File: libindex.html

package info (click to toggle)
slicot 5.9.1-2
links: PTS, VCS
area: main
in suites: forky, sid
size: 23,528 kB
sloc: fortran: 148,076; makefile: 964; sh: 57
file content (893 lines) | stat: -rw-r--r-- 37,771 bytes
<HTML>
<HEAD><title>On-Line SLICOT Overview</title></HEAD>
<BODY>

<H1>SLICOT LIBRARY INDEX</H1>
<HR>
To go to the beginning of a chapter click on the appropriate letter below: <p>
<center>
<A HREF = "#A"><B>A</B></A> ;
<A HREF = "#B"><B>B</B></A> ;
<A HREF = "#C"><B>C</B></A> ;
<A HREF = "#D"><B>D</B></A> ;
<A HREF = "#F"><B>F</B></A> ;
<A HREF = "#I"><B>I</B></A> ;
<A HREF = "#M"><B>M</B></A> ;
<A HREF = "#N"><B>N</B></A> ;
<A HREF = "#S"><B>S</B></A> ;
<A HREF = "#T"><B>T</B></A> ;
<A HREF = "#U"><B>U</B></A> ;
</center>
<BR>
or <A href="http://www.slicot.org/index.php?site=home">
<b>Return to SLICOT homepage</b></A>
<BR>
or <A href="support.html">
<b>Go to SLICOT Supporting Routines Index</b></A>
<p>
<HR>
<A NAME="A"><H2>A - Analysis Routines</H2></A>
<h3>AB - State-Space Analysis</h3>
<h4>Canonical and Quasi Canonical Forms</h4>
<PRE>
<A href="AB01MD.html">
<B>AB01MD</B></A>   Orthogonal controllability form for single-input system
<A href="AB01ND.html">
<B>AB01ND</B></A>   Orthogonal controllability staircase form for multi-input system
<A href="AB01OD.html">
<B>AB01OD</B></A>   Staircase form for multi-input system using orthogonal transformations
</PRE>
<h4>Continuous/Discrete Time</h4>
<PRE>
<A href="AB04MD.html">
<B>AB04MD</B></A>   Discrete-time <-> continuous-time conversion by bilinear transformation
</PRE>
<h4>Interconnections of Subsystems</h4>
<PRE>
<A href="AB05MD.html">
<B>AB05MD</B></A>   Cascade inter-connection of two systems in state-space form
<A href="AB05ND.html">
<B>AB05ND</B></A>   Feedback inter-connection of two systems in state-space form
<A href="AB05OD.html">
<B>AB05OD</B></A>   Rowwise concatenation of two systems in state-space form
<A href="AB05PD.html">
<B>AB05PD</B></A>   Parallel inter-connection of two systems in state-space form
<A href="AB05QD.html">
<B>AB05QD</B></A>   Appending two systems in state-space form
<A href="AB05RD.html">
<B>AB05RD</B></A>   Closed-loop system for a mixed output and state feedback control law
<A href="AB05SD.html">
<B>AB05SD</B></A>   Closed-loop system for an output feedback control law
</PRE>
<h4>Inverse and Dual Systems</h4>
<PRE>
<A href="AB07MD.html">
<B>AB07MD</B></A>   Dual of a given state-space representation
<A href="AB07ND.html">
<B>AB07ND</B></A>   Inverse of a given state-space representation
</PRE>
<h4>Poles, Zeros, Gain</h4>
<PRE>
<A href="AB08MD.html">
<B>AB08MD</B></A>   Normal rank of the transfer-function matrix of a state space model
<A href="AB08MZ.html">
<B>AB08MZ</B></A>   Normal rank of the transfer-function matrix of a state space model (complex case)
<A href="AB08ND.html">
<B>AB08ND</B></A>   System zeros and Kronecker structure of system pencil
<A href="AB08NW.html">
<B>AB08NW</B></A>   System zeros and singular and infinite Kronecker structure of system pencil
<A href="AB08NZ.html">
<B>AB08NZ</B></A>   System zeros and Kronecker structure of system pencil (complex case)
</PRE>
<h4>Model Reduction</h4>
<PRE>
<A href="AB09AD.html">
<B>AB09AD</B></A>   Balance & Truncate model reduction
<A href="AB09BD.html">
<B>AB09BD</B></A>   Singular perturbation approximation based model reduction
<A href="AB09CD.html">
<B>AB09CD</B></A>   Hankel norm approximation based model reduction
<A href="AB09DD.html">
<B>AB09DD</B></A>   Singular perturbation approximation formulas
<A href="AB09ED.html">
<B>AB09ED</B></A>   Hankel norm approximation based model reduction of unstable systems
<A href="AB09FD.html">
<B>AB09FD</B></A>   Balance & Truncate model reduction of coprime factors
<A href="AB09GD.html">
<B>AB09GD</B></A>   Singular perturbation approximation of coprime factors
<A href="AB09HD.html">
<B>AB09HD</B></A>   Stochastic balancing based model reduction
<A href="AB09ID.html">
<B>AB09ID</B></A>   Frequency-weighted model reduction based on balancing techniques
<A href="AB09JD.html">
<B>AB09JD</B></A>   Frequency-weighted Hankel norm approximation with invertible weights
<A href="AB09KD.html">
<B>AB09KD</B></A>   Frequency-weighted Hankel-norm approximation
<A href="AB09MD.html">
<B>AB09MD</B></A>   Balance & Truncate model reduction for the stable part
<A href="AB09ND.html">
<B>AB09ND</B></A>   Singular perturbation approximation based model reduction for the
         stable part
</PRE>
<h4>System Norms</h4>
<PRE>
<A href="AB13AD.html">
<B>AB13AD</B></A>   Hankel-norm of the stable projection
<A href="AB13BD.html">
<B>AB13BD</B></A>   H2 or L2 norm of a system
<A href="AB13CD.html">
<B>AB13CD</B></A>   H-infinity norm of a continuous-time stable system
