664 lines
21 KiB
JavaScript
664 lines
21 KiB
JavaScript
/**
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* LogarithmPlotter - 2D plotter software to make BODE plots, sequences and distribution functions.
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* Copyright (C) 2022 Ad5001
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <https://www.gnu.org/licenses/>.
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*/
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.pragma library
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.import "reference.js" as Reference
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const DERIVATION_PRECISION = 0.01
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const OPERATION_PRIORITY = {
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"+": 10, "-": 10,
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"*": 20, "/": 20
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}
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enum ASEType {
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UNKNOWN,
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VARIABLE,
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NUMBER,
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STRING,
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FUNCTION,
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CONSTANT,
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OPERATION,
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NEGATION // Example: -x.
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}
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class AbstractSyntaxElement {
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type = ASEType.UNKNOWN;
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execute(variables) {
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return null;
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}
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simplify() {
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return this;
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}
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derivate(variable) {
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return this;
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}
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integrate(variable) {
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return this;
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}
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toEditableString() {
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return "";
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}
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toLatex() {
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return "";
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}
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isConstant() {
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return true;
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}
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}
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class Variable extends AbstractSyntaxElement {
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type = ASEType.VARIABLE;
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constructor(variableName) {
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this.varName = variableName;
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}
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execute(variables) {
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if(variables.includes(this.varName)) {
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return variables[this.varName];
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} else {
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throw new EvalError("Unknown variable " + this.varName + ".");
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}
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}
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derivate(variable) {
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if(variable == this.varName)
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return new NumberElement(1);
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return this;
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}
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integrate(variable) {
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if(variable == this.varName)
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// <var>^2/2
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return new Operation(new Operation(this, '^', new NumberElement(2)), '/', new NumberElement(2));
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return this;
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}
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toEditableString() {
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return this.varName;
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}
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toLatex() {
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return this.varName;
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}
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isConstant() {
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return false;
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}
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}
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class ArrayVariable extends Variable {
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constructor(arrayName, astIndex) {
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super(arrayName + "[" + astIndex.toEditableString() + "]")
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this.arrayName = arrayName;
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this.astIndex = astIndex;
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}
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execute(variables) {
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if(variables.includes(this.arrayName)) {
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let index = this.astIndex.execute(variables)
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if(index % 1 != 0 || index < 0) { // Float index.
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throw new EvalError("Non-integer array index " + index + " used as array index for " + this.varName + ".");
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} else if(variables[this.arrayName].length <= index) {
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throw new EvalError("Out-of-range index " + index + " used as array index for " + this.varName + ".");
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} else {
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return variables[this.arrayName][index];
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}
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} else {
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throw new EvalError("Unknown variable " + this.varName + ".");
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}
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toLatex() {
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return this.varName;
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}
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}
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simplify() {
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return new ArrayVariable(this.arrayName, this.astIndex.simplify());
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}
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toLatex() {
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return this.arrayName + '\\left[' + this.astIndex.toLatex() + '\\right]';
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}
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isConstant() {
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return false;
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}
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}
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class Constant extends Variable {
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type = ASEType.CONSTANT;
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constructor(constant) {
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super(constant)
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}
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execute(variables) {
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if(Reference.CONSTANTS_LIST.includes(this.varName)) {
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return Reference.CONSTANTS[this.varName];
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} else {
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throw new EvalError("Unknown constant " + this.varName + ".");
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}
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}
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derivate(variable) {
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if(variable == this.varName)
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return new NumberElement(0);
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return this;
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}
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integrate(variable) {
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return new Operation(new Variable(variable), '^', this);
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}
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toEditableString() {
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return this.varName;
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}
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toLatex() {
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return this.varName;
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}
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isConstant() {
