1. EASIBEX-MATLAB : a simple tool to start with interval contractors
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EASIBEX-MATLAB : a simple tool to start with interval contractors
Fabrice LE BARS
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Description
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3. Description Main goals Target users
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Description
Main goals
Start using interval arithmetic and contractors
Quickly prototype and test new algorithms
Target users
Students
Scientists not specialist in programming
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4. Description Base and philosophy Simple MATLAB layer of IBEX
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Description
Base and philosophy
Simple MATLAB layer of IBEX
Non object-oriented naming conventions
Easily draw results thanks to MATLAB or VIBes
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5. Description Limitations Other options
19/02/2019
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
Once you are comfortable with intervals, contractors, C++ and object-oriented programming, use directly IBEX
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Demo
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Demo
Download and test
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8. Demo To define an EASIBEX-MATLAB interval An empty interval would be
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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]
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9. Demo To define a box 2 intervals can be added using And 2 boxes
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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]])
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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)
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11. Demo Interval matrix imatrix Contract y=Ax x = [[1,2];[0,1]];
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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)
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12. Demo C=AB Contract C=AB
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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)
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Questions?
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