Linear Algebra

A big matrix class written in C++.

Supported Operators

• + : Either adds two same sized matrices, or adds a constant to each element of the matrix

• - : Either subtracts from one matrix to other (same sized matrices), or subtracts a constant from each element of the matrix

• * : Either multiply two matrices (mxn * nxk = mxk), or scale the matrix by a constant

• / : Divides each element of the matrix by a constant

• == : Checks if two matrices are same

• != : Checks if two matrices are different

• = : Assignment operator

Syntactic Sugars

• += operator

• -= operator

• *= operator

• /= operator

Getters

• getRows(): Returns the number of rows

• getCols(): Returns the number of columns

• return_col(i): Returns the ith column of the matrix

• return_row(i): Returns the ith row of the matrix

Linear Algebra

• T(self=false) : Returns the transpose of the matrix, if self (default false), updates the matrix

• gaussianElimination(self=false) : Returns the row-echolon form of the matrix, if self (default false), updates the matrix

• inverse() : Returns the inverse of the matrix

• determinant() : Returns the determinant of the matrix (defined only on square matrices)

• qr_decomposition() : Returns matrices Q(orthogonal matrix) and R(upper triangular matrix) that satisfies Q*R = object using Gram-Schmidt equations(analytically). The algorithm fails to deliver correct Q and R when the object is singular.

• singular_value_decomposition() : Returns matrices U, E, V_T where U contains AA_T's eigenvectors, E contains the eigenvalues of A and V contains A_TA's eigenvectors using Jacobi Eigenvalue Algorithm (numerically).

• eigs() : Returns the eigenvalues of the matrix (utilizing Jacobi Eigenvalue Algorithm)

Util Functions

• clipCols(start, end, self=false) : Returns the columns between start and end (M[start:end]), if self (default false), updates the matrix

• clipRows(start, end, self=false) : Returns the rows between start and end, if self (default false), updates the matrix

• swapRows(i,j) : Swaps ith row with jth.

• swapCols(i,j) : Swaps ith column with jth.

• remove_row_col(i,j, self=false) : Returns a matrix that does not contain ith row and jth column of the object, if self (default false), updates the matrix (utilized while calculating the cofactor matrix)

• sum(axis=0, self=false) : Returns the sum of the elements in given axis

• frobeniusNorm() : Returns the Frobenius Norm of the matrix

• assignCol(m, col_num) : Assigns m to col_numth column of the matrix

• assignRow(m, row_num) : Assigns m to row_numth row of the matrix

• apply(function) : Applies the function to the each element of the matrix (mutates the object)

• printMatrix() : Prints the matrix with 2 precision

Free Functions

• eye(n) : Returns an identity matrix with size nxn

• zeros(n) : Returns a matrix of zeros with size nxn

• ones(n) : Returns a matrix of ones with size nxn

• diag(m) : Returns a matrix whose diagonal values are m

• matrixtoVector(m) : Returns the vector representation of matrix m