         (obsolete, replaced by AB13DD)
<A href="AB13DD.html">
<B>AB13DD</B></A>   L-infinity norm of a state space system
<A href="AB13HD.html">
<B>AB13HD</B></A>   L-infinity norm of a state space system in standard or
         in descriptor form
<A href="AB13ED.html">
<B>AB13ED</B></A>   Complex stability radius, using bisection
<A href="AB13FD.html">
<B>AB13FD</B></A>   Complex stability radius, using bisection and SVD
<A href="AB13ID.html">
<B>AB13ID</B></A>   Properness of the transfer function matrix of a descriptor system
<A href="AB13MD.html">
<B>AB13MD</B></A>   Upper bound on the structured singular value for a square
         complex matrix
</PRE>
<h3>AG - Generalized State-Space Analysis</h3>
<h4>Inverse and Dual Systems</h4>
<PRE>
<A href="AG07BD.html">
<B>AG07BD</B></A>   Descriptor inverse of a state-space or descriptor representation
</PRE>
<h4>Poles, Zeros, Gain</h4>
<PRE>
<A href="AG08BD.html">
<B>AG08BD</B></A>   Zeros and Kronecker structure of a descriptor system pencil
<A href="AG08BZ.html">
<B>AG08BZ</B></A>   Zeros and Kronecker structure of a descriptor system pencil (complex case)
</PRE>

<HR>
<A NAME="B"><H2>B - Benchmark and Test Problems</H2></A>
<h3>BB - State-space Models</h3>
<PRE>
<A href="BB01AD.html">
<B>BB01AD</B></A>   Benchmark examples for continuous-time Riccati equations
<A href="BB02AD.html">
<B>BB02AD</B></A>   Benchmark examples for discrete-time Riccati equations
<A href="BB03AD.html">
<B>BB03AD</B></A>   Benchmark examples of (generalized) continuous-time Lyapunov equations
<A href="BB04AD.html">
<B>BB04AD</B></A>   Benchmark examples of (generalized) discrete-time Lyapunov equations
</PRE>
<h3>BD - Generalized State-space Models</h3>
<PRE>
<A href="BD01AD.html">
<B>BD01AD</B></A>   Benchmark examples of continuous-time systems
<A href="BD02AD.html">
<B>BD02AD</B></A>   Benchmark examples of discrete-time systems
</PRE>
<HR>
<A NAME="C"><H2>C - Adaptive Control</H2></A>
<HR>
<A NAME="D"><H2>D - Data Analysis</H2></A>
<h3>DE - Covariances</h3>
<PRE>
<A href="DE01OD.html">
<B>DE01OD</B></A>   Convolution or deconvolution of two signals
<A href="DE01PD.html">
<B>DE01PD</B></A>   Convolution or deconvolution of two real signals using Hartley transform
</PRE>
<h3>DF - Spectra</h3>
<PRE>
<A href="DF01MD.html">
<B>DF01MD</B></A>   Sine transform or cosine transform of a real signal
</PRE>
<h3>DG - Discrete Fourier and Hartley Transforms</h3>
<PRE>
<A href="DG01MD.html">
<B>DG01MD</B></A>   Discrete Fourier transform of a complex signal
<A href="DG01ND.html">
<B>DG01ND</B></A>   Discrete Fourier transform of a real signal
<A href="DG01OD.html">
<B>DG01OD</B></A>   Scrambled discrete Hartley transform of a real signal
</PRE>
<h3>DK - Windowing</h3>
<PRE>
<A href="DK01MD.html">
<B>DK01MD</B></A>   Anti-aliasing window applied to a real signal
</PRE>
<HR>
<A NAME="F"><H2>F - Filtering</H2></A>
<h3>FB - Kalman Filters</h3>
<PRE>
<A href="FB01QD.html">
<B>FB01QD</B></A>   Time-varying square root covariance filter (dense matrices)
<A href="FB01RD.html">
<B>FB01RD</B></A>   Time-invariant square root covariance filter (Hessenberg form)
<A href="FB01SD.html">
<B>FB01SD</B></A>   Time-varying square root information filter (dense matrices)
<A href="FB01TD.html">
<B>FB01TD</B></A>   Time-invariant square root information filter (Hessenberg form)
<A href="FB01VD.html">
<B>FB01VD</B></A>   One recursion of the conventional Kalman filter
</PRE>
<h3>FD - Fast Recursive Least Squares Filters</h3>
<PRE>
<A href="FD01AD.html">
<B>FD01AD</B></A>   Fast recursive least-squares filter
</PRE>
<HR>
<A NAME="I"><H2>I - Identification</H2></A>
<h3>IB - Subspace Identification</h3>
<h4>Time Invariant State-space Systems</h4>
<PRE>
<A href="IB01AD.html">
<B>IB01AD</B></A>   Input-output data preprocessing and finding the system order
<A href="IB01BD.html">
<B>IB01BD</B></A>   Estimating the system matrices, covariances, and Kalman gain
<A href="IB01CD.html">
<B>IB01CD</B></A>   Estimating the initial state and the system matrices B and D
</PRE>
<h4>Wiener Systems</h4>
<PRE>
<A href="IB03AD.html">
<B>IB03AD</B></A>   Estimating a Wiener system by a Levenberg-Marquardt algorithm
         (Cholesky-based or conjugate gradients solver)
<A href="IB03BD.html">
<B>IB03BD</B></A>   Estimating a Wiener system by a MINPACK-like Levenberg-Marquardt
         algorithm
</PRE>
<HR>
<A NAME="M"><H2>M - Mathematical Routines</H2></A>
<h3>MB - Linear Algebra</h3>
<h4>Basic Linear Algebra Manipulations</h4>
<PRE>
<A href="MB01PD.html">
<B>MB01PD</B></A>   Matrix scaling (higher level routine)
<A href="MB01QD.html">
<B>MB01QD</B></A>   Matrix scaling (lower level routine)
<A href="MB01RB.html">
<B>MB01RB</B></A>   Computation of a triangle of matrix expression alpha*R + beta*A*B
