VERSOFT: Verification software in MATLAB / INTLAB

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The files below are written in MATLAB 7.4.0 (R2007a) using INTLAB, version 5.4. 

 

Download all   (Current version: VERSOFT_10, released Jan. 31, 2009)

 

VERSOFT: Guide

 

VERSOFT: Examples

 

INTLAB Primer

 

Files are grouped into three sections: real data, interval data, and uncommon problems.

Files marked by a black asterisk "*"  may yield albeit verified, yet unsatisfactory results.

 

Real (or complex) data only: Matrices

 

VERBASIS                       Verified basis of the range space of a rectangular real matrix  

 

VERORTH                                          Verified orthonormal basis of the range space of a rectangular real matrix  

 

VERNULL*                                        Verified null space of a rectangular real matrix  

 

VERRANK                     Verified bounds on the rank of a rectangular real matrix 

VERFULLCOLRANK                       Verified full column rank of a rectangular real matrix  

 

VERNORM2                                       Verified 2-norm of a rectangular complex (or real) matrix 

VERDISTSING                                   Verified 2-norm distance to the nearest singular matrix 

VERCONDNUM                                Verified 2-norm condition number of a square real matrix 

VERDET                       Verified determinant of a complex (or real) matrix 

VERRREF                                           Verified reduced row-echelon form (RREF) of a rectangular real matrix  

VERPINV                                            Verified pseudoinverse of a rectangular real matrix

VERORTHPROJ                                Verified orthogonal projection on the range space of a rectangular real matrix  

VERPD                                                 Verified positive definiteness of a real matrix

VERPMAT                                          Verified P-property of a real matrix

See VERINVERSE or INV for verified inverse matrix

 

See VERBASINTNPPROB for verified solution of an easy-looking NP-hard matrix problem

 

Use F=VERMATFUN ('sqrt(x)',A,1)  for verified square root  F of a symmetric positive definite matrix A   

 

Real (or complex) data only: Matrices: Eigenvalues and singular values

 

VEREIG                                               Verified eigenvalues and eigenvectors of a complex (or real) matrix  

 

VERSPECTRAD                                Verified spectral radius of a complex (or real) matrix 

 

VEREIGBACK                  Verified backward error analysis of eigenpairs

See VERSINGVAL or VERTHINSVD for verified singular values of a rectangular real matrix 

Real (or complex) data only: Matrices: Decompositions

 

VERRANKDEC                                Verified rank decomposition of a rectangular real matrix  

 

VERSPECTDEC                               Verified spectral decomposition of a symmetric real matrix

 

VERTHINSVD                 Verified thin singular value decomposition of a rectangular complex (or real) matrix   

VERPOLDEC                                    Verified polar decomposition of a square real matrix  

See VERCHOL  for verified Cholesky decomposition of a symmetric real matrix      

See VERQR for verified QR decomposition of a rectangular real matrix      

Real (or complex) data only: Matrix functions

 

VERMATFUN                  Verified matrix function of a square complex (or real) matrix   

 

Real data only: Linear systems (square)

 

See VERINTERVALHULL  or VERIFYLSS for  verified solution of a system of  linear equations

 

Real data only: Linear systems (rectangular)  

 

VERLINSYS                                       Verified description of all solutions of a system of linear equations   

 

VERLSQ                       Verified description of all linear squares solutions of a system of linear equations   

VERLININEQNN                               Verified nonnegative solution of a system of linear inequalities

See VERLINPROG for verified nonnegative solution of a system of linear equations 

Real data only: Matrix equations (rectangular)

 

See VERMATREQN  for verified solution of the matrix equation A*X*B+C*X*D=F (in particular, of the Sylvester or Lyapunov equation)                                      

 

Real data only: Optimization

 

VERLINPROG                 Verified linear programming (format min c'*x  s.t.  A*x=b, x>=0)

VERLINPROGG                              Verified linear programming (format min c'*x  s.t.  A*x=b, x>=0)

                                                             (An improved version of VERLINPROG; may be slower)

 

VERQUADPROG                             Verified convex quadratic programming (format min 0.5*x'*D*x+c'*x  s.t.  A*x>=b, x>=0)

VERLCPALL                                    Verified all solutions of a linear complementarity problem

 

Real (or complex) data only: Polynomials

 

VERROOTS                                        Verified roots of a complex (or real) polynomial

 

 

Interval (or real) data: Matrices

 

VERINVERSE                                   Verified inverse interval matrix

 

VERINVNONNEG              Verified nonnegative invertibility of an interval matrix

 

VERREGSING                                  Verified regularity/singularity of an interval matrix

 

VERPOSDEF                                     Verified positive definiteness of an interval matrix

 

VERHURWSTAB                              Verified Hurwitz stability of an interval matrix  

 

Interval (or real) data: Matrices: Eigenvalues and singular values

 

VEREIGSYM                                     Verified eigenvalues of a symmetric interval (or real) matrix  

 

VERSINGVAL                                   Verified singular values of a rectangular interval (or real) matrix  

 

VEREIGVAL                                      Verified real eigenvalue of an interval matrix

 

VEREIGVEC                                      Verified real eigenvector of an interval matrix

 

VERPERRVEC                  Verified Perron vector of a positive interval matrix

Interval (or real) data: Matrices: Decompositions

VERCHOL*                    Verified Cholesky decomposition of a symmetric interval (or real) matrix   

VERQR*                                             Verified QR decomposition of a rectangular interval (or real) matrix   

Interval (or real) data: Linear systems (square)

 

VERENCLINTHULL            Verified enclosure of the interval hull of the solution set  of a system of interval linear equations

VERINTERVALHULL                    Verified interval hull of the solution set of a system of interval linear equations

                  

VERHULLPARAM              Verified enclosure of the solution set of a family of parametric interval linear equations

VERHULLPATT                                Verified enclosure of the solution set of a system of interval linear equations  with equality of coefficients being taken into account

 

Interval (or real) data: Linear systems (rectangular)

 

VEROETTPRAG                               Verified solution of the Oettli-Prager inequality, and the data to it

 

VERTOLSOL                                     Verified tolerance solution of a system of interval linear equations

 

VERINTLININEQS                           Verified strong solution of a system of interval linear inequalities

 

Interval (or real) data: Matrix equations (rectangular)

 

VERMATREQN                                 Verified solution of the matrix equation A*X*B+C*X*D=F                                                                

                                                               (in particular, of the Sylvester or Lyapunov equation)       

 

 

Real data only: Uncommon problems

 

VERABSVALEQN                           Verified solution of the equation A*x+B*abs(x)=b

 

VERABSVALEQNALL         Verified all solutions of the equation A*x+B*abs(x)=b

VERBASINTNPPROB                     Verified solution of the basic NP-complete problem of interval computations

PLUSMINUSONESET                     Matrix of plus/minus-one vectors

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Last change: 2009-06-18