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return true;
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}
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}
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class NumberElement extends AbstractSyntaxElement {
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type = ASEType.NUMBER;
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constructor(number) {
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this.value = parseFloat(number);
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}
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derivate(variable) {
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return new NumberElement(0);
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}
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integrate(variable) {
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return new Variable(variable);
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}
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toEditableString() {
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return this.value.toString();
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}
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toLatex() {
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return this.value.toString();
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}
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isConstant() {
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return true;
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}
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}
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class StringElement extends AbstractSyntaxElement {
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type = ASEType.STRING;
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constructor(str) {
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this.str = str;
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}
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execute(variables) {
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return this.str
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}
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derivate(variable) {
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return this;
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}
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integrate(variable) {
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return this;
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}
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toEditableString() {
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return '"' + this.str + '"';
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}
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toLatex() {
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return this.str;
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}
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isConstant() {
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return true;
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}
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}
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class FunctionElement extends AbstractSyntaxElement {
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type = ASEType.FUNCTION;
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constructor(functionName, astArguments) {
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this.function = functionName;
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this.args = astArguments;
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}
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execute(variables) {
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if(this.function == "derivate") {
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return executeDerivative(variables)
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} else if(this.function == "integrate") {
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return executeIntegral(variables)
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} else if(Reference.FUNCTIONS_LIST.includes(this.function)) {
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let args = this.args.map(arg => arg.execute(variables));
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return Reference.FUNCTIONS[this.function](...args);
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} else {
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throw new EvalError("Unknown function " + this.function + ".");
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}
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}
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executeDerivative(variables) {
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// Calculate derivation.
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if(this.args.length == 2)
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if(this.args[1] instanceof Variable) {
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let d = this.args[1].varName; // derivative variable name.
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if(Object.keys(variables).includes(d)) {
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let plus = this.args[0].execute(Object.assign({}, variables, {d: variables[d]+DERIVATION_PRECISION/2}));
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let min = this.args[0].execute(Object.assign({}, variables, {d: variables[d]-DERIVATION_PRECISION/2}));
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return (plus-min)/DERIVATION_PRECISION
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} else
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throw new EvalError("Undefined variable " + d + ".");
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} else
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throw new EvalError(`Argument 1 of function derivate must be a variable.`)
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else
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throw new EvalError(`Function 'derivate' can only have 2 arguments. ${this.args.length} provided.`)
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}
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executeIntegral(variables) {
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// Calculate integral.
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// Using simons rule
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// https://en.wikipedia.org/wiki/Simpson%27s_rule
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let d, f, a, b;
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if(this.args.length == 2)
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// Integral(f,var) integral of f by var.
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if(this.args[1] instanceof Variable)
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if(Object.keys(variables).includes(d)) {
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d = this.args[1].varName; // derivative variable name.
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if(!Object.keys(variables).includes(d))
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throw new EvalError("Undefined variable " + d + ".")
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a = 0;
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b = variables[d];
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f = this.args[0].execute;
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} else
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else
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throw new EvalError(`Argument 2 of function derivate must be a variable.`)
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else if(this.args.length == 4)
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// Integral(a,b,f,var) integral from a to b of f by var.
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if(this.args[3] instanceof Variable)
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if(Object.keys(variables).includes(d)) {
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a = this.args[0].execute(variables);
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b = this.args[1].execute(variables);
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f = this.args[2].execute;
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d = this.args[3].varName; // derivative variable name.
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if(!Object.keys(variables).includes(d))
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throw new EvalError("Undefined variable " + d + ".");
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}
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else
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throw new EvalError(`Argument 4 of function derivate must be a variable.`)
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else
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throw new EvalError(`Function 'derivate' can only have 2 or 4 arguments. ${this.args.length} provided.`)
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// (b-a)/6*(f(a)+4*f((a+b)/2)+f(b))
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let f_a = f(Object.assign({}, variables, {d: a})), f_b = f(Object.assign({}, variables, {d: b}));
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let f_m = f(Object.assign({}, variables, {d: (a+b)/2}))
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return (b-a)/6*(f_a+4*f_m+f_b);
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}
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simplify() {
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let args = this.args.map(arg => arg.simplify(variables));
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let newFunc = new FunctionElement(this.function, args);
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let result;
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if(newFunc.isConstant() && (result = newFunc.execute({})) % 1 == 0) { // Simplification (e.g. cos(0), sin(π/2)...)
