplitz matrix

    MB02MD   Solution of Total Least-Squares problem using a SVD approach

    MB02ND   Solution of Total Least-Squares problem using a partial SVD approach

    MB02OD   Solution of op(A)*X = alpha*B, or X*op(A) = alpha*B, A triangular

    MB02PD   Solution of matrix equation op(A)*X = B, with error bounds
             and condition estimates

    MB02QD   Solution, optionally corresponding to specified free elements,
             of a linear least squares problem

    MB02RD   Solution of a linear system with upper Hessenberg matrix

    MB02RZ   Solution of a linear system with complex upper Hessenberg matrix

    MB02SD   LU factorization of an upper Hessenberg matrix

    MB02SZ   LU factorization of a complex upper Hessenberg matrix

    MB02TD   Condition number of an upper Hessenberg matrix

    MB02TZ   Condition number of a complex upper Hessenberg matrix

    MB02UD   Minimum norm least squares solution of op(R)*X = B, or X*op(R) = B,
             using singular value decomposition (R upper triangular)

    MB02VD   Solution of X*op(A) = B

#### Eigenvalues and Eigenvectors

    MB03LF   Eigenvalues and right deflating subspace of a real
             skew-Hamiltonian/Hamiltonian pencil in factored form

    MB03FZ   Eigenvalues and right deflating subspace of a complex
             skew-Hamiltonian/Hamiltonian pencil in factored form

    MB03LD   Eigenvalues and right deflating subspace of a real
             skew-Hamiltonian/Hamiltonian pencil

    MB03LP   Eigenvalues and right deflating subspace of a real
             skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)

    MB03LZ   Eigenvalues and right deflating subspace of a complex
             skew-Hamiltonian/Hamiltonian pencil

    MB3LZP   Eigenvalues and right deflating subspace of a complex
             skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)

    MB03MD   Upper bound for L singular values of a bidiagonal matrix

    MB03ND   Number of singular values of a bidiagonal matrix less than a bound

    MB03OD   Matrix rank determination by incremental condition estimation

    MB03PD   Matrix rank determination (row pivoting)

    MB03QD   Reordering of the diagonal blocks of a real Schur matrix

    MB03QG   Reordering of the diagonal blocks of principal subpencil of
             a real Schur-triangular matrix pencil

    MB03RD   Reduction of a real Schur matrix to a block-diagonal form

    MB03RZ   Reduction of a complex Schur matrix to a block-diagonal form

    MB03SD   Eigenvalues of a square-reduced Hamiltonian matrix

    MB03TD   Reordering the diagonal blocks of a matrix in (skew-)Hamiltonian Schur form

    MB03UD   Singular value decomposition of an upper triangular matrix

    MB03VD   Periodic Hessenberg form of a product of matrices

    MB03VW   Periodic Hessenberg form of a formal product of matrices

    MB03WD   Periodic Schur decomposition and eigenvalues of a product of
             matrices in periodic Hessenberg form

    MB03XD   Eigenvalues of a Hamiltonian matrix

    MB03XZ   Eigenvalues of a complex Hamiltonian matrix

    MB03XP   Periodic Schur decomposition and eigenvalues of a matrix product A*B,
             A upper Hessenberg and B upper triangular

    MB03YD   Periodic QR iteration

    MB03ZD   Stable and unstable invariant subspaces for a dichotomic Hamiltonian matrix

#### Decompositions and Transformations

    MB04AD   Eigenvalues and generalized symplectic URV decomposition of a real
             skew-Hamiltonian/Hamiltonian pencil in factored form

    MB04AZ   Eigenvalues of a complex skew-Hamiltonian/Hamiltonian pencil in factored form

    MB04BD   Eigenvalues and orthogonal decomposition of a real
             skew-Hamiltonian/Hamiltonian pencil

    MB04BP   Eigenvalues and orthogonal decomposition of a real
             skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)

    MB04BZ   Eigenvalues of a complex skew-Hamiltonian/Hamiltonian pencil

    MB04DL   Balancing a real matrix pencil, optionally avoiding large
             norms for the scaled (sub)matrices

    MB4DLZ   Balancing a complex matrix pencil, optionally avoiding large
             norms for the scaled (sub)matrices

    MB04DP   Balancing a real skew-Hamiltonian/Hamiltonian matrix pencil,
             optionally avoiding large norms for the scaled (sub)matrices

    MB4DPZ   Balancing a complex skew-Hamiltonian/Hamiltonian matrix pencil,
             optionally avoiding large norms for the scaled (sub)matrices

