File: support.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 (925 lines) | stat: -rw-r--r-- 43,547 bytes
parent folder | download | duplicates (2)
<HTML>
<HEAD><title>On-Line SLICOT Supporting Routines Overview</title></HEAD>
<BODY>

<H1>SLICOT SUPPORTING ROUTINES 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="..\libindex.html">
<b>Go to SLICOT LIBRARY INDEX</b></A>
<p>
<HR>
<A NAME="A"><H2>A - Analysis Routines</H2></A>
<h3>AB - State-Space Analysis</h3>
<h4>Poles, Zeros, Gain</h4>
<PRE>
<A href="AB08NX.html">
<B>AB08NX</B></A>   Construction of a reduced system with input/output matrix Dr of full 
         row rank, preserving transmission zeros
<A href="AB08NY.html">
<B>AB08NY</B></A>   Construction of a reduced system with input/output matrix Dr of full 
         row rank, preserving transmission zeros (extended variant)
<A href="AB8NXZ.html">
<B>AB8NXZ</B></A>   Construction of a reduced system with input/output matrix Dr of full 
         row rank, preserving transmission zeros (complex case)
</PRE>
<h4>Model Reduction</h4>
<PRE>
<A href="AB09AX.html">
<B>AB09AX</B></A>   Balance & Truncate model reduction with state matrix in real Schur form  
<A href="AB09BX.html">
<B>AB09BX</B></A>   Singular perturbation approximation based model reduction with state
         matrix in real Schur form 
<A href="AB09CX.html">
<B>AB09CX</B></A>   Hankel norm approximation based model reduction with state matrix
         in real Schur form 
<A href="AB09HX.html">
<B>AB09HX</B></A>   Stochastic balancing model reduction of stable systems
<A href="AB09HY.html">
<B>AB09HY</B></A>   Cholesky factors of the controllability and observability Grammians
<A href="AB09IX.html">
<B>AB09IX</B></A>   Accuracy enhanced balancing related model reduction
<A href="AB09IY.html">
<B>AB09IY</B></A>   Cholesky factors of the frequency-weighted controllability and 
         observability Grammians
<A href="AB09JV.html">
<B>AB09JV</B></A>   State-space representation of a projection of a left weighted 
         transfer-function matrix
<A href="AB09JW.html">
<B>AB09JW</B></A>   State-space representation of a projection of a right weighted 
         transfer-function matrix
<A href="AB09JX.html">
<B>AB09JX</B></A>   Check stability/antistability of finite eigenvalues
<A href="AB09KX.html">
<B>AB09KX</B></A>   Stable projection of V*G*W or conj(V)*G*conj(W)
</PRE>
<h4>System Norms</h4>
<PRE>
<A href="AB13AX.html">
<B>AB13AX</B></A>   Hankel-norm of a stable system with state matrix in real Schur form  
<A href="AB13DX.html">
<B>AB13DX</B></A>   Maximum singular value of a transfer-function matrix
</PRE>
<h3>AG - Generalized State-Space Analysis</h3>
<h4>Poles, Zeros, Gain</h4>
<PRE>
<A href="AG08BY.html">
<B>AG08BY</B></A>   Construction of a reduced system with input/output matrix Dr of full 
         row rank, preserving the finite Smith zeros
<A href="AG8BYZ.html">
<B>AG8BYZ</B></A>   Construction of a reduced system with input/output matrix Dr of full 
         row rank, preserving the finite Smith zeros (complex case)
</PRE>
<HR>
<A NAME="B"><H2>B - Benchmark and Test Problems</H2></A> 
<HR>
<A NAME="C"><H2>C - Adaptive Control</H2></A>
<HR>
<A NAME="D"><H2>D - Data Analysis</H2></A>
<h3>DE - Covariances</h3>
<h3>DF - Spectra</h3>
<h3>DG - Discrete Fourier Transforms</h3>
<h3>DK - Windowing</h3>
<HR>
<A NAME="F"><H2>F - Filtering</H2></A>
<h3>FB - Kalman Filters</h3>
<HR>
<A NAME="I"><H2>I - Identification</H2></A>
<h3>IB - Subspace Identification</h3>
<h4>Time Invariant State-space Systems</h4>
<PRE>
<A href="IB01MD.html">
<B>IB01MD</B></A>   Upper triangular factor in QR factorization of a
         block-Hankel-block matrix
<A href="IB01MY.html">
<B>IB01MY</B></A>   Upper triangular factor in fast QR factorization of a 
         block-Hankel-block matrix
<A href="IB01ND.html">
<B>IB01ND</B></A>   Singular value decomposition giving the system order
<A href="IB01OD.html">
<B>IB01OD</B></A>   Estimating the system order
<A href="IB01OY.html">
<B>IB01OY</B></A>   User's confirmation of the system order
<A href="IB01PD.html">
<B>IB01PD</B></A>   Estimating the system matrices and covariances
<A href="IB01PX.html">
<B>IB01PX</B></A>   Estimating the matrices B and D of a system using Kronecker products
<A href="IB01PY.html">
<B>IB01PY</B></A>   Estimating the matrices B and D of a system exploiting the structure
<A href="IB01QD.html">
<B>IB01QD</B></A>   Estimating the initial state and the matrices B and D of a system
<A href="IB01RD.html">
<B>IB01RD</B></A>   Estimating the initial state of a system
</PRE>
<HR>
<A NAME="M"><H2>M - Mathematical Routines</H2></A>
<h3>MA - Auxiliary Routines</h3>
<h4>Mathematical Scalar Routines</h4>
<PRE>
<A href="MA01AD.html">
<B>MA01AD</B></A>   Complex square root of a complex number in real arithmetic
<A href="MA01BD.html">
<B>MA01BD</B></A>   Safely computing the general product of K real scalars
<A href="MA01BZ.html">
<B>MA01BZ</B></A>   Safely computing the general product of K complex scalars
<A href="MA01CD.html">
<B>MA01CD</B></A>   Safely computing the sign of a sum of two real numbers represented
         using integer powers of a base
<A href="MA01DD.html">
<B>MA01DD</B></A>   Approximate symmetric chordal metric for two finite complex numbers
<A href="MA01DZ.html">
<B>MA01DZ</B></A>   Approximate symmetric chordal metric for two, possibly infinite, complex numbers
