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Added Gaussian elimination class

This commit is contained in:
Filip Znachor 2022-10-13 00:06:09 +02:00
parent 7e6b016f7a
commit d6af343db1
3 changed files with 217 additions and 5 deletions
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38
__tests__/matrix.ts
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@ -1,4 +1,4 @@
import { Matrix } from "../matrix";
import { GaussianElimination, Matrix } from "../matrix";
let A = new Matrix(
[1, 2, 3],
@ -30,4 +30,40 @@ test('A * B = C', () => {
test('B * A != C', () => {
expect(B.mul(A).eq(C)).toBe(false);
});
let D = new GaussianElimination(
new Matrix(
[1, 2, -1, 1, 2],
[2, 5, 0, 1, 5],
[3, 7, -1, 3, 9],
[1, 3, 1, 1, 5]
)
);
let D_solved = new Matrix(
[1, 2, -1, 1, 2],
[0, 1, 2, -1, 1],
[0, 0, 0, 1, 2],
[0, 0, 0, 0, 0]
);
test('D - Gaussian elimination', () => {
expect(D.solve().eq(D_solved)).toBe(true);
});
let E = new GaussianElimination(
new Matrix(
[1, 1, 3],
[2, -1, 4]
)
);
let E_solved = new Matrix(
[1, 1, 3],
[0, -3, -2]
);
test('E - Gaussian elimination', () => {
expect(E.solve().eq(E_solved)).toBe(true);
});

81
matrix.ts
View File

@ -3,9 +3,9 @@ export type RawMatrix = number[][];
export class Matrix {
rows: number;
cols: number;
matrix: RawMatrix;
rows!: number;
cols!: number;
matrix!: RawMatrix;
static zero(rows: number, cols: number) {
let matrix: RawMatrix = [];
@ -19,6 +19,10 @@ export class Matrix {
}
constructor(...matrix: RawMatrix) {
this.set(...matrix);
}
set(...matrix: RawMatrix) {
this.matrix = matrix;
this.rows = matrix.length;
if(matrix.length == 0) throw Error("Empty matrix");
@ -75,7 +79,7 @@ export class Matrix {
pow(power: number) {
for(let i=0; i<(power-1); i++)
this.matrix = this.mul(this).matrix;
this.set(...this.mul(this).matrix);
return this;
}
@ -104,4 +108,73 @@ export class Matrix {
return true;
}
in_stepped_shape() {
let pivot_index = -1;
for(let i=0; i<this.rows; i++) {
for(let j=0; j<this.cols; j++) {
console.log(this.matrix[i][j], pivot_index);
if(this.matrix[i][j] == 0) {
if(j > pivot_index) pivot_index = j;
} else if(pivot_index >= j) return false;
}
pivot_index++;
}
return true;
}
pivots() {
let pivots: number[] = [];
for(let i=0; i<this.rows; i++) {
let col = 0;
for(let j=0; j<this.cols; j++) {
if(this.matrix[i][j] != 0) break;
col++;
}
pivots.push(col);
}
return pivots;
}
}
export class GaussianElimination {
matrix: Matrix;
constructor(matrix: Matrix) {
this.matrix = matrix;
}
sort() {
let matrix = this.matrix.matrix;
let new_matrix = [matrix[0]];
let pivots = this.matrix.pivots();
for(let i=1; i<pivots.length; i++) {
if(pivots[i] < pivots[i-1]) new_matrix.unshift(matrix[i]);
else new_matrix.push(matrix[i]);
}
this.matrix.set(...new_matrix);
}
solve() {
for(let v_offset=0; v_offset<this.matrix.rows; v_offset++) {
this.sort();
let matrix = this.matrix.matrix;
let h_offset = this.matrix.pivots()[v_offset];
let first_number = matrix[v_offset][h_offset];
for(let i=1+v_offset; i<matrix.length; i++) {
let n = -matrix[i][h_offset]/first_number;
this.matrix.matrix[i] = matrix[i].map((c, j) => c + n*matrix[v_offset][j]);
}
}
return this.matrix;
}
mul_row(index: number, number: number, replace: boolean = false) {
let row = this.matrix.matrix[index].map(original => number * original);
if(replace) this.matrix.matrix[index] = row;
return row;
}
}

