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EASIBEX-MATLAB : a simple tool to start with interval contractors

EASIBEX-MATLAB : a simple tool to start with interval contractors. Fabrice LE BARS. Description. Description. Main goals Start using interval arithmetic and contractors Quickly prototype and test new algorithms Target users Students Scientists not specialist in programming. Description.

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EASIBEX-MATLAB : a simple tool to start with interval contractors

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  1. EASIBEX-MATLAB : a simple tool to start with interval contractors Fabrice LE BARS

  2. Description

  3. Description Main goals Start using interval arithmetic and contractors Quickly prototype and test new algorithms Target users Students Scientists not specialist in programming

  4. Description Base and philosophy Simple MATLAB layer of IBEX Non object-oriented naming conventions Easily draw results thanks to MATLAB or VIBes

  5. Description Limitations To keep it simple, not all IBEX features are available No guaranties w.r.t. rounding… Simplified function names to avoid object-oriented paradigms Other options EASIBEX-CPP is available if C++ is needed : see www.ensta-bretagne.fr/jaulin/easibex.html Once you are comfortable with intervals, contractors, C++ and object-oriented programming, use directly IBEX

  6. Demo

  7. Demo • Download and test • https://github.com/ENSTABretagneRobotics/EASIBEX-MATLAB/

  8. Demo To define an EASIBEX-MATLAB interval x=[-2,2] x(1,2) would be 2 An empty interval would be x=[NaN,NaN] Infinity x=[-Inf,Inf]

  9. Demo To define a box x=[[-2,2];[2,4];[-4,1]] x(2,:) would be [2,4] 2 intervals can be added using Z=i_Add([0,2],[-1,2]) And 2 boxes Z=i_Add([[0,1];[0,10];[0,10]],[[-1,0];[2,5];[-1,0]])

  10. Demo To contract 3 intervals Z=[-10,1], X=[0,2], Y=[-1,2] knowing the constraint Z=X+Y : [Z,X,Y]=i_Cadd([-10,1],[0,2],[-1,2]) To contract the vector x=[-10,10]*[0,10]*[-10,0] w.r.t. the q-relaxed intersection of the 4 vectors [-2,2]*[2,4]*[-4,1], [-1,5]*[-5,8]*[-7,2], [-1,1]*[0,2]*[1,2], [-2,2]*[2,8]*[-1,2], with q=2 : x = [[-10,10];[0,10];[-10,0]] y_j = {[[-2,2];[2,4];[-4,1]];[[-1,5];[-5,8];[-7,2]];[[-1,1];[0,2];[1,2]];[[-2,2];[2,8];[-1,2]]} x = i_C_q_in(x, 2, y_j)

  11. Demo Interval matrix imatrix x = [[1,2];[0,1]]; A = i_imatrix(2, 2, [[[0,1];[0,0]];[[0,0];[0,1]]]); i_Mulimatrixbox(A, x) Contract y=Ax y = [[2,3];[1,2]]; [v, M, u] = i_Cmulimatrixbox(y, A, x)

  12. Demo C=AB A = i_imatrix(2, 2, [[[0,1];[0,0]];[[0,0];[0,1]]]); B = i_imatrix(2, 2, [[[1,2];[0,0]];[[0,0];[1,2]]]); C = i_imatrix(2, 2, [[[2,3];[0,0]];[[0,0];[2,3]]]); i_Mul(A, B) Contract C=AB [M, P, Q] = i_Cmul(C, A, B)

  13. Questions?

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