LinearAlgae

A very simple linear algebra library I made for fun as an exercise for Elementary Linear Algebra. It can find REF, RREF, inverse, determinant, and LU factorization in O(m^2 * n), O(m^2 * n), O(m^3), O(m^3), and O(m^3) time complexity respectively. The product AB, where A has dimensions a x b and B has dimensions b x c, can be found in O(abc) time.

Everything below must be accessed from the LinearAlgae namespace.

Operations

Row Class Methods

Set jth entry

  void setEntry(int j, int val)

Parameter	Type	Description
j	integer	The jth entry in the row
val	float	The value to set the entry to

Returns void

Get jth entry

  float getEntry(int j)

Parameter	Type	Description
j	integer	The jth entry in the row

Returns a float representing the entry

Get size

  int getSize()

Returns an integer representing the size of the row

Get raw contents

  std::vector<float>* getRaw()

Returns std::vector<float>*; a pointer to the vector storing the entries

Matrix Class Methods

Construct a swap operation

  ElemOp swap(int a, int b)

Parameter	Type	Description
a	integer	Row on the LHS
b	integer	Row on the RHS

Returns ElemOp representing R_a <--> R_b

Construct a replace operation

  ElemOp replace(float a, int b, float c, int d)

Parameter	Type	Description
a	float	Coefficient of the left row
b	integer	Index of the left row
c	float	Coefficient of the right row
d	integer	Index of the right row and the row on the RHS

Returns ElemOp representing aR_b + cR_d --> R_d

Construct a scale operation

  ElemOp scale(float a, int b)

Parameter	Type	Description
a	float	Scaling factor
b	integer	Index of row

Returns ElemOp representing aR_b --> R_b

Apply an elementary operation

  void applyOperation(ElemOp op)

Parameter	Type	Description
op	ElemOp	The operation to apply

Returns void

Apply an elementary operation

  void applyOperation(ElemOp op)

Parameter	Type	Description
op	ElemOp	The operation to apply

Returns void

Set an entry

  void setEntry(int i, int j, float val)

Parameter	Type	Description
i	integer	The row
j	integer	The column
val	float	The value to set it to

Returns void

Get an entry

  float getEntry(int i, int j)

Parameter	Type	Description
i	integer	The row
j	integer	The column

Returns float representing the value at i, j

Get m

  int getM()

Returns int representing the dimension m (matrix is assumed to be m x n)

Get n

  int getN()

Returns int representing the dimension n (matrix is assumed to be m x n)

Get raw contents

  std::vector<Row>* getRaw()

Returns std::vector<Row>*; a pointer to the vector storing the rows

Utility Methods

Print a row

  void printRow(Row row)

Parameter	Type	Description
row	Row	The row to print

Returns void

Print a matrix

  void printMatrix(Matrix matrix)

Parameter	Type	Description
matrix	Matrix	The matrix to print

Returns void

Print an elementary operation

  void printOperation(ElemOp op)

Parameter	Type	Description
op	ElemOp	The operation to print

Returns void

Invert an elementary operation

  ElemOp inverseOperation(ElemOp op)

Parameter	Type	Description
op	ElemOp	The operation to invert

Returns an ElemOp representing the inverse of op

Construct an identity matrix

  Matrix createIdentityMatrix(int n)

Parameter	Type	Description
n	integer	Dimension of the identity matrix

Returns a Matrix representing I_n, the n x n identity matrix

Put a matrix into REF

  std::vector<ElemOp> REF(Matrix& matrix)

Parameter	Type	Description
matrix	Matrix	Matrix to REF

Directly modifies the matrix to put it into REF. Returns std::vector<ElemOp> representing the operations performed to row-reduce the matrix.

Put a matrix into RREF

  std::vector<ElemOp> RREF(Matrix& matrix)

Parameter	Type	Description
matrix	Matrix	Matrix to RREF

Directly modifies the matrix to put it into RREF. Returns std::vector<ElemOp> representing the operations performed to RREF the matrix.

Find the inverse of a matrix

  Matrix findInverse(Matrix mat)

Parameter	Type	Description
mat	Matrix	Matrix to invert

Returns a Matrix representing the inverse of mat.

Find the determinant of a matrix

  float findDeterminant(Matrix mat)

Parameter	Type	Description
mat	Matrix	Matrix to find the determinant of

Returns a float representing the determinant of mat

Find the LU factorization of a matrix

  std::pair<Matrix, Matrix> findLUFactorization(Matrix mat)

Parameter	Type	Description
mat	Matrix	Matrix to find the LU factorization of

Returns a std::pair<Matrix, Matrix> with the first element being L and the second element being U