    MB04ED   Eigenvalues and orthogonal decomposition of a real
             skew-Hamiltonian/skew-Hamiltonian pencil in factored form

    MB04FD   Eigenvalues and orthogonal decomposition of a real
             skew-Hamiltonian/skew-Hamiltonian pencil

    MB04FP   Eigenvalues and orthogonal decomposition of a real
             skew-Hamiltonian/skew-Hamiltonian pencil (applying transformations on panels of columns)

    MB04GD   RQ factorization of a matrix with row pivoting

    MB04ID   QR factorization of a matrix with a lower left zero triangle

    MB04IZ   QR factorization of a matrix with a lower left zero triangle (complex case)

    MB04JD   LQ factorization of a matrix with an upper right zero triangle

    MB04KD   QR factorization of a special structured block matrix

    MB04LD   LQ factorization of a special structured block matrix

    MB04MD   Balancing a general real matrix

    MB04ND   RQ factorization of a special structured block matrix

    MB04OD   QR factorization of a special structured block matrix (variant)

    MB04PB   Paige/Van Loan form of a Hamiltonian matrix

    MB04RD   Reduction of a real matrix pencil in generalized real Schur form to
             a block-diagonal form

    MB04RT   Solution of a generalized real Sylvester equation with matrix pairs
             in generalized real Schur form (blocked version)

    MB04RW   Solution of a generalized complex Sylvester equation with matrix pairs
             in generalized complex Schur form (blocked version)

    MB04RZ   Reduction of a complex matrix pencil in generalized complex Schur form to
             a block-diagonal form

    MB04TB   Symplectic URV decomposition of a real 2N-by-2N matrix

    MB04UD   Unitary column echelon form for a rectangular matrix

    MB04VD   Upper block triangular form for a rectangular pencil

    MB04XD   Basis for left/right null singular subspace of a matrix

    MB04YD   Partial diagonalization of a bidiagonal matrix

    MB04ZD   Transforming a Hamiltonian matrix into a square-reduced form

#### Matrix Functions

    MB05MD   Matrix exponential for a real non-defective matrix

    MB05ND   Matrix exponential and integral for a real matrix

    MB05OD   Matrix exponential for a real matrix, with accuracy estimate

### MC - Polynomial and Rational Function Manipulation

#### Scalar Polynomials

    MC01MD   The leading coefficients of the shifted polynomial

    MC01ND   Value of a real polynomial at a given complex point

    MC01OD   Coefficients of a complex polynomial, given its zeros

    MC01PD   Coefficients of a real polynomial, given its zeros

    MC01QD   Quotient and remainder polynomials for polynomial division

    MC01RD   Polynomial operation P(x) = P1(x) P2(x) + alpha P3(x)

    MC01SD   Scaling coefficients of a real polynomial for minimal variation

    MC01TD   Checking stability of a given real polynomial

    MC01VD   Roots of a quadratic equation with real coefficients

    MC01WD   Quotient and remainder polynomials for a quadratic denominator

    MC01XD   Roots of a third order polynomial

#### Polynomial Matrices

    MC03MD   Real polynomial matrix operation P(x) = P1(x) P2(x) + alpha P3(x)

    MC03ND   Minimal polynomial basis for the right nullspace of a polynomial matrix

### MD - Optimization

#### Unconstrained Nonlinear Least Squares

    MD03AD   Levenberg-Marquardt algorithm (Cholesky-based or conjugate
             gradients solver)

    MD03BD   Enhanced MINPACK-like Levenberg-Marquardt algorithm

## N - Nonlinear Systems

### NI - Interfaces to Nonlinear Solvers

#### ODE and DAE Solvers

    DAESolver    Interface to DAE Solvers

    ODESolver    Interface to ODE Solvers

#### Nonlinear Equation Solvers

    KINSOL    Interface to KINSOL solver for nonlinear systems of equations

#### Nonlinear Optimization Solvers

    FSQP    Interface to FSQP solver for nonlinear optimization

## S - Synthesis Routines

### SB - State-Space Synthesis

#### Eigenvalue/Eigenvector Assignment

    SB01BD    Pole assignment for a given matrix pair (A,B)

    SB01DD    Eigenstructure assignment for a controllable matrix pair (A,B) in
              orthogonal canonical form

    SB01MD    State feedback matrix of a time-invariant single-input system

#### Riccati Equations

    SB02MD    Solution of algebraic Riccati equations (Schur vectors method)

    SB02MT    Conversion of problems with coupling terms to standard problems

    SB02MX    Conversion of problems with coupling terms to standard problems
              (more flexibility)

    SB02ND    Optimal state feedback matrix for an optimal control problem

    SB02OD    Solution of algebraic Riccati equations (generalized Schur method)

