WCPHELP32.html

Example 3

Orthogonal interpolatory masks satisfy sum rules of order 2

(7.5.1)

(7.5.2)

(7.5.3)

(7.5.4)

(7.5.5)

(7.5.6)

(7.5.7)

(7.5.8)

(7.5.9)

$Make sure that the mask a={a(k)} is normalized so that sum_k a(k) = 1, i.e., subs(z=1,poly) = 1.$

$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$
$`assign`(eq3, {`+`(`*`(3, `*`(a101c2, `*`(`a201c-1`))), `*`(3, `*`(a101c1, `*`(`a201c-2`))), `*`(`/`(1, 3), `*`(a102c3)), `*`(3, `*`(a102c3, `*`(a202c3))), `*`(6, `*`(`^`(a102c3, 2))), `-`(`*`(`/`(1, ...$ (7.5.10)

(7.5.11)

`assign`(poly3, Matrix(%id = 152370960)) (7.5.12)

$Make sure that the mask a={a(k)} is normalized so that sum_k a(k) = 1, i.e., subs(z=1,poly) = 1.$

(7.5.13)

(7.5.14)

cg = [-0.38e2 / 0.297e3 0 0.83e2 / 0.297e3 0.64e2 / 0.297e3 0.1e1 / 0.3e1 0.26e2 / 0.99e2 0.1e1 / 0.27e2 0 0.2e1 / 0.27e2 -0.2e1 / 0.27e2 0 0; 0.8e1 / 0.297e3 0 -0.14e2 / 0.297e3 -0.10e2 / 0.297e3 0 0.1e1 / 0.11e2 0.118e3 / 0.297e3 0.1e1 / 0.3e1 0.8e1 / 0.297e3 0.67e2 / 0.297e3 0 -0.2e1 / 0.99e2;];

cg0 = [-2 -1 0 1 2 3];

(7.5.15)

(7.5.16)

`assign`(poly4, Matrix(%id = 187320416)) (7.5.17)

$Make sure that the mask a={a(k)} is normalized so that sum_k a(k) = 1, i.e., subs(z=1,poly) = 1.$

(7.5.18)

`assign`(res, Matrix(%id = 196457792))

cg1 = [-0.44e2 / 0.567e3 0 0.55e2 / 0.567e3 0.220e3 / 0.567e3 0.1e1 / 0.3e1 0.2e1 / 0.9e1 0.5e1 / 0.81e2 0 -0.4e1 / 0.81e2 0.2e1 / 0.81e2; 0.8e1 / 0.567e3 0 -0.10e2 / 0.567e3 -0.40e2 / 0.567e3 0 0.1e1 / 0.9e1 0.190e3 / 0.567e3 0.1e1 / 0.3e1 0.172e3 / 0.567e3 -0.5e1 / 0.567e3;];
cg2 = [-2 -1 0 1 2];

$Make sure that the mask a={a(k)} is normalized so that sum_k a(k) = 1, i.e., subs(z=1,poly) = 1.$
	(7.5.13)

$Make sure that the mask a={a(k)} is normalized so that sum_k a(k) = 1, i.e., subs(z=1,poly) = 1.$
	(7.5.18)



cg1 = [-0.44e2 / 0.567e3 0 0.55e2 / 0.567e3 0.220e3 / 0.567e3 0.1e1 / 0.3e1 0.2e1 / 0.9e1 0.5e1 / 0.81e2 0 -0.4e1 / 0.81e2 0.2e1 / 0.81e2; 0.8e1 / 0.567e3 0 -0.10e2 / 0.567e3 -0.40e2 / 0.567e3 0 0.1e1 / 0.9e1 0.190e3 / 0.567e3 0.1e1 / 0.3e1 0.172e3 / 0.567e3 -0.5e1 / 0.567e3;]; cg2 = [-2 -1 0 1 2];