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CCA (Computational Convex Analysis) >> plq > _plq_conv_on_interval

# _plq_conv_on_interval

Piecewise linear quadratic (plq), two-piece convexity on interval

### Calling Sequence

    plqco = _plq_conv_on_interval(f1,f2,x1,x3,x5)

### Parameters

f1

  One row of a plq function, on the interval (x1,x3].

f2

  The next row of the plq function, on the interval (x3,x5].

x1

  The open lower bound of f1.

x3

  The closed lower bound of f1, and the open upper bound of f2.

x5

  The closed upper bound of f2.

plqco

  A plq function that is the convex hull of f1 and f2 on (x1,x5].

### Description

Takes two adjacent pieces of a plq function, and the intervals over which they are defined, and returns a plq function that is defined over the domain of both of the pieces, and is the convex hull of both of the pieces.

### Examples

    plqf = [1,1,0,0; 4,0,0,1];
    f1 = plqf(1,:);
    f2 = plqf(2,:);
    x1=-2.5;
    x3=f1(1,1);
    x5=f2(1,1);
    result = _plq_conv_on_interval(f1,f2,x1,x3,x5); // [0.1270167,1,0,0; 4,0,0.2540333,-0.0161332]
    plq_plot(plqf, result, -2.5, 4);

### See Also

- plq_coDirect
- plq_function

### Authors

`Bryan Gardiner`, University of British Columbia, BC, Canada

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