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AB01MDOrthogonal controllability form for single-input systemAB01NDOrthogonal controllability staircase form for multi-input systemAB01ODStaircase form for multi-input system using orthogonal transformations

AB04MDDiscrete-time <-> continuous-time conversion by bilinear transformation

AB05MDCascade inter-connection of two systems in state-space formAB05NDFeedback inter-connection of two systems in state-space formAB05ODRowwise concatenation of two systems in state-space formAB05PDParallel inter-connection of two systems in state-space formAB05QDAppending two systems in state-space formAB05RDClosed-loop system for a mixed output and state feedback control lawAB05SDClosed-loop system for an output feedback control law

AB07MDDual of a given state-space representationAB07NDInverse of a given state-space representation

AB08MDNormal rank of the transfer-function matrix of a state space modelAB08MZNormal rank of the transfer-function matrix of a state space model (complex case)AB08NDSystem zeros and Kronecker structure of system pencilAB08NWSystem zeros and singular and infinite Kronecker structure of system pencilAB08NZSystem zeros and Kronecker structure of system pencil (complex case)

AB09ADBalance & Truncate model reductionAB09BDSingular perturbation approximation based model reductionAB09CDHankel norm approximation based model reductionAB09DDSingular perturbation approximation formulasAB09EDHankel norm approximation based model reduction of unstable systemsAB09FDBalance & Truncate model reduction of coprime factorsAB09GDSingular perturbation approximation of coprime factorsAB09HDStochastic balancing based model reductionAB09IDFrequency-weighted model reduction based on balancing techniquesAB09JDFrequency-weighted Hankel norm approximation with invertible weightsAB09KDFrequency-weighted Hankel-norm approximationAB09MDBalance & Truncate model reduction for the stable partAB09NDSingular perturbation approximation based model reduction for the stable part

AB13ADHankel-norm of the stable projectionAB13BDH2 or L2 norm of a systemAB13CDH-infinity norm of a continuous-time stable system (obsolete, replaced by AB13DD)AB13DDL-infinity norm of a state space systemAB13EDComplex stability radius, using bisectionAB13FDComplex stability radius, using bisection and SVDAB13IDProperness of the transfer function matrix of a descriptor systemAB13MDUpper bound on the structured singular value for a square complex matrix

AG07BDDescriptor inverse of a state-space or descriptor representation

AG08BDZeros and Kronecker structure of a descriptor system pencilAG08BZZeros and Kronecker structure of a descriptor system pencil (complex case)

BB01ADBenchmark examples for continuous-time Riccati equationsBB02ADBenchmark examples for discrete-time Riccati equationsBB03ADBenchmark examples of (generalized) continuous-time Lyapunov equationsBB04ADBenchmark examples of (generalized) discrete-time Lyapunov equations

BD01ADBenchmark examples of continuous-time systemsBD02ADBenchmark examples of discrete-time systems

DE01ODConvolution or deconvolution of two signalsDE01PDConvolution or deconvolution of two real signals using Hartley transform

DF01MDSine transform or cosine transform of a real signal

DG01MDDiscrete Fourier transform of a complex signalDG01NDDiscrete Fourier transform of a real signalDG01ODScrambled discrete Hartley transform of a real signal

DK01MDAnti-aliasing window applied to a real signal

FB01QDTime-varying square root covariance filter (dense matrices)FB01RDTime-invariant square root covariance filter (Hessenberg form)FB01SDTime-varying square root information filter (dense matrices)FB01TDTime-invariant square root information filter (Hessenberg form)FB01VDOne recursion of the conventional Kalman filter

FD01ADFast recursive least-squares filter

IB01ADInput-output data preprocessing and finding the system orderIB01BDEstimating the system matrices, covariances, and Kalman gainIB01CDEstimating the initial state and the system matrices B and D

IB03ADEstimating a Wiener system by a Levenberg-Marquardt algorithm (Cholesky-based or conjugate gradients solver)IB03BDEstimating a Wiener system by a MINPACK-like Levenberg-Marquardt algorithm