         or alpha*R + beta*B*A ( BLAS 3 version)
<A href="MB01RD.html">
<B>MB01RD</B></A>   Computation of matrix expression alpha*R + beta*A*X*trans(A)
<A href="MB01TD.html">
<B>MB01TD</B></A>   Product of two upper quasi-triangular matrices
<A href="MB01UD.html">
<B>MB01UD</B></A>   Computation of matrix expressions alpha*H*A or alpha*A*H,
         with H an upper Hessenberg matrix
<A href="MB01UX.html">
<B>MB01UX</B></A>   Computation of matrix expressions alpha*T*A or alpha*A*T, T quasi-triangular
<A href="MB01UY.html">
<B>MB01UY</B></A>   Computation of matrix expressions alpha*T*A or alpha*A*T, over T, T triangular
<A href="MB01UZ.html">
<B>MB01UZ</B></A>   Computation of matrix expressions alpha*T*A or alpha*A*T, over T, T triangular
         (complex version)
<A href="MB01WD.html">
<B>MB01WD</B></A>   Residuals of Lyapunov or Stein equations for Cholesky factored
         solutions
<A href="MB01XD.html">
<B>MB01XD</B></A>   Computation of the product U'*U or L*L', with U and L upper and
         lower triangular matrices (block algorithm)
<A href="MB01YD.html">
<B>MB01YD</B></A>   Symmetric rank k operation C := alpha*A*A' + beta*C, C symmetric
<A href="MB01ZD.html">
<B>MB01ZD</B></A>   Computation of matrix expressions H := alpha*T*H, or H := alpha*H*T,
         with H Hessenberg-like, T triangular
</PRE>
<h4>Linear Equations and Least Squares</h4>
<PRE>
<A href="MB02CD.html">
<B>MB02CD</B></A>   Cholesky factorization of a positive definite block Toeplitz matrix
<A href="MB02DD.html">
<B>MB02DD</B></A>   Updating Cholesky factorization of a positive definite block
         Toeplitz matrix
<A href="MB02ED.html">
<B>MB02ED</B></A>   Solution of T*X = B or X*T = B, with T a positive definite
         block Toeplitz matrix
<A href="MB02FD.html">
<B>MB02FD</B></A>   Incomplete Cholesky factor of a positive definite block Toeplitz matrix
<A href="MB02GD.html">
<B>MB02GD</B></A>   Cholesky factorization of a banded symmetric positive definite
         block Toeplitz matrix
<A href="MB02HD.html">
<B>MB02HD</B></A>   Cholesky factorization of the matrix T'*T, with T a banded
         block Toeplitz matrix of full rank
<A href="MB02ID.html">
<B>MB02ID</B></A>   Solution of over- or underdetermined linear systems with a full rank
         block Toeplitz matrix
<A href="MB02JD.html">
<B>MB02JD</B></A>   Full QR factorization of a block Toeplitz matrix of full rank
<A href="MB02JX.html">
<B>MB02JX</B></A>   Low rank QR factorization with column pivoting of a block Toeplitz matrix
<A href="MB02KD.html">
<B>MB02KD</B></A>   Computation of the product C = alpha*op( T )*B + beta*C, with T
         a block Toeplitz matrix
<A href="MB02MD.html">
<B>MB02MD</B></A>   Solution of Total Least-Squares problem using a SVD approach
<A href="MB02ND.html">
<B>MB02ND</B></A>   Solution of Total Least-Squares problem using a partial SVD approach
<A href="MB02OD.html">
<B>MB02OD</B></A>   Solution of op(A)*X = alpha*B, or X*op(A) = alpha*B, A triangular
<A href="MB02PD.html">
<B>MB02PD</B></A>   Solution of matrix equation op(A)*X = B, with error bounds
         and condition estimates
<A href="MB02QD.html">
<B>MB02QD</B></A>   Solution, optionally corresponding to specified free elements,
         of a linear least squares problem
<A href="MB02RD.html">
<B>MB02RD</B></A>   Solution of a linear system with upper Hessenberg matrix
<A href="MB02RZ.html">
<B>MB02RZ</B></A>   Solution of a linear system with complex upper Hessenberg matrix
<A href="MB02SD.html">
<B>MB02SD</B></A>   LU factorization of an upper Hessenberg matrix
<A href="MB02SZ.html">
<B>MB02SZ</B></A>   LU factorization of a complex upper Hessenberg matrix
<A href="MB02TD.html">
<B>MB02TD</B></A>   Condition number of an upper Hessenberg matrix
<A href="MB02TZ.html">
<B>MB02TZ</B></A>   Condition number of a complex upper Hessenberg matrix
<A href="MB02UD.html">
<B>MB02UD</B></A>   Minimum norm least squares solution of op(R)*X = B, or X*op(R) = B,
         using singular value decomposition (R upper triangular)
<A href="MB02VD.html">
<B>MB02VD</B></A>   Solution of X*op(A) = B
</PRE>
<h4>Eigenvalues and Eigenvectors</h4>
<PRE>
<A href="MB03LF.html">
<B>MB03LF</B></A>   Eigenvalues and right deflating subspace of a real
         skew-Hamiltonian/Hamiltonian pencil in factored form
<A href="MB03FZ.html">
<B>MB03FZ</B></A>   Eigenvalues and right deflating subspace of a complex
         skew-Hamiltonian/Hamiltonian pencil in factored form
<A href="MB03LD.html">
<B>MB03LD</B></A>   Eigenvalues and right deflating subspace of a real
         skew-Hamiltonian/Hamiltonian pencil
<A href="MB03LP.html">
<B>MB03LP</B></A>   Eigenvalues and right deflating subspace of a real
         skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)
<A href="MB03LZ.html">
<B>MB03LZ</B></A>   Eigenvalues and right deflating subspace of a complex
         skew-Hamiltonian/Hamiltonian pencil
<A href="MB3LZP.html">
<B>MB3LZP</B></A>   Eigenvalues and right deflating subspace of a complex
         skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)
<A href="MB03MD.html">
<B>MB03MD</B></A>   Upper bound for L singular values of a bidiagonal matrix
<A href="MB03ND.html">
<B>MB03ND</B></A>   Number of singular values of a bidiagonal matrix less than a bound
<A href="MB03OD.html">
<B>MB03OD</B></A>   Matrix rank determination by incremental condition estimation
<A href="MB03PD.html">
<B>MB03PD</B></A>   Matrix rank determination (row pivoting)
<A href="MB03QD.html">
<B>MB03QD</B></A>   Reordering of the diagonal blocks of a real Schur matrix
<A href="MB03QG.html">
<B>MB03QG</B></A>   Reordering of the diagonal blocks of principal subpencil of
         a real Schur-triangular matrix pencil
<A href="MB03RD.html">
<B>MB03RD</B></A>   Reduction of a real Schur matrix to a block-diagonal form
<A href="MB03RZ.html">
<B>MB03RZ</B></A>   Reduction of a complex Schur matrix to a block-diagonal form
<A href="MB03SD.html">
<B>MB03SD</B></A>   Eigenvalues of a square-reduced Hamiltonian matrix
<A href="MB03TD.html">
<B>MB03TD</B></A>   Reordering the diagonal blocks of a matrix in (skew-)Hamiltonian Schur form
<A href="MB03UD.html">
<B>MB03UD</B></A>   Singular value decomposition of an upper triangular matrix
<A href="MB03VD.html">
<B>MB03VD</B></A>   Periodic Hessenberg form of a product of matrices
<A href="MB03VW.html">
<B>MB03VW</B></A>   Periodic Hessenberg form of a formal product of matrices
<A href="MB03WD.html">
<B>MB03WD</B></A>   Periodic Schur decomposition and eigenvalues of a product of
         matrices in periodic Hessenberg form
<A href="MB03XD.html">
<B>MB03XD</B></A>   Eigenvalues of a Hamiltonian matrix
<A href="MB03XZ.html">
<B>MB03XZ</B></A>   Eigenvalues of a complex Hamiltonian matrix
<A href="MB03XP.html">
<B>MB03XP</B></A>   Periodic Schur decomposition and eigenvalues of a matrix product A*B,
         A upper Hessenberg and B upper triangular
<A href="MB03YD.html">
<B>MB03YD</B></A>   Periodic QR iteration
<A href="MB03ZD.html">
<B>MB03ZD</B></A>   Stable and unstable invariant subspaces for a dichotomic Hamiltonian matrix
</PRE>
<h4>Decompositions and Transformations</h4>
<PRE>
<A href="MB04AD.html">
<B>MB04AD</B></A>   Eigenvalues and generalized symplectic URV decomposition of a real
         skew-Hamiltonian/Hamiltonian pencil in factored form
<A href="MB04AZ.html">
<B>MB04AZ</B></A>   Eigenvalues of a complex skew-Hamiltonian/Hamiltonian pencil in factored form
<A href="MB04BD.html">
<B>MB04BD</B></A>   Eigenvalues and orthogonal decomposition of a real
         skew-Hamiltonian/Hamiltonian pencil
<A href="MB04BP.html">
<B>MB04BP</B></A>   Eigenvalues and orthogonal decomposition of a real
         skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)
<A href="MB04BZ.html">
<B>MB04BZ</B></A>   Eigenvalues of a complex skew-Hamiltonian/Hamiltonian pencil
<A href="MB04DL.html">
<B>MB04DL</B></A>   Balancing a real matrix pencil, optionally avoiding large
         norms for the scaled (sub)matrices
<A href="MB4DLZ.html">
<B>MB4DLZ</B></A>   Balancing a complex matrix pencil, optionally avoiding large
         norms for the scaled (sub)matrices
<A href="MB04DP.html">
<B>MB04DP</B></A>   Balancing a real skew-Hamiltonian/Hamiltonian matrix pencil,
         optionally avoiding large norms for the scaled (sub)matrices
<A href="MB4DPZ.html">
<B>MB4DPZ</B></A>   Balancing a complex skew-Hamiltonian/Hamiltonian matrix pencil,
         optionally avoiding large norms for the scaled (sub)matrices
<A href="MB04ED.html">
<B>MB04ED</B></A>   Eigenvalues and orthogonal decomposition of a real
         skew-Hamiltonian/skew-Hamiltonian pencil in factored form
<A href="MB04FD.html">
<B>MB04FD</B></A>   Eigenvalues and orthogonal decomposition of a real
         skew-Hamiltonian/skew-Hamiltonian pencil
<A href="MB04FP.html">
<B>MB04FP</B></A>   Eigenvalues and orthogonal decomposition of a real
         skew-Hamiltonian/skew-Hamiltonian pencil (applying transformations on panels of columns)
<A href="MB04GD.html">
<B>MB04GD</B></A>   RQ factorization of a matrix with row pivoting
<A href="MB04ID.html">
<B>MB04ID</B></A>   QR factorization of a matrix with a lower left zero triangle
<A href="MB04IZ.html">
<B>MB04IZ</B></A>   QR factorization of a matrix with a lower left zero triangle (complex case)
<A href="MB04JD.html">
<B>MB04JD</B></A>   LQ factorization of a matrix with an upper right zero triangle
<A href="MB04KD.html">
