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. 22, 2019). MIT license
included.
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