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d5b7741 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 | import OAI.Combinatorics.ContingencyTables.Sampling.UnitTrialProgram
import OAI.Combinatorics.ContingencyTables.Sampling.ProfilePublicProgram
namespace OAI
/-! # A single computed sampler for large and all-small rectangles -/
namespace ContingencyTables.ProfilePrograms
open MatchingFPRAS.TreeTyped DensePrograms
def parameterUnitWords (z : SamplingParameters) : ℕ :=
parameterTrials z*(parameterSteps z*parameterProposalWidth z)
def parameterUnitWordsRealizer : Realizer parameterUnitWords :=
composition (f := fun z : SamplingParameters =>
(parameterTrials z,parameterSteps z*parameterProposalWidth z))
(g := fun p : ℕ×ℕ => p.1*p.2) (pair parameterTrialsRealizer
(composition (f := fun z : SamplingParameters => (parameterSteps z,parameterProposalWidth z))
(g := fun p : ℕ×ℕ => p.1*p.2) (pair parameterStepsRealizer parameterProposalWidthRealizer) multiply)) multiply
theorem polynomial_parameterUnitWords : PolynomialTime parameterUnitWordsRealizer :=
polynomial_composition (polynomial_pair polynomial_parameterTrials
(polynomial_composition (polynomial_pair polynomial_parameterSteps polynomial_parameterProposalWidth)
polynomial_multiply)) polynomial_multiply
attribute [local irreducible] parameterUnitWords
abbrev SamplingWordInput := SamplingParameters×List Bool
def unitSamplingBits (z : SamplingWordInput) : List Bool :=
z.2.take (parameterUnitWords z.1)
def unitSamplingBitsRealizer : Realizer unitSamplingBits :=
composition (f := fun z : SamplingWordInput => (z.2,parameterUnitWords z.1))
(g := fun z : List Bool×ℕ => z.1.take z.2)
(pair (f := fun z : SamplingWordInput => z.2)
(g := fun z : SamplingWordInput => parameterUnitWords z.1) second
(composition (f := fun z : SamplingWordInput => z.1)
(g := parameterUnitWords) first parameterUnitWordsRealizer)) takeFast
theorem polynomial_unitSamplingBits : PolynomialTime unitSamplingBitsRealizer :=
polynomial_composition (polynomial_pair polynomial_second
(polynomial_composition polynomial_first polynomial_parameterUnitWords)) polynomial_takeFast
def unitSamplingInput (z : SamplingWordInput) : ProfileRetryData :=
(samplingRetryParameters z.1,unitSamplingBits z)
def unitSamplingInputRealizer : Realizer unitSamplingInput :=
pair (composition (f := fun z : SamplingWordInput => z.1) (g := samplingRetryParameters)
first samplingRetryParametersRealizer) unitSamplingBitsRealizer
theorem polynomial_unitSamplingInput : PolynomialTime unitSamplingInputRealizer :=
polynomial_pair (polynomial_composition polynomial_first polynomial_samplingRetryParameters)
polynomial_unitSamplingBits
def unitSamplingMatrix (z : SamplingWordInput) : MatrixCode := unitProfileRetry (unitSamplingInput z)
def unitSamplingMatrixRealizer : Realizer unitSamplingMatrix :=
composition (f := unitSamplingInput) (g := unitProfileRetry)
unitSamplingInputRealizer unitProfileRetryRealizer
theorem polynomial_unitSamplingMatrix : PolynomialTime unitSamplingMatrixRealizer :=
polynomial_composition polynomial_unitSamplingInput polynomial_unitProfileRetry
def parameterLargeIndices (row : Bool) (z : SamplingParameters) : List ℕ :=
largeIndices (marginThreshold z.1,if row then z.1.1 else z.1.2)
def parameterLargeIndicesRealizer (row : Bool) : Realizer (parameterLargeIndices row) := by
cases row with
| false =>
exact composition
(f := fun z : SamplingParameters => (marginThreshold z.1,z.1.2)) (g := largeIndices)
(pair (composition (f := fun z : SamplingParameters => z.1) (g := marginThreshold)
first marginThresholdRealizer) (composition first second)) largeIndicesRealizer
| true =>
exact composition
(f := fun z : SamplingParameters => (marginThreshold z.1,z.1.1)) (g := largeIndices)
(pair (composition (f := fun z : SamplingParameters => z.1) (g := marginThreshold)
