From de850676e79da39aec6f1ce0400cfa94cecbd744 Mon Sep 17 00:00:00 2001
From: mattkae <mattkae@protonmail.com>
Date: Sun, 19 Sep 2021 16:32:15 -0400
Subject: First commit

---
 posts/linear_system_solver.html  | 102 +++++++++++++++++++++++
 posts/linear_system_solver.html~ |  77 ++++++++++++++++++
 posts/linear_system_solver.js    | 172 +++++++++++++++++++++++++++++++++++++++
 posts/linear_system_solver.js~   | 106 ++++++++++++++++++++++++
 4 files changed, 457 insertions(+)
 create mode 100644 posts/linear_system_solver.html
 create mode 100644 posts/linear_system_solver.html~
 create mode 100644 posts/linear_system_solver.js
 create mode 100644 posts/linear_system_solver.js~

(limited to 'posts')

diff --git a/posts/linear_system_solver.html b/posts/linear_system_solver.html
new file mode 100644
index 0000000..a8b17e5
--- /dev/null
+++ b/posts/linear_system_solver.html
@@ -0,0 +1,102 @@
+
+<h2>Linear Systems Solver</h2>
+<h3>2021-08-01 by Matthew Kosarek</h3>
+<p>
+  I wanted to write a little algorithm to visually solve linear systems of equations for fun. I am only going to deal with 3x3 matrices for now, but I'll make it so that I can easily extend it to more matrices in the future if I think that would be cool.
+
+  <br/><br/>
+
+  <div id='equation_container'>
+    <div id='matrix_lhs'></div>
+    <label>&times;</label>
+    <div id='unknown_variables'></div>
+    <label>=</label>
+    <div id='matrix_rhs'></div>
+  </div>
+  
+  <div id='solution_container'>
+  </div>
+
+  <div id='actions_container'>
+    <button class='action_button'id='reset_button'>
+      Reset
+    </button>
+    <button class='action_button' id='solve_button'>
+      Solve
+    </button>
+  </div>
+  
+  <script src='/posts/linear_system_solver.js'></script>
+
+  <style>
+    #equation_container {
+        display: flex;
+        flex-direction: row;
+        align-items: center;
+        width: 100%;
+        justify-content: center;
+    }
+
+    #equation_container input {
+        width: 128px;
+    }
+
+    #equation_container > label {
+        padding: 1rem;
+    }
+
+    #matrix_lhs {
+        display: grid;
+        grid-gap: 1rem;
+        grid-template-columns: repeat(3, 1fr);
+    }
+
+    #unknown_variables {
+        display: grid;
+        grid-gap: 1rem;
+    }
+
+    #unknown_variables > input {
+        text-align: center;
+    }
+
+    #matrix_rhs {
+        display: grid;
+        grid-gap: 1rem;
+    }
+
+    #actions_container {
+        padding: 1rem;
+        text-align: center;
+    }
+
+    #solve_button {
+        background-color: lightgreen;
+    }
+
+    .augmented_matrix_container {
+        display: flex;
+        flex-direction: row;
+        width: 100%;
+        padding: 1rem;
+    }
+
+    .augmented_matrix_container input {
+        width: 128px;
+    }
+
+    .augmented_matrix_container > div:first-child {
+        display: grid;
+        grid-gap: 1rem;
+        grid-template-columns: repeat(3, 1fr);
+        padding-right: 0.5rem;
+        border-right: 1px dashed white;
+    }
+
+    .augmented_matrix_container > div:last-child {
+        display: grid;
+        grid-gap: 1rem;
+        padding-left: 0.5rem;
+    }
+  </style>
+</p>
diff --git a/posts/linear_system_solver.html~ b/posts/linear_system_solver.html~
new file mode 100644
index 0000000..a280a8b
--- /dev/null
+++ b/posts/linear_system_solver.html~
@@ -0,0 +1,77 @@
+
+<h2>Linear Systems Solver</h2>
+<h3>2021-08-01 by Matthew Kosarek</h3>
+<p>
+  I wanted to write a little algorithm to visually solve linear systems of equations for fun. I am only going to deal with 3x3 matrices for now, but I'll make it so that I can easily extend it to more matrices in the future if I think that would be cool.
