Matrix

Table of Contents

1. Installation

2. Development

   2.1. Linux

   2.2. Windows

3. Benchmarking

4. Testing

5. Quick Start Guide

   5.1. Initializers

   5.2. Slicing

   5.3. Printing/Viewing

   5.4. Indexing

   5.5. Operators

   5.6. Broadcasting

   5.7. Minimum, Maximum

   5.8. Mathematical Operations

   5.9. Statistical Operations

   5.10. Matrix Algebra

   5.11. Miscellaneous

Installation

This describes the installation process using cmake. As pre-requisites, you’ll
need git and cmake installed.

# Check out the library.
$ git clone https://github.com/mlcpp/Matrix.git && cd Matrix

# Make a build directory to place the build output.
$ cmake -E make_directory "build"

# Generate build system files with cmake.
$ cmake -E chdir "build" cmake -DCMAKE_BUILD_TYPE=Release ../

# Build the library.
$ cmake -DCMAKE_BUILD_TYPE=Release -S . -B "build"

On a unix system, the build directory should now look something like this:

/Matrix
  /build
    /examples
      /abs
      /addition
      ...

Development

Linux

Prerequisites

1. C++ compiler (gcc or clang)
2. git
3. clang-format
4. make (for Makefiles)
5. cmake (version 3.13 or higher)

# Check out the library.
$ git clone https://github.com/mlcpp/Matrix.git && cd Matrix

# Create build directory.
$ mkdir build

# Enter into build directory.
$ cd build

# Run CMake. This step will generate a Makefile in the build/ folder.
$ cmake ../

# Compile all files and place the binaries inside build/examples/ folder.
$ make

# Compile single file and place the binary inside build/examples/ folder.
$ make <file_name_without_extension>

Windows

Prerequisites

1. C++ compiler (mingw-gcc)
2. git (msysgit)
3. clang-format
4. mingw-make or mingw32-make (for Makefiles)
5. cmake (version 3.13 or higher)

Add these tools to PATH.

Note: Run the following commands in msysgit terminal.

# Check out the library.
$ git clone https://github.com/mlcpp/Matrix.git && cd Matrix

# Create build directory.
$ mkdir build

# Enter into build directory.
$ cd build

# Run CMake. This step will generate a Makefile in the build/ folder.
$ cmake ../

# Compile all files and place the binaries inside build/examples/ folder.
$ mingw-make                                          # use mingw32-make if using 32-bit Windows

# Compile single file and place the binary inside build/examples/ folder.
$ mingw-make <file_name_without_extension>            # use mingw32-make if using 32-bit Windows

Benchmarking

To compile g_benchmark binaries:

Linux: make benchmarks

Windows: mingw32-make benchmarks

Testing

To compile g_test binaries:

Linux: make tests

Windows: mingw32-make tests

Quick Start Guide

This guide contains detailed explanation of all the methods and functions available and how to use them.

More detailed information about how to use these methods and functions is available in /examples.

Note: Here d-type means any C++ data type.

Initializers

Many initializer functions are provided that return Matrix object.

Function	Parameters	Return value	Description
matrix.init()	1 Parameter: Type: d-type/std::vector<d-type>/std::vector<std::vector<d-type>>/std::vector<std::vector<std::string>> Job: value(s) of elements in the Matrix object	Matrix object	Creates a Matrix object of same dimensions and values as provided in the parameter.
matrix.eye()	1 Parameter: Type: int Job: Size of the identity matrix	Matrix object	Creates an identity Matrix object of the size given as parameters.
matrix.zeros()	2 Parameters: Type: int; int Job: Number of rows; Number of columns	Matrix object	Creates a Matrix object of all elements 0 of the size given as parameters.
matrix.ones()	2 Parameters: Type: int; int Job: Number of rows; Number of columns	Matrix object	Creates a Matrix object of all elements 1 of the size given as parameters.
matrix.genfromtxt()	2 Parameters: Type: std::string;char Job: Path of the .csv file	Matrix object	Creates a Matrix object with data elements as in the given file.

Slicing

Matrix objects can be sliced like NumPy arrays.

Function	Parameters	Return value	Description
Matrix.slice()	4 Parameter: Type: int; int; int; int Job: Starting row index; Ending row index; Starting column index; Ending column index	Matrix object	Slices the Matrix object according to the indices provided.
Matrix.slice_select()	4 Parameter: Type: Matrix<d-type1>; Matrix<d-type2>; d-type2; int Job: Matrix to select values on; Matrix to select values from; value to select; column index on which to select	Matrix object	Slices the Matrix object to get all rows which have value(3rd parameter) in second Matrix object and one column(4th parameter)

Printing/Viewing

A number of methods are provided to print/view a Matrix object in different ways.

Function	Parameters	Return value	Description
Matrix.print()	0 Parameters	void	Prints the whole Matrix object onto the console.
Matrix.head()	0 Parameters	void	Prints first 5 rows of the Matrix object onto the console.
Matrix.tail()	0 Parameters	void	Prints first 5 rows of the Matrix object onto the console.
Matrix.view()	2 Parameters: Type: int; int Job: row index; column index	void	Prints the value on the provided index.
Matrix.view()	4 Parameters: Type: int; int; int; int ob: Starting row index; Ending row index; Starting column index; Ending column index	void	Prints the Matrix object according to the indices provided.

Indexing

Indexing can be used to get or assign value to a particular element.

