diff --git a/.idea/misc.xml b/.idea/misc.xml index a165cb3..cbb200f 100644 --- a/.idea/misc.xml +++ b/.idea/misc.xml @@ -1,6 +1,6 @@ - + \ No newline at end of file diff --git a/.idea/project.iml b/.idea/project.iml index 47baa8c..d34aa22 100644 --- a/.idea/project.iml +++ b/.idea/project.iml @@ -6,5 +6,14 @@ + + + + + + + + + \ No newline at end of file diff --git a/in.txt b/in.txt new file mode 100644 index 0000000..090b2e8 --- /dev/null +++ b/in.txt @@ -0,0 +1,5 @@ +4 4 +0 0 2 0 +0 1 5 1 +0 0 6 0 +0 0 12 0 \ No newline at end of file diff --git a/out.txt b/out.txt new file mode 100644 index 0000000..af5f51f --- /dev/null +++ b/out.txt @@ -0,0 +1 @@ +Infinite solutions \ No newline at end of file diff --git a/src/solver/AugmentedMatrix.java b/src/solver/AugmentedMatrix.java new file mode 100644 index 0000000..c5477d9 --- /dev/null +++ b/src/solver/AugmentedMatrix.java @@ -0,0 +1,152 @@ +package solver; + +import java.lang.reflect.Array; +import java.text.DecimalFormat; +import java.util.ArrayList; +import java.util.Arrays; +import java.util.InputMismatchException; +import java.util.Scanner; + +public class AugmentedMatrix { + private Row[] matrix; + private String decimalPattern = "#.####"; + + // We don't always need swapHistory, so method which uses this field must check whether it is initialized or not. + private ArrayList swapHistory; + + + AugmentedMatrix(double[][] matrix) { + setMatrix(matrix); + } + + AugmentedMatrix() {} + + public void readMatrix(Scanner scanner) throws InputMismatchException { + int n = scanner.nextInt(); + int m = scanner.nextInt(); + matrix = new Row[n]; + for (int i = 0; i < n; i++) { + matrix[i] = new Row(m); + for (int j = 0; j < m; j++) { + this.set(i, j, scanner.nextDouble()); + } + } + } + + public void set(int i, int j, double value) { + matrix[i].set(j, value); + } + + public double get(int i, int j) { + return matrix[i].get(j); + } + + + public String fancyPrint(String decimalPattern) { + if(decimalPattern == null) { + decimalPattern = this.decimalPattern; + } + StringBuilder sb = new StringBuilder(); + double[] row; + for (int i = 0; i < matrix.length; i++) { + row = matrix[i].getRow(); + sb.append("["); + for(int j =0; j < row.length; j++) { + sb.append(new DecimalFormat(decimalPattern).format(row[j])); + sb.append(", "); + } + sb.delete(sb.length()-2, sb.length()); + sb.append("]"); + sb.append("\n"); + } + return sb.toString(); + } + + @Override + public String toString() { + return fancyPrint(null); + } + + public void swapRows(int firstRowIndex, int secondRowIndex) { + Row temp = matrix[firstRowIndex]; + matrix[firstRowIndex] = matrix[secondRowIndex]; + matrix[secondRowIndex] = temp; + } + + private void addSwapHistoryEntry(int prevIndex, int nextIndex) { + // Initialization check + if(swapHistory==null) { + swapHistory = new ArrayList<>(); + } + swapHistory.add(new SwapInfo(prevIndex, nextIndex)); + } + + public void clearSwapHistory() { + swapHistory.clear(); + } + + public void swapColumns(int firstColumnIndex, int secondColumnIndex) { + swapColumns(firstColumnIndex, secondColumnIndex, true); + } + + public void swapColumns(int firstColumnIndex, int secondColumnIndex, boolean writeLog) { + double coeff1, coeff2; + for(Row row : matrix) { + coeff1 = row.get(firstColumnIndex); + coeff2 = row.get(secondColumnIndex); + row.set(firstColumnIndex, coeff2); + row.set(secondColumnIndex, coeff1); + } + if(writeLog) { + addSwapHistoryEntry(firstColumnIndex, secondColumnIndex); + } + } + + public ArrayList getSwapHistory() { + return swapHistory; + } + + public double[][] getMatrixCopy() { + double[][] copy = new double[matrix.length][]; + for(int i = 0; i < matrix.length; i++) { + copy[i] = matrix[i].getRow(); + } + return copy; + } + + public void setMatrix(double[][] matrix) { + this.matrix = new Row[matrix.length]; + for(int i = 0; i < matrix.length; i++) { + this.matrix[i] = new Row(matrix[i]); + } + } + + public Row getRow(int index) { + return