</PRE>
<h4>Mathematical Vector/Matrix Routines</h4>
<PRE>
<A href="MA02AD.html">
<B>MA02AD</B></A>   Transpose of a matrix
<A href="MA02AZ.html">
<B>MA02AZ</B></A>   (Conjugate) transpose of a complex matrix
<A href="MA02BD.html">
<B>MA02BD</B></A>   Reversing the order of rows and/or columns of a matrix
<A href="MA02BZ.html">
<B>MA02BZ</B></A>   Reversing the order of rows and/or columns of a matrix (complex case)
<A href="MA02CD.html">
<B>MA02CD</B></A>   Pertranspose of the central band of a square matrix 
<A href="MA02CZ.html">
<B>MA02CZ</B></A>   Pertranspose of the central band of a square matrix (complex case)
<A href="MA02DD.html">
<B>MA02DD</B></A>   Pack/unpack the upper or lower triangle of a symmetric matrix 
<A href="MA02ED.html">
<B>MA02ED</B></A>   Construct a triangle of a symmetric matrix, given the other triangle 
<A href="MA02ES.html">
<B>MA02ES</B></A>   Construct a triangle of a skew-symmetric real matrix, given the 
         other triangle
<A href="MA02EZ.html">
<B>MA02EZ</B></A>   Construct a triangle of a (skew-)symmetric/Hermitian complex matrix,
         given the other triangle
<A href="MA02FD.html">
<B>MA02FD</B></A>   Hyperbolic plane rotation 
<A href="MA02GD.html">
<B>MA02GD</B></A>   Column interchanges on a real matrix 
<A href="MA02GZ.html">
<B>MA02GZ</B></A>   Column interchanges on a complex matrix 
<A href="MA02HD.html">
<B>MA02HD</B></A>   Check if a matrix is a scalar multiple of an identity-like matrix
<A href="MA02HZ.html">
<B>MA02HZ</B></A>   Check if a complex matrix is a scalar multiple of an identity-like matrix
<A href="MA02ID.html">
<B>MA02ID</B></A>   Matrix 1-, Frobenius, or infinity norms of a skew-Hamiltonian matrix
<A href="MA02IZ.html">
<B>MA02IZ</B></A>   Matrix 1-, Frobenius, or infinity norms of a complex skew-Hamiltonian matrix
<A href="MA02JD.html">
<B>MA02JD</B></A>   Test if a matrix is an orthogonal symplectic matrix
<A href="MA02JZ.html">
<B>MA02JZ</B></A>   Test if a matrix is a unitary symplectic matrix
<A href="MA02MD.html">
<B>MA02MD</B></A>   Norms of a real skew-symmetric matrix
<A href="MA02MZ.html">
<B>MA02MZ</B></A>   Norms of a complex skew-symmetric matrix
<A href="MA02NZ.html">
<B>MA02NZ</B></A>   Two rows and columns permutation of a (skew-)symmetric/Hermitian
         complex matrix
<A href="MA02OD.html">
<B>MA02OD</B></A>   Number of zero rows of a real (skew-)Hamiltonian matrix
<A href="MA02OZ.html">
<B>MA02OZ</B></A>   Number of zero rows of a complex (skew-)Hamiltonian matrix
<A href="MA02PD.html">
<B>MA02PD</B></A>   Number of zero rows and columns of a real matrix
<A href="MA02PZ.html">
<B>MA02PZ</B></A>   Number of zero rows and columns of a complex matrix
<A href="MA02RD.html">
<B>MA02RD</B></A>   Sorting a real vector and rearranging another vector
<A href="MA02SD.html">
<B>MA02SD</B></A>   Smallest nonzero absolute value of the elements of a real matrix
<A href="MB01KD.html">
<B>MB01KD</B></A>   Rank 2k operation alpha*A*trans(B) - alpha*B*trans(A) + beta*C,
         with A and C skew-symmetric matrices
<A href="MB01LD.html">
<B>MB01LD</B></A>   Computation of matrix expression alpha*R + beta*A*X*trans(A) with 
         skew-symmetric matrices R and X
<A href="MB01MD.html">
<B>MB01MD</B></A>   Matrix-vector operation alpha*A*x + beta*y, with A a skew-symmetric matrix
<A href="MB01ND.html">
<B>MB01ND</B></A>   Rank 2 operation alpha*x*trans(y) - alpha*y*trans(x) + A, with A a 
         skew-symmetric matrix
<A href="MB01SD.html">
<B>MB01SD</B></A>   Rows and/or columns scaling of a matrix 
<A href="MB01SS.html">
<B>MB01SS</B></A>   Symmetric scaling of a symmetric matrix 
</PRE>
<h3>MB - Linear Algebra</h3>
<h4>Basic Linear Algebra Manipulations</h4>
<PRE>
<A href="MB01OC.html">
<B>MB01OC</B></A>   Computation of matrix expression alpha R + beta ( op(H) X + X op(H)' ) 
         with R, X symmetric and H upper Hessenberg
<A href="MB01OD.html">
<B>MB01OD</B></A>   Computation of matrix expression alpha R + beta ( op(H) X op(E)' + op(E) X op(H)' )  
         with R, X symmetric, H upper Hessenberg, and E upper triangular
<A href="MB01OE.html">
<B>MB01OE</B></A>   Computation of matrix expression alpha R + beta ( op(H) op(E)' + op(E) op(H)' )
          with R symmetric, H upper Hessenberg, and E upper triangular
<A href="MB01OH.html">
<B>MB01OH</B></A>   Computation of matrix expression alpha R + beta ( op(H) op(A)' + op(A) op(H)' ) 
         with R symmetric, and A, H upper Hessenberg
<A href="MB01OO.html">
<B>MB01OO</B></A>   Computation of P or P' with P = op(H) X op(E)' with X symmetric, 
         H upper Hessenberg, and E upper triangular
<A href="MB01OS.html">
<B>MB01OS</B></A>   Computation of matrix expression P = H X or P = X H, with X symmetric and 
         H upper Hessenberg
<A href="MB01OT.html">
<B>MB01OT</B></A>   Computation of matrix expression alpha R + beta ( op(E) op(T)' + op(T) op(E)' ) 
         with R symmetric and E, T upper triangular
<A href="MB01RH.html">
<B>MB01RH</B></A>   Computation of matrix expression alpha R + beta op(H) X op(H)' 
         with R, X symmetric and H upper Hessenberg
<A href="MB01RT.html">
<B>MB01RT</B></A>   Computation of matrix expression alpha R + beta op(E) X op(E)'  
         with R, X symmetric and E upper triangular
<A href="MB01RU.html">
<B>MB01RU</B></A>   Computation of matrix expression alpha*R + beta*A*X*trans(A)
         (MB01RD variant)