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return new NumberElement(result);
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} else {
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return newFunc;
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}
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}
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derivate(variable) {
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//TODO: Use DERIVATIVES elements in reference.
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return new FunctionElement("derivate", this, variable);
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}
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integrate(variable) {
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//TODO: Use INTEGRALS elements in reference.
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return new FunctionElement("integrate", this, variable);
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}
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toEditableString() {
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return this.function + '(' + this.args.map(arg => arg.toEditableString()).join(', ') + ')';
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}
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toLatex() {
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switch(this.function) {
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case "sqrt":
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return '\\sqrt{' + this.args.map(arg => arg.toLatex()).join(', ') + '}';
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case "abs":
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return '\\left|' + this.args.map(arg => arg.toLatex()).join(', ') + '\\right|';
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case "floor":
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return '\\left\\lfloor' + this.args.map(arg => arg.toLatex()).join(', ') + '\\right\\rfloor';
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case "ceil":
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return '\\left\\lceil' + this.args.map(arg => arg.toLatex()).join(', ') + '\\right\\rceil';
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default:
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return '\\mathrm{' + this.function + '}\\left(' + this.args.map(arg => arg.toLatex()).join(', ') + '\\right)';
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}
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}
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isConstant() {
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if(this.function == "derivate")
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return this.args[0].isConstant();
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else if(this.function == "integrate")
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return this.args.length == 4 && this.args[0].isConstant() && this.args[1].isConstant() && this.args[2].isConstant();
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else
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return this.args.every(x => x.isConstant());
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}
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}
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class Operation extends AbstractSyntaxElement {
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type = ASEType.OPERATION;
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constructor(leftHand, operation, rightHand) {
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this.leftHand = leftHand;
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this.ope = operation;
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this.rightHand = rightHand;
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}
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evaluate(variables) {
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switch(this.ope) {
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case '+':
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return this.leftHand.evaluate(variables) + this.rightHand.evaluate(variables);
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case '-':
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return this.leftHand.evaluate(variables) - this.rightHand.evaluate(variables);
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case '*':
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return this.leftHand.evaluate(variables) * this.rightHand.evaluate(variables);
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case '/':
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return this.leftHand.evaluate(variables) / this.rightHand.evaluate(variables);
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case '%':
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return this.leftHand.evaluate(variables) % this.rightHand.evaluate(variables);
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case '^':
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return Math.pow(this.leftHand.evaluate(variables), this.rightHand.evaluate(variables));
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default:
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throw new EvalError("Unknown operator " + ope + ".");
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}
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}
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simplify() {
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let leftHand = this.leftHand.simplify();
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let rightHand = this.rightHand.simplify();
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let newOpe = new Operation(leftHand, this.ope, rightHand);
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if(leftHand.isConstant() && rightHand.isConstant() && Math.abs(newOpe.execute({})) < 1000000) {
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// Do not simplify to too big numbers
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switch(this.ope) {
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case '+':
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case '-':
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case '*':
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case '^':
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case '%':
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return new NumberElement(newOpe.execute({}));
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case '/':
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if(result % 1 == 0)
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return new NumberElement(newOpe.execute({}));
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else {
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let simplified = simplifyFraction(leftHand.number, rightHand.number)
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return new Operation(new NumberElement(simplified[0]), '/', new NumberElement(simplified[1]))
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}
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return this.leftHand.evaluate(variables) / this.rightHand.evaluate(variables);
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return Math.pow(this.leftHand.evaluate(variables), this.rightHand.evaluate(variables));
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default:
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throw new EvalError("Unknown operator " + ope + ".");
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}
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} else {
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// Simplifications of +- 0 or *1
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switch(this.ope) {
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case '+':