For example, let there is a Matrix object named mat. If we want to get the value at index (5,3) we can do this as follows:

double val = mat(5,3);

Similarly, if we want to assign the value to index (5,3) we can do this by:

mat(5,3) = 10.54;

Operators

Support for almost all standard C++ operators is provided. This includes:

• Arithmetic operators (+, -, \*, /)
• Compound assignment operatos (+=, -=, \*=, /=)
• Increment and decrement operators (++, --)
• Relational and Comparison operators (==, !=, <, >, <=, >=)
• Unary Minus (-)

Broadcasting

Broadcasting is in-built in the Basic Mathematical operations i.e., addition, subtraction, multiplication and division.

Following binary operations are possible:

• Matrix = Matrix @ Matrix
• Matrix = Matrix @ Vector
• Matrix = Matrix @ Scalar

where, @ is any operator from (+, -, *, /)

Note: Vector is a Matrix object where row length or column length is equal to 1.

Following unary operations are possible:

• Matrix = @Matrix

where, @ is any operator from (-)

Minimum, Maximum

Function	Parameters	Return value	Description
matrix.min()	2 Parameters: Type: Matrix; std::string Job: Matrix to find minimum; dimension across which to find minimum	Matrix object	Method to get the minimum value along an axis
matrix.max()	2 Parameters: Type: Matrix; std::string Job: Matrix to find maximum; dimension across which to find maximum	Matrix object	Method to get the maximum value along an axis
matrix.argmin()	2 Parameters: Type: Matrix; std::string Job: Matrix to find index of minimum; dimension across which to find index of minimum	Matrix object	Method to get the index of minimum value along an axis
matrix.argmax()	2 Parameters: Type: Matrix; std::string Job: Matrix to find index of maximum; dimension across which to find index of maximum	Matrix object	Method to get the index of maximum value along an axis

Mathematical Operations

Function	Parameters	Return value	Description
matrix.sqrt()	1 Parameter: Type: Matrix Job: Matrix object to apply method on	Matrix object	Method to get the sqrt of each element of aMatrix object
matrix.power()	2 Parameters: Type: Matrix; double Job: Matrix object to apply method on; power of Matrix elements	Matrix object	Method to calculate power of each element of a Matrix object
matrix.power()	2 Parameters: Type: Matrix; Matrix Job: Matrix object to apply method on; power of Matrix elements	Matrix object	Method to calculate power of each element of a Matrix object
matrix.exp()	1 Parameter: Type: Matrix Job: Matrix object to apply method on	Matrix object	Method to calculate exponential of all elements in the Matrix object
matrix.log()	1 Parameter: Type: Matrix Job: Matrix object to apply method on	Matrix object	Method to calculate natural logarithm of all elements in the in the Matrix object
matrix.abs()	1 Parameter: Type: Matrix Job: Matrix object to apply method on	Matrix object	Method to get absolute value of all elements in the in the Matrix object

Note: Broadcasting in power() methods works in the same way as in Basic Mathematical operations.

Statistical Operations

Function	Parameters	Return value	Description
matrix.sum()	2 Parameters: Type: Matrix; std::string Job: Matrix object to apply method on; Dimension on which to calculate sum	Matrix object	Method to calculate the sum over an axis of aMatrix object
matrix.mean()	2 Parameters: Type: Matrix; std::string Job: Matrix object to apply method on; Dimension on which to calculate mean	Matrix object	Method to calculate the mean over an axis of a Matrix object
matrix.std()	2 Parameters: Type: Matrix; std::string Job: Matrix object to apply method on; Dimension on which to calculate standard deviation	Matrix object	Method to calculate the standard deviation over an axis of a Matrix object

Matrix Algebra

Function	Parameters	Return value	Description
Matrix.transpose()	0 Parameters	Matrix object	Method to return the Tranpose of aMatrix object
matrix.matmul()	2 Parameters: Type: Matrix; Matrix Job: First Matrix for matrix multiplication; Second Matrix for matrix multiplication	Matrix object	Method to calculate matrix multiplication
matrix.determinant()	2 Parameters: Type: Matrix; int Job: Matrix object to calculate determinant of; Size of the Matrix object	double	Method to calculate the Determinant of a Matrix object
matrix.inverse()	1 Parameter: Type: Matrix Job: Matrix object to calculate inverse of	Matrix object	Method to calculate the Inverse of a Matrix object

Miscellaneous

Function	Parameters	Return value	Description
matrix.concatenate()	3 Parameters: Type: Matrix; Matrix; std::string Job: Matrix to concatenate on; Matrix which is to be concatenated; Dimension on which to concatenate	Matrix object	Method to concatenate/join two Matrix objects
Matrix.get()	0 Parameters	std::vector<std::vector<d-type>>	Method to get the Matrix object as a 2D vector
Matrix.get_row()	1 Parameter: Type: int Job: row index	std::vector<d-type>	Method to get a row of a Matrix object in the form of a vector
Matrix.get_col()	1 Parameter: Type: int Job: column index	std::vector<d-type>	Method to get a column of a Matrix object in the form of a vector
matrix.delete_()	3 Parameters: Type: Matrix; int; std::string Job: Matrix to delete row/column of; index to be deleted; Dimension on which to delete	Matrix object	Method to delete a row or column of a Matrix object
matrix.reciprocal()	1 Parameter: Type: Matrix Job: Matrix object to apply method on	Matrix object	Method to calculate reciprocal of all elements in the Matrix object
Matrix.row_length()	0 Parameters	int	Method to get the number of rows in a Matrix object
Matrix.col_length()	0 Parameters	int	Method to get the number of columns in a Matrix object