<A href="MB01RW.html">
<B>MB01RW</B></A>   Computation of matrix expression alpha*A*X*trans(A), X symmetric (BLAS 2)
<A href="MB01RX.html">
<B>MB01RX</B></A>   Computing a triangle of the matrix expressions alpha*R + beta*A*B 
         or alpha*R + beta*B*A
<A href="MB01RY.html">
<B>MB01RY</B></A>   Computing a triangle of the matrix expressions alpha*R + beta*H*B 
         or alpha*R + beta*B*H, with H an upper Hessenberg matrix
<A href="MB01UW.html">
<B>MB01UW</B></A>   Computation of matrix expressions alpha*H*A or alpha*A*H,
         overwritting A, with H an upper Hessenberg matrix
<A href="MB01VD.html">
<B>MB01VD</B></A>   Kronecker product of two matrices
<A href="MB01XY.html">
<B>MB01XY</B></A>   Computation of the product U'*U or L*L', with U and L upper and 
         lower triangular matrices (unblock algorithm)
<A href="SB03OV.html">
<B>SB03OV</B></A>   Construction of a complex plane rotation to annihilate a real number,
         modifying a complex number
<A href="SG03BY.html">
<B>SG03BY</B></A>   Computing a complex plane rotation in real arithmetic 
<A href="SG03BR.html">
<B>SG03BR</B></A>   Computing a complex plane rotation in real arithmetic (SG03BY version
         - adaptation of LAPACK ZLARTG)
</PRE>
<h4>Linear Equations and Least Squares</h4>
<PRE>
<A href="MB02CU.html">
<B>MB02CU</B></A>   Bringing the first blocks of a generator in proper form
         (extended version of MB02CX)
<A href="MB02CV.html">
<B>MB02CV</B></A>   Applying the MB02CU transformations on other columns / rows of 
         the generator
<A href="MB02CX.html">
<B>MB02CX</B></A>   Bringing the first blocks of a generator in proper form
<A href="MB02CY.html">
<B>MB02CY</B></A>   Applying the MB02CX transformations on other columns / rows of 
         the generator
<A href="MB02NY.html">
<B>MB02NY</B></A>   Separation of a zero singular value of a bidiagonal submatrix
<A href="MB02QY.html">
<B>MB02QY</B></A>   Minimum-norm least squares solution, given a rank-revealing
         QR factorization
<A href="MB02UU.html">
<B>MB02UU</B></A>   Solution of linear equations using LU factorization with complete pivoting
<A href="MB02UV.html">
<B>MB02UV</B></A>   LU factorization with complete pivoting
<A href="MB02UW.html">
<B>MB02UW</B></A>   Solution of linear equations of order at most 2 with possible scaling 
         and perturbation of system matrix
<A href="MB02WD.html">
<B>MB02WD</B></A>   Solution of a positive definite linear system A*x = b, or f(A, x) = b,
         using conjugate gradient algorithm
<A href="MB02XD.html">
<B>MB02XD</B></A>   Solution of a set of positive definite linear systems, A'*A*X = B, or
         f(A)*X = B, using Gaussian elimination
<A href="MB02YD.html">
<B>MB02YD</B></A>   Solution of the linear system A*x = b, D*x = 0, D diagonal
</PRE>
<h4>Eigenvalues and Eigenvectors</h4>
<PRE>
<A href="MB03AD.html">
<B>MB03AD</B></A>   Reducing the first column of a real Wilkinson shift polynomial for a 
         product of matrices to the first unit vector
<A href="MB03AB.html">
<B>MB03AB</B></A>   Reducing the first column of a real Wilkinson shift polynomial for a  
         product of matrices to the first unit vector (variant with explicit shifts)
<A href="MB03AE.html">
<B>MB03AE</B></A>   Reducing the first column of a real Wilkinson shift polynomial for a  
         product of matrices to the first unit vector (variant with partial evaluation, 
         Hessenberg factor is the first one)
<A href="MB03AF.html">
<B>MB03AF</B></A>   Reducing the first column of a real Wilkinson shift polynomial for a  
         product of matrices to the first unit vector (variant, Hessenberg factor is the 
         last one)
<A href="MB03AG.html">
<B>MB03AG</B></A>   Reducing the first column of a real Wilkinson shift polynomial for a  
         product of matrices to the first unit vector (variant with evaluation, 
         Hessenberg factor is the first one)
<A href="MB03AH.html">
<B>MB03AH</B></A>   Reducing the first column of a real Wilkinson shift polynomial for a  
         product of matrices to the first unit vector (variant with partial evaluation, 
         Hessenberg factor is the last one)
<A href="MB03AI.html">
<B>MB03AI</B></A>   Reducing the first column of a real Wilkinson shift polynomial for a  
         product of matrices to the first unit vector (variant with evaluation, 
         Hessenberg factor is the last one)
<A href="MB03BA.html">
<B>MB03BA</B></A>   Computing maps for Hessenberg index and signature array
<A href="MB03BB.html">
<B>MB03BB</B></A>   Eigenvalues of a 2-by-2 matrix product via a complex single shifted 
         periodic QZ algorithm
<A href="MB03BC.html">
<B>MB03BC</B></A>   Product singular value decomposition of K-1 triangular factors of 
         order 2
<A href="MB03BD.html">
<B>MB03BD</B></A>   Finding eigenvalues of a generalized matrix product in 
         Hessenberg-triangular form
<A href="MB03BE.html">
<B>MB03BE</B></A>   Applying iterations of a real single shifted periodic QZ algorithm 
         to a 2-by-2 matrix product
<A href="MB03BF.html">
<B>MB03BF</B></A>   Applying iterations of a real single shifted periodic QZ algorithm 
         to a 2-by-2 matrix product, with Hessenberg factor the last one
<A href="MB03BZ.html">
<B>MB03BZ</B></A>   Finding eigenvalues of a complex generalized matrix product in
         Hessenberg-triangular form