    SB02PD    Solution of continuous algebraic Riccati equations (matrix sign
              function method) with condition and forward error bound estimates

    SB02QD    Condition and forward error for continuous Riccati equation solution

    SB02RD    Solution of algebraic Riccati equations (refined Schur vectors method)
              with condition and forward error bound estimates

    SB02SD    Condition and forward error for discrete Riccati equation solution

#### Lyapunov Equations

    SB03MD    Solution of Lyapunov equations and separation estimation

    SB03OD    Solution of stable Lyapunov equations (Cholesky factor)

    SB03OZ    Solution of stable complex Lyapunov equations (Cholesky factor)

    SB03PD    Solution of discrete Lyapunov equations and separation estimation

    SB03QD    Condition and forward error for continuous Lyapunov equations

    SB03RD    Solution of continuous Lyapunov equations and separation estimation

    SB03SD    Condition and forward error for discrete Lyapunov equations

    SB03TD    Solution of continuous Lyapunov equations, condition and forward error
              estimation

    SB03UD    Solution of discrete Lyapunov equations, condition and forward error
              estimation

#### Sylvester Equations

    SB04MD    Solution of continuous Sylvester equations (Hessenberg-Schur method)

    SB04ND    Solution of continuous Sylvester equations (one matrix in Schur form)

    SB04OD    Solution of generalized Sylvester equations with separation estimation

    SB04PD    Solution of continuous or discrete Sylvester equations (Schur method)

    SB04QD    Solution of discrete Sylvester equations (Hessenberg-Schur method)

    SB04RD    Solution of discrete Sylvester equations (one matrix in Schur form)

#### Deadbeat Control

    SB06ND    Minimum norm deadbeat control state feedback matrix

#### Transfer Matrix Factorization

    SB08CD    Left coprime factorization with inner denominator

    SB08DD    Right coprime factorization with inner denominator

    SB08ED    Left coprime factorization with prescribed stability degree

    SB08FD    Right coprime factorization with prescribed stability degree

    SB08GD    State-space representation of a left coprime factorization

    SB08HD    State-space representation of a right coprime factorization

    SB08MD    Spectral factorization of polynomials (continuous-time case)

    SB08ND    Spectral factorization of polynomials (discrete-time case)

#### Realization Methods

    SB09MD    Closeness of two multivariable sequences

#### Optimal Regulator Problems

    SB10AD    H-infinity optimal controller using modified Glover's and Doyle's
              formulas (continuous-time)

    SB10DD    H-infinity (sub)optimal state controller for a discrete-time system

    SB10ED    H2 optimal state controller for a discrete-time system

    SB10FD    H-infinity (sub)optimal state controller for a continuous-time system

    SB10HD    H2 optimal state controller for a continuous-time system

    SB10MD    D-step in the D-K iteration for continuous-time case

    SB10ID    Positive feedback controller for a continuous-time system

    SB10KD    Positive feedback controller for a discrete-time system

    SB10ZD    Positive feedback controller for a discrete-time system (D <> 0)

#### Controller Reduction

    SB16AD    Stability/performance enforcing frequency-weighted controller reduction

    SB16BD    Coprime factorization based state feedback controller reduction

    SB16CD    Coprime factorization based frequency-weighted state feedback
              controller reduction

### SG - Generalized State-Space Synthesis

#### Riccati Equations

    SG02AD    Solution of algebraic Riccati equations for descriptor systems

    SG02CW    Residual of continuous- or discrete-time (generalized) algebraic
              Riccati equations

    SG02CX    Line search parameter minimizing the residual of (generalized)
              continuous- or discrete-time algebraic Riccati equations

    SG02ND    Optimal state feedback matrix for an optimal control problem

#### Generalized Lyapunov Equations

    SG03AD    Solution of generalized Lyapunov equations and separation estimation

    SG03BD    Solution of stable generalized Lyapunov equations (Cholesky factor)

    SG03BZ    Solution of stable generalized complex Lyapunov equations (Cholesky factor)

## T - Transformation Routines

### TB - State-Space

#### State-Space Transformations

    TB01ID   Balancing a system matrix for a given triplet

    TB01IZ   Balancing a system matrix for a given triplet (complex case)

    TB01KD   Additive spectral decomposition of a state-space system

    TB01LD   Spectral separation of a state-space system

    TB01MD   Upper/lower controller Hessenberg form

    TB01ND   Upper/lower observer Hessenberg form

    TB01PD   Minimal, controllable or observable block Hessenberg realization

    TB01PX   Minimal, controllable or observable block Hessenberg realization (variant)

