VERSOFT: Verification software in MATLAB / INTLAB


 

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). MIT license included.

 

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
 
 

Download all

 

Last change: 2016-07-26

 

[CNW:Counter]