<A href="MB03CD.html">
<B>MB03CD</B></A>   Exchanging eigenvalues of a real 2-by-2, 3-by-3 or 4-by-4 block upper 
         triangular pencil (factored version)
<A href="MB03CZ.html">
<B>MB03CZ</B></A>   Exchanging eigenvalues of a complex 2-by-2 upper triangular pencil 
         (factored version)
<A href="MB03DD.html">
<B>MB03DD</B></A>   Exchanging eigenvalues of a real 2-by-2, 3-by-3 or 4-by-4 block upper 
         triangular pencil
<A href="MB03DZ.html">
<B>MB03DZ</B></A>   Exchanging eigenvalues of a complex 2-by-2 upper triangular pencil
<A href="MB03ED.html">
<B>MB03ED</B></A>   Reducing a real 2-by-2 or 4-by-4 block (anti-)diagonal 
         skew-Hamiltonian/Hamiltonian pencil to generalized Schur form and moving 
         eigenvalues with negative real parts to the top (factored version)
<A href="MB03FD.html">
<B>MB03FD</B></A>   Reducing a real 2-by-2 or 4-by-4 block (anti-)diagonal 
         skew-Hamiltonian/Hamiltonian pencil to generalized Schur form and moving 
         eigenvalues with negative real parts to the top
<A href="MB03GD.html">
<B>MB03GD</B></A>   Exchanging eigenvalues of a real 2-by-2 or 4-by-4 block upper 
         triangular skew-Hamiltonian/Hamiltonian pencil (factored version)
<A href="MB03GZ.html">
<B>MB03GZ</B></A>   Exchanging eigenvalues of a complex 2-by-2 skew-Hamiltonian/
         Hamiltonian pencil in structured Schur form (factored version)
<A href="MB03HD.html">
<B>MB03HD</B></A>   Exchanging eigenvalues of a real 2-by-2 or 4-by-4 skew-Hamiltonian/
         Hamiltonian pencil in structured Schur form
<A href="MB03HZ.html">
<B>MB03HZ</B></A>   Exchanging eigenvalues of a complex 2-by-2 skew-Hamiltonian/
         Hamiltonian pencil in structured Schur form
<A href="MB03ID.html">
<B>MB03ID</B></A>   Moving eigenvalues with negative real parts of a real 
         skew-Hamiltonian/Hamiltonian pencil in structured Schur form to the 
         leading subpencil (factored version)
<A href="MB03IZ.html">
<B>MB03IZ</B></A>   Moving eigenvalues with negative real parts of a complex 
         skew-Hamiltonian/Hamiltonian pencil in structured Schur form to the 
         leading subpencil (factored version)
<A href="MB03JD.html">
<B>MB03JD</B></A>   Moving eigenvalues with negative real parts of a real 
         skew-Hamiltonian/Hamiltonian pencil in structured Schur form to the 
         leading subpencil
<A href="MB03JP.html">
<B>MB03JP</B></A>   Moving eigenvalues with negative real parts of a real 
         skew-Hamiltonian/Hamiltonian pencil in structured Schur form to the 
         leading subpencil (applying transformations on panels of columns)
<A href="MB03JZ.html">
<B>MB03JZ</B></A>   Moving eigenvalues with negative real parts of a complex 
         skew-Hamiltonian/Hamiltonian pencil in structured Schur form to the 
         leading subpencil
<A href="MB3JZP.html">
<B>MB3JZP</B></A>   Moving eigenvalues with negative real parts of a complex 
         skew-Hamiltonian/Hamiltonian pencil in structured Schur form to the 
         leading subpencil (applying transformations on panels of columns)
<A href="MB03KA.html">
<B>MB03KA</B></A>   Moving diagonal blocks at a specified position in a formal matrix 
         product to another position
<A href="MB03KB.html">
<B>MB03KB</B></A>   Swapping pairs of adjacent diagonal blocks of sizes 1 and/or 2 in 
         a formal matrix product
<A href="MB03KC.html">
<B>MB03KC</B></A>   Reducing a 2-by-2 formal matrix product to periodic 
         Hessenberg-triangular form
<A href="MB03KD.html">
<B>MB03KD</B></A>   Reordering the diagonal blocks of a formal matrix product using 
         periodic QZ algorithm
<A href="MB03KE.html">
<B>MB03KE</B></A>   Solving periodic Sylvester-like equations with matrices of order 
         at most 2
<A href="MB03NY.html">
<B>MB03NY</B></A>   The smallest singular value of A - jwI
<A href="MB03OY.html">
<B>MB03OY</B></A>   Matrix rank determination by incremental condition estimation, during 
         the pivoted QR factorization process 
<A href="MB3OYZ.html">
<B>MB3OYZ</B></A>   Matrix rank determination by incremental condition estimation, during 
         the pivoted QR factorization process (complex case) 
<A href="MB03PY.html">
<B>MB03PY</B></A>   Matrix rank determination by incremental condition estimation, during 
         the pivoted RQ factorization process (row pivoting) 
<A href="MB3PYZ.html">
<B>MB3PYZ</B></A>   Matrix rank determination by incremental condition estimation, during 
         the pivoted RQ factorization process (row pivoting, complex case) 
<A href="MB03QV.html">
<B>MB03QV</B></A>   Eigenvalues of an upper quasi-triangular matrix pencil
<A href="MB03QW.html">
<B>MB03QW</B></A>   Standardization and eigenvalues of a 2-by-2 diagonal block pair of
         an upper quasi-triangular matrix pencil
<A href="MB03QX.html">
<B>MB03QX</B></A>   Eigenvalues of an upper quasi-triangular matrix
<A href="MB03QY.html">
<B>MB03QY</B></A>   Transformation to Schur canonical form of a selected 2-by-2 diagonal
         block of an upper quasi-triangular matrix
<A href="MB03RX.html">
<B>MB03RX</B></A>   Reordering the diagonal blocks of a principal submatrix of a real Schur 
         form matrix
<A href="MB03RY.html">
<B>MB03RY</B></A>   Tentative solution of Sylvester equation -AX + XB = C (A, B in real 
         Schur form)
<A href="MB03RW.html">
