Vector warmup

• Topic: basic operations, functions, vectors, timing

• Task:

  1. Create matrices as list tables and numpy arrays.

  2. Test what happens, when you make changes to these.

  3. You should run into some problems, try to fix them.

  4. Test how vectorization affects numeric efficiency by increasing the size of your matrices.

• Template: vectors.py

• Further reading:

  • https://en.wikipedia.org/wiki/Array_programming

vectors.py

vectors.add_scalar(matrix, scalar)

Adds a scalar to a matrix.

The function checks whether the given matrix is a true numpy array or just a table made of lists.

If the matrix is an array, the operation is executed as a single vector command. If the matrix is a table, the only option is to loop over all elements.

Parameters:

• matrix (list or array) – the matrix

• scalar (float) – added value

vectors.change_center_element(matrix, value)

Change the center element of the matrix to the given value.

The given matrix is not affected. Instead, a new matrix is returned.

Parameters:

• matrix (list or array) – the matrix

• value (float) – new value

Returns:

new matrix

Return type:

array or list

vectors.change_center_element_in_place(matrix, value)

Change the center element of the matrix to the given value.

The change is derectly applied on the given matrix.

Parameters:

• matrix (list or array) – the matrix

• value (float) – new value

vectors.main(nx, ny, printout=True)

The main function.

Creates a matrix both as a list of lists and a numpy array and performs similar operations on both.

The first operation is changing the center element of the matrix using either change_center_element() or change_center_element_in_place().

The second operation is multiplying the matrix with a scalar with multiply_by_scalar().

The function times the multiplication for both matrices and returns the required time in seconds.

Note

This function is incomplete!

Parameters:

• nx (int) – number of columns (horizontal size)

• ny (int) – number of rows (vertical size)

• printout (bool) – if True, the matrices are printed after each step

Returns:

multiplication time for a table, for a matrix

Return type:

float, float

vectors.matrix(nx, ny)

Create a matrix of ones as a numpy array.

Note

This function is incomplete!

Parameters:

• nx (int) – number of columns (horizontal size)

• ny (int) – number of rows (vertical size)

Returns:

matrix of ones

Return type:

list

vectors.matrix_as_lists(nx, ny)

Create a ‘matrix’ of ones as a list of lists.

Parameters:

• nx (int) – number of columns (horizontal size)

• ny (int) – number of rows (vertical size)

Returns:

table of ones

Return type:

list

vectors.multiply_by_scalar(matrix, scalar)

Multiplies the matrix by a scalar.

The function checks whether the given matrix is a true numpy array or just a table made of lists.

If the matrix is an array, the operation is executed as a single vector command. If the matrix is a table, the only option is to loop over all elements.

Parameters:

• matrix (list or array) – the matrix

• scalar (float) – multiplier

vectors.print_matrix(matrix, name)

Prints a matrix in a tabulated format.

For numpy arrays, printing automatically produces a nice matrix-like representation, but lists are printed on one line. This function will tabulate both.

Parameters:

• matrix (list or array) – the matrix

• name (str) – the title printed before the actual matrix