Welcome to Numc, a library for the Python programming language, adding support for very large and multi-dimensional matrix operations. The Numc package also provides an easy, convenient, and efficient way for these operations. This repository is developed in UC Berkeley CS61C as a class project by Rory Na and Stephen Yang.

Follow the following steps in order to create a matrix in the python terminal. Import the Numc package: import Numc as nc

To create a new matrix, use the following syntax: nc.Matrix([[a, b, c], … ]) where a, b, and c are integers or double-precision float numbers in the C language. You may create the matrix in any reasonable dimensions, by concatenating the numbers(a, b, c) or the rows [a, b, c]. You need to use commas to separate the values. nc.Matrix(m, n) where m and n are the rows and the columns of the matrix. The matrix will be filled with all zeros. nc.Matrix(m, n, val) where m and n are the rows and the columns of the matrix and val is the value that the matrix will be filled with.

Example usage:

a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
The variable a is now assigned to a representation of a 3x3 matrix with elements [1, -2, 3.0] in the first row, [-4, -5, 6] in the second row, and [7.0, 8, -9] in the third row.
b = nc.Matrix(3, 3)
The variable b is now assigned to a representation of a 3x3 matrix with elements [0, 0, 0] in the first row, [0, 0, 0] in the second row, and [0, 0, 0] in the third row.
c = nc.Matrix(3, 3, 2)
The variable c is now assigned to a representation of a 3x3 matrix with elements [2, 2, 2] in the first row, [2, 2, 2] in the second row, and [2, 2, 2] in the third row.

a = b + c, where a, b, and c are matrices. Corresponding method in numc.c: Matrix61c_add Corresponding method in matrix.c: add_matrix Description: This operation adds two pre- allocated matrices.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> b = nc.Matrix(3, 3, 2)
>>> a + b
[[3.0, 0.0, 5.0], [-2.0, -3.0, 8.0], [9.0, 10.0, -7.0]]

a = b - c, where a, b, and c are matrices. Corresponding method in numc.c: Matrix61c_sub Corresponding method in matrix.c: sub_matrix Description: This operation subtracts two pre- allocated matrices.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> b = nc.Matrix(3, 3, 2)
>>> a - b
[[-1.0, -4.0, 1.0], [86.0, -7.0, 4.0], [5.0, 6.0, -11.0]]

a = b * c, where a, b, and c are matrices. Corresponding method in numc.c: Matrix61c_multiply Corresponding method in matrix.c: mul_matrix Description: This operation multiplies two pre- allocated matrices.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> b = nc.Matrix(3, 3, 2)
>>> a * b
[[4.0, 4.0, 4.0], [178.0, 178.0, 178.0], [12.0, 12.0, 12.0]]

a = - b, where a and b are matrices. Corresponding method in numc.c: Matrix61c_neg Corresponding method in matrix.c: neg_matrix Description: This operation negates two pre- allocated matrices.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> -a
[[-1.0, 2.0, -3.0], [4.0, 5.0, -6.0], [-7.0, -8.0, 9.0]]

a = abs(b), where a and b are matrices. Corresponding method in numc.c: Matrix61c_abs Corresponding method in matrix.c: abs_matrix Description: This operation takes the absolute value of a pre-allocated matrix.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> abs(a)
[[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]]

a = a ** n, where a is a matrix and n is an integer. Corresponding method in numC: Matrix61c_pow Corresponding method in matrix.c: pow_matrix Description: This operation returns the nth power of a pre-allocated matrix.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> a ** 0
[[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
>>> a ** 1
[[1.0, -2.0, 3.0], [-4.0, -5.0, 6.0], [7.0, 8.0, -9.0]]
>>> a ** 2
[[30.0, 32.0, -36.0], [58.0, 81.0, -96.0], [-88.0, -126.0, 150.0]]

a.get(i, j), where a is a matrix, i, and j are integer indices. Corresponding method in numC: Matrix61c_get_value Corresponding method in matrix.c: get Description: This operation retrieves an element from a matrix.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> a.get(1, 0)
-4.0

a.set(i, j, val), where a is a matrix, val is a new double-precision float, and i and j are integers. Corresponding method in numC: Matrix61c_set_value Corresponding method in matrix.c: set Description: This operation sets an element of a pre-allocated matrix to a new value.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> a.set(1, 0, 88)
>>>

a[i][j] / a[i, j] / a[i, j:k] / a[i:j, k] / a[i:j, k:l], where a is a matrix, i, j, k and l are integer indices. Corresponding method in numC: Matrix61c_subscript Corresponding method in matrix.c: N/A Description: This operation returns the slice of a pre-allocated matrix. The sliced matrix shares data with its parent matrix.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>>a[1]
[88.0, -5.0, 6.0]
>>> a[1][0]
88.0
>>> a[1: 3]
[[88.0, -5.0, 6.0], [7.0, 8.0, -9.0]]
>>> a[2, 2]
-9.0
>>> a[1: 3, 2]
[6.0, -9.0]
>>> a[2, 0:1]
7.0
>>> a[1: 2, 0: 1]
-5.0

a[i][j] / a[i, j] / a[i, j:k] / a[i:j, k] / a[i:j, k:l] = val/ b, where a and b are matrices, i, j, k and val are integer indices. where a is a matrix and i and j are integers. Corresponding method in numC:Matrix61c_set_subscript Corresponding method in matrix.c: N/A Description: This operation sets the slice of a pre-allocated matrix into a new value or matrix. The sliced matrix shares data with its parent matrix, so the new values are reflected in the parent matrix.

Example usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>> a[1] = [10, 11, 12]
>>> a[1][0] = 13
>>> a[1: 3] = [[14, 15, 16], [17, 18, 19]]
>>> a[2, 2] = 20
>>> a[1: 3, 2] = [21, 22]
>>> a[2, 0:1] = 23
>>> a[1: 2, 0: 1] = 24

a.shape, where a is a matrix. Corresponding method in numC: get_shape() Corresponding method in matrix.c: N/A Description: This operation retrieves the shape of a pre-assigned matrix.

Example Usage:

>>> a = nc.Matrix([[1, -2, 3.0], [-4, -5, 6], [7.0, 8, -9]])
>>>a.shape
(3, 3)

• Note that the dimensions need to be correct for corresponding operations for the operation to proceed.

The plugin supports SIMD, OpenMP, cache blocking and loop unrolling rendering you unprecedentedly fast performance improvements in large operations, such as taking a large square or multiplying large matrices.