<B>MB03RW</B></A>   Tentative solution of Sylvester equation -AX + XB = C (A, B in complex
         Schur form)
<A href="MB03TS.html">
<B>MB03TS</B></A>   Swapping two diagonal blocks of a matrix in (skew-)Hamiltonian 
         canonical Schur form
<A href="MB03VY.html">
<B>MB03VY</B></A>   Generating orthogonal matrices for reduction to periodic 
         Hessenberg form of a product of matrices
<A href="MB03WA.html">
<B>MB03WA</B></A>   Swapping two adjacent diagonal blocks in a periodic real Schur canonical form
<A href="MB03WX.html">
<B>MB03WX</B></A>   Eigenvalues of a product of matrices, T = T_1*T_2*...*T_p,
         with T_1 upper quasi-triangular and T_2, ..., T_p upper triangular 
<A href="MB03XS.html">
<B>MB03XS</B></A>   Eigenvalues and real skew-Hamiltonian Schur form of a skew-Hamiltonian matrix
<A href="MB03XU.html">
<B>MB03XU</B></A>   Panel reduction of columns and rows of a real (k+2n)-by-(k+2n) matrix by 
         orthogonal symplectic transformations
<A href="MB03YA.html">
<B>MB03YA</B></A>   Annihilation of one or two entries on the subdiagonal of a Hessenberg matrix 
         corresponding to zero elements on the diagonal of a triangular matrix
<A href="MB03YT.html">
<B>MB03YT</B></A>   Periodic Schur factorization of a real 2-by-2 matrix pair (A,B) 
         with B upper triangular
<A href="MB03ZA.html">
<B>MB03ZA</B></A>   Reordering a selected cluster of eigenvalues of a given matrix pair in 
         periodic Schur form
<A href="MB05MY.html">
<B>MB05MY</B></A>   Computing an orthogonal matrix reducing a matrix to real Schur form T, 
         the eigenvalues, and the upper triangular matrix of right eigenvectors 
         of T 
<A href="MB05OY.html">
<B>MB05OY</B></A>   Restoring a matrix after balancing transformations
</PRE>
<h4>Decompositions and Transformations</h4>
<PRE>
<A href="MB04CD.html">
<B>MB04CD</B></A>   Reducing a special real block (anti-)diagonal skew-Hamiltonian/
         Hamiltonian pencil in factored form to generalized Schur form
<A href="MB04DB.html">
<B>MB04DB</B></A>   Applying the inverse of a balancing transformation for a real 
         skew-Hamiltonian/Hamiltonian matrix pencil
<A href="MB4DBZ.html">
<B>MB4DBZ</B></A>   Applying the inverse of a balancing transformation for a complex 
         skew-Hamiltonian/Hamiltonian matrix pencil
<A href="MB04DD.html">
<B>MB04DD</B></A>   Balancing a real Hamiltonian matrix
<A href="MB04DZ.html">
<B>MB04DZ</B></A>   Balancing a complex Hamiltonian matrix
<A href="MB04DI.html">
<B>MB04DI</B></A>   Applying the inverse of a balancing transformation for a real Hamiltonian matrix
<A href="MB04DS.html">
<B>MB04DS</B></A>   Balancing a real skew-Hamiltonian matrix
<A href="MB04DY.html">
<B>MB04DY</B></A>   Symplectic scaling of a Hamiltonian matrix
<A href="MB04HD.html">
<B>MB04HD</B></A>   Reducing a special real block (anti-)diagonal skew-Hamiltonian/
         Hamiltonian pencil to generalized Schur form
<A href="MB04IY.html">
<B>MB04IY</B></A>   Applying the product of elementary reflectors used for QR factorization
         of a matrix having a lower left zero triangle
<A href="MB04NY.html">
<B>MB04NY</B></A>   Applying an elementary reflector to a matrix C = ( A  B ), from the right, 
         where A has one column
<A href="MB04OY.html">
<B>MB04OY</B></A>   Applying an elementary reflector to a matrix C = ( A'  B' )', from the 
         left, where A has one row
<A href="MB04OW.html">
<B>MB04OW</B></A>   Rank-one update of a Cholesky factorization for a 2-by-2 block matrix
<A href="MB04OX.html">
<B>MB04OX</B></A>   Rank-one update of a Cholesky factorization
<A href="MB04PA.html">
<B>MB04PA</B></A>   Special reduction of a (skew-)Hamiltonian like matrix
<A href="MB04PU.html">
<B>MB04PU</B></A>   Computation of the Paige/Van Loan (PVL) form of a Hamiltonian matrix 
         (unblocked algorithm)
<A href="MB04PY.html">
<B>MB04PY</B></A>   Applying an elementary reflector to a matrix from the left or right
<A href="MB04QB.html">
<B>MB04QB</B></A>   Applying a product of symplectic reflectors and Givens rotations to two 
         general real matrices
<A href="MB04QC.html">
<B>MB04QC</B></A>   Premultiplying a real matrix with an orthogonal symplectic block reflector
<A href="MB04QF.html">
<B>MB04QF</B></A>   Forming the triangular block factors of a symplectic block reflector
<A href="MB04QS.html">
<B>MB04QS</B></A>   Multiplication with a product of symplectic reflectors and Givens rotations
<A href="MB04QU.html">
<B>MB04QU</B></A>   Applying a product of symplectic reflectors and Givens rotations to two 
         general real matrices (unblocked algorithm)
<A href="MB04RB.html">
<B>MB04RB</B></A>   Reduction of a skew-Hamiltonian matrix to Paige/Van Loan (PVL) form 
         (blocked version)
<A href="MB04RU.html">
<B>MB04RU</B></A>   Reduction of a skew-Hamiltonian matrix to Paige/Van Loan (PVL) form 
         (unblocked version)
<A href="MB04RS.html">
<B>MB04RS</B></A>   Solution of a generalized real Sylvester equation with matrix pairs in
         generalized real Schur form
<A href="MB04RV.html">
<B>MB04RV</B></A>   Solution of a generalized complex Sylvester equation with matrix pairs in 
         generalized complex Schur form
<A href="MB04SU.html">
<B>MB04SU</B></A>   Symplectic QR decomposition of a real 2M-by-N matrix
<A href="MB04TS.html">
<B>MB04TS</B></A>   Symplectic URV decomposition of a real 2N-by-2N matrix (unblocked version)
