verifiable lagrange

basic/verifiable_Lagrange_interpolation/.gitignore

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+target

basic/verifiable_Lagrange_interpolation/README.md

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+# **Verifiable Lagrange interpolation**
+
+Lagrange interpolation is a mathematical technique used to approximate a function that passes through a given set of points. It takes an input set of data points and computes a polynomial that passes through all of them. 
+
+Given a set of $n+1$ data points (or interpolation nodes) $X_0, X_1, ..., X_n$ with corresponding function values $Y_0, Y_1, ..., Y_n$, Lagrange interpolation seeks to find a polynomial of degree at most $n$ that passes through all these points.
+
+Below, we provide a brief review of the implementation of a Lagrange interpolation in Python, which we will then convert to Cairo to transform it into a verifiable ZKML (Lagrange interpolation), using the Orion library. 
+
+Content overview:
+
+1. Lagrange interpolation with Python: We start with the basic implementation of Lagrange interpolation using Python.
+2. Convert your model to Cairo: In the subsequent stage, we will create a new scarb project and replicate our model to Cairo which is a language for creating STARK-provable programs.
+3. Implementing Lagrange interpolation using Orion: To catalyze our development process, we will use the Orion Framework to construct the key functions to build our verifiable Lagrange interpolation.

basic/verifiable_Lagrange_interpolation/Scarb.toml

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+[package]
+name = "lagrange"
+version = "0.1.0"
+description = "Verifiable Lagrange Interpolation"
+
+[dependencies]
+orion = { git = "https://github.com/gizatechxyz/orion.git", rev = "v0.1.9" }
+
+[scripts]
+test = "scarb cairo-test -f lagrange_test"

basic/verifiable_Lagrange_interpolation/notebooks/src/generated.cairo

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+mod X;
+mod Y;
+mod x;
+mod y;

basic/verifiable_Lagrange_interpolation/notebooks/src/generated/X.cairo

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+use array::{ArrayTrait, SpanTrait};
+use orion::operators::tensor::{core::{Tensor, TensorTrait}};
+use orion::operators::tensor::FP16x16Tensor;
+use orion::numbers::fixed_point::implementations::fp16x16::core::{FP16x16, FixedTrait};
+
+fn X() -> Tensor<FP16x16>{
+
+let mut shape = ArrayTrait::new();
+shape.append(11);
+let mut data = ArrayTrait::new();
+data.append(FixedTrait::new(327680, false));
+data.append(FixedTrait::new(311642, false));
+data.append(FixedTrait::new(265098, false));
+data.append(FixedTrait::new(192605, false));
+data.append(FixedTrait::new(101258, false));
+data.append(FixedTrait::new(0, false));
+data.append(FixedTrait::new(101258, true));
+data.append(FixedTrait::new(192605, true));
+data.append(FixedTrait::new(265098, true));
+data.append(FixedTrait::new(311642, true));
+data.append(FixedTrait::new(327680, true));
+let tensor = TensorTrait::<FP16x16>::new(shape.span(), data.span());
+return tensor;
+}

basic/verifiable_Lagrange_interpolation/notebooks/src/generated/Y.cairo

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+use array::{ArrayTrait, SpanTrait};
+use orion::operators::tensor::{core::{Tensor, TensorTrait}};
+use orion::operators::tensor::FP16x16Tensor;
+use orion::numbers::fixed_point::implementations::fp16x16::core::{FP16x16, FixedTrait};
+
+fn Y() -> Tensor<FP16x16>{
+
+let mut shape = ArrayTrait::new();
+shape.append(11);
+let mut data = ArrayTrait::new();
+data.append(FixedTrait::new(2520, false));
+data.append(FixedTrait::new(2775, false));
+data.append(FixedTrait::new(3774, false));
+data.append(FixedTrait::new(6800, false));
+data.append(FixedTrait::new(19347, false));
+data.append(FixedTrait::new(65536, false));
+data.append(FixedTrait::new(19347, false));
+data.append(FixedTrait::new(6800, false));
+data.append(FixedTrait::new(3774, false));
+data.append(FixedTrait::new(2775, false));
+data.append(FixedTrait::new(2520, false));
+let tensor = TensorTrait::<FP16x16>::new(shape.span(), data.span());
+return tensor;
+}