first marginThresholdRealizer) (composition first first)) largeIndicesRealizer
theorem polynomial_parameterLargeIndices (row : Bool) : PolynomialTime (parameterLargeIndicesRealizer row) := by
cases row with
| false => exact polynomial_composition (polynomial_pair
(polynomial_composition polynomial_first polynomial_marginThreshold)
(polynomial_composition polynomial_first polynomial_second)) polynomial_largeIndices
| true => exact polynomial_composition (polynomial_pair
(polynomial_composition polynomial_first polynomial_marginThreshold)
(polynomial_composition polynomial_first polynomial_first)) polynomial_largeIndices
def hasLargeRectangle (z : SamplingParameters) : Bool :=
decide (0<(parameterLargeIndices true z).length) && decide (0<(parameterLargeIndices false z).length)
def hasLargeRectangleRealizer : Realizer hasLargeRectangle :=
composition (f := fun z : SamplingParameters =>
(decide (0<(parameterLargeIndices true z).length),decide (0<(parameterLargeIndices false z).length)))
(g := fun p : Bool×Bool => p.1 && p.2)
(pair
(composition (f := fun z : SamplingParameters => (0,(parameterLargeIndices true z).length))
(g := fun p : ℕ×ℕ => decide (p.1<p.2))
(pair (constant 0) (composition (f := parameterLargeIndices true) (g := List.length)
(parameterLargeIndicesRealizer true) listLength)) less)
(composition (f := fun z : SamplingParameters => (0,(parameterLargeIndices false z).length))
(g := fun p : ℕ×ℕ => decide (p.1<p.2))
(pair (constant 0) (composition (f := parameterLargeIndices false) (g := List.length)
(parameterLargeIndicesRealizer false) listLength)) less)) boolAnd
theorem polynomial_hasLargeRectangle : PolynomialTime hasLargeRectangleRealizer :=
polynomial_composition (polynomial_pair
(polynomial_composition (polynomial_pair (polynomial_constant 0)
(polynomial_composition (polynomial_parameterLargeIndices true) polynomial_listLength)) polynomial_less)
(polynomial_composition (polynomial_pair (polynomial_constant 0)
(polynomial_composition (polynomial_parameterLargeIndices false) polynomial_listLength)) polynomial_less))
polynomial_boolAnd
def samplingMatrixAll (z : SamplingParameters×List Bool) : MatrixCode :=
if hasLargeRectangle z.1 then samplingMatrix z else unitSamplingMatrix z
def samplingMatrixAllRealizer : Realizer samplingMatrixAll :=
choose (composition (f := fun z : SamplingParameters×List Bool => z.1) (g := hasLargeRectangle)
first hasLargeRectangleRealizer) samplingMatrixRealizer unitSamplingMatrixRealizer
theorem polynomial_samplingMatrixAll : PolynomialTime samplingMatrixAllRealizer :=
polynomial_choose (polynomial_composition polynomial_first polynomial_hasLargeRectangle)
polynomial_samplingMatrix polynomial_unitSamplingMatrix
def publicSamplingAll (z : List MatchingFPRAS.Symbol×List Bool) : List MatchingFPRAS.Symbol :=
GreedyFeasibleTable.printMatrix (samplingMatrixAll (parsedSampling z.1,z.2))
def publicSamplingAllRealizer : Realizer publicSamplingAll :=
composition (f := fun z : List MatchingFPRAS.Symbol×List Bool =>
samplingMatrixAll (parsedSampling z.1,z.2)) (g := GreedyFeasibleTable.printMatrix)
(composition (f := fun z : List MatchingFPRAS.Symbol×List Bool => (parsedSampling z.1,z.2))
(g := samplingMatrixAll) (pair (composition (f := fun z : List MatchingFPRAS.Symbol×List Bool => z.1)
(g := parsedSampling) first parsedSamplingRealizer) second) samplingMatrixAllRealizer)
GreedyFeasibleTable.printMatrixRealizer
theorem polynomial_publicSamplingAll : PolynomialTime publicSamplingAllRealizer :=
polynomial_composition (polynomial_composition (polynomial_pair
(polynomial_composition polynomial_first polynomial_parsedSampling) polynomial_second)
polynomial_samplingMatrixAll) GreedyFeasibleTable.polynomial_printMatrix
end ContingencyTables.ProfilePrograms
end OAI
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