<A href="MB04TU.html">
<B>MB04TU</B></A>   Applying a row-permuted Givens transformation to two row vectors
<A href="MB04WD.html">
<B>MB04WD</B></A>   Generating an orthogonal basis spanning an isotropic subspace
<A href="MB04WP.html">
<B>MB04WP</B></A>   Generating an orthogonal symplectic matrix which performed the reduction 
         in MB04PU
<A href="MB04WR.html">
<B>MB04WR</B></A>   Generating orthogonal symplectic matrices defined as products of symplectic 
         reflectors and Givens rotations
<A href="MB04WU.html">
<B>MB04WU</B></A>   Generating an orthogonal basis spanning an isotropic subspace 
         (unblocked version)
<A href="MB04XY.html">
<B>MB04XY</B></A>   Applying Householder transformations for bidiagonalization (stored 
         in factored form) to one or two matrices, from the left
<A href="MB04YW.html">
<B>MB04YW</B></A>   One QR or QL iteration step onto an unreduced bidiagonal submatrix 
         of a bidiagonal matrix
</PRE>
<h3>MC - Polynomial and Rational Function Manipulation</h3>
<h4>Scalar Polynomials</h4>
<PRE>
<A href="MC01PY.html">
<B>MC01PY</B></A>   Coefficients of a real polynomial, stored in decreasing order, 
         given its zeros         
</PRE>
<h4>Polynomial Matrices</h4>
<PRE>
<A href="MC03NX.html">
<B>MC03NX</B></A>   Construction of a pencil sE-A related to a given polynomial matrix  
</PRE>
<h3>MD - Optimization</h3>
<h4>Unconstrained Nonlinear Least Squares</h4>
<PRE>
<A href="MD03BX.html">
<B>MD03BX</B></A>   QR factorization with column pivoting and error vector 
         transformation
<A href="MD03BY.html">
<B>MD03BY</B></A>   Finding the Levenberg-Marquardt parameter
</PRE>
<HR>
<A NAME="N"><H2>N - Nonlinear Systems</H2></A>
<h3>NF - Wiener Systems</h3>
<h4>Wiener Systems Identification</h4>
<PRE>
<A href="NF01AD.html">
<B>NF01AD</B></A>   Computing the output of a Wiener system  
<A href="NF01AY.html">
<B>NF01AY</B></A>   Computing the output of a set of neural networks
<A href="NF01BD.html">
<B>NF01BD</B></A>   Computing the Jacobian of a Wiener system  
<A href="NF01BP.html">
<B>NF01BP</B></A>   Finding the Levenberg-Marquardt parameter
<A href="NF01BQ.html">
<B>NF01BQ</B></A>   Solution of the linear system J*x = b, D*x = 0, D diagonal
<A href="NF01BR.html">
<B>NF01BR</B></A>   Solution of the linear system op(R)*x = b, R block upper 
         triangular stored in a compressed form
<A href="NF01BS.html">
<B>NF01BS</B></A>   QR factorization of a structured Jacobian matrix
<A href="NF01BU.html">
<B>NF01BU</B></A>   Computing J'*J + c*I, for the Jacobian J given in a
         compressed form
<A href="NF01BV.html">
<B>NF01BV</B></A>   Computing J'*J + c*I, for a full Jacobian J (one output
         variable)
<A href="NF01BW.html">
<B>NF01BW</B></A>   Matrix-vector product x <-- (J'*J + c*I)*x, for J in a
         compressed form
<A href="NF01BX.html">
<B>NF01BX</B></A>   Matrix-vector product x <-- (A'*A + c*I)*x, for a
         full matrix A
<A href="NF01BY.html">
<B>NF01BY</B></A>   Computing the Jacobian of the error function for a neural 
         network (for one output variable)
</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="SB01BX.html">
<B>SB01BX</B></A>   Choosing the closest real (complex conjugate) eigenvalue(s) to
         a given real (complex) value
<A href="SB01BY.html">
<B>SB01BY</B></A>   Pole placement for systems of order 1 or 2
<A href="SB01FY.html">
<B>SB01FY</B></A>   Inner denominator of a right-coprime factorization of an unstable system
         of order 1 or 2
</PRE>
<h4>Riccati Equations</h4>
<PRE>
<A href="SB02MU.html">
<B>SB02MU</B></A>   Constructing the 2n-by-2n Hamiltonian or symplectic matrix for
         linear-quadratic optimization problems
<A href="SB02RU.html">
<B>SB02RU</B></A>   Constructing the 2n-by-2n Hamiltonian or symplectic matrix for
         linear-quadratic optimization problems (efficient and accurate
         version of SB02MU)
<A href="SB02OY.html">
<B>SB02OY</B></A>   Constructing and compressing the extended Hamiltonian or symplectic 
         matrix pairs for linear-quadratic optimization problems
</PRE>
<h4>Lyapunov Equations</h4>
<PRE>
<A href="SB03MV.html">
<B>SB03MV</B></A>   Solving a discrete-time Lyapunov equation for a 2-by-2 matrix
<A href="SB03MW.html">
<B>SB03MW</B></A>   Solving a continuous-time Lyapunov equation for a 2-by-2 matrix
<A href="SB03MX.html">
<B>SB03MX</B></A>   Solving a discrete-time Lyapunov equation with matrix A quasi-triangular
<A href="SB03MY.html">
<B>SB03MY</B></A>   Solving a continuous-time Lyapunov equation with matrix A quasi-triangular
<A href="SB03OT.html">
<B>SB03OT</B></A>   Solving (for Cholesky factor) stable continuous- or discrete-time 
         Lyapunov equations, with A quasi-triangular and R triangular
<A href="SB03OS.html">
<B>SB03OS</B></A>   Solving (for Cholesky factor) stable continuous- or discrete-time 
         complex Lyapunov equations, with matrices S and R triangular
<A href="SB03OU.html">
<B>SB03OU</B></A>   Solving (for Cholesky factor) stable continuous- or discrete-time 
         Lyapunov equations, with A in real Schur form and B rectangular
<A href="SB03OY.html">
<B>SB03OY</B></A>   Solving (for Cholesky factor) stable 2-by-2 continuous- or discrete-time
         Lyapunov equations, with matrix A having complex conjugate eigenvalues
<A href="SB03QX.html">
