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(* Examples *)
<<"SDPB.m";
(* The following is the example in the manual *)
(* Maximize {a,b}.{0,-1} = -b over {a,b} such that {a,b}.{1,0}=a=1 and
E^(-x)(a(1+x^4) + b(x^4/12 + x^2)) >= 0 for all x>=0
Equivalently,
1+x^4 + b(x^4/12 + x^2) >= 0 for all x >= 0
The prefactor DampedRational[1,{},1/E,x] doesn't affect the answer,
but does affect the choice of sample scalings and bilinear basis.
*)
testSDP[datFile_] := Module[
{
pols = {PositiveMatrixWithPrefactor[DampedRational[1,{}, 1/E,x], {{{1 + x^4, x^4/12 + x^2}}}]},
norm = {1, 0},
obj = {0, -1}
},
WriteBootstrapSDP[datFile, SDP[obj, norm, pols]];];
(* A similar computation to the above, except with nontrivial matrix semidefiniteness constraints *)
testSDPMatrix[datFile_] := Module[
{
pols = {
PositiveMatrixWithPrefactor[
DampedRational[1, {}, 1/E, x],
{{{1 + x^4, 1 + x^4/12 + x^2}, {x^2, x/5}},
{{x^2, x/5}, {2 + x^4, x^4/3 + 2*x^2}}}],
PositiveMatrixWithPrefactor[
DampedRational[1, {}, 1/E, x],
{{{1 + 3x^4/4, 1 + x^4/12 + x^2}, {x^2, 1/2 + x/5}},
{{x^2, 1/2 + x/5}, {2 + 3x^4/5, x^4/3 + 2*x^2}}}]
},
norm = {1, 0},
obj = {0, -1}
},
WriteBootstrapSDP[datFile, SDP[obj, norm, pols]];];
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