<B>MB04KD</B></A>   QR factorization of a special structured block matrix
<A href="MB04LD.html">
<B>MB04LD</B></A>   LQ factorization of a special structured block matrix
<A href="MB04MD.html">
<B>MB04MD</B></A>   Balancing a general real matrix
<A href="MB04ND.html">
<B>MB04ND</B></A>   RQ factorization of a special structured block matrix
<A href="MB04OD.html">
<B>MB04OD</B></A>   QR factorization of a special structured block matrix (variant)
<A href="MB04PB.html">
<B>MB04PB</B></A>   Paige/Van Loan form of a Hamiltonian matrix
<A href="MB04RD.html">
<B>MB04RD</B></A>   Reduction of a real matrix pencil in generalized real Schur form to
         a block-diagonal form
<A href="MB04RT.html">
<B>MB04RT</B></A>   Solution of a generalized real Sylvester equation with matrix pairs
         in generalized real Schur form (blocked version)
<A href="MB04RW.html">
<B>MB04RW</B></A>   Solution of a generalized complex Sylvester equation with matrix pairs
         in generalized complex Schur form (blocked version)
<A href="MB04RZ.html">
<B>MB04RZ</B></A>   Reduction of a complex matrix pencil in generalized complex Schur form to
         a block-diagonal form
<A href="MB04TB.html">
<B>MB04TB</B></A>   Symplectic URV decomposition of a real 2N-by-2N matrix
<A href="MB04UD.html">
<B>MB04UD</B></A>   Unitary column echelon form for a rectangular matrix
<A href="MB04VD.html">
<B>MB04VD</B></A>   Upper block triangular form for a rectangular pencil
<A href="MB04XD.html">
<B>MB04XD</B></A>   Basis for left/right null singular subspace of a matrix
<A href="MB04YD.html">
<B>MB04YD</B></A>   Partial diagonalization of a bidiagonal matrix
<A href="MB04ZD.html">
<B>MB04ZD</B></A>   Transforming a Hamiltonian matrix into a square-reduced form
</PRE>
<h4>Matrix Functions</h4>
<PRE>
<A href="MB05MD.html">
<B>MB05MD</B></A>   Matrix exponential for a real non-defective matrix
<A href="MB05ND.html">
<B>MB05ND</B></A>   Matrix exponential and integral for a real matrix
<A href="MB05OD.html">
<B>MB05OD</B></A>   Matrix exponential for a real matrix, with accuracy estimate
</PRE>
<h3>MC - Polynomial and Rational Function Manipulation</h3>
<h4>Scalar Polynomials</h4>
<PRE>
<A href="MC01MD.html">
<B>MC01MD</B></A>   The leading coefficients of the shifted polynomial
<A href="MC01ND.html">
<B>MC01ND</B></A>   Value of a real polynomial at a given complex point
<A href="MC01OD.html">
<B>MC01OD</B></A>   Coefficients of a complex polynomial, given its zeros
<A href="MC01PD.html">
<B>MC01PD</B></A>   Coefficients of a real polynomial, given its zeros
<A href="MC01QD.html">
<B>MC01QD</B></A>   Quotient and remainder polynomials for polynomial division
<A href="MC01RD.html">
<B>MC01RD</B></A>   Polynomial operation P(x) = P1(x) P2(x) + alpha P3(x)
<A href="MC01SD.html">
<B>MC01SD</B></A>   Scaling coefficients of a real polynomial for minimal variation
<A href="MC01TD.html">
<B>MC01TD</B></A>   Checking stability of a given real polynomial
<A href="MC01VD.html">
<B>MC01VD</B></A>   Roots of a quadratic equation with real coefficients
<A href="MC01WD.html">
<B>MC01WD</B></A>   Quotient and remainder polynomials for a quadratic denominator
<A href="MC01XD.html">
<B>MC01XD</B></A>   Roots of a third order polynomial
</PRE>
<h4>Polynomial Matrices</h4>
<PRE>
<A href="MC03MD.html">
<B>MC03MD</B></A>   Real polynomial matrix operation P(x) = P1(x) P2(x) + alpha P3(x)
<A href="MC03ND.html">
<B>MC03ND</B></A>   Minimal polynomial basis for the right nullspace of a polynomial matrix
</PRE>
<h3>MD - Optimization</h3>
<h4>Unconstrained Nonlinear Least Squares</h4>
<PRE>
<A href="MD03AD.html">
<B>MD03AD</B></A>   Levenberg-Marquardt algorithm (Cholesky-based or conjugate
         gradients solver)
<A href="MD03BD.html">
<B>MD03BD</B></A>   Enhanced MINPACK-like Levenberg-Marquardt algorithm
</PRE>
<HR>
<A NAME="N"><H2>N - Nonlinear Systems</H2></A>
<h3>NI - Interfaces to Nonlinear Solvers</h3>
<h4>ODE and DAE Solvers</h4>
<PRE>
<A href="DAESolver.html">
<B>DAESolver</B></A>    Interface to DAE Solvers
<A href="ODESolver.html">
<B>ODESolver</B></A>    Interface to ODE Solvers
</PRE>
<h4>Nonlinear Equation Solvers</h4>
<PRE>
<A href="KINSOL.html">
<B>KINSOL</B></A>    Interface to KINSOL solver for nonlinear systems of equations
</PRE>
<h4>Nonlinear Optimization Solvers</h4>
<PRE>
<A href="FSQP.html">
<B>FSQP</B></A>    Interface to FSQP solver for nonlinear optimization
</PRE>
<HR>
<A NAME="S"><H2>S - Synthesis Routines</H2></A>
<h3>SB - State-Space Synthesis</h3>
<h4>Eigenvalue/Eigenvector Assignment</h4>
<PRE>
<A href="SB01BD.html">
<B>SB01BD</B></A>    Pole assignment for a given matrix pair (A,B)
<A href="SB01DD.html">
<B>SB01DD</B></A>    Eigenstructure assignment for a controllable matrix pair (A,B) in