<B>SB03QX</B></A>   Forward error bound for continuous-time Lyapunov equations
<A href="SB03QY.html">
<B>SB03QY</B></A>   Separation and Theta norm for continuous-time Lyapunov equations
<A href="SB03SX.html">
<B>SB03SX</B></A>   Forward error bound for discrete-time Lyapunov equations
<A href="SB03SY.html">
<B>SB03SY</B></A>   Separation and Theta norm for discrete-time Lyapunov equations
</PRE>
<h4>Sylvester Equations</h4>
<PRE>
<A href="SB03MU.html">
<B>SB03MU</B></A>   Solving a discrete-time Sylvester equation for an m-by-n matrix X, 
         1 <= m,n <= 2
<A href="SB03OR.html">
<B>SB03OR</B></A>   Solving quasi-triangular continuous- or discrete-time Sylvester equations, 
         for an n-by-m matrix X, 1 <= m <= 2
<A href="SB04MR.html">
<B>SB04MR</B></A>   Solving a linear algebraic system whose coefficient matrix (stored 
         compactly) has zeros below the second subdiagonal
<A href="SB04MU.html">
<B>SB04MU</B></A>   Constructing and solving a linear algebraic system whose coefficient 
         matrix (stored compactly) has zeros below the second subdiagonal 
<A href="SB04MW.html">
<B>SB04MW</B></A>   Solving a linear algebraic system whose coefficient matrix (stored 
         compactly) has zeros below the first subdiagonal
<A href="SB04MY.html">
<B>SB04MY</B></A>   Constructing and solving a linear algebraic system whose coefficient 
         matrix (stored compactly) has zeros below the first subdiagonal
<A href="SB04NV.html">
<B>SB04NV</B></A>   Constructing right-hand sides for a system of equations in 
         Hessenberg form solved via SB04NX
<A href="SB04NW.html">
<B>SB04NW</B></A>   Constructing the right-hand side for a system of equations in 
         Hessenberg form solved via SB04NY 
<A href="SB04NX.html">
<B>SB04NX</B></A>   Solving a system of equations in Hessenberg form with two consecutive 
         offdiagonals and two right-hand sides 
<A href="SB04NY.html">
<B>SB04NY</B></A>   Solving a system of equations in Hessenberg form with one offdiagonal 
         and one right-hand side 
<A href="SB04OW.html">
<B>SB04OW</B></A>   Solving a periodic Sylvester equation with matrices in periodic Schur form
<A href="SB04PX.html">
<B>SB04PX</B></A>   Solving a discrete-time Sylvester equation for matrices of order <= 2
<A href="SB04PY.html">
<B>SB04PY</B></A>   Solving a discrete-time Sylvester equation with matrices in Schur form
<A href="SB04QR.html">
<B>SB04QR</B></A>   Solving a linear algebraic system whose coefficient matrix (stored 
         compactly) has zeros below the third subdiagonal
<A href="SB04QU.html">
<B>SB04QU</B></A>   Constructing and solving a linear algebraic system whose coefficient 
         matrix (stored compactly) has zeros below the third subdiagonal
<A href="SB04QY.html">
<B>SB04QY</B></A>   Constructing and solving a linear algebraic system whose coefficient 
         matrix (stored compactly) has zeros below the first subdiagonal
         (discrete-time case)
<A href="SB04RV.html">
<B>SB04RV</B></A>   Constructing right-hand sides for a system of equations in 
         Hessenberg form solved via SB04RX
<A href="SB04RW.html">
<B>SB04RW</B></A>   Constructing the right-hand side for a system of equations in 
         Hessenberg form solved via SB04RY 
<A href="SB04RX.html">
<B>SB04RX</B></A>   Solving a system of equations in Hessenberg form with two consecutive 
         offdiagonals and two right-hand sides (discrete-time case) 
<A href="SB04RY.html">
<B>SB04RY</B></A>   Solving a system of equations in Hessenberg form with one offdiagonal 
         and one right-hand side (discrete-time case) 
</PRE>
<h4>Optimal Regulator Problems</h4>
<PRE>
<A href="SB10JD.html">
<B>SB10JD</B></A>    Conversion of a descriptor state-space system into regular 
          state-space form
<A href="SB10LD.html">
<B>SB10LD</B></A>    Closed-loop system matrices for a system with robust controller
<A href="SB10PD.html">
<B>SB10PD</B></A>    Normalization of a system for H-infinity controller design
<A href="SB10QD.html">
<B>SB10QD</B></A>    State feedback and output injection matrices for an H-infinity
          (sub)optimal state controller (continuous-time)
<A href="SB10RD.html">
<B>SB10RD</B></A>    H-infinity (sub)optimal controller matrices using state feedback
          and output injection matrices (continuous-time)
<A href="SB10SD.html">
<B>SB10SD</B></A>    H2 optimal controller matrices for a normalized discrete-time system
<A href="SB10TD.html">
<B>SB10TD</B></A>    H2 optimal controller matrices for a discrete-time system
<A href="SB10UD.html">
<B>SB10UD</B></A>    Normalization of a system for H2 controller design
<A href="SB10VD.html">
<B>SB10VD</B></A>    State feedback and output injection matrices for an H2 optimal
          state controller (continuous-time)
<A href="SB10WD.html">
<B>SB10WD</B></A>    H2 optimal controller matrices using state feedback and
          output injection matrices (continuous-time)
<A href="SB10YD.html">
<B>SB10YD</B></A>    Fitting frequency response data with a stable, minimum phase
          SISO system
<A href="SB10ZP.html">
<B>SB10ZP</B></A>    Transforming a SISO system into a stable and minimum phase one
</PRE>
<h4>Controller Reduction</h4>
<PRE>
<A href="SB16AY.html">
<B>SB16AY</B></A>    Cholesky factors of the frequency-weighted controllability and 
          observability Grammians for controller reduction
<A href="SB16CY.html">