basic/verifiable_Lagrange_interpolation/notebooks/src/generated/x.cairo

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+use array::{ArrayTrait, SpanTrait};
+use orion::operators::tensor::{core::{Tensor, TensorTrait}};
+use orion::operators::tensor::FP16x16Tensor;
+use orion::numbers::fixed_point::implementations::fp16x16::core::{FP16x16, FixedTrait};
+
+fn x() -> Tensor<FP16x16>{
+
+let mut shape = ArrayTrait::new();
+shape.append(100);
+let mut data = ArrayTrait::new();
+data.append(FixedTrait::new(327680, true));
+data.append(FixedTrait::new(321060, true));
+data.append(FixedTrait::new(314440, true));
+data.append(FixedTrait::new(307820, true));
+data.append(FixedTrait::new(301200, true));
+data.append(FixedTrait::new(294581, true));
+data.append(FixedTrait::new(287961, true));
+data.append(FixedTrait::new(281341, true));
+data.append(FixedTrait::new(274721, true));
+data.append(FixedTrait::new(268101, true));
+data.append(FixedTrait::new(261482, true));
+data.append(FixedTrait::new(254862, true));
+data.append(FixedTrait::new(248242, true));
+data.append(FixedTrait::new(241622, true));
+data.append(FixedTrait::new(235002, true));
+data.append(FixedTrait::new(228383, true));
+data.append(FixedTrait::new(221763, true));
+data.append(FixedTrait::new(215143, true));
+data.append(FixedTrait::new(208523, true));
+data.append(FixedTrait::new(201903, true));
+data.append(FixedTrait::new(195284, true));
+data.append(FixedTrait::new(188664, true));
+data.append(FixedTrait::new(182044, true));
+data.append(FixedTrait::new(175424, true));
+data.append(FixedTrait::new(168804, true));
+data.append(FixedTrait::new(162185, true));
+data.append(FixedTrait::new(155565, true));
+data.append(FixedTrait::new(148945, true));
+data.append(FixedTrait::new(142325, true));
+data.append(FixedTrait::new(135705, true));
+data.append(FixedTrait::new(129086, true));
+data.append(FixedTrait::new(122466, true));
+data.append(FixedTrait::new(115846, true));
+data.append(FixedTrait::new(109226, true));
+data.append(FixedTrait::new(102606, true));
+data.append(FixedTrait::new(95987, true));
+data.append(FixedTrait::new(89367, true));
+data.append(FixedTrait::new(82747, true));
+data.append(FixedTrait::new(76127, true));
+data.append(FixedTrait::new(69507, true));
+data.append(FixedTrait::new(62888, true));
+data.append(FixedTrait::new(56268, true));
+data.append(FixedTrait::new(49648, true));
+data.append(FixedTrait::new(43028, true));
+data.append(FixedTrait::new(36408, true));
+data.append(FixedTrait::new(29789, true));
+data.append(FixedTrait::new(23169, true));
+data.append(FixedTrait::new(16549, true));
+data.append(FixedTrait::new(9929, true));
+data.append(FixedTrait::new(3309, true));
+data.append(FixedTrait::new(3309, false));
+data.append(FixedTrait::new(9929, false));
+data.append(FixedTrait::new(16549, false));
+data.append(FixedTrait::new(23169, false));
+data.append(FixedTrait::new(29789, false));
+data.append(FixedTrait::new(36408, false));
+data.append(FixedTrait::new(43028, false));
+data.append(FixedTrait::new(49648, false));
+data.append(FixedTrait::new(56268, false));
+data.append(FixedTrait::new(62888, false));
+data.append(FixedTrait::new(69507, false));
+data.append(FixedTrait::new(76127, false));
+data.append(FixedTrait::new(82747, false));
+data.append(FixedTrait::new(89367, false));
+data.append(FixedTrait::new(95987, false));
+data.append(FixedTrait::new(102606, false));
+data.append(FixedTrait::new(109226, false));
+data.append(FixedTrait::new(115846, false));
+data.append(FixedTrait::new(122466, false));
+data.append(FixedTrait::new(129086, false));
+data.append(FixedTrait::new(135705, false));
+data.append(FixedTrait::new(142325, false));
+data.append(FixedTrait::new(148945, false));
+data.append(FixedTrait::new(155565, false));
+data.append(FixedTrait::new(162185, false));
+data.append(FixedTrait::new(168804, false));
+data.append(FixedTrait::new(175424, false));
+data.append(FixedTrait::new(182044, false));
+data.append(FixedTrait::new(188664, false));
+data.append(FixedTrait::new(195284, false));
+data.append(FixedTrait::new(201903, false));
+data.append(FixedTrait::new(208523, false));
+data.append(FixedTrait::new(215143, false));
+data.append(FixedTrait::new(221763, false));
+data.append(FixedTrait::new(228383, false));
+data.append(FixedTrait::new(235002, false));
+data.append(FixedTrait::new(241622, false));
+data.append(FixedTrait::new(248242, false));
+data.append(FixedTrait::new(254862, false));
+data.append(FixedTrait::new(261482, false));
+data.append(FixedTrait::new(268101, false));
+data.append(FixedTrait::new(274721, false));
+data.append(FixedTrait::new(281341, false));
+data.append(FixedTrait::new(287961, false));
+data.append(FixedTrait::new(294581, false));
+data.append(FixedTrait::new(301200, false));
+data.append(FixedTrait::new(307820, false));
+data.append(FixedTrait::new(314440, false));
+data.append(FixedTrait::new(321060, false));
+data.append(FixedTrait::new(327680, false));
+let tensor = TensorTrait::<FP16x16>::new(shape.span(), data.span());
+return tensor;
+}