          orthogonal canonical form
<A href="SB01MD.html">
<B>SB01MD</B></A>    State feedback matrix of a time-invariant single-input system
</PRE>
<h4>Riccati Equations</h4>
<PRE>
<A href="SB02MD.html">
<B>SB02MD</B></A>    Solution of algebraic Riccati equations (Schur vectors method)
<A href="SB02MT.html">
<B>SB02MT</B></A>    Conversion of problems with coupling terms to standard problems
<A href="SB02MX.html">
<B>SB02MX</B></A>    Conversion of problems with coupling terms to standard problems
          (more flexibility)
<A href="SB02ND.html">
<B>SB02ND</B></A>    Optimal state feedback matrix for an optimal control problem
<A href="SB02OD.html">
<B>SB02OD</B></A>    Solution of algebraic Riccati equations (generalized Schur method)
<A href="SB02PD.html">
<B>SB02PD</B></A>    Solution of continuous algebraic Riccati equations (matrix sign
          function method) with condition and forward error bound estimates
<A href="SB02QD.html">
<B>SB02QD</B></A>    Condition and forward error for continuous Riccati equation solution
<A href="SB02RD.html">
<B>SB02RD</B></A>    Solution of algebraic Riccati equations (refined Schur vectors method)
          with condition and forward error bound estimates
<A href="SB02SD.html">
<B>SB02SD</B></A>    Condition and forward error for discrete Riccati equation solution
</PRE>
<h4>Lyapunov Equations</h4>
<PRE>
<A href="SB03MD.html">
<B>SB03MD</B></A>    Solution of Lyapunov equations and separation estimation
<A href="SB03OD.html">
<B>SB03OD</B></A>    Solution of stable Lyapunov equations (Cholesky factor)
<A href="SB03OZ.html">
<B>SB03OZ</B></A>    Solution of stable complex Lyapunov equations (Cholesky factor)
<A href="SB03PD.html">
<B>SB03PD</B></A>    Solution of discrete Lyapunov equations and separation estimation
<A href="SB03QD.html">
<B>SB03QD</B></A>    Condition and forward error for continuous Lyapunov equations
<A href="SB03RD.html">
<B>SB03RD</B></A>    Solution of continuous Lyapunov equations and separation estimation
<A href="SB03SD.html">
<B>SB03SD</B></A>    Condition and forward error for discrete Lyapunov equations
<A href="SB03TD.html">
<B>SB03TD</B></A>    Solution of continuous Lyapunov equations, condition and forward error
          estimation
<A href="SB03UD.html">
<B>SB03UD</B></A>    Solution of discrete Lyapunov equations, condition and forward error
          estimation
</PRE>
<h4>Sylvester Equations</h4>
<PRE>
<A href="SB04MD.html">
<B>SB04MD</B></A>    Solution of continuous Sylvester equations (Hessenberg-Schur method)
<A href="SB04ND.html">
<B>SB04ND</B></A>    Solution of continuous Sylvester equations (one matrix in Schur form)
<A href="SB04OD.html">
<B>SB04OD</B></A>    Solution of generalized Sylvester equations with separation estimation
<A href="SB04PD.html">
<B>SB04PD</B></A>    Solution of continuous or discrete Sylvester equations (Schur method)
<A href="SB04QD.html">
<B>SB04QD</B></A>    Solution of discrete Sylvester equations (Hessenberg-Schur method)
<A href="SB04RD.html">
<B>SB04RD</B></A>    Solution of discrete Sylvester equations (one matrix in Schur form)
</PRE>
<h4>Deadbeat Control</h4>
<PRE>
<A href="SB06ND.html">
<B>SB06ND</B></A>    Minimum norm deadbeat control state feedback matrix
</PRE>
<h4>Transfer Matrix Factorization</h4>
<PRE>
<A href="SB08CD.html">
<B>SB08CD</B></A>    Left coprime factorization with inner denominator
<A href="SB08DD.html">
<B>SB08DD</B></A>    Right coprime factorization with inner denominator
<A href="SB08ED.html">
<B>SB08ED</B></A>    Left coprime factorization with prescribed stability degree
<A href="SB08FD.html">
<B>SB08FD</B></A>    Right coprime factorization with prescribed stability degree
<A href="SB08GD.html">
<B>SB08GD</B></A>    State-space representation of a left coprime factorization
<A href="SB08HD.html">
<B>SB08HD</B></A>    State-space representation of a right coprime factorization
<A href="SB08MD.html">
<B>SB08MD</B></A>    Spectral factorization of polynomials (continuous-time case)
<A href="SB08ND.html">
<B>SB08ND</B></A>    Spectral factorization of polynomials (discrete-time case)
</PRE>
<h4>Realization Methods</h4>
<PRE>
<A href="SB09MD.html">
<B>SB09MD</B></A>    Closeness of two multivariable sequences

</PRE>
<h4>Optimal Regulator Problems</h4>
<PRE>
<A href="SB10AD.html">
<B>SB10AD</B></A>    H-infinity optimal controller using modified Glover's and Doyle's
          formulas (continuous-time)
<A href="SB10DD.html">
<B>SB10DD</B></A>    H-infinity (sub)optimal state controller for a discrete-time system
<A href="SB10ED.html">
<B>SB10ED</B></A>    H2 optimal state controller for a discrete-time system
<A href="SB10FD.html">
<B>SB10FD</B></A>    H-infinity (sub)optimal state controller for a continuous-time system