+
+  <br/><br/>
+
+  <div id='equation_container'>
+    <div id='matrix_lhs'></div>
+    <label>&times;</label>
+    <div id='unknown_variables'></div>
+    <label>=</label>
+    <div id='matrix_rhs'></div>
+  </div>
+  
+  <div id='solution_container'>
+  </div>
+
+  <div id='actions_container'>
+    <button class='action_button'id='reset_button'>
+      Reset
+    </button>
+    <button class='action_button' id='solve_button'>
+      Solve
+    </button>
+  </div>
+  
+  <script src='/posts/linear_system_solver.js'></script>
+
+  <style>
+    #equation_container {
+        display: flex;
+        flex-direction: row;
+        align-items: center;
+        width: 100%;
+        justify-content: center;
+    }
+
+    #equation_container input {
+        width: 128px;
+    }
+
+    #equation_container > label {
+        padding: 1rem;
+    }
+
+    #matrix_lhs {
+        display: grid;
+        grid-gap: 1rem;
+        grid-template-columns: repeat(3, 1fr);
+    }
+
+    #unknown_variables {
+        display: grid;
+        grid-gap: 1rem;
+    }
+
+    #unknown_variables > input {
+        text-align: center;
+    }
+
+    #matrix_rhs {
+        display: grid;
+        grid-gap: 1rem;
+    }
+
+    #actions_container {
+        padding: 1rem;
+        text-align: center;
+    }
+
+    #solve_button {
+        background-color: lightgreen;
+    }
+  </style>
+</p>
diff --git a/posts/linear_system_solver.js b/posts/linear_system_solver.js
new file mode 100644
index 0000000..9eb901f
--- /dev/null
+++ b/posts/linear_system_solver.js
@@ -0,0 +1,172 @@
+var $ = window.$,
+    rows = 3,
+    columns = 3,
+    currentLhs = [], // rows x columns matrix
+    currentRhs = []; // rows x 1 matrix
+    solutionContainer = $('#solution_container');
+
+function main() {
+    $('#reset_button').on('click', onResetClicked);
+    $('#solve_button').on('click', onSolveClicked);
+    resetView();
+}
+
+function resetView() {
+    renderLHS();
+    renderUnknowns();
+    renderRHS();
+
+    currentLhs = [];
+    currentRhs = [];
+    for (var r = 0; r < rows; r++) {
+        for (var c = 0; c < columns; c++) {
+            currentLhs.push(0);
+        }
+    }
+
+    for (var otherR = 0; otherR < rows; otherR++) {
+        currentRhs.push(0);
+    }
+
+    solutionContainer.empty();
+}
+
+// Renders for the input container.
+function renderLHS() {
+    var lhs = $('#matrix_lhs').empty(),
+        addCell = function(index) {
+            $('<input>').type('number').val(0).on('change',  function(event) {
+                currentLhs[index] = Number(event.target.value);
+            }).appendTo(lhs);
+        };
+
+    for (var r = 0; r < rows; r++) {
+        for (var c = 0; c < columns; c++) {
+            addCell((r * rows) + c);
+        }
+    }
+}
+
+function renderUnknowns() {
+    var unknownsContainer = $('#unknown_variables').empty();
+
+    for (var r = 0; r < columns; r++) {
+        var cell = $('<input>').disabled(true).val(String.fromCharCode('x'.charCodeAt(0) + r).toUpperCase());
+        unknownsContainer.append(cell);
+    }
+}
+
+function renderRHS() {
+    var rhs = $('#matrix_rhs').empty(),
+        addCell = function(index) {
+            $('<input>').type('number').val(0).on('change', function(event) {
+                currentRhs[index] = Number(event.target.value);
+            }).appendTo(rhs);
+        };
+
+    for (var r = 0; r < rows; r++) {
+        addCell(r);
+    }
+}
+
+// Renders for the augmented matrix container
+function renderAugmentedMatrix(lhs, rhs) {
+    var container = $('<div>').addClass('augmented_matrix_container'),
+        lhsContainer = $('<div>').appendTo(container),
+        rhsContainer = $('<div>').appendTo(container),
+        addLhsCell = function(index) {
+            $('<input>').type('number').val(lhs[index]).disabled(true).appendTo(lhsContainer);
+        },
+        addRhsCell = function(index) {
+            $('<input>').type('number').val(rhs[index]).disabled(true).appendTo(rhsContainer);
+        };
+    
+    for (var r = 0; r < rows; r++) {
+        for (var c = 0; c < columns; c++) {
+            addLhsCell(r * rows + c);
+        }
+    }
+
+    for (var otherR = 0; otherR < rows; otherR++) {
+        addRhsCell(otherR);
+    }
+
+    return container;
+}
+
+// Solver helper functions
+function findLargestValue(c, rowStart) {
+    var largestValue = 0,
+        largestRow = -1;
+    for (var r = rowStart; r < rows; r++) {
+        var currValue = Math.abs(currentLhs[r * rows + c]);
+        if (currValue > largestValue) {
+            largestValue = currValue;
+            largestRow = r;
+        }
+    }
