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<H1>SLICOT SUPPORTING ROUTINES INDEX</H1>
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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> ;
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or <A href="http://www.slicot.org/index.php?site=home">
<b>Return to SLICOT homepage</b></A>
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or <A href="..\libindex.html">
<b>Go to SLICOT LIBRARY INDEX</b></A>
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<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>