<A href="SB10HD.html">
<B>SB10HD</B></A>    H2 optimal state controller for a continuous-time system
<A href="SB10MD.html">
<B>SB10MD</B></A>    D-step in the D-K iteration for continuous-time case
<A href="SB10ID.html">
<B>SB10ID</B></A>    Positive feedback controller for a continuous-time system
<A href="SB10KD.html">
<B>SB10KD</B></A>    Positive feedback controller for a discrete-time system
<A href="SB10ZD.html">
<B>SB10ZD</B></A>    Positive feedback controller for a discrete-time system (D <> 0)

</PRE>
<h4>Controller Reduction</h4>
<PRE>
<A href="SB16AD.html">
<B>SB16AD</B></A>    Stability/performance enforcing frequency-weighted controller reduction
<A href="SB16BD.html">
<B>SB16BD</B></A>    Coprime factorization based state feedback controller reduction
<A href="SB16CD.html">
<B>SB16CD</B></A>    Coprime factorization based frequency-weighted state feedback
          controller reduction
</PRE>
<h3>SG - Generalized State-Space Synthesis</h3>
<h4>Riccati Equations</h4>
<PRE>
<A href="SG02AD.html">
<B>SG02AD</B></A>    Solution of algebraic Riccati equations for descriptor systems
<A href="SG02CW.html">
<B>SG02CW</B></A>    Residual of continuous- or discrete-time (generalized) algebraic
          Riccati equations
<A href="SG02CX.html">
<B>SG02CX</B></A>    Line search parameter minimizing the residual of (generalized)
          continuous- or discrete-time algebraic Riccati equations
<A href="SG02ND.html">
<B>SG02ND</B></A>    Optimal state feedback matrix for an optimal control problem
</PRE>
<h4>Generalized Lyapunov Equations</h4>
<PRE>
<A href="SG03AD.html">
<B>SG03AD</B></A>    Solution of generalized Lyapunov equations and separation estimation
<A href="SG03BD.html">
<B>SG03BD</B></A>    Solution of stable generalized Lyapunov equations (Cholesky factor)
<A href="SG03BZ.html">
<B>SG03BZ</B></A>    Solution of stable generalized complex Lyapunov equations (Cholesky factor)
</PRE>
<HR>
<A NAME="T"><H2>T - Transformation Routines</H2></A>
<h3>TB - State-Space</h3>
<h4>State-Space Transformations</h4>
<PRE>
<A href="TB01ID.html">
<B>TB01ID</B></A>   Balancing a system matrix for a given triplet
<A href="TB01IZ.html">
<B>TB01IZ</B></A>   Balancing a system matrix for a given triplet (complex case)
<A href="TB01KD.html">
<B>TB01KD</B></A>   Additive spectral decomposition of a state-space system
<A href="TB01LD.html">
<B>TB01LD</B></A>   Spectral separation of a state-space system
<A href="TB01MD.html">
<B>TB01MD</B></A>   Upper/lower controller Hessenberg form
<A href="TB01ND.html">
<B>TB01ND</B></A>   Upper/lower observer Hessenberg form
<A href="TB01PD.html">
<B>TB01PD</B></A>   Minimal, controllable or observable block Hessenberg realization
<A href="TB01PX.html">
<B>TB01PX</B></A>   Minimal, controllable or observable block Hessenberg realization (variant)
<A href="TB01TD.html">
<B>TB01TD</B></A>   Balancing state-space representation by permutations and scalings
<A href="TB01UD.html">
<B>TB01UD</B></A>   Controllable block Hessenberg realization for a state-space representation
<A href="TB01UY.html">
<B>TB01UY</B></A>   Controllable block Hessenberg realization for a standard multi-input system
<A href="TB01WD.html">
<B>TB01WD</B></A>   Reduction of the state dynamics matrix to real Schur form
<A href="TB01WX.html">
<B>TB01WX</B></A>   Orthogonal similarity transformation of a standard system to one
         with state matrix in a Hessenberg form
<A href="TB01ZD.html">
<B>TB01ZD</B></A>   Controllable realization for single-input systems
</PRE>
<h4>State-Space to Polynomial Matrix Conversion</h4>
<PRE>
<A href="TB03AD.html">
<B>TB03AD</B></A>   Left/right polynomial matrix representation of a state-space representation
</PRE>
<h4>State-Space to Rational Matrix Conversion</h4>
<PRE>
<A href="TB04AD.html">
<B>TB04AD</B></A>   Transfer matrix of a state-space representation
<A href="TB04BD.html">
<B>TB04BD</B></A>   Transfer matrix of a state-space representation, using the pole-zeros method
<A href="TB04CD.html">
<B>TB04CD</B></A>   Transfer matrix of a state-space representation in the pole-zero-gain form
</PRE>
<h4>State-Space to Frequency Response</h4>
<PRE>
<A href="TB05AD.html">
<B>TB05AD</B></A>   Frequency response matrix of a state-space representation
</PRE>
<h3>TC - Polynomial Matrix</h3>
<h4>Polynomial Matrix Transformations</h4>
<PRE>
<A href="TC01OD.html">
<B>TC01OD</B></A>   Dual of a left/right polynomial matrix representation
</PRE>
<h4>Polynomial Matrix to State-Space Conversion</h4>
<PRE>
<A href="TC04AD.html">
<B>TC04AD</B></A>   State-space representation for left/right polynomial matrix representation
</PRE>
<h4>Polynomial Matrix to  Frequency Response</h4>
<PRE>
<A href="TC05AD.html">