basic/verifiable_Lagrange_interpolation/notebooks/src/generated/y.cairo

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+use array::{ArrayTrait, SpanTrait};
+use orion::operators::tensor::{core::{Tensor, TensorTrait}};
+use orion::operators::tensor::FP16x16Tensor;
+use orion::numbers::fixed_point::implementations::fp16x16::core::{FP16x16, FixedTrait};
+
+fn y() -> Tensor<FP16x16>{
+
+let mut shape = ArrayTrait::new();
+shape.append(100);
+let mut data = ArrayTrait::new();
+data.append(FixedTrait::new(2520, false));
+data.append(FixedTrait::new(3257, false));
+data.append(FixedTrait::new(3016, false));
+data.append(FixedTrait::new(2402, false));
+data.append(FixedTrait::new(1805, false));
+data.append(FixedTrait::new(1449, false));
+data.append(FixedTrait::new(1436, false));
+data.append(FixedTrait::new(1778, false));
+data.append(FixedTrait::new(2433, false));
+data.append(FixedTrait::new(3321, false));
+data.append(FixedTrait::new(4344, false));
+data.append(FixedTrait::new(5402, false));
+data.append(FixedTrait::new(6402, false));
+data.append(FixedTrait::new(7267, false));
+data.append(FixedTrait::new(7934, false));
+data.append(FixedTrait::new(8366, false));
+data.append(FixedTrait::new(8544, false));
+data.append(FixedTrait::new(8473, false));
+data.append(FixedTrait::new(8176, false));
+data.append(FixedTrait::new(7692, false));
+data.append(FixedTrait::new(7074, false));
+data.append(FixedTrait::new(6385, false));
+data.append(FixedTrait::new(5696, false));
+data.append(FixedTrait::new(5080, false));
+data.append(FixedTrait::new(4609, false));
+data.append(FixedTrait::new(4354, false));
+data.append(FixedTrait::new(4376, false));
+data.append(FixedTrait::new(4732, false));
+data.append(FixedTrait::new(5465, false));
+data.append(FixedTrait::new(6608, false));
+data.append(FixedTrait::new(8179, false));
+data.append(FixedTrait::new(10184, false));
+data.append(FixedTrait::new(12615, false));
+data.append(FixedTrait::new(15450, false));
+data.append(FixedTrait::new(18654, false));
+data.append(FixedTrait::new(22179, false));
+data.append(FixedTrait::new(25970, false));
+data.append(FixedTrait::new(29959, false));
+data.append(FixedTrait::new(34073, false));
+data.append(FixedTrait::new(38233, false));
+data.append(FixedTrait::new(42359, false));
+data.append(FixedTrait::new(46366, false));
+data.append(FixedTrait::new(50173, false));
+data.append(FixedTrait::new(53702, false));
+data.append(FixedTrait::new(56878, false));
+data.append(FixedTrait::new(59635, false));
+data.append(FixedTrait::new(61914, false));
+data.append(FixedTrait::new(63668, false));
+data.append(FixedTrait::new(64858, false));
+data.append(FixedTrait::new(65460, false));
+data.append(FixedTrait::new(65460, false));
+data.append(FixedTrait::new(64858, false));
+data.append(FixedTrait::new(63668, false));
+data.append(FixedTrait::new(61914, false));
+data.append(FixedTrait::new(59635, false));
+data.append(FixedTrait::new(56878, false));
+data.append(FixedTrait::new(53702, false));
+data.append(FixedTrait::new(50173, false));
+data.append(FixedTrait::new(46366, false));
+data.append(FixedTrait::new(42359, false));
+data.append(FixedTrait::new(38233, false));
+data.append(FixedTrait::new(34073, false));
+data.append(FixedTrait::new(29959, false));
+data.append(FixedTrait::new(25970, false));
+data.append(FixedTrait::new(22179, false));
+data.append(FixedTrait::new(18654, false));
+data.append(FixedTrait::new(15450, false));
+data.append(FixedTrait::new(12615, false));
+data.append(FixedTrait::new(10184, false));
+data.append(FixedTrait::new(8179, false));
+data.append(FixedTrait::new(6608, false));
+data.append(FixedTrait::new(5465, false));
+data.append(FixedTrait::new(4732, false));
+data.append(FixedTrait::new(4376, false));
+data.append(FixedTrait::new(4354, false));
+data.append(FixedTrait::new(4609, false));
+data.append(FixedTrait::new(5080, false));
+data.append(FixedTrait::new(5696, false));
+data.append(FixedTrait::new(6385, false));
+data.append(FixedTrait::new(7074, false));
+data.append(FixedTrait::new(7692, false));
+data.append(FixedTrait::new(8176, false));
+data.append(FixedTrait::new(8473, false));
+data.append(FixedTrait::new(8544, false));
+data.append(FixedTrait::new(8366, false));
+data.append(FixedTrait::new(7934, false));
+data.append(FixedTrait::new(7267, false));
+data.append(FixedTrait::new(6402, false));
+data.append(FixedTrait::new(5402, false));
+data.append(FixedTrait::new(4344, false));
+data.append(FixedTrait::new(3321, false));
+data.append(FixedTrait::new(2433, false));
+data.append(FixedTrait::new(1778, false));
+data.append(FixedTrait::new(1436, false));
+data.append(FixedTrait::new(1449, false));
+data.append(FixedTrait::new(1805, false));
+data.append(FixedTrait::new(2402, false));
+data.append(FixedTrait::new(3016, false));
+data.append(FixedTrait::new(3257, false));
+data.append(FixedTrait::new(2520, false));
+let tensor = TensorTrait::<FP16x16>::new(shape.span(), data.span());
+return tensor;
+}