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case '-':
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if(leftHand.type == ASEType.NUMBER && leftHand.value == 0)
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return rightHand;
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else if(rightHand.type == ASEType.NUMBER && rightHand.value == 0) {
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if(ope == '-') leftHand.value = -leftHand.value;
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return leftHand;
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} else
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return newOpe
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case '*':
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if((leftHand.type == ASEType.NUMBER && leftHand.value == 0) || (rightHand.type == ASEType.NUMBER && rightHand.value == 0))
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return new NumberElement(0);
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else if(leftHand.type == ASEType.NUMBER && leftHand.value == 1)
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return rightHand;
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else if(rightHand.type == ASEType.NUMBER && rightHand.value == 1)
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return leftHand;
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else
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return newOpe
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case '^':
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if(rightHand.type == ASEType.NUMBER && rightHand.value == 0)
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return new NumberElement(1);
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else if(rightHand.type == ASEType.NUMBER && rightHand.value == 1)
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return new NumberElement(leftHand.value);
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else
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return newOpe;
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case '/':
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if(rightHand.type == ASEType.NUMBER && rightHand.value == 1)
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return new NumberElement(leftHand.value);
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else
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return newOpe;
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case '%':
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return newOpe;
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default:
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throw new EvalError("Unknown operator " + ope + ".");
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}
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}
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}
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derivate(variable) {
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switch(this.ope) {
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case '-':
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case '+':
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return new Operation(this.leftHand.derivate(variable), this.ope, this.rightHand.derivate(variable));
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case '*':
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return new Operation(
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new Operation(this.leftHand, '*', this.rightHand.derivate(variable)),
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'+',
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new Operation(this.leftHand.derivate(variable), '*', this.rightHand),
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);
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case '/':
|
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return new Operation(
|
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new Operation(
|
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new Operation(this.leftHand, '*', this.rightHand.derivate(variable)),
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'-',
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new Operation(this.leftHand.derivate(variable), '*', this.rightHand),
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),
|
|
'/',
|
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new Operation(this.rightHand, '^', new NumberElement(2))
|
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);
|
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case '^':
|
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case '%':
|
|
return new FunctionElement("derivate", this.toEditableString());
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default:
|
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throw new EvalError("Unknown operator " + ope + ".");
|
|
}
|
|
}
|
|
|
|
integrate(variable) {
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switch(this.ope) {
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case '-':
|
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case '+':
|
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return new Operation(this.leftHand.integrate(variable), this.ope, this.rightHand.integrate(variable));
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case '*':
|
|
return new Operation(
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new Operation(this.leftHand.derivate(variable), '*', this.rightHand),
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'+',
|
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new Operation(this.leftHand, '*', this.rightHand.derivate(variable))
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);
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case '/':
|
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return new Operation(
|
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new Operation(this.leftHand.derivate(variable), '*', this.rightHand),
|
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'+',
|
|
new Operation(this.leftHand, '*', this.rightHand.derivate(variable))
|
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);
|
|
case '^':
|
|
case '%':
|
|
return new FunctionElement("integrate", this.toEditableString());
|
|
default:
|
|
throw new EvalError("Unknown operator " + ope + ".");
|
|
}
|
|
}
|
|
|
|
toEditableString() {
|
|
let leftString = this.leftHand.toEditableString();
|
|
let rightString = this.rightHand.toEditableString();
|
|
if(this.leftHand.type == ASEType.OPERATION && OPERATION_PRIORITY[this.ope] > OPERATION_PRIORITY[this.leftHand.ope])
|
|
leftString = "(" + leftString + ")"
|
|
if(this.rightHand.type == ASEType.OPERATION && OPERATION_PRIORITY[this.ope] > OPERATION_PRIORITY[this.rightHand.ope])
|
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rightString = "(" + rightString + ")"
|
|
return leftString + " " + this.ope + " " + rightString;
|
|
}
|
|
|
|
|
|
toLatex() {
|
|
switch(this.ope) {
|
|
case '-':
|
|
case '+':
|
|
return this.leftHand.toLatex() + this.ope + this.rightHand.toLatex();
|
|
case '*':
|
|
return this.leftHand.toLatex() + " \\times " + this.rightHand.toLatex();
|
|
case '%':
|
|
return this.leftHand.toLatex() + " \\mathrm{mod} " + this.rightHand.toLatex();
|
|
case '/':
|
|
return "\\frac{" + this.leftHand.toLatex() + "}{" + this.rightHand.toLatex() + "}"
|
|
case '^':
|
|
return this.leftHand.toLatex() + "^{" + this.rightHand.toLatex() + "}";
|
|
default:
|
|
throw new EvalError("Unknown operator " + ope + ".");
|
|
}
|
|
return this.leftHand.toLatex() + ope + this.rightHand.toLatex();
|
|
}
|
|
|
|
isConstant() {
|
|
return this.leftHand.isConstant() && this.rightHand.isConstant();
|
|
}
|
|
}
|
|
|
|
function simplifyFraction(num,den) {
|
|
// More than gcd because it allows decimals fractions.