MB01PDMatrix scaling (higher level routine)MB01QDMatrix scaling (lower level routine)MB01RBComputation of a triangle of matrix expression alpha*R + beta*A*B or alpha*R + beta*B*A ( BLAS 3 version)MB01RDComputation of matrix expression alpha*R + beta*A*X*trans(A)MB01TDProduct of two upper quasi-triangular matricesMB01UDComputation of matrix expressions alpha*H*A or alpha*A*H, with H an upper Hessenberg matrixMB01UXComputation of matrix expressions alpha*T*A or alpha*A*T, T quasi-triangularMB01WDResiduals of Lyapunov or Stein equations for Cholesky factored solutionsMB01XDComputation of the product U'*U or L*L', with U and L upper and lower triangular matrices (block algorithm)MB01YDSymmetric rank k operation C := alpha*A*A' + beta*C, C symmetricMB01ZDComputation of matrix expressions H := alpha*T*H, or H := alpha*H*T, with H Hessenberg-like, T triangular

MB02CDCholesky factorization of a positive definite block Toeplitz matrixMB02DDUpdating Cholesky factorization of a positive definite block Toeplitz matrixMB02EDSolution of T*X = B or X*T = B, with T a positive definite block Toeplitz matrixMB02FDIncomplete Cholesky factor of a positive definite block Toeplitz matrixMB02GDCholesky factorization of a banded symmetric positive definite block Toeplitz matrixMB02HDCholesky factorization of the matrix T'*T, with T a banded block Toeplitz matrix of full rankMB02IDSolution of over- or underdetermined linear systems with a full rank block Toeplitz matrixMB02JDFull QR factorization of a block Toeplitz matrix of full rankMB02JXLow rank QR factorization with column pivoting of a block Toeplitz matrixMB02KDComputation of the product C = alpha*op( T )*B + beta*C, with T a block Toeplitz matrixMB02MDSolution of Total Least-Squares problem using a SVD approachMB02NDSolution of Total Least-Squares problem using a partial SVD approachMB02ODSolution of op(A)*X = alpha*B, or X*op(A) = alpha*B, A triangularMB02PDSolution of matrix equation op(A)*X = B, with error bounds and condition estimatesMB02QDSolution, optionally corresponding to specified free elements, of a linear least squares problemMB02RDSolution of a linear system with upper Hessenberg matrixMB02RZSolution of a linear system with complex upper Hessenberg matrixMB02SDLU factorization of an upper Hessenberg matrixMB02SZLU factorization of a complex upper Hessenberg matrixMB02TDCondition number of an upper Hessenberg matrixMB02TZCondition number of a complex upper Hessenberg matrixMB02UDMinimum norm least squares solution of op(R)*X = B, or X*op(R) = B, using singular value decomposition (R upper triangular)MB02VDSolution of X*op(A) = B

MB03LFEigenvalues and right deflating subspace of a real skew-Hamiltonian/Hamiltonian pencil in factored formMB03FZEigenvalues and right deflating subspace of a complex skew-Hamiltonian/Hamiltonian pencil in factored formMB03LDEigenvalues and right deflating subspace of a real skew-Hamiltonian/Hamiltonian pencilMB03LPEigenvalues and right deflating subspace of a real skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)MB03LZEigenvalues and right deflating subspace of a complex skew-Hamiltonian/Hamiltonian pencilMB3LZPEigenvalues and right deflating subspace of a complex skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)MB03MDUpper bound for L singular values of a bidiagonal matrixMB03NDNumber of singular values of a bidiagonal matrix less than a boundMB03ODMatrix rank determination by incremental condition estimationMB03PDMatrix rank determination (row pivoting)MB03QDReordering of the diagonal blocks of a real Schur matrixMB03QGReordering of the diagonal blocks of principal subpencil of a real Schur-triangular matrix pencilMB03RDReduction of a real Schur matrix to a block-diagonal formMB03SDEigenvalues of a square-reduced Hamiltonian matrixMB03TDReordering the diagonal blocks of a matrix in (skew-)Hamiltonian Schur formMB03UDSingular value decomposition of an upper triangular matrixMB03VDPeriodic Hessenberg form of a product of matricesMB03WDPeriodic Schur decomposition and eigenvalues of a product of matrices in periodic Hessenberg formMB03XDEigenvalues of a Hamiltonian matrixMB03XZEigenvalues of a complex Hamiltonian matrixMB03XPPeriodic Schur decomposition and eigenvalues of a matrix product A*B, A upper Hessenberg and B upper triangularMB03YDPeriodic QR iterationMB03ZDStable and unstable invariant subspaces for a dichotomic Hamiltonian matrix