<B>TC05AD</B></A>   Transfer matrix of a left/right polynomial matrix representation
</PRE>
<h3>TD - Rational  Matrix</h3>
<h4>Rational Matrix to Polynomial Matrix Conversion</h4>
<PRE>
<A href="TD03AD.html">
<B>TD03AD</B></A>   Left/right polynomial matrix representation for a proper transfer matrix
</PRE>
<h4>Rational Matrix to State-Space Conversion</h4>
<PRE>
<A href="TD04AD.html">
<B>TD04AD</B></A>   Minimal state-space representation for a proper transfer matrix
</PRE>
<h4>Rational Matrix to Frequency Response</h4>
<PRE>
<A href="TD05AD.html">
<B>TD05AD</B></A>   Evaluation of a transfer function for a specified frequency
</PRE>
<h3>TF - Time Response</h3>
<PRE>
<A href="TF01MD.html">
<B>TF01MD</B></A>   Output response of a linear discrete-time system
<A href="TF01ND.html">
<B>TF01ND</B></A>   Output response of a linear discrete-time system (Hessenberg matrix)
<A href="TF01OD.html">
<B>TF01OD</B></A>   Block Hankel expansion of a multivariable parameter sequence
<A href="TF01PD.html">
<B>TF01PD</B></A>   Block Toeplitz expansion of a multivariable parameter sequence
<A href="TF01QD.html">
<B>TF01QD</B></A>   Markov parameters of a system from transfer function matrix
<A href="TF01RD.html">
<B>TF01RD</B></A>   Markov parameters of a system from state-space representation
</PRE>
<h3>TG - Generalized State-space</h3>
<h4>Generalized State-space Transformations</h4>
<PRE>
<A href="TG01AD.html">
<B>TG01AD</B></A>   Balancing the matrices of the system pencil corresponding to a
         descriptor triple
<A href="TG01AZ.html">
<B>TG01AZ</B></A>   Balancing the matrices of the system pencil corresponding to a
         descriptor triple (complex case)
<A href="TG01BD.html">
<B>TG01BD</B></A>   Orthogonal reduction of a descriptor system to the generalized
         Hessenberg form
<A href="TG01CD.html">
<B>TG01CD</B></A>   Orthogonal reduction of a descriptor system pair (A-sE,B)
         to the QR-coordinate form
<A href="TG01DD.html">
<B>TG01DD</B></A>   Orthogonal reduction of a descriptor system pair (C,A-sE)
         to the RQ-coordinate form
<A href="TG01ED.html">
<B>TG01ED</B></A>   Orthogonal reduction of a descriptor system to a SVD coordinate
         form
<A href="TG01FD.html">
<B>TG01FD</B></A>   Orthogonal reduction of a descriptor system to a SVD-like
         coordinate form
<A href="TG01FZ.html">
<B>TG01FZ</B></A>   Orthogonal reduction of a descriptor system to a SVD-like
         coordinate form (complex case)
<A href="TG01GD.html">
<B>TG01GD</B></A>   Reduced descriptor representation without non-dynamic modes
<A href="TG01HD.html">
<B>TG01HD</B></A>   Orthogonal reduction of a descriptor system to the controllability
         staircase form
<A href="TG01ID.html">
<B>TG01ID</B></A>   Orthogonal reduction of a descriptor system to the observability
         staircase form
<A href="TG01JD.html">
<B>TG01JD</B></A>   Irreducible descriptor representation
<A href="TG01JY.html">
<B>TG01JY</B></A>   Irreducible descriptor representation (blocked version)
<A href="TG01LD.html">
<B>TG01LD</B></A>   Finite-infinite decomposition of a descriptor system
<A href="TG01MD.html">
<B>TG01MD</B></A>   Finite-infinite generalized real Schur form decomposition of a descriptor system
<A href="TG01ND.html">
<B>TG01ND</B></A>   Finite-infinite block-diagonal decomposition of a descriptor system
<A href="TG01OD.html">
<B>TG01OD</B></A>   Reducing a SISO descriptor system with E nonsingular so that
         the obtained feedthrough term has a sufficiently large magnitude
<A href="TG01OZ.html">
<B>TG01OZ</B></A>   Reducing a complex SISO descriptor system with E nonsingular so that
         the obtained feedthrough term has a sufficiently large magnitude
<A href="TG01PD.html">
<B>TG01PD</B></A>   Bi-domain spectral splitting of a subpencil of a descriptor system
<A href="TG01QD.html">
<B>TG01QD</B></A>   Three-domain spectral splitting of a subpencil of a descriptor system
<A href="TG01WD.html">
<B>TG01WD</B></A>   Reduction of the descriptor dynamics matrix pair to generalized
         real Schur form
</PRE>
<HR>
<A NAME="U"><H2>U - Utility Routines</H2></A>
<h3>UD - Numerical Data Handling</h3>
<PRE>
<A href="UD01BD.html">
<B>UD01BD</B></A>   Reading a matrix polynomial
<A href="UD01CD.html">
<B>UD01CD</B></A>   Reading a sparse matrix polynomial
<A href="UD01DD.html">
<B>UD01DD</B></A>   Reading a sparse real matrix
<A href="UD01MD.html">
<B>UD01MD</B></A>   Printing a real matrix
<A href="UD01MZ.html">
<B>UD01MZ</B></A>   Printing a real matrix (complex case)
<A href="UD01ND.html">
<B>UD01ND</B></A>   Printing a matrix polynomial
<A href="UE01MD.html">
<B>UE01MD</B></A>   Default machine-specific parameters for (skew-)Hamiltonian computation routines
</PRE>
<HR>
</BODY>
</HTML>