Basic linear algebra operations using Java.
sh project.sh run compiles and runs the program from the main class.
Uses Fraction class from this repo
Constructs a Matrix instance. Takes an int for rows and columns, and an array of type Fraction to create a Matrix with specific entries. If an array of entries is given and the length does not match the size of the Matrix instance, throws an exception.
// construct a 3x4 matrix with all zero entries
Matrix m1 = new Matrix(3, 4);
// construct a 2x2 matrix with specific entries
Fraction[] entries = {new Fraction(1, 2), new Fraction(1, 3), new Fraction(1, 4), new Fraction(1, 5)};
Matrix m2 = new Matrix(2, 2, entries);Sets all entries in the Matrix instance to a random integer between 0 and the int that it takes.
// construct a 3x3 matrix
Matrix m = new Matrix(3, 3);
m.randomize(10); // set all entries to a random number between 0 and 10Prints the Matrix instance to the console.
// construct a 3x3 matrix
Matrix m = new Matrix(3, 3);
// set all entries to a random number between 0 and 10
m.randomize(10);
m.showSelf(); // prints 'm' to consoleReturns a Matrix instance that is the sum of the two Matrix instances. Throws an exception if the arrays have different sizes. Takes another Matrix instance.
// construct two 3x3 matrices
Matrix m1 = new Matrix(3, 3);
Matrix m2 = new Matrix(3, 3);
// randomize entries in all matrices
m1.randomize(10);
m2.randomize(10);
Matrix sum = m1.add(m2); // returns the result of m1 + m2Returns a Matrix instance that is the difference of the two Matrix instances. Throws an exception if the arrays have different sizes. Takes another Matrix instance.
// construct two 3x3 matrices
Matrix m1 = new Matrix(3, 3);
Matrix m2 = new Matrix(3, 3);
// randomize entries in all matrices
m1.randomize(10);
m2.randomize(10);
Matrix difference = m1.subtract(m2); // returns the result of m1 - m2Returns a Matrix instance that is the product of the two Matrix instances. Throws an exception if the arrays have incompatible sizes. Takes another Matrix instance.
// construct two 3x3 matrices
Matrix m1 = new Matrix(3, 3);
Matrix m2 = new Matrix(3, 3);
// randomize entries in all matrices
m1.randomize(10);
m2.randomize(10);
Matrix product = m1.multiply(m2); // returns the result of m1 * m2Returns a Matrix instance that is scaled to the given scalar. Takes a Fraction instance.
// construct a 3x3 matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
// create scalar fraction
Fraction scalar = new Fraction(5, 1);
Matrix scaledMatrix = m1.scale(scalar); // scales all entries in m1 by 5Returns an array of type Fraction that corresponds to the entries in the specified column. Takes an int.
// construct a 3x3 matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
Matrix getColumn = m1.getColumn(0); // returns the 0th column of matrix m1Returns the transpose of the current Matrix instance.
// construct a 3x3 matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
Matrix mTranspose = m1.transpose(); // returns the transpose of Matrix 'm1'Returns a Matrix instance that is the minor of the matrix in relation to the given entry position. Takes an int for entryRow and an int for entryColumn.
// construct a 3x3 matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
Matrix minor = m1.minor(0, 0); // returns the minor of Matrix 'm1' in relation to the entry in the 1st column and 1st rowReturns a Fraction instance that is the determinant of the given Matrix. Finds the determinant using Laplace expansion, complexity is O(n!). Throws an exception if the Matrix is not square (if rows != columns).
// construct a 3x3 matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
Fraction det = m1.determinant(); // returns the determinant of m1Returns a Matrix instance that is the result of an elementary row operation. Takes row at position int operatorRow, multiplies it by Fraction multiplier and adds it to row at position int operatingRow.
// construct a 3x3 matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
// make multiplier Fraction
Fraction mult = new Fraction(2, 1);
Matrix operated = m1.rowOperation(0, 1, mult); // returns m1 after adding 2*row1 to row2Returns a Fraction instance that is the determinant of the given Matrix. Uses .makeUpperTriangular() so complexity is O(n3).
// construct a 3x3 matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
Fraction det = m1.fastDeterminant(); // returns the determinant of m1Returns a Matrix instance that is the inverse of the given Matrix. Uses .fastDeterminant(), .minorMatrix(), .transpose(), and .scale() as helper functions.
// construct a 3x3 matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
Matrix inverse = m1.inverse(); // returns the inverse of m1Checks if two Matrix instances are equal to each other. Returns a boolean.
// construct two 3x3 matrices
Matrix m1 = new Matrix(3, 3);
Matrix m2 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
m2.randomize(10);
m1.isEqualTo(m2); // <- returns a booleanChecks if a Matrix instance is ortogonal. Returns a boolean.
// construct a square matrix
Matrix m1 = new Matrix(3, 3);
// randomize entries
m1.randomize(10);
m1.isOrthogonal(); // <- returns a boolean