103
tsconfig.json Normal file
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@ -0,0 +1,103 @@
{
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// "disableSourceOfProjectReferenceRedirect": true, /* Disable preferring source files instead of declaration files when referencing composite projects. */
// "disableSolutionSearching": true, /* Opt a project out of multi-project reference checking when editing. */
// "disableReferencedProjectLoad": true, /* Reduce the number of projects loaded automatically by TypeScript. */
/* Language and Environment */
"target": "es2016", /* Set the JavaScript language version for emitted JavaScript and include compatible library declarations. */
// "lib": [], /* Specify a set of bundled library declaration files that describe the target runtime environment. */
// "jsx": "preserve", /* Specify what JSX code is generated. */
// "experimentalDecorators": true, /* Enable experimental support for TC39 stage 2 draft decorators. */
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// "jsxFactory": "", /* Specify the JSX factory function used when targeting React JSX emit, e.g. 'React.createElement' or 'h'. */
// "jsxFragmentFactory": "", /* Specify the JSX Fragment reference used for fragments when targeting React JSX emit e.g. 'React.Fragment' or 'Fragment'. */
// "jsxImportSource": "", /* Specify module specifier used to import the JSX factory functions when using 'jsx: react-jsx*'. */
// "reactNamespace": "", /* Specify the object invoked for 'createElement'. This only applies when targeting 'react' JSX emit. */
// "noLib": true, /* Disable including any library files, including the default lib.d.ts. */
// "useDefineForClassFields": true, /* Emit ECMAScript-standard-compliant class fields. */
// "moduleDetection": "auto", /* Control what method is used to detect module-format JS files. */
/* Modules */
"module": "commonjs", /* Specify what module code is generated. */
// "rootDir": "./", /* Specify the root folder within your source files. */
// "moduleResolution": "node", /* Specify how TypeScript looks up a file from a given module specifier. */
// "baseUrl": "./", /* Specify the base directory to resolve non-relative module names. */
// "paths": {}, /* Specify a set of entries that re-map imports to additional lookup locations. */
// "rootDirs": [], /* Allow multiple folders to be treated as one when resolving modules. */
// "typeRoots": [], /* Specify multiple folders that act like './node_modules/@types'. */
// "types": [], /* Specify type package names to be included without being referenced in a source file. */
// "allowUmdGlobalAccess": true, /* Allow accessing UMD globals from modules. */
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// "resolveJsonModule": true, /* Enable importing .json files. */
// "noResolve": true, /* Disallow 'import's, 'require's or '<reference>'s from expanding the number of files TypeScript should add to a project. */
/* JavaScript Support */
// "allowJs": true, /* Allow JavaScript files to be a part of your program. Use the 'checkJS' option to get errors from these files. */
// "checkJs": true, /* Enable error reporting in type-checked JavaScript files. */
// "maxNodeModuleJsDepth": 1, /* Specify the maximum folder depth used for checking JavaScript files from 'node_modules'. Only applicable with 'allowJs'. */
/* Emit */
// "declaration": true, /* Generate .d.ts files from TypeScript and JavaScript files in your project. */
// "declarationMap": true, /* Create sourcemaps for d.ts files. */
// "emitDeclarationOnly": true, /* Only output d.ts files and not JavaScript files. */
// "sourceMap": true, /* Create source map files for emitted JavaScript files. */
// "outFile": "./", /* Specify a file that bundles all outputs into one JavaScript file. If 'declaration' is true, also designates a file that bundles all .d.ts output. */
// "outDir": "./", /* Specify an output folder for all emitted files. */
// "removeComments": true, /* Disable emitting comments. */
// "noEmit": true, /* Disable emitting files from a compilation. */
// "importHelpers": true, /* Allow importing helper functions from tslib once per project, instead of including them per-file. */
// "importsNotUsedAsValues": "remove", /* Specify emit/checking behavior for imports that are only used for types. */
// "downlevelIteration": true, /* Emit more compliant, but verbose and less performant JavaScript for iteration. */
// "sourceRoot": "", /* Specify the root path for debuggers to find the reference source code. */
// "mapRoot": "", /* Specify the location where debugger should locate map files instead of generated locations. */
// "inlineSourceMap": true, /* Include sourcemap files inside the emitted JavaScript. */
// "inlineSources": true, /* Include source code in the sourcemaps inside the emitted JavaScript. */
// "emitBOM": true, /* Emit a UTF-8 Byte Order Mark (BOM) in the beginning of output files. */
// "newLine": "crlf", /* Set the newline character for emitting files. */
// "stripInternal": true, /* Disable emitting declarations that have '@internal' in their JSDoc comments. */
// "noEmitHelpers": true, /* Disable generating custom helper functions like '__extends' in compiled output. */
// "noEmitOnError": true, /* Disable emitting files if any type checking errors are reported. */
// "preserveConstEnums": true, /* Disable erasing 'const enum' declarations in generated code. */
// "declarationDir": "./", /* Specify the output directory for generated declaration files. */
// "preserveValueImports": true, /* Preserve unused imported values in the JavaScript output that would otherwise be removed. */
/* Interop Constraints */
// "isolatedModules": true, /* Ensure that each file can be safely transpiled without relying on other imports. */
// "allowSyntheticDefaultImports": true, /* Allow 'import x from y' when a module doesn't have a default export. */
"esModuleInterop": true, /* Emit additional JavaScript to ease support for importing CommonJS modules. This enables 'allowSyntheticDefaultImports' for type compatibility. */
// "preserveSymlinks": true, /* Disable resolving symlinks to their realpath. This correlates to the same flag in node. */
"forceConsistentCasingInFileNames": true, /* Ensure that casing is correct in imports. */
/* Type Checking */
"strict": true, /* Enable all strict type-checking options. */
// "noImplicitAny": true, /* Enable error reporting for expressions and declarations with an implied 'any' type. */
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// "strictFunctionTypes": true, /* When assigning functions, check to ensure parameters and the return values are subtype-compatible. */
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// "alwaysStrict": true, /* Ensure 'use strict' is always emitted. */
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/* Completeness */
// "skipDefaultLibCheck": true, /* Skip type checking .d.ts files that are included with TypeScript. */
"skipLibCheck": true /* Skip type checking all .d.ts files. */
}
}