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// SPDX-License-Identifier: AGPL-3.0-or-later

import assert from "node:assert";

import { describe, it } from "node:test";

import { MonomialBasis } from "../src/analysis/monomial_basis.js";

describe("MonomialBasis (Graded-Lexicographical Monomial Indexing)", () => {

it("should generate correct graded-lex ordering for 2 variables, order 2", () => {

const basis = MonomialBasis.get(2, 2);

assert.strictEqual(basis.totalMonomials, 6); // binom(2+2, 2) = 6

// Invariants: index 0 is constant, indices 1..2 are coordinate variables

assert.deepStrictEqual(basis.exponents[0], [0, 0]);

assert.deepStrictEqual(basis.exponents[1], [1, 0]);

assert.deepStrictEqual(basis.exponents[2], [0, 1]);

assert.deepStrictEqual(basis.exponents[3], [2, 0]);

assert.deepStrictEqual(basis.exponents[4], [1, 1]);

assert.deepStrictEqual(basis.exponents[5], [0, 2]);

assert.strictEqual(basis.variableIndex(0), 1);

assert.strictEqual(basis.variableIndex(1), 2);

assert.deepStrictEqual(Array.from(basis.degrees), [0, 1, 1, 2, 2, 2]);

assert.strictEqual(basis.indexOf([0, 0]), 0);

assert.strictEqual(basis.indexOf([1, 1]), 4);

assert.strictEqual(basis.indexOf([3, 0]), -1); // Exceeds order 2

});

it("should precompute exact multiplication table for polynomial products", () => {

const basis = MonomialBasis.get(2, 2);

const table = basis.mulTable!;

assert.ok(table !== null);

const M = basis.totalMonomials;

const mul = (i: number, j: number) => table[i * M + j]!;

// 1 * x0 = x0 (0 * 1 = 1)

assert.strictEqual(mul(0, 1), 1);

// x0 * x1 = x0*x1 (1 * 2 = 4)

assert.strictEqual(mul(1, 2), 4);

// x0 * x0 = x0^2 (1 * 1 = 3)

assert.strictEqual(mul(1, 1), 3);

// x1 * x1 = x1^2 (2 * 2 = 5)

assert.strictEqual(mul(2, 2), 5);

// x0^2 * x0 = x0^3 (degree 3 > 2 => -1 truncated)

assert.strictEqual(mul(3, 1), -1);

// x0*x1 * x1 = x0*x1^2 (degree 3 > 2 => -1 truncated)

assert.strictEqual(mul(4, 2), -1);

});

it("should precompute variable restriction maps correctly", () => {

const basis = MonomialBasis.get(2, 2);

// Restricting variable 0 (x0) to 0

const target0 = basis.restrictTarget[0]!;

const deg0 = basis.restrictDegree[0]!;

// Constant [0, 0] (idx 0) -> [0, 0] (idx 0), deg 0

assert.strictEqual(target0[0], 0);

assert.strictEqual(deg0[0], 0);

// x0 [1, 0] (idx 1) -> [0, 0] (idx 0), deg 1

assert.strictEqual(target0[1], 0);

assert.strictEqual(deg0[1], 1);

// x1 [0, 1] (idx 2) -> [0, 1] (idx 2), deg 0

assert.strictEqual(target0[2], 2);

assert.strictEqual(deg0[2], 0);

// x0*x1 [1, 1] (idx 4) -> [0, 1] (idx 2), deg 1

assert.strictEqual(target0[4], 2);

assert.strictEqual(deg0[4], 1);

// x0^2 [2, 0] (idx 3) -> [0, 0] (idx 0), deg 2

assert.strictEqual(target0[3], 0);

assert.strictEqual(deg0[3], 2);

});

it("should precompute time integration maps correctly", () => {

const basis = MonomialBasis.get(2, 2);

// Integrating with respect to variable 0

const target0 = basis.integrateTarget[0]!;

const div0 = basis.integrateDivisor[0]!;

// 1 [0, 0] (idx 0) -> x0 [1, 0] (idx 1), divisor 1

assert.strictEqual(target0[0], 1);

assert.strictEqual(div0[0], 1);

// x0 [1, 0] (idx 1) -> x0^2 [2, 0] (idx 3), divisor 2

assert.strictEqual(target0[1], 3);

assert.strictEqual(div0[1], 2);

// x1 [0, 1] (idx 2) -> x0*x1 [1, 1] (idx 4), divisor 1

assert.strictEqual(target0[2], 4);

assert.strictEqual(div0[2], 1);

// x0^2 [2, 0] (idx 3) -> x0^3 (degree 3 > 2 => -1), divisor 3

assert.strictEqual(target0[3], -1);

assert.strictEqual(div0[3], 3);

});

it("should precompute variable differentiation maps correctly", () => {

const basis = MonomialBasis.get(2, 2);

// Differentiating with respect to variable 0 (x0)

const target0 = basis.diffTarget[0]!;

const mult0 = basis.diffMultiplier[0]!;

// 1 [0, 0] (idx 0) -> derivative is 0 (-1)

assert.strictEqual(target0[0], -1);

assert.strictEqual(mult0[0], 0);

// x0 [1, 0] (idx 1) -> 1 [0, 0] (idx 0), mult 1

assert.strictEqual(target0[1], 0);

assert.strictEqual(mult0[1], 1);

// x1 [0, 1] (idx 2) -> derivative wrt x0 is 0 (-1)

assert.strictEqual(target0[2], -1);

assert.strictEqual(mult0[2], 0);

// x0^2 [2, 0] (idx 3) -> 2*x0 [1, 0] (idx 1), mult 2

assert.strictEqual(target0[3], 1);

assert.strictEqual(mult0[3], 2);

// x0*x1 [1, 1] (idx 4) -> x1 [0, 1] (idx 2), mult 1

assert.strictEqual(target0[4], 2);

assert.strictEqual(mult0[4], 1);

// x1^2 [0, 2] (idx 5) -> derivative wrt x0 is 0 (-1)

assert.strictEqual(target0[5], -1);

assert.strictEqual(mult0[5], 0);

});

it("should reuse cached MonomialBasis instances", () => {

const b1 = MonomialBasis.get(3, 3);

const b2 = MonomialBasis.get(3, 3);

assert.strictEqual(b1, b2);

// binom(3+3, 3) = 20

assert.strictEqual(b1.totalMonomials, 20);

});

});