MB04ADEigenvalues and generalized symplectic URV decomposition of a real skew-Hamiltonian/Hamiltonian pencil in factored formMB04AZEigenvalues of a complex skew-Hamiltonian/Hamiltonian pencil in factored formMB04BDEigenvalues and orthogonal decomposition of a real skew-Hamiltonian/Hamiltonian pencilMB04BPEigenvalues and orthogonal decomposition of a real skew-Hamiltonian/Hamiltonian pencil (applying transformations on panels of columns)MB04BZEigenvalues of a complex skew-Hamiltonian/Hamiltonian pencilMB04DLBalancing a real matrix pencil, optionally avoiding large norms for the scaled (sub)matricesMB4DLZBalancing a complex matrix pencil, optionally avoiding large norms for the scaled (sub)matricesMB04DPBalancing a real skew-Hamiltonian/Hamiltonian matrix pencil, optionally avoiding large norms for the scaled (sub)matricesMB4DPZBalancing a complex skew-Hamiltonian/Hamiltonian matrix pencil, optionally avoiding large norms for the scaled (sub)matricesMB04EDEigenvalues and orthogonal decomposition of a real skew-Hamiltonian/skew-Hamiltonian pencil in factored formMB04FDEigenvalues and orthogonal decomposition of a real skew-Hamiltonian/skew-Hamiltonian pencilMB04FPEigenvalues and orthogonal decomposition of a real skew-Hamiltonian/skew-Hamiltonian pencil (applying transformations on panels of columns)MB04GDRQ factorization of a matrix with row pivotingMB04IDQR factorization of a matrix with a lower left zero triangleMB04IZQR factorization of a matrix with a lower left zero triangle (complex case)MB04JDLQ factorization of a matrix with an upper right zero triangleMB04KDQR factorization of a special structured block matrixMB04LDLQ factorization of a special structured block matrixMB04MDBalancing a general real matrixMB04NDRQ factorization of a special structured block matrixMB04ODQR factorization of a special structured block matrix (variant)MB04PBPaige/Van Loan form of a Hamiltonian matrixMB04TBSymplectic URV decomposition of a real 2N-by-2N matrixMB04UDUnitary column echelon form for a rectangular matrixMB04VDUpper block triangular form for a rectangular pencilMB04XDBasis for left/right null singular subspace of a matrixMB04YDPartial diagonalization of a bidiagonal matrixMB04ZDTransforming a Hamiltonian matrix into a square-reduced form

MB05MDMatrix exponential for a real non-defective matrixMB05NDMatrix exponential and integral for a real matrixMB05ODMatrix exponential for a real matrix, with accuracy estimate

MC01MDThe leading coefficients of the shifted polynomialMC01NDValue of a real polynomial at a given complex pointMC01ODCoefficients of a complex polynomial, given its zerosMC01PDCoefficients of a real polynomial, given its zerosMC01QDQuotient and remainder polynomials for polynomial divisionMC01RDPolynomial operation P(x) = P1(x) P2(x) + alpha P3(x)MC01SDScaling coefficients of a real polynomial for minimal variationMC01TDChecking stability of a given real polynomialMC01VDRoots of a quadratic equation with real coefficientsMC01WDQuotient and remainder polynomials for a quadratic denominatorMC01XDRoots of a third order polynomial

