From 850af24aa2c2ae32df177cc8f503942f8412fc2c Mon Sep 17 00:00:00 2001
From: Matthew Ellison <m_ellison@ymail.com>
Date: Thu, 3 Feb 2022 22:01:37 +0000
Subject: [PATCH] Added function to calculate determinants

---
 .../com/mattrixwv/matrix/IntegerMatrix.java   | 148 ++++++++++++++++++
 1 file changed, 148 insertions(+)

diff --git a/src/main/java/com/mattrixwv/matrix/IntegerMatrix.java b/src/main/java/com/mattrixwv/matrix/IntegerMatrix.java
index a9cde9a..4ab474f 100644
--- a/src/main/java/com/mattrixwv/matrix/IntegerMatrix.java
+++ b/src/main/java/com/mattrixwv/matrix/IntegerMatrix.java
@@ -58,6 +58,57 @@ public class IntegerMatrix{
 		//Return the new grid
 		return newGrid;
 	}
+	private boolean isSquare(){
+		if(getNumRows() == 0){
+			return false;
+		}
+		else{
+			return getNumRows() == getNumCols();
+		}
+	}
+	//Returns a matrix with the supplied row and column removed
+	private IntegerMatrix laplaceExpansionHelper(int row, int col){
+		//Make sure the matrix is square
+		if(!isSquare()){
+			throw new InvalidGeometryException("A matrix must be square for you to perform Laplace Expansion");
+		}
+		//Make sure the matrix is large enough to have this operation performed
+		if((getNumRows() <= 1) || (getNumCols() <= 1)){
+			throw new InvalidGeometryException("A matrix must be at least 2x2 for you to perform Laplace Expansion: " + getNumRows() + "x" + getNumCols());
+		}
+		//Make sure the row is valid
+		if((row < 0) || (row >= getNumRows())){
+			throw new InvalidCoordinatesException("An invalid row number was supplied: " + row + ". The matrix contains " + getNumRows() + " rows");
+		}
+		//Make sure the col is valid
+		if((col < 0) || (col >= getNumCols())){
+			throw new InvalidCoordinatesException("An invalid column number was supplied: " + col + ". The matrix contains " + getNumCols() + " columns");
+		}
+
+
+		//Create a new matrix that is one row and column smaller than the existing row
+		int[][] newGrid = new int[getNumRows() - 1][getNumCols() - 1];
+		//Traverse the matrix and set the values in the new matrix, skipping elements in the given row and col
+		for(int workingRow = 0, newRow = 0;workingRow < getNumRows();++workingRow){
+			//Skip the row we are expanding
+			if(workingRow == row){
+				continue;
+			}
+			for(int workingCol = 0, newCol = 0;workingCol < getNumCols();++workingCol){
+				//Skip the column we are expanding
+				if(workingCol == col){
+					continue;
+				}
+				newGrid[newRow][newCol] = grid[workingRow][workingCol];
+				++newCol;
+			}
+			++newRow;
+		}
+
+
+		//Return the new matrix
+		return new IntegerMatrix(newGrid);
+	}
 
 	//Constructors
 	public IntegerMatrix(){
@@ -492,6 +543,103 @@ public class IntegerMatrix{
 		//Return the new matrix
 		return new IntegerMatrix(newGrid);
 	}
+	public int det(){
+		return determinant();
+	}
+	public int determinant(){
+		//Make sure the matrix is square
+		if(!isSquare()){
+			throw new InvalidGeometryException("A matrix must be square for it to have a determinant");
+		}
+		//?Don't have to worry about a matrix existing. isSquare takes care of 0x0 matrix
+
+		//Determine the formula do use for the determinant
+		int det = 0;
+		switch(getNumRows()){
+			//If the matrix is 1x1 return the number
+			case 1 : det = grid[0][0]; break;
+			//If the matrix is 2x2 use the formula
+			case 2 : {
+					det = (grid[0][0] * grid[1][1]) - (grid[0][1] * grid[1][0]);
+				}
+				break;
+			//If the matrix is 3x3 use the formula
+			case 3 : {
+					det = (grid[0][0] * grid[1][1] * grid[2][2]) + (grid[0][1] * grid[1][2] * grid[2][0]) + (grid[0][2] * grid[1][0] * grid[2][1]) -
+						(grid[2][0] * grid[1][1] * grid[0][2]) - (grid[2][1] * grid[1][2] * grid[0][0]) - (grid[2][2] * grid[1][0] * grid[0][1]);
+				}
+				break;
+			//If the matrix is larger break it down and try again
+			default : {
+					//Find the row/column with the largest number of 0's
+					int zerosLocation = 0;
+					int maxNumZeros = 0;
+					boolean zerosRow = true;
+					//Check the rows
+					for(int row = 0;row < getNumRows();++row){
+						int numZeros = 0;
+						for(int col = 0;col < getNumCols();++col){
+							if(grid[row][col] == 0){
+								++numZeros;
+							}
+						}
+						if(numZeros > maxNumZeros){
+							maxNumZeros = numZeros;
+							zerosLocation = row;
+							zerosRow = true;
+						}
+					}
+					//Check the columns
+					for(int col = 0;col < getNumCols();++col){
+						int numZeros = 0;
+						for(int row = 0;row < getNumRows();++row){
+							if(grid[row][col] == 0){
+								++numZeros;
+							}
+						}
+						if(numZeros > maxNumZeros){
+							maxNumZeros = numZeros;
+							zerosLocation = col;
+							zerosRow = false;
+						}
+					}
+
+					//If the largest number of zeros were found in a row
+					if(zerosRow){
+						//Set a variable to make sure the appropriate + or - is applied to the scalar
+						int multiplier = 1;
+						if((zerosLocation % 2) == 1){
+							multiplier = -1;
+						}
+						//Go through every column in the optimal row using the formula
+						for(int col = 0;col < getNumCols();++col){
+							if(grid[zerosLocation][col] != 0){
+								det += (multiplier * grid[zerosLocation][col] * laplaceExpansionHelper(zerosLocation, col).determinant());
+							}
+							multiplier = -multiplier;
+						}
+					}
+					//If the largest number of zeros were found in a column
+					else{
+						//Set a variable to make sure the appropriate + or - is applied to the scalar
+						int multiplier = 1;
+						if((zerosLocation % 2) == 1){
+							multiplier = -1;
+						}
+						//Go through every row in the coptimal column using the formula
+						for(int row = 0;row < getNumRows();++row){
+							if(grid[row][zerosLocation] != 0){
+								det += (multiplier * grid[row][zerosLocation] * laplaceExpansionHelper(row, zerosLocation).determinant());
+							}
+							multiplier = -multiplier;
+						}
+					}
+				}
+		}
+
+		//Return the determinant
+		return det;
+	}
 
 	//Object funtions
 	@Override