SLICOT LIBRARY INDEX
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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