MC03MDReal polynomial matrix operation P(x) = P1(x) P2(x) + alpha P3(x)MC03NDMinimal polynomial basis for the right nullspace of a polynomial matrix

MD03ADLevenberg-Marquardt algorithm (Cholesky-based or conjugate gradients solver)MD03BDEnhanced MINPACK-like Levenberg-Marquardt algorithm

DAESolverInterface to DAE SolversODESolverInterface to ODE Solvers

KINSOLInterface to KINSOL solver for nonlinear systems of equations

FSQPInterface to FSQP solver for nonlinear optimization

SB01BDPole assignment for a given matrix pair (A,B)SB01DDEigenstructure assignment for a controllable matrix pair (A,B) in orthogonal canonical formSB01MDState feedback matrix of a time-invariant single-input system

SB02MDSolution of algebraic Riccati equations (Schur vectors method)SB02MTConversion of problems with coupling terms to standard problemsSB02MXConversion of problems with coupling terms to standard problems (more flexibility)SB02NDOptimal state feedback matrix for an optimal control problemSB02ODSolution of algebraic Riccati equations (generalized Schur method)SB02PDSolution of continuous algebraic Riccati equations (matrix sign function method) with condition and forward error bound estimatesSB02QDCondition and forward error for continuous Riccati equation solutionSB02RDSolution of algebraic Riccati equations (refined Schur vectors method) with condition and forward error bound estimatesSB02SDCondition and forward error for discrete Riccati equation solution

SB03MDSolution of Lyapunov equations and separation estimationSB03ODSolution of stable Lyapunov equations (Cholesky factor)SB03PDSolution of discrete Lyapunov equations and separation estimationSB03QDCondition and forward error for continuous Lyapunov equationsSB03RDSolution of continuous Lyapunov equations and separation estimationSB03SDCondition and forward error for discrete Lyapunov equationsSB03TDSolution of continuous Lyapunov equations, condition and forward error estimationSB03UDSolution of discrete Lyapunov equations, condition and forward error estimation

SB04MDSolution of continuous Sylvester equations (Hessenberg-Schur method)SB04NDSolution of continuous Sylvester equations (one matrix in Schur form)SB04ODSolution of generalized Sylvester equations with separation estimationSB04PDSolution of continuous or discrete Sylvester equations (Schur method)SB04QDSolution of discrete Sylvester equations (Hessenberg-Schur method)SB04RDSolution of discrete Sylvester equations (one matrix in Schur form)

SB06NDMinimum norm deadbeat control state feedback matrix

SB08CDLeft coprime factorization with inner denominatorSB08DDRight coprime factorization with inner denominatorSB08EDLeft coprime factorization with prescribed stability degreeSB08FDRight coprime factorization with prescribed stability degreeSB08GDState-space representation of a left coprime factorizationSB08HDState-space representation of a right coprime factorizationSB08MDSpectral factorization of polynomials (continuous-time case)SB08NDSpectral factorization of polynomials (discrete-time case)

SB09MDCloseness of two multivariable sequences

SB10ADH-infinity optimal controller using modified Glover's and Doyle's formulas (continuous-time)SB10DDH-infinity (sub)optimal state controller for a discrete-time systemSB10EDH2 optimal state controller for a discrete-time systemSB10FDH-infinity (sub)optimal state controller for a continuous-time systemSB10HDH2 optimal state controller for a continuous-time systemSB10MDD-step in the D-K iteration for continuous-time caseSB10IDPositive feedback controller for a continuous-time systemSB10KDPositive feedback controller for a discrete-time systemSB10ZDPositive feedback controller for a discrete-time system (D <> 0)

SB16ADStability/performance enforcing frequency-weighted controller reductionSB16BDCoprime factorization based state feedback controller reductionSB16CDCoprime factorization based frequency-weighted state feedback controller reduction

SG02ADSolution of algebraic Riccati equations for descriptor systemsSG02CWResidual of continuous- or discrete-time (generalized) algebraic Riccati equationsSG02CXLine search parameter minimizing the residual of (generalized) continuous- or discrete-time algebraic Riccati equationsSG02NDOptimal state feedback matrix for an optimal control problem