+    return {
+        row: largestRow,
+        value: largestValue
+    };
+}
+
+function swapRows(r1, r2) {
+    if (r1 === r2) {
+        return;
+    }
+
+    for (var c = 0; c < columns; c++) {
+        var temp = currentLhs[r1 * row + c];
+        currentLhs[r1 * rows + c] = currentLhs[r2 * row + c];
+        currentLhs[r2 * rows + c] = temp;
+    }
+
+    var rhsTmp = currentRhs[r1];
+    currentRhs[r1] = currentRhs[r2];
+    currentRhs[r2] = rhsTmp;
+}
+
+function multiplyRow(r, scale) {
+    for (var c = 0; c < columns; c++) {
+      currentLhs[r * rows + c] *= scale;
+    }
+
+    currentRhs[r] *= scale;
+}
+
+function addRow(r, a) {
+    for (var c = 0; c < columns; c++) {
+      currentLhs[r * rows + c] += a;
+    }
+
+    currentRhs[r] += a;
+}
+
+// Callbacks for actions
+function onResetClicked() {
+    resetView();
+}
+
+function onSolveClicked() {
+    var rowStart = 0;
+    for (var c = 0; c < columns; c++) {
+        var largestForColumn = findLargestValue(c, rowStart);
+        if (largestForColumn.row >= 0) {
+            swapRows(rowStart, largestForColumn.row);
+            multiplyRow(rowStart, 1.0 / largestForColumn.value);
+
+            for (var r = 0; r < rows; r++) {
+                if (r === rowStart) continue;
+
+            }
+        }
+
+        rowStart++;
+    }
+
+    solutionContainer.append(renderAugmentedMatrix(currentLhs, currentRhs));
+    solutionContainer.append(renderAugmentedMatrix(currentLhs, currentRhs));
+}
+
+main();
diff --git a/posts/linear_system_solver.js~ b/posts/linear_system_solver.js~
new file mode 100644
index 0000000..33fc026
--- /dev/null
+++ b/posts/linear_system_solver.js~
@@ -0,0 +1,106 @@
+var $ = window.$,
+    rows = 3,
+    columns = 3,
+    currentLhs = [], // rows x columns matrix
+    currentRhs = []; // rows x 1 matrix
+    solutionContainer = $('#solution_container');
+
+function main() {
+    $('#reset_button').on('click', onResetClicked);
+    $('#solve_button').on('click', onSolveClicked);
+    resetView();
+}
+
+function resetView() {
+    renderLHS();
+    renderUnknowns();
+    renderRHS();
+
+    currentLhs = [];
+    currentRhs = [];
+    for (var r = 0; r < rows; r++) {
+        for (var c = 0; c < columns; c++) {
+            currentLhs.push(0);
+        }
+    }
+
+    for (var otherR = 0; otherR < rows; otherR++) {
+        currentRhs.push(0);
+    }
+
+    solutionContainer.empty();
+}
+
+// Renders for the input container.
+function renderLHS() {
+    var lhs = $('#matrix_lhs').empty(),
+        addCell = function(index) {
+            $('<input>').type('number').val(0).on('change',  function(event) {
+                currentLhs[index] = Number(event.target.value);
+            }).appendTo(lhs);
+        };
+
+    for (var r = 0; r < rows; r++) {
+        for (var c = 0; c < columns; c++) {
+            addCell((r * rows) + c);
+        }
+    }
+}
+
+function renderUnknowns() {
+    var unknownsContainer = $('#unknown_variables').empty();
+
+    for (var r = 0; r < columns; r++) {
+        var cell = $('<input>').disabled(true).val(String.fromCharCode('x'.charCodeAt(0) + r).toUpperCase());
+        unknownsContainer.append(cell);
+    }
+}
+
+function renderRHS() {
+    var rhs = $('#matrix_rhs').empty(),
+        addCell = function(index) {
+            $('<input>').type('number').val(0).on('change', function(event) {
+                currentRhs[index] = Number(event.target.value);
+            }).appendTo(rhs);
+        };
+
+    for (var r = 0; r < rows; r++) {
+        addCell(r);
+    }
+}
+
+// Renders for the solution container
+function renderAugmentedMatrix(lhs, rhs) {
+    var container = $('<div>').addClass('augmented_matrix_container'),
+        lhsContainer = $('<div>').appendTo(container),
+        rhsContainer = $('<div>').appendTo(container),
+        addLhsCell = function(index) {
+            $('<input>').type('number').val(lhs[index]).disabled(true).appendTo(lhsContainer);
+        },
+        addRhsCell = function(index) {
+            $('<input>').type('number').val(rhs[index]).disabled(true).appendTo(rhsContainer);
+        };
+    
+    for (var r = 0; r < rows; r++) {
+        for (var c = 0; c < columns; c++) {
+            addLhsCell(r * rows + c);
+        }
+    }
+
+    for (var otherR = 0; otherR < rows; otherR++) {
+        addRhsCell(otherR);
+    }
+
+    return container;
+}
+
+// Callbacks for actions
+function onResetClicked() {
+    resetView();
+}
+
+function onSolveClicked() {
+    solutionContainer.append(renderAugmentedMatrix(currentLhs, currentRhs));
+}
+
+main();
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