this.matrix[index]; + } + + public Row getColumnCopy(int index) { + int rows = size()[0]; // Number of rows + Row col = new Row(rows); + for(int i = 0; i < rows; i++) { + col.set(i, matrix[i].get(index)); + } + return col; + } + + + + /** + * Get dimensions of Augmented matrix + * @return size()[0] - number of rows, size()[1] - number of columns + */ + public int[] size() { + int[] size = new int[2]; + size[0] = matrix.length; + // Consider that all rows have the same size, according to the class initialization + size[1] = matrix[0].size(); + return size; + } + + +} diff --git a/src/solver/LinearEquationSolver.java b/src/solver/LinearEquationSolver.java new file mode 100644 index 0000000..d2f5eda --- /dev/null +++ b/src/solver/LinearEquationSolver.java @@ -0,0 +1,297 @@ +package solver; + +import java.text.DecimalFormat; +import java.util.ArrayList; +import java.util.Arrays; + +enum SystemType { + NO_SOLUTIONS, + SINGLE_SOLUTION, + INFINITE_NUMBER_OF_SOLUTIONS, + UNKNOWN_ERROR +} + +public class LinearEquationSolver { + private AugmentedMatrix matrix; + private StringBuilder logs; + private String result; + private SystemType resultType; + private String decimalPattern = "#.#####"; + + LinearEquationSolver(AugmentedMatrix matrix) { + this.matrix = new AugmentedMatrix(matrix.getMatrixCopy()); + this.logs = new StringBuilder(); + } + + /** + * It is step 1 of solving System of Linear Equations: transforming matrix to upper triangular form + */ + private void transformToUpperTriangularForm() { + Row currentRow; double currentCoefficient; + Row nextRow; double nextCoefficient; + double multiplicator; + int n = matrix.size()[0]; // number of rows + int m = matrix.size()[1]; // number of cols + int rowNum, colNum; + // If there are no special cases, then rowNum = colNum (transforming to diagonal form) + for(rowNum = 0, colNum = 0; rowNum < n && colNum < m-1; rowNum++, colNum++) { + currentRow = matrix.getRow(rowNum); + currentCoefficient = currentRow.get(colNum); + + + // Search for the row with non-zero coefficent + int columnOffset = 0; boolean foundInColumn = false; + double coeff; int innerColNum = colNum; + while(currentCoefficient == 0 && innerColNum < m-1) { + + // If a current coefficient is zero, then we should find row with non-zero coefficient below + if (currentCoefficient == 0) { + foundInColumn = false; + int nextRowNum; + for (nextRowNum = rowNum; nextRowNum < n; nextRowNum++) { + coeff = matrix.getRow(nextRowNum).get(innerColNum); + if (coeff != 0) { + // Found row with non-zero i-th coefficient + foundInColumn = true; + break; + } + } + + if(foundInColumn) { + // We should swap rows + // These variables can be equal if previous column was filled with zeros, + // but on this column this row have non-zero coefficient + if(rowNum != nextRowNum) { + this.matrix.swapRows(rowNum, nextRowNum); + logMessage(String.format("R%d <-> R%d", rowNum, nextRowNum)); + } + // If innerColNum != colNum -> we found non-zero coefficient in other column, we should swap columns + if(innerColNum != colNum) { + matrix.swapColumns(colNum, innerColNum); + logMessage(String.format("C%d <-> C%d", colNum, innerColNum)); + } + // Update currentRow and currentCoefficient variables after all swaps + currentRow = matrix.getRow(rowNum); // rowNum after swap references to nextRowNum + currentCoefficient = currentRow.get(colNum); + break; + } else { + innerColNum++; + } + + } + + } + + // If after all (full search of non-zero coefficient in whole matrix) we have zero-coefficient + // We should end up with matrix processing - matrix already transformed + if(currentCoefficient == 0) { + return; + } + + // Make coefficient equal to one by dividing entire row by this coefficient + if(currentCoefficient != 1.0) { + currentRow.divide(currentCoefficient); + logMessage(String.format("R%d / %s -> R%d", rowNum, new DecimalFormat(decimalPattern).format(currentCoefficient), rowNum)); + } + + // Perform actions to zero coefficients in other rows + for(int j = rowNum + 1; j < n; j++) { + nextRow = matrix.getRow(j); + nextCoefficient = nextRow.get(colNum); + currentCoefficient = currentRow.get(colNum); // it must always be equal to one + // nextCoefficient should be zero + if(nextCoefficient != 0) { + multiplicator = nextCoefficient / currentCoefficient * (-1); + nextRow.add(currentRow.multiply(multiplicator, false)); + logMessage(String.format("%s * R%d + R%d -> R%d", new DecimalFormat(decimalPattern).format(multiplicator), rowNum, j, j)); + } + } + } + } + + /** + * It is step 2 of solving System of Linear Equations: reduction of non-diagonal members of upper triangular form of matrix + */ + private void reduceNonDiagonalCoefficients() { + // Start from the end + int rowNum, colNum, nextRowNum; + int n = matrix.size()[0]; + int coefficientIndex = -1; + double currentCoefficient, nextCoefficient, multiplicator; + Row row; Row nextRow; + for(rowNum = n-1; rowNum >= 0; rowNum--) { + + // Find first non-zero element + row = matrix.getRow(rowNum); + for(int i = 0; i < row.size()-1; i++) { + if(row.get(i) != 0) { + coefficientIndex = i; + break; + } + } + + + // If entire row filled with zeros - stop processing, go to the next iteration + if(coefficientIndex == -1) { + continue; + } + + // Start subtracting this row from rows above + for(nextRowNum = rowNum - 1; nextRowNum >= 0; nextRowNum--) { + currentCoefficient = row.get(coefficientIndex); + nextRow = matrix.getRow(nextRowNum); + nextCoefficient = nextRow.get(coefficientIndex); + if (nextCoefficient != 0) { + multiplicator = nextCoefficient / currentCoefficient * (-1); + nextRow.add(row.multiply(multiplicator, false)); + logMessage(String.format("%s * R%d + R%d -> R%d", new DecimalFormat(decimalPattern).format(multiplicator), rowNum, nextRowNum, nextRowNum)); + } + } + + } + } + + + /** + * It is step 3 of solving System of Linear Equations: checking for number of solutions + * + * In this method it is essential that matrix has a pseudo-diagonal form (after 1st and 2nd steps were completed) + * + * @return SystemType enum + */ + private SystemType checkResult() { + // Checking for no solution + int rowNum, index; + int n = matrix.size()[0]; // number of rows + int m = matrix.size()[1]; // number of columns + Row currentRow; + for(rowNum = n-1; rowNum >=0; rowNum--) { + currentRow = matrix.getRow(rowNum); + if(currentRow.isZeroFilled()) { + continue; // Zero rows are insignificant for us + } + + // Getting first non-zero element + index = currentRow.getIndexOfFirstNonZeroElement(); + + // If first non-zero element located in a last column - the system is inconsistent + if(index == m-1) { + return SystemType.NO_SOLUTIONS; + } + + // Check for infinite number of solutions + + // We look at last non-trivial row and get the matrix[i][j] first non-zero element, if j - is last column of + // non-augmented matrix - then we have single solution, if j - is not the last column of the non-augmented + // matrix - there is infinite number of solutions + // Example: + // 1 0 0 | 4 1 0 0 | 4 + // 0 1 0 | 5 0 1 0 | 5 + // 0 0 0 | 0 0 0 1 | 0 + // 0 0 0 | 0 0 0 0 | 0 + // INFINITE SOLUTIONS SINGLE SOLUTION + int cols = m -1; // number of columns of non-augmented matrix + if(index+1 != cols) { + return SystemType.INFINITE_NUMBER_OF_SOLUTIONS; + } + + // All other ways were considered -> only one variant + // We have single solution + return SystemType.SINGLE_SOLUTION; + } + + return SystemType.UNKNOWN_ERROR; + } + + /** + * It is step 4 of solving System of Linear Equations: get original columns' order in matrix by looking at swap history + * + * Look at swap history and do reverse actions in desc order to get original column positions. + */ + public void revokeColumnsSwap() { + int[] reversedSwapIndexes; + ArrayList swapHistory = matrix.getSwapHistory(); + try { + for (int i = swapHistory.size() - 1; i >= 0; i--) { + reversedSwapIndexes = swapHistory.get(i).getReversedSwapInfo(); + matrix.swapColumns(reversedSwapIndexes[0], reversedSwapIndexes[1], false); + logMessage(String.format("Reverse: C%d <-> C%d", reversedSwapIndexes[0], reversedSwapIndexes[1])); + } + matrix.clearSwapHistory(); + } catch(NullPointerException e) { + // Ignore: + // It means that we haven't swapped any columns and swapHistory is not initialized yet + // (we do not initialize swapHistory to preserve memory, i know that in general this is possibly stupid =) ) + return; + } + } + + private void transformToDiagonalForm() { + transformToUpperTriangularForm(); + reduceNonDiagonalCoefficients(); + resultType = checkResult(); + revokeColumnsSwap(); + } + + private void logMessage(String msg) { + // System.out.println(msg); + logs.append(msg); + logs.append("\n"); + } + + /** + * Get coefficients of single solution + * + * @return solution - array of coefficients + */ + private double[] getSingleSolution() { + int n = matrix.size()[0]; // Number of rows + int m = matrix.size()[1]; // Number of columns of augmented matrix + double[] solution = new double[m-1]; + int solutionIndex; + for(int rowNum = 0; rowNum < n; rowNum++) { + if(matrix.getRow(rowNum).isZeroFilled()) { + continue; + } + + solutionIndex = matrix.getRow(rowNum).getIndexOfFirstNonZeroElement(); + solution[solutionIndex] = matrix.getRow(rowNum).get(m-1); + } + return solution; + } + + public String getLogs() { + return this.logs.toString(); + } + + public String getResult() { + return result; + } + + + public LinearEquationSolver solve() { + transformToDiagonalForm(); + switch(resultType) { + case NO_SOLUTIONS: + result = "No solutions"; + return this; + case INFINITE_NUMBER_OF_SOLUTIONS: + result = "Infinite solutions"; + return this; + case SINGLE_SOLUTION: + double[] res = getSingleSolution(); + StringBuilder sb = new StringBuilder(); + for(double coefficient: res) { + sb.append(new DecimalFormat(decimalPattern).format(coefficient)); + sb.append("\n"); + } + sb.deleteCharAt(sb.length()-1); + result = sb.toString(); + } + return this; + } + + public AugmentedMatrix getMatrix() { + return matrix; + } +} diff --git a/src/solver/Main.java b/src/solver/Main.java index 4404714..74b9ca1 100644 --- a/src/solver/Main.java +++ b/src/solver/Main.java @@ -1,7 +1,106 @@ package solver; +import java.io.File; +import java.io.FileNotFoundException; +import java.io.FileWriter; +import java.io.IOException; +import java.util.InputMismatchException; +import java.util.Scanner; + public class Main { + + static String getHelp() { + String helpMsg = "This program is intended to solve Linear Equations with any amount of variables using Gauss-Jordan Elimination. \n\n" + + "Options: " + + "\n\t * -in [pathToFile] reads file with the first number - number of equations and variables, and augmented matrix of linear equation" + + "\n\t * -out [pathToFile] writes results to the output file " + + "\n\t * -h shows help information " + + "\n\nExample: \njava Solver -in in.txt -out out.txt" + + "\n\nExample of in.txt:\n" + + "3\n" + + "1 1 2 9\n" + + "2 4 -3 1\n" + + "3 6 -5 0"; + return helpMsg; + } + + /** + * Program should start with necessary options -in [pathToFileWithMatrix] and -out [pathToOutputFile] + * Example: > java Solver -in in.txt -out out.txt + * @param args + */ public static void main(String[] args) { - System.out.print("Hello world!"); + // Getting and handling console parameters + String inputFile=""; + String outputFile=""; + for(int i = 0; i < args.length; i++) { + try { + switch (args[i]) { + case "-in": + inputFile = args[i + 1]; + break; + case "-out": + outputFile = args[i + 1]; + break; + case "-h" : + System.out.println(getHelp()); + return; + + } + } catch (ArrayIndexOutOfBoundsException e) { + System.err.println("Invalid command line options, use '-h' option to see help"); + return; + } + } + + if(inputFile.isEmpty() || outputFile.isEmpty()) { + System.err.println("Invalid command line options, use '-h' option to see help"); + return; + } + + System.out.println("Input File: " + inputFile + "\nOutput File: " + outputFile); + + // Working with input file + File file = new File(inputFile); + AugmentedMatrix matrix = new AugmentedMatrix(); + try(Scanner fileScanner = new Scanner(file);) { + matrix.readMatrix(fileScanner); + } catch(FileNotFoundException e) { + System.out.println("File: " + file.getAbsolutePath() + " doesn't exist"); + return; + } catch (InputMismatchException e) { + System.err.println("Invalid structure of input file: " + file.getAbsolutePath()); + return; + } + + if(matrix.size()[0] == 0 || matrix.size()[1] == 0) { + System.err.println("Invalid structure of input file: " + file.getAbsolutePath()); + return; + } + + // Input matrix output + System.out.println("Input matrix:"); + System.out.println(matrix); + + + // Solving equation + System.out.println("Start solving linear equation."); + LinearEquationSolver solver = new LinearEquationSolver(matrix); + String res = solver.solve().getResult(); + System.out.println("Rows manipulation:"); + System.out.println(solver.getLogs()); + + System.out.println("Resulting matrix:"); + System.out.println(solver.getMatrix()); + + System.out.println("The solution is: (" + res.replaceAll("\n", ", ") + ")"); + + // Output writing + try(FileWriter fileWriter = new FileWriter(outputFile)) { + fileWriter.write(res); + System.out.println("Saved to " + outputFile); + } catch(IOException e) { + System.err.println("Result cannot be written to the output file, please try other output file"); + } } } \ No newline at end of file diff --git a/src/solver/Row.java b/src/solver/Row.java new file mode 100644 index 0000000..6143ea2 --- /dev/null +++ b/src/solver/Row.java @@ -0,0 +1,106 @@ +package solver; + +import java.util.Arrays; + +public class Row { + private double[] row; + + Row(double[] row) { + setRow(row); + } + + Row(int m) { + row = new double[m]; + } + + + Row divide(double v) { + if(v == 0){ + throw new java.lang.ArithmeticException("Division by zero"); + } + for(int i = 0; i < row.length; i++) { + row[i] = row[i] / v; + } + return this; + } + + Row multiply(double v, boolean inplace) { + Row curRow; + if(inplace) { + curRow = this; + } else { + curRow = new Row(row.length); + } + for(int i = 0; i < row.length; i++) { + curRow.set(i, row[i] * v); + } + return curRow; + } + + Row multiply(double v) { + return multiply(v, true); + } + + Row subtract(Row row) { + for(int i = 0; i < this.row.length; i++) { + this.row[i] = this.row[i] - row.get(i); + } + return this; + } + + Row add(Row row) { + return add(row, true); + } + + Row add(Row nextRow, boolean inplace) { + Row curRow; + if(inplace) { + curRow = this; + } else { + curRow = new Row(row.length); + } + for(int i = 0; i < row.length; i++) { + curRow.set(i, curRow.get(i) + nextRow.get(i)); + } + return curRow; + } + + public double[] getRow() { + return Arrays.copyOf(row, row.length); + } + + public void setRow(double[] row) { + this.row = Arrays.copyOf(row, row.length); + } + + public void set(int j, double value) { + this.row[j] = value; + } + + public double get(int j) { + return this.row[j]; + } + + public boolean isZeroFilled() { + for(int i = 0; i < row.length; i++) { + if( row[i] != 0) { + return false; + } + } + return true; + } + + public int getIndexOfFirstNonZeroElement() { + for(int i = 0; i < row.length; i++) { + if(row[i] != 0 ) { + return i; + } + } + + return -1; + } + + public int size() { + return this.row.length; + } +} diff --git a/src/solver/SwapInfo.java b/src/solver/SwapInfo.java new file mode 100644 index 0000000..7c65dc2 --- /dev/null +++ b/src/solver/SwapInfo.java @@ -0,0 +1,19 @@ +package solver; + +public class SwapInfo { + private int prevIndex; + private int nextIndex; + + SwapInfo(int prevIndex, int nextIndex) { + this.prevIndex = prevIndex; + this.nextIndex = nextIndex; + } + + public int[] getSwapInfo() { + return new int[]{prevIndex, nextIndex}; + } + + public int[] getReversedSwapInfo() { + return new int[]{nextIndex, prevIndex}; + } +}