SG03ADSolution of generalized Lyapunov equations and separation estimationSG03BDSolution of stable generalized Lyapunov equations (Cholesky factor)

TB01IDBalancing a system matrix for a given tripletTB01IZBalancing a system matrix for a given triplet (complex case)TB01KDAdditive spectral decomposition of a state-space systemTB01LDSpectral separation of a state-space systemTB01MDUpper/lower controller Hessenberg formTB01NDUpper/lower observer Hessenberg formTB01PDMinimal, controllable or observable block Hessenberg realizationTB01PXMinimal, controllable or observable block Hessenberg realization (variant)TB01TDBalancing state-space representation by permutations and scalingsTB01UDControllable block Hessenberg realization for a state-space representationTB01UYControllable block Hessenberg realization for a standard multi-input systemTB01WDReduction of the state dynamics matrix to real Schur formTB01WXOrthogonal similarity transformation of a standard system to one with state matrix in a Hessenberg formTB01ZDControllable realization for single-input systems

TB03ADLeft/right polynomial matrix representation of a state-space representation

TB04ADTransfer matrix of a state-space representationTB04BDTransfer matrix of a state-space representation, using the pole-zeros methodTB04CDTransfer matrix of a state-space representation in the pole-zero-gain form

TB05ADFrequency response matrix of a state-space representation

TC01ODDual of a left/right polynomial matrix representation

TC04ADState-space representation for left/right polynomial matrix representation

TC05ADTransfer matrix of a left/right polynomial matrix representation

TD03ADLeft/right polynomial matrix representation for a proper transfer matrix

TD04ADMinimal state-space representation for a proper transfer matrix

TD05ADEvaluation of a transfer function for a specified frequency

TF01MDOutput response of a linear discrete-time systemTF01NDOutput response of a linear discrete-time system (Hessenberg matrix)TF01ODBlock Hankel expansion of a multivariable parameter sequenceTF01PDBlock Toeplitz expansion of a multivariable parameter sequenceTF01QDMarkov parameters of a system from transfer function matrixTF01RDMarkov parameters of a system from state-space representation

TG01ADBalancing the matrices of the system pencil corresponding to a descriptor tripleTG01AZBalancing the matrices of the system pencil corresponding to a descriptor triple (complex case)TG01BDOrthogonal reduction of a descriptor system to the generalized Hessenberg formTG01CDOrthogonal reduction of a descriptor system pair (A-sE,B) to the QR-coordinate formTG01DDOrthogonal reduction of a descriptor system pair (C,A-sE) to the RQ-coordinate formTG01EDOrthogonal reduction of a descriptor system to a SVD coordinate formTG01FDOrthogonal reduction of a descriptor system to a SVD-like coordinate formTG01FZOrthogonal reduction of a descriptor system to a SVD-like coordinate form (complex case)TG01GDReduced descriptor representation without non-dynamic modesTG01HDOrthogonal reduction of a descriptor system to the controllability staircase formTG01IDOrthogonal reduction of a descriptor system to the observability staircase formTG01JDIrreducible descriptor representationTG01JYIrreducible descriptor representation (blocked version)TG01LDFinite-infinite decomposition of a descriptor systemTG01MDFinite-infinite generalized real Schur form decomposition of a descriptor systemTG01NDFinite-infinite block-diagonal decomposition of a descriptor systemTG01PDBi-domain spectral splitting of a subpencil of a descriptor systemTG01QDThree-domain spectral splitting of a subpencil of a descriptor systemTG01WDReduction of the descriptor dynamics matrix pair to generalized real Schur form

UD01BDReading a matrix polynomialUD01CDReading a sparse matrix polynomialUD01DDReading a sparse real matrixUD01MDPrinting a real matrixUD01MZPrinting a real matrix (complex case)UD01NDPrinting a matrix polynomialUE01MDDefault machine-specific parameters for (skew-)Hamiltonian computation routines