Preliminary#

Vectors#

fib-o-mat ships a Vector class which represent a 2-dim mathematical vector or point in euclidean space. A vector can be constructed in various ways:

Vector() creates a null-vector

Vector(x=1, y=2) = Vector(1, 2) creates a cartesian vector with (1, 2) as components

Vector(np.array([1, 2])) creates the same vector as above from a numpy array

Vector([1, 2]) creates the same vector as above from a list

Vector((1, 2)) creates the same vector as above from a tuple

Vector(r=1, phi=np.pi) creates a vector from polar coordinates

Vector(Vector(1, 2)) copies the passed vector object

Vector support the usual mathematical operations

u = Vector(1, 2)
v = Vector(3, 4)

print(u + v)  # result in Vector(4, 6)
print(u - v)  # result in Vector(-2, -2)
print(4 * u)  # result in Vector(4, 8)
print(u / 2)  # result in Vector(0.5, 1)

print(u + (1, 2))  # results also in Vector(4, 6)
print(u + [1, 2])  # results also in Vector(4, 6)
print(u + np.array((1, 2)))  # results also in Vector(4, 6)

print(u.dot(v)) # prints the dot product between u and v, in this case 9

Vectors can be accessed component-wise

print(u.x, u.y)  # prints "1, 2"
print(u[0], u[1])  # prints "1, 2", too. u[0] = u.x, u[1] = u.y

w = Vector(r=1, phi=np.pi)
print(u.r, u.phi)  # prints 1, 3.14159

Warning

Vector values cannot be changed by accessing its elements. E.g. u.x = 5 is not working. To change a component, a new Vector must be constructed new_u = Vector(x=5, y=u.y)

Further, some other properties of the vector can be accessed

print(v.length)  # prints out the norm (length) of the vector
print(v.angle_about_x_axis)  # prints the angle of the vector and the positive x-axis. the result will be in [0, 2pi]

print(u.close_to(v))  # returns True, if u is nearly v and otherwise False.

print(angle_between(u, v))  # prints the angle between u and v

Some other operations which can be applied to vectors

u_rot = u.rotated(np.pi/2)  # rotated the vector counterclockwise by np.pi/2 around the origin.
u_mir = u.mirrored([1, 0])  # mirrors the vector at the positive x-axis
u_norm = u.normalized()  # returns a vector pointing in the same direction as `u` but with length = 1

Vector can be converted to a numpy array with

np_array = np.asarray(u)

To describe dimensioned vectors, the DimVector class exist. This class supports the same function and methods as given above for the Vector class.

Todo

Add example here.

All the code snippets above are combined here: viggge/fib-o-mat/-/blob/master/examples/vectors.py.

Note

Not all methods on and with vectors are introduced above. Please consult the module reference for all available functions and methods.

Physical units#

fibomat uses the pint library to represent physical units. All functionality is encapsulated in the units submodule.

A unit can be constructed with

length_unit = U_('µm')
dose_unit = U_('ions / nm**2')

Quantities can be defined nearly identical

length = Q_('1 nm')
dose = Q_('10 ions / nm**2')

 another_length = 10 * length_unit  # equal to 10 * U_('µm')

# three version to create a dimensioned vector
dim_vector = (3, 4) * U_('µm')
dim_vector2 = Vector(3, 4) * U_('µm')
dim_vector3 = DimVector(3 * U_('µm'), 4 * U_('µm'))

Quantities can be scaled and scale factors can be calculated

length_in_um = scale_to(U_('µm'), length)  # NOTE: length_in_um is a float now and NOT a quantity anymore

scale_factor = scale_factor(U_('µm'), U_('nm'))  # scale factor (float) to scale from nm to µm

Alternatively, all functions and methods defined in the pint module itself can be used

length_in_um = length.m_as('µm')  # identical to scale_to(U_('µm'), length)
# ...

Examples given in: viggge/fib-o-mat/-/blob/master/examples/units.py.

Immutability#

All classes besides the Sample, Site and the lattice builder classes are immutable. This means, once an object is constructed, it cannot be changed or altered anymore.

For example, the x component of Vector can be read but not set or the rotated() method returns a rotated Vector but will not change the original one.