SDPResult -- result of a semidefinite programming computation

Description

This type encapsulates the result of a semidefinite programming computation.

i1 : R = QQ[x][t];

i2 : f = x^2 - 3*x - t;

i3 : sol = solveSOS (f, -t, RoundTol=>12)

o3 = MomentMatrix   2x2 matrix over RR_53           
     GramMatrix     2x2 matrix over QQ              
     Monomials      2x1 matrix over QQ[x]           
     Parameters     1x1 matrix over QQ              
     Status         SDP solved, primal-dual feasible

o3 : SDPResult

i4 : peek sol

o4 = SDPResult{GramMatrix => | 9/4  -3/2 |               }
                             | -3/2 1    |
               MomentMatrix => | 1   1.5  |
                               | 1.5 2.25 |
               Monomials => | 1 |
                            | x |
               Parameters => | -9/4 |
               Status => SDP solved, primal-dual feasible

The fields can be extracted with the operator #.

i5 : sol#GramMatrix

o5 = | 9/4  -3/2 |
     | -3/2 1    |

              2       2
o5 : Matrix QQ  <-- QQ

If the Gram matrix is different from null, then the sum-of-squares polynomial can be recovered with sosPoly.

i6 : sosPoly sol

      9    2      2
o6 = (-)(- -x + 1)
      4    3

o6 : SOSPoly

Methods that use an object of class SDPResult:

recoverSolution(SDPResult) -- see recoverSolution -- factor a rank one positive semidefinite matrix
net(SDPResult)
status(SDPResult)
sosPoly(SDPResult) -- see sosPoly -- make an SOS polynomial

For the programmer

The object SDPResult is a type, with ancestor classes HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SumsOfSquares/SOSdoc.m2:221:0.