|
|
let mult = 1;
|
|
if(num%1 != 0)
|
|
mult = Math.max(mult,Math.pow(10,num.toString().split('.')[1].length))
|
|
else if(den%1 != 0)
|
|
mult = Math.max(mult,Math.pow(10,den.toString().split('.')[1].length))
|
|
let a = Math.abs(num*mult);
|
|
let b = Math.abs(den*mult);
|
|
let gcd = 0
|
|
if (b > a) {let temp = a; a = b; b = temp;}
|
|
while (gcd == 0) {
|
|
if (b == 0) gcd = a;
|
|
a %= b;
|
|
if (a == 0) gcd = b;
|
|
b %= a;
|
|
}
|
|
return [num*mult/gcd, den*mult/gcd]
|
|
}
|
|
|
|
class Negation extends AbstractSyntaxElement {
|
|
type = ASEType.NEGATION;
|
|
|
|
constructor(variableName) {
|
|
this.varName = variableName;
|
|
}
|
|
|
|
execute(variables) {
|
|
if(variables.includes(this.varName)) {
|
|
return variables[this.varName];
|
|
} else {
|
|
throw new EvalError("Unknown variable " + this.varName + ".");
|
|
}
|
|
}
|
|
|
|
derivate(variable) {
|
|
if(variable == this.varName)
|
|
return new NumberElement(1);
|
|
return this;
|
|
}
|
|
|
|
integrate(variable) {
|
|
if(variable == this.varName)
|
|
// <var>^2/2
|
|
return new Operation(new Operation(this, '^', new NumberElement(2)), '/', new NumberElement(2));
|
|
return this;
|
|
}
|
|
|
|
toEditableString() {
|
|
return this.varName;
|
|
}
|
|
|
|
toLatex() {
|
|
return this.varName;
|
|
}
|
|
|
|
isConstant() {
|
|
return false;
|
|
}
|
|
}
|
|
|
|
class Negation extends AbstractSyntaxElement {
|
|
type = ASEType.NEGATION;
|
|
|
|
constructor(expression) {
|
|
this.expression = expression;
|
|
}
|
|
|
|
execute(variables) {
|
|
if(variables.includes(this.arrayName)) {
|
|
let index = this.astIndex.execute(variables)
|
|
if(index % 1 != 0 || index < 0) { // Float index.
|
|
throw new EvalError("Non-integer array index " + index + " used as array index for " + this.varName + ".");
|
|
} else if(variables[this.arrayName].length <= index) {
|
|
throw new EvalError("Out-of-range index " + index + " used as array index for " + this.varName + ".");
|
|
} else {
|
|
return variables[this.arrayName][index];
|
|
}
|
|
} else {
|
|
throw new EvalError("Unknown variable " + this.varName + ".");
|
|
}
|
|
|
|
toLatex() {
|
|
return this.varName;
|
|
}
|
|
}
|
|
|
|
simplify() {
|
|
return new Negation(this.expression.simplify());
|
|
}
|
|
|
|
derivate(variable) {
|
|
return new Negation(this.expression.derivate(variable));
|
|
}
|
|
|
|
integrate(variable) {
|
|
return new Negation(this.expression.integrate(variable));
|
|
}
|
|
|
|
toLatex() {
|
|
return '-' + this.expression.toLatex();
|
|
}
|
|
|
|
isConstant() {
|
|
return this.expression.isConstant();
|
|
}
|
|
}
|