basic/verifiable_Lagrange_interpolation/src/generated.cairo

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+mod X;
+mod Y;
+mod x;
+mod y;

basic/verifiable_Lagrange_interpolation/src/generated/X.cairo

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+use array::{ArrayTrait, SpanTrait};
+use orion::operators::tensor::{core::{Tensor, TensorTrait}};
+use orion::operators::tensor::FP16x16Tensor;
+use orion::numbers::fixed_point::implementations::fp16x16::core::{FP16x16, FixedTrait};
+
+fn X() -> Tensor<FP16x16>{
+
+let mut shape = ArrayTrait::new();
+shape.append(11);
+let mut data = ArrayTrait::new();
+data.append(FixedTrait::new(327680, false));
+data.append(FixedTrait::new(311642, false));
+data.append(FixedTrait::new(265098, false));
+data.append(FixedTrait::new(192605, false));
+data.append(FixedTrait::new(101258, false));
+data.append(FixedTrait::new(0, false));
+data.append(FixedTrait::new(101258, true));
+data.append(FixedTrait::new(192605, true));
+data.append(FixedTrait::new(265098, true));
+data.append(FixedTrait::new(311642, true));
+data.append(FixedTrait::new(327680, true));
+let tensor = TensorTrait::<FP16x16>::new(shape.span(), data.span());
+return tensor;
+}

basic/verifiable_Lagrange_interpolation/src/generated/Y.cairo

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+use array::{ArrayTrait, SpanTrait};
+use orion::operators::tensor::{core::{Tensor, TensorTrait}};
+use orion::operators::tensor::FP16x16Tensor;
+use orion::numbers::fixed_point::implementations::fp16x16::core::{FP16x16, FixedTrait};
+
+fn Y() -> Tensor<FP16x16>{
+
+let mut shape = ArrayTrait::new();
+shape.append(11);
+let mut data = ArrayTrait::new();
+data.append(FixedTrait::new(2520, false));
+data.append(FixedTrait::new(2775, false));
+data.append(FixedTrait::new(3774, false));
+data.append(FixedTrait::new(6800, false));
+data.append(FixedTrait::new(19347, false));
+data.append(FixedTrait::new(65536, false));
+data.append(FixedTrait::new(19347, false));
+data.append(FixedTrait::new(6800, false));
+data.append(FixedTrait::new(3774, false));
+data.append(FixedTrait::new(2775, false));
+data.append(FixedTrait::new(2520, false));
+let tensor = TensorTrait::<FP16x16>::new(shape.span(), data.span());
+return tensor;
+}