<B>SB16CY</B></A>    Cholesky factors of controllability and observability Grammians
          of coprime factors of a state-feedback controller
</PRE>
<h3>SG - Generalized State-Space Synthesis</h3>
<h4>Generalized Lyapunov Equations</h4>
<PRE>
<A href="SG02CV.html">
<B>SG02CV</B></A>   Computation of residual matrix for a continuous-time or discrete-time 
         reduced Lyapunov equation
<A href="SG03AX.html">
<B>SG03AX</B></A>   Solving a generalized discrete-time Lyapunov equation with 
         A quasi-triangular and E upper triangular
<A href="SG03AY.html">
<B>SG03AY</B></A>   Solving a generalized continuous-time Lyapunov equation with 
         A quasi-triangular and E upper triangular
<A href="SG03BU.html">
<B>SG03BU</B></A>   Solving (for Cholesky factor) stable generalized discrete-time 
         Lyapunov equations with A quasi-triangular, and E, B upper triangular
<A href="SG03BS.html">
<B>SG03BS</B></A>   Solving (for Cholesky factor) stable generalized discrete-time 
         complex Lyapunov equations with A, E, and B upper triangular
<A href="SG03BV.html">
<B>SG03BV</B></A>   Solving (for Cholesky factor) stable generalized continuous-time 
         Lyapunov equations with A quasi-triangular, and E, B upper triangular
<A href="SG03BT.html">
<B>SG03BT</B></A>   Solving (for Cholesky factor) stable generalized continuous-time 
         complex Lyapunov equations with A, E, and B upper triangular
<A href="SG03BX.html">
<B>SG03BX</B></A>   Solving (for Cholesky factor) stable generalized 2-by-2 Lyapunov equations
</PRE>
<h4>Generalized Sylvester Equations</h4>
<PRE>
<A href="SG03BW.html">
<B>SG03BW</B></A>   Solving a generalized Sylvester equation with A quasi-triangular 
         and E upper triangular, for X m-by-n, n = 1 or 2
</PRE>
<HR>
<A NAME="T"><H2>T - Transformation Routines</H2></A>
<h3>TB - State-Space</h3>
<h4>State-Space Transformations</h4>
<PRE>
<A href="TB01KX.html">
<B>TB01KX</B></A>   Additive spectral decomposition of the transfer-function matrix of a standard system
<A href="TB01UX.html">
<B>TB01UX</B></A>   Observable-unobservable decomposition of a standard system
<A href="TB01VD.html">
<B>TB01VD</B></A>   Conversion of a discrete-time system to output normal form
<A href="TB01VY.html">
<B>TB01VY</B></A>   Conversion of the output normal form of a discrete-time system 
         to a state-space representation
<A href="TB01XD.html">
<B>TB01XD</B></A>   Special similarity transformation of the dual state-space system
<A href="TB01XZ.html">
<B>TB01XZ</B></A>   Special similarity transformation of the dual state-space system 
         (complex case)
<A href="TB01YD.html">
<B>TB01YD</B></A>   Special similarity transformation of a state-space system 
</PRE>
<h4>State-Space to Rational Matrix Conversion</h4>
<PRE>
<A href="TB04BV.html">
<B>TB04BV</B></A>   Strictly proper part of a proper transfer function matrix 
<A href="TB04BW.html">
<B>TB04BW</B></A>   Sum of a rational matrix and a real matrix 
<A href="TB04BX.html">
<B>TB04BX</B></A>   Gain of a SISO linear system, given (A,b,c,d), its poles and zeros
</PRE>
<h3>TC - Polynomial Matrix</h3>
<h3>TD - Rational  Matrix</h3>
<h3>TF - Time Response</h3>
<PRE>
<A href="TF01MX.html">
<B>TF01MX</B></A>   Output response of a linear discrete-time system, given a 
         general system matrix (each output is a column of the result)
<A href="TF01MY.html">
<B>TF01MY</B></A>   Output response of a linear discrete-time system, given the
         system matrices (each output is a column of the result)
</PRE>
<h3>TG - Generalized State-space</h3>
<h4>Generalized State-space Transformations</h4>
<PRE>
<A href="TG01HU.html">
<B>TG01HU</B></A>   Staircase controllability representation of a multi-input descriptor system
<A href="TG01HX.html">
<B>TG01HX</B></A>   Orthogonal reduction of a descriptor system to a system with
         the same transfer-function matrix and without uncontrollable finite 
         eigenvalues
<A href="TG01HY.html">
<B>TG01HY</B></A>   Orthogonal reduction of a descriptor system to a system with
         the same transfer-function matrix and without uncontrollable finite 
         eigenvalues (blocked version)
<A href="TG01KD.html">
<B>TG01KD</B></A>   Orthogonal equivalence transformation of a SISO descriptor system
         with E upper triangular (TG01OA version with more complex interface)
<A href="TG01KZ.html">
<B>TG01KZ</B></A>   Unitary equivalence transformation of a complex SISO descriptor system
         with E upper triangular (TG01OB version with more complex interface)
<A href="TG01LY.html">
<B>TG01LY</B></A>   Finite-infinite decomposition of a structured descriptor system
<A href="TG01NX.html">
<B>TG01NX</B></A>   Block-diagonal decomposition of a descriptor system in 
         generalized real Schur form
<A href="TG01OA.html">
<B>TG01OA</B></A>   Orthogonal equivalence transformation of a SISO descriptor system
         with E upper triangular, so that B becomes parallel to the first unit vector
         and E keeps its structure
<A href="TG01OB.html">
<B>TG01OB</B></A>   Unitary equivalence transformation of a complex SISO descriptor system
         with E upper triangular, so that B becomes parallel to the first unit vector
         and E keeps its structure
</PRE>
<HR>
<A NAME="U"><H2>U - Utility Routines</H2></A>
<h3>UD - Numerical Data Handling</h3>
<HR>
</BODY>
</HTML>