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better solver and free variable restrictions
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@menocsk27
menocsk27 committed Dec 3, 2024
1 parent b86fa8b commit f039f5a
Showing 1 changed file with 80 additions and 34 deletions.
114 changes: 80 additions & 34 deletions frontend/public/js/proof/rules/cd/linear/linear.js
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Original file line number Diff line number Diff line change
Expand Up @@ -46,10 +46,6 @@ function solve(data) {
sum = Fraction(sum).add(Fraction(matrix[i][j]).mul(Fraction(solutions[j])));
}
solutions[i] = Fraction(matrix[i][numCols - 1]).sub(Fraction(sum)).div(Fraction(matrix[i][i]));

if (Fraction(solutions[i]).abs().lt(tolerance)) {
solutions[i] = Fraction(0);
}
}

return solutions;
Expand Down Expand Up @@ -87,13 +83,13 @@ function solve(data) {
matrix.forEach((row) => {
let nonZeroFound = false;
for (let j = 0; j < numCols; j++) {
if (Fraction(row[j]).abs().gt(0)) {
if (!Fraction(row[j]).equals(0)) {
free--;
nonZeroFound = true;
break;
}
}
if (!nonZeroFound && Fraction(row[numCols]).abs().gt(0)) {
if (!nonZeroFound && !Fraction(row[numCols]).equals(0)) {
hasSolution = false; // No solution if a row has all zeros and a non-zero constant
}
});
Expand All @@ -113,24 +109,35 @@ function solve(data) {
let numRows = system.length;
let numCols = system[0].length;

//system.forEach(row => console.log(row.map(c => Fraction(c).toFraction()).join(" ")));
// gaussian elimination based on https://matrixcalc.org/slu.html
let offset = 0;

for (let i = 0; i < numRows; i++) {
let maxRow = i;
for (let k = i + 1; k < numRows; k++) {
if (Fraction(system[k][i]).abs().gt(system[maxRow][i])) {
maxRow = k;
}
if (i + offset >= numCols) {
break; // can't reduce anymore
}
[system[i], system[maxRow]] = [system[maxRow], system[i]];

if (Fraction(system[i][i + offset]).equals(0)) { // avoids divisions by zero
let pivot = i;
for (let k = i + 1; k < numRows; k++) {
if (!Fraction(system[k][i + offset]).equals(0)) {
pivot = k;
break;
}
}

if (pivot === i) { // no suitable replacement found
offset += 1;
i -= 1;
continue;
}
[system[i], system[pivot]] = [system[pivot], system[i]];
}

for (let k = i + 1; k < numRows; k++) {
let c = Fraction(-1).mul(system[k][i]).div(system[i][i]);
for (let j = i; j < numCols; j++) {
let c = Fraction(-1).mul(system[k][i + offset]).div(system[i][i + offset]);
for (let j = i + offset; j < numCols; j++) {
system[k][j] = Fraction(system[k][j]).add(c.mul(system[i][j]));
if (Fraction(system[k][j]).abs().lt(tolerance)) {
system[k][j] = Fraction(0);
}
}
}
}
Expand Down Expand Up @@ -200,6 +207,7 @@ function vis(plot, solution) {

function visByType(solution) {
const leftControls = document.querySelector('.bar-left');
leftControls.innerHTML = ""
const question = document.createElement('a');
question.setAttribute("class", "bar-button")
question.setAttribute("data-position", "top")
Expand All @@ -208,14 +216,14 @@ function visByType(solution) {
switch (solution.type) {
case 'unique solution':
question.setAttribute("data-tooltip",
`The conclusion equation shares, and therefore intersects <br>
`The conclusion equation shares, (and therefore intersects) <br>
the solution of the premise equation system.`
);
visualizeUniqueSolution(plot, solution);
break;
case 'infinite solutions':
question.setAttribute("data-tooltip",
`The conclusion equation shares, and therefore intersects <br>
`The conclusion equation shares (and therefore intersects) <br>
the solution of the premise equation system. <br>
This holds regardless of which variables are selected as free.`
);
Expand All @@ -224,7 +232,8 @@ function visByType(solution) {
case 'no solution':
question.setAttribute("data-tooltip",
`The premise equation system has no solution, meaning that <br>
at least two lines do not intersect`
at least two lines do not intersect as they don't share their <br>
solution space.`
);
visualizeNoSolutions(plot, solution);
break;
Expand Down Expand Up @@ -353,24 +362,57 @@ function visualizeUniqueSolution(plot, _data) {
return { plot: p, hl };
}

function getFreeVariables(data) {
const echelon = data.echelon;
const numberFree = data.free;
const dependent = [];

let free = [];
let offset = 0;

for (let i = 0; i < echelon.length; i++) {
if (i + offset >= echelon[0].length) {
break; // can't reduce anymore
}

if (!Fraction(echelon[i][i + offset]).equals(0)) {
dependent.push(vars[i + offset])
} else {
free.push(vars[i + offset]);
offset += 1;
i -= 1;
continue;
}
}

if (free.length === 0) {
free = vars.slice(vars.length -(numberFree));
}

return { dependent, free }
}

function visualizeInfiniteSolutions(plot, _data) {
const dependent = vars.slice(0, -(_data.free));
const matrix = _data.matrix;
const { dependent, free } = getFreeVariables(_data);
const solutions = _data.solutions;
const independent = {};
vars.slice(vars.length - _data.free).forEach(varName => {

free.forEach(varName => {
const slider = document.getElementById(`slider-${varName}`);
independent[varName] = parseFloat(slider.value);
document.getElementById(`sol-${varName}`).innerHTML = `${varName} = ${slider.value}`;
});

document.getElementById(plot).innerHTML = '';
const solutions = _data.solutions;
const matrix = _data.matrix;

const dependentValues = {}; // Store computed values for dependent variables

// Iterate over solutions in reverse to handle dependencies correctly
for (let i = solutions.length - 1; i >= 0; i--) {
const sol = solutions[i];
const dependentVar = dependent[i];

let terms = sol.slice(0, -1);
let constantTerm = Fraction(sol[sol.length - 1].c);
let equationParts = [];
Expand Down Expand Up @@ -398,12 +440,14 @@ function visualizeInfiniteSolutions(plot, _data) {
const varName = dependentVar;
const independentTermsPreview = equationPreviewParts.join(" + ");
let solved = independentTermsPreview;

if (equationPreviewParts.length === 1) {
solved = ` - ${solved}`;
} else {
solved = ` - (${solved})`;
}

if (equationPreviewParts.length !== 0) {
if (equationPreviewParts.length === 1) {
solved = ` - ${solved}`;
} else {
solved = ` - (${solved})`;
}
}

if (constantTerm !== 0) {
solved = `${f(constantTerm)}${solved}`;
Expand Down Expand Up @@ -590,14 +634,16 @@ export class LinearCD {
freeVarsContainer.style = 'display:grid';

const sliders = {};

vars.slice(vars.length - data.free).forEach((varName, i) => {

const { _ , free} = getFreeVariables(data);

free.forEach((varName, i) => {
if (sliders[varName] === undefined) {
// create select to replace free variable
const select = document.createElement('select');
select.id = `select-free-${i}`;
select.style = "display:block;";
vars.forEach(vName => select.add(new Option(vName, vName)));
vars.forEach(v => select.add(new Option(v, v)));
select.value = varName;

// create slider to specify free variable value
Expand Down

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