    TB01TD   Balancing state-space representation by permutations and scalings

    TB01UD   Controllable block Hessenberg realization for a state-space representation

    TB01UY   Controllable block Hessenberg realization for a standard multi-input system

    TB01WD   Reduction of the state dynamics matrix to real Schur form

    TB01WX   Orthogonal similarity transformation of a standard system to one
             with state matrix in a Hessenberg form

    TB01ZD   Controllable realization for single-input systems

#### State-Space to Polynomial Matrix Conversion

    TB03AD   Left/right polynomial matrix representation of a state-space representation

#### State-Space to Rational Matrix Conversion

    TB04AD   Transfer matrix of a state-space representation

    TB04BD   Transfer matrix of a state-space representation, using the pole-zeros method

    TB04CD   Transfer matrix of a state-space representation in the pole-zero-gain form

#### State-Space to Frequency Response

    TB05AD   Frequency response matrix of a state-space representation

### TC - Polynomial Matrix

#### Polynomial Matrix Transformations

    TC01OD   Dual of a left/right polynomial matrix representation

#### Polynomial Matrix to State-Space Conversion

    TC04AD   State-space representation for left/right polynomial matrix representation

#### Polynomial Matrix to Frequency Response

    TC05AD   Transfer matrix of a left/right polynomial matrix representation

### TD - Rational Matrix

#### Rational Matrix to Polynomial Matrix Conversion

    TD03AD   Left/right polynomial matrix representation for a proper transfer matrix

#### Rational Matrix to State-Space Conversion

    TD04AD   Minimal state-space representation for a proper transfer matrix

#### Rational Matrix to Frequency Response

    TD05AD   Evaluation of a transfer function for a specified frequency

### TF - Time Response

    TF01MD   Output response of a linear discrete-time system

    TF01ND   Output response of a linear discrete-time system (Hessenberg matrix)

    TF01OD   Block Hankel expansion of a multivariable parameter sequence

    TF01PD   Block Toeplitz expansion of a multivariable parameter sequence

    TF01QD   Markov parameters of a system from transfer function matrix

    TF01RD   Markov parameters of a system from state-space representation

### TG - Generalized State-space

#### Generalized State-space Transformations

    TG01AD   Balancing the matrices of the system pencil corresponding to a
             descriptor triple

    TG01AZ   Balancing the matrices of the system pencil corresponding to a
             descriptor triple (complex case)

    TG01BD   Orthogonal reduction of a descriptor system to the generalized
             Hessenberg form

    TG01CD   Orthogonal reduction of a descriptor system pair (A-sE,B)
             to the QR-coordinate form

    TG01DD   Orthogonal reduction of a descriptor system pair (C,A-sE)
             to the RQ-coordinate form

    TG01ED   Orthogonal reduction of a descriptor system to a SVD coordinate
             form

    TG01FD   Orthogonal reduction of a descriptor system to a SVD-like
             coordinate form

    TG01FZ   Orthogonal reduction of a descriptor system to a SVD-like
             coordinate form (complex case)

    TG01GD   Reduced descriptor representation without non-dynamic modes

    TG01HD   Orthogonal reduction of a descriptor system to the controllability
             staircase form

    TG01ID   Orthogonal reduction of a descriptor system to the observability
             staircase form

    TG01JD   Irreducible descriptor representation

    TG01JY   Irreducible descriptor representation (blocked version)

    TG01LD   Finite-infinite decomposition of a descriptor system

    TG01MD   Finite-infinite generalized real Schur form decomposition of a descriptor system

    TG01ND   Finite-infinite block-diagonal decomposition of a descriptor system

    TG01OD   Reducing a SISO descriptor system with E nonsingular so that
             the obtained feedthrough term has a sufficiently large magnitude

    TG01OZ   Reducing a complex SISO descriptor system with E nonsingular so that
             the obtained feedthrough term has a sufficiently large magnitude

    TG01PD   Bi-domain spectral splitting of a subpencil of a descriptor system

    TG01QD   Three-domain spectral splitting of a subpencil of a descriptor system

    TG01WD   Reduction of the descriptor dynamics matrix pair to generalized
             real Schur form

## U - Utility Routines

### UD - Numerical Data Handling

    UD01BD   Reading a matrix polynomial

    UD01CD   Reading a sparse matrix polynomial

    UD01DD   Reading a sparse real matrix

    UD01MD   Printing a real matrix

    UD01MZ   Printing a real matrix (complex case)

    UD01ND   Printing a matrix polynomial

    UE01MD   Default machine-specific parameters for (skew-)Hamiltonian computation routines