Example 1 

Compute the L2 smoothness of cadinal B-spline function with dilation d.
The mask for cardinal B-spline of order m and dilation factor d is given by: The L2 smoothness should be equal to m-1/2 

> restart; 1
 

> read
 

> `assign`(d, 2); 1; `assign`(m, 2); 1
 

 

`assign`(d, 2)
`assign`(m, 2) (10.3.1)
 

> `assign`(poly, D1BSplineMask(d, m)); 1
 

`assign`(poly, `*`(`^`(`+`(`/`(1, 2), `*`(`/`(1, 2), `*`(z))), 2))) (10.3.2)
 

> D1Nu2Mask(poly, d, m); 1
 

1.500000000 (10.3.3)
 

> `assign`(poly2, convert(`<,>`(poly), Matrix)); 1
 

`assign`(poly2, Matrix(%id = 196454100)) (10.3.4)
 

> D1CriticalExponentV2(poly2, d, m); 1
D1CriticalExponentV2(poly2, d, m); 1
D1CriticalExponentV2(poly2, d, m); 1
 

1.500000000 (10.3.5)
 

> `assign`(d, 3); 1; `assign`(m, 10); 1
 

 

`assign`(d, 3)
`assign`(m, 10) (10.3.6)
 

> `assign`(poly, D1BSplineMask(d, m)); 1
 

`assign`(poly, `*`(`^`(`+`(`/`(1, 3), `*`(`/`(1, 3), `*`(z)), `*`(`/`(1, 3), `*`(`^`(z, 2)))), 10))) (10.3.7)
 

> D1Nu2Mask(poly, d, m); 1
 

9.500000000 (10.3.8)
 

> D1CriticalExponentV2(convert(`<,>`(poly), Matrix), d, m); 1
 

9.499999995 (10.3.9)
 

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